Location of terror response facilities: A game between state and terrorist

We study a leader follower game with two players: a terrorist and a state where the later one installs facilities that provide support in case of a terrorist attack. While the Terrorist attacks one of the metropolitan areas to maximize his utility, the State, which acts as a leader, installs the facilities such that the metropolitan area attacked is the one that minimizes her disutility (i.e., minimizes ‘loss’). We solve the problem efficiently for one facility and we formulate it as a mathematical programming problem for a general number of facilities. We demonstrate the problem via a case study of the 20 largest metropolitan areas in the United States.     

Sparse pseudorandom distributions

The existence of sparse pseudorandom distributions is proved. These are probability distributions concentrated in a very small set of strings, yet it is infeasible for any polynomial-time algorithm to distinguish between truly random coins and coins selected according to these distributions. It is shown that such distributions can be generated by (nonpolynomial) probabilistic algorithms, while probabilistic polynomial-time algorithms cannot even approximate all the pseudorandom distributions. Moreover, we show the existence of evasive pseudorandom distributions which are not only sparse, but also have the property that no polynomial-time algorithm may find an element in their support, except for a negligible probability. All these results are proved independently of any intractability assumption.     

Simple Constructions of Almost k-wise Independent Random Variables

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity.     

Rapid liquid chromatography-ultraviolet determination of organic acids and phenolic compounds in red wine and must

A reversed-phase liquid chromatography-ultraviolet (LC-UV) method is proposed for the rapid simultaneous analysis of the main carboxylic acids and polyphenols in must and wine. Good resolution was obtained for citric, tartaric, malic, lactic, acetic, caffeic, ellagic and gallic acids, (-)-epicatechin, quercetin and resveratrol. A novel silica-based column containing ether-linked phenyl groups, with polar end-capping and suitable for low-pH aqueous mobile phases was used and found to be superior to others tested. The method employed a mixture of 0.2% TFA in water and acetonitrile as eluents, showed linearity and precision, and was applied to samples of must and wine.     

Form fluctuations of carbosilane dendrimers in dilute solution: a study using neutron spin echo spectroscopy

A series of carbosilane dendrimers with perfluorinated end groups has been prepared. The structure of these molecules in dilute solution is studied using small angle neutron scattering. For generations g<3 we find a non-spherical shape of the particles and a tendency for aggregation. This result is supported by the analysis of the diffusion coefficient obtained from photon correlation spectroscopy. The overall shape of the molecules is that of a core-shell particle. The generation 4 molecule is obtained as a compact sphere. Neutron spin echo spectroscopy reveals a relaxation time which is attributed to the form fluctuations of this particle.     

Rigidity of circle domains whose boundary hasσ-finite linear measure

Summary Let be a circle domain in the Riemann sphere whose boundary has -finite linear measure. We show that is rigid in the sense that any conformal homeomorphism of onto any other circle domain is equal to the restriction of a Möbius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle, domains whose boundary is a Cantor set of (Hausdorff) dimension one.Oblatum 19-VI-1992 & 2-IV-1993Supported by NSF and Sloan Foundation     

Statistical mechanics of bilayer membrane with a fixed projected area

The equilibrium and fluctuation methods for determining the surface tension, sigma, and bending modulus, kappa, of a bilayer membrane with a fixed projected area are discussed. In the fluctuation method the elastic coefficients sigma and kappa are measured from the amplitude of thermal fluctuations of the planar membrane, while in the equilibrium method the free energy required to deform the membrane is considered. The latter approach is used to derive new expressions for sigma and kappa (as well as for the saddle-splay modulus), which relate them to the pair-interactions between the amphiphiles forming the membrane. We use linear response theory to argue that the two routes lead to similar values for sigma and kappa. This argument is confirmed by Monte Carlo simulations of a model membrane whose elastic coefficients are calculated using both methods.     

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.