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    <description>recent bookmarks from cshalizi</description>
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    <title>[2509.15855] What does it mean for a system to compute?</title>
    <dc:date>2026-01-30T12:10:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2509.15855</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can identify which aspects of the dynamic system match the input and output of the computation that it performs, as well as the aspects of the dynamic system that match the intermediate logical variables of that computation. In contrast, in many naturally occurring dynamical systems that we understand to be computers, even though we neither designed nor constructed them - such as the human brain - it is not a priori clear how to identify the computation we presume to be encoded in the dynamic system. Regardless of their origin, dynamical systems capable of computation can, in principle, be mapped onto corresponding abstract computational machines that perform the same operations. In this paper, we begin by surveying a wide range of dynamic systems whose computational properties have been studied. We then introduce a very broadly applicable framework for identifying what computations(s) are emulated by a given dynamic system. After an introduction, we summarize key examples of dynamical systems whose computational properties have been studied. We then introduce a very broadly applicable framework that defines the computation performed by a given dynamical system in terms of maps between that system's evolution and the evolution of an abstract computational machine. We illustrate this framework with several examples from the literature, in particular discussing why some of those examples do not fully fall within the remit of our framework. We also briefly discuss several related issues, such as uncomputability in dynamical systems, and how to quantify the value of computation in naturally occurring computers."]]></description>
<dc:subject>dynamical_systems computational_statistics physics_of_information wolpert.david_h. in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:afe7eeac6956/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:physics_of_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wolpert.david_h."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03555-1">
    <title>Measure-Theoretic Time-Delay Embedding | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:25:12+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03555-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The celebrated Takens’ embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic and that observations are noise-free, limiting its applicability in real-world scenarios. Motivated by these limitations, we formulate a measure-theoretic generalization that adopts an Eulerian description of the dynamics and recasts the embedding as a pushforward map between spaces of probability measures. Our mathematical results leverage recent advances in optimal transport. Building on the proposed measure-theoretic time-delay embedding theory, we develop a computational procedure that aims to reconstruct the full state of a dynamical system from time-lagged partial observations, engineered with robustness to handle sparse and noisy data. We evaluate our measure-based approach across several numerical examples, ranging from the classic Lorenz-63 system to real-world applications such as NOAA sea surface temperature reconstruction and ERA5 wind field reconstruction."]]></description>
<dc:subject>to:NB to_read state-space_reconstruction dynamical_systems stochastic_processes re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ddcab3885772/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_reconstruction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03547-1">
    <title>Error Bounds in a Smooth Metric for Brownian Approximation of Dynamical Systems via Stein’s Method | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:24:23+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03547-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We adapt Stein’s method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of smooth test functions under a functional correlation decay bound. For systems with a sufficiently fast polynomial rate of correlation decay, the error bound is of order 
$O(N^{−1/2})$, under an additional condition on the linear growth of variance. Applications include a family of interval maps with neutral fixed points and unbounded derivatives, and two-dimensional dispersing Sinai billiards."]]></description>
<dc:subject>to:NB central_limit_theorem stochastic_processes dynamical_systems ergodic_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4134e9e7c64c/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03537-3">
    <title>Large Deviation Principle for Slow-Fast Systems with Infinite-Dimensional Mixed Fractional Brownian Motion | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:22:29+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03537-3</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This work is concerned with the large deviation principle (LDP) for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H \in (1/2, 1)$. We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply Khasminskii’s averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components. Finally, the moderate deviation principle (MDP) for the slow-fast systems is established based on the proof of the proposed LDP."]]></description>
<dc:subject>to:NB dynamical_systems large_deviations stochastic_processes long-range_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:58caae221a90/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
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<item rdf:about="https://link.springer.com/article/10.1007/s10955-025-03546-2">
    <title>Maximal large deviations for sequential dynamical systems | Journal of Statistical Physics</title>
    <dc:date>2025-12-26T14:20:00+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10955-025-03546-2</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We establish a maximal large deviation principle for sequential dynamical systems with arbitrarily slow polynomial decay of correlations. We apply our result to a larger class of sequential interval maps, including Liverani-Saussol-Vaienti maps, intermittent maps with critical points, and Lasota-Yorke convex maps. We also recover several classical results on large deviations for these maps."]]></description>
<dc:subject>to:NB large_deviations extreme_values dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7b14f0809bdc/</dc:identifier>
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<item rdf:about="https://link.springer.com/article/10.1007/s00332-002-0506-0">
    <title>For Differential Equations with r Parameters, 2r+1 Experiments Are Enough for Identification | Journal of Nonlinear Science</title>
    <dc:date>2025-12-11T19:25:13+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s00332-002-0506-0</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly choose external inputs to help excite the system, how many experiments are sufficient in order to obtain all the information that is potentially available about the parameters? This paper shows that the best possible answer (assuming exact measurements) is 2r+1 experiments, where r is the number of parameters. Moreover, a generic set of such experiments suffices."]]></description>
<dc:subject>to:NB have_read via:mraginsky have_read_decades_ago dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ffaae5a2b942/</dc:identifier>
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<item rdf:about="https://direct.mit.edu/books/oa-monograph/6009/Mathematical-Models-of-MeaningA-Dynamic-Systems">
    <title>Mathematical Models of Meaning: A Dynamic Systems Approach to Possible World Semiotics | Books Gateway | MIT Press</title>
    <dc:date>2025-11-05T20:10:28+00:00</dc:date>
    <link>https://direct.mit.edu/books/oa-monograph/6009/Mathematical-Models-of-MeaningA-Dynamic-Systems</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A mathematical model of meaning that captures the dynamics and diversity of meaning-oriented agents.
"In Mathematical Models of Meaning, Paul Kockelman offers answers to the following kinds of questions: What is meaning? What is the relation between meaning, information, value, and purpose? What ingredients are necessary for a system to exhibit meaning? What behaviors, and capacities for behavior, are particular to meaning-oriented agents? Is there a relatively simple mathematical model that can adequately capture the dynamics—and diversity—of meaning-oriented agents? And finally, how can we best bridge the divide between interpretive paradigms that are qualitative and context rich and formal methods that are quantitative and domain general?
