arXiv research

Study axisymmetric surfaces in Euclidean space for energy minimization.

The paper constructs surfaces with prescribed mean curvature in a specific space.

Study rotational surfaces with prescribed Gauss curvature in 3D space.

Analyzes Berry phases and connection matrices on Siegel-Jacobi spaces.

Study connects symmetries in dynamical systems to phase plane representations.

Review of information plane analyses in neural networks, highlighting mixed results and methodological challenges.

We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution of structure constants of the metric Lie algebra with respect to an evolving or…

We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.

Poisson plane and sphere --- homogeneous spaces of Poisson groups E(2) and SU(2) (resp.) --- have phase spaces (corresponding symplectic groupoids), in which a free Hamiltonian is naturally defined. We solve the equations of motion and point out some unexpected features: free motion on the plane is bounded (periodic) a…

A new era in radioastronomy will begin with the upcoming large-scale surveys planned at the Australian Square Kilometre Array Pathfinder (ASKAP). ASKAP started its Early Science program in October 2017 and several target fields were observed during the array commissioning phase. The SCORPIO field was the first observed…

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularit…

Motivated by the work of Leznov--Mostovoy, we classify the linear deformations of standard $2n$-dimensional phase space that preserve the obvious symplectic $\mathfrak{o}(n)$-symmetry. As a consequence, we describe standard phase space, as well as $T^{*}S^{n}$ and $T^{*}\mathbb{H}^{n}$ with their standard symplectic fo…

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 …

Stochastic Gradient Descent phases explained for deep networks.

We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Haus…

New IP analysis for deep neural networks using Rényi's entropy and tensor kernels.

Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.

A new model of V1 using orientation, frequency, and phase.

New phases identified in neural scaling laws with compute limits.

A new image completion method inspired by brain cells.

New analysis of Muon and SignSGD on matrix-valued least squares problems.

We obtain all possible solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation exactly, containing configurations made of walls, vortices and monopoles in the Higgs phase. We use supersymmetric U(N_C) gauge theories with eight supercharges with N_F fundamental hypermultiplets in the strong coupling limit. The moduli…

DPI quantifies phase differences in 1D and multidimensional signals using Riesz transform.

Unsupervised learning is a discipline of machine learning which aims at discovering patterns in big data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many body systems…

Study local and global aspects of complex plane curve embeddings.

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

The study explores conformal planes with finite areas.

Consumers with low demand, like households, are generally supplied single-phase power by connecting their service mains to one of the phases of a distribution transformer. The distribution companies face the problem of keeping a record of consumer connectivity to a phase due to uninformed changes that happen. The exact…

In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e. if $\mathcal{M}$ occupies the whole phase space we recover the E.Hopf rigidity. …

Researchers create new triply periodic minimal surfaces by gluing saddle towers.

The paper confirms isoperimetric conjectures on cubes and Gaussian slabs.

The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.

New measures of asymmetry for triangles help evaluate electric power quality.

Global stability bounds for matrix frames in phase retrieval problems.

By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [$y$], inflation [$π$] and nominal interest rate [$…

Gradient descent dynamics in quadratic regression models are analyzed, revealing five phases: monotonic, catapult, periodic, chaotic, and divergent.

Characterizes RFF regression in large $n,p,N$ setting, providing precise learning phases and double descent curve.

A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized i…

ML PCA detects phase transitions in muon spectroscopy data.

This paper investigates a paradigm for offering artificial intelligence as a service (AI-aaS) on software-defined infrastructures (SDIs). The increasing complexity of networking and computing infrastructures is already driving the introduction of automation in networking and cloud computing management systems. Here we …

Automated surgical workflow analysis and understanding can assist surgeons to standardize procedures and enhance post-surgical assessment and indexing, as well as, interventional monitoring. Computer-assisted interventional (CAI) systems based on video can perform workflow estimation through surgical instruments' recog…

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundament…

Torus graphs analyze multivariate phase coupling among brain signals.

PCA improves detection of phase transitions in muon spectroscopy data from various materials.

The phase space of a compact, irreducible, simply connected, Riemannian symmetric space admits a natural family of Kähler polarizations parametrized by the upper half plane $S$. Using this family, geometric quantization, including the half-form correction, produces the field $H^{corr}\rightarrow S$ of quantum Hilbert s…

This paper presents a Bayesian approach to symbol and phase inference in a phase-unsynchronized digital receiver. It primarily extends [Quinn 2011] to the multi-symbol case, using the variational Bayes (VB) approximation to deal with the combinatorial complexity of the phase inference in this case. The work provides a …

Few years ago we developed jointly with I.Dynnikov new discretization of complex analysis (DCA) based on the two-dimensional manifolds with colored black/white triangulation. Especially deep results were obtained for the Euclidean plane with equilateral triangle lattice. In the present work we develop a DCA theory for …

This paper introduces SRPR for robust phase retrieval with smoothed loss functions.