Related papers: Distributional Boundary Values: Some New Perspecti…
We present sufficient conditions for the existence of positive solutions for a class of fractional singular boundary value problems in presence of Caputo fractional derivative. Further, the nonlinearity involved has singularity with respect…
We investigate the Berezin integral of non-compactly supported quantities. In the framework of supermanifolds with corners, we give a general, explicit and coordinate-free repesentation of the boundary terms introduced by an arbitrary…
We give a new proof of VC bounds where we avoid the use of symmetrization and use a shadow sample of arbitrary size. We also improve on the variance term. This results in better constants, as shown on numerical examples. Moreover our bounds…
All famous machine learning algorithms that comprise both supervised and semi-supervised learning work well only under a common assumption: the training and test data follow the same distribution. When the distribution changes, most…
We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
Let $X$ be a compact smooth manifold with boundary. In this article, we study the spaces $\mathcal V^\dagger(X)$ and $\mathcal V^\ddagger(X)$ of so called boundary generic and traversally generic vector fields on $X$ and the place they…
Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the…
In this work, we analyze the conditions under which information about the context of an input $X$ can improve the predictions of deep learning models in new domains. Following work in marginal transfer learning in Domain Generalization…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
This paper completes the foundations of neatly integrable normal distribution theory on manifolds with boundary. Normal distributions are those which contain vectors transverse to the boundary along its entirety. The theory is observed to…
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
Learning domain-invariant representations has become a popular approach to unsupervised domain adaptation and is often justified by invoking a particular suite of theoretical results. We argue that there are two significant flaws in such…
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination have been the most used, but their legitimacy has been…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on…