arXiv research

Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.

Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.

Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite fraction of all pairs of elements. The coexistence of an eigenvalue spectrum predic…

We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study the parameter estimation problem under such one-parameter models. We demonstrate…

There are non-vanishing price responses across different stocks in correlated financial markets. We further study this issue by performing different averages, which identify active and passive cross-responses. The two average cross-responses show different characteristic dependences on the time lag. The passive cross-r…

The non-vanishing conjecture implies the abundance conjecture in certain cases.

We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…

We prove the non-vanishing of the CMC flux of the boundaries of certain Riemannian manifolds with constant mean curvature.

It is well known that combining multiple hedge fund alpha streams yields diversification benefits to the resultant portfolio. Additionally, crossing trades between different alpha streams reduces transaction costs. As the number of alpha streams increases, the relative turnover of the portfolio decreases as more trades…

The paper constructs metrics on compact manifolds using Aubin's deformations.

We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg-Witten invariant of connected sums of 4-manifolds with positive first Betti number. The non-vanishing theorem enables us to find many new examples of 4-manifolds with non-trivial stable cohomotopy Seiberg-Witten invariants and it also gives a …

The paper explores statistical limits for detecting correlation in tree structures.

New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.

Study shows non-vanishing Stiefel-Whitney classes and absence of spin^C structures in certain hyperbolic manifolds.

Paper proves non-extendability of quasimorphism and non-vanishing of Reznikov's class.

Paper tackles robust graph matching in dense graphs with AMP type algorithm.

Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.

In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.

Study confirms optimal bounds for group cohomology of Lie groups.

We solve Euler equations on graph manifolds, classifying steady flows with Morse-Bott Bernoulli functions.

Study non-vanishing $\ell^2$-Betti numbers for specific groups.

We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai's sutured manifold theory. It is hoped that the non-vanis…

Study shows non-abelian free groups' 4th cohomology is non-zero.

The problem on the minimal number (with respect to deformation) of intersection points of two closed curves on a surface is solved. Following the Nielsen approach, we define classes of intersection points and essential classes of intersection points, which "are preserved under deformation" and whose total number is cal…

We study the problem of the execution of a moderate size order in an illiquid market within the framework of a solvable Markovian model. We suppose that in order to avoid impact costs, a trader decides to execute her order through a unique trade, waiting for enough liquidity to accumulate at the best quote. We find tha…

In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model coupled to a non-dynamical gauge field with Kahler target space X being a G-manifold. Our main objective is to furnish a purely physical interpretation of the equivariant cohomology of the chiral de Rham complex…

We study the first uniformly finite homology group of Block and Weinberger for uniformly locally finite graphs, with coefficients in $\mathbb{Z}$ and $\mathbb{Z}_2$. When the graph is a tree, or coefficients are in $\mathbb{Z}_2$, a characterisation of the group is obtained. In the general case, we describe three pheno…

New type of maps studied with non-vanishing torsion.

We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that this invariant can distinguish some links for which the ordinary Milnor invaria…

We show the non-vanishing of cohomology groups of sufficiently small congruence lattices in $SL(1,D)$, where $D$ is a quaternion division algebras defined over a number field $E$ contained inside a solvable extension of a totally real number field. As a corollary, we obtain new examples of compact, arithmetic, hyperbol…

We show that surface bundles over surfaces with base and fiber of genus at least 2 have non-vanishing simplicial volume.

We state and prove a generalization of the Poincaré-Hopf index theorem for manifolds with boundary. We then apply this result to non-vanishing complex vector fields.

We prove a non-vanishing result for the $L_{q,p}$-cohomology of complete simply-connected Riemannian manifolds with pinched negative curvature.

The study finds hyperbolic manifolds without spin^c structures in dimensions 5 and above.

We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant.

We determine the isomorphism classes of symmetric symplectic manifolds of dimension at least 4 which are connected, simply-connected and have a curvature tensor which has only one non-vanishing irreducible component -- the Ricci tensor.

The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.

The affine-additive group is hyperbolic with a non-vanishing 4-capacity.

We prove that the mean curvature $τ$ of the slices given by a constant mean curvature foliation can be used as a time function, i.e. $τ$ is smooth with non-vanishing gradient.

We construct examples of $S^1$-manifolds with finite second homotopy group and non-vanishing $\hat A$-genus. This is related to the classification of positive quaternionic Kaehler manifolds.

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are given.

New rigidity result for non-orientable manifolds with scalar curvature constraints.

We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.

We show that a compact embedded minimal or constant mean curvature annulus with non-vanishing Gaussian curvature which is tangent to two spheres of same radius or tangent to a sphere and meeting a plane in constant contact angle is rotational.

Using the knot Floer homology filtration, we define invariants associated to a knot in a three-manifold possessing non-vanishing Floer co(homology) classes. In the case of the Ozsvath-Szabo contact invariant we obtain an invariant of knots in a contact three-manifold. This invariant provides an upper bound for the Thur…

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $κ_μ$ (relatively to a suitable riemannian metric $μ$) is zero. In the transversally orientable case…

The study explores Legendrian invariants and half Giroux torsion in contact structures.

We observe inequalities involving the Herzlich volume of a 4-dimensional asymptotically complex hyperbolic Einstein manifold and its Euler characteristic provided the metrics is either Kaehler or selfdual. In the selfdual case we have to assume furthermore that the Kronheimer-Mrowka invariant is non vanishing.