Breaking chaotic shift key communication via adaptive key identification

This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter's parameter (key). By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.     

The Conjugate Nets, Cartan Submanifolds, and Laplace Transformations in Space Forms

In this paper we establish the geometric theory of conjugate nets, Cartan submanifolds, and Laplace transformations in sphere and pseudo-sphere spaces. The corresponding theory in cases of projective and Euclidean spaces has been established by Chern, Kamran and Tenenblat.     

Accelerated Poisson-Boltzmann calculations for static and dynamic systems

We report here an efficient implementation of the finite difference Poisson-Boltzmann solvent model based on the Modified Incomplete Cholsky Conjugate Gradient algorithm, which gives rather impressive performance for both static and dynamic systems. This is achieved by implementing the algorithm with Eisenstat's two optimizations, utilizing the electrostatic update in simulations, and applying prudent approximations, including: relaxing the convergence criterion, not updating Poisson-Boltzmann-related forces every step, and using electrostatic focusing. It is also possible to markedly accelerate the supporting routines that are used to set up the calculations and to obtain energies and forces. The resulting finite difference Poisson-Boltzmann method delivers efficiency comparable to the distance-dependent dielectric model for a system tested, HIV Protease, making it a strong candidate for solution-phase molecular dynamics simulations. Further, the finite difference method includes all intrasolute electrostatic interactions, whereas the distance dependent dielectric calculations use a 15-A cutoff. The speed of our numerical finite difference method is comparable to that of the pair-wise Generalized Born approximation to the Poisson-Boltzmann method.     

On the Action of the Dual Group on the Cohomology of Perverse Sheaves on the Affine Grassmannian

It was proved by Ginzburg, Mirkovic and Vilonen that the G(O)-equivariant perverse sheaves on the affine Grassmannian of a connected reductive group G form a tensor category equivalent to the tensor category of finite dimensional representations of the dual group G . In this paper we construct explicitly the action of G on the global cohomology of a perverse sheaf.     

A Duality Theorem for Étale p-Torsion Sheaves on Complete Varieties over a Finite Field

Let X be an arbitrary variety over a finite field k and p=char k,n N. We will construct a complex of étale sheaves on X together with trace isomorphism from the highest étale cohomology group of this complex onto Z/pⁿZ such that for every constructible Z/pⁿZ-sheaf on X the Yoneda pairing is a nondegenerate pairing of finite groups. If X is smooth, this complex is the Gersten resolution of the logarithmic de Rham–Witt sheaf introduced by Gros and Suwa. The proof is based on the special case proven by Milne when the sheaf is constant and X is smooth, as well as on a purity theorem which in turn follows from a theorem about the cohomological dimension of C_i-fields due to Kato and Kuzumaki. If the existence of the Lichtenbaum complex is proven, the theorem will be the p-part of a general duality theorem for varieties over finite fields.     

A Note on Error Bounds for Convex and Nonconvex Programs

Given a single feasible solution and a single infeasible solution of a mathematical program, we provide an upper bound to the optimal dual value. We assume that satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.     

Cyclic Cohomology of étale Groupoids: The General Case

We give a general method for computing the cyclic cohomology of crossed products by étale groupoids, extending the Feigin–Tsygan–Nistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor, and Tsygan for the convolution algebra C _c (G) of an étale groupoid, removing the Hausdorffness condition and including the computation of hyperbolic components. Examples like group actions on manifolds and foliations are considered.     

SO(2) Symmetry of a Maxwell p-Form Theory

We find a universal SO(2) symmetry of a p-form Maxwell theory for both odd and even p. For odd p, it corresponds to the duality rotations but for even p, it defines a new set of transformations which is not related to duality rotations. In both cases, a symmetry group defines a subgroup of the O(2,1) group of R-linear canonical transformations which has also a natural representation on the level of quantization condition for p-brane dyons.     

Asymptotic properties of the fenchel dual functional and applications to decomposition problems

We study dual functionals which have two fundamental properties. Firstly, they have a good asymptotical behavior. Secondly, to each dual sequence of subgradients converging to zero, one can associate a primal sequence which converges to an optimal solution of the primal problem. Furthermore, minimal conditions for the convergence of the Gauss-Seidel methods are given and applied to such kinds of functionals.