In the present paper, we identify several distributions from Physics and study their applicability to phenomena such as distribution of income, wealth, and expenditure. Firstly, we apply logistic distribution to these data and we find that it fits very well the annual data for the entire income interval including for upper income segment of population. Secondly, we apply Fermi-Dirac distribution to these data. We seek to explain possible correlations and analogies between economic systems and statistical thermodynamics systems. We try to explain their behaviour and properties when we correlate physical variables with macroeconomic aggregates and indicators. Then we draw some analogies between parameters of the Fermi-Dirac distribution and macroeconomic variables. Thirdly, as complex systems are modelled using polynomial distributions, we apply polynomials to the annual sets of data and we find that it fits very well also the entire income interval. Fourthly, we develop a new methodology to approach dynamically the income, wealth, and expenditure distribution similarly with dynamical complex systems. This methodology was applied to different time intervals consisting of consecutive years up to 35 years. Finally, we develop a mathematical model based on a Hamiltonian that maximises utility function applied to Ramsey model using Fermi-Dirac and polynomial utility functions. We find some theoretical connections with time preference theory. We apply these distributions to a large pool of data from countries with different levels of development, using different methods for calculation of income, wealth, and expenditure.

Die Tourenbildung beschäftigt sich mit der Konstruktion kostengünstiger Transportrouten zur Belieferung von Verbrauchern. Sie ist eine der weitreichensten Erfolgsgeschichten des Operations Research. Das starke Interesse an diesen Problemen durch Industrie und Forschung liegt zum einen am wirtschaftlichen Potenzial der Tourenbildung und -optimierung, zum anderen macht ihr Reichtum an Struktur sie zu einem faszinierenden Forschungsgebiet. In der vorliegenden Arbeit soll ein Überblick über einige, u. a. auch neuere mathematische Modell- und Lösungsansätze gegeben werden. Auf Grund der hohen Anzahl der Veröffentlichungen auf diesem Gebiet wird nicht zwingend ein Anspruch auf die vollständige Darlegung aller möglichen Problemstellungen im Zusammenhang mit dem TSP sowie dem VRP und deren Lösungsansätze erhoben. An den gegebenen Stellen wird statt dessen auf weiterführende Literatur verwiesen.

>Magister Scientiae - MSc / This dissertation studies the computation methods of pricing of Asian options. Asian options are options in which the underlying variable is the average price over a period of time. Because of this, Asian options have a lower volatility and this render them cheaper relative to their European counterparts. Asian options belong to the so-called path-dependent derivatives; they are among the most difficult to price and hedge both analytically and numerically. In practice, it is only discrete Asian options that are traded, however continuous Asian options are used for studying purposes. Several approaches have been proposed in the literature, including Monte Carlo simulations, tree-based methods, Taylor’s expansion, partial differential equations, and analytical ap- proximations among others. When using partial differential equations for pricing of continuous time Asian options, the high dimensionality is problematic. In this dissertation we focus on the discrete time methods. We start off by explaining the binomial tree method, and our last chapter presents the very exciting and relatively simple method of Tsao and Huang, using Taylor approximations. The main papers that are used in this dissertation are articles by Jan Vecer (2001); LCG Rogers (1995); Eric Benhamou (2001); Gianluca Fusai (2007); Kamizono, Kariya and Nakatsuma (2006) and Tsao and Huang (2007). The author has provided computations, including graphs and tables dispersed over the different chapters, to demonstrate the utility of the methods. We observe various parameters of influence such as correlation, volatility, strike, etc. A further contribution by the author of this dissertation is, in particular, in Chapter 5, in the presentation of the work of Tsao et al. Here we have provided slightly more detailed explanations and again some further computational tables.

Synchronizace inflačních cyklů je jednou z podmínek teorie optimální měnové unie, a jelikož bude jednoho dne valná většina členských států EU používat euro, zdá se analýza konvergence jejich inflačních měr jako rozumná i z dnešního pohledu. Používáme data měřítka harmonizovaného indexu spotřebitelských cen, jakož i velmi flexibilní model zdánlivě nesouvisejících regresních modelů a podáváme důkaz o všeobecně rozšířeném, setrvalém a robustním výskytu konvergence inflace v celé EU mezi lety 1999 a 2016. Navíc nám naše metodologie umožňuje zahrnout do modelu řadu dummy proměnných indikujících konkrétní období s možným dopadem na konvergenci inflace. V tomto smyslu ukazujeme, že měnové režimy zaměřené na cenovou stabilitu (inflační cílování, opatření omezující pohyb měnového kurzu) mají příznivý dopad, období globální finanční krize a nulové dolní meze se obecně nejeví jako rušivé, zatímco efekt zavádění společného evropského práva zůstává nejistý. Naše hlavní závěry implikují, že synchronizace inflace zřejmě nepředstavuje problém pro další rozšíření Eurozóny.

