Related papers: Generalization of Pigeon Hole Bound
Frames play significant role in various areas of science and engineering. In this paper, we introduce the concepts of frames for $End_{\mathcal{A}}^{\ast}(\mathcal{H, K})$ and their generalizations. Moreover, we obtain some new results for…
Boundary groupoids were introduced by the second author, which can be used to model many analysis problems on singular spaces. In order to investigate index theory on boundary groupoids, we introduce the notion of {\em a deformation from…
We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$…
We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables…
We generalize a result of Galatius and Venkatesh which relates the graded module of cohomology of locally symmetric spaces to the graded homotopy ring of the derived Galois deformation rings, by removing certain assumptions, and in…
We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil [H.E. Andersen and O. Geil, Evaluation codes from order domain theory, Finite Fields Appl., 14 (2008), pp. 92-123] for primary codes are consequences of…
Caire, Taricco and Biglieri presented a detailed analysis of bit interleaved coded modulation, a simple and popular technique used to improve system performance, especially in the context of fading channels. They derived an upper bound to…
Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of…
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized K\"ahler…
In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical…
The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…
A problem of further generalization of generalized Choi maps $\Phi_{[a,b,c]}$ acting on $\mathbb{M}_3$ introduced by Cho, Kye and Lee is discussed. Some necessary conditions for positivity of the generalized maps are provided as well as…
For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poisson structures the linear holonomy is defined for…
In 1991, J. Thomson obtained a celebrated decomposition theorem for $P^t(\mu),$ the closed subspace of $L^t(\mu)$ spanned by the analytic polynomials, when $1 \le t < \i.$ In 2008, J. Brennan \cite{b08} generalized Thomson's theorem to…
We extend the deformation to the normal cone and tangent groupoid constructions from finite-dimensional manifolds to infinite-dimensional Banach and Fredholm manifolds. Next, we generalize the concept of Fredholm filtrations to get a more…
In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the…
We first extend the construction of generalized barycentric coordinates (GBC) based on the vertices on the boundary of a polygon $\Omega$ to a new kind of GBCs based on vertices inside the $\Omega$ of interest. For clarity, the standard…
The weight hierarchy of generalized Reed-Muller codes over arbitrary finite fields was determined by Heijnen and Pellikaan. In this paper we produce curves over finite fields with many points which are closely related to this weight…