An exact solution approach for the interdiction median problem with fortification

Systematic approaches to security investment decisions are crucial for improved homeland security. We present an optimization modeling approach for allocating protection resources among a system of facilities so that the disruptive effects of possible intentional attacks to the system are minimized. This paper is based upon the p-median service protocol for an operating set of p facilities. The primary objective is to identify the subset of q facilities which, when fortified, provides the best protection against the worst-case loss of r non-fortified facilities. This problem, known as the r-interdiction median problem with fortification (IMF), was first formulated as a mixed-integer program by Church and Scaparra [R.L. Church, M.P. Scaparra, Protecting critical assets: The r-interdiction median problem with fortification, Geographical Analysis 39 (2007) 129–146]. In this paper, we reformulate the IMF as a maximal covering problem with precedence constraints, which is amenable to a new solution approach. This new approach produces good approximations to the best fortification strategies. Furthermore, it provides upper and lower bounds that can be used to reduce the size of the original model. The reduced model can readily be solved to optimality by general-purpose MIP solvers. Computational results on two geographical data sets with different structural characteristics show the effectiveness of the proposed methodology for solving IMF instances of considerable size.     

Deciphering the Spectral Tuning Mechanism in Proteorhodopsin: The Dominant Role of Electrostatics Instead of Chromophore Geometry

Proteorhodopsin (PR) is a photoactive proton pump found in marine bacteria. There are two phenotypes of PR exhibiting an environmental adaptation to the ocean's depth which tunes their maximum absorption: blue-absorbing proteorhodopsin (BPR) and green-absorbing proteorhodopsin (GPR). This blue/green color-shift is controlled by a glutamine to leucine substitution at position 105 which accounts for a 20 nm shift. Typically, spectral tuning in rhodopsins is rationalized by the external point charge model but the Q105L mutation is charge neutral. To study this tuning mechanism, we employed the hybrid QM/MM method with sampling from molecular dynamics. Our results reveal that the positive partial charge of glutamine near the C₁₄−C₁₅ bond of retinal shortens the effective conjugation length of the chromophore compared to the leucine residue. The derived mechanism can be applied to explain the color regulation in other retinal proteins and can serve as a guideline for rational design of spectral shifts.     

Comparative macrocycle binding of the anticancer drug phenanthriplatin by cucurbit[<Emphasis Type="Italic">n</Emphasis>]urils, β-cyclodextrin and <Emphasis Type="Italic">para</Emphasis>-sulfonatocalix[4]arene: a <Superscript>1</Superscript>H NMR and molecular modelling study

The potential anticancer drug phenanthriplatin, [cis-(NH₃)₂(phenanthridine)Cl]⁺, forms supramolecular complexes with cucurbit[n]urils (CB[n], n?=?7 or 8), β-cyclodextrin and para-sulfonatocalix[4]arene (sCX[4]) as determined by ¹H NMR spectroscopy and molecular modeling. The results show that cucurbit[7]uril binds over the long arm of the drug, where hydrophobic effects and two hydrogen bonds stabilise binding. For cucurbit[8]uril, two phenanthriplatin molecules can bind simultaneously within the macrocycle’s cavity. Unfortunately, Na⁺ was able to displace the drug from both CB[7] and CB[8] making the macrocycles unsuitable as delivery vehicles for phenanthriplatin. Drug binding to β-cyclodextrin occurs at the portal of the macrocycle with no part of the phenanthriplatin located within the cavity. Phenanthriplatin binding to sCX[4] occurs in a 2-to-1, macrocycle-to-drug, ratio with the formation of a capsule-like complex where each sCX[4] binds over opposing ends of the drug. The results indicate that para-sulfonatocalix[4]arene is the only suitable macrocycle of the four studied for further research into phenanthriplatin drug delivery.     

