arXiv research

Develops methods to calculate global index of real polynomials.

The paper explores global index formulas for one-dimensional holomorphic foliations.

Global balance index measures systemic risk in financial networks.

Global Morse index theorem applied to Jacobi fields on CMC surfaces.

We define the "localized index" of longitudinal elliptic operators on Lie groupoids associated to Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of …

Study XRP network, propose Flow Index to analyze transaction frequencies.

Formula for index in Lorentzian spacetimes.

Study creates a global living index to assess quality of life.

The index theorem connects anomalies on a domain wall to global integrals.

Study examines cross-training neural networks for financial index prediction.

We consider a hyperbolic Dirac-type operator with growing potential on a a spatially non-compact globally hyperbolic manifold. We show that the Atiyah-Patodi-Singer boundary value problem for such operator is Fredholm and obtain a formula for this index in terms of the local integrals and the relative eta-invariant int…

We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators th…

This study analyzes dynamic connectedness in global supply chain infrastructure portfolios, identifying key risk factors and extreme events.

We investigated the critical dynamics on the daily Taiwan stock exchange index (TSE) from 1971 to 2005, and the 5-min intraday data from 1996 to 2005. A global persistence exponent $θ_{p}$ was defined for non-equilibrium critical phenomena \cite{Janssen,Majumdar}, and describing dynamic behavior in an economic index \c…

Study reveals 2020 stock crashes were mostly endogenous, not exogenous.

Reformulates mod-two APS index using domain-wall fermion.

Gradient descent dynamics studied for DEQs in linear and single-index models.

Wavelet analysis reveals financialization effects on oil-food price correlation.

Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.

We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemann…

Researchers extend Gamma index theorem to non-compact spacetimes.

We prove that the half-integer valued local index of an isolated umbilic point on a $C^{3+α}$-smooth convex surface in Euclidean 3-space is less than two. The approach is to study the co-kernel of an associated Riemann-Hilbert boundary value problem. The link between the local and global is a semi-local technique that …

Local index formula for Lorentzian Dirac operators on spacetimes.

Introduces Levi core for CR manifolds, linking it to global invariants.

New theorem bounds group quotient size to subgroups index.

We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin$^c$-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit spaces. One special case is an index defined in terms of multiplicities of discrete…

Given a Lorentzian manifold $(M,g)$, a geodesic $γ$ in $M$ and a timelike Jacobi field $\mathcal Y$ along $γ$, we introduce a special class of instants along $γ$ that we call $\mathcal Y$-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the $\mathcal Y$-pseudo conjugate insta…

Paper establishes a new formula for Atiyah-Patodi-Singer index using eta invariants.

In this paper we are concerned with harmonic maps and minimal immersions defined on compact Riemannian manifolds and with values in homogenous strongly harmonic manifolds. We show some results on the Morse index by varying these maps along suitable conformal vector fields. We obtain also that they are global maxima on …

This paper analyses how Time Series Analysis techniques can be applied to capture movement of an exchange traded index in a stock market. Specifically, Seasonal Auto Regressive Integrated Moving Average (SARIMA) class of models is applied to capture the movement of Nifty 50 index which is one of the most actively excha…

In this paper, an equality between the Hochs-Mathai type index and the Atiyah-Patodi-Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group actions. As a technical preparation, a problem concerning the Fredholm property …

Herd behavior is an important economic phenomenon, especially in the context of the recent financial crises. In this paper, herd behavior in global stock markets is investigated with a focus on intercontinental comparison. Since most existing herd behavior indices do not provide a comparative method, we propose a new h…

We show that in any triangulated 3-manifold, every index n topologically minimal surface can be transformed to a surface which has local indices (as computed in each tetrahedron) that sum to at most n. This generalizes classical theorems of Kneser and Haken, and more recent theorems of Rubinstein and Stocking, and is t…

We prove an extension of the Index Theorem for Morse-Sturm systems of the form $-V''+RV=0$, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint. The result is then applied to the case of a Jacobi equation along a geodesic in…

We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for the area functional, in particular it has index one. We also obtain an inequality…

We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing …

We exhibit sufficient conditions for a finite collection of periodic orbits of a Reeb flow on a closed $3$-manifold to bound a positive global surface of section with genus zero. These conditions turn out to be $C^\infty$-generically necessary. Moreover, they involve linking assumptions on periodic orbits with Conley-Z…

Improved genetic algorithm optimizes SVR for robust long-term stock index forecasting.

The study examines how global economic policy uncertainty affects crude oil futures volatility.

Reverses simplification of risk measurement, focusing on portfolio covariance.

Model forecasts global stock market volatility using dynamic graphs and all trading days.

In this paper the correlation between education, research and macroeconomic strength of countries at a global scale is analyzed on the basis of statistical data published by the UNIDO and OECD. It uses sets of composite indicators describing the economical performance and competitiveness as well as those relevant for h…

DFR models dynamic distributional data with weighted Fréchet means.

PLS-Lasso integrates dimension reduction into regression for financial index tracking.

New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk $D$ that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeom…

The paper studies global invertibility of maps on Finsler manifolds.

We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond the regime where effective estimates are at disposal.