arXiv research

Researchers resolved ambiguities in gravitational radiation charges.

Study of homogeneous spacetimes with isotropic symmetry and their symmetries.

Defines null G-structures on Lorentzian manifolds and explores their symmetries.

Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to improve the predictive ability and biological interpretability of biomarkers. Here, we…

Study proposes active learning method for estimating robust regions in uncertain function evaluations.

Unified perspective on Hopfield networks with attention module.

Let $M^7$ be a smooth manifold equipped with a $G_2$-structure $φ$, and $Y^3$ be an closed compact $φ$-associative submanifold. In \cite{McL}, R. McLean proved that the moduli space $\bm_{Y,φ}$ of the $φ$-associative deformations of $Y$ has vanishing virtual dimension. In this paper, we perturb $φ$ into a $G_2$-structu…

BM$^2$ learns Schrödinger bridges using neural networks.

The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\to\Bm(c)$ be a null hypersurface of a space-time with constant sectional curvature $c$, endowed with a Screen Integrable and Conformal rigging $N$. The (Marginally) Trapped Submanifolds we are intere…

AFS-BM improves model accuracy by dynamically selecting features.

A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form $ψ_i=|\langle\bm{a}_i,\bm{x}\rangle|$. This problem, also known as phase retrieval from magnitude-onl…

We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs ov…

Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the sca…

Statistical analysis of financial data most focused on testing the validity of Brownian motion (Bm). Analysis performed on several time series have shown deviation from the Bm hypothesis, that is at the base of the evaluation of many financial derivatives. We inquiry in the behavior of measures of performance based on …

This paper presents a new algorithm, termed \emph{truncated amplitude flow} (TAF), to recover an unknown vector $\bm{x}$ from a system of quadratic equations of the form $y_i=|\langle\bm{a}_i,\bm{x}\rangle|^2$, where $\bm{a}_i$'s are given random measurement vectors. This problem is known to be \emph{NP-hard} in genera…

Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, non-differentiability of the discrete units prohibits using the reparameterization trick, essential for lo…

I explain an open conjecture by Braverman/Milatovic/Shubin (BMS) on the positivity of square integrable solutions $f$ of $(-Δ+1)f\geq 0$ on a geodescially complete Riemannian manifold, and its connection to essential self-adjointness problems of covariant Schrödinger operators. The latter conjecture has remained open f…

Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.

New findings show independent subordination is not relevant for accurate option pricing.

Paper proves finite BMS measure for SPR groups in higher rank Lie groups.

Paper analyzes strategic underreporting in competitive insurance markets.

The paper proves a unique conformal measure for Anosov groups and shows local mixing.

Maps dBKP solutions to MS system solutions, defining Einstein-Weyl structures.

A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. However, regularization often shrinks the estimator for relevant features, which leads to incorrect feature selection. Motivated by the above-mentioned issue…

Paper identifies problematic baselines in Shapley value explanations and proposes a reweighting mechanism.

The paper approximates rough lognormal model using Markovian processes.

After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the complex length l_V and the complex twist tau_V,W parameters define a holomorphic embedding of the quasifuchsian space QF of punctured tori into C^2. It is called the complex Fenchel-Nielsen coordinates of QF. For a complex number c, let Q_gam…

A new sampler and temperature estimation method enable efficient learning of Boltzmann Machines.

Study automorphisms and subgroups of exceptional Lie group E8.

This paper provides a tutorial on Boltzmann Machines and Deep Belief Networks.

Hybrid framework combines PGMs and TNs for complex probabilistic modeling.

In this article we propose a model for stochastic delay differential equation with jumps (SDDEJ) in a differentiable manifold $M$ endowed with a connection $\nabla$. In our model, the continuous part is driven by vector fields with a fixed delay and the jumps are assumed to come from a distinct source of (càdlàg) noise…

Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) prin…

This paper introduces a novel real-time Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM) for big data classification task. The study of real-time algorithms addresses several major concerns, which are namely: accuracy, memory consumption, and ability to stretch assumptions and time complexity. Attaining a fa…

Paper proves Brunn-Minkowski inequality and curvature dimension condition are equivalent in weighted Riemannian manifolds.

Let $\M$ be a smooth connected non-compact manifold endowed with a smooth measure $μ$ and a smooth locally subelliptic diffusion operator $L$ satisfying $L1=0$, and which is symmetric with respect to $μ$. We show that if $L$ satisfies, with a non negative curvature parameter $ρ_1$, the generalized curvature inequality …

Study on Neural Tangent Kernel of Matrix Product States and their convergence.

A new model captures option price dynamics using sub-fractional Brownian motion.

Imputation method respects manifold structure for missing data.

Generative Fractional Diffusion Models improve image diversity and quality.

We study the geometric properties of holomorphic distributions of totally null $m$-planes on a $(2m+ε)$-dimensional complex Riemannian manifold $(\mathcal{M}, \bm{g})$, where $ε\in {0,1}$ and $m \geq 2$. In particular, given such a distribution $\mathcal{N}$, say, we obtain algebraic conditions on the Weyl tensor and t…

CAP-BM learns complex-valued data's amplitude and phase distributions.

New tractor geometry derived from asymptotically flat spacetimes.

Study equidistribution for flows on geometrically finite convergence group actions.

We use the correlation matrix of stocks returns in order to create maps of the São Paulo Stock Exchange (BM&F-Bovespa), Brazil's main stock exchange. The data reffer to the year 2010, and the correlations between stock returns lead to the construction of a minimum spanning tree and of asset graphs with a variety of thr…

Revises Schwarzschild manifold rigidity proof for spin manifolds.

Let $\mathcal{M}^{\mathrm{st}}$ ($\mathcal{M}^{\mathrm{pst}}$) be a moduli space of stable (polystable) bundles with fixed determinant on a complex surface with $b_1=1$, $p_g=0$, and let $Z\subset \mathcal{M}^{\mathrm{st}}$ be a pure $k$-dimensional analytic set. We prove a general formula for the homological boundary …

The paper models US inflation and hyperinflation using monetary and GDP data.