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Although evidence integration to the boundary model has successfully explained a wide range of behavioral and neural data in decision making under uncertainty, how animals learn and optimize the boundary remains unresolved. Here, we propose…

There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long distance movement state and a resting or local movement state. Here a mathematical description of this…

Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…

An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit…

We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account {as a…

This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…

Quadrupedal animals employ diverse galloping strategies to optimize speed, stability, and energy efficiency. However, the biomechanical mechanisms that enable adaptive gait transitions during high-speed locomotion under load remain poorly…

The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…

In sequential decision-making environments, the primary approaches for training agents are Reinforcement Learning (RL) and Imitation Learning (IL). Unlike RL, which relies on modeling a reward function, IL leverages expert demonstrations,…

World models aim to improve robotic decision making by predicting the consequences of actions. However, in practice, their predictions often become unreliable once the robot encounters states outside the training distribution, limiting…

In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…

Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…

In this work, we introduce PIPER: Primitive-Informed Preference-based Hierarchical reinforcement learning via Hindsight Relabeling, a novel approach that leverages preference-based learning to learn a reward model, and subsequently uses…

Tripartite mutual information (TMI) is an efficient observable to quantify the ability of scrambler for unitary time-evolution operator with quenched many-body Hamiltonian. In this paper, we give numerical demonstrations of the TMI in…

Drift analysis is a powerful tool for analyzing the time complexity of evolutionary algorithms. However, it requires manual construction of drift functions to bound hitting time for each specific algorithm and problem. To address this…

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $\delta$, the so called refraction period. This prevents the optimal exercise times…

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture…

Animals learn tasks requiring a sequence of actions over time. Waiting a given time before taking an action is a simple example. Mimicry is a complex example, e.g. in humans, humming a brief tune you have just heard. Re-experiencing a…

Pre-trained Language Models have recently emerged in Information Retrieval as providing the backbone of a new generation of neural systems that outperform traditional methods on a variety of tasks. However, it is still unclear to what…

In this paper, we study the optimal multiple stopping problem under the filtration consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions rather than an RCLL process. We…