Vertex enumeration (VE) algorithms explore the problem of listing some or all solutions that lie at corners of a convex polyhedron defined by a set of linear inequalities. Many algorithms have been developed for general polytopes. The most successful of these, from both an empirical and theoretical viewpoint, are based on pivoting. Dyer [24] gives an algorithm for simple polytopes which runs in time O (mn^2) per vertex. In this thesis we concentrate on the VE problem for certain special classes of polyhedron. We also address the problem of (approximately) counting the vertices without listing them. Pivoting algorithms rely on the correspondence between vertices and feasible bases and are consequently inefficient in the presence of a high degree of degeneracy such as frequently occurs in network polyhedra. Provan [79] gives a high-level description of a VE algorithm for such polyhedra which has running time that is quadratic in the number of vertices. W e describe an implementation of Provan's algorithm, present some computational results on transportation and assignment polytopes and discuss some practical difficulties with the algorithm. We then present an algorithmic description of a VE method via the dual Fourier-Motzkin (F-M) elimination method. One of the difficulties with F-M is that the number of constraints introduced in eliminating variables grows exponentially; we show that, for linear inequality systems with at most two variables per constraint, denoted LI(2), the growth is exponential in the number of variables but linear in the number of constraints. We go on to prove results which characterize the basis structure for LI(2) and dual LI(2) systems and hence develop a new pivoting algorithm for enumerating vertices of polyhedra associated with dual LI(2) systems. Counting the vertices of general polyhedra is #P-complete [24] and thus approximate counting procedures are of interest. In particular, some fpras for counting vertices of polyhedra associated with 0-1 Permanent, Down Sets, Independent Sets, 0-1 Knapsack Problems, 2 by n transportation problems, matroids and matchings in a non-bipartite graph are developed.

Based on the geometric analysis of Gaussian elimination (GE) found in Neal and Poole (Linear Algebra Appl. 173 (1992) 239-264) and Poole and Neal (Linear Algebra Appl. 149 (1991) 249-272; 162-164 (1992) 309-324), a new pivoting strategy, Rook's pivoting (RP), was introduced in Neal and Poole (Linear Algebra Appl. 173 (1992) 239-264) which encourages stability in the back-substitution phase of GE while controlling the growth of round-off error during the sweep-out. In fact, Foster (J. Comput. Appl. Math. 86 (1997) 177-194) has previously shown that RP, as with complete pivoting, cannot have exponential growth error. Empirical evidence presented in Neal and Poole (Linear Algebra Appl. 173 (1992) 239-264) showed that RP produces computed solutions with consistently greater accuracy than partial pivoting. That is, Rook's pivoting is, on average, more accurate than partial pivoting, with comparable costs. Moreover, the overhead to implement Rook's pivoting in a scalar or serial environment is only about three times the overhead to implement partial pivoting. The theoretical proof establishing this fact is presented here, and is empirically confirmed in this paper and supported in Foster (J. Comput. Appl. Math. 86 (1997) 177-194).

At the onset of cell division microtubules growing from spindle pole bodies (SPB) interact with each other to form the mitotic spindle enabling proper chromosome positioning and segregation. However, the exact mechanism of microtubule dynamics and microtubule associated proteins (MAPs) underlying spindle assembly is still not well understood. We developed an in vivo method to observe spindle assembly in the fission yeast Schizosaccharomyces pombe by inducing depolymerization of already formed and grown spindles by subjecting the cells to low temperatures, followed by subsequent repolymerization at a permissive temperature. We observed that microtubules pivot, i.e., perform angular movement around the SPB in a random manner, exploring the intranuclear space. Eventually microtubules extending from opposite SPBs come into contact and establish an antiparallel connection thus reassembling the spindle. Mutant approaches revealed that deletion of ase1 and klp5 did not prevent spindle reassembly, however introduced aberrations during the spindle formation. Amazingly, cut7p showed direct colocalization with microtubule overlap during spindle reassembly. Abrogation of cut7p led to inability to form a functional spindle. Thus, cut7p is the main regulator of spindle formation in fission yeast. None of the mutant strains affected microtubule pivoting, confirming that microtubule pivoting is a random movement unrelated to MAPs.

Bedding angle is a fundamental property of a particulate system that describes the resistance to rolling motion of a single grain. Mean trends of the bedding angle of sand have been described in the literature. This research expands upon the work to date by investigating the distribution of bedding angle for sands. Experimental measurements of bedding angle distributions are made for eight sands. Additionally, a theoretical description of the variability of bedding angle as a function of random grain size is developed and implemented numerically. The shape of the bedding angle distribution is found to be simulated well from the numerical simulations; the mean value of bedding angle is best predicted from particle roundness and empirical relationships. Together, these procedures provide a means of predicting the complete distribution of bedding angle for any given sand.

