arXiv research

Algorithm improves multi-agent learning with noisy observations.

Community detection using both graphs and social networks is the focus of many algorithms. Recent methods aimed at optimizing the so-called modularity function proceed by maximizing relations within communities while minimizing inter-community relations. However, given the NP-completeness of the problem, these algorith…

Algorithm reduces regret in multi-agent bandits through gossiping.

New method improves community detection for large networks.

New compression method reduces communication in Federated Learning from non-iid data.

CNNs reconstruct medium properties from wave probing responses.

The study predicts how discussions in mental disorder Reddit communities affect users' emotional states.

Paper extends Aronson-Bénilan estimates for porous medium equations on manifolds with negative curvature.

New digital currency aims for equal wealth distribution.

DSGD with OAC-MAC scheme achieves better convergence in noisy wireless networks.

The paper analyzes gradient estimates for a nonlinear heat equation on graphs.

Researchers study fractional porous medium equation on hyperbolic space.

Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.

Study nonnegative solutions on Riemannian manifolds using fractional porous medium equation.

Study improves Harnack estimates for porous medium equation under geometric flow.

Frank-Wolfe algorithms have recently regained the attention of the Machine Learning community. Their solid theoretical properties and sparsity guarantees make them a suitable choice for a wide range of problems in this field. In addition, several variants of the basic procedure exist that improve its theoretical proper…

Optimizes wireless power control using graph neural networks and counterfactual optimization.

Study self shrinkers with medium entropy in 4D space.

Researchers solve porous medium equation on noncompact manifolds with Ricci curvature.

In this paper we study gradient estimates for the positive solutions of the porous medium equation: $u_t=Δu^m$ where $m>1$, which is a nonlinear version of the heat equation. We derive local gradient estimates of the Li-Yau type for positive solutions of porous medium equations on Riemannian manifolds with Ricci curv…

In this paper, we prove Perelman type $\mathcal{W}$-entropy formulae and global differential Harnack estimates for positive solutions to porous medium equation on the closed Riemannian manifolds with Ricci curvature bounded below. As applications, we derive Harnack inequalities and Laplacian estimates.

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income)classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker-Planck counterpart, we derived a unified formula for desc…

Toda flow explained as a porous medium equation.

In this paper we study the porous medium equation (PME) coupled with the Ricci flow on complete manifolds with bounded nonnegative curvature operator. In particular, we derive Aronson-Bénilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions to the PME, with a linear forcing term, under the…

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $u_t=Δ_φ(u^p)$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the $m$-dimensional Bakry-Emery Ricci curvature is bounded from below, we obtain gradient estimates which…

We study the long-time behaviour of nonnegative solutions of the Porous Medium Equation posed on Cartan-Hadamard manifolds having very large negative curvature, more precisely when the sectional or Ricci curvatures diverge at infinity more than quadratically in terms of the geodesic distance to the pole. We find an une…

The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.

We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on negatively curved Riemannian manifolds. We show existence of solutions taking as initial condition a finite Radon measure, not necessarily positive. We then establish uniqueness in the class of nonnegative …

In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discove…

We consider the porous medium equation with power-type reaction terms $u^p$ on negatively curved Riemannian manifolds, and solutions corresponding to bounded, nonnegative and compactly supported data. If $p>m$, small data give rise to global-in-time solutions while solutions associated to large data blow up in finite t…

In this paper, we investigate some new local Aronson-Bénilan type gradient estimates for positive solutions of the porous medium equation $u_{t}=Δu^{m},$ under Ricci flow. As application, the related Harnack inequalities are derived. Our results generalize known results. These results in the paper can be regard as …

We use machine learning for designing a medium frequency trading strategy for a portfolio of 5 year and 10 year US Treasury note futures. We formulate this as a classification problem where we predict the weekly direction of movement of the portfolio using features extracted from a deep belief network trained on techni…

In this paper, by employ the cutoff function and the maximum principle, some Hamilton-Souplet-Zhang type gradient estimates for porous medium type equation are deduced. As a special case, an Hamilton-Souplet-Zhang type gradient estimates of the heat equation is derived which is different from the result of Souplet-Zhan…

Study proposes a hybrid method for medium-term load forecasting.

Cryptocurrencies show stable prices as a medium of exchange.

Study analyzes order transitions in high, medium, and low market cap stocks using Markov chains.

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

Study reconstructs Riemannian metric from Cherenkov radiation in complex media.

Being one of the most important factors of economic growth of the country, innovations became one of the key vectors in Russian economic policy. In this field technology parks are one of the most effective instruments which can provide growth of innovative activity in sectors, regions and economies. In this paper, we m…

Study shows conditions for nonexistence of solutions in Riemannian geometry.

Weight Squeezing transfers knowledge from large models to smaller ones, improving performance and speed.

This paper identifies critical cases for evaluating PV investment impacts on MV networks efficiently.

New approach for fair graph clustering using semidefinite relaxation.

Recursive filtering predicts wireless interference levels accurately.

This paper challenges the conventional wisdom of trend-following by showing that the medium-term horizon adds little value once short- and long-term components are included.

Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…

AI traders learn to exploit meta-orders from slower traders, increasing their profits.