arXiv research

End-to-end learning of codes for secure BPSK communication in Gaussian wiretap channel.

Adversarial examples in machine learning for images are widely publicized and explored. Illustrations of misclassifications caused by slightly perturbed inputs are abundant and commonly known (e.g., a picture of panda imperceptibly perturbed to fool the classifier into incorrectly labeling it as a gibbon). Similar atta…

While research on adversarial examples in machine learning for images has been prolific, similar attacks on deep learning (DL) for radio frequency (RF) signals and their mitigation strategies are scarcely addressed in the published work, with only one recent publication in the RF domain [1]. RF adversarial examples (Ad…

Classifies modules of surface-knots in terms of their properties.

Curvature defined for Hilbert modules and Kasparov modules.

Proves finiteness and holonomicity of skein modules for 3-manifolds.

Defines super projective modules and explores their properties.

A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is …

We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the or…

Paper compares skein modules to Kauffman bracket modules.

Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach "algebra situs." When looking at the panorama of skein modules we see, past the rolling hills of homologies and homotopies, distant mountains - the Kauffman bracket skein mo…

Generalized Steinberg module presentation for Gaussian and Eisenstein integers.

Enhanced Alexander module detects linking numbers in links.

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called 2-crossed module bundle gerbe, which is a crossed module bundle gerbe equipped with an extra sructure. It is shown that s…

Combinatorial approach to compute satellite knot invariants using graph theory.

New sl(2) action defined on a mathematical module.

Studies modules over a category of Jacobi diagrams in handlebodies.

Enhances knot and link invariants using quandle modules.

Introduces admissible skein modules for non-semisimple categories.

Let $\{T_1, \ldots, T_n\}$ be a set of $n$ commuting bounded linear operators on a Hilbert space $\mathcal{H}$. Then the $n$-tuple $(T_1, \ldots, T_n)$ turns $\mathcal{H}$ into a module over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \raro \clh, \quad \quad …

This paper generalizes L2 cohomology theory for complex manifolds.

Study Kauffman bracket skein modules of Seifert fibered spaces.

Formula for interleaving distance of rectangle persistence modules.

Introduces Floer lasagna modules using link Floer homology.

Researchers create a Fredholm module on fractal shapes like the Cantor set.

We show that the Kauffman bracket skein module of a cylinder over the torus embeds as a subalgebra of the noncommutative torus. Using this we derive nice formulas for the Jones-Wenzl idempotents and analyze the structure of the Kauffman bracket skein module of the unknot as a module over the Kauffman bracket skein modu…

New knot theory module shows torsion-ness in number theory.

Study quandle modules over geometric quandles and their relation to Lie-Yamaguti representations.

The multivariate Alexander module of a link L has several subsets that admit quandle operations defined using the module operations. One of them, the fundamental multivariate Alexander quandle, determines the link module sequence of L.

A complex vector space $V$ is a prehomogeneous $G$-module if $G$ acts rationally on $V$ with a Zariski-open orbit. The module is called etale if $\dim V=\dim G$. We study etale modules for reductive algebraic groups $G$ with one-dimensional center. For such $G$, even though every etale module is a regular prehomogeneou…

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h…

Study on skein module dimensions at irreducible representations.

This document contains tables with the classification of prehomogeneous modules for reductive algebraic groups with up to two simple factors due to Sato, Kimura and many others, as well as corresponding tables of the étale modules appearing in this list, determined by the author. It is intended as a convenient referenc…

The paper studies deformations of cohesive modules on complex manifolds.

Some neural network modules are more critical to performance than others.

We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.

The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry''. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohom…

Study meromorphic open-string vertex algebras and modules over Riemannian manifolds.

Researchers compute the Kauffman bracket skein module of a specific 3-manifold.

New (co)homology theory for symmetric quandles developed.

Classifies extended Abelian Chern-Simons theories using quadratic modules.

Enhanced bikei modules distinguish unoriented and non-orientable surface-links.

We improve our previous results on indefinite Kasparov modules, which provide a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. In particular, we can weaken the assumptions that are imposed on indefinite Kasparov modules. Using a new theorem by Lesch an…

Corrects a paper on Alexander modules and answers a related question.

The space of m-ary differential operators acting on weighted densities is a (m+1)-parameter family of modules over the Lie algebra of vector fields. For almost all the parameters, we construct a canonical isomorphism between this space and the corresponding space of symbols as sl(2)-modules. This yields to the notion o…

Given a Heegaard splitting of a closed 3-manifold, the skein modules of the two handlebodies are modules over the skein algebra of their common boundary surface. The zeroth Hochschild homology of the skein algebra of a surface with coefficients in the tensor product of the skein modules of two handlebodies is interpret…

The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S^3-K, considered as a module over the (commutative) Laurent polynomial ring, and the Blanchfield linking pairing defined on this module. From the perspective of the…