"Partially grounded in a pragmatist approach, this book rethinks the semiotic, statistical, and logical currents of Charles Sanders Peirce’s thought in relation to more recent developments in allied traditions. Putting possible worlds, as well as social relations, at the center of significance, it focuses on the emergence of meaningful behavior among relatively distributed agents that choose in real time, learn over developmental time, or evolve over phylogenetic time."]]></description>
<dc:subject>to:NB books:noted semiotics semantics philosophy_of_mind dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7ef64e018c38/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:philosophy_of_mind"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
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<item rdf:about="https://link.springer.com/article/10.1007/BF01295322">
    <title>Subshifts of finite type and sofic systems | Monatshefte für Mathematik</title>
    <dc:date>2025-08-08T03:11:31+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/BF01295322</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[--- Finally read, after literally decades of citing it.  (It is indeed as my teachers and co-authors claimed it to be.)]]></description>
<dc:subject>to:NB have_read sofic_processes symbolic_dynamics dynamical_systems markov_models automata_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e99618a1664e/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sofic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
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<item rdf:about="https://martinuzzifrancesco.github.io/posts/a-brief-introduction-to-reservoir-computing/">
    <title>A brief introduction to Reservoir Computing | Francesco Martinuzzi</title>
    <dc:date>2025-08-07T15:03:08+00:00</dc:date>
    <link>https://martinuzzifrancesco.github.io/posts/a-brief-introduction-to-reservoir-computing/</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>to:NB to_read reservoir_computing dynamical_systems prediction re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b949b5cf35ce/</dc:identifier>
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<item rdf:about="https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1221051/full">
    <title>Frontiers | Learning from the past: reservoir computing using delayed variables</title>
    <dc:date>2025-08-07T15:02:29+00:00</dc:date>
    <link>https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1221051/full</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Reservoir computing is a machine learning method that is closely linked to dynamical systems theory. This connection is highlighted in a brief introduction to the general concept of reservoir computing. We then address a recently suggested approach to improve the performance of reservoir systems by incorporating past values of the input signal or of the reservoir state variables into the readout used to forecast the input or cross-predict other variables of interest. The efficiency of this extension is illustrated by a minimal example in which a three-dimensional reservoir system based on the Lorenz-63 model is used to predict the variables of a chaotic Rössler system."]]></description>
<dc:subject>to:NB prediction dynamical_systems reservoir_computing parlitz.ulrich</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:127371a086a7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:reservoir_computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:parlitz.ulrich"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.nature.com/articles/s41467-024-45187-1">
    <title>Emerging opportunities and challenges for the future of reservoir computing | Nature Communications</title>
    <dc:date>2025-08-07T14:44:41+00:00</dc:date>
    <link>https://www.nature.com/articles/s41467-024-45187-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Reservoir computing originates in the early 2000s, the core idea being to utilize dynamical systems as reservoirs (nonlinear generalizations of standard bases) to adaptively learn spatiotemporal features and hidden patterns in complex time series. Shown to have the potential of achieving higher-precision prediction in chaotic systems, those pioneering works led to a great amount of interest and follow-ups in the community of nonlinear dynamics and complex systems. To unlock the full capabilities of reservoir computing towards a fast, lightweight, and significantly more interpretable learning framework for temporal dynamical systems, substantially more research is needed. This Perspective intends to elucidate the parallel progress of mathematical theory, algorithm design and experimental realizations of reservoir computing, and identify emerging opportunities as well as existing challenges for large-scale industrial adoption of reservoir computing, together with a few ideas and viewpoints on how some of those challenges might be resolved with joint efforts by academic and industrial researchers across multiple disciplines."]]></description>
<dc:subject>to:NB reservoir_computing re:codename:catherine_wheel to_read prediction dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:951abc62d069/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:reservoir_computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2407.14781">
    <title>[2407.14781] Bernstein-von Mises theorems for time evolution equations</title>
    <dc:date>2025-07-28T14:19:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.14781</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider a class of infinite-dimensional dynamical systems driven by non-linear parabolic partial differential equations with initial condition θ modelled by a Gaussian process `prior' probability measure. Given discrete samples of the state of the system evolving in space-time, one obtains updated `posterior' measures on a function space containing all possible trajectories. We give a general set of conditions under which these non-Gaussian posterior distributions are approximated, in Wasserstein distance for the supremum-norm metric, by the law of a Gaussian random function. We demonstrate the applicability of our results to periodic non-linear reaction diffusion equations
\[
\frac{\partial}{\partial t} u - \nabla u = f(u)
\[
\[
u(0) = \theta
\]
where f is any smooth and compactly supported reaction function. In this case the limiting Gaussian measure can be characterised as the solution of a time-dependent Schrödinger equation with `rough' Gaussian initial conditions whose covariance operator we describe."]]></description>
<dc:subject>to:NB stochastic_processes dynamical_systems central_limit_theorem nickl.richard gaussian_processes bayesian_consistency</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4df4e0251977/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:central_limit_theorem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nickl.richard"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gaussian_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesian_consistency"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://kording.substack.com/p/attractors-are-usually-not-mechanisms">
    <title>Attractors are usually not mechanisms - by Konrad Kording</title>
    <dc:date>2025-07-28T14:13:48+00:00</dc:date>
    <link>https://kording.substack.com/p/attractors-are-usually-not-mechanisms</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>have_read explanation neuroscience dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c73ea5935fa0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2505.13755">
    <title>[2505.13755] Panda: A pretrained forecast model for universal representation of chaotic dynamics</title>
    <dc:date>2025-06-15T16:04:59+00:00</dc:date>
    <link>https://arxiv.org/abs/2505.13755</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of 2×104 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen real world chaotic systems, and nonlinear resonance patterns in cross-channel attention heads. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics."]]></description>
<dc:subject>to:NB neural_networks large_language_models_(so_called) color_me_skeptical dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9f87c6cff54a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_language_models_(so_called)"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2409.12179">
    <title>[2409.12179] Computational Dynamical Systems</title>
    <dc:date>2025-01-22T15:37:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2409.12179</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that 'chaotic' dynamical systems (more precisely, Axiom A systems) and 'integrable' dynamical systems (more generally, measure-preserving systems) cannot robustly simulate universal Turing machines, although such machines can be robustly simulated by other kinds of dynamical systems. Subsequently, we show that any Turing machine that can be encoded into a structurally stable one-dimensional dynamical system must have a decidable halting problem, and moreover an explicit time complexity bound in instances where it does halt. More broadly, our work elucidates what it means for one 'machine' to simulate another, and emphasizes the necessity of defining low-complexity 'encoders' and 'decoders' to translate between the dynamics of the simulation and the system being simulated. We highlight how the notion of a computational dynamical system leads to questions at the intersection of computational complexity theory, dynamical systems theory, and real algebraic geometry."
]]></description>
<dc:subject>to:NB dynamical_systems computational_complexity via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2e3e742c5941/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2410.10103">
    <title>[2410.10103] Causal Discovery in Nonlinear Dynamical Systems using Koopman Operators</title>
    <dc:date>2024-10-21T12:54:10+00:00</dc:date>
    <link>https://arxiv.org/abs/2410.10103</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that causal mechanisms manifest as particular flows of observables between function subspaces. While the flow map definition is a clear generalization of the standard definition of causal mechanism given in the structural causal model framework, the flow maps are complicated objects that are not tractable to work with in practice. By contrast, the equivalent Koopman definition lends itself to a straightforward data-driven algorithm that can quantify multivariate causal relations in high-dimensional nonlinear dynamical systems. The coupled Rossler system provides examples and demonstrations throughout our exposition. We also demonstrate the utility of our data-driven Koopman causality measure by identifying causal flow in the Lorenz 96 system. We show that the causal flow identified by our data-driven algorithm agrees with the information flow identified through a perturbation propagation experiment. Our work provides new theoretical insights into causality for nonlinear dynamical systems, as well as a new toolkit for data-driven causal analysis."]]></description>
<dc:subject>to_read causal_discovery dynamical_systems koopman_operators via:rvenkat in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3a66836a1377/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:koopman_operators"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:rvenkat"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/pii/002437959190021N">
    <title>Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems - ScienceDirect</title>
    <dc:date>2023-05-22T18:19:08+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/pii/002437959190021N</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We establish a number of properties associated with the dynamical system $Ḣ= [H,[H, N]]$, where $H$ and $N$ are symmetric $n$ by $n$ matrices and $[A, B] = AB − BA$. The most important of these come from the fact that this equation is equivalent to a certain gradient flow on the space of orthogonal matrices. We are especially interested in the role of this equation as an analog computer. For example, we show how to map the data associated with a linear programming problem into $H(0)$ and $N$ in such a way as to have  $Ḣ= [H[H, N]]$
 evolve to a solution of the linear programming problem. This result can be applied to find systems which solve a variety of genetic combinatorial optimization problems, and it even provides an algorithm for diagonalizing symmetric matrices."

--- This sounds wild.
--- ("via" is indirect)]]></description>
<dc:subject>to:NB dynamical_systems linear_algebra optimization re:in_soviet_union_optimization_problem_solves_you brockett.r.w. via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:26419d95ecee/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:in_soviet_union_optimization_problem_solves_you"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:brockett.r.w."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://hrl.harvard.edu/publications/brockett94dynamical.pdf">
    <title>Dynamical Systems and their Associated Automata</title>
    <dc:date>2023-05-22T18:16:31+00:00</dc:date>
    <link>http://hrl.harvard.edu/publications/brockett94dynamical.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper studies problems related to the construction of a robust correspondence between an automaton and a continuous-time dynamical system of the input-output type.
Two general methods, based on ideas from topology, are considered. They can be distinguished on the basis of the time scale on which they operate. The slow time scale method
utilizes the relationship between the fundamental group of a space and the corresponding
deck transformations acting on the covering space. The fast time scale method is based on
a suitable topological characterization of pulses and identifies pulses with transitions between the domains of attraction of stable equilibria. As compared with the standard digital
electronics paradigm, these results provide a more general conceptual scheme for building
robustness into calculating mechanism. The results obtained suggest new ways to interpret
neurobiological signal processing."

--- I probably should've known about this during my dissertation!]]></description>
<dc:subject>to:NB automata_theory dynamical_systems re:dissertation brockett.r.w. via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0fdd5dd9a411/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:dissertation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:brockett.r.w."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.jstor.org/stable/2171879">
    <title>A Rational Route to Randomness on JSTOR</title>
    <dc:date>2023-05-08T19:12:32+00:00</dc:date>
    <link>https://www.jstor.org/stable/2171879</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The concept of adaptively rational equilibrium (A.R.E.) is introduced. Agents adapt their beliefs over time by choosing from a finite set of different predictor or expectations functions. Each predictor is a function of past observations and has a performance or fitness measure which is publicly available. Agents make a rational choice concerning the predictors based upon their past performance. This results in a dynamics across predictor choice which is coupled to the equilibrium dynamics of the endogenous variables. As a simple, but typical, example we consider a cobweb type demand-supply model where agents can choose between rational and naive expectations. In an unstable market with (small) positive information costs for rational expectations, a high intensity of choice to switch predictors leads to highly irregular equilibrium prices converging to a strange attractor. The irregularity of the equilibrium time paths is explained by the existence of a so-called homoclinic orbit and its associated complicated dynamical phenomena. Thus local instability and global complicated dynamics may be a feature of a fully rational notion of equilibrium."
]]></description>
<dc:subject>have_read cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 economics learning_in_games prediction brock.william_a. hommes.cars dynamical_systems chaos in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:69c12a7b5294/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:economics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_in_games"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:brock.william_a."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hommes.cars"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chaos"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2304.05794">
    <title>[2304.05794] Systemic risk measured by systems resiliency to initial shocks</title>
    <dc:date>2023-04-27T14:45:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2304.05794</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The study of systemic risk is often presented through the analysis of several measures referring to quantities used by practitioners and policy makers. Almost invariably, those measures evaluate the size of the impact that exogenous events can exhibit on a financial system without analysing the nature of initial shock. Here we present a symmetric approach and propose a set of measures that are based on the amount of exogenous shock that can be absorbed by the system before it starts to deteriorate. For this purpose, we use a linearized version of DebtRank that allows to clearly show the onset of financial distress towards a correct systemic risk estimation. We show how we can explicitly compute localized and uniform exogenous shocks and explained their behavior though spectral graph theory. We also extend analysis to heterogeneous shocks that have to be computed by means of Monte Carlo simulations. We believe that our approach is more general and natural and allows to express in a standard way the failure risk in financial systems."]]></description>
<dc:subject>to:NB networks dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cfa6a95f2b6b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/abs/pii/S0020019097001105">
    <title>Finite automata-models for the investigation of dynamical systems - ScienceDirect</title>
    <dc:date>2023-04-24T22:07:58+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/abs/pii/S0020019097001105</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We describe a method to measure the complexity of a dynamical system. By complexity we mean the intrinsic information processing abilities which we believe to be visible only on an infinitesimal scale. The complexity measure is based on concepts from information theory and from the theory of formal languages."]]></description>
<dc:subject>to:NB have_read automata_theory dynamical_systems complexity_measures re:dissertation cleaning_out_the_filing_cabinet_for_the_first_time_since_2005</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7be4910aff26/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:complexity_measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:dissertation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/BF01025993">
    <title>Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators | SpringerLink</title>
    <dc:date>2023-04-24T22:02:59+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/BF01025993</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit-cycle oscillators with distributed native frequencies. In particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power-law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above. This peculiar feature is demonstrated by numerical simulations mainly through finite-size scaling analyses. In the course of exploring its origin, we encounter a new concept termed a “correlation frequency” which provides a natural interpretation of the finite-size scaling laws. A comment is given on a recent theory by Kuramoto and Nishikawa to clarify why it contradicts our results."]]></description>
<dc:subject>to:NB networks dynamical_systems synchronization phase_transitions cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7d2f206d0789/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:synchronization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:phase_transitions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.33.1134">
    <title>Phys. Rev. A 33, 1134 (1986) - Independent coordinates for strange attractors from mutual information</title>
    <dc:date>2023-04-24T21:53:56+00:00</dc:date>
    <link>https://journals.aps.org/pra/abstract/10.1103/PhysRevA.33.1134</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction. An N logN algorithm for calculating I is presented. As proposed by Shaw, a minimum in I is found to be a good criterion for the choice of time delay in phase-portrait reconstruction from time-series data. This criterion is shown to be far superior to choosing a zero of the autocorrelation function."]]></description>
<dc:subject>have_read state-space_reconstruction dynamical_systems time_series information_theory fraser.andrew_m. swinney.harry_l. have_taught cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7c8c3564ea61/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_reconstruction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fraser.andrew_m."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:swinney.harry_l."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_taught"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.51.3871">
    <title>Phys. Rev. E 51, 3871 (1995) - Symbol sequence statistics in noisy chaotic signal reconstruction</title>
    <dc:date>2023-04-24T21:48:32+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.51.3871</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A method is discussed for reconstructing chaotic systems from noisy signals using a symbolic approach. The state space of the dynamical system is partitioned into subregions and a symbol is assigned to each subregion. Consequently, an orbit in a continuous state space is converted into a long symbol string. The probabilities of occurrence for different symbol sequences constitute the symbol sequence statistics. The symbol sequence statistics are easily measured from the signal output and are used as the target for reconstruction (i.e., for assessing the goodness of fit of proposed models). Reliable reconstructions were achieved given a noisy chaotic signal, provided the general class of the model of the underlying dynamics is known. Both observational and dynamical noise were considered, and they were not limited to small amplitudes. Substantial noise produces a strong bias in the symbol sequence statistics, but such bias can be tracked and effectively eliminated by including the noise characteristics in the model. This is demonstrated by the robust reconstruction of the Hénon and Ikeda maps even when the signal to noise ratio is ≊1. Applications of this method include extracting control parameters for nonlinear dynamical systems and nonlinear model evaluation from experimental data."]]></description>
<dc:subject>symbolic_dynamics dynamical_systems time_series statistical_inference_for_stochastic_processes cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 have_read re:dissertation estimation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:04d216b60071/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:symbolic_dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:dissertation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/nlin/0212015">
    <title>[nlin/0212015] Local dimension and finite time prediction in spatiotemporal chaotic systems</title>
    <dc:date>2023-04-24T21:46:32+00:00</dc:date>
    <link>https://arxiv.org/abs/nlin/0212015</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as having high predictability and vice-versa. This conclusion is reached by using methods from dynamical systems theory and Bayesian modelling. We emphasize in this work the consequences for short time forecasting and examine the relevance for factor analysis. Although we concentrate on coupled map lattices and coupled nonlinear oscillators for convenience, any other spatially distributed system could be used instead, such as turbulent fluid flows."]]></description>
<dc:subject>to_reread prediction spatio-temporal_statistics dynamical_systems factor_analysis cleaning_out_the_filing_cabinet_for_the_first_time_since_2005 have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a72594c17206/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_reread"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:factor_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cleaning_out_the_filing_cabinet_for_the_first_time_since_2005"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2201.05624">
    <title>[2201.05624] Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next</title>
    <dc:date>2023-03-24T18:51:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2201.05624</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved."]]></description>
<dc:subject>dynamical_systems simulation neural_networks differential_equations in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3f6c3e712506/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:differential_equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2008.00690">
    <title>[2008.00690] Counting equilibria of large complex systems by instability index</title>
    <dc:date>2023-03-15T15:06:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2008.00690</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider a nonlinear autonomous system of N≫1 degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such systems generically undergo an abrupt transition from a trivial phase portrait with a single stable equilibrium into a topologically non-trivial regime of 'absolute instability' where equilibria are on average exponentially abundant, but typically all of them are unstable, unless the dynamics is purely gradient. When interactions increase even further the stable equilibria eventually become on average exponentially abundant unless the interaction is purely solenoidal. We further calculate the mean proportion of equilibria which have a fixed fraction of unstable directions."]]></description>
<dc:subject>to:NB dynamical_systems high-dimensional_probability</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d6fd3c8acda5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_probability"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.nature.com/articles/s41598-017-00810-8">
    <title>Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems | Scientific Reports</title>
    <dc:date>2023-01-23T03:35:12+00:00</dc:date>
    <link>https://www.nature.com/articles/s41598-017-00810-8</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) where the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems."]]></description>
<dc:subject>to:NB artificial_intelligence dynamical_systems emergence color_me_skeptical via:rvenkat</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:55f81a741912/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:artificial_intelligence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:emergence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:rvenkat"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journal.r-project.org/archive/2014/RJ-2014-023/index.html">
    <title>phaseR: An R Package for Phase Plane Analysis of Autonomous ODE Systems (Grayling, 2014)</title>
    <dc:date>2022-12-02T15:46:52+00:00</dc:date>
    <link>https://journal.r-project.org/archive/2014/RJ-2014-023/index.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When modelling physical systems, analysts will frequently be confronted by differential equations which cannot be solved analytically. In this instance, numerical integration will usually be the only way forward. However, for autonomous systems of ordinary differential equations (ODEs) in one or two dimensions, it is possible to employ an instructive qualitative analysis foregoing this requirement, using so-called phase plane methods. Moreover, this qualitative analysis can even prove to be highly useful for systems that can be solved analytically, or will be solved numerically anyway. The package phaseR allows the user to perform such phase plane analyses: determining the stability of any equilibrium points easily, and producing informative plots."]]></description>
<dc:subject>to:NB have_skimmed R dynamical_systems to_teach</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a925ecd44c4a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:R"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.science.org/doi/10.1126/sciadv.abm8310">
    <title>Network structural origin of instabilities in large complex systems | Science Advances</title>
    <dc:date>2022-08-31T23:22:25+00:00</dc:date>
    <link>https://www.science.org/doi/10.1126/sciadv.abm8310</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks show nonnormality and that nonnormality can give rise to reactivity—the capacity of a linearly stable system to amplify its response to perturbations, oftentimes exciting nonlinear instabilities. Here, we identify network structural properties underlying the pervasiveness of nonnormality and reactivity in real directed networks, which we establish using the most extensive dataset of such networks studied in this context to date. The identified properties are imbalances between incoming and outgoing network links and paths at each node. On the basis of this characterization, we develop a theory that quantitatively predicts nonnormality and reactivity and explains the observed pervasiveness. We suggest that these results can be used to design, upgrade, control, and manage networks to avoid or promote network instabilities."]]></description>
<dc:subject>to:NB dynamical_systems networks motter.adilson</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4311381b447f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:motter.adilson"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://jmlr.org/papers/v23/20-617.html">
    <title>Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems</title>
    <dc:date>2022-07-15T12:27:42+00:00</dc:date>
    <link>https://jmlr.org/papers/v23/20-617.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of learning a nonlinear dynamical system governed by a nonlinear state equation ht+1=ϕ(ht,ut;θ)+wtht+1=ϕ(ht,ut;θ)+wt. Here θθ is the unknown system dynamics, htht is the state, utut is the input and wtwt is the additive noise vector. We study gradient based algorithms to learn the system dynamics θθ from samples obtained from a single finite trajectory. If the system is run by a stabilizing input policy, then using a mixing-time argument we show that temporally-dependent samples can be approximated by i.i.d. samples. We then develop new guarantees for the uniform convergence of the gradient of the empirical loss induced by these i.i.d. samples. Unlike existing works, our bounds are noise sensitive which allows for learning the ground-truth dynamics with high accuracy and small sample complexity. When combined, our results facilitate efficient learning of a broader class of nonlinear dynamical systems as compared to the prior works. We specialize our guarantees to entrywise nonlinear activations and verify our theory in various numerical experiments."]]></description>
<dc:subject>dynamical_systems equations_of_motion_from_a_time_series in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:83b6712533b8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.04217">
    <title>[2206.04217] Decomposition of Boolean networks: An approach to modularity of biological systems</title>
    <dc:date>2022-06-11T04:50:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.04217</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network satisfying certain conditions, there is a unique collection of subnetworks so that the network can be reconstructed from these subnetworks by an extension operation. The main result of the paper is that this structural decomposition induces a corresponding decomposition of the network dynamics. The theory is motivated by the search for a mathematical framework to formalize the hypothesis that biological systems are modular, widely accepted in the life sciences, but not well-defined and well-characterized. As an example of how dynamic modularity could be used for the efficient identification of phenotype control, the control strategies for the network can be found by identifying controls in its modules, one at a time."]]></description>
<dc:subject>to:NB gene_expression_data_analysis dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5fcfb6485173/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gene_expression_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.94.015005">
    <title>Rev. Mod. Phys. 94, 015005 (2022) - Collective nonlinear dynamics and self-organization in decentralized power grids</title>
    <dc:date>2022-06-06T13:04:31+00:00</dc:date>
    <link>https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.94.015005</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The ongoing transition to renewable energy supply comes with a restructuring of power grids, changing their effective interaction topologies, more and more strongly decentralizing them and substantially modifying their input, output, and response characteristics. All of these changes imply that power grids become increasingly affected by collective, nonlinear dynamic phenomena, structurally and dynamically more distributed and less predictable in space and time, more heterogeneous in its building blocks, and as a consequence less centrally controllable. Here cornerstone aspects of data-driven and mathematical modeling of collective dynamical phenomena emerging in real and model power grid networks by combining theories from nonlinear dynamics, stochastic processes and statistical physics, anomalous statistics, optimization, and graph theory are reviewed. The mathematical background required for adequate modeling and analysis approaches is introduced, an overview of power system models is given, and a range of collective dynamical phenomena are focused on, including synchronization and phase locking, flow (re)routing, Braess’s paradox, geometric frustration, and spreading and localization of perturbations and cascading failures, as well as the nonequilibrium dynamics of power grids, where fluctuations play a pivotal role."]]></description>
<dc:subject>dynamical_systems networks self-organization synchronization kurths.jurgen re:blackouts_and_alienation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:436a84efd0d7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:self-organization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:synchronization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kurths.jurgen"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:blackouts_and_alienation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.06601">
    <title>[2203.06601] Dynamics on higher-order networks: A review</title>
    <dc:date>2022-06-06T12:57:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.06601</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions. Higher-order networks, where a link can connect more than two nodes, have therefore emerged as a new frontier in network science. Since group interactions are common in social, biological, and technological systems, higher-order networks have recently led to important new discoveries across many fields of research. We here review these works, focusing in particular on the novel aspects of the dynamics that emerges on higher-order networks. We cover a variety of dynamical processes that have thus far been studied, including different synchronization phenomena, contagion processes, the evolution of cooperation, and consensus formation. We also outline open challenges and promising directions for future research."]]></description>
<dc:subject>to:NB networks dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:39465def7bde/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2008.02915">
    <title>[2008.02915] Kernel Ordinary Differential Equations</title>
    <dc:date>2022-02-15T14:55:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2008.02915</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA too. We demonstrate the efficacy of our method through numerous ODE examples."]]></description>
<dc:subject>equations_of_motion_from_a_time_series dynamical_systems kernel_methods statistics nonparametrics splines in_NB have_skimmed</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8188454a9772/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_skimmed"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.11231">
    <title>[2107.11231] Optimization on manifolds: A symplectic approach</title>
    <dc:date>2021-08-17T14:16:01+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.11231</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>dynamical_systems geometry optimization jordan.michael_i. via:rvenkat</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:879a72440557/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:jordan.michael_i."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:rvenkat"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.10242">
    <title>[2101.10242] Between Synchrony and Turbulence: Intricate Hierarchies of Coexistence Patterns</title>
    <dc:date>2021-08-06T15:39:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.10242</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Coupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of so-called chimera states, states of coexisting synchronized and unsynchronized oscillators, provided a possible link between the two and definitely showed that different parts of the same ensemble can sustain qualitatively different forms of motion. Here, we demonstrate that globally coupled identical oscillators can express a range of coexistence patterns more comprehensive than chimeras. A hierarchy of such states evolves from the fully synchronized solution in a series of cluster-splittings. At the far end of this hierarchy, the states further collide with their own mirror-images in phase space -- rendering the motion chaotic, destroying some of the clusters and thereby producing even more intricate coexistence patterns. A sequence of such attractor collisions can ultimately lead to full incoherence of only single asynchronous oscillators. Chimera states, with one large synchronized cluster and else only single oscillators, are found to be just one step in this transition from low- to high-dimensional dynamics."]]></description>
<dc:subject>to:NB dynamical_systems synchronization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ded08487b315/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:synchronization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.014409">
    <title>Phys. Rev. E 104, 014409 (2021) - Choosing dynamical systems that predict weak input</title>
    <dc:date>2021-07-22T15:42:39+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.014409</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Somehow, our brain and other organisms manage to predict their environment. Behind this must be an input-dependent dynamical system, or recurrent neural network, whose present state reflects the history of environmental input. The design principles for prediction—in particular, what kinds of attractors allow for greater predictive capability—are still unknown. We offer some clues to design principles using an attractor picture when the environment perturbs the system's state weakly, motivating and developing some theory for continuous-time time-varying linear reservoirs along the way. Reservoirs that inherently support only stable fixed points are generically good predictors, while reservoirs with limit cycles are good predictors for noisy periodic input."]]></description>
<dc:subject>to:NB prediction dynamical_systems design_for_a_brain</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4b0cfbc8d859/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:design_for_a_brain"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.00177">
