相关论文: Climbing on Pyramids
This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…
Segmentation algorithms based on an energy minimisation framework often depend on a scale parameter which balances a fit to data and a regularising term. Irregular pyramids are defined as a stack of graphs successively reduced. Within this…
In this chapter the physical aspects of the global optimization of the geometry of atomic clusters are elucidated. In particular, I examine the structural principles that determine the nature of the lowest-energy structure, the physical…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
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…
We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
Discrete energy minimization is a ubiquitous task in computer vision, yet is NP-hard in most cases. In this work we propose a multiscale framework for coping with the NP-hardness of discrete optimization. Our approach utilizes algebraic…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well known quantum mechanical tunneling property which enables small bodies to penetrate…
Avraham et al. [AFK+15] presented an alternative approach to parametric search, called \emph{bifurcation}, that performs faster under certain circumstances. Intuitively, when the underlying decider execution can be rolled back cheaply and…
We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work…
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve…
We present an iterative algorithm that finds the optimal measurement for extracting the accessible information in any quantum communication scenario. The maximization is achieved by a steepest-ascent approach toward the extremal point,…
A method is presented that can find the global minimum of very complex condensed matter systems. It is based on the simple principle of exploring the configurational space as fast as possible and of avoiding revisiting known parts of this…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…