arXiv research

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

Study analyzes household capital risk and poverty trapping, deriving a new function for capital deficit distribution.

Deep neural networks map brain lesions to deficits for better brain function understanding.

Sharp upper bounds derived for Alexandrov-Fenchel deficit using weighted Minkowski integral formulas.

In the class of smoothly embedded surfaces of sphere type we prove that the isoperimetric deficit can be controlled by the Willmore deficit.

Sharp bounds for curve isoperimetric deficit derived.

In his paper "Shapes of Polyhedra and Triangulations of the Sphere", Thurston found that the set of shapes of convex polyhedra with prescribed cone-deficits has a complex hyperbolic structure. Inspired by his work, this paper studies the set of shapes of centrally symmetric octahedra with prescribed cone-deficits. We s…

The accurate diagnosis and assessment of neurodegenerative disease and traumatic brain injuries (TBI) remain open challenges. Both cause cognitive and functional deficits due to focal axonal swellings (FAS), but it is difficult to deliver a prognosis due to our limited ability to assess damaged neurons at a cellular le…

Study inequalities involving torsional rigidity and spherical deficit on Riemannian manifolds.

The paper improves inequalities for nearly spherical sets using quermassintegrals.

Quantitative estimates for $Q$-curvature near minimizing metrics on Riemannian manifolds.

The paper analyzes risk measures and optimal reserve allocation strategies.

In this paper we provide a Bonnesen-style inequality which gives a lower bound for the isoperimetric deficit corresponding to a closed convex curve in terms of some geometrical invariants of this curve. Moreover we give a geometrical interpretation for the case when equality holds.

We relate the total curvature and the isoperimetric deficit of a curve $γ$ in a two-dimensional space of constant curvature with the area enclosed by the evolute of $γ$. We provide also a Gauss-Bonnet theorem for a special class of evolutes.

New proof of log-Brunn-Minkowski inequality for zonoids and convex bodies.

Study on spectral stability of an embedded annulus under curve shortening and Ricci flows.

The aim of this paper is to give not only an explicit upper bound of the total Q-curvature but also an induced isoperimetric deficit formula for the complete conformal metrics on $\mathbb R^n$, $n\ge 3$ with scalar curvature being nonnegative near infinity and Q-curvature being absolutely convergent.

This study analyzes public debts and deficits between European countries. The statistical evidence here seems in general to reveal that sovereign debts and government deficits of countries within European Monetary Unification-in average- are getting worse than countries outside European Monetary Unification, in particu…

We construct knot invariants on the basis of ascribing Euclidean geometric values to a triangulation of sphere S^3 where the knot lies. The main new feature of this construction compared to the author's earlier papers on manifold invariants is that now nonzero "deficit angles" (in the terminology of Regge calculus) can…

The paper proves reverse inequalities in various geometric settings using curvature radius data.

In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$ under the assumption that the constant discount rate $ν\in (0,1)$. More specifical…

Successful implementation of California's Renewable Portfolio Standard (RPS) mandating 33 percent renewable energy generation by 2020 requires inclusion of a robust strategy to mitigate increased risk of energy deficits (blackouts) due to short time-scale (sub 1 hour) intermittencies in renewable energy sources. Of the…

A sharp quantitative polygonal isoperimetric inequality is obtained.

The aim of the present article is to offer a strictly mathematical, statistical treatment of the current account balances in EU and in the Eurozone. Based on Eurostat data, an overview of the total and annual balances is first made for different collections among the EU countries. Then, using the Mathematica technical …

We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral t…

Study stability of rigid motions and Möbius transformations on spheres, proving new rigidity estimates.

One of the main issues affecting the Italian NHS is the healthcare deficit: according to current agreements between the Italian State and its Regions, public funding of regional NHS is now limited to the amount of regional deficit and is subject to previous assessment of strict adherence to constraint on regional healt…

The study optimizes cell membranes' shapes based on curvature and proves existence of minimizers.

We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are obtained in the genera…

Softmax temperature influences model representation rank and performance.

The paper proves stability for scalar-flat metrics on manifolds with boundary.

Optimally stabilizes Möbius group maps in spheres across dimensions.

The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation requires the evaluation of the overshoot/undershoot distributions of the surplus proce…

We postulates, and then show experimentally, that liquidity deficit is the driving force of the markets. In the first part of the paper a kinematic of liquidity deficit is developed. The calculus-like approach, which is based on Radon--Nikodym derivatives and their generalization, allows us to calculate important chara…

Quantitative stability for nearly minimizing Yamabe metrics.

Paper finds eigenvalue bounds for hyperbolic space domains.

The study proves stability of quermassintegral inequalities in hyperbolic space.

New proofs and inequalities for capillarity problems quantify asymmetries.

The paper evaluates integrals of planes and their relation to convex set angles.

Paper examines stability of minimizing metrics on manifolds with boundary.

We are concerned about the coarse and precise aspects of a priori estimates for Green's function of a regular domain for the Laplacian-Betrami operator on any $3\le n$-dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and s…

Early and accurate identification of parkinsonian syndromes (PS) involving presynaptic degeneration from non-degenerative variants such as Scans Without Evidence of Dopaminergic Deficit (SWEDD) and tremor disorders, is important for effective patient management as the course, therapy and prognosis differ substantially …

The paper develops a model for sovereign debt dynamics with explicit maturity structure.

Given a simple closed plane curve $Γ$ of length $L$ enclosing a compact convex set $K$ of area $F$, Hurwitz found an upper bound for the isoperimetric deficit, namely $L^2-4πF\leq π|F_{e}|$, where $F_{e}$ is the algebraic area enclosed by the evolute of $Γ$. In this note we improve this inequality finding strictly posi…

Similar to humans and animals, deep artificial neural networks exhibit critical periods during which a temporary stimulus deficit can impair the development of a skill. The extent of the impairment depends on the onset and length of the deficit window, as in animal models, and on the size of the neural network. Deficit…

We give conditions on a knot on which the Morton-Franks-Williams inequality is not sharp. As applications, we show infinitely many examples of knots where the inequality is not sharp and also prove (by giving examples) that the deficit of the inequality can be arbitrarily large.

Study compares nonsmooth spaces with integrable Ricci bounds.

Veterans with mild traumatic brain injury (mTBI) have reported auditory and visual dysfunction that persists beyond the acute incident. The etiology behind these symptoms is difficult to characterize with current clinical imaging. These functional deficits may be caused by shear injury or micro-bleeds, which can be det…