    <title>[2106.00177] Solutions of the Multivariate Inverse Frobenius--Perron Problem</title>
    <dc:date>2021-07-01T13:31:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.00177</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We address the inverse Frobenius--Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map, that is, a map under which the uniform distribution on the d-dimensional hypercube as invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via 1-dimensional examples, and then use the factorization to present solutions in 1 and 2 dimensions induced by a range of uniform maps."]]></description>
<dc:subject>to:NB dynamical_systems ergodic_theory computational_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cc12c18854a0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.08525">
    <title>[2106.08525] A Feynman-Kac Type Theorem for ODEs: Solutions of Second Order ODEs as Modes of Diffusions</title>
    <dc:date>2021-06-28T04:35:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.08525</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this article, we prove a Feynman-Kac type result for a broad class of second order ordinary differential equations. The classical Feynman-Kac theorem says that the solution to a broad class of second order parabolic equations is the mean of a particular diffusion. In our situation, we show that the solution to a system of second order ordinary differential equations is the mode of a diffusion, defined through the Onsager-Machlup formalism. One potential utility of our result is to use Monte Carlo type methods to estimate the solutions of ordinary differential equations. We conclude with examples of our result illustrating its utility in numerically solving linear second order ODEs."]]></description>
<dc:subject>to:NB stochastic_processes dynamical_systems path_integrals_for_classical_stochastic_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a427215fa02e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:path_integrals_for_classical_stochastic_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.03523">
    <title>[2106.03523] A stylised view on structural and functional connectivity in dynamical processes in networks</title>
    <dc:date>2021-06-10T02:03:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.03523</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The relationship of network structure and dynamics is one of most extensively investigated problems in the theory of complex systems of the last years. Understanding this relationship is of relevance to a range of disciplines -- from Neuroscience to Geomorphology. A major strategy of investigating this relationship is the quantitative comparison of a representation of network architecture (structural connectivity) with a (network) representation of the dynamics (functional connectivity). Analysing such SC/FC relationships has over the past years contributed substantially to our understanding of the functional role of network properties, such as modularity, hierarchical organization, hubs and cycles.
"Here, we show that one can distinguish two classes of functional connectivity -- one based on simultaneous activity (co-activity) of nodes the other based on sequential activity of nodes. We delineate these two classes in different categories of dynamical processes -- excitations, regular and chaotic oscillators -- and provide examples for SC/FC correlations of both classes in each of these models. We expand the theoretical view of the SC/FC relationships, with conceptual instances of the SC and the two classes of FC for various application scenarios in Geomorphology, Freshwater Ecology, Systems Biology, Neuroscience and Social-Ecological Systems.
"Seeing the organization of a dynamical processes in a network either as governed by co-activity or by sequential activity allows us to bring some order in the myriad of observations relating structure and function of complex networks."]]></description>
<dc:subject>to:NB dynamical_systems networks functional_connectivity synchronization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:23617071a49b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:functional_connectivity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:synchronization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2004.07774">
    <title>[2004.07774] Computing all identifiable functions of parameters for ODE models</title>
    <dc:date>2021-06-10T01:59:57+00:00</dc:date>
    <link>https://arxiv.org/abs/2004.07774</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Parameter identifiability is a structural property of an ODE model for recovering the values of parameters from the data (i.e., from the input and output variables). This property is a prerequisite for meaningful parameter identification in practice. In the presence of nonidentifiability, it is important to find all functions of the parameters that are identifiable. The existing algorithms check whether a given function of parameters is identifiable or, under the solvability condition, find all identifiable functions. However, this solvability condition is not always satisfied, which presents a challenge. Our first main result is an algorithm that computes all identifiable functions without any additional assumptions, which is the first such algorithm as far as we know. Our second main result concerns the identifiability from multiple experiments (with generically different inputs and initial conditions among the experiments). For this problem, we prove that the set of functions identifiable from multiple experiments is what would actually be computed by input-output equation-based algorithms (whether or not the solvability condition is fulfilled), which was not known before. We give an algorithm that not only finds these functions but also provides an upper bound for the number of experiments to be performed to identify these functions. We provide an implementation of the presented algorithms."]]></description>
<dc:subject>to:NB partial_identification dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5bfa1f9f20be/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:partial_identification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1809.05243">
    <title>[1809.05243] Random Fixed Points, Limits and Systemic risk</title>
    <dc:date>2021-05-18T14:00:45+00:00</dc:date>
    <link>https://arxiv.org/abs/1809.05243</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i th FP equation depends on the j th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random neighbor components. We obtain finite dimensional limit FP equations (in a much smaller dimensional space), whose solutions approximate the solution of the random FP equations for almost all realizations, in the asymptotic limit (number of components increase). Our techniques are different from the traditional mean-field methods, which deal with stochastic FP equations in the space of distributions to describe the stationary distributions of the systems. In contrast our focus is on realization-wise FP solutions. We apply the results to study systemic risk in a large financial heterogeneous network with many small institutions and one big institution, and demonstrate some interesting phenomenon."

--- This _sounds_ weird, but possibly interesting, in a "what does a generic randomly-wired system do anyway?" vein.]]></description>
<dc:subject>to:NB dynamical_systems stochastic_processes macro_from_micro color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:27faf6ca4b62/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macro_from_micro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2007.04890">
    <title>[2007.04890] Emergent stability in complex network dynamics</title>
    <dc:date>2021-05-13T14:11:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.04890</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any design for stability. What then are the naturally emerging organizing principles of complex-system stability? Encoded within the system's stability matrix, the Jacobian, the answer is obscured by the scale and diversity of the relevant systems, their broad parameter space, and their nonlinear interaction mechanisms. To make advances, here we uncover emergent patterns in the structure of the Jacobian, rooted in the interplay between the network topology and the system's intrinsic nonlinear dynamics. These patterns help us analytically identify the few relevant control parameters that determine a system's dynamic stability. Complex systems, we find, exhibit discrete stability classes, from asymptotically unstable, where stability is unattainable, to sensitive, in which stability abides within a bounded range of the system's parameters. Most crucially, alongside these two classes, we uncover a third class, asymptotically stable, in which a sufficiently large and heterogeneous network acquires a guaranteed stability, independent of parameters, and therefore insensitive to external perturbation. Hence, two of the most ubiquitous characteristics of real-world networks - scale and heterogeneity - emerge as natural organizing principles to ensure stability in the face of changing environmental conditions."]]></description>
<dc:subject>to:NB dynamical_systems networks color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:444ba86026f9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.053304">
    <title>Phys. Rev. E 103, 053304 (2021) - Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization</title>
    <dc:date>2021-05-13T06:00:36+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.053304</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Optimization is at the heart of machine learning, statistics, and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as spin glasses. Proximal algorithms form a class of methods that are broadly applicable and are particularly well-suited to nonsmooth, constrained, large-scale, and distributed optimization problems. There are essentially five proximal algorithms currently known, each proposed in seminal work: Forward-backward splitting, Tseng splitting, Douglas-Rachford, alternating direction method of multipliers, and the more recent Davis-Yin. These methods sit on a higher level of abstraction compared to gradient-based ones, with deep roots in nonlinear functional analysis. In this paper we show that all of these methods are actually different discretizations of a single differential equation, namely, the simple gradient flow which dates back to Cauchy (1847). An important aspect behind many of the success stories in machine learning relies on “accelerating” the convergence of first-order methods. However, accelerated methods are notoriously difficult to analyze, counterintuitive, and without an underlying guiding principle. We show that similar discretization schemes applied to Newton's equation with an additional dissipative force, which we refer to as accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms—the majority of which are new although some recover known cases in the literature. Furthermore, we extend these methods to stochastic settings, allowing us to make connections with Langevin and Fokker-Planck equations. Similar ideas apply to gradient descent, heavy ball, and Nesterov's method which are simpler. Our results therefore provide a unified framework from which several important optimization methods are nothing but simulations of classical dissipative systems."]]></description>
<dc:subject>optimization dynamical_systems in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3a8a4c951da0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2007.07447">
    <title>[2007.07447] Motifs for processes on networks</title>
    <dc:date>2021-05-12T18:32:10+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.07447</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as "motifs" that occur frequently in real-world networks and may contribute by various mechanisms to important functions in these systems. However, these mechanisms are unknown for many of these motifs. We propose to distinguish between "structure motifs" (i.e., graphlets) in networks and "process motifs" (which we define as structured sets of walks) on networks and consider process motifs as building blocks of processes on networks. Using the steady-state covariances and steady-state correlations in a multivariate Ornstein--Uhlenbeck process on a network as examples, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks."]]></description>
<dc:subject>to:NB network_data_analysis dynamical_systems porter.mason_a. to_teach:baby-nets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:71edf40dff9d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:porter.mason_a."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:baby-nets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-072020-084434">
