相关论文: Reduced Dependency Spaces for Existential Paramete…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…

Dependence logics are a modern family of logics of independence and dependence which mimic notions of database theory. In this paper, we aim to initiate the study of enumeration complexity in the field of dependence logics and thereby get a…

A vertex of a plane digraph is bimodal if all its incoming edges (and hence all its outgoing edges) are consecutive in the cyclic order around it. A plane digraph is bimodal if all its vertices are bimodal. Bimodality is at the heart of…

Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…

Property Specification Patterns (PSPs) have been proposed to solve recurring specification needs, to ease the formalization of requirements, and enable automated verification thereof. In this paper, we extend PSPs by considering Boolean as…

We introduce BEDS (Bayesian Emergent Dissipative Structures), a formal framework for analyzing inference systems that must maintain beliefs continuously under energy constraints. Unlike classical computational models that assume perfect…

We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…

The alternation of existential and universal quantifiers in a quantified boolean formula (QBF) generates dependencies among variables that must be respected when evaluating the formula. Dependency schemes provide a general framework for…

We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems…

Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter…

We introduce the notion of a Real Equation System (RES), which lifts Boolean Equation Systems (BESs) to the domain of extended real numbers. Our RESs allow arbitrary nesting of least and greatest fixed-point operators. We show that each RES…

Hamkins and Kikuchi (2016 and 2017) show that in both set theory and class theory the definable subset ordering of the universe interprets a complete and decidable theory. If $\mathcal{M}$ is a model of set theory, then $\langle M,…

Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…

We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…

Among the biggest challenges in property-based testing (PBT) is the constrained random generation problem: given a predicate on program values, randomly sample from the set of all values satisfying that predicate, and only those values.…

The persistence of excitation (PE) condition is sufficient to ensure parameter convergence in adaptive estimation problems. Recent results on adaptive estimation in reproducing kernel Hilbert spaces (RKHS) introduce PE conditions for RKHS.…

We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs…

Probabilistic circuits (PCs) are a prominent representation of probability distributions with tractable inference. While parameter learning in PCs is rigorously studied, structure learning is often more based on heuristics than on…

A fundamental challenge in synthesis from examples is designing a learning algorithm that poses the minimal number of questions to an end user while guaranteeing that the target hypothesis is discovered. Such guarantees are practically…