Related papers: Stochastic modeling of a serial killer
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
We study a continuous time branching process where an individual splits into two daughters with rate b and dies with rate a, starting from a single individual at t=0. We show that the model can be mapped exactly to a random walk problem…
This paper introduces a statistical model for the arrival times of connection events in a computer network. Edges between nodes in a network can be interpreted and modelled as point processes where events in the process indicate information…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of…
Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of…
The underlying reasons behind modern terrorism are seemingly complex and intangible. Despite diverse causal mechanisms, research has shown that there exists general statistical patterns at the global scale that can shed light on human…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
In this paper, we study a spatial model for dormancy in a random environment via a two-type branching random walk in continuous-time, where individuals switch between dormant and active states depending on the current state of a fluctuating…
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…
We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [Perra \textit{et al.} Sci. Rep. srep00469 (2012)]. For realistic activity distributions with a power-law…
The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that…
We present and analyze a model of the frequency of severe terrorist attacks, which generalizes the recently proposed model of Johnson et al. This model, which is based on the notion of self-organized criticality and which describes how…
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly,…
This study presents a comprehensive statistical analysis of criminal complaint data from the New York City Police Department (NYPD) spanning 47 years (1963-2025) [1]. Using a dataset of 438,556 complaint records, we employed exploratory…
We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study…