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We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
We investigate non-degenerate Lagrangians of the form $$ \int f(u_x, u_y, u_t) dx dy dt $$ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of hydrodynamic…
In this paper an attempt is made to extend the concept of the exponentially stable adaptive control to one class of multi-input-multi-output (MIMO) plants with matched nonlinearity and unknown piecewise constant parameters. Within the…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e. bosonic into fermionic or…
Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. In this paper, we study the translation of LGCA on quantum computers (QC) using computational basis…
A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related…
In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven XY lattice of dissipative two-level systems. A commonly used mean-field ansatz, in which spatial correlations are neglected,…
Standard accuracy on binary reasoning benchmarks hides critical failure modes: prior collapse, inconsistency under paraphrase, and inability to reason about parameter-dependent dynamics. We present ChaosBench-Logic v2, a 40,886-question…
Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations…
The evolution of organismal populations is not typically thought of in terms of classical mechanics. However, many of the conceptual models used to approximate evolutionary trajectories have implicit parallels to dynamic physical systems.…
We study the stability properties of a control system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback…
Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com putations update internal states and…
We study the pairwise entanglement present in a quantum computer that simulates a dynamically localized system. We show that the concurrence is exponentially sensitive to changes in the Hamiltonian of the simulated system. Moreover,…
Mutation testing has been demonstrated to be one of the most powerful fault-revealing tools in the tester's tool kit. Much previous work implicitly assumed it to be sufficient to re-compute mutant suites per release. Sadly, this makes…
This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
We investigate discrete-time conewise linear systems (CLS) for which all the solutions exhibit a finite number of switches. By switches, we mean transitions of a solution from one cone to another. Our interest in this class of CLS comes…
We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…
The co-optimization of a robot's body and brain presents a coupled challenge: the morphology constrains which control strategies are effective, while the control determines how well the morphology performs. To address this, we combine…