We prove a theorem in 3-dimensional topological field theory: Reshetikhin–Turaev theory admits nonzero boundary iff it is Turaev–Viro theory. The proof immediately implies characterization of fusion categories terms dualizability. Our results rely on (special case of) the cobordism hypothesis with singularities. main applies to physics, where an obstruction gapped quantum system admitting Appen...

We analyze the freezing transition in a system of hard particles with a very long-ranged repulsion. The long-range repulsion makes first-order freezing transitions continuous, but leaves the initial stages of the crystallization unchanged: the crystal phase must still nucleate. The coexistence between bulk phases is replaced by microphase separation.

Skeletonization will probably become as valuable a tool for shape analysis in 3D, as it is in 2D. We present a topology preserving 3D skeletonization method which computes both surface and curve skeletons whose voxels are labelled with the D6 distance to the original background. The surface skeleton preserves all shape information, so (close to) complete recovery of the object is possible. The ...

The Angel-Devil game is an infinite game played on an infinite chess board: In each move the Angel, a generalized chess king, jumps from his current square to some location at distance at most k, while his opponent, the Devil, blocks squares trying to strand the Angel. The Angel wins if he manages to fly on forever. It is a long-standing open question whether some Angel of sufficiently large po...

A particular higher-derivative extension of the Einstein-Hilbert action in three spacetime dimensions is shown to be equivalent at the linearized level to the (unitary) Pauli-Fierz action for a massive spin-2 field. A more general model, which also includes "topologically-massive" gravity as a special case, propagates the two spin-2 helicity states with different masses. We discuss the extensio...

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...

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...

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...