The paper examines the hypothesis that the devaluation of the domestic currency leads to the higher exchange rate pass-through at the zero lower bound since the interest rate channel cannot offset effects of the depreciation in that situation. Time-varying vector autoregression with stochastic volatility is used to identify the development of the pass-through. The hypothesis is tested on the Czech dataset because the Czech Republic is considered as the prototypical small open economy with inflation targeting. The assumption of higher pass-through to consumer prices at the zero lower bound is rejected. Obtained results confirm that the deprecation stimulates output growth slightly more when the interest rate is close to zero. Our estimations imply that the exchange rate commitment of the Czech National Bank increased the price level by 0.116 % and contributed to the output growth by 0.781 %.

Dans ce travail, nous présentons trois nouveaux algorithmes pour le problème de la clique de poids maximum. Les trois algorithmes dépendent d'un ordre initial des sommets. Deux ordres sont considérés, l'un en fonction de la pondération des sommets et l'autre en fonction de la taille voisinage des sommets. Le premier algorithme, que nous avons appelé BITCLIQUE, est une algorithme de séparation et évaluation. Il réunit efficacement plusieurs idées déjà utilisées avec succès pour résoudre le problème, comme l'utilisation d'une heuristique de coloration pondérée en nombres entiers pour l'évaluation ; et l'utilisation de vecteurs de bits pour simplifier les opérations sur le graphe. L'algorithme proposé surpasse les algorithmes par séparation et évaluation de l'état de l'art sur la plupart des instances considérées en terme de nombre de sous-problèmes énumérés ainsi que en terme de temps d'exécution. La seconde version est un algorithme des poupées russes, BITRDS, qui intègre une stratégie d'évaluation et de ramification de noeuds basée sur la coloration pondérée. Les simulations montrent que BITRDS réduit à la fois le nombre de sous-problèmes traités et le temps d'exécution par rapport à l'algorithme de l'état de l'art basée sur les poupées russes sur les graphes aléatoires avec une densité supérieure à 50%. Cette différence augmente à la mesure que la densité du graphe augmente. D'ailleurs, BITRDS est compétitif avec BITCLIQUE avec une meilleure performance sur les instances de graphes aléatoires avec une densité comprise entre 50% et 80%. Enfin, nous présentons une coopération entre la méthode poupées russes et la méthode de ``Resolution Search''. L'algorithme proposé, appelé BITBR, utilise au même temps la coloration pondérée et les limites supérieures donnés par les poupées pour trouver un ``nogood''. L'algorithme hybride réduit le nombre d'appels aux heuristiques de coloration pondérée, atteignant jusqu'à 1 ordre de grandeur par rapport à BITRDS. Plusieurs simulations sont réalisées avec la algorithmes proposés et les algorithmes de l'état de l'art. Les résultats des simulations sont rapportés pour chaque algorithme en utilisant les principaux instances disponibles dans la littérature. Enfin, les orientations futures de la recherche sont discutées. / In this work, we present three new exact algorithms for the maximum weight clique problem. The three algorithms depend on an initial ordering of the vertices. Two ordering are considered, as a function of the weights of the vertices or the weights of the neighborhoods of the vertices. This leads to two versions of each algorithm. The first one, called BITCLIQUE, is a combinatorial Branch & Bound algorithm. It effectively combines adaptations of several ideas already successfully employed to solve the problem, such as the use of a weighted integer coloring heuristic for pruning and branching, and the use of bitmap for simplifying the operations on the graph. The proposed algorithm outperforms state-of-the-art Branch & Bound algorithms in most instances of the considered in terms of the number of enumerated subproblems as well in terms of computational time The second one is a Russian Dolls, called BITRDS, which incorporates the pruning and branching strategies based on weighted coloring. Computational tests show that BITRDS reduces both the number of enumerated subproblems and execution time when compared to the previous state-of-art Russian Dolls algorithm for the problem in random graph instances with density above 50%. As graph density increases, this difference increases. Besides, BITRDS is competitive with BITCLIQUE with better performance in random graph instances with density between 50% and 80%. Finally, we present a cooperation between the Russian Dolls method and the Resolution Search method. The proposed algorithm, called BITBR, uses both the weighted coloring and upper bounds given by the dolls to find a nogood. The hybrid algorithm reduces the number of coloring heuristic calls, reaching up to 1 order of magnitude when compared with BITRDS. However, this reduction decreases the execution time only in a few instances. Several computational experiments are carried out with the proposed and state-of-the-art algorithms. Computational results are reported for each algorithm using the main instances available in the literature. Finally, future directions of research are discussed.

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The binding of different proteins involved in processes such as transcription, replication and chromatin compaction to regions of the genome is regulated by the structure of DNA. Thus, DNA structure acts as the crucial link modulating evolutionary selection of the DNA sequence based on its own function, and the function of the proteins it encodes. The aim of this work is to examine the role of intrinsic, sequence-dependent structural variations vis-a -vis the protein-induced variations, in allowing DNA to assume geometries necessary for binding by proteins. For this purpose, we carried out analyses of datasets of X-ray crystal structures of free and protein-bound DNA, and molecular dynamics simulation studies of few free DNA structures and a protein-DNA complex. Each of the projects described below will appear as a separate chapter in the thesis. Analysis of X-ray crystal structure datasets Dataset of high-resolution X-ray crystal structures of free and protein-bound DNA This project was initiated with the aim of investigating the variation in A-and B-forms of DNA and the role they play in the binding of proteins. However, a survey of the existing literature indicated that the terms ‘A-DNA’ and ‘B-DNA’ were being used rather loosely and several different parameters at the local structural level were being used by various investigators to characterise these structures. Hence a systematic study was taken up to analyse all high-resolution free DNA structures comprising of sufficient number of contiguous Watson-Crick basepairs, irrespective of how they were classified by the existing databases. We also carried out a study of double-helical, Watson-Crick basepaired, free RNA structures for comparison. The structures in the RNA dataset were observed to rigidly assume the A-form and hence the average values of different parameters for that dataset were used to characterise the A-form. The analysis of free DNA and RNA structures was accompanied by an analysis of protein-bound DNA crystal structures. DNA structures bound to the helix-turn-helix motif in proteins were also analysed separately. The analysis of free DNA and RNA structures allowed us to pinpoint the parameters suitable for discriminating A-and B-forms of DNA at the local structural level. The results illustrated that the free DNA molecule, even in the crystalline state, samples a large amount of conformational space, encompassing both the A-and the B-forms. Most protein-bound DNA structures, including those with large, smooth curvature, were observed to assume the B-form. The A-form was observed to be limited to a small number of dinucleotide steps in DNA structures bound to the proteins belonging to a few specific families. Thus our study highlighted the structural versatility of B-form DNA, which allowed it to take up a range of global geometries to accommodate most DNA-binding protein motifs. Dataset of X-ray crystal structures of the nucleosome The study of high-resolution structures of free and protein-bound DNA was followed by an analysis of a dataset of X-ray crystal structures of the nucleosome, which is the fundamental repeating unit of the eukaryotic chromosome, and has been shown to play an important role in transcription regulation. Our results indicated that there is an ensemble of dinucleotide and trinucleotide level parameters that can give rise to similar global nucleosome structures. We therefore raise doubts about the use of the best resolved nucleosome structure as the template to calculate the energy required by putative nucleosome-forming sequences for adopting the nucleosome structure. Based on our results, we have proposed that the local and global level structural variability of DNA may act as a significant factor influencing the formation of nucleosomes in the vicinity of high-plasticity genes, and in determining the probability of binding by regulatory proteins. Molecular dynamics simulation studies of free and protein-bound DNA structures The analysis of crystal structure databases was complemented by molecular dynamics (MD) studies to investigate the dynamic evolution of the DNA structure in its free and protein-bound states. The following three simulation studies were carried out: Study to examine the biological relevance of the presence of 5-methyl group in thymine nucleotides An investigation of the biological relevance of the 5-methyl group in thymine nucleotides was carried out. For this purpose, comparison of molecular dynamics studies on structures with sequences d(CGCAAAUUUGCG)2and d(CGCAAATTTGCG)2was carried out. Our results showed that the presence of the thymine 5-methyl group was necessary for the A-tract to assume characteristic properties such as a narrow minor groove. It was also shown to modulate local level structural parameters and consequently, the curvature of the longer DNA fragment in which the A-tract was embedded. The analysis also provided possible explanation for the experimentally observed interaction of A-tracts with drugs and DNase-I in the presence and the absence of the thymine 5-methyl group. This project was the first of a series of MD studies, and hence several protocols were tested before finalising the correct protocol. Simulations were carried out using the Berendsen temperature equilibration scheme as well as the Langevin temperature equilibration scheme on both the structures. The Langevin temperature equilibration scheme was found to be unsuitable for nucleic acid simulations, as it caused long-term and possibly permanent disruption of the double-helical structure at the terminal and the neighbouring two positions in the sequence. The Berendsen temperature equilibration scheme was not observed to cause such disruptions. Simulations were also carried out on both structures, with or without initialising the initial ion positions. The position of minimum electrostatic potential, where AMBER8 placed the first counterion, was observed to act as a minimum energy trap from which the counterion could not escape even during the course of several nanoseconds of simulation. Hence, the actual simulations were carried out using the Berendsen temperature equilibration scheme, and after randomisation of initial ion positions. The results of protocol testing have been reported in an appendix. Study of DNA bending and curvature An analysis of DNA bending and curvature was carried out, by MD simulation on structures of three, ∼thirty basepair long sequences, namely, d(G-3(CA4T4G)-C)2, d(G-3(CT4A4G)-C)2and d(T-GACTA5T-GACTA6T-GACTA5T-G). For each molecule, snapshots belonging to a particular global geometry (linear, curved, bent in a particular direction etc.) were grouped together, and the average values of the dinucleotide step parameters for different groups were compared. It was observed that for all the three molecules, the average values for groups corresponding to different global geometries were within 1of each other, indicating that ensemble average values of dinucleotide level parameters are incapable of predicting the global geometry of a DNA molecule. Study of the TraR-Trabox complex The study on DNA bending and curvature was followed by simulations of a protein-DNA complex comprising of the bacterial quorum sensing transcription factor TraR with its promoter region known as Trabox. Simulations of a protein-free wild-type Trabox and a Trabox with two mutations in the spacer region were also carried out. Grouping of DNA snapshots in all the three simulations based on average values of dinucleotide parameters in the spacer region shows how selection of the ‘right’ DNA geometry by proteins works at several levels. The number of snapshots of free mutated Trabox assuming a geometry favourable for protein-binding in terms of average twist alone are less than one-fourth of the corresponding number for free wild-type Trabox. When one applies further selection criteria in terms of other parameters such as roll and slide, the number of mutated Trabox snapshots with a geometry favourable for protein-binding drops to less than 0.5%ofthe total number of MD snapshots. Thus our results highlight how sequence-dependent changes in the structrure of DNA regions, adjacent to those that directly hydrogen-bond to proteins, can also critically influence processes such as transcription. General Conclusion Overall, our results indicate that intrinsic, sequence-dependent structural variations in free B-DNA allow it to sample a large volume of the double-helical conformational space, and assume global geometries that can accomodate most DNA-binding proteins.

