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La structure de projet se retrouve dans de nombreux contextes de l'industrie et des services. Il s'agit de réaliser un ensemble d'activités pouvant être connectées par des liens logiques de séquence (antériorité), en faisant appel à des ressources disponibles en quantité limitée. L'objectif est la minimisation d'un critère généralement lié à la durée ou au coût du projet. La plupart des problèmes d'ordonnancement de projet dans la littérature considèrent une unité de temps commune pour la détermination des dates d'exécution des activités et pour l'évaluation instantanée du respect des capacités des ressources qu'elles utilisent. Or, s'il est souvent nécessaire en pratique d'obtenir un calendrier détaillé des plages d'exécution des activités, l'utilisation des ressources peut être évaluée sur un horizon plus agrégé, comme par exemple les quarts de travail des employés. Dans cette thèse, un nouveau modèle intégrant ces deux échelles de temps est présenté afin de définir le problème d'ordonnancement de projet avec agrégation périodique des contraintes de ressources (PARCPSP). Ce problème est étudié du point de vue de la théorie de la complexité et des propriétés structurelles sont établies, mettant notamment en évidence des différences majeures avec le problème classique d'ordonnancement de projet sous contraintes de ressources (RCPSP). De ces propriétés sont dérivées des formulations exactes basées sur la programmation linéaire en nombres entiers, comparées en termes de qualité de la relaxation linéaire. Par ailleurs, plusieurs heuristiques, telles que des algorithmes de liste, ou une méthode approchée basée sur une résolution itérative qui exploite différentes échelles de temps, sont proposées. Les résultats expérimentaux montrent l'intérêt de ces différentes méthodes et illustrent la difficulté du problème. / The project structure arises in many fields of industry and services. It consists in performing a set of activities that may be linked by precedence relations, and use resources whose capacity is limited. The objective is to minimize a criterion usually linked to the duration or the cost of the project. Most of project scheduling problems in the literature assume that the same time scale should be used to determine activity start and completion dates and check resource constraints at each time. However, although it is often required in practice to build a precise schedule specifying the execution range of each activity, the resource usage can be evaluated on an aggregated basis, like worker shifts. In this thesis, a new model that enables the integration of these two time scales is presented in order to define the periodically aggregated resource-constrained project scheduling problem (PARCPSP). This problem is studied within the framework of complexity theory and several structural properties are established, highlighting major differences with the standard resource-constrained project scheduling problem (RCPSP). These properties allow deriving exact formulations based on integer linear programming, whose linear relaxations are compared. Moreover, several heuristics, such as schedule generations schemes, or an approached method based on a multi time scale iterative process, are proposed. Experimental results show the interest of these different methods and point out the intractability of the problem.

We explore the problem of transforming plane triangulations using simultaneous diagonal flips. Wagner showed that any n-vertex plane triangulation can be transformed to any other plane triangulation on equal number of vertices using a finite sequence of diagonal flips. Later on it has been established that O(n) individual flips suffice to complete this transformation. Bose et al. showed that the transformation can also be done in 4 × ( 2 / log 54/53 + 2 / log 6/5 ) logn + 2 ≈ 327.1 log n simultaneous flips. This bound is asymptotically tight. We present two algorithms to improve the leading coefficient of this bound for transforming any plane triangulation into any other. The first of the two algorithms lowers this bound down to 4 × ( 2 / log 12/11 + 2 / log 9/7 ) logn + 2 ≈ 85.8 log n. By processing and preprocessing the interior and exterior of the triangulation’s Hamiltonian cycle parallelly in an interlaced fashion, we make further improvement of the algorithm from ≈ 327.1 log n down to 12 / log 6/5 logn + 2 ≈ 45.6 log n.

