This paper generalizes Lanchester’s equations of warfare to partial differential equations involving time and two spatial variables. Unlike in Lanchester’s original ordinary differential equations, the distribution of armies over the battlefield must be considered. Four different modes of attack are introduced, generalizing Lanchester’s equations for area fire and for direct fire. The effect of...

In this document, we study a 3-polygraphic translation for the proofs of SKS, a formal system for classical propositional logic. We prove that the free 3-category generated by this 3-polygraph describes the proofs of classical propositional logic modulo structural bureaucracy. We give a 3-dimensional generalization of Penrose diagrams and use it to provide several pictures of a proof. We sketch...

Three dimensional Einstein gravity with negative cosmological constant −1/l2 deformed by a gravitational Chern-Simons action with coefficient 1/μ is studied in an asymptotically AdS3 spacetime. It is argued to violate unitary or positivity for generic μ due to negativeenergy massive gravitons. However at the critical value μl = 1, the massive gravitons disappear and BTZ black holes all have mas...

The Internet is proving to be a popular medium for the distribution of stereoscopic images. The availability of low cost LCD shutter glasses and the high update rate of PC monitors are also factors driving this increased popularity. However, current methods of distributing stereoscopic media have a number of problems when compared to 2D media transmission, such as higher bandwidth requirements,...

We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in particular as homothetic time-dependent solutions to Newton’s equations of motion and as stationary states in the One Component Plasma model. Concentrating mainly o...

Cells in vivo exist within the context of a multicellular tissue, where their behavior is governed by homo- and heterotypic cell-cell interactions, the material properties of the extracellular matrix, and the distribution of various soluble and physical factors. Most methods currently used to study and manipulate cellular behavior in vitro, however, sacrifice physiological relevance for experim...

MOTIVATION Currently a substantial research effort is devoted to automated representation of metabolic and gene networks. Automatic visualization plays a significant role in such efforts, and becomes an important problem on its own. Graphical visualization of metabolic pathways has to be information dense and not 'overloaded', recognizable and unified, close to traditional and algebraically con...

Formal specifications are difficult to understand for a number of reasons. When the developer of a large specification explains it to another person, he typically includes mformatlon in his explanation that is is not present, even Implicitly. in the specification itself. One useful form of information presents the specification In terms of an evolution from simpler specificattons. TypIcally a s...

While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of [1, 2, 3]. In this work we demonstrate the existence of “cyclic”, or Zn, non-pe...

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site "horseshoe"-shaped structure, which is always unstable in the bulk, while at the surface it is ...