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81.
S.?BoettcherEmail author 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(4):439-445
A reduction procedure to obtain ground states of spin
glasses on sparse graphs is developed and tested on the
hierarchical lattice associated with the Migdal-Kadanoff
approximation for low-dimensional lattices. While more generally
applicable, these rules here lead to a complete reduction of the
lattice. The stiffness exponent governing the scaling of the
defect energy E with system
size L, (E) ~L
y, is obtained as
y
3 = 0.25546(3) by reducing the equivalent
of lattices up to L =
2100 in d = 3, and as y
4 = 0.76382(4) for up to
L =
235 in d = 4. The reduction rules allow the
exact determination of the ground state energy, entropy, and
also provide an approximation to the overlap distribution. With
these methods, some well-know and some new features of diluted
hierarchical lattices are calculated. 相似文献
82.
D. Stauffer A. Aharony L. da Fontoura Costa J. Adler 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,32(3):395-399
Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N2 bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N2. The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled
neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is
connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q
3. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time.
Received 12 January 2003 Published online 11 April 2003
RID="a"
ID="a"e-mail: stauffer@thp.uni-koeln.de 相似文献
83.
ShiHongCHENG 《数学学报(英文版)》2003,19(1):177-186
We give an Edgeworth expansion for densities of order statistics with fixed rank k.The Edgeworth expansion for densities of extreme values is then obtained as a special case k=1. 相似文献
84.
Baha-Eldin Khaledi Subhash Kochar 《Annals of the Institute of Statistical Mathematics》2001,53(3):620-630
Consider a multivariate mixture model where the random variables X
1, ..., X
n
given (1, ...,
n
), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X
i
's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models. 相似文献
85.
Stanisaw Gnot Ewaryst Rafajowicz Agnieszka Urbaska-Motyka 《Annals of the Institute of Statistical Mathematics》2001,53(2):370-379
In the paper we consider a random linear model for observations provided by spatially located sensors measuring signals coming from one source. For this model a set of sufficient and complete statistics are found, and it is shown that the maximum likelihood estimators of unknown parameters (characteristics of the source) are functions of those statistics. The problem of nonnegative estimators of variance components of the model is shortly discussed. Comparisons of the mean squared errors of several estimators are given. Numerical example concerning hunting for defects in solar cells is considered in details. 相似文献
86.
O.V. Borisov F. Hakem T.A. Vilgis J.-F. Joanny A. Johner 《The European physical journal. E, Soft matter》2001,6(1):37-47
We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely
charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule
in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge
density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the
oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening
length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree
of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density
may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain
Coulombic repulsion by the counterions localized near the surface.
Received 12 April 2001 相似文献
87.
研究了双模最小关联混态在不同参数情况下的量子统计性质.发现在一定的参数范围内双模最小关联混态的二阶相干性违反经典的Cauchy-Schwartz不等式,呈现非经典性相关;同时对双模最小关联混态的压缩特性、亚泊松分布等非经典性质进行了分析,通过数值计算得出,每模光子的压缩性及其亚泊松分布均与参数d的取值密切相关. 相似文献
88.
E. Scalas U. Garibaldi S. Donadio 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(2):271-272
This erratum corrects a mistake in reference [E. Scalas, U. Garibaldi, S. Donadio, Eur. Phys. J. B 53, 267 (2006)].
In that paper,
we needed an aperiodic version of the BDY game, but, in formula (1),
we incorrectly presented
a periodic transition matrix of period 2 in the special case of g = 2 agents.
Here, we present the right aperiodic version. 相似文献
89.
Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space
should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity
of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels
growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for
the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture
holds exactly up to energies E
N
< β
c
N, where β
c
is the critical temperature. We also explain the more complex behaviour that sets in at higher energies.
Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from
Physics and Biology” and by the European Science Foundation in the Programme RDSES. 相似文献
90.
B. Dybiec L. Schimansky-Geier 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(3):313-320
We study the stationary probability density of a Brownian particle in a potential with a single-well subject to the purely
additive thermal and dichotomous noise sources. We find situations where bimodality of stationary densities emerges due to
presence of dichotomous noise. The solutions are constructed using stochastic dynamics (Langevin equation) or by discretization
of the corresponding Fokker-Planck equations. We find that in models with both noises being additive the potential has to
grow faster than |x| in order to obtain bimodality. For potentials ∝|x| stationary solutions are always of the double exponential
form. 相似文献