arXiv research

In this paper we explore the functional correlation approach to operational risk. We consider networks with heterogeneous a-priori conditional and unconditional failure probability. In the limit of sparse connectivity, self-consistent expressions for the dynamical evolution of order parameters are obtained. Under equil…

Proposes using GANs to solve phase retrieval problems.

Study on critical Lagrangian phase singularities in mean curvature flow.

There is an increasing need for monitoring and controlling uncertainties brought by distributed energy resources in distribution grids. For such goal, accurate multi-phase topology is the basis for correlating measurements in unbalanced distribution networks. Unfortunately, such topology knowledge is often unavailable …

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the…

Phase segregation, the process by which the components of a binary mixture spontaneously separate, is a key process in the evolution and design of many chemical, mechanical, and biological systems. In this work, we present a data-driven approach for the learning, modeling, and prediction of phase segregation. A direct …

Paper confirms conjecture for projective manifolds in supercritical phase.

Combines deep learning and iterative methods for robust phase retrieval.

Algorithm samples constrained stochastic differential equations.

We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …

New methods reveal compatible liquid crystal phases in 3D.

Study connects symmetries in dynamical systems to phase plane representations.

This paper proposes an approach to the joint modeling of the short-time Fourier transform magnitude and phase spectrograms with a deep generative model. We assume that the magnitude follows a Gaussian distribution and the phase follows a von Mises distribution. To improve the consistency of the phase values in the time…

Study phase transition in liquid crystal droplets using mathematical analysis.

Machine learning classifies topological phases in leaky photonic lattices.

Study on unique solutions to one-phase free boundary problems.

Extends phase retrieval methods to handle sensing vector errors.

Deep learning tackles low-photon nanoscale holographic phase retrieval.

New phase harmonic covariance models capture non-Gaussian properties of stationary processes.

Develops new strategy for Hessian estimates in Lagrangian mean curvature equation.

In order to model volatile real-world network behavior, we analyze phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-flipping dynamics, and find the probability that no more than q% of nodes…

Characterizes kernel interpolation in large dimensions, revealing optimal and sub-optimal regions.

Study shows thresholding scheme converges for mean curvature flow of convex sets.

Proposes a new binary classification model inspired by fluid phase separation.

The paper examines how gradient descent stabilizes low-rank matrix factorization in noisy conditions.

Proves smoothness and estimates for special Lagrangian solutions with semi-convexity.

The paper studies phase transitions in Information Bottleneck for representation learning.

Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.

Large GD stepsizes improve margins and speed up training for non-homogeneous networks.

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP) in methods such as PhaseLift and compete with recently developed non-convex techn…

Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.

We analyze the linear response of a market network to shocks based on the bipartite market model we introduced in an earlier paper, which we claimed to be able to identify the time-line of the 2009-2011 Eurozone crisis correctly. We show that this model has three distinct phases that can broadly be categorized as "stab…

Phase synchronisation in multichannel EEG is known as the manifestation of functional brain connectivity. Traditional phase synchronisation studies are mostly based on time average synchrony measures hence do not preserve the temporal evolution of the phase difference. Here we propose a new method to show the existence…

Global stability bounds for matrix frames in phase retrieval problems.

M. M. Nekhoroshev put forward the problem of to find the Complex Germ on a isotropic invariant torus with respect to Hamiltonian phases flows which come from k-functions in involution. This statement was partially solved in [9] establishing that if certain simplectic operator has a simple spectrum then the complex germ…

Study on line bundle flow on Kähler surfaces converging to a singular solution.

Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since tradi…

We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure…

PH-VAE models heavy-tailed data with flexible Phase-Type distributions.

Early SGD hyperparameters affect deep neural network training, showing a break-even point.

Study on combustion theory solutions, proving nondegeneracy and stability in limit.

CDLF predicts product life-cycles in cold-start phases with high accuracy.

Hypothesis testing is an important problem with applications in target localization, clinical trials etc. Many active hypothesis testing strategies operate in two phases: an exploration phase and a verification phase. In the exploration phase, selection of experiments is such that a moderate level of confidence on the …

DP-SGD can update fewer coordinates while maintaining privacy.

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graph…

Persistent entropy detects phase transitions in complex systems.

We explain how neural networks learn to solve modular addition tasks.

Proposes an online model for LLM cascading with adaptive API selection.