Related papers: Subminimal Paths on a Stochastic Graph
Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems…
After a rapid introduction to the physical motivations and a succinct presentation of heuristic results, this survey summarises the main mathematical results known on the Edwards-Anderson and the Sherrington-Kirkpatrick models of spin…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The…
The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
A new quantum spin model with frustration, the `Union Jack' model on the square lattice, is analyzed using spin-wave theory. For small values of the frustrating coupling $\alpha$, the system is N{\' e}el ordered as usual, while for large…
Reachability analysis is a popular method to give safety guarantees for stochastic cyber-physical systems (SCPSs) that takes in a symbolic description of the system dynamics and uses set-propagation methods to compute an overapproximation…
Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
Stochastic model checking is a technique for analyzing systems that possess probabilistic characteristics. However, its scalability is limited as probabilistic models of real-world applications typically have very large or infinite state…
The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By…
We discuss the issue of temperature chaos in the Sherrington--Kirkpatrick spin glass mean field model. We numerically compute probability distributions of the overlap among (equilibrium) configurations at two different values of the…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…