相关论文: Feasibility and stability in large Lotka Volterra …

We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…

In the framework of Lotka-Volterra dynamics with evolutionary parameter variation, it is shown that a system of two competing species which is evolutionarily unstable, if left to themselves, is stabilized by a commmon predator preying on…

Since 2008, the network analysis of financial systems is one of the most important subjects in economics. In this paper, we have used the complexity approach and Random Matrix Theory (RMT) for analyzing the global banking network. By…

The reward model (RM) that represents human preferences plays a crucial role in optimizing the outputs of large language models (LLMs), e.g., through reinforcement learning from human feedback (RLHF) or rejection sampling. However, a long…

Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an…

A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…

We present new a stability result for periodic solutions of the periodic predator prey Lotka Volterra model, based on boundaries for the average of the coexistence states. Our result complements previous one in the literature.

The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…

The increasing deployment of Large Language Models (LLMs) in various applications necessitates a rigorous evaluation of their robustness against adversarial attacks. In this paper, we present a comprehensive study on the robustness of GPT…

In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…

We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend…

Mays celebrated theoretical work of the 70s contradicted the established paradigm by demonstrating that complexity leads to instability in biological systems. Here Mays random-matrix modelling approach is generalized to realistic…

Metagenomic data has significantly advanced microbiome research by employing ecological models, particularly in personalised medicine. The generalised Lotka-Volterra (gLV) model is commonly used to understand microbial interactions and…

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

Learning systems are typically optimized by minimizing loss or maximizing reward, assuming that improvements in these signals reflect progress toward the true objective. However, when feedback reliability is unobservable, this assumption…

The primary challenge in deploying Large Language Model (LLM) is ensuring its harmlessness. Red team can identify vulnerabilities by attacking LLM to attain safety. However, current efforts heavily rely on single-round prompt designs and…

For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This…

We consider the Generalized Lotka-Volterra system of equations with all-to-all, random asymmetric interactions describing high-dimensional, very diverse and well-mixed ecosystems. We analyze the multiple equilibria phase of the model and…

Large Language Models (LLMs) can be deployed in situations where they process positive/negative interactions with other agents. We study how this is done under the sociological framework of social balance, which explains the emergence of…

As large language models (LLMs) are increasingly deployed in high-stakes and operational settings, evaluation strategies based solely on aggregate accuracy are often insucient to characterize system reliability. This study proposes a…