Related papers: Scaling law in target-hunting processes

We study target-searching processes on a percolation, on which a hunter tracks a target by smelling odors it emits. The odor intensity is supposed to be inversely proportional to the distance it propagates. The Monte Carlo simulation is…

Primate visual system samples different parts of the world unevenly. The part of the visual scene corresponding to the eye center is represented densely, while away from the center the sampling becomes progressively sparser. Such…

Animal behavior and neural recordings show that the brain is able to measure both the intensity of an odor and the timing of odor encounters. However, whether intensity or timing of odor detections is more informative for olfactory-driven…

Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general…

Finding a target in a complex environment is a fundamental challenge in nature, from chemical reactions to sperm reaching an egg. An effective strategy to reduce the time needed to reach a target is to deploy many searchers, increasing the…

Locating and intercepting a moving target from possibly delayed, intermittent sensory signals is a paradigmatic problem in decision-making under uncertainty, and a fundamental challenge for, e.g., animals seeking prey or mates and…

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare…

We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice…

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in…

Consider a target moving at a constant velocity on a unit-circumference circle, starting at an arbitrary location. To acquire the target, any region of the circle can be probed to obtain a noisy measurement of the target's presence, where…

Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…

We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this…

Forest-fire waiting times, defined as the time between successive events above a certain size in a given region, are calculated for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact…

Monte Carlo Tree Search (MCTS) is a branch of stochastic modeling that utilizes decision trees for optimization, mostly applied to artificial intelligence (AI) game players. This project imagines a game in which an AI player searches for a…

Data scaling has revolutionized fields like natural language processing and computer vision, providing models with remarkable generalization capabilities. In this paper, we investigate whether similar data scaling laws exist in robotics,…

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a…

Monte Carlo Tree Search (MCTS) is particularly adapted to domains where the potential actions can be represented as a tree of sequential decisions. For an effective action selection, MCTS performs many simulations to build a reliable tree…

Scaling up neural models has yielded significant advancements in a wide array of tasks, particularly in language generation. Previous studies have found that the performance of neural models frequently adheres to predictable scaling laws,…

Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…

Adaptive sampling and planning in robotic environmental monitoring are challenging when the target environmental process varies over space and time. The underlying environmental dynamics require the planning module to integrate future…