Using 3 fb-1 of pp collision data collected at √s = 7 and 8 TeV by the LHCb experiment in the 2011 and 2012 data taking periods, the decays B⁰s → ϕπ+π- and B⁰d → ϕπ+π- have been studied in the π+π- invariant mass range below 1600 MeV/c². The B⁰s,d → ϕπ+π- branching fractions are determined to be: B(B⁰s → ϕπ+π-;mππ < 1600) = [3:72 ± 0:18 ± 0:38 ± 0:38] x 10-6 B(B⁰d → ϕπ+π-,mππ < 1600) = [1:75 ± 0:25 ± 0:42 ± 0:14] x 10-7 where the first uncertainty is statistical, the second is systematic, and the third comes from the normalisation mode B⁰s → ϕϕ. From the π+π- mass distribution and fits to angular distributions, the resonant decay mode B⁰s → ϕf₀(980) is observed and the branching fraction is measured to be: B(B⁰s → ϕf₀(980); f₀(980) → π+π-) = [1:23 ± 0:15 ± 0:12 ± 0:12] x 10-6 The fit also requires contributions from B⁰s → ϕf2(1270). A search for a P-wave contribution from B⁰s → ϕρ⁰(770) finds evidence at ~ 4σ but confirmation will require more data. An upper limit of the B⁰s → ϕρ⁰(770) decay branching fraction at 90% C.L. is measured to be: B(B⁰s → ϕρ⁰(770)) < 4 x 10-7.

This thesis investigates how breaking apart selection interference (‘Hill-Robertson’ effects) that arises between linked loci can select for higher levels of recombination. Specifically, it mainly studies how the presence of both advantageous and deleterious mutation affects selection for recombination. These evolutionary advantages are subsequently investigated with regards to sex resisting asexual invasion in a subdivided population. i) KEIGHTLEY and OTTO (2006) showed a strong advantage to recombination in breaking apart selection interference, if it acts across multiple, linked loci subject to recurrent deleterious mutation. Their model is modified to consider selection acting on recombination if a small proportion of mutations are advantageous. This leads to a greater increase in selection acting on a recombination modifier, compared to cases where only deleterious mutations are present. ii) Branching-process methods are developed to quantify how likely it is that a deleterious mutant hitchhikes with a selective sweep, and how recombination between the two loci affects this process. This is compared to the neutral hitchhiking model, to determine how levels of linked neutral diversity would differ between the two scenarios. A simple application with regards to human genetic data is provided. iii) Population subdivision can maintain costly sex, as a consequence of restricted gene flow slowing the spread of invading asexuals, which leads to an excessive accumulation of deleterious alleles. However, previous work did not quantify whether costly sex can be maintained with realistic levels of population subdivision. Simulations in this thesis show that the level of population subdivision (as measured by Fst) needed to maintain costly sex decreases with larger population size; however critical Fst values found are generally high, compared to surveys of geographicallyclose populations. The lowest levels of population subdivision that maintained sex were found if mutation is both advantageous and deleterious, and demes were arranged in a one-dimensional stepping-stone formation. iv) An analytical method is developed to calculate how long it takes an advantageous mutation (such as an invading asexual) to spread through a subdivided population. The flexibility of the methods created means that they can be applied to different types of stepping-stone populations. It is shown how to formulate the fixation time for one-dimensional and two-dimensional structures, with analytical methods showing a good fit to simulation data.

Neutrino-nucleon scattering is an effective way to investigate the inner structure of the nucleon, to extract the Standard Model parameters and to explore heavy quarks production dynamics. In the last decades, several experiments have been constructed to study weak interactions of neutrinos with nucleons. One of them was CERN-WA95 experiment operated by the CHORUS collaboration. It is based on a hybrid detector with nuclear emulsion as a target followed by electronic devices. Nuclear emulsion provides three dimensional spatial information with an outstanding resolution of the order of one micron. Therefore, it is ideal to detect short-lived particles. A special technique has been developed to reconstruct events in the emulsion which allows to perform a detailed investigation of events such as charmed hadrons production by neutrinos. As a result, the backround in the selected charm sample is up to six times lower compared to similar experiments. Such a method also permits to make direct measurements of some quantities instead of model fittings. This thesis is devoted to the study of the muonic decays of charmed hadrons and their production in emulsion. Manual inspection of charm events gives a complete reconstruction of charm decay topology. The extraction of the inclusive muonic branching ratio is based on the ratios per number of charged daughters in charm decay. Such an approach allows to separetely measure the muonic branching ratios for neutral and charged charm particles. Finally, normalization of the events with a muon in the final state to the charged current events gives dimuon production rate which is found compatible with the previous experiments. On top of that, preliminary results are shown for Bjorken x distribution and for a direct measurement of the Vcd Cabbibo-Kabayashi-Maskawa matrix element.

