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Mode-locking is a process in which different modes of an optical resonator establish, through nonlinear interactions, stable synchronization. This self-organization underlies light sources that enable many modern scientific applications,…
In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the…
We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the…
We introduce aligned probing, a novel interpretability framework that aligns the behavior of language models (LMs), based on their outputs, and their internal representations (internals). Using this framework, we examine over 20 OLMo,…
Prior research indicates that LID model performance significantly declines on accented speech; however, the specific causes, extent, and characterization of these errors remain under-explored. (i) We identify a common failure mode on…
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Automatic or assisted workflow composition is a field of intense research for applications to the world wide web or to business process modeling. Workflow composition is traditionally addressed in various ways, generally via theorem proving…
We use the feedback loop of McKeon \& Sharma (2010), where the nonlinear term in the Navier-Stokes equations is treated as an intrinsic forcing of the linear resolvent operator, to educe the structure of fluctuations in the range of scales…
Autonomous driving is an emerging technology that has advanced rapidly over the last decade. Modern transportation is expected to benefit greatly from a wise decision-making framework of autonomous vehicles, including the improvement of…
We study the two-dimensional disordered topological superconductor with Hubbard interactions. When the magnitude of the pairing potential is tuned to special values, this interacting model is exactly solvable even when disorders are imposed…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
Obtaining prescribed accuracy bounds in super-twisting sliding mode control loops often falls short in terms of the applicability of the controller in high-performance systems. This is due to the fact that the selection of the controller…
We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power…
In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for…
We analyze the convergence properties of a modified barrier method for solving bound-constrained optimization problems where evaluations of the objective function and its derivatives are affected by bounded and non-diminishing noise. The…
We study the surface plasmon modes of an arbitrarily shaped nanoparticle in the electrostatic limit. We first deduce an eigenvalue equation for these modes, expressed in terms of the Dirichlet-Neumann operators. We then use the properties…
A method of exciting coherent spatial modes of Bose-condensed trapped atoms is considered. The method is based on the resonance modulation of the trapping potential. The population dynamics of coherent modes is analysed. The method makes it…
We consider the Steklov problem on differential $p$-forms defined by M. Karpukhin and present geometric eigenvalue bounds in the setting of warped product manifolds in various scenarios. In particular, we obtain Escobar type lower bounds…
Vision-Language Models (VLMs) achieve strong cross-modal performance, yet recent evidence suggests they over-rely on textual descriptions while under-utilizing visual evidence -- a phenomenon termed ``text shortcut learning.'' We propose an…