In this thesis, we undertake a combinatorial study of certain aspects of triangulations of cartesian products of simplices, particularly in relation to their relevance in toric algebra and to their underlying product structure. The first chapter reports joint work with Samu Potka. The object of study is a class of homogeneous toric ideals called cut ideals of graphs, that were introduced by Sturmfels and Sullivant 2006. Apart from their inherent appeal to combinatorial commutative algebra, these ideals also generalize graph statistical models for binary data and are related to some statistical models for phylogenetic trees. Specifically, we consider minimal free resolutions for the cut ideals of trees. We propose a method to combinatorially estimate the Betti numbers of the ideals in this class. Using this method, we derive upper bounds for some of the Betti numbers, given by formulas exponential in the number of vertices of the tree. Our method is based on a common technique in commutative algebra whereby arbitrary homogeneous ideals are deformed to initial monomial ideals, which are easier to analyze while conserving some of the information of the original ideals. The cut ideal of a tree on n vertices turns out to be isomorphic to the Segre product of the cut ideals of its n-1 edges (in particular, its algebraic properties do not depend on its shape). We exploit this product structure to deform the cut ideal of a tree to an initial monomial ideal with a simple combinatorial description: it coincides with the edge ideal of the incomparability graph of the power set of the edges of the tree. The vertices of the incomparability graph are subsets of the edges of the tree, and two subsets form an edge whenever they are incomparable. In order to obtain algebraic information about these edge ideals, we apply an idea introduced by Dochtermann and Engström in 2009 that consists in regarding the edge ideal of a graph as the (monomial) Stanley-Reisner ideal of the independence complex of the graph. Using Hochster\''s formula for computting Betti numbers of Stanley-Reisner ideals by means of simplicial homology, the computation of the Betti numbers of these monomial ideals is turned to the enumeration of induced subgraphs of the incomparability graph. That the resulting values give upper bounds for the Betti numbers of the cut ideals of trees is an important well-known result in commutative algebra. In the second chapter, we focus on some combinatorial features of triangulations of the point configuration obtained as the cartesian product of two standard simplices. These were explored in collaboration with César Ceballos and Arnau Padrol, and had a two-fold motivation. On the one hand, we intended to understand the influence of the product structure on the set of triangulations of the cartesian product of two point configurations; on the other hand, the set of all triangulations of the product of two simplices is an intricate and interesting object that has attracted attention both in discrete geometry and in other fields of mathematics such as commutative algebra, algebraic geometry, enumerative geometry or tropical geometry. Our approach to both objectives is to examine the circumstances under which a triangulation of the polyhedral complex given by the the product of an (n-1)-simplex times the (k-1)-skeleton of a (d-1)-simplex extends to a triangulation of an (n-1)-simplex times a (d-1)-simplex. We refer to the former as a partial triangulation of the product of two simplices. Our main result says that if d >= k > n, a partial triangulation always extends to a uniquely determined triangulation of the product of two simplices. A somewhat unexpected interpretation of this result is as a finiteness statement: it asserts that if d is sufficiently larger than n, then all partial triangulations are uniquely determined by the (compatible) triangulations of its faces of the form “(n-1)-simplex times n-simplex”. Consequently, one can say that in this situation ‘\''triangulations of an (n-1)-simplex times a (d-1)-simplex are not much more complicated than triangulations of an (n-1)-simplex times an n-simplex\''\''. The uniqueness assertion of our main result holds already when d>=k>=n. However, the same is not true for the existence assertion; namely, there are non extendable triangulations of an (n-1)-simplex times the boundary of an n-simplex that we explicitly construct. A key ingredient towards this construction is a triangulation of the product of two (n-1)-simplices that can be seen as its ``second simplest triangulation\''\'' (the simplest being its staircase triangulation). It seems to be knew, and we call it the Dyck path triangulation. This triangulation displays symmetry under the cyclic group of order n that acts by simultaneously cycling the indices of the points in both factors of the product. Next, we exhibit a natural extension of the Dyck path triangulation to a triangulation of an (n-1)-simplex times an n-simplex that, in a sense, enjoys some sort of ‘\''rigidity\''\'' (it also seems new). Performing a ‘\''local modification\''\'' on the restriction of this extended triangulation to the polyhedral complex given by (n-1)-simplex times the boundary of an n-simplex yields the non-extendable partial triangulation. The thesis includes two appendices on basic commutative algebra and triangulations of point configuration, included to make it slightly self-contained.

