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We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to…
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
Neutron and X-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of a model-dependent methods. This…
Large data applications rely on storing data in massive, sparse graphs with millions to trillions of nodes. Graph-based methods, such as node prediction, aim for computational efficiency regardless of graph size. Techniques like localized…
In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…
A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…
We consider weighted tiling systems to represent functions from graphs to a commutative semiring such as the Natural semiring or the Tropical semiring. The system labels the nodes of a graph by its states, and checks if the neighbourhood of…
Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating…
Graphene is of great scientific interest due to a variety of unique properties such as ballistic transport, spin selectivity, the quantum hall effect, and other quantum properties. Nanopatterning and atomic scale modifications of graphene…
Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient…
We consider probe-based quantum thermometry and show that machine classification can provide model-independent estimation with quantifiable error assessment. Our approach is based on the k-nearest-neighbor algorithm. The machine is trained…
Inverse problems are of great importance in astrophysics for deriving information about the physical characteristics of hot optically thin plasma sources from their EUV and X-ray spectra. We describe and test an iterative method developed…
We present a framework for learning Node Embeddings from Static Subgraphs (NESS) using a graph autoencoder (GAE) in a transductive setting. NESS is based on two key ideas: i) Partitioning the training graph to multiple static, sparse…
Graph attention networks learn neighbor importance through data-dependent coefficients, but standard layers lack explicit control over unreliable feature dimensions and use fixed sharpness of attention coefficient distributions. This paper…
In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
The network alignment (or graph matching) problem refers to recovering the node-to-node correspondence between two correlated networks. In this paper, we propose a network alignment algorithm which works without using a seed set of…