Exact Algorithms for Different Classes of Vehicle Routing Problems

We deal with five problems arising in the field of logistics: the Asymmetric TSP (ATSP), the TSP with Time Windows (TSPTW), the VRP with Time Windows (VRPTW), the Multi-Trip VRP (MTVRP), and the Two-Echelon Capacitated VRP (2E-CVRP). The ATSP requires finding a lest-cost Hamiltonian tour in a digraph. We survey models and classical relaxations, and describe the most effective exact algorithms from the literature. A survey and analysis of the polynomial formulations is provided. The considered algorithms and formulations are experimentally compared on benchmark instances. The TSPTW requires finding, in a weighted digraph, a least-cost Hamiltonian tour visiting each vertex within a given time window. We propose a new exact method, based on new tour relaxations and dynamic programming. Computational results on benchmark instances show that the proposed algorithm outperforms the state-of-the-art exact methods. In the VRPTW, a fleet of identical capacitated vehicles located at a depot must be optimally routed to supply customers with known demands and time window constraints. Different column generation bounding procedures and an exact algorithm are developed. The new exact method closed four of the five open Solomon instances. The MTVRP is the problem of optimally routing capacitated vehicles located at a depot to supply customers without exceeding maximum driving time constraints. Two set-partitioning-like formulations of the problem are introduced. Lower bounds are derived and embedded into an exact solution method, that can solve benchmark instances with up to 120 customers. The 2E-CVRP requires designing the optimal routing plan to deliver goods from a depot to customers by using intermediate depots. The objective is to minimize the sum of routing and handling costs. A new mathematical formulation is introduced. Valid lower bounds and an exact method are derived. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.

Longitudinal evolution of cognitive functions in patients with multiple system atrophy: a prospective study

Introduction and Background: Multiple system atrophy (MSA) is a sporadic, adult-onset, progressive neurodegenerative disease characterized clinically by parkinsonism, cerebellar ataxia, and autonomic failure. We investigated cognitive functions longitudinally in a group of probable MSA patients, matching data with sleep parameters. Patients and Methods: 10 patients (7m/3f) underwent a detailed interview, a general and neurological examination, laboratory exams, MRI scans, a cardiovascular reflexes study, a battery of neuropsychological tests, and video-polysomnographic recording (VPSG). Patients were revaluated (T1) a mean of 16±5 (range: 12-28) months after the initial evaluation (T0). At T1, the neuropsychological assessment and VPSG were repeated. Results: The mean patient age was 57.8±6.4 years (range: 47-64) with a mean age at disease onset of 53.2±7.1 years (range: 43-61) and symptoms duration at T0 of 60±48 months (range: 12-144). At T0, 7 patients showed no cognitive deficits while 3 patients showed isolated cognitive deficits. At T1, 1 patient worsened developing multiple cognitive deficits from a normal condition. At T0 and T1, sleep efficiency was reduced, REM latency increased, NREM sleep stages 1-2 slightly increased. Comparisons between T1 and T0 showed a significant worsening in two tests of attention and no significant differences of VPSG parameters. No correlation was found between neuropsychological results and VPSG findings or RBD duration. Discussion and Conclusions: The majority of our patients do not show any cognitive deficits at T0 and T1, while isolated cognitive deficits are present in the remaining patients. Attention is the cognitive function which significantly worsened. Our data confirm the previous findings concerning the prevalence, type and the evolution of cognitive deficits in MSA. Regarding the developing of a condition of dementia, our data did not show a clear-cut diagnosis of dementia. We confirm a mild alteration of sleep structure. RBD duration does not correlate with neuropsychological findings.

