Related papers: Mixed Random Sampling of Frames method for countin…
Emergence of robustness in biological networks is a paramount feature of evolving organisms, but a study of this property in vivo, for any level of representation such as Genetic, Metabolic, or Neuronal Networks, is a very hard challenge.…
The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use…
Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the…
Quantum Monte Carlo is an efficient technique for finding the ground-state energy and related properties of small molecules. A major challenge remains in accurate determination of a molecule's geometry, i.e. the optimal location of its…
To maximize the accuracy of background simulation and event reconstruction, high-energy neutrino telescopes require detailed knowledge of light propagation over a large volume of detection medium. If light scattering and absorption leng ths…
The observation that some subgraphs, called motifs, appear more often in real networks than in their randomized counterparts has attracted much attention in the scientific community. In the prevalent approach the detection of motifs is…
Quasi-Monte Carlo methods are a way of improving the efficiency of Monte Carlo methods. Digital nets and sequences are one of the low discrepancy point sets used in quasi-Monte Carlo methods. This thesis presents the three new results…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Fiber network modeling can be used for studying mechanical properties of paper. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be…
Network motifs are small building blocks of complex networks. Statistically significant motifs often perform network-specific functions. However, the precise nature of the connection between motifs and the global structure and function of…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
We consider feature representation learning problem of molecular graphs. Graph Neural Networks have been widely used in feature representation learning of molecular graphs. However, most existing methods deal with molecular graphs…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods…
Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic…