相关论文: Region graph partition function expansion and appr…

Systems with many interacting stochastic constituents are fully characterized by their free energy. Computing this quantity is therefore the objective of various approaches, notably perturbative expansions, which are applied in problems…

Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…

Enhanced sampling techniques have become an essential tool in computational chemistry and physics, where they are applied to sample activated processes that occur on a time scale that is inaccessible to conventional simulations. Despite…

Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for…

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…

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to…

Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…

This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…

Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs…

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…

We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…

Scene graph generation aims to interpret an input image by explicitly modelling the potential objects and their relationships, which is predominantly solved by the message passing neural network models in previous methods. Currently, such…

We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…

We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency…

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal…

We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help…

In this paper, we propose a simple but effective method for fast image segmentation. We re-examine the locality-preserving character of spectral clustering by constructing a graph over image regions with both global and local connections.…

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…

In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This…