The VIMOS-VLT Deep Survey: the evolution of type-1 AGN

Quasars and AGN play an important role in many aspects of the modern cosmology. Of particular interest is the issue of the interplay between AGN activity and formation and evolution of galaxies and structures. Studies on nearby galaxies revealed that most (and possibly all) galaxy nuclei contain a super-massive black hole (SMBH) and that between a third and half of them are showing some evidence of activity (Kormendy and Richstone, 1995). The discovery of a tight relation between black holes mass and velocity dispersion of their host galaxy suggests that the evolution of the growth of SMBH and their host galaxy are linked together. In this context, studying the evolution of AGN, through the luminosity function (LF), is fundamental to constrain the theories of galaxy and SMBH formation and evolution. Recently, many theories have been developed to describe physical processes possibly responsible of a common formation scenario for galaxies and their central black hole (Volonteri et al., 2003; Springel et al., 2005a; Vittorini et al., 2005; Hopkins et al., 2006a) and an increasing number of observations in different bands are focused on collecting larger and larger quasar samples. Many issues remain however not yet fully understood. In the context of the VVDS (VIMOS-VLT Deep Survey), we collected and studied an unbiased sample of spectroscopically selected faint type-1 AGN with a unique and straightforward selection function. Indeed, the VVDS is a large, purely magnitude limited spectroscopic survey of faint objects, free of any morphological and/or color preselection. We studied the statistical properties of this sample and its evolution up to redshift z 4. Because of the contamination of the AGN light by their host galaxies at the faint magnitudes explored by our sample, we observed that a significant fraction of AGN in our sample would be missed by the UV excess and morphological criteria usually adopted for the pre-selection of optical QSO candidates. If not properly taken into account, this failure in selecting particular sub-classes of AGN could, in principle, affect some of the conclusions drawn from samples of AGN based on these selection criteria. The absence of any pre-selection in the VVDS leads us to have a very complete sample of AGN, including also objects with unusual colors and continuum shape. The VVDS AGN sample shows in fact redder colors than those expected by comparing it, for example, with the color track derived from the SDSS composite spectrum. In particular, the faintest objects have on average redder colors than the brightest ones. This can be attributed to both a large fraction of dust-reddened objects and a significant contamination from the host galaxy. We have tested these possibilities by examining the global spectral energy distribution of each object using, in addition to the U, B, V, R and I-band magnitudes, also the UV-Galex and the IR-Spitzer bands, and fitting it with a combination of AGN and galaxy emission, allowing also for the possibility of extinction of the AGN flux. We found that for 44% of our objects the contamination from the host galaxy is not negligible and this fraction decreases to 21% if we restrict the analysis to a bright subsample (M1450 <-22.15). Our estimated integral surface density at IAB < 24.0 is 500 AGN per square degree, which represents the highest surface density of a spectroscopically confirmed sample of optically selected AGN. We derived the luminosity function in B-band for 1.0 < z < 3.6 using the 1/Vmax estimator. Our data, more than one magnitude fainter than previous optical surveys, allow us to constrain the faint part of the luminosity function up to high redshift. A comparison of our data with the 2dF sample at low redshift (1 < z < 2.1) shows that the VDDS data can not be well fitted with the pure luminosity evolution (PLE) models derived by previous optically selected samples. Qualitatively, this appears to be due to the fact that our data suggest the presence of an excess of faint objects at low redshift (1.0 < z < 1.5) with respect to these models. By combining our faint VVDS sample with the large sample of bright AGN extracted from the SDSS DR3 (Richards et al., 2006b) and testing a number of different evolutionary models, we find that the model which better represents the combined luminosity functions, over a wide range of redshift and luminosity, is a luminosity dependent density evolution (LDDE) model, similar to those derived from the major Xsurveys. Such a parameterization allows the redshift of the AGN density peak to change as a function of luminosity, thus fitting the excess of faint AGN that we find at 1.0 < z < 1.5. On the basis of this model we find, for the first time from the analysis of optically selected samples, that the peak of the AGN space density shifts significantly towards lower redshift going to lower luminosity objects. The position of this peak moves from z 2.0 for MB <-26.0 to z 0.65 for -22< MB <-20. This result, already found in a number of X-ray selected samples of AGN, is consistent with a scenario of “AGN cosmic downsizing”, in which the density of more luminous AGN, possibly associated to more massive black holes, peaks earlier in the history of the Universe (i.e. at higher redshift), than that of low luminosity ones, which reaches its maximum later (i.e. at lower redshift). This behavior has since long been claimed to be present in elliptical galaxies and it is not easy to reproduce it in the hierarchical cosmogonic scenario, where more massive Dark Matter Halos (DMH) form on average later by merging of less massive halos.

