Solving hard industrial combinatorial problems with SAT

The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis. Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible: - Reducing the complex constraints into propositional clauses. - Enriching the SAT Solver language. The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators. The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems. However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered

Genetic control of meiosis surveillance mechanisms in mammals

Meiosis is a specialized cell division that generates haploid gametes and is critical for successful sexual reproduction. During the extended meiotic prophase I, homologous chromosomes progressively pair, synapse and desynapse. These chromosomal dynamics are tightly integrated with meiotic recombination (MR), during which programmed DNA double-strand breaks (DSBs) are formed and subsequently repaired. Consequently, parental chromosome arms reciprocally exchange, ultimately ensuring accurate homolog segregation and genetic diversity in the offspring. Surveillance mechanisms carefully monitor the MR and homologous chromosome synapsis during meiotic prophase I to avoid producing aberrant chromosomes and defective gametes. Errors in these critical processes would lead to aneuploidy and/or genetic instability. Studies of mutation in mouse models, coupled with advances in genomic technologies, lead us to more clearly understand how meiosis is controlled and how meiotic errors are linked to mammalian infertility. Here, we review the genetic regulations of these major meiotic events in mice and highlight our current understanding of their surveillance mechanisms. Furthermore, we summarize meiotic prophase genes, the mutations that activate the surveillance system leading to meiotic prophase arrest in mouse models, and their corresponding genetic variants identified in human infertile patients. Finally, we discuss their value for the diagnosis of causes of meiosis-based infertility in humans

Classification of plane germs: metric and valorative properties

In this memory we follow the geometric approach of Casas’ boof [1] for studying of the singularities of plane germs of curves, which updates Enriques’ works to modern standards and reviews the modern development of the theorey from the point of view of infinitely near points. This memory has a two sided goal: on one hand, we want to acquire skills with the tools and concepts of the singularity theory and the valuative theory, both the classical ones and the more recent ones. On the other hand, we want to study in depth the different implicit concepts and notions involved in the Favre and Jonsson’s new approach, such as the ultrametric space structure of the set of irreducible germs of plane curves and the tree structure of the valuations

Meiosis in a Bottle : New Approaches to Overcome Mammalian Meiocyte Study Limitations

The study of meiosis is limited because of the intrinsic nature of gametogenesis in mammals. One way to overcome these limitations would be the use of culture systems that would allow meiotic progression in vitro. There have been some attempts to culture mammalian meiocytes in recent years. In this review we will summarize all the efforts to-date in order to culture mammalian sperm and oocyte precursor cells

Un Mateix camí amb dreceres diferents en funció del sexe: gametogènesi femenina

En humans, les aneuploïdies s'originen principalment a causa d'errors en la gametogènesi femenina. Aquest fenomen fa de l'oogènesi un tema d'estudi atractiu, tot i que per la dificultat que comporta l'obtenció de mostres no existeixen molts estudis al respecte. En aquest treball, es resumeix l'estat actual del problema, i es para especial atenció a les diferències existents entre la gametogènesi masculina i femenina que puguin explicar l'origen d'aquest important problema per a la societat actual.In humans, aneuploidy is mainly originated by errors produced during female gametogenesis. This phenomenon makes oogenesis such an attractive research topic, but due to the difficulties involving sample collection, not many studies have been performed in human oocytes. In this paper, a summary of the current knowledge about human female meiosis is provided, specially focusing on the differences between male and female gametogenesis that may explain the origin of such an important topic for Western society

p53 Controls Meiotic Prophase Progression and Crossover Formation

Meiosis initiates with the formation of double strand breaks (DSBs) throughout the genome. To avoid genomic instability, these DSBs need to be correctly repaired by homologous recombination. Surveillance mechanisms involving the DNA damage response (DDR) pathway ATM-CHK2-p53 can detect the persistence of unrepaired DBSs and activate the recombination-dependent arrest at the pachytene stage. However, a complete understanding of p53 functions under normal physiological conditions remains lacking. Here, we report a detailed analysis of the p53 role during meiotic prophase in mice spermatocytes. We show that the absence of p53 regulates prophase progression by slowing down the pachytene stage when the recombination-dependent arrest occurs. Furthermore, our results show that p53 is necessary for proper crossover (CO) formation and localization. Our study contributes to a deeper understanding of p53 roles during the meiotic prophase

A parametric approach for smaller and better encodings of cardinality constraints

