Pattern Hit-and-Run for sampling efficiently on polytopes

Pattern Hit-and-Run (PHR) is a Markov chain Monte Carlo sampler for a target distribution that was originally designed for general sets embedded in a box. A specific set of interest to many applications is a polytope intersected with discrete or mixed continuous/discrete lattices. PHR requires an acceptance/rejection mechanism along a bidirectional walk to guarantee feasibility. We remove this inefficiency by utilizing the linearity of the constraints defining the polytope, so each iteration of PHR can be efficiently implemented even though the variables are allowed to be integer valued. Moreover, PHR converges to a uniform distribution in polynomial time for a class of discrete polytopes.     

Selective and periodic inventory routing problem for waste vegetable oil collection

We consider a biodiesel production company that collects waste vegetable oil from source points that generate waste in large amounts. The company uses the collected waste as raw material for biodiesel production. The manager of this company needs to decide which of the present source points to include in the collection program, which of them to visit on each day, which periodic routing schedule to repeat over an infinite horizon and how many vehicles to operate such that the total collection, inventory and purchasing costs are minimized while the production requirements and operational constraints are met. For this selective and periodic inventory routing problem, we propose two different formulations, compare them and apply the better performing one on a real-world problem with 36 scenarios. We generate lower bounds using a partial linear relaxation model, and observe that the solutions obtained through our model are within 3.28% of optimality on the average. Several insights regarding the customer selection, routing and purchasing decisions are acquired with sensitivity analysis.     

Cobalt(II)/(III) complexes bearing a tetradentate thiosemicarbazone: Synthesis,experimental and theoretical characterization,and electrochemical and antioxidant properties

New cobalt complexes, Co1 and Co2 , were synthesized starting from acetylacetone-S-methylthiosemicarbazone. The square planar cobalt(II) and octahedral cobalt(III) complexes were characterized by FT-IR, UV–visible, ¹H NMR, and X-ray diffraction spectroscopies and mass spectrometry. Frontier orbitals of the complexes were theoretically obtained to better understand the complex structures and intermolecular interactions. The electrochemical behaviors of Co1 and Co2 were investigated and the results were evaluated by comparing with each other and with similar published compounds to determine their possible usage in various electrochemical technologies, such as energy storage devices, electrocatalysts, and electrosensors. Metal-based oxidation at around 0 V and metal-based reduction at around −1.0 V indicated that these complexes are valuable for the proposed applications. By determining the trolox equivalent antioxidant capacity and the radical scavenging activity of the cobalt complexes, the compatibility between the antioxidant qualification, redox, and theoretical calculation results was discussed.     

A genetic algorithm for flow shop scheduling problems

Many scheduling problems are NP-hard problems. For such NP-hard combinatorial optimization problems, heuristics play a major role in searching for near-optimal solutions. In this paper we develop a genetic algorithm-based heuristic for the flow shop scheduling problem with makespan as the criterion. The performance of the algorithm is compared with the established NEH algorithm. Computational experience indicates that genetic algorithms can be good techniques for flowshop scheduling problems.     

4‐Amino‐3,5‐diethyl‐4H‐1,2,4‐triazole at 100 K: chains of edge‐fused R44(10) and R44(20) rings

The title compound, C₆H₁₂N₄, has four crystallographically independent molecules in the asymmetric unit. Intermolecular N—H...N hydrogen bonds involving amino groups and triazole N atoms form a three‐dimensional framework involving R₄⁴(10) and R₄⁴(20) rings. The hydrogen bonding is supported by weak C—H...π interactions.     

Convex graph invariant relaxations for graph edit distance

Mathematical Programming - The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to...     

Reinforcing thermosets with crystallizable solvents

This study demonstrates an approach to generate reinforcement in thermosetting polymers through crystal growth of crystallizable solvents. Emphasis is to identify the reaction conditions, which lead to suitable reinforcement in selected compounds. Crystallization behavior and miscibility of dimethylsulfone (DMS) in diglycidylether of bisphenol‐A epoxy monomer was investigated. Small angle laser scattering and optical microscopy were utilized to monitor phase separation and crystallization of DMS at different isothermal conditions during the cure process. It is shown that DMS crystals grow anisotropically to form faceted geometries and demonstrate possible structures to anchor into the epoxy matrix. The growth mechanism and the agility of crystals are shown to be affected by the cure reaction as well as depth of supercooling. A completely cured sample with 15 wt % DMS shows a broad map of rich morphologies from nanoscale particles to uniformly distributed macroscale, discontinuous fiber‐like crystals generated only by altering the curing conditions. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 840–849, 2010