Related papers: Random walks on binary strings applied to the soma…
In a cellular medium, the plasmic membrane is a place of interactions between the cell and its direct external environment. A classic model describes it as a fluid mosaic. The fluid phase of the membrane allows a lateral degree of freedom…
Sood and Grassberger studied in [Phys. Rev. Lett. 99, 098701 (2007)] random walks on random graphs that are biased towards a fixed target point. They put forward a critical bias strength b_c such that a random walker on an infinite graph…
The mammalian adaptive immune system has evolved over millions of years to become an incredibly effective defense against foreign antigens. The adaptive immune system's humoral response creates plasma B cells and memory B cells, each with…
Immune cells learn about their antigenic targets using tactile sense: during recognition, a highly organized yet dynamic motif, named immunological synapse, forms between immune cells and antigen-presenting cells (APCs). Via synapses,…
The adaptive immune system constantly remodels its lymphocyte repertoire for better protection against future pathogens. Its ability to improve antigen recognition on the fly relies on somatic mutation and selective expansion of B…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
Immune cells have evolved to recognize and eliminate pathogens, and the efficiency of this process can be measured in a Petri dish. Yet, even if the cells are time-lapse recorded and tracked with high resolution, it is difficult to judge…
In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
B cells and the antibodies they produce are vital to health and survival, motivating research on the details of the mutational and evolutionary processes in the germinal centers (GC) from which mature B cells arise. It is known that B cells…
We quantify the VDJ recombination and somatic hypermutation processes in human B-cells using probabilistic inference methods on high-throughput DNA sequence repertoires of human B-cell receptor heavy chains. Our analysis captures the…
It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs $\hat C$. This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals. For a…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension $d$, a random walk with an absorbing state is defined which relates to the spectrum of the $k$-dimensional…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…