Related papers: Broadcasting in random recursive dags
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree <k>, and p(s) undergoes a…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via…
Dominating broadcasting is a domination-type structure that models a transmission antenna network. In this paper, we study a limited version of this structure, that was proposed as a common framework for both broadcast and classical…
We study distributed plurality consensus among $n$ nodes, each of which initially holds one of $k$ opinions. The goal is to eventually agree on the initially dominant opinion. We consider an asynchronous communication model in which each…
We consider a recursively defined random set of points and its barycenter, where the random set is constructed by the following inductive rule: Given a realization of $n-1$ points, one of them is picked at random and serves as a source the…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability…
We consider uniformly random set partitions of size $n$ with exactly $k$ blocks, and uniformly random permutations of size $n$ with exactly $k$ cycles, under the regime where $n-k \sim t\sqrt{n}$, $t>0$. In this regime, there is a simple…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…
Motivated by the study of random temporal networks, we introduce a class of random trees that we coin \emph{uniform temporal trees}. A uniform temporal tree is obtained by assigning independent uniform $[0,1]$ labels to the edges of a…
Rooted trees with probabilities are convenient to represent a class of random processes with memory. They allow to describe and analyze variable length codes for data compression and distribution matching. In this work, the Leaf-Average…
Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can…
Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
We consider the problem of selecting $k$ seed nodes in a network to maximize the minimum probability of activation under an independent cascade beginning at these seeds. The motivation is to promote fairness by ensuring that even the least…