Doctor of Philosophy / Department of Computing and Information Sciences / Xinming (Simon) Ou / Enterprise network security management is a vitally important task, more so now than ever before. Networks grow ever larger and more complex, and corporations, universities, government agencies, etc. rely heavily on the availability of these networks. Security in enterprise networks is constantly threatened by thousands of known software vulnerabilities, with thousands more discovered annually in a wide variety of applications. An overwhelming amount of data is relevant to the ongoing protection of an enterprise network. Previous works have addressed the identification of vulnerabilities in a given network and the aggregated collection of these vulnerabilities in an attack graph, clearly showing how an attacker might gain access to or control over network resources. These works, however, do little to address how to evaluate or properly utilize this information. I have developed a comprehensive approach to enterprise network security management. Compared with previous methods, my approach realizes these issues as a uniform desire for provable mitigation of risk within an enterprise network. Attack graph simplification is used to improve user comprehension of the graph data and to enable more efficient use of the data in risk assessment. A sound and effective quantification of risk within the network produces values that can form a basis for valuation policies necessary for the application of a SAT solving technique. SAT solving resolves policy conflicts and produces an optimal reconfiguration, based on the provided values, which can be verified by a knowledgeable human user for accuracy and applicability within the context of the enterprise network. Empirical study shows the effectiveness and efficiency of these approaches, and also indicates promising directions for improvements to be explored in future works. Overall, this research comprises an important step toward a more automated security management initiative.

The shortest path problem in graphs is both a classic combinatorial optimization problem and a practical problem that admits many applications. Techniques for preprocessing a graph are useful for reducing shortest path query times. This dissertation studies the foundations of a class of algorithms that use preprocessed landmark information and the triangle inequality to guide A* search in graphs. A new heuristic is presented for solving shortest path queries that enables the use of higher order polygon inequalities. We demonstrate this capability by leveraging distance information from two landmarks when visiting a vertex as opposed to the common single landmark paradigm. The new heuristic’s novel feature is that it computes and stores a reduced amount of preprocessed information (in comparison to previous landmark-based algorithms) while enabling more informed search decisions. We demonstrate that domination of this heuristic over its predecessor depends on landmark selection and that, in general, the denser the landmark set, the better heuristic performs. Due to the reduced memory requirement, this new heuristic admits much denser landmark sets. We conduct experiments to characterize the impact that landmark configurations have on this new heuristic, demonstrating that centrality-based landmark selection has the best tradeoff between preprocessing and runtime. Using a developed graph library and static information from benchmark road map datasets, the algorithm is compared experimentally with previous landmark-based shortest path techniques in a fixed-memory environment to demonstrate a reduction in overall computational time and memory requirements. Experimental results are evaluated to detail the significance of landmark selection and density, the tradeoffs of performing preprocessing, and the practical use cases of the algorithm.

The extended finite state machine (EFSM) is a powerful modelling approach that has been applied to represent a wide range of systems. Despite its popularity, testing from an EFSM is a substantial problem for two main reasons: path feasibility and path test case generation. The path feasibility problem concerns generating transition paths through an EFSM that are feasible and satisfy a given test criterion. In an EFSM, guards and assignments in a path‟s transitions may cause some selected paths to be infeasible. The problem of path test case generation is to find a sequence of inputs that can exercise the transitions in a given feasible path. However, the transitions‟ guards and assignments in a given path can impose difficulties when producing such data making the range of acceptable inputs narrowed down to a possibly tiny range. While search-based approaches have proven efficient in automating aspects of testing, these have received little attention when testing from EFSMs. This thesis proposes an integrated search-based approach to automatically test from an EFSM. The proposed approach generates paths through an EFSM that are potentially feasible and satisfy a test criterion. Then, it generates test cases that can exercise the generated feasible paths. The approach is evaluated by being used to test from five EFSM cases studies. The achieved experimental results demonstrate the value of the proposed approach.

In recent years, Multi-hop Wireless Networks (MHWNs) have experienced an explosion of deployment due to the increasing demand for continuous connectivity regardless of the physical location. Internet predominant transport protocols, i.e. Transmission Control Protocol (TCP), face performance degradation in MHWNs because of the high loss and link failure rates. Several solutions have been proposed which are based on network state estimation or use information from MAC layer (called metrics) in a cross-layer manner to better comprehend the network state. The first part of this thesis provides a survey and comprehensive definition of common metrics from Physical, MAC, Network and Transport layers and thus provides a multi-criteria and hierarchical classification. After that, the effectiveness in reflecting network information of MAC metrics is also investigated in a systematic way by simulating various network situations and measuring the MAC metrics. Thus, the good MAC metric for congestion control which is coupled with the network contention level and the medium induced losses will be found out. From the results of the effectiveness study, new rate control schemes for transport protocols are proposed which adapt efficiently the source bit rate depending on the network condition provided by some MAC metrics. Through an extensive set of simulations, the performance of the proposed rate control schemes in MHWNs is investigated thoroughly with several network situations.