    <title>Analysis and Interventions in Large Network Games | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2021-05-06T13:49:30+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-072020-084434</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We review classic results and recent progress on equilibrium analysis, dynamics, and optimal interventions in network games with both continuous and discrete strategy sets. We study strategic interactions in deterministic networks as well as networks generated from a stochastic network formation model. For the former case, we review a unifying framework for analysis based on the theory of variational inequalities. For the latter case, we highlight how knowledge of the stochastic network formation model can be used by a central planner to design interventions for large networks in a computationally efficient manner when exact network data are not available."]]></description>
<dc:subject>to:NB dynamical_systems networks control_theory_and_control_engineering game_theory re:in_soviet_union_optimization_problem_solves_you</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4256d40d9911/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:game_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:in_soviet_union_optimization_problem_solves_you"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-061820-083817">
    <title>Model Reduction Methods for Complex Network Systems | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2021-05-06T13:48:38+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-061820-083817</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics."]]></description>
<dc:subject>to:NB dynamical_systems networks dimension_reduction graph_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b03640a0c4ff/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graph_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-071020-010108">
    <title>Koopman Operators for Estimation and Control of Dynamical Systems | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2021-05-06T13:46:57+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-071020-010108</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A common way to represent a system's dynamics is to specify how the state evolves in time. An alternative viewpoint is to specify how functions of the state evolve in time. This evolution of functions is governed by a linear operator called the Koopman operator, whose spectral properties reveal intrinsic features of a system. For instance, its eigenfunctions determine coordinates in which the dynamics evolve linearly. This review discusses the theoretical foundations of Koopman operator methods, as well as numerical methods developed over the past two decades to approximate the Koopman operator from data, for systems both with and without actuation. We pay special attention to ergodic systems, for which especially effective numerical methods are available. For nonlinear systems with an affine control input, the Koopman formalism leads naturally to systems that are bilinear in the state and the input, and this structure can be leveraged for the design of controllers and estimators."

]]></description>
<dc:subject>dynamical_systems control_theory_and_control_engineering ergodic_theory in_NB koopman_operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:adc64525a4f6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:koopman_operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2104.09299">
    <title>[2104.09299] Complex networks of interacting stochastic tipping elements: cooperativity of phase separation in the large-system limit</title>
    <dc:date>2021-04-21T19:45:48+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.09299</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are sub-dominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erdös-Rényi, Barabási-Albert and Watts-Strogatz networks of different size and with different coupling parameters."]]></description>
<dc:subject>to:NB dynamical_systems networks macro_from_micro re:do-institutions-evolve to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f7b3f6fc4328/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macro_from_micro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:do-institutions-evolve"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.10224">
    <title>[2005.10224] The Random Feature Model for Input-Output Maps between Banach Spaces</title>
    <dc:date>2021-04-20T13:21:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.10224</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Well known to the machine learning community, the random feature model, originally introduced by Rahimi and Recht in 2008, is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to the real line. In this paper, we instead propose a methodology for use of the random feature model as a data-driven surrogate for operators that map an input Banach space to an output Banach space. Although the methodology is quite general, we consider operators defined by partial differential equations (PDEs); here, the inputs and outputs are themselves functions, with the input parameters being functions required to specify the problem, such as initial data or coefficients, and the outputs being solutions of the problem. Upon discretization, the model inherits several desirable attributes from this infinite-dimensional, function space viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions. We view the random feature model as a non-intrusive data-driven emulator, provide a mathematical framework for its interpretation, and demonstrate its ability to efficiently and accurately approximate the nonlinear parameter-to-solution maps of two prototypical PDEs arising in physical science and engineering applications: viscous Burgers' equation and a variable coefficient elliptic equation."]]></description>
<dc:subject>random_features analysis via:rvenkat approximation in_NB have_read dynamical_systems re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:81171133ef9a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_features"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:rvenkat"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.158102">
    <title>Phys. Rev. Lett. 126, 158102 (2021) - Collective Synchronous Spiking in a Brain Network of Coupled Nonlinear Oscillators</title>
    <dc:date>2021-04-18T15:48:15+00:00</dc:date>
    <link>https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.158102</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and phase coupling between modes are taken into account. The nonlinear behavior of the modes participating in the network are the result of the nonresonant dynamics of weakly evanescent cortical waves that, as shown recently, adhere to an inverse frequency–wave number dispersion relation when propagating through an inhomogeneous anisotropic media characteristic of the brain cortex. This description provides a missing link between simplistic models of synchronization in networks of small amplitude phase coupled oscillators and in networks built with various empirically fitted models of pulse or amplitude coupled spiking neurons. Overall the phase-amplitude coupling mechanism presented in the Letter shows significantly more efficient synchronization compared to current standard approaches and demonstrates an emergence of collective synchronized spiking from subthreshold oscillations that neither phase nor amplitude coupling alone are capable of explaining."]]></description>
<dc:subject>to:NB dynamical_systems synchronization neural_data_analysis neuroscience</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8d9a55d2591e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:synchronization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neuroscience"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12513">
    <title>Nonstationary space–time covariance functions induced by dynamical systems - Senoussi - - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2021-04-12T03:43:08+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12513</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article provides a novel approach to nonstationarity by considering a bridge between differential equations and spatial fields. We consider the dynamical transformation of a given spatial process undergoing the action of a temporal flow of space diffeomorphisms. Such dynamical deformations are shown to be connected to certain classes of ordinary and partial differential equations. The natural question arises of how such dynamical diffeomorphisms convert the original spatial covariance function, specifically if the original covariance is spatially stationary or isotropic. We first challenge this question from a general perspective, and then turn into the special cases of both d‐dimensional Euclidean spaces, and hyperspheres. Several examples of dynamical diffeomorphisms defined in these spaces are given and some emphasis has been put on the stationary reducibility problem. We provide a simple illustration to show the performance of the maximum likelihood estimation of the parameters of a family of dynamically deformed covariance functions."]]></description>
<dc:subject>to:NB spatio-temporal_statistics variance_estimation dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9c55ada68f8c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variance_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.05202">
    <title>[2012.05202] Tâtonnement, Approach to Equilibrium and Excess Volatility in Firm Networks</title>
    <dc:date>2021-04-12T03:00:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.05202</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study the conditions under which input-output networks can dynamically attain competitive equilibrium, where markets clear and profits are zero. We endow a classical firm network model with simple dynamical rules that reduce supply/demand imbalances and excess profits. We show that the time needed to reach equilibrium diverges as the system approaches an instability point beyond which the Hawkins-Simons condition is violated and competitive equilibrium is no longer realisable. We argue that such slow dynamics is a source of excess volatility, through accumulation and amplification of exogenous shocks. Factoring in essential physical constraints, such as causality or inventory management, we propose a dynamically consistent model that displays a rich variety of phenomena. Competitive equilibrium can only be reached after some time and within some region of parameter space, outside of which one observes periodic and chaotic phases, reminiscent of real business cycles. This suggests an alternative explanation of the excess volatility that is of purely endogenous nature. Other regimes include deflationary equilibria and intermittent crises characterised by bursts of inflation. Our model can be calibrated using highly disaggregated data on individual firms and prices, and may provide a powerful tool to describe out-of-equilibrium economies."]]></description>
<dc:subject>to:NB economics dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d7186c0e3e52/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:economics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.05100">
    <title>[2102.05100] On structural and practical identifiability</title>
    <dc:date>2021-03-17T20:23:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.05100</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has a long tradition. Computationally efficient methods to detect and cure it have been developed recently. Practical non-identifiability on the other hand has not been investigated at the same conceptually clear level. We argue that practical identifiability is more challenging than structural identifiability when it comes to modelling experimental data. We discuss that the classical approach based on the Fisher information matrix has severe shortcomings. As an alternative, we propose using the profile likelihood, which is a powerful approach to detect and resolve practical non-identifiability."]]></description>
<dc:subject>to:NB identifiability dynamical_systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:09293a0b0fd9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:identifiability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://doi.org/10.1111/sjos.12513">
    <title>Nonstationary Space‐time Covariance Functions induced by Dynamical Systems - Senoussi - - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2021-01-19T18:42:24+00:00</dc:date>
    <link>https://doi.org/10.1111/sjos.12513</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper provides a novel approach to nonstationarity by considering a bridge between differential equations and spatial fields. We consider the dynamical transformation of a given spatial process undergoing the action of a temporal flow of space diffeomorphisms. Such dynamical deformations are shown to be connected to certain classes of ordinary and partial differential equations.