Neutrino-nucleon scattering is an effective way to investigate the inner structure of the nucleon, to extract the Standard Model parameters and to explore heavy quarks production dynamics. In the last decades, several experiments have been constructed to study weak interactions of neutrinos with nucleons. One of them was CERN-WA95 experiment operated by the CHORUS collaboration. It is based on a hybrid detector with nuclear emulsion as a target followed by electronic devices. Nuclear emulsion provides three dimensional spatial information with an outstanding resolution of the order of one micron. Therefore, it is ideal to detect short-lived particles. A special technique has been developed to reconstruct events in the emulsion which allows to perform a detailed investigation of events such as charmed hadrons production by neutrinos. As a result, the backround in the selected charm sample is up to six times lower compared to similar experiments. Such a method also permits to make direct measurements of some quantities instead of model fittings. This thesis is devoted to the study of the muonic decays of charmed hadrons and their production in emulsion. Manual inspection of charm events gives a complete reconstruction of charm decay topology. The extraction of the inclusive muonic branching ratio is based on the ratios per number of charged daughters in charm decay. Such an approach allows to separetely measure the muonic branching ratios for neutral and charged charm particles. Finally, normalization of the events with a muon in the final state to the charged current events gives dimuon production rate which is found compatible with the previous experiments. On top of that, preliminary results are shown for Bjorken x distribution and for a direct measurement of the Vcd Cabbibo-Kabayashi-Maskawa matrix element.

Rejecting approaches with a directionality parameter, mainstream minimalism has adopted the notion of strict (or unidirectional) branching. Within optimality theory however, constraints have recently been proposed that presuppose that the branching direction scheme is language specific. I show that a syntactic analysis of Chechen word order and relative clauses using strict branching and movement triggered by feature checking seems very unlikely, whereas a directionality approach works well. I argue in favor of a mixed directionality approach for Chechen, where the branching direction scheme depends on the phrase type. This observation leads to the introduction of context variants of existing markedness constraints, in order to describe the branching processes in terms of optimality theory. The paper discusses how and where the optimality theory selection of the branching directions can be implemented within a minimalist derivation.

This thesis is about solving the manpower planning problem concerning stangand transitioning of pilots. The objective of the planning is to have enoughpilots to satisfy the demand while minimizing the cost. The main decisions totake are how many pilots to hire, which pilots to train and which courses toschedule. The planning problems that arise are both large and dicult whichmakes it important to use ecient solution methods. Seniority rules betweenpairs of pilots are the most complicating factor.A major part in the solution process is the solving of mixed integer programs.The emphasis in the thesis is to develop and test adaptations of the branch andbound algorithm to solve mixed integer programs faster. One of these is abranching principle that takes a problem specic structure into account. Agraph of implications is constructed from the seniority rules and this graph isthen used to estimate the impact of each branching candidate. The implementedmethods outperform the software XPRESS on some instances, while for mostinstances the performance is comparable.

Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation of an undirected graph, has rank equal to the maximum number of vertices covered by a matching in the associated graph. The branching matrix, a representation of a directed graph, has rank equal to the maximum number of vertices covered by a branching in the associated graph. A mixed graph has both undirected and directed edges, and the matching forest problem for mixed graphs, introduced by Giles, is a generalization of the matching problem and the branching problem. A mixed graph can be represented by the matching forest matrix, and the rank of the matching forest matrix is related to the size of a matching forest in the associated mixed graph. The Tutte matrix and the branching matrix have indeterminate entries, and we describe algorithms that evaluate the indeterminates as rationals in such a way that the rank of the evaluated matrix is equal to the rank of the indeterminate matrix. Matroids in the context of graphs are discussed, and matroid formulations for the matching, branching, and matching forest problems are given.

