Related papers: Optimal combinations of imperfect objects
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
Consider a collection of objects, some of which may be `bad', and a test which determines whether or not a given sub-collection contains no bad objects. The non-adaptive pooling (or group testing) problem involves identifying the bad…
In this paper we describe a general approach to optimal imperfect maintenance activities of a repairable equipment with independent components. Most of the existing works on optimal imperfect maintenance activities of a repairable equipment…
We consider the problem of reproducing one quantum measurement given the ability to perform another. We give a general framework and specific protocols for this problem. For example, we show how to use available "imperfect" devices a small…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
An important issue in additive manufacturing is the reliability and reproducibility of parts. One major problem in achieving this are uncontrolled local variations in the obtained material properties which arise in the complex manufacturing…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
Reassembling 3D broken objects is a challenging task. A robust solution that generalizes well must deal with diverse patterns associated with different types of broken objects. We propose a method that tackles the pairwise assembly of 3D…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many…
The dynamics of real-world applications and systems require efficient methods for improving infeasible solutions or restoring corrupted ones by making modifications to the current state of a system in a restricted way. We propose a new…
State of the art quantum computing architectures are founded on the decision to use scalable but faulty quantum hardware in conjunction with an efficient error correcting code capable of tolerating high error rates. The promised effect of…