Related papers: Scaling law in target-hunting processes

Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually…

We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…

Purpose: In recent years Monte-Carlo sampling methods, such as Monte Carlo tree search, have achieved tremendous success in model free reinforcement learning. A combination of the so called upper confidence bounds policy to preserve the…

Monte Carlo Tree Search is a popular method for solving decision making problems. Faster implementations allow for more simulations within the same wall clock time, directly improving search performance. To this end, we present an…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…

We consider the ANTS problem [Feinerman et al.] in which a group of agents collaboratively search for a target in a two-dimensional plane. Because this problem is inspired by the behavior of biological species, we argue that in addition to…

We present in this article an analysis of some of the properties of the density field realized in numerical simulations for power-law initial power-spectra in the case of a critical density universe. We compare our numerical results in the…

Chase-escape percolation is a variation of the standard epidemic spread models. In this model, each site can be in one of three states: unoccupied, occupied by a single prey, or occupied by a single predator. Prey particles spread to…

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees.…

We present a new Monte Carlo scheme for the efficient simulation of multi-polymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler,…

Two mobile agents, starting at arbitrary, possibly different times from arbitrary locations in the plane, have to meet. Agents are modeled as discs of diameter 1, and meeting occurs when these discs touch. Agents have different labels which…

Much current research in AI and games is being devoted to Monte Carlo search (MCS) algorithms. While the quest for a single unified MCS algorithm that would perform well on all problems is of major interest for AI, practitioners often know…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…

We address the challenge of training diffusion models to sample from unnormalized energy distributions in the absence of data, the so-called diffusion samplers. Although these approaches have shown promise, they struggle to scale in more…

The quality of Large Language Model (LLM) pretraining depends on multiple factors, including the compute budget and the choice of optimization algorithm. Empirical scaling laws are widely used to predict loss as model size and training data…

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling…

We present a limited empirical study of scaling laws for transfer learning in transformer models. More specifically, we examine a scaling law that incorporates a "transfer gap" term, indicating the effectiveness of pre-training on one…

Animals use stereo sampling of odor concentration to localize sources and follow odor trails. We analyze the dynamics of a bilateral model that depends on the simultaneous comparison between odor concentrations detected by left and right…

Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…