相关论文: Star-collision in random hypergraphs
Unitarity of evolution in gravitational collapses implies existence of macroscopic stable horizonless objects. With such objects in mind, we study the effects of anisotropy of pressures on the stability of stars. We consider stars in four…
The dense, clustered environment in which massive stars form can lead to interactions with neighboring stars. It has been hypothesized that collisions and mergers may contribute to the growth of the most massive stars. In this paper we…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
In the binomial random graph $\mathcal{G}(n,p)$, when $p$ changes from $(1-\varepsilon)/n$ (subcritical case) to $1/n$ and then to $(1+\varepsilon)/n$ (supercritical case) for $\varepsilon>0$, with high probability the order of the largest…
The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We present the results of the first study of global oscillations of relativistic stars with both elastic crusts and interpenetrating superfluid components. For simplicity, we focus on the axial quasi-normal modes. Our results demonstrate…
We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
The purpose of this paper is to introduce a model to study structures which are widely present in public transportation networks. We show that, through hypergraphs, one can describe these structures and investigate the relation between…
The relations between observable stellar parameters are usually assumed to be deterministic. That is, given an infinitely precise measurement of independent variable, `$x$', and some model, the value of dependent variable, `$y$' can be…
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable…
Using cosmological hydrodynamical simulations, we investigate the effects of hierarchical aggregation on the triggering of star formation in galactic-like objects. We include a simple star formation model to transform the cold gas in dense…
We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…
Random hypergraphs extend the classical notion of random graphs by allowing hyperedges to join more than two vertices, making them well-suited for modeling higher-order interactions in complex systems. Despite their broad applicability,…
Massive stars are known to have a high multiplicity, with examples of higher order multiples among the nearest and best studied objects. In this paper we study hierarchical multiple systems (an inner binary as a component of a wider binary)…
A transversal coalition in a hypergraph $H$ is a partition of the vertex set $U$ into two subsets $U_1$ and $U_2$ such that neither $U_1$ nor $U_2$ alone intersects every hyperedge of $H$, but their union, $U_1 \cup U_2$, intersects every…
We study giant molecular cloud (GMC) collisions and their ability to trigger star cluster formation. We further develop our three dimensional magnetized, turbulent, colliding GMC simulations by implementing star formation sub-grid models.…
We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra…