arXiv research

Proves additivity of Casson-Seiberg-Witten invariant for a specific 4-manifold.

Study of Khovanov homology invariants from $U(1) imes U(1)$-equivariant algebra.

The paper calculates a specific invariant for a manifold with a circle action.

Let $(X,o)$ be a complex normal surface singularity with rational homology sphere link and let $\widetilde{X}$ be one of its good resolutions. Fix an effective cycle $Z$ supported on the exceptional curve and also a possible Chern class $l'\in H^2(\widetilde{X},\mathbb{Z})$. Define ${\rm Eca}^{l'}(Z)$ as the space of e…

Study of multiplicative connections in Lie groupoids.

In an earlier paper, we studied manifolds $M$ endowed with a generalized F structure $Φ\in End(TM\oplus T^*M)$, skew-symmetric with respect to the pairing metric, such that $Φ^3+Φ=0$. Furthermore, if $Φ$ is integrable (in some well-defined sense), $Φ$ is a generalized CRF structure. In the present paper we study quasi-…

No Lagrangian Klein bottles found in $S^2 imes S^2$.

Optimizes treatment allocation in networks considering indirect effects.

Formulae prove equivalence of two invariants on specific 4-manifolds.

Let N_1, N_2, M be smooth manifolds with dim N_1 + dim N_2 +1 = dim M$ and let phi_i, for i=1,2, be smooth mappings of N_i to M with Im phi_1 and Im phi_2 disjoint. The classical linking number lk(phi_1,phi_2) is defined only when phi_1*[N_1] = phi_2*[N_2] = 0 in H_*(M). The affine linking invariant alk is a generaliza…

The IM effect helps detect anomalies by memorizing inliers early.

Humans are capable of building holistic representations for images at various levels, from local objects, to pairwise relations, to global structures. The interpretation of structures involves reasoning over repetition and symmetry of the objects in the image. In this paper, we present the Program-Guided Image Manipula…

New algorithm optimizes unimodal bandits using empirical divergence.

New strategies avoid forced exploration for unimodal bandits.

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]

Discussion of "2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization" by V. Koltchinskii [arXiv:0708.0083]

Let $-\im\Lie_\T$ (essentially Lie derivative with respect to $\T$, a smooth nowhere zero real vector field) and $P$ be commuting differential operators, respectively of orders 1 and $m\geq 1$, the latter formally normal, both acting on sections of a vector bundle over a closed manifold. It is shown that if $P+(-i\Lie_…

A new framework maximizes influence spread in social networks by accounting for inter-community diffusion.

Proposes EDESH-SA for better inventory management under uncertainty.

The rise of Online Social Networks (OSNs) has caused an insurmountable amount of interest from advertisers and researchers seeking to monopolize on its features. Researchers aim to develop strategies for determining how information is propagated among users within an OSN that is captured by diffusion or influence model…

We compare the homology groups $H_n ^{IC}(X)$ of the chain complex of integral currents with compact support of a metric space $X$ with the singular Lipschitz homology $H^L_n (X)$ and with ordinary singular homology. If $X$ satisfies certain cone inequalities all these homology theories coincide. On the other hand, for…

Language models perform worse with implicit reward models than explicit ones.

New method recovers relative rates in spatial compositional data from IMS.

Optimized strategies for graph-structured bandits reduce regret efficiently.

Prove existence of $SO(3) imes SO(8)$-invariant Einstein metric on $S^3 imes S^7$

The well-known Influence Maximization (IM) problem has been actively studied by researchers over the past decade, with emphasis on marketing and social networks. Existing research have obtained solutions to the IM problem by obtaining the influence spread and utilizing the property of submodularity. This paper is based…

Grid homology invariant proved for lens space links.

The based loop space homology of a special family of homogeneous spaces, flag manifolds of connected compact Lie groups is studied. First, the rational homology of the based loop space on a complete flag manifold is calculated together with its Pontrjagin structure. Second, it is shown that the integral homology of the…

This paper concerns the problem of existence of taut foliations among 3-manifolds. Since the contribution of David Gabai, we know that closed 3-manifolds with non-trivial second homology group admit a taut foliations. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite di…

New families of Brieskorn spheres bound rational homology balls.

MONSTOR estimates influence in unseen networks with high accuracy.

ALTBI enhances outlier detection by maximizing the inlier-memorization effect.

We examine surgery on a knot in $S^3$ to determine surgery obstructions to Seifert fibered integral homology spheres. We find such surgery obstructions using Heegaard Floer, Knot Floer homology and the mapping cone formula for computing Heegaard Floer homology of surgery on a knot. Here however, we take a different app…

Smooth approximation of integral cycles in manifolds.

The paper finds new graph covers with exceptionally low degree.

Incompatible operations affect Khovanov homology and spectral sequences.

We prove that an integral homology 3-sphere is S^3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S^3. As an application we show that an irreducible integral homology sphere which is not S^3 is the cyclic branched cover of odd prime order of at most four knots in S^3…

Classifies surgeries on torus knots and cables that bound rational homology balls.

We will announce some results on the values of quantum sl_2 invariants of knots and integral homology spheres. Lawrence's universal sl_2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl_2. This implies an integrality result on the…

We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial …

Generalizes Seifert algorithm to integral homology spheres.

In a previous article, we constructed an invariant Z for null-homologous knots in rational homology spheres, from equivariant intersections in configuration spaces. Here we present an equivalent definition of Z in terms of configuration space integrals, we prove that Z is multiplicative under connected sum, and we prov…

Ozsváth, Rasmussen and Szabó constructed odd Khovanov homology. It is a link invariant which has the same reduction modulo 2 as (even) Khovanov homology. Szabó introduced a spectral sequence with mod 2 coefficients from mod 2 Khovanov homology to another link homology. He got his spectral sequence from a chain complex …

A new diffeomorphism invariant of integral homology 3-spheres is defined using a non-abelian 'quaternionic' version of the Seiberg-Witten equations.

We define a notion of isotropic surfaces in $\mathbb{O}$, i.e. on which some canonical symplectic forms vanish. Using the cross-product in $\mathbb{O}$ we define a map $ρ\colon Gr\_2(\mathbb{O})\to S^6$ from the Grassmannian of $\mathbb{O}$ to $S^6$. This allows us to associate to each surface $Σ$ of $\mathbb{O}$ a fun…