Accurate, timely replication of a DNA molecule is a pivotal moment in the life cycle of every living organism. Any temporal or spatial defect putting the fine-tuned replication machinery off balance causes the so-called replication stress. As the replication machinery consists mainly of enzymes and other proteins, it is not surprising that many of the obstacles most severely blocking the replication machinery progress are of protein origin. Therefore, specialized proteases responsible for relieving replication stress matured during evolution. However, neither the full repertoire of proteolytic enzymes and their particular substrates taking place in countering the DNA replication stress nor detailed molecular mechanisms involved remain unknown. This thesis describes how conserved putative aspartic proteases of the Ddi1-like family engage in countering DNA replication stress via a proteolysis dependent mechanism. We structurally and biophysically characterized yeast and human members of the Ddi1-like family, explored their interactions with ubiquitin and polyubiquitin chains, and identified hypersensitivity to DNA replication inhibitor hydroxyurea in a yeast strain double deleted for DDI1 gene together with a DNA dependent metalloprotease WSS1. Detailed analysis of the DDI1 role in hydroxyurea...

The rapid development of the gene engineering techniques, especially methods for in vitro directed evolution and combinatorial mutagenesis, has triggered the generation of new binding agents to almost any antigen of interest as an alternative to broadly used antibodies. These so-called non-Ig scaffolds are often derived from proteins with useful biophysical properties. While the therapeutic market is still dominated by monoclonal antibodies, the easy option of desired customization of non-Ig binders by conventional methods of gene engineering predestine them largely for the use in the diagnostic area. The ABD scaffold, derived from a three-helix bundle of albumin-binding domain of streptococcal protein G, represents one of the small non-Ig scaffolds. In our laboratory, we have established a highly complex combinatorial library developed on the ABD scaffold. This ABD scaffold-derived library was used to generate unique binders of human prostate cancer (PCa) biomarkers PSP94, KLK2, KLK11 for the more precise diagnosis of PCa. The second part of the thesis describes the generation of ABD-derived binders selectively recognizing different phenotypes of circulating tumor cells as a binding component of the cell capture zone of microfluidic chip for lung adenocarcinoma diagnosis. Beside this already...

<p>Recent innovations in combinatorial dynamical systems permit them to be studied with algorithmic methods. One such method from topological data analysis, called persistent homology, allows one to summarize the changing homology of a sequence of simplicial complexes. This dissertation explicates three methods for capturing and summarizing changes in combinatorial dynamical systems through the lens of persistent homology. The first places the Conley index in the persistent homology setting. This permits one to capture the persistence of salient features of a combinatorial dynamical system. The second shows how to capture changes in combinatorial dynamical systems at different resolutions by computing the persistence of the Conley-Morse graph. Finally, the third places Conley's notion of continuation in the combinatorial setting and permits the tracking of isolated invariant sets across a sequence of combinatorial dynamical systems. </p>

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In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific real-life applications. Owning to their specific nature, these problems are different from those discussed in the literature. For each of these problems, we present a mathematical programming formulation, analyze the problem to determine its useful, inherent structural properties, and develop an efficient methodology for its solution by exploiting these properties. The first problem that we address is the course timetabling problem encountered at Virginia Tech. The course timetabling problem for a university is a difficult problem and has been studied by many researchers over the years. As a result, a plethora of models and approaches have been reported in the literature. However, most of these studies have focused on applications pertaining to course scheduling for a single or at most few departments of a university. The sheer size of the university-wide timetabling problem that we address, involving thousands of courses to be scheduled in hundreds of classrooms in each semester, makes it a challenging problem. We employ an appropriate decomposition technique that relies on some inherent structural properties of the problem both during the modeling and algorithmic development phases. We show the superiority of the schedules generated by our methodology over those that are currently being used. Also, our methodology requires only a reasonable amount of computational time in solving this large-size problem. A facility layout problem involving arbitrary-shaped departments is the second problem that we investigate in this dissertation. We designate this problem as the arbitrary-shaped facility layout problem (ASFLP). The ASFLP deals with arranging a given set of departments (facilities, workstations, machines) within the confines of a given floor space, in order to optimize a desired metric, which invariably relates to the material handling cost. The topic of facility planning has been addressed rather extensively in the literature. However, a major limitation of most of the work reported in the literature is that they assume the shape of a department to be a rectangle (or even a square). The approach that relies on approximating an arbitrary-shaped department by a rectangle might result in an unattractive solution. The key research questions for the ASFLP are: (1) how to accurately model the arbitrary-shaped departments, and (2) how to effectively and efficiently determine the desired layout. We present a mixed-integer programming model that maintains the arbitrary shapes of the departments. We use a meta-heuristic to solve the large-size instances of the ASFLP in a reasonable amount of time. The third problem that we investigate is a supply chain scheduling problem. This problem involves two stages of a supply chain, specifically, a manufacturer and one or more customers. The key issue is to achieve an appropriate coordination between the production and distribution functions of the manufacturer so as to minimize the sum of the shipping and job tardiness costs. We, first, address a single customer problem, and then, extend our analysis to the case of multiple customers. For the single-customer problem, we present a polynomial-time algorithm to solve it to optimality. For the multiple-customer problem, we prove that this problem is NP-hard and solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. We propose a branch-and-bound-based methodology for this problem that exploits its structural properties. Results of an extensive computational experimentation are presented that show the following: (1) our algorithms are efficient to use and effective to implement; and (2) significant benefits accrue as a result of integrating the production and distribution functions. / Ph. D.

