Related papers: Generalization of Pigeon Hole Bound
Motivated by the computations done in \cite{C1}, where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category $\mathsf{Bun}_{G,M}$ of principal…
We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements…
Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
Marginal MAP inference involves making MAP predictions in systems defined with latent variables or missing information. It is significantly more difficult than pure marginalization and MAP tasks, for which a large class of efficient and…
Generalized M\"obius-Listing bodies and surfaces are generalizations of the classic M\"obius band. The original motivation is that for solutions of boundary value problems the knowledge of the domain is essential. In previous papers cutting…
Building upon the application of flags to network coding introduced by Liebhold, Nebe, and Vazquez-Castro, we develop a variant of this coding technique that uses degenerate flags. The information set is a metric affine space isometric to…
In this short note we consider several widely used L^2-orthogonal Helmholtz decompositions for bounded domains in R^3. It is well known that one part of the decompositions is a subspace of the space of functions with zero mean. We refine…
Symmetric cohomology of groups, defined by M. Staic in [2], is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which…
In fragments of first order arithmetic, definable maps on finite domains could behave very differently from finite maps. Here combinatorial properties of $\Sigma_{n+1}$-definable maps on finite domains are compared in the absence of…
R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2)…
A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.
In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.
There has been considerable effort to better understand the generalization capabilities of deep neural networks both as a means to unlock a theoretical understanding of their success as well as providing directions for further improvements.…
We prove partial and full boundary regularity for manifold constrained $p(x)$-harmonic maps.
A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It turns out that such a generalization can be based on integral…
We compute supersymmetric contributions to pion leptonic (\pi_{l2}) decays in the Minimal Supersymmetric Standard Model (MSSM). When R-parity is conserved, the largest contributions to the ratio R_{e/\mu} = \Gamma[ \pi^+ \to e^+…
We define a scale of Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, $p\in[1,\infty]$, that are invariant under suitable Fourier integral operators of order zero. This builds on work by Smith for $p=1$. We also introduce a notion of…
We establish local to global results for a function space which is larger than the well known BMO space, and was also introduced by John and Nirenberg.
The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.