Related papers: Quantifier Elimination for Statistical Problems
An open question contributed by Yu. Orlov to a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel, A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…
We study the connectedness structure of the proper Pareto solution sets, the Pareto solution sets, the weak Pareto solution sets of polynomial vector variational inequalities, as well as the connectedness structure of the efficient solution…
Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of unsupervised learning is to find the probability distribution that would best describe the available data, and…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces,…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
We present in this paper a general algorithm for solving first-order formulas in particular theories called "decomposable theories". First of all, using special quantifiers, we give a formal characterization of decomposable theories and…
Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We…