An integer linear programming formulation and heuristics for the minmax relative regret robust shortest path problem

The well-known Shortest Path problem (SP) consists in finding a shortest path from a source to a destination such that the total cost is minimized. The SP models practical and theoretical problems. However, several shortest path applications rely on uncertain data. The Robust Shortest Path problem (RSP) is a generalization of SP. In the former, the cost of each arc is defined by an interval of possible values for the arc cost. The objective is to minimize the maximum relative regret of the path from the source to the destination. This problem is known as the minmax relative regret RSP and it is NP-Hard. We propose a mixed integer linear programming formulation for this problem. The CPLEX branch-and-bound algorithm based on this formulation is able to find optimal solutions for all instances with 100 nodes, and has an average gap of 17 % on the instances with up to 1,500 nodes. We also develop heuristics with emphasis on providing efficient and scalable methods for solving large instances for the minmax relative regret RSP, based on Pilot method and random-key genetic algorithms. To the best of our knowledge, this is the first work to propose a linear formulation, an exact algorithm and metaheuristics for the minmax relative regret RSP.     

On local regularization for an inverse problem of option pricing

We explore the theoretical and numerical application of local regularization methods to an ill-posed inverse problem arising from financial option pricing. In addition, we provide an algorithm and show results through numerical examples.     

Dried blood spot on‐card derivatization: an alternative form of sample handling to overcome the instability of thiorphan in biological matrix

Thiorphan, the active metabolite of racecadotril, can undergo oxidation in biological matrices such as blood and plasma. In bioanalysis, a general approach for the stabilization of such a molecule is to derivatize the thiol group to a more stable thioether, often requiring complex handling procedures at the clinical site. In this research, the concept of dried blood spot (DBS) on‐card derivatization was evaluated to stabilize thiorphan. DBS cards were in‐house pre‐treated with 2‐bromo‐3′‐methoxyacetophenone and left to dry prior to blood spotting. Thiorphan was shown to be effectively derivatized to thiorphan–methoxyacetophenone once applied on the in‐house pre‐treated cards. Thiorphan–methoxyacetophenone was extracted by soaking a 6 mm DBS punch in methanol containing the internal standard (thiorphan–methoxyacetophenone‐D₅). Chromatographic separation was achieved on a Waters XBridge C₁₈ column with a gradient elution of 5 m m NH₄HCO₃ and methanol in 2.5 min and detection by ESI(+)/MS/MS. A linear (weighted 1/x²) relationship was obtained over a concentration range of 5.00–600.00 ng/mL. The assay met regulatory guidelines acceptance criteria for sensitivity, selectivity, precision and accuracy, matrix effect, recovery, dilution integrity and multiple stability evaluations. The DBS on‐card derivatization has shown to be an easy and reliable alternative form of sample collection for the quantification of thiorphan. Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis and characterization of functionalized water soluble cationic poly(ester amide)s

A new family of positively charged, water soluble and functional amino acid‐based poly(ester amide)s ( Arg‐AG PEA ) consisting of four building blocks (L ‐Arginine, DL ‐2‐Allylglycine, oligoethylene glycol, and aliphatic diacid) were synthesized by the solution copolycondensation. Functional pendant carbon–carbon double bonds located in the DL ‐2‐allylglycine unit were incorporated into these Arg‐AG PEAs, and the double bond contents could be adjusted by tuning the feed ratio of L ‐arginine to DL ‐2‐allylglycine monomers. Chemical structures of this new functional Arg‐AG PEA family were confirmed by Fourier transform infrared spectroscopy (FTIR) and nuclear magnetic resonance (NMR) spectra. The thermal property of these polymers was investigated; increasing the methylene chain in both the amino acid and diacid segments resulted in a reduction in the polymer glass‐transition temperature. All these cationic Arg‐AG PEAs had good solubility in water and polar organic solvents. The cytotoxity of Arg‐AG PEAs was evaluated by 3‐(4,5‐Dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide (MTT) assay. These preliminary MTT results indicated that Arg‐AG PEAs were nontoxic to bovine aortic endothelial cells (BAECs). © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3758–3766, 2010     

Effects of several lanthanide trichloride hydrates on the melting behavior and spherulitic superstructure of poly(ethylene oxide)

Binary mixtures of poly(ethylene oxide) (PEO) with the trichloride hydrates of lanthanum, cerium, europium, terbium, and ytterbium have been studied with calorimetry, polarized optical microscopy, and infrared spectroscopy. Melting‐point depression of the PEO‐rich phase occurs in all cases. At sufficiently high concentrations of the low molecular weight lanthanide complex, crystallization of the polymer is absent. The lighter lanthanides with larger ionic radii, such as lanthanum and cerium, are more effective in suppressing PEO crystallization from solution or the molten state because they are more oxophilic. The spherulitic superstructure of PEO disappears at rather low concentrations of the lanthanide salts, between 2 and 8 mol % Ln³⁺. Lanthanum and terbium are most efficient at disrupting the formation of PEO spherulites, and europium is least efficient. Infrared spectroscopy identifies twisting and wagging vibrational absorptions of CH₂ groups in the polymer that are sensitive to the morphologies of these mixtures. Modifications of the PEO infrared absorbances in the presence of these five lanthanide salts correlate more closely with the presence or absence of major PEO melting, not the formation of a spherulitic superstructure. The phase behavior is rather simple, with no evidence of eutectic solidification upon cooling from the molten state. Multiple melting endotherms are observed in the differential scanning calorimetry heating traces of binary mixtures containing 8 mol % Yb³⁺ and between 10 and 20 mol % Eu³⁺, but the concentration dependence of these first‐order endothermic transitions is not characteristic of eutectic phase behavior. The presence of trivalent cations, such as Eu³⁺ or Yb³⁺, in these complexes perturbs the crystallization kinetics of PEO upon cooling from the molten state, as well as the melting behavior upon heating. Ion–dipole or electrostatic interactions between the lanthanide cation and the ether oxygen of PEO might alter the surface free energy at the periphery of the crystalline lamellae and perturb the chain‐folding characteristics of PEO. Consequently, coupling between the amorphous matrix and the PEO crystallites is strengthened, and this provides stability for the existence of multiple‐chain‐folded crystals composed of rather thin lamellae that could be responsible for multiple melting behavior. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2200–2213, 2003     

Photoluminescence from CdS Quantum Dots in Silica Gel

CdS semiconductor nanocrystals were grown as quantum dots (QDs) inside a silica matrix obtained by the sol-gelmethod and assisted in the mother liquid by high powerultrasounds. Small-angle neutron scattering (SANS) accountsfor a 3.6 nm crystal size homogeneously distributed. Optical excitation from the third harmonic of a Nd:YAG ns laser wasfocused on the sample to study the photoluminescence (PL) atroom temperature. The PL spectrum shows radiative processfrom intrinsic transitions and a broad band corresponding tothe traps. Variable stripe length (VSL) method was used to measure the optical gain spectra by the growth of theamplified luminescence. A broad optical gain spectrumproduced by the biexciton-exciton transitions revealing thestimulated emission from the CdS QDs. It is also observed ared-shift of the PL emission crystal size-dependent.