"The natural question arises of how such dynamical diffeomorphisms convert the original spatial covariance function, specifically if the original covariance is spatially stationary or isotropic. We first challenge this question from a general perspective, and then turn into the special cases of both d‐dimensional Euclidean spaces, and hyperspheres. Several examples of dynamical diffeomorphisms defined in these spaces are given and some emphasis has been put on the stationary reducibility problem. We provide a simple illustration to show the performance of the maximum likelihood estimation of the parameters of a family of dynamically deformed covariance functions."]]></description>
<dc:subject>non-stationarity dynamical_systems statistics covariance_estimation spatio-temporal_statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:981a9aed08f8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:non-stationarity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:covariance_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatio-temporal_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2002.02250">
    <title>[2002.02250] Uncovering differential equations from data with hidden variables</title>
    <dc:date>2020-12-26T17:46:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2002.02250</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data-set of temperature time series provided by the Réseau de Transport d'Électricité (RTE). Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables."]]></description>
<dc:subject>equations_of_motion_from_a_time_series sparsity linear_regression dynamical_systems inference_to_latent_objects in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3ba9d3e1c481/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inference_to_latent_objects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.06391">
    <title>[2012.06391] Learning physically consistent mathematical models from data using group sparsity</title>
    <dc:date>2020-12-15T01:36:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.06391</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a statistical learning framework based on group-sparse regression that can be used to 1) enforce conservation laws, 2) ensure model equivalence, and 3) guarantee symmetries when learning or inferring differential-equation models from measurement data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas like biology, high noise levels, sensor-induced correlations, and strong inter-system variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn "biologically plausible and physically consistent" models rather than models that simply fit the data best. We present a novel group Iterative Hard Thresholding (gIHT) algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling."]]></description>
<dc:subject>to:NB dynamical_systems statistical_inference_for_stochastic_processes sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7760c0b795d9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.08641">
    <title>[1901.08641] Gibbs posterior convergence and the thermodynamic formalism</title>
    <dc:date>2020-12-12T20:03:25+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.08641</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard Bayesian inference. We place a prior over a model class consisting of a parametrized family of Gibbs measures on a mixing shift of finite type. This model class generalizes (hidden) Markov chain models by allowing for long range dependencies, including Markov chains of arbitrarily large orders. We characterize the asymptotic behavior of the Gibbs posterior distribution on the parameter space as the number of observations tends to infinity. In particular, we define a limiting variational problem over the space of joinings of the model system with the observed system, and we show that the Gibbs posterior distributions concentrate around the solution set of this variational problem. In the case of properly specified models our convergence results may be used to establish posterior consistency. This work establishes tight connections between Gibbs posterior inference and the thermodynamic formalism, which may inspire new proof techniques in the study of Bayesian posterior consistency for dependent processes."]]></description>
<dc:subject>to:NB bayesian_consistency statistical_inference_for_stochastic_processes dynamical_systems large_deviations ergodic_theory nobel.andrew</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2ed738a0f046/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesian_consistency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nobel.andrew"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.05601">
    <title>[2012.05601] Bayes posterior convergence for loss functions via almost additive Thermodynamic Formalism</title>
    <dc:date>2020-12-12T20:01:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.05601</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical systems from ergodic observations, where the Bayesian procedure is based on the Gibbs posterior inference, a decision process generalization of standard Bayesian inference where the likelihood is replaced by the exponential of a loss function. In the case of direct observation and almost-additive loss functions, we prove an exponential convergence of the a posteriori measures a limit measure. Our estimates on the Bayes posterior convergence for direct observation are related but complementary to those in a recent paper by K. McGoff, S. Mukherjee and A. Nobel. Our approach makes use of non-additive thermodynamic formalism and large deviation properties instead of joinings."]]></description>
<dc:subject>to:NB bayesian_consistency dynamical_systems statistical_inference_for_stochastic_processes large_deviations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ca38875160c1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesian_consistency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:large_deviations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.04556">
    <title>[2012.04556] Finding nonlinear system equations and complex network structures from data: a sparse optimization approach</title>
    <dc:date>2020-12-12T03:25:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.04556</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system equations and structure based solely on measured time series. Recently, methods based on sparse optimization have been developed. For example, the principle of exploiting sparse optimization such as compressive sensing to find the equations of nonlinear dynamical systems from data was articulated in 2011 by the Nonlinear Dynamics Group at Arizona State University. This article presents a brief review of the recent progress in this area. The basic idea is to expand the equations governing the dynamical evolution of the system into a power series or a Fourier series of a finite number of terms and then to determine the vector of the expansion coefficients based solely on data through sparse optimization. Examples discussed here include discovering the equations of stationary or nonstationary chaotic systems to enable prediction of dynamical events such as critical transition and system collapse, inferring the full topology of complex networks of dynamical oscillators and social networks hosting evolutionary game dynamics, and identifying partial differential equations for spatiotemporal dynamical systems. Situations where sparse optimization is effective and those in which the method fails are discussed. Comparisons with the traditional method of delay coordinate embedding in nonlinear time series analysis are given and the recent development of model-free, data driven prediction framework based on machine learning is briefly introduced."]]></description>
<dc:subject>to:NB dynamical_systems time_series sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2a830c8c26f9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.01068">
    <title>[2012.01068] Reduced-Order Models for Coupled Dynamical Systems: Koopman Operator and Data-driven Methods</title>
    <dc:date>2020-12-04T21:40:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.01068</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we demonstrate a link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parametrizations of weakly coupled dynamical systems. Such parametrizations yield a set of stochastic integro-differential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integro-differential equations can be recast as a simpler multilevel Markovian model, and we establish an intutive link with the formalism of a generalized Langevin equation. This link helps setting up a clear connection between the top-down, equations-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings support, on the one hand, the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parametrizations."]]></description>
<dc:subject>stochastic_processes dynamical_systems macro_from_micro in_NB koopman_operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c3a153af7d79/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:macro_from_micro"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:koopman_operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2002.09922">
    <title>[2002.09922] Steering complex networks toward desired dynamics</title>
    <dc:date>2020-12-02T01:45:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2002.09922</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great practical interest in many areas of science, as well as providing insight into the interplay between network structure and dynamical behavior. We propose a pinning protocol for imposing specific dynamic evolutions compatible with the equations of motion on a networked system. The method does not impose any restrictions on the local dynamics, which may vary from node to node, nor on the interactions between nodes, which may adopt in principle any nonlinear mathematical form and be represented by weighted, directed or undirected, links. We first explore our method on small synthetic networks of chaotic oscillators, which allows us to unveil a correlation between the ordered sequence of pinned nodes and their topological influence in the network. We then consider a 12-species trophic web network, which is a model of a mammalian food web. By pinning a relatively small number of species, one can make the system abandon its spontaneous evolution from its (typically uncontrolled) initial state towards a target dynamics, or periodically control it so as to make the populations evolve within stipulated bounds. The relevance of these findings for environment management and conservation is discussed."]]></description>
<dc:subject>to:NB control_theory_and_control_engineering dynamical_systems networks re:in_soviet_union_optimization_problem_solves_you</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e392bf3ff108/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:in_soviet_union_optimization_problem_solves_you"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.11122">
    <title>[2011.11122] Controlling symmetries and clustered dynamics of complex networks</title>
