arXiv research

In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative $1$-Lipschitz functions with Dirichlet boundary condition around zero, which is called boundary concentration phenomena. We first examine relation between boundary concen…

We investigate different concentration-compactness phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in $R^{2m}$, then that of a closed manifold and, finally, the particular case of the sphere $S^{2m}$. In all cases we allow the sign of the Q-curvature to vary, …

We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequa…

The aim of this paper is to analyze the processes of polarization and agglomeration, to explain the mechanisms and causes of these phenomena in order to identify similarities and differences. As the main implication of this study should be noted that both process pretend to explain the concentration of economic activit…

The paper shows how solutions of perturbed Dirac operators concentrate near singular sets.

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…

New deficit functions link elliptic and parabolic inequalities, proving log Sobolev.

We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle_{\textbf{g}}u+h.u=f .u^{\frac{n+2}{n-2}}$ on a compact riemannian manifold in the limit case normally not solved by variational methods. For this purpose, we use a concept of "critical function" that was original…

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our…

We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle_{\textbf{g}}u+h.u = f.u^{\frac{n+2}{n-2}}$ on a compact riemannian manifold in the limit case normally not solved by variational methods. For this purpose, we use a concept of "critical function" that was original…

Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Ha…

Wave maps can have multiple bubbling solutions at blow-up points.

Consistent estimator derived for confounding strength in observational data.

High-dimensional spectroscopy data makes ML models achieve near-perfect accuracy, even when chemical distinctions are absent.

This paper shows DPPs can outperform random coresets in machine learning tasks.

With this study we want to test the validity of the well known "Verdoorn's Law" which considers the relationship between the growth of productivity and output in the case of the Portuguese economy at a regional and sectoral levels (NUTs II) for the period 1995-1999. The importance of some additional variables in the or…

Theory explains power-law distributions without complex models.

In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the second smallest eigenvalue of the Laplacian is at least 1/4, then the distances on the surface are highly concentrated around the minimal poss…

The paper argues against the inefficiency of explaining deep learning phenomena.

Our work connects parameter magnitudes and Hessian eigenspaces in deep neural nets.

Most environmental phenomena, such as wind profiles, ozone concentration and sunlight distribution under a forest canopy, exhibit nonstationary dynamics i.e. phenomenon variation change depending on the location and time of occurrence. Non-stationary dynamics pose both theoretical and practical challenges to statistica…

Impersonators on Online Social Networks such as Instagram are playing an important role in the propagation of the content. These entities are the type of nefarious fake accounts that intend to disguise a legitimate account by making similar profiles. In addition to having impersonated profiles, we observed a considerab…

Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classification of the market crisis p…

The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In this note we discuss short …

Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.

The paper studies how adding a 'Gauge Mass' term breaks gauge symmetry in Yang-Mills-Higgs systems and analyzes the resulting behavior.

The paper explores higher property T in lattices and its connections to geometric phenomena.

Theory for algebraic data on categories via concentration structures.

Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.

In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…

Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.

Study Finsler metric measure manifolds' concentration properties.

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In general, in order to solve PDEs that represent real systems to an acceptable degr…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.

Geometric approach to thermodynamics of chemical reaction networks.

New method improves missing mass concentration bounds.

Surfaces in 3-manifolds concentrate at curvature critical points.

Analyzes magnetic Laplacian on hyperbolic surfaces, highlighting key quantum phenomena.

The paper provides stability guarantees for non-parametric maximum likelihood estimation using statistical mechanics.

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromo…

Sharp concentration bounds for i.i.d. variables.

Study exotic phenomena in small 4-manifolds using diffeomorphisms.

We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for $L^1$-norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.

The paper studies hyperbolic phenomena on closed surfaces using bicorn curves.

Knowing and modelling the migration phenomena and especially the social and economic consequences have a theoretical and practical importance, being related to their consequences for development, economic progress (or as appropriate, regression), environmental influences etc. One of the causes of migration, especially …

A new model CDTM improves text classification by concentrating document topics.

Simplified proof of Gaussian concentration inequality using covariance.