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.     

Graft copolymerization. I. Grafting of hydroxyalkyl methacrylates on poly(vinyl alcohol)

New graft copolymers were synthesized by grafting hydroxyethyl methacrylate and hydroxpropyl methacrylate on poly(vinyl alcohol) in aqueous solution with Ce⁺⁴ions as initiator. The dependence of the percentage of grafting and monomer conversion on the concentration of the monomer, on the concentration of the initiator, on the total concentration of the reactants, and on temperature and duration of the reaction were investigated. Some basic properties of the graft copolymers and some preliminary permeation measurements of water vapors through films, made from these copolymers, are also reported.     

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     

Boolean logic functions of a synthetic peptide network

Living cells can process rapidly and simultaneously multiple extracellular input signals through the complex networks of evolutionary selected biomolecular interactions and chemical transformations. Recent approaches to molecular computation have increasingly sought to mimic or exploit various aspects of biology. A number of studies have adapted nucleic acids and proteins to the design of molecular logic gates and computational systems, while other works have affected computation in living cells via biochemical pathway engineering. Here we report that de novo designed synthetic peptide networks can also mimic some of the basic logic functions of the more complex biological networks. We show that segments of a small network whose graph structure is composed of five nodes and 15 directed edges can express OR, NOR, and NOTIF logic.     

Adsorption of fast green and erythrosin-B to montmorillonite modified with crystal violet

Adsorption of erythrosin-B (EB) and fast green (FG) to a non-charged organosmectite based on crystal violet adsorbed up to 100% of the cation exchange capacity (CEC) was tested. Adsorption isotherms of EB and FG were prepared at 3, 24 and 50°C. All isotherms are of H-type reaching loads of approximately up to 20% of the original CEC of the crude montmorillonite (up to 0.15 and 0.10 mol dye kg^–1 clay for EB and FG, respectively). Adsorption decreases with temperature, indicating an exothermic process. Enthalpy was evaluated using van’t Hoff equation, yielding approximately –20 kJ mol^–1 for both dyes.     

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.