De Novo Design of secondary structures: Synthesis and conformational studies

Chemists have long sought to extrapolate the power of biological catalysis and recognition to synthetic systems. These efforts have focused largely on low molecular weight catalysts and receptors; however, biological systems themselves rely almost exclusively on polymers, proteins and RNA, to perform complex chemical functions. Proteins and RNA are unique in their ability to adopt compact, well-ordered conformations, and specific folding provides precise spatial orientation of the functional groups that comprise the “active site”. These features suggest that identification of new polymer backbones with discrete and predictable folding propensities (“foldamers”) will provide a basis for design of molecular machines with unique capabilities. The foldamer approach complements current efforts to design unnatural properties into polypeptides and polynucleotides. The aim of this thesis is the synthesis and conformational studies of new classes of foldamers, using a peptidomimetic approach. Moreover their attitude to be utilized as ionophores, catalysts, and nanobiomaterials were analyzed in solution and in the solid state. This thesis is divided in thematically chapters that are reported below. It begins with a very general introduction (page 4) which is useful, but not strictly necessary, to the expert reader. It is worth mentioning that paragraph I.3 (page 22) is the starting point of this work and paragraph I.5 (page 32) isrequired to better understand the results of chapters 4 and 5. In chapter 1 (page 39) is reported the synthesis and conformational analysis of a novel class of foldamers containing (S)-β3-homophenylglycine [(S)-β3-hPhg] and D- 4-carboxy-oxazolidin-2-one (D-Oxd) residues in alternate order is reported. The experimental conformational analysis performed in solution by IR, 1HNMR, and CD spectroscopy unambiguously proved that these oligomers fold into ordered structures with increasing sequence length. Theoretical calculations employing ab initio MO theory suggest a helix with 11-membered hydrogenbonded rings as the preferred secondary structure type. The novel structures enrich the field of peptidic foldamers and might be useful in the mimicry of native peptides. In chapter 2 cyclo-(L-Ala-D-Oxd)3 and cyclo-(L-Ala-DOxd) 4 were prepared in the liquid phase with good overall yields and were utilized for bivalent ions chelation (Ca2+, Mg2+, Cu2+, Zn2+ and Hg2+); their chelation skill was analyzed with ESI-MS, CD and 1HNMR techniques and the best results were obtained with cyclo-(L-Ala-D-Oxd)3 and Mg2+ or Ca2+. Chapter 3 describes an application of oligopeptides as catalysts for aldol reactions. Paragraph 3.1 concerns the use of prolinamides as catalysts of the cross aldol addition of hydroxyacetone to aromatic aldeydes, whereas paragraphs 3.2 and 3.3 are about the catalyzed aldol addition of acetone to isatins. By means of DFT and AIM calculations, the steric and stereoelectronic effects that control the enantioselectivity in the cross-aldol addition of acetone to isatin catalysed by L-proline have been studied, also in the presence of small quantities of water. In chapter 4 is reported the synthesis and the analysis of a new fiber-like material, obtained from the selfaggregation of the dipeptide Boc-L-Phe-D-Oxd-OBn, which spontaneously forms uniform fibers consisting of parallel infinite linear chains arising from singleintermolecular N-H···O=C hydrogen bonds. This is the absolute borderline case of a parallel β-sheet structure. Longer oligomers of the same series with general formula Boc-(L-Phe-D-Oxd)n-OBn (where n = 2-5), are described in chapter 5. Their properties in solution and in the solid state were analyzed, in correlation with their attitude to form intramolecular hydrogen bond. In chapter 6 is reported the synthesis of imidazolidin-2- one-4-carboxylate and (tetrahydro)-pyrimidin-2-one-5- carboxylate, via an efficient modification of the Hofmann rearrangement. The reaction affords the desired compounds from protected asparagine or glutamine in good to high yield, using PhI(OAc)2 as source of iodine(III).

