79,585 research outputs found
Secret Sharing Schemes with a large number of players from Toric Varieties
A general theory for constructing linear secret sharing schemes over a finite
field \Fq from toric varieties is introduced. The number of players can be as
large as for . We present general methods for obtaining
the reconstruction and privacy thresholds as well as conditions for
multiplication on the associated secret sharing schemes.
In particular we apply the method on certain toric surfaces. The main results
are ideal linear secret sharing schemes where the number of players can be as
large as . We determine bounds for the reconstruction and privacy
thresholds and conditions for strong multiplication using the cohomology and
the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1203.454
Quantum Codes from Toric Surfaces
A theory for constructing quantum error correcting codes from Toric surfaces
by the Calderbank-Shor-Steane method is presented. In particular we study the
method on toric Hirzebruch surfaces. The results are obtained by constructing a
dualizing differential form for the toric surface and by using the cohomology
and the intersection theory of toric varieties. In earlier work the author
developed methods to construct linear error correcting codes from toric
varieties and derive the code parameters using the cohomology and the
intersection theory on toric varieties. This method is generalized in section
to construct linear codes suitable for constructing quantum codes by the
Calderbank-Shor-Steane method. Essential for the theory is the existence and
the application of a dualizing differential form on the toric surface. A.R.
Calderbank, P.W. Shor and A.M. Steane produced stabilizer codes from linear
codes containing their dual codes. These two constructions are merged to obtain
results for toric surfaces. Similar merging has been done for algebraic curves
with different methods by A. Ashikhmin, S. Litsyn and M.A. Tsfasman.Comment: IEEE copyrigh
A separable approximation dynamic programming algorithm for economic dispatch with transmission losses
Copyright @ 2002 University of Belgrade - This article can be accessed from the link below.The standard way to solve the static economic dispatch problem with transmission losses is the penalty factor method. The problem is solved iteratively by a Lagrange multiplier method or by dynamic programming, using values obtained at one iteration to compute penalty factors for the next until stability is attained. A new iterative method is proposed for the case where transmission losses are represented by a quadratic formula (i.e., by the traditional B-coefficients). A separable approximation is made at each iteration, which is much closer to the initial problem than the penalty factor approximation. Consequently, lower cost solutions may be obtained in some cases, and convergence is faster
Alternative method to find orbits in chaotic systems
We present here a new method which applies well ordered symbolic dynamics to
find unstable periodic and non-periodic orbits in a chaotic system. The method
is simple and efficient and has been successfully applied to a number of
different systems such as the H\'enon map, disk billiards, stadium billiard,
wedge billiard, diamagnetic Kepler problem, colinear Helium atom and systems
with attracting potentials. The method seems to be better than earlier applied
methods.Comment: 5 pages, uuencoded compressed tar PostScript fil
Comments on "State equation for the three-dimensional system of 'collapsing' hard spheres"
A recent paper [I. Klebanov et al. \emph{Mod. Phys. Lett. B} \textbf{22}
(2008) 3153; arXiv:0712.0433] claims that the exact solution of the
Percus-Yevick (PY) integral equation for a system of hard spheres plus a step
potential is obtained. The aim of this paper is to show that Klebanov et al.'s
result is incompatible with the PY equation since it violates two known cases:
the low-density limit and the hard-sphere limit.Comment: 4 pages; v2: title chang
Reduction of the hydrophobic attraction between charged solutes in water
We examine the effective force between two nanometer scale solutes in water
by Molecular Dynamics simulations. Macroscopic considerations predict a strong
reduction of the hydrophobic attraction between solutes when the latter are
charged. This is confirmed by the simulations which point to a surprising
constancy of the effective force between oppositely charged solutes at contact,
while like charged solutes lead to significantly different behavior between
positive and negative pairs. The latter exhibit the phenomenon of ``like-charge
attraction" previously observed in some colloidal dispersions.Comment: 4 pages, 5 figure
Competition of hydrophobic and Coulombic interactions between nano-sized solutes
The solvation of charged, nanometer-sized spherical solutes in water, and the
effective, solvent-induced force between two such solutes are investigated by
constant temperature and pressure Molecular Dynamics simulations of model
solutes carrying various charge patterns. The results for neutral solutes agree
well with earlier findings, and with predictions of simple macroscopic
considerations: substantial hydrophobic attraction may be traced back to strong
depletion (``drying'') of the solvent between the solutes. This hydrophobic
attraction is strongly reduced when the solutes are uniformly charged, and the
total force becomes repulsive at sufficiently high charge; there is a
significant asymmetry between anionic and cationic solute pairs, the latter
experiencing a lesser hydrophobic attraction. The situation becomes more
complex when the solutes carry discrete (rather than uniform) charge patterns.
Due to antagonistic effects of the resulting hydrophilic and hydrophobic
``patches'' on the solvent molecules, water is once more significantly depleted
around the solutes, and the effective interaction reverts to being mainly
attractive, despite the direct electrostatic repulsion between solutes.
Examination of a highly coarse-grained configurational probability density
shows that the relative orientation of the two solutes is very different in
explicit solvent, compared to the prediction of the crude implicit solvent
representation. The present study strongly suggests that a realistic modeling
of the charge distribution on the surface of globular proteins, as well as the
molecular treatment of water are essential prerequisites for any reliable study
of protein aggregation.Comment: 20 pages, 25 figure
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