27 papers · ranked by Valyu relevance
Agus Hasan
Title: Graphical abstract
Jordan Cotler, Semon Rezchikov
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'…
Chenyu Dong, Davide Faranda, Adriano Gualandi, Valerio Lucarini + 1 more
'Gianmarco Mengaldo'] Title: Significance In many complex systems, predictability can be substantially state-dependent. We propose here a purely data-driven approach for estimating the local predictability at different time scales. The effectiveness of our approach is validated against existing knowledge, and its…
Sean T. Vittadello, Léo P. M. Diaz, Yujing Liu, Adriana Zanca + 1 more
'Michael P. H. Stumpf'] An adult human body is made up of some 30 to 40 trillion cells, all of which stem from a single fertilized egg cell. The process by which the right cells appear to arrive in their right numbers at the right time at the right place – development – is only understood in the roughest of outlines.…
Farhan Khodaee, Rohola Zandie, Yufan Xia, Elazer R. Edelman
We propose a new theory for aging based on dynamical systems and provide a data-driven computational method to quantify the changes at the cellular level. We use ergodic theory to decompose the dynamics of changes during aging and show that aging is fundamentally a dissipative process within biological systems, akin to…
Usha Kadiyala, David Sprinzak, Nicholas A. M. Monk, Shannon E. Taylor + 6 more
'Shannon E. Taylor' 'Berta Verd' 'Katharina F. Sonnen' 'Lauren Moon' 'Adrienne H. K. Roeder' 'Ruben Perez-Carrasco' 'Pau Formosa-Jordan'] Title: ABSTRACT Developmental biology seeks to unravel the intricate regulatory mechanisms orchestrating the transformation of a single cell into a complex, multicellular organism.…
Enrique Morales, Cesar Bordehore, Héctor M. Pastor, David García-García
Stella Architect (iSee Systems) offers an object-oriented environment that facilitates the development of dynamic models. Stella, however, does not support some of the advanced mathematical tools that can be found in mathematical software such as R. Moreover, R is open source, contains numerous libraries and resources…
John Guckenheimer
in which b, λ, k, a are parameters with k large. Their description of dynamical behavior now known as chaos in this dissipative dynamical system was a landmark in dynamical systems theory. Littlewood's "monster paper" containing the details of their investigation finally appeared twelve years later in the journal Acta…
Sean T. Vittadello, Léo Diaz, Yujing Liu, Adriana Zanca + 1 more
An adult human body is made up of some 30 to 40 trillion cells, all of which stem from a single fertilized egg cell. The process by which the right cells appear to arrive in their right numbers at the right time at the right place - development - is only understood in the roughest of outlines. This process does not…
Matthew Foreman
This note discusses dynamical systems–systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called the study of the smooth behavior and ergodic theory. We then introduce the…
Sergio Cobo-López, Matthew Witt, Lucas J. Carbajal, Forest L. Rohwer + 1 more
All dynamical systems are transient. The dynamics of our world at biogeochemical, ecological, and astronomical scales exist in a transient state because the Earth, Sun, and universe are evolving toward thermodynamic equilibrium. However, predicting the tipping points associated with major dynamical shifts in these…
Stefano Giampiccolo, Giovanni Iacca, Luca Marchetti
Dynamical systems play a central role across the quantitative sciences, offering a powerful mathematical framework to describe, analyze, and predict the evolution of complex processes over time. In Systems Biology, dynamical systems provide a foundation for modeling and predicting the intricate behaviors of biological…
Yeachan Park
Narrow Networks Authors: ['Yeachan Park'] In the field of machine learning, comprehending the intricate training dynamics of neural networks poses a significant challenge. This paper explores the training dynamics of neural networks, particularly whether these dynamics can be expressed in a general closed-form…
Daniel Durstewitz, Georgia Koppe, Max Ingo Thurm
Mechanistic and computational models in neuroscience usually take the form of systems of differential or time-recursive equations. The spatio-temporal behavior of such systems is the subject of dynamical systems theory (DST). DST provides a powerful mathematical toolbox for describing and analyzing neurobiological…
Jiri Petrzela
Biological, engineering, economic, social, medical, environmental, and other systems exhibit time evolution. These observable objects can be either naturally inspired or artificial, isolated or non-autonomous, and truly deterministic or stochastic. Some of them can be, after appropriately executed simplification…
Subhrajit Sinha, Parvathi Kooloth
— In this work, we propose a novel approach to investigate symmetry breaking in dynamical systems. In particular, we use the notion of information transfer, which provides a measure of the entropy transfer between any pair of observables in a system, to predict symmetry breaking. We show that as a system loses…
Denizhan Pak, Randall D. Beer
Organisms must manage a trade-off between robustness and flexibility as they enact adaptive behaviors. One way organisms achieve this is by navigating a network of quasi-stable behavioral states. Evidence for such behavioral states has been observed in many organisms, and new methods for detecting these states have…
Jane Kondev, Marc Kirschner, Hernan G. Garcia, Gabriel L. Salmon + 1 more
Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which…
Jonathan V. Krispin
The present article focuses on presentations from the second topical cluster from the 2024 Theory and Philosophy Conference held by the ABAI-Cultural Systems. The cultural systems cluster was comprised of two primary talks-“Unhinging Design from Darwinian and Skinnerian Selection” (Wasserman, [37]), and a second…
Mohsen Farshad
Providing a simple description of entropy as the foundation of thermodynamics is necessary for researchers in explaining physical phenomena in the universe. Here we dive deep into the meaning of entropy starting from the basics and ending with the Newton's second law of motion which may be rooted in a hidden dimension…
Authors not listed
Molecular dynamics (MD) and hybrid quantum–classical (QM/MM) methods provide powerful tools for simulating chemical and biological systems, yet their application to long-timescale, strongly coupled processes remains limited by non-integrability, chaotic sensitivity, and extreme time-scale separation. These limitations…
Eric Koessler, Arkajit Mandal, Pengfei Huo
We derive the L-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the L-MFE method that satisfies this exact…
Serguei Saavedra, Yuguang Yang, Christopher P. Kempes, Chengyi Long + 3 more
Understanding the selecting and generating forces operating across the self-organization of ecological systems is synonymous with understanding principles of life itself. Three prominent hypotheses in ecological research—Lotka’s Maximum Power Principle, Odum and Pinkerton’s Intermediate Efficiency Principle, and…
Authors not listed
The GENERIC framework provides a robust structure for nonequilibrium dynamics but lacks a principled method to select reversible ($L$) and irreversible ($M$) brackets. Similarly, finite-time optimizations minimizing path-averaged reciprocal temperature exist but remain isolated. Here, we introduce the \textbf{Entropy…
Authors not listed
A framework for catalysis based on categorical aperture selection rather than temporal acceleration is presented. Traditional catalysis theory describes catalysts as agents that accelerate reactions by lowering activation energies, implicitly treating time as the fundamental variable and reaction rate enhancement as…
Stephen Goldup, Ivan Aprahamian
All chemists are familiar with the idea that, at equilibrium steady state, the relative concentrations of species present in a system are predicted by the corresponding equilibrium constants, which are in turn related to the relative free energy difference of the system components. There is also no net flux between…
Authors not listed
This paper formally defines an operational isomorphism between spectral damping in molecular vibronic systems and neuromodulatory control in biological sensory systems. Without asserting causal continuity or physical identity across scales, we show that both domains instantiate the same class of output-selective…