    <dc:date>2020-11-25T15:41:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.11122</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of synchronization with nodes clustered in a desired way. Our approach consists of perturbing the original network connectivity, either by adding new edges or by adding/removing links together with modifying their weights. By solving suitable optimization problems, we furthermore guarantee that changes made on the existing topology are minimal. The conditions for the stability of the enforced pattern are derived for the general case, and the performance of the method is illustrated with paradigmatic examples. Our results are relevant to all the practical situations in which coordination of the networked systems into diverse groups may be desirable, such as for teams of robots, unmanned autonomous vehicles, power grids and central pattern generators."]]></description>
<dc:subject>to:NB dynamical_systems networks control_theory_and_control_engineering re:in_soviet_union_optimization_problem_solves_you</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ece0572ed180/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:in_soviet_union_optimization_problem_solves_you"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.11371">
    <title>[2011.11371] Ordinary differential equations (ODE): metric entropy and nonasymptotic theory for noisy function fitting</title>
    <dc:date>2020-11-25T14:38:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.11371</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper establishes novel results on the metric entropy of ODE solution classes. In addition, we establish a nonasymptotic theory concerning noisy function fitting for nonparametric least squares and least squares based on Picard iterations. Our results on the metric entropy provide answers to "how do the degree of smoothness and the "size" of a class of ODEs affect the "size" of the associated class of solutions?" We establish a general upper bound on the covering number of solution classes associated with the higher order Picard type ODEs, y(m)(x)=f(x,y(x),y′(x),...,y(m−1)(x)). This result implies, the covering number of the underlying solution class is (basically) bounded from above by the covering number of the class  that f ranges over. This general bound (basically) yields a sharp scaling when f is parameterized by a K−dimensional vector of coefficients belonging to a ball and the noisy recovery is essentially no more difficult than estimating a K−dimensional element in the ball. For m=1, when  is an infinitely dimensional smooth class, the solution class ends up with derivatives whose magnitude grows factorially fast -- "a curse of smoothness". We introduce a new notion called the "critical smoothness parameter" to derive an upper bound on the covering number of the solution class. When the sample size is large relative to the degree of smoothness, the rate of convergence associated with the noisy recovery problem obtained by applying this "critical smoothness parameter" based approach improves the rate obtained by applying the general upper bound on the covering number (and vice versa)."]]></description>
<dc:subject>to:NB dynamical_systems time_series curve_fitting to_read statistics learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1bac398887af/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:curve_fitting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.09573">
    <title>[2011.09573] Learning Recurrent Neural Net Models of Nonlinear Systems</title>
    <dc:date>2020-11-23T17:26:33+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.09573</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the following learning problem: Given sample pairs of input and output signals generated by an unknown nonlinear system (which is not assumed to be causal or time-invariant), we wish to find a continuous-time recurrent neural net with hyperbolic tangent activation function that approximately reproduces the underlying i/o behavior with high confidence. Leveraging earlier work concerned with matching output derivatives up to a given finite order, we reformulate the learning problem in familiar system-theoretic language and derive quantitative guarantees on the sup-norm risk of the learned model in terms of the number of neurons, the sample size, the number of derivatives being matched, and the regularity properties of the inputs, the outputs, and the unknown i/o map."
]]></description>
<dc:subject>to:NB raginsky.maxim learning_theory dynamical_systems to_read learning_under_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e20380910c33/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:raginsky.maxim"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-053018-023659">
    <title>Discrete Event Systems: Modeling, Observation, and Control | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2020-11-19T05:23:41+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-053018-023659</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article begins with an introduction to the modeling of discrete event systems, a class of dynamical systems with discrete states and event-driven dynamics. It then focuses on logical discrete event models, primarily automata, and reviews observation and control problems and their solution methodologies. Specifically, it discusses diagnosability and opacity in the context of partially observed discrete event systems. It then discusses supervisory control for both fully and partially observed systems. The emphasis is on presenting fundamental results first, followed by a discussion of current research directions."

]]></description>
<dc:subject>to:NB dynamical_systems control_theory_and_control_engineering automata_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2b962984d03a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-053018-023717">
    <title>Formal Methods for Control Synthesis: An Optimization Perspective | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2020-11-19T05:23:14+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-053018-023717</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In control theory, complicated dynamics such as systems of (nonlinear) differential equations are controlled mostly to achieve stability. This fundamental property, which can be with respect to a desired operating point or a prescribed trajectory, is often linked with optimality, which requires minimizing a certain cost along the trajectories of a stable system. In formal verification (model checking), simple systems, such as finite-state transition graphs that model computer programs or digital circuits, are checked against rich specifications given as formulas of temporal logics. The formal synthesis problem, in which the goal is to synthesize or control a finite system from a temporal logic specification, has recently received increased interest. In this article, we review some recent results on the connection between optimal control and formal synthesis. Specifically, we focus on the following problem: Given a cost and a correctness temporal logic specification for a dynamical system, generate an optimal control strategy that satisfies the specification. We first provide a short overview of automata-based methods, in which the dynamics of the system are mapped to a finite abstraction that is then controlled using an automaton corresponding to the specification. We then provide a detailed overview of a class of methods that rely on mapping the specification and the dynamics to constraints of an optimization problem. We discuss advantages and limitations of these two types of approaches and suggest directions for future research."]]></description>
<dc:subject>control_theory_and_control_engineering automata_theory dynamical_systems in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ea873961191f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:control_theory_and_control_engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:automata_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-053018-023744">
    <title>System Identification: A Machine Learning Perspective | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2020-11-19T05:21:49+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-053018-023744</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Estimation of functions from sparse and noisy data is a central theme in machine learning. In the last few years, many algorithms have been developed that exploit Tikhonov regularization theory and reproducing kernel Hilbert spaces. These are the so-called kernel-based methods, which include powerful approaches like regularization networks, support vector machines, and Gaussian regression. Recently, these techniques have also gained popularity in the system identification community. In both linear and nonlinear settings, kernels that incorporate information on dynamic systems, such as the smoothness and stability of the input–output map, can challenge consolidated approaches based on parametric model structures. In the classical parametric setting, the complexity of the model (the model order) needs to be chosen, typically from a finite family of alternatives, by trading bias and variance. This (discrete) model order selection step may be critical, especially when the true model does not belong to the model class. In regularization-based approaches, model complexity is controlled by tuning (continuous) regularization parameters, making the model selection step more robust. In this article, we review these new kernel-based system identification approaches and discuss extensions based on nuclear and  norms."]]></description>
<dc:subject>to:NB nonparametrics statistics learning_theory dynamical_systems to_teach:childs_garden_of_statistical_learning_theory learning_under_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:72d9379f7c5e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aos/1597370663">
    <title>McGoff , Nobel : Empirical risk minimization and complexity of dynamical models</title>
    <dc:date>2020-11-19T04:45:26+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aos/1597370663</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A dynamical model consists of a continuous self-map T:→T:X→X of a compact state space X and a continuous observation function f:→ℝf:X→R. This paper considers the fitting of a parametrized family of dynamical models to an observed real-valued stochastic process using empirical risk minimization. The limiting behavior of the minimum risk parameters is studied in a general setting. We establish a general convergence theorem for minimum risk estimators and ergodic observations. We then study conditions under which empirical risk minimization can effectively separate signal from noise in an additive observational noise model. The key condition in the latter results is that the family of dynamical models has limited complexity, which is quantified through a notion of entropy for families of infinite sequences that connects covering number based entropies with topological entropy studied in dynamical systems. We establish close connections between entropy and limiting average mean widths for stationary processes, and discuss several examples of dynamical models."]]></description>
<dc:subject>learning_theory dynamical_systems state_estimation nobel.andrew to_teach:childs_garden_of_statistical_learning_theory have_read in_NB learning_under_dependence</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8d0c6a1757d4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nobel.andrew"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>