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It is shown that when the initial particles probability density is discontinuous the emerging currents appear instantaneously, and although the density beyond the discontinuity is initially negligible the currents there have a finite value.…
We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement…
We study property testing of (di)graph properties in bounded-degree graph models. The study of graph properties in bounded-degree models is one of the focal directions of research in property testing in the last 15 years. However, despite…
A computable structure A is x-computably categorical for some Turing degree x, if for every computable structure B isomorphic to A there is an isomorphism f:B -> A with f computable in x. A degree x is a degree of categoricity if there is a…
The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains…
In a previous paper, the author introduced the idea of intrinsic density --- a restriction of asymptotic density to sets whose density is invariant under computable permutation. We prove that sets with well-defined intrinsic density (and…
We study connections between classical asymptotic density and c.e. sets. We prove that a c.e. Turing degree d is not low if and only if d contains a c.e. set A of density 1 which has no computable subsets of density 1, giving a natural…
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts for the maximal smallest degree of a subgraph containing a…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Ne\v{s}et\v{r}il and Ossona de Mendez. These classes are defined by the fact that the maximum average degree of a…
Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…
We show that a randomly perturbed digraph, where we start with a dense digraph $D_\alpha$ and add a small number of random edges to it, will typically contain a fixed orientation of a bounded degree spanning tree. This answers a question…
We prove that for each $k\ge0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, so that the expected number of vertices of degree $k$ is asymptotically $d_k n$, and moreover…
The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…
Throughout the paper, an analytic field means a non-archimedean complete real-valued one, and our main objective is to extend to these fields the basic theory of transcendental extensions. One easily introduces a topological analogue of the…
With complex networks emerging as an effective tool to tackle multidisciplinary problems, models of network generation have gained an importance of their own. These models allow us to extensively analyze the data obtained from real-world…
This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…