Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time.

     

Moment Identifiability of Homoscedastic Gaussian Mixtures

Foundations of Computational Mathematics - We consider the problem of identifying a mixture of Gaussian distributions with the same unknown covariance matrix by their sequence of moments up to...     

A paradigmatic system to study the transition from zero/Hopf to double-zero/Hopf bifurcation

A two-d.o.f.?system experiencing codimension-three double-zero/Hopf bifurcation is considered. This is a special bifurcation which simultaneously involves a defective and a nondefective pair of critical eigenvalues, therefore, requiring a perturbation method specifically tailored on it. A nonstandard version of the multiple scale method is implemented, in which fractional power expansions, both for state-variables and time are used, and high-order arbitrary amplitudes are introduced. Bifurcation equations are obtained, governing the slow flow on the center manifold, which turns out to be tangent to the space spanned by the four critical eigenvectors. These are used to analyze the transition from codimension-three to codimension-two single-zero/Hopf bifurcations, occurring when the modulus of the damping is increased from small to order-one values. Bifurcation charts are obtained, displaying the role of quasi-periodic motions in the transition.     

Non-degeneracy and uniqueness of solutions to singular mean field equations on bounded domains

The aim of this paper is to complete the program initiated in [51], [23] and then carried out by several authors concerning non-degeneracy and uniqueness of solutions to mean field equations. In particular, we consider mean field equations with general singular data on non-smooth domains. The argument is based on the Alexandrov–Bol inequality and on the eigenvalues analysis of linearized singular Liouville-type problems.     

Generalized Langevin Equations for Systems with Local Interactions

Journal of Statistical Physics - We present a new method to approximate the Mori–Zwanzig (MZ) memory integral in generalized Langevin equations describing the evolution of smooth observables...     

The effect of point mutations on copper(II) complexes with peptide fragments encompassing the 106–114 region of human prion protein

Abstract  

The tetrapeptides Ac-SKHM-NH₂, Ac-TKHM-NH₂, Ac-MKHS-NH₂, Ac-S(OMe)KHM-NH₂, and Ac-MKHS(OMe)-NH₂ and the nonapeptides Ac-KTNSKHMAG-NH₂ and Ac-KTNMKHSAG-NH₂ were synthesized and their copper(II) complexes were studied by potentiometric, UV–Vis, circular dichroism (CD), and electron paramagnetic resonance (EPR) spectroscopic methods. These peptides mimic the 109–112 and 106–114 residues of the sequence of human prion protein. The imidazole-N donor atoms of histidyl residues were found to be the primary metal binding sites of all peptide fragments. This binding mode provides a good possibility for the cooperative deprotonation and metal ion coordination of two amide functions preceding histidine. The (N_im,N⁻,N⁻)-bonded species predominate in the pH range 5.5–7.0 and the free coordination sites of these species make possible the metal binding of weakly coordinating side chains. The comparison of the potentiometric and spectroscopic results revealed the stabilizing role of the oxygen donors of seryl, threonyl, or methoxyseryl residues of Ac-SKHM-NH₂, Ac-TKHM-NH₂, Ac-S(OMe)KHM-NH₂, and Ac-KTNSKHMAG-NH₂ containing the mutations in position 109. These interactions were, however, not observed in the peptides containing the specific amino acids in other locations of the peptide sequence.     

Preparation and optical characterization of two photoactive poly(bisphenol a ethoxylate diacrylate) copolymers containing designed amino‐nitro‐substituted azobenzene units,obtained via classical and frontal polymerization,using novel ionic liquids as initiators

The frontal polymerization (FP) of bisphenol A ethoxylate diacrylate (BPAEDA) was carried with and without the presence of two different azobenzene comonomers by means of an external heating source. The first azomonomer (MDR‐1) is a derivative of disperse red‐1, N‐ethyl‐N‐(2‐hydroxyethyl)‐4‐(4‐nitrophenylazo)aniline, whereas the second (E)‐2‐(4‐((4‐nitrophenyl)diazenyl)phenyl)‐5,8,11‐trioxa‐2‐azatridecan‐13‐yl methacrylate (4PEGMAN) comes from the azo‐dye N‐methyl‐N‐{4‐[(E)‐(4‐nitrophenyl)diazenyl]phenyl}‐N‐(11‐hydroxy‐3,6,9‐trioxaundecas‐1‐yl) amine. In this work, an ionic liquid trihexyltetradecylphosphonium persulfate was used as initiator. This compound produced stable propagating polymerization fronts with good velocities and moderate maximum temperature values. Moreover, this initiator prevented bubble formation and was found to be the most efficient when it was used in lower amounts with respect to other initiators, such as benzoyl peroxide, 2,2′‐azobisisobutyronitrile, aliquat persulfate®, and tetrabutylphosphonium persulfate. The thermal properties of the obtained polymers and copolymers were determined by thermogravimetric analysis and differential scanning calorimetry. The nonlinear optical (NLO) characterizations of the developed BPAEDA/MDR‐1 and BPAEDA/4PEGMAN copolymers were performed according to the Z‐Scan technique in film samples prepared by classical polymerization. It has been proven that samples with higher 4PEGMAN content (0.26 mol %) exhibited outstanding cubic NLO‐activity with positive NLO‐refractive coefficients in the promising range of n₂ = +3.2 × 10^?4 esu. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Asymptotic Estimates for the p-Laplacian on Infinite Graphs with Decaying Initial Data

Potential Analysis - We consider the Cauchy problem for the evolutive discrete p-Laplacian in infinite graphs, with initial data decaying at infinity. We prove optimal sup and gradient bounds for...     

Hexa-peri-benzocoronene with two extra K-regions in an ortho-configuration

There are three possible isomers for hexa-peri-hexabenzocoronene (HBC) with two extra K-regions, but only two of them have been reported, namely with the meta- and para-configurations. Herein, we describe the synthesis of HBC 4 with two extra K-regions in the ortho-configuration, forming a longer zigzag edge compared with the other two isomers. The structure of 4 was validated by laser desorption/ionization time-of-flight mass analysis and nuclear magnetic resonance spectra, as well as Raman and infrared spectroscopies supported by density functional theory calculations. The optical properties of 4 were investigated by UV/vis absorption and ultrafast transient absorption spectroscopy. Together with the analysis of aromaticity, the influence of the zigzag edge on the π-conjugation pathway and HOMO–LUMO gaps of the three isomers were investigated.

We reported the synthesis of hexa-peri-benzocoronene (HBC) with two extra K-regions adopting an ortho-configuration. The systematical study provides deep insights about the effect of zigzag edge on the π-conjugated pathway and molecular design.