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Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important since it reveals which hypergraph properties cannot be…

Combinatorics · Mathematics 2024-06-14 Aida Abiad , Antonina P. Khramova

We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…

Algebraic Geometry · Mathematics 2007-05-23 Duco van Straten , Christian Sevenheck

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

Machine Learning · Computer Science 2014-11-25 Xiaojun Chang , Feiping Nie , Zhigang Ma , Yi Yang , Xiaofang Zhou

Let ($\Omega^{\ast}(M), d$) be the de Rham cochain complex for a smooth compact closed manifolds $M$ of dimension $n$. For an odd-degree closed form $H$, there are a twisted de Rham cochain complex $(\Omega^{\ast}(M), d+H_\wedge)$ and its…

Algebraic Topology · Mathematics 2010-05-06 Weiping Li , Xiugui Liu , He Wang

Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…

Numerical Analysis · Mathematics 2016-11-16 Silvia Noschese , Lothar Reichel

We are interested in computing the Bredon cohomology with coefficients in the constant Mackey functor $\underline{ \mathbb{F}_2}$ for equivariant $\text{Rep}(C_2)$ spaces, in particular for Grassmannian manifolds of the form…

Algebraic Topology · Mathematics 2025-03-14 Eric Hogle

We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…

Algebraic Topology · Mathematics 2018-01-09 Zbigniew Błaszczyk , Marek Kaluba

We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $\theta$-deformed Riemannian manifolds. It can be summarized as a category…

Quantum Algebra · Mathematics 2022-01-24 Yang Liu

We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.

Functional Analysis · Mathematics 2009-09-25 Peter G. Casazza , Nigel J. Kalton , Denka Kutzarova , M. Mastylo

As needed for the construction of rank $n$ continuous frames on a right quaternionic Hilbert space the so-called S-spectrum of a right quaternionic operator is studied. Using the S-spectrum, as for the case of complex Hilbert spaces, along…

Mathematical Physics · Physics 2015-07-03 M. Khokulan , K. Thirulogasanthar , B. Muraleetharan

We present a new approach for constructing covariant symplectic structures for geometrical theories, based on the concept of adjoint operators. Such geometric structures emerge by direct exterior derivation of underlying symplectic…

Mathematical Physics · Physics 2016-09-07 R. Cartas-Fuentevilla

We study a spectral sequence approximating Lie algebroid cohomology associated to a Lie subalgebroid. This is a simultaneous generalisation of several classical constructions in differential geometry, including the Leray-Serre spectral…

Differential Geometry · Mathematics 2024-10-25 Ioan Mărcuţ , Andreas Schüßler

Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…

Classical Analysis and ODEs · Mathematics 2024-01-15 Lucas Dunckley , Bryn Davies

We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…

Mesoscale and Nanoscale Physics · Physics 2023-07-06 Tommy Tai , Ching Hua Lee

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

Symplectic Geometry · Mathematics 2019-12-02 Alberto Della Vedova

In this paper we define a new category of almost complex riemannian 4- manifolds and discuss some basic properties of such pseudo symplectic manifolds. Some motivation based on the Seiberg - Witten theory is imposed.

Differential Geometry · Mathematics 2007-05-23 Nik. A. Tyurin

We develop in this work the first polytopal complexes of differential forms. These complexes, inspired by the Discrete De Rham and the Virtual Element approaches, are discrete versions of the de Rham complex of differential forms built on…

Numerical Analysis · Mathematics 2025-01-22 Francesco Bonaldi , Daniele A. Di Pietro , Jerome Droniou , Kaibo Hu

We determine the invariants characterizing the $Sp(n)$-orbits in the real Grassmannian $Gr^\R(2k,4n)$ of the $2k$-dimensional complex and $\Sigma$-complex subspaces of a $4n$-dimensional Hermitian quaternionic vector space. A…

Differential Geometry · Mathematics 2022-02-01 Massimo Vaccaro

The main goal of our paper is the study of several classes of submanifolds of generalized complex manifolds. Along with the generalized complex submanifolds defined by Gualtieri and Hitchin (we call these ``generalized Lagrangian…

Differential Geometry · Mathematics 2019-11-14 Oren Ben-Bassat , Mitya Boyarchenko

The quantum homology of the monotone complex quadric surface splits into the sum of two fields. We outline a proof of the following statement: The unities of these fields give rise to distinct symplectic quasi-states defined by asymptotic…

Symplectic Geometry · Mathematics 2010-06-15 Yakov Eliashberg , Leonid Polterovich