Related papers: Saturating directed spaces
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
Approximate stationarity conditions provide necessary optimality conditions without requiring additional assumptions by demanding that a perturbed stationarity system possesses solutions as the involved perturbations tend to zero. Together…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…
In this paper, we present a construction from a Reedy category $C$ of a direct category $\operatorname{Down}(C)$ and a functor $\operatorname{Down}(C) \to C$, which exhibits $C$ as an $(\infty,1)$-categorical localization of…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
Our previous paper introduces topological notions of normal crossings symplectic divisor and variety and establishes that they are equivalent, in a suitable sense, to the desired geometric notions. Friedman's d-semistability condition is…
In this submission, we explore the use of equality saturation to optimize concurrent computations. A concurrent environment gives rise to new optimization opportunities, like extracting a common concurrent subcomputation. To our knowledge,…
The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…
In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function…
Categories of locally ordered spaces are especially well-adapted to the realization of most precubical sets, though their colimits are not so easy to determine (in comparison with colimits in the category of d-spaces for example). We use…
This article characterizes topological duals of spaces of cadlag processes. We obtain extensions of functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis. In particular, we obtain…
Disjoint-paths logic, denoted $\mathsf{FO}$+$\mathsf{dp}$, extends first-order logic ($\mathsf{FO}$) with atomic predicates $\mathsf{dp}_r[(x_1,y_1),\ldots,(x_r,y_r)]$, expressing the existence of vertex-disjoint paths between $x_i$ and…
Optimizing a network of maps among a collection of objects/domains (or map synchronization) is a central problem across computer vision and many other relevant fields. Compared to optimizing pairwise maps in isolation, the benefit of map…
We effectively bound T-singularities on non-rational projective surfaces with an arbitrary amount of T-singularities and ample canonical class. This fully generalizes the previous work for the case of one singularity, and illustrates the…