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We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed…
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a…
Urban systems are primarily relational. The uneven intensities and distribution of flows between systems of cities results in hierarchically organised complex networks of urban exchange. Distinct urban spatial structures reflect the…
The universal behavior of magnetic impurities in a metal is proved with the help of skeleton diagrams. The energy scales are derived from the structure of the skeleton diagrams. A minimal set of skeleton diagrams is sorted out that scales…
The amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of what really drives the processes behind urbanisation. In this…
Gravitational-collapse-based explanations of the cosmic web lead to problems in estimating the total mass in the universe. A first-principles several-scales model is developed here for the structural organisation of cosmic matter in a flat…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
In multi-criteria graph traversal, paths are compared via Pareto dominance, an ordering that identifies which paths are non-dominated, but says nothing about which path to expand next or when the search may stop. As a result, existing…
Following H. Tomita and C. Murakami we propose an analytical model to predict critical probability of percolation. It is based on the excursion set theory which allows us to consider N-dimensional bounded regions. Details are given for the…
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…
We propose a decision criterion for segmenting the cosmic web into different structure types (voids, sheets, filaments, and clusters) on the basis of their respective probabilities and the strength of data constraints. Our approach is…
We study kinetic transport through modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it indicates…
The scatter in the apparent magnitude of type Ia supernovae induced by stochastic gravitational lensing is highly dependent on the nonlinear growth of cosmological structure. In this paper, we show that such a dependence can potentially be…
We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph…
Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…
3D Voronoi's tessellation method was first applied to identify groups of galaxies in the structure of a supercluster. The sample under consideration consists of more than 7000 galaxies of the Local Supercluster (LS) with radial velocities…
The phase space distribution of matter out to $\sim 100 \rm Mpc$ is probed by two types of observational data: galaxy redshift surveys and peculiar motions of galaxies. Important information on the process of structure formation and…
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…
The online increasing subsequence problem is a stochastic optimisation task with the objective to maximise the expected length of subsequence chosen from a random series by means of a nonanticipating decision strategy. We study the…
We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows…