Imprinting of molecular recognition sites through electropolymerization of functionalized Au nanoparticles: development of an electrochemical TNT sensor based on pi-donor-acceptor interactions

Electrochemical sensors for the analysis of TNT with enhanced sensitivities are described. The enhanced sensitivities are achieved by tailoring pi-donor-acceptor interactions between TNT and pi-donor-modified electrodes or pi-donor-cross-linked Au nanoparticles linked to the electrode. In one configuration a p-aminothiophenolate monolayer-modified electrode leads to the analysis of TNT with a sensitivity corresponding to 17 ppb (74 nM). In the second configuration, the cross-linking of Au NPs by oligothioaniline bridges to the electrode yields a functionalized electrode that detects TNT with a sensitivity that corresponds to 460 ppt (2 nM). Most impressively, the imprinting of molecular TNT recognition sites into the pi-donor oligoaniline-cross-linked Au nanoparticles yields a functionalized electrode with a sensitivity that corresponds to 46 ppt (200 pM). The electrode reveals high selectivity, reusability, and stability.     

A spline for your saddle

Pinpointing extrema on a multidimensional hypersurface is an important generic problem with a broad scope of application in statistical mechanics, biophysics, chemical reaction dynamics, and quantum chemistry. Local minima of the hypersurface correspond to metastable structures and are usually the most important points to look for. They are relatively easy to find using standard minimizing algorithms. A considerably more difficult task is the location of saddle points. The saddle points most sought for are those which form the lowest barriers between given minima and are usually required for determining rates of rare events. We formulate a path functional minimum principle for the saddle point. We then develop a cubic spline method for applying this principle and locating the saddle point(s) separating two local minima on a potential hypersurface. A quasi-Newton algorithm is used for minimization. The algorithm does not involve second derivatives of the hypersurface and the number of potential gradients evaluated is usually less than 10% of the number of potential evaluations. We demonstrate the performance of the method on several standard examples and on a concerted exchange mechanism for self-diffusion in diamond. Finally, we show that the method may be used for solving large constrained minimization problems which are relevant for self-consistent field iterations in large systems.     

Structural and algorithmic properties for parametric minimum cuts

We consider the minimum s, t-cut problem in a network with parametrized arc capacities. Following the seminal work of Gallo et?al. (SIAM J. Comput. 18(1):30–55, 1989), classes of this parametric problem have been shown to enjoy the nice Structural Property that minimum cuts are nested, and the nice Algorithmic Property that all minimum cuts can be computed in the same asymptotic time as a single minimum cut by using a clever Flow Update step to move from one value of the parameter to the next. We present a general framework for parametric minimum cuts that extends and unifies such results. We define two conditions on parametrized arc capacities that are necessary and sufficient for (strictly) decreasing differences of the parametric cut function. Known results in parametric submodular optimization then imply the Structural Property. We show how to construct appropriate Flow Updates in linear time under the above conditions, implying that the Algorithmic Property also holds under these conditions. We then consider other classes of parametric minimum cut problems, without decreasing differences, for which we establish the Structural and/or the Algorithmic Property, as well as other cases where nested minimum cuts arise.     

On sequential commitment in the price-dependent newsvendor model

We investigate the effect of sequential commitment in the decentralized newsvendor model with price-dependent demand. Sequential commitment allows the self-profit maximizing parties to commit to contract parameters (e.g., wholesale price, retail price, buyback price and order quantity) sequentially and alternately, and we investigate its effect on the equilibrium profits of the channel and its members. Sequential commitment introduces more flexibility to contracting in the supply chain and our analysis can provide some insight to channel members who follow a bargaining process to determine the values of contract parameters. We show that the introduction of sequential commitment to the price-dependent (PD) newsvendor model with buybacks can significantly improve the manufacturer’s and the channel expected profits, but it can also decrease the retailer’s expected profit. Finally, we demonstrate that with sequential commitment, under some conditions, the choice of the first mover is endogenized and we identify the unique sequence of commitments by channel members that would arise in equilibrium.     

A generalized linear production model: A unifying model

We introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producersS is not restricted to be the vector sum of the resources held by the members ofS. We provide sufficient conditions for the non-emptiness of the core of the associated generalized linear production game, and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem. Our generalized linear production model is a proper generalization of the linear production model introduced by Owen, and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework. We use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non-empty core. We further employ our model to prove the non-emptiness of the core of two other classes of cooperative games, which were not previously studied in the literature, and we also use our generalized model to provide an alternative proof for the non-emptiness of the core of the class of minimum cost spanning tree games. Thus, it appears that the generalized linear production model is a unifying model which can be used to explain the non-emptiness of the core of cooperative games generated by various, seemingly different, optimization models.This research was partially done while the author was visiting the Graduate School of Business Administration at Tel-Aviv University. The research was partially supported by Natural Sciences and Engineering Research Council Canada Grant A4181 and by SSHRC leave fellowship 451-83-0030.Dedicated to George B. Dantzig.     

A new exchange property for matroids and its application to max-min-problems

We provide a new characterization for matroids which is useful for sensitivity analysis and for solving certain max min matroid optimization problems.

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Zusammenfassung Es wird eine neue Charakterisierung von Matroiden angegeben, welche für eine Sensitivitätsanalyse und für eine Lösung von Max-Min-Optimierungsproblemen für Matroide nützlich ist.

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Research was partially supported by National Science and Engineering Research Council of Canada Grant A4181.     

Role of quantum statistics in multi-particle decay dynamics

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.     

Schur complement preconditioners for anisotropic problems

We present two new variants of Schur complement domain decompositionpreconditioners suitable for 2D anisotropic problems. Thesevariants are based on adaptations of the probing idea, describedby Chan et al (1992 Fifth Int. Symp. on Domain DecompositionMethods for Partial Differential Equations, Philadelphia: SIAM,pp 236-249), used in conjunction with a coarse grid approximationas introduced by Bramble et al (1986 Math. Comput. 47, 103-134).The new methods are specifically designed for situations wherethe coupling between neighbouring interfaces is stronger thanthe coupling within an interface. Taking into account this strongcoupling, one variant uses a multicolour probing technique toavoid distortion in the probe approximations that appear whenusing the method proposed by Chan et al. The second techniqueuses additional probe matrices to approximate not only the couplingwithin the interfaces but also the coupling between interfacepoints across the subdomains. This latter procedure looks somewhatlike an alternating line relaxation method for anisotropic problems,see Brandt (1977 Math. Comput.. 31, 333-390). To assess therelevance of the new preconditioners, we compare their numericalbehaviour with well known robust preconditioners such as thebalanced Neumann-Neumann method proposed by Mandel (1993 Commun.Numer. Methods Eng.. 9, 233-241).