Related papers: Optimising structure in a networked Lanchester Mod…
In this paper, a non-linear Lanchester-type model involving supply units is introduced. The model describes a battle where the Blue party consisting of one armed force $B$ is fighting against the Red party. The Red party consists of $n$…
In this work, we introduce a nonlinear Lanchester model of NCW-type and study a problem of finding the optimal fire allocation for this model. A Blue party $B$ will fight against a Red party consisting of $A$ and $R$, where $A$ is an…
In this paper, we introduce a non-linear Lanchester model of NCW-type and investigate an optimization problem for this model, where only the Red force is supplied by several supply agents. Optimal fire allocation of the Blue force is sought…
The outcomes of warfare have rarely only been characterised by the quantity and quality of individual combatant force elements. The ability to manoeuvre and adapt across force elements through effective Command and Control (C2) can allow…
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…
In this paper is presented a framework for treating uncertainty in optimal decision problems occuring in combat situations, in order to robustly select the optimal strategy. A stochastic version of the popular Lanchester's aimed-fire model…
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…
In this work we study the interplay between the dynamics of a model of diffusion governed by a mechanism of imitation and its underlying structure. The dynamics of the model can be quantified by a macroscopic observable which permits the…
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,…
Maximizing the damage by attacking specific nodes of the combat network can efficiently disrupt enemies' defense capability, protect our critical units, and enhance the resistance to the destruction of system-of-system~(SOS). However, the…
We consider a model of adversarial dynamics consisting of three populations, labelled Blue, Green and Red, which evolve under a system of first order nonlinear differential equations. Red and Blue populations are adversaries and interact…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
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…
We introduce a new optimization framework to maximize the expected spread of cascades in networks. Our model allows a rich set of actions that directly manipulate cascade dynamics by adding nodes or edges to the network. Our motivating…
The goal of this thesis is to develop the optimisation and generalisation theoretic foundations of learning in artificial neural networks. On optimisation, a new theoretical framework is proposed for deriving architecture-dependent…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
We consider a network where strategic agents, who are contesting for allocation of resources, are divided into fixed groups. The network control protocol is such that within each group agents get to share the resource and across groups they…
Highly optimized tolerance is a model of optimization in engineered systems, which gives rise to power-law distributions of failure events in such systems. The archetypal example is the highly optimized forest fire model. Here we give an…
Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…