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Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is…
In this paper we investigate the behavior of trajectories of one class of rational $p$-adic dynamical systems in complex $p$-adic field $\C_p$. We studied Siegel disks and attractors of such dynamical systems. We found the basin of the…
Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring…
We study almost automorphic solutions of the discrete delayed neutral dynamic system% \[ x(t+1)=A(t)x(t)+\Delta Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))) \] by means of a fixed point theorem due to Krasnoselskii. Using discrete variant of…
Inverse Constraint Learning (ICL) is the problem of inferring constraints from safe (i.e., constraint-satisfying) demonstrations. The hope is that these inferred constraints can then be used downstream to search for safe policies for new…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…
Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…
Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This…
Interpretability methods aim to understand the algorithm implemented by a trained model (e.g., a Transofmer) by examining various aspects of the model, such as the weight matrices or the attention patterns. In this work, through a…
We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…
It was previously shown that control-flow refinement can be achieved by a program specializer incorporating property-based abstraction, to improve termination and complexity analysis tools. We now show that this purpose-built specializer…
We consider the problem of proving that each point in a given set of states ("target set") can indeed be reached by a given nondeterministic continuous-time dynamical system from some initial state. We consider this problem for abstract…
This paper deals with existence and robust stability of hybrid limit cycles for a class of hybrid systems given by the combination of continuous dynamics on a flow set and discrete dynamics on a jump set. For this purpose, the notion of…
This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is…
Deep reinforcement learning has demonstrated remarkable achievements across diverse domains such as video games, robotic control, autonomous driving, and drug discovery. Common methodologies in partially-observable domains largely lean on…
Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential…
Planning and extension of water distribution systems (WDSs) plays a key role in the development of smart cities, driven by challenges such as urbanization and climate change. In this context, the correct estimation of physically correct…