Related papers: Optimal combinations of imperfect objects
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
Decomposition, i.e. independently analyzing possible subgames, has proven to be an essential principle for effective decision-making in perfect information games. However, in imperfect information games, decomposition has proven to be…
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the…
Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are…
The encoding of classical data in a physical support can be done up to some level of accuracy due to errors and the imperfection of the writing process. Moreover, some degradation of the storage data can happen over the time because of…
By suitable examples we illustrate an algorithm for composition of inverse problems.
Electrical component obsolescence poses a major issue especially within systems with large life cycles. Thus, finding the optimal management solution for each obsolescence case is as crucial as knowing what to consider when faced with an…
Many present day quantum optics experiments, particularly in optical quantum information processing, rely on number-resolving photo-detection as a basic building block. In this paper we demonstrate that a simple classical optimisation…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of…
In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller.…
A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
Numerical optimization of complex systems benefits from the technological development of computing platforms in the last twenty years. Unfortunately, this is still not enough, and a large computational time is still necessary when…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…