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The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical…
We demonstrate direct evidence for ferromagnetic order at defect structures in highly oriented pyrolytic graphite with magnetic force microscopy at room temperature. Magnetic impurities have been excluded as the origin of the magnetic…
We study the magnetic and thermodynamic properties of a spin-$1/2$ Ising system containing three layers, each of which is composed exclusively of one out of two possible types of atoms, \textbf{A} or \textbf{B}. The \textbf{A-A} and…
Carbon materials are attracting increasing attention due to the novelty of the associated physical properties and the potential applications in high-tech devices. The possibility to achieve outstanding properties in macroscopic carbon…
Graph models, like other machine learning models, have implicit and explicit biases built-in, which often impact performance in nontrivial ways. The model's faithfulness is often measured by comparing the newly generated graph against the…
As impermeable to gas molecules and at the same time transparent to high-energy ions, graphene has been suggested as a window material for separating a high-vacuum ion beam system from targets kept at ambient conditions. However,…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
The two-dimensional Ising model defined on square lattices with diamond-type bond-decorations is employed to study the nature of the ferromagnetic phase transitions of inhomogeneous systems. The model is studied analytically under the…
The 2d ferromagnetic Ising model was solved by Onsager on the square lattice in 1944, and an explicit expression of the free energy density $f$ is presently available for some other planar lattices. But an exact derivation of the critical…
We study thermodynamic properties of an antiferromagnetic Ising model on the inverse perovskite lattice by using Monte Carlo simulations. The lattice structure is composed of corner-sharing octahedra and contains three-dimensional…
We study the one dimensional Ising model with ferromagnetic, long range interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an external random filed. we assume that the random field is given by a collection of independent…
Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph and motivated by social and biological networks, we study the problem of…
We study the Independent Set (IS) problem in $H$-free graphs, i.e., graphs excluding some fixed graph $H$ as an induced subgraph. We prove several inapproximability results both for polynomial-time and parameterized algorithms.…
We study phase ordering dynamics in the three-dimensional nearest-neighbor Ising model, following rapid quenches from infinite to zero temperature. Results on various aspects, viz., domain growth, persistence, aging and pattern, have been…
Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised…
In this note we extend the analysis of a previous paper by the author to the Random Cluster model. The main result being that the pressure of the finite range ferromagnetic Ising model is analytic as a function of the inverse temperature in…
Ordered distributions of carbon and substitutional dopant (A) atoms over the sites of a graphene lattice and problem of their stability are considered theoretically. The ranges of values of interatomic-interaction parameters providing the…
We propose a method to find out the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field $B_s = +\infty$, $B_{t} =…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…