Related papers: Berezovsky number
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
We review the theory of loss networks, including recent results on their dynamical behaviour. We give also some new results.
We investigate the heterogeneity of outcomes of repeated instances of percolation experiments in complex networks using a message passing approach to evaluate heterogeneous, node dependent probabilities of belonging to the giant or…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Let $b$ be a numeration base. A $b$-Niven number is one that is divisible by the sum of its base $b$ digits. We introduce high degree $b$-Niven numbers. These are $b$-Niven numbers that have a power greater than $1$ that is $b$-Niven…
The Turaev genus and dealternating number of a link are two invariants that measure how far away a link is from alternating. We determine the Turaev genus of a torus knot with five or fewer strands either exactly or up to an error of at…
This mini-project models propagation of shocks, in time point, through links in connected banks. In particular, financial network of 100 banks out of which 15 are shocked to default (that is, 85.00% of the banks are solvent) is modelled…
We introduce the Orchard crossing number, which is defined in a similar way to the well-known rectilinear crossing number. We compute the Orchard crossing number for some simple families of graphs. We also prove some properties of this…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
In paper the method for estimation of available bandwidth is supposed which does not demand the advanced utilities. Our method is based on the measurement of network delay $D$ for packets of different sizes $W$. The simple expression for…
This is a review of current research in Markov chains as toric statistical models. Its content is mixture of background information, results from the relevant recent literature, new results, and work in progress.
We define a new Hurwitz problem which is essentially a small core of the simple Hurwitz problem. The corresponding Hurwitz numbers have simpler formulae, satisfy effective recursion relations and determine the simple Hurwitz numbers. We…
A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers.…
We introduce and study a new kind of congruent number problem on the right trapezoid.
In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of…
In a set equipped with a binary operation, (S,*), a subset U is defined to be avoidable if there exists a partition {A,B} of S such that no element of U is the product of two distinct elements of A or of two distinct elements of B. For more…
Markov numbers are integers that appear in the solution triples of the Diophantine equation, $x^2+y^2+z^2=3xyz$, called the Markov equation. A classical topic in number theory, these numbers are related to many areas of mathematics such as…
The paper focuses on the bribery network emphasizing harassment bribery. A bribery network ends with the police officer whose utility from the bribe is positive and the approving officer in the network. The persistent nature of corruption…