Related papers: Binary distributions of concentric rings
We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings (Stone & Leigh 2019). Using these outcome distribution functions, we present in this paper…
The distribution of distances in the star graph $ST_n$, ($1<n\in\Z$), is established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given by the distances to the identity…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We construct an $S_3$-symmetric probability distribution on $\{(a,b,c) \in \mathbb{Z}_{\geq 0}^3 \: : \: a+b+c =n \}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots,n\}$ with mean…
Algebraic statistics for binary random variables is concerned with highly structured algebraic varieties in the space of 2x2x...x2-tensors. We demonstrate the advantages of representing such varieties in the coordinate system of binary…
We prove Bernstein-type matrix concentration inequalities for linear combinations with matrix coefficients of binary random variables satisfying certain $\ell_\infty$-independence assumptions, complementing recent results by Kaufman, Kyng…
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. Kamiya, Takemura and Kuriki (2006) generalized the elliptically contoured…
The evolution of close binary stars in mass asymmetry (transfer) coordinate is considered. The conditions for the formation of stable symmetric binary stars are analyzed. The role of symmetrization of asymmetric binary star in the…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
The formation of a binary system surrounded by disks is the most common outcome of stellar formation. Hence studying and understanding the formation and the evolution of binary systems and associated disks is a cornerstone of star formation…
Stellar models of massive single stars are still plagued by major uncertainties. Testing and calibrating against observations is essential for their reliability. For this purpose one preferably uses observed stars that have never…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
We define a class of algebras describing links of binary isolating formulas on a set of realizations for a family of 1-types of a complete theory. We prove that a set of labels for binary isolating formulas on a set of realizations for a…
Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree…
Many problems in contemporary astrophysics---from understanding the formation of black holes to untangling the chemical evolution of galaxies---rely on knowledge about binary stars. This, in turn, depends on discovery and characterization…
Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…