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A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
Pedestrian trajectory prediction plays an important role in autonomous driving systems and robotics. Recent work utilizing prominent deep learning models for pedestrian motion prediction makes limited a priori assumptions about human…
The mesochronic velocity is the average of the velocity field along trajectories generated by the same velocity field over a time interval of finite duration. In this paper we classify initial conditions of trajectories evolving in…
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…
In this paper the asymptotic behavior of trajectories of discontinuous vector fields is studied. The vector fields are defined on a two-dimensional Riemannian manifold $M$ and the confinement of trajectories on some suitable compact set $K$…
We define a deterministic integral with respect to irregular paths as a limit of standard line integrals and completely describe a class of all paths for which this integral exists for functions with H\"older exponent in the range of (0,1].…
Existing drift detection methods focus on designing sensitive test statistics. They treat the detection threshold as a fixed hyperparameter, set once to balance false alarms and late detections, and applied uniformly across all datasets and…
Classically, the dynamics in a non-globally hyperbolic spacetime is ill posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second order operator acting on a Hilbert space defined on static…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by…
When deploying autonomous systems in unknown and changing environments, it is critical that their motion planning and control algorithms are computationally efficient and can be reapplied online in real time, whilst providing theoretical…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen [15]. The presence of sensitivity, which is an indispensable feature of chaotic dynamics, is a crucial property that arises…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…