Le crowdsourcing est une pratique permettant aux entreprises de faire appel à l’intelligence humaine à grande échelle afin d’apporter des solutions à des problématiques qu’elles souhaitent externaliser. Les problématiques externalisées sont de plus en plus complexes et ne peuvent être résolues individuellement. Nous proposons dans cette thèse une approche appelée SocialCrowd, contribuant à améliorer la qualité des résultats de crowdsourcing. Elle consiste à faire collaborer les participants afin d’unir leur capacité de résolution et apporter des solutions aux problèmes externalisés de plus en plus complexes. Les groupes collaboratifs sont mis en compétition, via des rétributions attrayantes, afin d’obtenir de meilleures résolutions. Par ailleurs, il est nécessaire de protéger les données privées des groupes en compétition. Nous utilisons les réseaux sociaux comme support de fuite de données. Nous proposons une approche basée sur l’algorithme Dijkstra pour estimer la probabilité de propagation de données privées d’un membre sur le réseau social. Ce calcul est complexe étant donné la taille des réseaux sociaux. Une parallélisation du calcul est proposée suivant le modèle MapReduce. Un algorithme de classification basé sur le calcul de propagation dans les réseaux sociaux est proposé permettant de regrouper les participants en groupes collaboratifs et compétitifs tout en minimisant les fuites de données d’un groupe vers l’autre. Comme ce problème de classification est d’une complexité combinatoire, nous avons proposé un algorithme de classification basé sur les algorithmes d’optimisation combinatoires tels que le recuit simulé et les algorithmes génétiques. Etant donnée le nombre important de solutions possible, une approche basée sur le modèle du Soft Constraint Satisfaction Problem (SCSP) est proposée pour classer les différentes solutions. / Crowdsourcing is the practice of allowing companies to use human intelligence scale to provide solutions to issues they want to outsource. Outsourced issues are increasingly complex and cannot be resolved individually. We propose in this thesis an approach called SocialCrowd, helping to improve the quality of the results of crowdsourcing. It compromise to collaborate participants to unite solving ability and provide solutions to outsourced problems more and more complex. Collaborative groups are put in competition through attractive remuneration, in order to obtain better resolution. Furthermore, it is necessary to protect the private information of competing groups. We use social media as a support for data leakage. We propose an approach based on Dijkstra algorithm to estimate the propagation probability of private data member in the social network. Given the size of social networks, this computation is complex. Parallelization of computing is proposed according to the MapReduce model. A classification algorithm based on the calculation of propagations in social networks is proposed for grouping participants in collaborative and competitive groups while minimizing data leaks from one group to another. As this classification problem is a combinatorial complexity, we proposed a classification algorithm based on combinatorial optimization algorithms such as simulated annealing and genetic algorithms. Given the large number of feasible solutions, an approach based on the model of Soft Constraint Satisfaction Problem (SCSP) is proposed to classify the different solutions.