Related papers: Boolean-valued models as a foundation for locally …

This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work…

This paper investigates locally linear regression for locally stationary time series and develops theoretical results for locally linear smoothing and transfer learning. Existing analyses have focused on local constant estimators and given…

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…

Non-locality is being intensively studied in various PDE-contexts and in variational problems. The numerical approximation also looks challenging, as well as the application of these models to Continuum Mechanics and Image Analysis, among…

We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the…

This paper studies convex problems of Bolza in the conjugate duality framework of Rockafellar. We parameterize the problem by a general Borel measure which has direct economic interpretation in problems of financial economics. We derive a…

The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the…

We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ is a (strict) functor taking values in the category of commutative…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and…

In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…

The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector…

We prove a few representer theorems for a localised version of the regularised and multiview support vector machine learning problem introduced by H.Q. Minh, L. Bazzani, and V. Murino, Journal of Machine Learning Research, 17(2016) 1-72,…

The notion of multivariate total positivity has proved to be useful in finance and psychology but may be too restrictive in other applications. In this paper we propose a concept of local association, where highly connected components in a…

We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are…

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational…

We introduce the new notion of convolution of a (smooth or generalized) valuation on a group $G$ and a valuation on a manifold $M$ acted upon by the group. In the case of a transitive group action, we prove that the spaces of smooth and…

The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…

Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…