Related papers: Discrete Lanchester attrition models: the case of …

Lanchester's model of combat has certain deficiencies in its standard form arising from the neglect of the influence of random fluctuations. Several approaches to rectify this have been proposed and various results are scattered throughout…

The classical Lanchester's model is shortly reviewed and analysed, with particular attention to the critical issues that intrinsically arise from the mathematical formalization of the problem. We then generalize a particular version of such…

The war of attrition in game theory is a model of a stand-off situation between two opponents where the winner is determined by its persistence. We model a stand-off between a predator and a prey when the prey is hiding and the predator is…

One of the most notable aspects of mathematical modeling is that it sheds light on the complexities arising from changes in parameters and their real-world implications, thus gaining better insight into the dynamics of economic, political,…

An overview of Lanchester combat models, emphasising their pedagogical possibilities. After a description of the aimed-fire model and comments on the literature, we introduce briefly a range of further topics: a discrete equivalent, the…

We propose a framework for examining the effects of infections with self-replicating malware on military forces engaged in kinetic combat. The framework uses models, in which kinetic attrition is represented by a Lanchester model coupled…

We present a generalisation of the classical Lanchester model for directed fire between two combat forces but now employing networks for the manoeuvre of Blue and Red forces, and the pattern of engagement between the two. The model…

Major revolts have recently erupted in parts of the Middle East with substantial international repercussions. Predicting, coping with and winning those revolts have become a grave problem for many regimes and for world powers. We propose a…

Data scarcity drives the need for more sample-efficient large language models. In this work, we use the double descent phenomenon to holistically compare the sample efficiency of discrete diffusion and autoregressive models. We show that…

Deep neural networks (DNNs) are highly susceptible to adversarial examples--subtle, imperceptible perturbations that can lead to incorrect predictions. While detection-based defenses offer a practical alternative to adversarial training,…

Deep learning models have been used for a wide variety of tasks. They are prevalent in computer vision, natural language processing, speech recognition, and other areas. While these models have worked well under many scenarios, it has been…

Deep Neural Networks (DNNs) have shown remarkable performance in a diverse range of machine learning applications. However, it is widely known that DNNs are vulnerable to simple adversarial perturbations, which causes the model to…

Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…

Machine learning models are now widely deployed in real-world applications. However, the existence of adversarial examples has been long considered a real threat to such models. While numerous defenses aiming to improve the robustness have…

Deep neural networks are at the forefront of machine learning research. However, despite achieving impressive performance on complex tasks, they can be very sensitive: Small perturbations of inputs can be sufficient to induce incorrect…

We make a methodological contribution by introducing a new dimension of traffic conflict severity: the probability that a driver is in a defensive state. This behavioural probability reflects an internal response to perceived risk and is…

Modern classification algorithms are susceptible to adversarial examples--perturbations to inputs that cause the algorithm to produce undesirable behavior. In this work, we seek to understand and extend adversarial examples across domains…

The "War of Attrition" is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a…

The principle of least action, a fundamental principle in variational mechanics with broad applicability to classical physical systems, is employed to formulate a novel attrition model for combat dynamics. This formulation extends the…

Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…