Genomic and transcriptional analysis of allergen genes in apple (Malus x domestica)

Apple consumption is highly recomended for a healthy diet and is the most important fruit produced in temperate climate regions. Unfortunately, it is also one of the fruit that most ofthen provoks allergy in atopic patients and the only treatment available up to date for these apple allergic patients is the avoidance. Apple allergy is due to the presence of four major classes of allergens: Mal d 1 (PR-10/Bet v 1-like proteins), Mal d 2 (Thaumatine-like proteins), Mal d 3 (Lipid transfer protein) and Mal d 4 (profilin). In this work new advances in the characterization of apple allergen gene families have been reached using a multidisciplinary approach. First of all, a genomic approach was used for the characterization of the allergen gene families of Mal d 1 (task of Chapter 1), Mal d 2 and Mal d 4 (task of Chapter 5). In particular, in Chapter 1 the study of two large contiguos blocks of DNA sequences containing the Mal d 1 gene cluster on LG16 allowed to acquire many new findings on number and orientation of genes in the cluster, their physical distances, their regulatory sequences and the presence of other genes or pseudogenes in this genomic region. Three new members were discovered co-localizing with the other Mal d 1 genes of LG16 suggesting that the complexity of the genetic base of allergenicity will increase with new advances. Many retrotranspon elements were also retrieved in this cluster. Due to the developement of molecular markers on the two sequences, the anchoring of the physical and the genetic map of the region has been successfully achieved. Moreover, in Chapter 5 the existence of other loci for the Thaumatine-like protein family in apple (Mal d 2.03 on LG4 and Mal d 2.02 on LG17) respect the one reported up to now was demonstred for the first time. Also one new locus for profilins (Mal d 4.04) was mapped on LG2, close to the Mal d 4.02 locus, suggesting a cluster organization for this gene family, as is well reported for Mal d 1 family. Secondly, a methodological approach was used to set up an highly specific tool to discriminate and quantify the expression of each Mal d 1 allergen gene (task of Chapter 2). In aprticular, a set of 20 Mal d 1 gene specific primer pairs for the quantitative Real time PCR technique was validated and optimized. As a first application, this tool was used on leaves and fruit tissues of the cultivar Florina in order to identify the Mal d 1 allergen genes that are expressed in different tissues. The differential expression retrieved in this study revealed a tissue-specificity for some Mal d 1 genes: 10/20 Mal d 1 genes were expressed in fruits and, indeed, probably more involved in the allergic reactions; while 17/20 Mal d 1 genes were expressed in leaves challenged with the fungus Venturia inaequalis and therefore probably interesting in the study of the plant defense mechanism. In Chapter 3 the specific expression levels of the 10 Mal d 1 isoallergen genes, found to be expressed in fruits, were studied for the first time in skin and flesh of apples of different genotypes. A complex gene expression profile was obtained due to the high gene-, tissue- and genotype-variability. Despite this, Mal d 1.06A and Mal d 1.07 expression patterns resulted particularly associated with the degree of allergenicity of the different cultivars. They were not the most expressed Mal d 1 genes in apple but here it was hypotized a relevant importance in the determination of allergenicity for both qualitative and quantitative aspects of the Mal d 1 gene expression levels. In Chapter 4 a clear modulation for all the 17 PR-10 genes tested in young leaves of Florina after challenging with the fungus V. inaequalis have been reported but with a peculiar expression profile for each gene. Interestingly, all the Mal d 1 genes resulted up-regulated except Mal d 1.10 that was down-regulated after the challenging with the fungus. The differences in direction, timing and magnitude of induction seem to confirm the hypothesis of a subfunctionalization inside the gene family despite an high sequencce and structure similarity. Moreover, a modulation of PR-10 genes was showed both in compatible (Gala-V. inaequalis) and incompatible (Florina-V. inaequalis) interactions contribute to validate the hypothesis of an indirect role for at least some of these proteins in the induced defense responses. Finally, a certain modulation of PR-10 transcripts retrieved also in leaves treated with water confirm their abilty to respond also to abiotic stress. To conclude, the genomic approach used here allowed to create a comprehensive inventory of all the genes of allergen families, especially in the case of extended gene families like Mal d 1. This knowledge can be considered a basal prerequisite for many further studies. On the other hand, the specific transcriptional approach make it possible to evaluate the Mal d 1 genes behavior on different samples and conditions and therefore, to speculate on their involvement on apple allergenicity process. Considering the double nature of Mal d 1 proteins, as apple allergens and as PR-10 proteins, the gene expression analysis upon the attack of the fungus created the base for unravel the Mal d 1 biological functions. In particular, the knowledge acquired in this work about the PR-10 genes putatively more involved in the specific Malus-V. inaequalis interaction will be helpful, in the future, to drive the apple breeding for hypo-allergenicity genotype without compromise the mechanism of response of the plants to stress conditions. For the future, the survey of the differences in allergenicity among cultivars has to be be thorough including other genotypes and allergic patients in the tests. After this, the allelic diversity analysis with the high and low allergenic cultivars on all the allergen genes, in particular on the ones with transcription levels correlated to allergencity, will provide the genetic background of the low ones. This step from genes to alleles will allow the develop of molecular markers for them that might be used to effectively addressed the apple breeding for hypo-allergenicity. Another important step forward for the study of apple allergens will be the use of a specific proteomic approach since apple allergy is a multifactor-determined disease and only an interdisciplinary and integrated approach can be effective for its prevention and treatment.

