Related papers: On Generalized Ordered Sets: A constructive develo…
A novel paradigm for sorting is introduced, based upon resetting. Using simple examples, we demonstrate that sorting is achieved by resetting the velocity component(s) or orientation of the particles, rather than position. The objects to be…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
Monotone triangles are a rich extension of permutations that biject with alternating sign matrices. The notions of weak order and descent sets for permutations are generalized here to monotone triangles, and shown to enjoy many analogous…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…
We describe all inequalities among generalized diagonals in positive semi-definite matrices. These turn out to be governed by a simple partial order on the symmetric group. This provides an analogue of results of Drake, Gerrish, and…
We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences and most of the usual construction of…
The theme of the first two sections, is to prepare the framework of how from a ``complicated'' family of so called index models $I \in K_1$ we build many and/or complicated structures in a class $K_2$. The index models are…
An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…
In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.
We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability…
In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…