Many real life problems can be formulated as constraint satisfaction problems <i>(CSPs)</i>. Backtracking search algorithms are usually employed to solve <i>CSPs</i> and in backtracking search the choice of branching strategies can be critical since they specify how a search algorithm can instantiate a variable and how a problem can be reduced into subproblems; that is, they define a search tree. In spite of the apparent importance of the branching strategy, there have been only a few empirical studies about different branching strategies and they all have been tested exclusively for numerical constraints. In this thesis, we employ the three most commonly used branching strategies in solving finite domain <i>CSPs</i>. These branching strategies are described as follows: first, a branching strategy with strong commitment assigns its variables in the early stage of the search as in k-Way branching; second, 2-Way branching guides a search by branching one side with assigning a variable and the other with eliminating the assigned value; third, the domain splitting strategy, based on the least commitment principle, branches by dividing a variable's domain rather than by assigning a single value to a variable. In our experiments, we compared the efficiency of different branching strategies in terms of their execution times and the number of choice points in solving finite domain <i>CSPs</i>. Interestingly, our experiments provide evidence that the choice of branching strategy for finite domain problems does not matter much in most cases--provided we are using an effective variable ordering heuristic--as domain splitting and 2-Way branching end up simulating k-Way branching. However, for an optimization problem with large domain size, the branching strategy with the least commitment principle can be more efficient than the other strategies. This empirical study will hopefully interest other practitioners to take different branching schemes into consideration in designing heuristics.

The interface crack branching phenomena, including thermal effects, has been investigated by using complex variable method and Stroh's dislocation theory, extended to thermo-elasticity in matrix notation. As one of the most catastrophic failure modes in structures like laminated and sandwich composites in aerospace and marine construction, thin film in electronic packaging, rotators in high speed engine of aircraft and reactor in nuclear power station, the study of interface crack branching has become a topic not only having theoretical importance, but also having practical significance. A unified approach is presented to address the thermoelastic interface crack problems in dissimilar anisotropic bimaterial composites, and a compact closed form solution is formulated by analytical continuation principle of complex analysis. Employing the contour integral method, an explicit solution to the interaction between the dislocations and the interface crack is obtained. By modeling the branched portion as a continuous distribution of the dislocations, the thermoelastic interface crack branching problem is then converted to a set of semi-coupled singular integral equations and solved by Gauss-Jacobi integration schemes. The influence of material property mismatches between the two constituents and the thermal loading effects on the interface crack branching are demonstrated by extensive numerical simulation. Some useful criteria for predicting the interface crack branching growth and guidance for optimal composites design are suggested. Further, a contact model to eliminate the overlapping between the two surfaces of an interface crack is also proposed and some new parameters which could influence the interpenetrating phenomena are also discovered. The technique to extend the current method to three dimensional problems is also outlined. Furthermore, the C++ source code has been implemented to manipulate the complicated complex operations for numerically solving the singular integral equations in complex matrix form.

Light is the fundamental source of energy and information throughout the plant life cycle. Light signals regulate plant architecture and branching, key processes that determine biomass production and grain yield. Low red (R) to far-red (FR) light ratios (R:FR) perceived by phytochromes serve as a warning signal about impending competition for light resources and lead to shade avoidance responses (SARs), including reduced branching. The R:FR regulates branching in both a bud autonomous and non-bud autonomous manner, however a detailed mechanistic understanding of the process remains unclear. We hypothesized that high R:FR promotes bud outgrowth by differentially regulating branching-related genes (transcriptome) within the axillary bud and that increased apical dominance under low R:FR or with phyB deficiency is mediated by auxin or other novel signal/s. We analyzed the branching phenotype of Arabidopsis Columbia-60000 ecotype in response to different R:FR treatments and conducted a microarray study to identify early (within 3 hours) changes in the transcriptome of buds from different rosette positions in response to altered R:FR. Physiological experiments were also conducted to determine if auxin concentration, transport rate, sensitivity, and establishment of an auxin transport stream were important in determining the branching phenotype of shade avoiding plants. The results revealed that the duration of low R:FR determines plant architecture and the branching phenotype and that bud outgrowth is regulated by the R:FR in a spatial and temporal manner. Low R:FR promoted the elongation of branches at top rosette nodes while it suppressed the outgrowth of axillary buds at lower nodes. High R:FR could reverse the effects of previous low R:FR by promoting the outgrowth of buds from lower axils within 24 hours of treatment. Transcriptomic analysis revealed that the R:FR differentially regulated the expression of genes related to hormone biosynthesis/transport/signaling, cell-cycle regulation and cell wall modification. Cis-elements responsive to light and hormone signaling pathways were overrepresented in several gene clusters. Apical dominance related studies discovered that loss of phyB function results in a slower auxin transport rate, fewer xylem parenchyma cells, and reduced sensitivity to auxin. These results, in addition to estimates of correlative inhibition, suggested that auxin is at least partially responsible for increased apical dominance under low R:FR or with phyB deficiency, but may be acting in conjunction with other undefined regulators.