Transcriptional functions of DNA Topoisomerases at a genome-wide scale and a single gene levels

The DNA topology is an important modifier of DNA functions. Torsional stress is generated when right handed DNA is either over- or underwound, producing structural deformations which drive or are driven by processes such as replication, transcription, recombination and repair. DNA topoisomerases are molecular machines that regulate the topological state of the DNA in the cell. These enzymes accomplish this task by either passing one strand of the DNA through a break in the opposing strand or by passing a region of the duplex from the same or a different molecule through a double-stranded cut generated in the DNA. Because of their ability to cut one or two strands of DNA they are also target for some of the most successful anticancer drugs used in standard combination therapies of human cancers. An effective anticancer drug is Camptothecin (CPT) that specifically targets DNA topoisomerase 1 (TOP 1). The research project of the present thesis has been focused on the role of human TOP 1 during transcription and on the transcriptional consequences associated with TOP 1 inhibition by CPT in human cell lines. Previous findings demonstrate that TOP 1 inhibition by CPT perturbs RNA polymerase (RNAP II) density at promoters and along transcribed genes suggesting an involvement of TOP 1 in RNAP II promoter proximal pausing site. Within the transcription cycle, promoter pausing is a fundamental step the importance of which has been well established as a means of coupling elongation to RNA maturation. By measuring nascent RNA transcripts bound to chromatin, we demonstrated that TOP 1 inhibition by CPT can enhance RNAP II escape from promoter proximal pausing site of the human Hypoxia Inducible Factor 1 (HIF-1) and c-MYC genes in a dose dependent manner. This effect is dependent from Cdk7/Cdk9 activities since it can be reversed by the kinases inhibitor DRB. Since CPT affects RNAP II by promoting the hyperphosphorylation of its Rpb1 subunit the findings suggest that TOP 1inhibition by CPT may increase the activity of Cdks which in turn phosphorylate the Rpb1 subunit of RNAP II enhancing its escape from pausing. Interestingly, the transcriptional consequences of CPT induced topological stress are wider than expected. CPT increased co-transcriptional splicing of exon1 and 2 and markedly affected alternative splicing at exon 11. Surprisingly despite its well-established transcription inhibitory activity, CPT can trigger the production of a novel long RNA (5’aHIF-1) antisense to the human HIF-1 mRNA and a known antisense RNA at the 3’ end of the gene, while decreasing mRNA levels. The effects require TOP 1 and are independent from CPT induced DNA damage. Thus, when the supercoiling imbalance promoted by CPT occurs at promoter, it may trigger deregulation of the RNAP II pausing, increased chromatin accessibility and activation/derepression of antisense transcripts in a Cdks dependent manner. A changed balance of antisense transcripts and mRNAs may regulate the activity of HIF-1 and contribute to the control of tumor progression After focusing our TOP 1 investigations at a single gene level, we have extended the study to the whole genome by developing the “Topo-Seq” approach which generates a map of genome-wide distribution of sites of TOP 1 activity sites in human cells. The preliminary data revealed that TOP 1 preferentially localizes at intragenic regions and in particular at 5’ and 3’ ends of genes. Surprisingly upon TOP 1 downregulation, which impairs protein expression by 80%, TOP 1 molecules are mostly localized around 3’ ends of genes, thus suggesting that its activity is essential at these regions and can be compensate at 5’ ends. The developed procedure is a pioneer tool for the detection of TOP 1 cleavage sites across the genome and can open the way to further investigations of the enzyme roles in different nuclear processes.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.