Using Estimated Missing Spatial Data with the 2-Median Model

Spatial operations research problems seek best locations, often points of minimum aggregate weighted distance, requiring georeferenced data as input. Frequently maps of such data are incomplete, with holes in their geographic distributions. Spatial statistical procedures are available to complete these data sets with best estimates of the missing values. Impacts such imputations have on 2-median facility location–allocation solutions are explored. The sampling distribution of the spatial mean and standard distance of these medians are studied. Population density is used as the weight attribute in determining location-allocation solutions because it can be accurately described with a relatively simple spatial statistical model.     

Force-extension behavior of folding polymers

The elastic response of flexible polymers made of elements which can be either folded or unfolded, having different lengths in these two states, is discussed. These situations are common for biopolymers as a result of folding interactions intrinsic to the monomers, or as a result of binding of other smaller molecules along the polymer length. Using simple flexible-chain models, we show that even when the energy ε associated with maintaining the folded state is comparable to k _B T, the elastic response of such a chain can mimic usual polymer linear elasticity, but with a force scale enhanced above that expected from the flexibility of the chain backbone. We discuss recent experiments on single-stranded DNA, chromatin fiber and double-stranded DNA with proteins weakly absorbed along its length which show this effect. Effects of polymer semiflexiblity and torsional stiffness relevant to experiments on proteins binding to dsDNA are analyzed. We finally discuss the competition between electrostatic self-repulsion and folding interactions responsible for the complex elastic response of single-stranded DNA. Received 7 August 2002 and Received in final form 7 March 2003 / Published online: 15 April 2003 RID="a" ID="a"e-mail: jmarko@uic.edu     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar     

Universal properties of shortest paths in isotropically correlated random potentials

We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2ν - ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations. Received 20 December 2002 / Received in final form 10 April 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: schorr@lusi.uni-sb.de     

Correction value to charged Bekenstein-Hawking black hole entropy

Recently, based on the study of black hole Hawking radiation with the tunnel effect method, we found that the radiation spectrum of the black hole is not a strict pure thermal spectrum. It is a very interesting problem to determine how the departure of the black hole radiation spectrum from the pure thermal spectrum affects entropy. We calculate the partition function by the energy spectrum obtained using tunnel effect. Using the relation between the partition function and entropy, we derive the correction value to Bekenstein-Hawking entropy of the charged black hole. Furthermore, we obtain the conditions that various thermodynamic quantities must satisfy, when phase transition of the charged black hole occurs. Supported by the Natural Science Foundation of Shanxi Province of China (Grant No. 2006011012) and the Doctoral Sustentation Fund of Shanxi Datong University of China     

On the Skitovich–Darmois Theorem for Compact Abelian Groups

Let X be a separable compact Abelian group, Aut(X) the group of topological automorphisms of X, f _n: XX a homomorphism f _n(x)=nx, and X ⁽ⁿ⁾=Im f _n. Denote by I(X) the set of idempotent distributions on X and by (X) the set of Gaussian distributions on X. Consider linear statistics L ₁= ₁( ₁)+ ₂( ₂) and L ₂= ₁( ₁)+ ₂( ₂), where _j are independent random variables taking on values in X and with distributions _j, and _j, _jAut(X). The following results are obtained. Let X be a totally disconnected group. Then the independence of L ₁ and L ₂ implies that ₁, ₂I(X) if and only if X possesses the property: for each prime p the factor-group X/X ^(p) is finite. If X is connected, then there exist independent random variables _j taking on values in X and with distributions _j, and _j, _jAut(X) such that L ₁ and L ₂ are independent, whereas ₁, ₂(X) * I(X).     

Evolution of imitation networks in Minority Game model

The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erd?s-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost epsilon, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive epsilon makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erd?s-Rényi substrate for any epsilon and for Barabási-Albert scale-free substrate for large enough epsilon. A brief comparison with empirical data is provided.     

The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions

We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of ordering (quasi-long-range order) below a certain temperature and a size-dependent mean value of magnetisation in the low-temperature phase that goes to zero (according to the Mermin-Wagner-Hohenberg theorem) in the thermodynamic limit. We focus our attention on the asymptotic behaviour of the spin-spin correlation function and the probability distribution of magnetisation. The analytic approach is based on the spin-wave approximation valid for the low-temperature regime and an expansion in the parameters which characterise the deviation from completely homogeneous configuration of impurities. We further support the analytic considerations by Monte Carlo simulations performed for different concentrations of impurities and compare analytic and MC results. We present as the main quantitative result of the work the exponent of the spin-spin correlation function power law decay. It is non universal depending not only on temperature as in the pure model but also on concentration of magnetic sites. This exponent characterises also the vanishing of magnetisation with increasing lattice size.     

Interacting gaps model,dynamics of order book,and stock-market fluctuations

Inspired by order-book models of financial fluctuations, we investigate the Interacting gaps model, which is the schematic one-dimensional system mimicking the order-book dynamics. We find by simulations the power-law tail in return distribution, power-law decay of volatility autocorrelation with exponent 0.5 and Hurst exponent close to 1/2. Surprisingly, when we make a mean-field approximation, i.e. replace the one-dimensional system by effectively infinite-dimensional one, we obtain analytically the return exponent 5/2, in perfect accord with one-dimensional simulations.     

Preparation and performance of polysulfone-sulfonated poly(ether ether ketone) blend ultrafiltration membranes. Part I

Ultrafiltration membranes were prepared from blends with polysulfone (PSf) and sulfonated poly(ether ether ketone) (SPEEK) by phase inversion technique. The blend membranes were prepared with polymer composition from 0 to15 wt%. Sulfonated poly(ether ether ketone) was used to improve the performance and permeability of blended membranes. The effects of polymer composition on compaction, pure water flux, water content, and membrane hydraulic resistance were studied. The membranes were also subjected to the determination of pore statistics and molecular weight cut-off (MWCO) determination studies by using different molecular weight of proteins. The porosity, pore size of the membranes increased with increasing concentrations of SPEEK in the casting solution. Similarly, the MWCOs of the blend membranes ranged from 20 to 45 kDa, depending on the various polymer blend compositions. The pure water flux of the PSf/SPEEK blend membranes increases from 16.7 to 61.5 l m⁻² h, when the concentration of SPEEK increased from 0 to 15 wt%. Scanning electron microscope (SEM) results qualitative evidence for the trends observed for the pore statistics and MWCO studies.