This master thesis deals with penetration testing and ethical hacking. Regarding to the layout of the thesis there was prepared appropiate enviroment to realize Red/Blue team exercise, where Red team is in a role of the attacker and Blue team is in a role of defender of the network infrastructure. Whole infrastructure is implemented in a cloud virtual enviroment of VMware vSphere. Second part of the thesis consists of preparation and creation of the exercise to test web application security. Third part of the thesis is dedicating to the automatization of redteaming. Main focus of this master thesis is to demonstrate different attack vectors how to attack the network infrastructure and web applications and use of the defense mechanisms to avoid this kinds of attacks.

At the onset of cell division microtubules growing from spindle pole bodies (SPB) interact with each other to form the mitotic spindle enabling proper chromosome positioning and segregation. However, the exact mechanism of microtubule dynamics and microtubule associated proteins (MAPs) underlying spindle assembly is still not well understood. We developed an in vivo method to observe spindle assembly in the fission yeast Schizosaccharomyces pombe by inducing depolymerization of already formed and grown spindles by subjecting the cells to low temperatures, followed by subsequent repolymerization at a permissive temperature. We observed that microtubules pivot, i.e., perform angular movement around the SPB in a random manner, exploring the intranuclear space. Eventually microtubules extending from opposite SPBs come into contact and establish an antiparallel connection thus reassembling the spindle. Mutant approaches revealed that deletion of ase1 and klp5 did not prevent spindle reassembly, however introduced aberrations during the spindle formation. Amazingly, cut7p showed direct colocalization with microtubule overlap during spindle reassembly. Abrogation of cut7p led to inability to form a functional spindle. Thus, cut7p is the main regulator of spindle formation in fission yeast. None of the mutant strains affected microtubule pivoting, confirming that microtubule pivoting is a random movement unrelated to MAPs.

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No / Anterior cruciate ligament (ACL) injuries are a major problem among female athletes. Screening for the risk of ACL injuries tends to focus on landing tasks, which may be limited in sports where changing direction is the main action involved in noncontact ACL injuries such as soccer. To investigate whether there is a relationship between single-legged landing (SLL), cutting (90° cuts), and pivoting (180° turns) in terms of the characteristics of dynamic valgus. Study Design: Controlled laboratory study. Methods: Twenty female soccer players (mean ± SD: age, 21.0 ± 3.9 years; height, 1.65 ± 0.08 m; mass, 58.4 ± 6.4 kg) performed a minimum of 6 trials of SLL from a 0.3-m drop height and cutting and pivoting all on the right leg. Kinematics and kinetics were calculated from 3-dimensional motion analysis. Results: Strong correlations were found for peak knee abduction angles between tasks (R = 0.63-0.86, P < .01), whereas only moderate correlations between SLL and cutting (R = 0.46, P < .05), cutting and pivoting (R = 0.56, P < .05), and SLL and pivoting (R = 0.43, P > .05) were found between tasks for peak knee abduction moments. Conclusion: The results suggest that female athletes who exhibit poor SLL mechanics perform the same during various changing direction tasks. Clinical Relevance: The results support the use of existing screening tests that involve landing tasks to identify at-risk athletes for noncontact ACL injuries.

Supervised learning tasks like building a classifier, estimating the error rate of the predictors, are typically performed with labeled data. In most cases, obtaining labeled data is costly as it requires manual labeling. On the other hand, unlabeled data is available in abundance. In this thesis, we discuss methods to perform supervised learning tasks with no labeled data. We prove consistency of the proposed methods and demonstrate its applicability with synthetic and real world experiments. In some cases, small quantities of labeled data maybe easily available and supplemented with large quantities of unlabeled data (semi-supervised learning). We derive the asymptotic efficiency of generative models for semi-supervised learning and quantify the effect of labeled and unlabeled data on the quality of the estimate. Another independent track of the thesis is efficient computational methods for nonnegative tensor factorization (NTF). NTF provides the user with rich modeling capabilities but it comes with an added computational cost. We provide a fast algorithm for performing NTF using a modified active set method called block principle pivoting method and demonstrate its applicability to social network analysis and text mining.

Czech and Vietnamese are the national languages of the Czech Republic and Vietnam, re- spectively. The distinctive features and the shortage of resources renders Czech-Vietnamese machine translation into a difficult task, leading to the fact that no effort has been put into developing a translation tool specifically for the language pair. In this thesis, we develop phrase-based statistical machine translation systems for the language pair and investigate the potential to improve the translation quality with pivoting. Pivoting refers to a set of ma- chine translation approaches through which a natural language, called pivoting language, is introduced to solve the problem of data scarcity between source and target languages, one of the most challenging problems of statistical machine translation. Selecting English as the sole pivoting language for Czech-Vietnamese translation, we prepare training and test- ing corpora for the three language pairs. All possible corpus sources are explored regarding each specific language pair. The next step is to improve quality of the training corpora through normalizing and filtering. Various experiments with pivoting methods are carried out to analyse the performance of pivoting methods in a realistic working condition.