arXiv research

New metrics boost A/B-test power by up to 210%.

The paper studies automorphisms of free groups with a North-South dynamics.

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on $M$ …

The paper argues for a social-economic approach to AI development.

Study shows insurance industry in North Macedonia declined 10% due to COVID-19.

Paper disproves symmetry of stars at infinity in a specific graph.

Sharp eigenvalue bounds on metric measure spaces extend Cheng's theorem.

In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on the existence of Kähler metrics of constant scalar curvature. In the third part…

The paper discusses quantifying realism in generated images.

Let $\varphi$ be a hyperbolic outer automorphism of a non-abelian free group $F_N$ such that $\varphi$ and $\varphi^{-1}$ admit absolute train track representatives. We prove that $\varphi$ acts on the space of projectivized geodesic currents on $F_N$ with generalized uniform North-South dynamics.

Introduces new Hermitian metrics linking to Gauduchon and balanced metrics.

We study obstructions to the existence of closed Fedosov's star products on a given Kähler manifold. In our previous paper, we proved that the Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of Connes-Flato-Sternheimer) Fedosov's star product only if it is a zero of the Cahen-Gutt moment…

In this paper we complete the study started in [Pi2] of evolution by inverse mean curvature flow of star-shaped hypersurface in non-compact rank one symmetric spaces. We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the quaternionic hyperbolic space. We p…

Novel Hodge theory developed for Carrollian bundles, addressing black hole event horizons.

We consider the action of a pseudo-Anosov mapping class on $\mathcal{PML}(S)$. This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples of families of pseudo-Anosov mapping classes where the rate go…

Let X=G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this action when X is an irreducible hermitian symmetric space of compact …

We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the complex hyperbolic space. We prove that the flow is defined for any positive time, the evolving hypersurface stays star-shaped and mean convex. Moreover the induced metric converges, after rescaling, to…

The study examines evolving star-shaped hypersurfaces in hyperbolic spaces, influenced by ambient geometry.

Let $a>b>0$ and $f$ be a conformal map from $B_a\setminus B_b\subseteq R^2$ into $\R^n$, with $|\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\frac{\partial f}{\partial r},$ and $e_2=r^{-1}e^{-u}\frac{\partial f}{\partialθ}$ is a moving frame on $f(B_a\setminus B_b)$. It satisfies the following equation $$d\s…

Study of infinity in Teichmüller space using Thurston boundary.

In this paper, we study the discrete Morse flow for the Ricci flow on football, which is the 2-sphere with removed north and south poles and with the metric $g_0$ of constant scalar curvature, and and for Porous media equation on a bounded regular domain in the plane. We show that with a suitable assumption about $g(0)…

A Deep Zero-Inflated Model for Detecting North Atlantic Right Whale Presence

The study uses symplectic capacities to bound the systole on the sphere.

New hyperbolicity concepts expand manifold study.

The paper models star dynamics using Ricci flow and Perelman entropy, revealing chaotic behavior.

Introduces Star-Shaped deviation measures for risk analysis.

We prove uniform north-south dynamics type results for the action of $\varphi\in Out(F_{N})$ on the space of projectivized geodesic currents $\mathbb{P}Curr(S)=\mathbb{P}Curr(F_{N})$, where $\varphi$ is induced by a pseudo-Anosov homeomorphism on a compact surface S with boundary such that $π_{1}(S)=F_{N}$. As an appli…

New model forecasts power consumption with high accuracy over months to years.

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.

Let $Ω$ be a star-shaped bounded domain in $(\mathbb{S}^{n}, ds^{2})$ with smooth boundary. In this article, we give a sharp lower bound for the first non-zero eigenvalue of the Steklov eigenvalue problem in $Ω.$ This result is the generalization of a result given by Kuttler and Sigillito for a star-shaped bounded doma…

Study on octonionic Nahm's equations and their moduli space properties.

Algorithm achieves optimal regret for unknown Lipschitz convex losses.

This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland.

New star-shaped acceptability indexes generalize existing methods.

Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.

In this paper we define currents relative to a free factor system. We prove that a fully irreducible outer automorphism relative to a free factor system acts with uniform north-south dynamics on a subspace of the space of projective relative currents.

Classifies star products on Lie algebroid duals and extends to projectable quantizations.

Let (M, g, omega) be a compact, almost-Kaehler Einstein 4-manifold of negative star-scalar curvature. Then (M, omega) is a MINIMAL symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N # (-CP_2).

We report on time-varying network connectedness within three banking systems: North America, the EU, and ASEAN. The original method by Diebold and Yilmaz is improved by using exponentially weighted daily returns and ridge regularization on vector autoregression (VAR) and forecast error variance decomposition (FEVD). We…

The paper constructs a star product on a symplectically reduced phase space for a lattice gauge model.

New set-valued star-shaped risk measures introduced for better risk assessment.

Flow turns star-shaped curves into circles.

The paper studies dynamic star-shaped risk measures and their representation.

Study star products on Poisson manifolds compatible with reduction.

We classify SO(n)-equivariant principal bundles over $S^n$ in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant $(Π, G)$-bundles over cohomogeneity one manifolds.

Intrinsic formulation of noncommutative geometry for quantum gravity.

We investigate the relative market efficiency in financial market data, using the approximate entropy(ApEn) method for a quantification of randomness in time series. We used the global foreign exchange market indices for 17 countries during two periods from 1984 to 1998 and from 1999 to 2004 in order to study the effic…

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.