554 research outputs found
Properties of dense partially random graphs
We study the properties of random graphs where for each vertex a {\it
neighbourhood} has been previously defined. The probability of an edge joining
two vertices depends on whether the vertices are neighbours or not, as happens
in Small World Graphs (SWGs). But we consider the case where the average degree
of each node is of order of the size of the graph (unlike SWGs, which are
sparse). This allows us to calculate the mean distance and clustering, that are
qualitatively similar (although not in such a dramatic scale range) to the case
of SWGs. We also obtain analytically the distribution of eigenvalues of the
corresponding adjacency matrices. This distribution is discrete for large
eigenvalues and continuous for small eigenvalues. The continuous part of the
distribution follows a semicircle law, whose width is proportional to the
"disorder" of the graph, whereas the discrete part is simply a rescaling of the
spectrum of the substrate. We apply our results to the calculation of the
mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review
On the duality relation for correlation functions of the Potts model
We prove a recent conjecture on the duality relation for correlation
functions of the Potts model for boundary spins of a planar lattice.
Specifically, we deduce the explicit expression for the duality of the n-site
correlation functions, and establish sum rule identities in the form of the
M\"obius inversion of a partially ordered set. The strategy of the proof is by
first formulating the problem for the more general chiral Potts model. The
extension of our consideration to the many-component Potts models is also
given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.
Cloud-Chamber Observations of Some Unusual Neutral V Particles Having Light Secondaries
From six cloud-chamber photographs of unusual V0 decay events, the following conclusions are drawn: (1) there is a neutral V particle that decays into two particles lighter than κ mesons with a Q value too small to be consistent with a θ0(π, π, 214 Mev) particle; (2) some of these events cannot be explained in terms of the decay of a τ0(π0, π-, π+, Q∼80 Mev) particle; (3) these events can be explained by any one of a number of three-body decay schemes, but two different types of V particles must be postulated if two-body decays are assumed
Maximum principle and mutation thresholds for four-letter sequence evolution
A four-state mutation-selection model for the evolution of populations of
DNA-sequences is investigated with particular interest in the phenomenon of
error thresholds. The mutation model considered is the Kimura 3ST mutation
scheme, fitness functions, which determine the selection process, come from the
permutation-invariant class. Error thresholds can be found for various fitness
functions, the phase diagrams are more interesting than for equivalent
two-state models. Results for (small) finite sequence lengths are compared with
those for infinite sequence length, obtained via a maximum principle that is
equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure
Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case
Let be a prime number, for some positive integer , be a
positive integer such that , and let \k be a primitive
multiplicative character of order over finite field \fq. This paper
studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2
case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function).
Firstly, the classification of the Gauss sums in index 2 case is presented.
Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2
case with order being general even integer (i.e. N=2^{r}\cd N_0 where
are positive integers and is odd.) is obtained. Thus, the
problem of explicit evaluation of Gauss sums in index 2 case is completely
solved
Killer cell immunoglobulin-like receptor ligand mismatching and outcome after haploidentical transplantation with post-transplant cyclophosphamide
The propagator for the step potential and delta function potential using the path decomposition expansion
We present a derivation of the propagator for a particle in the presence of
the step and delta function potentials. These propagators are known, but we
present a direct path integral derivation, based on the path decomposition
expansion and the Brownian motion definition of the path integral. The
derivation exploits properties of the Catalan numbers, which enumerate certain
classes of lattice paths.Comment: 11 pages, 3 figure
A unified approach to combinatorial key predistribution schemes for sensor networks
There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified framework to study these kinds of schemes. To do so, we define a new, general class of designs, termed “partially balanced t-designs”, that is sufficiently general that it encompasses almost all of the designs that have been proposed for combinatorial key predistribution schemes. However, this new class of designs still has sufficient structure that we are able to derive general formulas for the metrics of the resulting key predistribution schemes. These metrics can be evaluated for a particular scheme simply by substituting appropriate parameters of the underlying combinatorial structure into our general formulas. We also compare various classes of schemes based on different designs, and point out that some existing proposed schemes are in fact identical, even though their descriptions may seem different. We believe that our general framework should facilitate the analysis of proposals for combinatorial key predistribution schemes and their comparison with existing schemes, and also allow researchers to easily evaluate which scheme or schemes present the best combination of performance metrics for a given application scenario
Information-theoretic interpretation of quantum error-correcting codes
Quantum error-correcting codes are analyzed from an information-theoretic
perspective centered on quantum conditional and mutual entropies. This approach
parallels the description of classical error correction in Shannon theory,
while clarifying the differences between classical and quantum codes. More
specifically, it is shown how quantum information theory accounts for the fact
that "redundant" information can be distributed over quantum bits even though
this does not violate the quantum "no-cloning" theorem. Such a remarkable
feature, which has no counterpart for classical codes, is related to the
property that the ternary mutual entropy vanishes for a tripartite system in a
pure state. This information-theoretic description of quantum coding is used to
derive the quantum analogue of the Singleton bound on the number of logical
bits that can be preserved by a code of fixed length which can recover a given
number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in
Phys. Rev.
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