Adequate encodings for high-level constraints are a key ingredient for the application of SAT technology. In particular, cardinality constraints state that at most (at least, or exactly) k out of n propositional variables can be true. They are crucial in many applications. Although sophisticated encodings for cardinality constraints exist, it is well known that for small n and k straightforward encodings without auxiliary variables sometimes behave better, and that the choice of the right trade-off between minimizing either the number of variables or the number of clauses is highly application-dependent. Here we build upon previous work on Cardinality Networks to get the best of several worlds: we develop an arc-consistent encoding that, by recursively decomposing the constraint into smaller ones, allows one to decide which encoding to apply to each sub-constraint. This process minimizes a function λ·num- vars + num-clauses, where λ is a parameter that can be tuned by the user. Our careful experimental evaluation shows that (e.g., for λ = 5) this new technique produces much smaller encodings in variables and clauses, and indeed strongly improves SAT solvers' performance.Postprint (author’s final draft

Proteïna ATR : vigilant la meiosi (Premi Aposta UAB 2011)

Totes les nostres cèl·lules tenen dos còpies de cada cromosoma excepte les sexuals perquè, en unir-se l'òvul i l'espermatozoide, generin altre cop un individu amb tota la dotació genètica, meitat de la mare, meitat del pare. El procés pel qual les cèl·lules sexuals, o gàmetes, redueixen el seu nombre de cromosomes a la meitat s'anomena meiosi. Aquesta, a més a més, té la missió d'aportar variabilitat a l'espècie combinant els gens del pare i de la mare. Per fer-ho, es generen trencaments en els cromosomes del propi individu que són reparats mitjançant mecanismes de recombinació homòloga. El problema és que aquests trencaments han de ser reparats correctament perquè no es produeixin mutacions heretables que puguin conduir a malalties o malformacions. Aquest projecte del grup de recerca dirigit pel Dr. Ignasi Roig, guardonat amb un Premi Aposta 2011 de la UAB, pretén estudiar les funcions i els mecanismes d'acció de la proteïna ATR, implicada en la reparació del dany en l'ADN, durant la meiosi.Todas nuestras células tienen dos copias de cada cromosoma excepto las sexuales para que, al unirse el óvulo y el espermatozoide, generen de nuevo un individuo con toda la dotación genética, mitad de la madre, mitad del padre. El proceso por el cual las células sexuales, o gametos, reducen su número de cromosomas a la mitad se llama meiosis. Esta, además, tiene la misión de aportar variabilidad a la especie combinando los genes del padre y de la madre. Para ello, se generan roturas en los cromosomas del propio individuo que son reparados mediante mecanismos de recombinación homóloga. El problema es que estas roturas deben ser reparadas correctamente para que no se produzcan mutaciones heredables que puedan conducir a enfermedades o malformaciones. Este proyecto del grupo de investigación dirigido por el Dr. Ignasi Roig, galardonado con un Premio Aposta 2011 de la UAB, pretende estudiar las funciones y los mecanismos de acción de la proteína ATR, implicada en la reparación del daño en el ADN, durante la meiosis

ATM Promotes the Obligate XY Crossover and both Crossover Control and Chromosome Axis Integrity on Autosomes

During meiosis in most sexually reproducing organisms, recombination forms crossovers between homologous maternal and paternal chromosomes and thereby promotes proper chromosome segregation at the first meiotic division. The number and distribution of crossovers are tightly controlled, but the factors that contribute to this control are poorly understood in most organisms, including mammals. Here we provide evidence that the ATM kinase or protein is essential for proper crossover formation in mouse spermatocytes. ATM deficiency causes multiple phenotypes in humans and mice, including gonadal atrophy. Mouse Atm−/− spermatocytes undergo apoptosis at mid-prophase of meiosis I, but Atm−/− meiotic phenotypes are partially rescued by Spo11 heterozygosity, such that ATM-deficient spermatocytes progress to meiotic metaphase I. Strikingly, Spo11+/−Atm−/− spermatocytes are defective in forming the obligate crossover on the sex chromosomes, even though the XY pair is usually incorporated in a sex body and is transcriptionally inactivated as in normal spermatocytes. The XY crossover defect correlates with the appearance of lagging chromosomes at metaphase I, which may trigger the extensive metaphase apoptosis that is observed in these cells. In addition, control of the number and distribution of crossovers on autosomes appears to be defective in the absence of ATM because there is an increase in the total number of MLH1 foci, which mark the sites of eventual crossover formation, and because interference between MLH1 foci is perturbed. The axes of autosomes exhibit structural defects that correlate with the positions of ongoing recombination. Together, these findings indicate that ATM plays a role in both crossover control and chromosome axis integrity and further suggests that ATM is important for coordinating these features of meiotic chromosome dynamics