相关论文: Graph's Topology and Free Energy of a Spin Model o…

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy…

We use a free energy functional theory to elucidate general properties of heterogeneously ordering, fast folding proteins, and we test our conclusions with lattice simulations. We find that both structural and energetic heterogeneity can…

The study of spins and particles on graphs has broad applications, from the dynamics of interacting systems on networks to combinatorial problems. Here, we study the large-$n$ limit of the $O(n)$ model on graphs, which is considerably more…

A general theoretical framework is developed using free energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from non-uniformity in native…

There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…

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…

We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity…

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy…

We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…

We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree…

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…

Thirty years ago, Stanley showed that an O(n) spin model on a lattice tends to a spherical model as $n\to\infty$. This means that at any temperature the corresponding free energies coincide. This fundamental result, providing the basis for…

Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randi\'c energy,…

Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of…

We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy…

The topological structure of the power grid plays a key role in the reliable delivery of electricity and price settlement in the electricity market. Incorporation of new energy sources and loads into the grid over time has led to its…

We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…

A detailed comparison is made between the field-theoretic and geometric definitions of topological charge density on the lattice. Their renormalizations with respect to continuum are analysed. The definition of the topological…

Graphene has been studied in detail due to its mechanical, electrical, and thermal properties. It is well documented that the introduction of dopants or defects in the lattice can be used to tune material properties for a specific…