When is a Function Securely Computable?

A subset of a set of terminals that observe correlated signals seek to compute a given function of the signals using public communication. It is required that the value of the function be kept secret from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the "aided secret key" capacity of an associated secrecy generation model, for which a single-letter characterization is provided

Polarised and Unpolarised Charmonium Production at Higher Orders in v

We study the unpolarised and polarised hadro-production of charmonium in non-relativistic QCD (NRQCD) at low transverse momentum, including sufficiently higher orders in the relative velocity, $v$, so as to study the ratio of $\chi_{c1}$ and $\chi_{c2}$ production rates.Comment: 4 pages, 1 Postscript figure, LaTeX, Presented at the QCD97 Euroconference, Montpellier, July 3-9, 1997, to appear in Nuclear Physics B Proceedings Supplemen

Dynamic Motion Planning for Aerial Surveillance on a Fixed-Wing UAV

We present an efficient path planning algorithm for an Unmanned Aerial Vehicle surveying a cluttered urban landscape. A special emphasis is on maximizing area surveyed while adhering to constraints of the UAV and partially known and updating environment. A Voronoi bias is introduced in the probabilistic roadmap building phase to identify certain critical milestones for maximal surveillance of the search space. A kinematically feasible but coarse tour connecting these milestones is generated by the global path planner. A local path planner then generates smooth motion primitives between consecutive nodes of the global path based on UAV as a Dubins vehicle and taking into account any impending obstacles. A Markov Decision Process (MDP) models the control policy for the UAV and determines the optimal action to be undertaken for evading the obstacles in the vicinity with minimal deviation from current path. The efficacy of the proposed algorithm is evaluated in an updating simulation environment with dynamic and static obstacles.Comment: Accepted at International Conference on Unmanned Aircraft Systems 201

Drinfeld center of planar algebra

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N \subset M$ is a subfactor realization of $P$, then the Drinfeld center of the $N$-$N$-bimodule category generated by $_N L^2 (M)_M$, is equivalent to the category of Hilbert affine representations of $P$ satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras.Comment: 32 page

Perturbations of planar algebras

We analyze the effect of pivotal structures (on a 2-category) on the planar algebra associated to a 1-cell as in \cite{Gho08} and come up with the notion of {\em perturbations of planar algebras by weights} (a concept that appeared earlier in Michael Burns' thesis \cite{Bur03}); we establish a one-to-one correspondence between weights and pivotal structures. Using the construction of \cite{Gho08}, to each bifinite bimodule over $II_1$-factors, we associate a {\em bimodule planar algebra} in such a way that extremality of the bimodule corresponds to sphericality of the planar algebra. As a consequence of this, we reproduce an extension of Jones' theorem (\cite{Jon}) (of associating `subfactor planar algebras' to extremal subfactors). Conversely, given a bimodule planar algebra, we construct a bifinite bimodule whose associated bimodule planar algebra is the one which we start with, using perturbations and Jones-Walker-Shlyakhtenko-Kodiyalam-Sunder method of reconstructing an extremal subfactor from a subfactor planar algebra. The perturbation technique helps us to construct an example of a family of non-spherical planar algebras starting from a particular spherical one; we also show that this family is associated to a known family of subfactors constructed by Jones.Comment: 28 page

Effect of Muons on the Phase Transition in Magnetised Proto-Neutron Star Matter

We study the effect of inclusion of muons and the muon neutrinos on the phase transition from nuclear to quark matter in a magnetised proto-neutron star and compare our results with those obtained by us without the muons. We find that the inclusion of muons changes slightly the nuclear density at which transition occurs.However the dependence of this transition density on various chemical potentials, temperature and the magnetic field remains quantitatively the same.Comment: LaTex2e file with four postscript figure