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Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of…

We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…

We propose a simple deterministic dynamic equation and reveal the mechanism of large-scale endless evolvement of spatial density inhomogeneity in active nematic. We determine the phase regions analytically. The interplay of density,…

We characterize a class of Markovian dynamics using the concept of divisible dynamical map. Moreover we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a…

Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…

We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…

In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…

Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…

Trans-membrane gradients and fluxes of cations (H+, Na+, K+, etc.) were deemed to be the rationale of electrical activities of aerobic cells/organelles, as per classical perceptions. Murburn concept (an umbrella of theorization based in…

It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…

We develop a deformation-based framework for analyzing static billiard systems through the Jacobian determinant computed in noncanonical angular coordinates. Although these systems are conservative, the determinant is not identically equal…

Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…

Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study…

A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the splitting exist and the splitting…