A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting bi…
We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-connected compact Lie groups. The square root of the Reidemeister torsion is used as a density on the moduli space of flat connecti…
Neural network models transform physical systems into latent Gaussian distributions.
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform be…
New method for flux quantization on phase space stacks.
We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie-Marques-Neves and Marques-Neves-Song, respectively. We …
We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a uniformly distributed random variable) defined on a closed, bounded interval Ω\subset …
We prove that the density function of the gradient of a sufficiently smooth function , obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of $φ=\exp\left(\frac{i…
New findings confirm parallels to De Giorgi's conjecture for phase transitions in higher dimensions.
Study proves existence of a specific type of flow in geometry.
We study the phase field method for the volume preserving mean curvature flow. Given an initial hypersurface we proved the existence of the weak solution for the volume preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula and the density up…
New study shows low-degree polynomial algorithms struggle at clause densities close to Fix's.
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function φ(X)---specifically, φ(X)=exp(iS(X)/τwhere τis a free parameter. In this work, we prove a novel result using the higher-orde…
Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Ca…
Study on combustion theory solutions, proving nondegeneracy and stability in limit.
Neural net reconstructs dark matter density from halo velocities.
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error …
Stable solutions to a specific equation are one-dimensional.
Study phase transitions in noisy transformer dynamics on spheres.
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them,…
We study the phase transition of dynamical herd behaviors for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior with three different values of the scaling exponent 3.11 (one time lag = 1 minute), 2.81 (30 minut…
The Sinkhorn-Knopp algorithm converges quickly but the number of iterations is poorly understood.
Machine learning predicts critical points for directed percolation models.
New method uses transport maps for efficient Bayesian inference.
The article applies Occam's Razor to non-parametric model building, minimizing the number of bits for data encoding.
New proof confirms De Giorgi's conjecture about phase-field approximation of Willmore functional.
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
New insights into binary perceptron reveal phase transitions and algorithmic thresholds.
The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a Hermitian geometry on the big phase space. Using the approach of Dijkgraaf and …
In this paper we propose new algorithm to reduce autocorrelation in Markov chain Monte-Carlo algorithms for euclidean field theories on the lattice. Our proposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restricted Boltzmann machine. We examine the validity of the algorithm by employing the phi-fourth t…
Symplectic forms from two phase spaces are proven equivalent.
Given an odd vector field on a supermanifold and a -invariant density on , under certain compactness conditions on , the value of the integral is determined by the value of on any neighborhood of the vanishing locus of . We present a formula for the integral in the case where…
Study shows zero level sets of solutions to Allen-Cahn equation are minimal surfaces with zero mean curvature.
The phase space of relativistic particle mechanics is defined as the 1st jet space of motions regarded as timelike 1-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally on the odd-dimensional phase space a generalized contact structure. In the paper infinitesimal sy…
A probing scheme is considered with an accessible and controllable qubit, used to probe an out-of equilibrium system consisting of a second qubit interacting with an environment. Quantum spontaneous synchronization between the probe and the system emerges in this model and, by tuning the probe frequency, can occur both…
Bayesian and simulation methods predict credit default probabilities.
In this paper, a unified susceptible-exposed-infected-susceptible-aware (SEIS-A) framework is proposed to combine epidemic spreading with individuals' on-line self-consultation behaviors. An epidemic spreading prediction model is established based on the SEIS-A framework. The prediction process contains two phases. In …
DenSNet learns electron densities for molecular dynamics, enabling accurate spectroscopic predictions.
EG-LF-MCMC infers posterior densities without likelihoods.
Introduces a new phase space for 2D supersymmetric sigma models.
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical mechanical system and arbitrary initial conditions, there exists a conservative …
New normalizing flows model molecular crystal structures.
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…
Method reconstructs financial networks from aggregate data, revealing critical link density.
The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w …
Proposes using continuum percolation to analyze data manifolds and improve generative models.
A neural network learns phase space properties for time series analysis.
Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter space, thus enabling chains to achieve a faster convergence rate when measured in n…