arXiv subjects

Vasili Baranau

Publications and source records attributed to Vasili Baranau.

4 recordsLinked to original sources

arXiv2025

What is the most optimal diffusion?

What is the fastest possible "diffusion"? A trivial answer would be "a process that converts a Dirac delta-function into a uniform distribution infinitely fast". Below, we consider a more reasonable formulation: a process that maximizes differential entropy of a probability density function (pdf) $f(\vec{x}, t)$ at every time $t$, under certain restrictions. Specifically, we focus on a case when the rate of the Kullback-Leibler divergence $D_{\text{KL}}$ is fixed. If $Δ(\vec{x}, t, d{t}) = \frac{\partial f}{ \partial t} d{t}$ is the pdf change at a time step $d{t}$, we maximize the differential entropy $H[f + Δ]$ under the restriction $D_{\text{KL}}(f + Δ|| f) = A^2 d{t}^2$, $A = \text{const} > 0$. It leads to the following equation: $\frac{\partial f}{ \partial t} = - κf (\ln{f} - \int f \ln{f} d{\vec{x}})$, with $κ= \frac{A}{\sqrt{ \int f \ln^2{f} d{\vec{x}} - \left( \int f \ln{f} d{\vec{x}} \right)^2 } }$. Notably, this is a non-local equation, so the process is different from the Itô diffusion and a corresponding Fokker-Planck equation. We show that the normal and exponential distributions are solutions to this equation, on $(-\infty; \infty)$ and $[0; \infty)$, respectively, both with $\text{variance} \sim e^{2 A t}$, i.e. diffusion is highly anomalous. We numerically demonstrate for sigmoid-like functions on a segment that the entropy change rate $\frac{d H}{d t}$ produced by such an optimal "diffusion" is, as expected, higher than produced by the "classical" diffusion.

cond-mat.stat-mech↗

arXiv2022

Fast and Precise Binary Instance Segmentation of 2D Objects for Automotive Applications

In this paper, we focus on improving binary 2D instance segmentation to assist humans in labeling ground truth datasets with polygons. Humans labeler just have to draw boxes around objects, and polygons are generated automatically. To be useful, our system has to run on CPUs in real-time. The most usual approach for binary instance segmentation involves encoder-decoder networks. This report evaluates state-of-the-art encoder-decoder networks and proposes a method for improving instance segmentation quality using these networks. Alongside network architecture improvements, our proposed method relies upon providing extra information to the network input, so-called extreme points, i.e. the outermost points on the object silhouette. The user can label them instead of a bounding box almost as quickly. The bounding box can be deduced from the extreme points as well. This method produces better IoU compared to other state-of-the-art encoder-decoder networks and also runs fast enough when it is deployed on a CPU.

cs.CV↗

arXiv2021

Configurational entropy of polydisperse systems can never reach zero

We present examples of systems whose configurational entropy $S_{\text{conf}}$ can never reach zero and is instead limited from below by the entropy of mixing $S_{\text{mix}}$ of the corresponding ideal gas. We use $S_{\text{conf}}$ defined through the local minima of the potential energy landscape, $S_{\text{conf}}^{\text{PEL}}$. We show that this happens in mean-field models, in collections of hard spheres with infinitesimal polydispersity, and for one-dimensional hard rods. We demonstrate that these results match recent advances in understanding the configurational entropy defined in the free energy landscape, $S_{\text{conf}}^{\text{FEL}}$. We demonstrate that if $\min( S_{\text{conf}}^{\text{FEL}} ) = 0$, then for an arbitrary system $\min( S_{\text{conf}}^{\text{PEL}} ) = A N + S_{\text{mix}}$, where $N$ is the number of particles and $A$ is some constant determined by the interaction potential. We discuss which implications these results have on the Adam--Gibbs (AG) and RFOT relations and show that the latter retain a physically meaningful shape for both configurational entropies, $S_{\text{conf}}^{\text{FEL}}$ and $S_{\text{conf}}^{\text{PEL}}$.

cond-mat.stat-mech↗

arXiv2017

Another resolution of the configurational entropy paradox as applied to hard spheres

Recently, Ozawa and Berthier [J. Chem. Phys., 2017, 146, 014502] studied the configurational and vibrational entropies $S_c$ and $S_v$ from the relation $S_{tot}=S_c+S_v$ for polydisperse mixtures of spheres. They noticed that because $S_{tot}/N$ shall contain the mixing entropy per particle $k_B s_m$ and $S_v/N$ shall not, the configurational entropy per particle $S_c/N$ shall diverge in the thermodynamic limit for continuous polydispersity due to the diverging $s_m$. They also provided a resolution for this paradox and related problems-it relies on a careful redefining of $S_c$ and $S_v$. Here, we note that the relation $S_{tot}=S_c+S_v$ is essentially a geometric relation in the phase space and shall hold without redefining $S_c$ and $S_v$. We also note that the total entropy per particle $S_{tot}/N$ diverges with $N \to \infty$ with continuous polydispersity as well. The usual way to avoid this and other difficulties with $S_{tot}/N$ is to work with the excess entropy $ΔS_{tot}$ (relative to the ideal gas of the same polydispersity). Speedy [Mol. Phys., 1998, 95, 169] applied this approach to the relation above and wrote this relation as $ΔS_{tot}=S_c+ΔS_v$. This form has flows as well, because $S_v/N$ does not contain the $k_B s_m$ term and the latter is introduced into $ΔS_v/N$ instead. Here, we suggest that this relation shall actually be written as $ΔS_{tot}=Δ_c S_c+Δ_v S_v$, where $Δ=Δ_c+Δ_v$ while $Δ_c S_c=S_c-k_B N s_m$ and $Δ_v S_v=S_v-k_B N[1+\ln(V/Λ^d N)+U/N k_B T]$ with $Λ$ standing for the de Broglie wavelength. In this form, all the terms per particle are always finite for $N \to \infty$ and continuous when introducing a small polydispersity to a monodisperse system. We also suggest that the Adam-Gibbs and related relations shall in fact contain $Δ_c S_c/N$ instead of $S_c/N$.

cond-mat.stat-mech↗