Related papers: Concentration effects of BV gradients have gradien…

Biological cells estimate concentration gradients of signaling molecules with a precision that is limited not only by sensing noise, but additionally by the cell's own stochastic motion. We ask for the theoretical limits of gradient…

We use colloidal suspensions encapsulated in emulsion droplets to model confined glass-forming liquids with tunable boundary mobility. We show dynamics in these idealized systems are governed by physical interactions with the boundary.…

In view of solving convex optimization problems with noisy gradient input, we analyze the asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we focus on the widely studied class of mirror descent schemes…

Some physically interesting weak-gravitational effects and phenomena are reviewed and briefly discussed: particle geometric phases due to the time-dependent spin-rotation couplings, non-inertial gravitational wave in rotating reference of…

We investigate the electronic confinement in bilayer graphene by topological loops of different shapes. These loops are created by lateral gates acting via gap inversion on the two graphene sheets. For large-area loops the spectrum is well…

In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the…

Using a method Raman of spectroscopy and considering a non-uniformity of allocation of vacancies in a monocrystal, it is shown that lines with the small intensity (caused by presence of vacancies) have a major intensity in the sample of a…

Policy gradient methods have been frequently applied to problems in control and reinforcement learning with great success, yet existing convergence analysis still relies on non-intuitive, impractical and often opaque conditions. In…

We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some energy function. We show that this simple…

It is well-known that the convergence of a family of smooth functions does not imply the convergence of its gradients. In this work, we show that if the family is definable in an o-minimal structure (for instance semialgebraic, subanalytic,…

Spatio-temporal pattern formation in complex systems presents rich nonlinear dynamics which leads to the emergence of periodic nonequilibrium structures. One of the most prominent equations for the theoretical and numerical study of the…

We demonstrate theoretically and experimentally coherence-induced polarization changes in generic and higher-order vector vortex beams with polarization singularity. The prominent depolarization on decreasing transverse correlation-width in…

We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is…

We consider the behavior of gradient flow and of discrete and noisy gradient descent. It is commonly noted that the addition of noise to the process of discrete gradient descent can affect the trajectory of gradient descent. In previous…

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…

Interference phenomena are the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive…

We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of…

An overlooked conservation law for near-inertial waves propagating in a steady background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this…

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they…

Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…