Related papers: Mode-Locking in Driven Disordered Systems as a Bou…
We develop an analytic approach which allows us to study the behaviour of spin models with competing interactions and $p$-fold spin anisotropy, $D$, in the limit where the pinning potential which results from $D$ is large. This is an…
We consider the optimal stopping problem for a Gauss-Markov process conditioned to adopt a prescribed terminal distribution. By applying a time-space transformation, we show it is equivalent to stopping a Brownian bridge pinned at a random…
Policy-based reinforcement learning methods suffer from the policy collapse problem. We find valued-based reinforcement learning methods with {\epsilon}-greedy mechanism are capable of enjoying three characteristics, Closed-form Diversity,…
The discovery of topological insulators has opened new prospects for robust signal transport for electronic, phononic, and photonic devices. Though transport of topological protected edge states is robust to disorder, large fluctuations and…
We use a generalization of Hoeffding's inequality to show concentration results for the free energy of disordered pinning models, assuming only that the disorder has a finite exponential moment. We also prove some concentration inequalities…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
Precise behavioral control of large language models (LLMs) is critical for complex applications. However, existing methods often incur high training costs, lack natural language controllability, or compromise semantic coherence. To bridge…
In recent years, artificial neural networks have been increasingly studied as feedback controllers for guidance problems. While effective in complex scenarios, they lack the verification guarantees found in classical guidance policies.…
In this paper we address the solution of the popular Wordle puzzle, using new reinforcement learning methods, which apply more generally to adaptive control of dynamic systems and to classes of Partially Observable Markov Decision Process…
We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i -…
Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck:…
This paper concerns the behavior of time-periodic solutions to 1D dissipative autonomous semilinear hyperbolic PDEs under the influence of small time-periodic forcing. We show that the phenomenon of forced frequency locking happens…
Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set. This theorem is realized in practice using so called…
Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The…
Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At…
Ratchet dynamics of topological solitons of the forced and damped discrete double sine-Gordon system are studied. Directed transport occurring both in regular and in chaotic regions of the phase space and its dependence on damping,…
Solutions of a 1-D free-interface problem modeling solid combustion front propagating in combustible mixture with periodically varying concentration of reactant exhibit classical phenomenon of mode locking. Numerical simulation shows a…
Periodic boundary conditions are not always used in the study of disordered systems, but it can be advantageous to apply them to mimick thermodynamically large systems. In this case, polarization and its cumulants can not be obtained…
We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking…
We derive several upper bounds for the superfluid stiffness $D_s$ for Bose and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insight into the non-trivial…