arXiv research

Researchers resolved ambiguities in gravitational radiation charges.

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

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.

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…

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…

Study equidistribution for flows on geometrically finite convergence group actions.

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…

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 …

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 analyzes strategic underreporting in competitive insurance markets.

In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift and fractional diffusion. Since the DO process is a semi-martingale,…

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.

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

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

Hybrid framework combines PGMs and TNs for complex probabilistic modeling.

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

The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{é}nez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $\tildeγ$ of order four on $G$ and $H$ is a fixed point…

In this paper, we establish that, for statistically convex-cocompact actions, contracting elements are exponentially generic in counting measure. Among others, the following exponential genericity results are obtained as corollaries for the set of hyperbolic elements in relatively hyperbolic groups, the set of rank-1 e…

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.

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to expon…

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.

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

In this work we define a new pseudometric in $\mathcal K^n_*$, the hyperspace of all non-degenerated compact convex sets of $\mathbb R^n$, which is invariant under similarities. We will prove that the quotient space generated by this pseudometric (which is the orbit space generated by the natural action of the group of…

New tractor geometry derived from asymptotically flat spacetimes.

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 …

In this paper we give a complete description of the space $ \QF $ of quasifuchsian punctured torus groups in terms of what we call {\em pleating invariants}. These are natural invariants of the boundary $\bch$ of the convex core of the associated hyperbolic 3-manifold $M$ and give coordinates for the non-Fuchsian group…