Related papers: Number partitioning as random energy model

We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware-efficient quantum algorithms for solving binary…

Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…

We prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size $n$ decorated by an Ising configuration with a weight proportional to the energy of this configuration. To do so, we establish…

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…

The consideration of the N-body gravitational problem equations can give to us some class of boundary-value problems defined on the "beem's" construction. One can considere it as weak or so-called finite element method's approximation with…

The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to…

Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…

Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…

Data clustering is an instrumental tool in the area of energy resource management. One problem with conventional clustering is that it does not take the final use of the clustered data into account, which may lead to a very suboptimal use…

Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…

We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti-Sommers representation of the…

We propose a new class of phenomenological models for dynamic glass transitions. The system consists of an ensemble of mesoscopic regions to which local energies are allocated. At each time step, a region is randomly chosen and a new local…

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We…

Local energy markets empower prosumers to form coalitions for energy trading. However, the optimal partitioning of the distribution grid into such coalitions remains unclear, especially in constrained grids with stochastic production and…

In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and…

We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.

In this study, we extend the lower bound on the average of the local energy of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] obtained for a symmetric distribution to an asymmetric one. Compared with the…

An appropriate model for the random energy landscape in organic glasses is a spatially correlated Gaussian field, generated by randomly located and oriented dipoles and quadrupoles. Correlation properties of energetic disorder directly…

We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a…

We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…