24 papers · ranked by Valyu relevance
X. T. Hou, X. Huang, Paris Perdikaris
Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce the Continuous Flow Operator (CFO), a framework that learns continuoustime PDE…
Samuel J. Abplanalp, Eric A. Reavis, Thanh P. Le, Michael F. Green
Ecological momentary assessment (EMA) is a frequently used approach among clinical researchers to collect naturalistic data in real time. EMA data can provide insights into the temporal dynamics of psychological processes. Traditional methods used to analyze EMA data, such as hierarchical linear modeling and multilevel…
Keisuke Kawano, Takuro Kutsuna, Naoki Hayashi, Yasushi Esaki + 1 more
'Hidenori Tanaka'] In many real-world scenarios, such as single-cell RNA sequencing, data are observed only as discrete-time snapshots spanning finite time intervals and subject to noisy timestamps, with no continuous trajectories available. Recovering the underlying continuous-time dynamics from these snapshots with…
Shuyun Jiao, David Waxman
There are many instances, in subjects such as biology, where a population number, or related quantity, changes in discrete time. For the population number at time n = 0, 1, 2, . . ., written xn, we show that some exactly soluble cases of xn can be related to a different problem, where the number of individuals changes…
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…
Sergey Kryzhevich
We give explicit criteria of solvability for families of linear systems on time scales. We introduce a new method of embedding a time scale into a non-autonomous system of ODEs. This will be the first step to implementing the structural stability result obtained by one of the co-authors together with V. A. Pliss to…
Jorge I. Poveda, Andrew R. Teel
H ybrid dynamical systems, which combine continuous-time and discrete-time dynamics, are pervasive in modern engineering. They naturally arise in cyber-physical systems (CPS) that integrate physical processes with digital components, spanning domains such as transportation [[1]], power grids [[2]], robotics [[3]], and…
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…
Sharma Yamijala, M. Belen Oviedo, Bryan Wong
This review focuses on the application of Density Functional Tight Binding (DFTB) to electronic-excited states, which has attracted significant attention for extending the computationally efficient approach to the time domain. The chapter highlights the use of real-time time-dependent-DFTB to probe the electron…
Henning Kirchberg, Abraham Nitzan, Hong Qian
We considered discrete and continuous representations of a thermodynamic process in which a random walker (e.g., a molecular motor on a molecular track) uses periodically pumped energy (work) to pass N sites and move energetically downhill while dissipating heat. Interestingly, we found that, starting from a discrete…
Marc Mangel, Alan Brown, Paul Bogdan
Variability is inherent to cyber systems. Here, we introduce ideas from stochastic population biology to describe the properties of two broad kinds of cyber systems. First, we assume that each of N0 components can be in only one of two states: functional or nonfunctional. We model this situation as a Markov process…
Authors not listed
Strong coupling and environmental memory render many open quantum systems intractable to classical computation. To overcome this barrier, we present a variational quantum algorithm capable of solving generalized form time-local quantum master equations directly on Noisy Intermediate-Scale Quantum (NISQ) processors. Our…
Esteban A. Hernandez-Vargas
Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient…
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…
Miguel A. Durán-Olivencia
Background Models of evolutionary dynamics have long been dominated by a paradigm of gradualism, yet the fossil record consistently points to a history defined by punctuation. This disconnect between theory and data has left major macroevolutionary events, such as punctuated equilibria, explosive radiations, and mass…
Duncan Bossion, Sutirtha Chowdhury, Pengfei Huo
We present the rigorous theoretical framework of the generalized spin mapping representation for non- adiabatic dynamics. This formalism is based on the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space in the state representation. The…
Tadashige Iwao, Yoshihiro Kimura, Tetsuya Iida
Understanding structural similarities across dynamical systems at different scales remains a central problem in nonlinear science [1, 3]. Here we propose a modeling framework for cross-scale morphogenetic dynamics, termed Generalized Morphogenesis Theory (GMT), based on a flow-inertia formulation: where S denotes…
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…
Antonio Carlos Costa, Massimo Vergassola
Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales. This immense variability hampers quantitative reasoning and renders the identification of universal principles elusive. Through data analysis and theory, we here show that slow non-ergodic drives generally give rise to heavy-tailed…
Karnamohit Ranka, Christine M. Isborn
Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate…
Karnamohit Ranka, Christine M. Isborn
Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate…
Gianmarco Ducci, Gennaro Vitucci, Philippe Chatelain, Renaud Ronsse
Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient - in order to spare their metabolic resources - and robust to perturbations. This paper investigates the relationship between both aspects, i.e. mechanical performance and stability in flapping…
Authors not listed
Machine olfaction—the artificial replication of the sense of smell—faces significant challenges due to the absence of large, standardized training datasets. Unlike vision, language, and audio models, which benefit from extensive corpora such as ImageNet, GLUE, and AudioSet, olfaction lacks scaled equivalents and…
Soheil Saghafi, Pejman Sanaei
Resonance and synchronized rhythm are important phenomena and can be either constructive or destructive in dynamical systems in the nature, specifically in biology. There are many examples showing that the human’s body organs must maintain their rhythm in order to function properly. For instance, in the brain…