Theoretical links between median and coverage location problems

The relationship between the maximal covering problem and the P-median problem is reviewed. It is shown that two multiple coverage models, themaximumexpectedcoverageproblem (MECP) and thebackupcoverageproblem (BACOP), are special cases of thevectorassignmentP-medianproblem (VAPMP). This relationship is utilized to solve both MECP and BACOP on test sets from the literature. Computational experience is reported.     

Polarization detection of trapped electrons via interaction with polarized atoms

Electrons were trapped in an electrostatic quadrupole trap with superimposed homogeneous magnetic field. The electrons were polarized by spin exchange with a polarized atomic beam. The free trapped electron polarization was converted to a change in the electron translational energy via spin-dependent inelastic collisions with the atomic beam, and the electron translational temperature was monitored. Discussed are the development of this variation of the measurement technique, characteristics of electron storage, and the electron-polarized atom inelastic interaction as a function of electron temperature and time. The method has been applied to the detection of the (g-2) resonance of free, stored electrons.     

Designing robust coverage networks to hedge against worst-case facility losses

In order to design a coverage-type service network that is robust to the worst instances of long-term facility loss, we develop a facility location–interdiction model that maximizes a combination of initial coverage by p facilities and the minimum coverage level following the loss of the most critical r facilities. The problem is formulated both as a mixed-integer program and as a bilevel mixed-integer program. To solve the bilevel program optimally, a decomposition algorithm is presented, whereby the original bilevel program is decoupled into an upper level master problem and a lower level subproblem. After sequentially solving these problems, supervalid inequalities can be generated and appended to the upper level master in an attempt to force it away from clearly dominated solutions. Computational results show that when solved to optimality, the bilevel decomposition algorithm is up to several orders of magnitude faster than performing branch and bound on the mixed-integer program.     

Representation theory and homological stability

We introduce the idea of representation stability   (and several variations) for a sequence of representations _Vn$V_n$ of groups _Gn$G_n$. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Representation stability also provides a framework in which to find and to predict patterns, from classical representation theory (Littlewood–Richardson and Murnaghan rules, stability of Schur functors), to cohomology of groups (pure braid, Torelli and congruence groups), to Lie algebras and their homology, to the (equivariant) cohomology of flag and Schubert varieties, to combinatorics (the (n+1)ⁿ⁻¹${(n+1)}^{n-1}$ conjecture). The majority of this paper is devoted to exposing this phenomenon through examples. In doing this we obtain applications, theorems and conjectures.     

Charge transfer reaction of multi-charged oxygen ions with O2

The rate of transfer of electrons from O₂ to O²⁺ and O³⁺ has been measured at energies ? 2 eV using a stored ion technique. The rate for O²⁺ is k = 1.0(0.3) × 10^?9 cm³/s and for O³⁺, k = 2.5(0.3) × 10^?9 cm³/s, compared to calculated Langevin rates of 1.8 × 10^?9 cm³/s and 2.7 × 10^?9 cm³/s respectively.     

A chelating gel for collection of copper from seawater

An affinity Chromatographic gel is coupled to carboxymethyl(imino)-bis(ethyl-enenitrilo) tetraacetic acid (DTPA) by a carbodiimide reaction. This gel is successful in extracting copper from seawater with high selectivity over alkaline earths such as mag-nesium. It is useful over a wide range of pH (4–9), and is stable and reversible over a period of nine months. Up to 20 μmol of copper can be adsorbed and recovered with greater than 99% efficiency with gel—DTPA prepared from 1 g of dry gel.     

Additions of substituted phenylthiyl radicals to substituted α-methylstyrenes : Ground state and transition state electronic effects

The radical addition of substituted thiophenols to α-methylstyrene and substituted α-methylstyrenes has been investigated at 70°. Relative reactivities of pairs of thiophenols competing with individual alkenes can be utilized to obtain Hammett correlations. The interplay of substituent effects in alkene and thiyl radical leads to examples of non-linear rho values. Rationales for this behavior will be offered in terms of variable contributions from ground state and transition state electronic factors as well as in terms of possible mechanistic changes.