Dans le contexte actuel marqué par l’instabilité des marchés, les clients sont de plus en plus exigeants. un client qui n’est pas approvisionné à une date souhaitée peut soit remettre son achat à plus tard, soit aller chercher le produit chez un concurrent. de plus, l’entreprise doit faire face à de multiples imprévisibilités internes, de la concurrence ou d’événements extérieurs. ces aléas induisent de l'incertitude dans la planification de la production et génèrent des sources nombreuses de retard, de désynchronisation et de pertes de productivité. ce travail de thèse s’intègre dans la problématique de la planification de la production dans un environnement incertain. nous étudions des problèmes de la planification des réapprovisionnements pour un système d’assemblage à plusieurs niveaux, quand les délais d’approvisionnement sont incertains. nous avons choisi comme indicateur de performance l’espérance du coût total moyen qui est égal à la somme du coût de stockage des composants, le coût de rupture du produit fini et le coût de stockage du produit fini. des propriétés théoriques, des modèles analytiques ainsi que des méthodes d’optimisation ont été proposés. nous avons montré que la résolution du problème ne dépend pas seulement de la méthode de résolution et du nombre de niveaux, mais aussi du coût de rupture en produit fini et de la structure du système d’assemblage. / In the current industrial context, the offer is largely higher than the demand. Therefore, the customers are more and more exigent. To distance themselves, companies need to offer to their customers the best quality products, the best costs, and with controlled lead times as short as possible. Last years, the struggle for reducing costs was accentuated within companies. However, stocks represent an important financial asset, and therefore, it is essential to control them. In addition, a bad management of stocks led either to delays in delivery, which generate additional production costs, either to the unnecessary inventory. The latter one can occur at different levels (from components at the last level to finished product), it costs money and immobilize funds. That is why, planners have to look for efficient methods of production and supply planning, to know exactly for each component, and when to order and in which quantity.The aim of this doctoral thesis is to investigate the supply planning in an uncertain environment. We are interested in a replenishment planning for multi-level assembly systems under a fixed demand and uncertainty of components lead times.We consider that each component has a fixed unit inventory cost; the finished product has an inventory cost and a backlogging cost per unit of time. Then, a general mathematical model for replenishment planning of multi-level assembly systems, genetic algorithm and branch and bound method are presented to calculate and to optimize the expected value of the total cost which equals to the sum of the inventory holding costs for the components, the backlogging and the inventory holding costs for the finished product. We can state by the different results that the convergence of the GA doesn't depend only on the number of components in the last level but also on the number of levels, the type of the BOM and the backlogging cost for the finished product.