We give a short introduction to various concepts related to the theory of p-harmonic functions on Rn, and some modern generalizations of these concepts to general metric spaces. The article Björn-Björn-Lehrbäck [6] serves as the starting point of our discussion. In [6], among other things, estimates of the variational capacity for thin annuli in metric spaces are given under the assumptions of a Poincaré inequality and an annular decay property. Most of the parameters in the various results of the article are proven to be sharp by counterexamples at the end of the article. The main result of this thesis is the verification of the sharpness of a parameter. At the center of our discussion will be a concrete metric subspace of weighted Rn, namely the so-called weighted bow-tie, where the weight function is assumed to be radial. A similar space was used in [6] to verify the sharpness of several parameters. We show that under the assumption that the variational p-capacity is nonzero for any ball centered at the origin, the p-Poincaré inequality holds in Rn if and only if it holds on the corresponding bow-tie Finally, we consider a concrete weight function, show that it is a Muckenhoupt A1 weight, and use this to construct a counterexample establishing the sharpness of the parameter in the above mentioned result from [6].

En 1991, Philippe Brunet publie une traduction inédite de la poétesse grecque archaïque du VII ème siècle avant J.-C., Sappho. Dans cette traduction, celui-ci a tenté d'imiter et de faire ressentir le mètre grec en français. La difficulté de cette entreprise réside dans le fait que le français n'est pas une langue à accent de mot et qu'il ne ressent pas la quantité des syllabes. Les mètres poétiques du français se basent en effet sur le nombre des syllabes et non sur leur quantité. À la Renaissance, une telle tentative d'imitation du mètre grec avait déjà été entreprise par Jean-Antoine de Baïf. Mais celui-ci, oubliant les particularités accentuelles du français, n'a pas réussi à développer un système adéquat. Philippe Brunet quant à lui a su utiliser ces règles accentuelles françaises pour faire ressentir à son lecteur quelque chose du rythme quantitatif grec. Se servant autant de l'accent tonique que de l'accent initial, son système respecte dans son ensemble la langue française tout en créant un rythme nouveau. Une fois cette traduction comparée à d'autres, on peut également voir à quel point ses recherches sémantiques et prosodiques aident à la réalisation de ce rythme particulier. M ots-clé : Sappho, grec, traduction, rythme, mètre, métrique, accent. / In 1991, Philippe Brunet published a new translation of the seventh century B.C. archaic Greek poet, Sappho. In this translation, he attempted to imitate and instigate the feel of the Greek meter in French. The difficulty of this project stands in the fact that the French language is not one of word accentuation and it doesn't take into account the syllables quantity. The poetic meters in French are indeed based on the syllables number and not on their quantity. During the Renaissance, a similar imitation experiment had already been attempted by Jean-Antoine de Baïf. But dismissing the accentual particularities of the French language, he failed to develop an adequate system. Meanwhile, Phillipe Brunet was able to use the French accentual rules to make his read feel about the quantitative Greek rhythm. Using the tonic accent as well as the initial accent, his system fully respects the French language while creating a new rhythm. When this translation is compared to others, we can see how much his sematic and prosodic research help to the creation of this peculiar system.

The pivot tables is one of the most effective metric access method optimized for a number of distance computations in similarity search. In this work the new modification of the pivot tables method was proposed that is besides distance computations optimized also for a number of I/O operations. Proposed Clustered pivot tables method is indexing clusters of similar objects that were created by another metric access method - the M-tree. The indexing of clustered objects has a positive effect for searching within indexed database. Whereas the clusters are paged in second memory, page containing such cluster, which do not satisfy particular query, is not accessed in second memory at all. Non-relevant objects, that are out of the query range, are not loaded into memory, what has the effect of decreasing number of I/O operations and total volume of transferred data. The correctness of proposed approach was experimentally proved and experimental results of proposed method was compared to selected metric access methods.

The goal of the present thesis is to introduce on a Riemannian Spin- manifold a system of partial differential equations for spinor-valued differ- ential forms called Killing equations. We study basic properties of several types of Killing fields and relationships among them. We provide a simple construction of Killing spinor-valued forms from Killing spinors and Killing forms. We also review the construction of metric cone and discuss the re- lationship between Killing spinor-valued forms on the base manifold and parallel spinor-valued forms on the metric cone.

The aim of this thesis is to build the foundations of generalized ordinary differ- ential equation theory in metric spaces. While differential equations in metric spaces have been studied before, the chosen approach cannot be extended to in- clude more general types of integral equations. We introduce a definition which combines the added generality of metric spaces with the strength of Kurzweil's generalized ordinary differential equations. Additionally, we present existence and uniqueness theorems which offer new results even in the context of Euclidean spaces.

On étudie les fonctions multivaluées vers un espace de Hilbert. Après avoir introduit unebonne notion de p énergie, on donne une définition possible d’espace de Sobolev et on prouveun théorème d’existence des p minimiseurs. Puis on considère les fonctions bivaluées de deuxvariables, stationnaires pour les déformations au départ et à l’arrivée. On démontre qu’ellessont localement lipschitziennes et on utilise cette régularité pour montrer la convergence fortedans W1,2 vers leur unique éclatement en un point. L’ensemble de branchement d’une tellefonction est la réunion localement finie de courbes analytiques qui se rencontrent en faisantdes angles égaux. Nous donnons aussi un exemple de fonction discontinue et stationnaireseulement pour les déformations au départ.Dans un deuxième temps, on prouve qu’il n’existe pas de rétraction uniformément continuede l’espace des champs vectoriels continus vers le sous-espace de ceux dont la divergence estnulle en un sens distributionnel. On généralise ce résultat en toute codimension en utilisant lanotion de m charge et à tout ensemble X ⊂ Rn vérifiant une hypothèse géométrique mineure. / We study multiple valued functions with values in a Hilbert space. We introduce a possibledefinition of Sobolev spaces and the rightful notion of p energy. We prove the existence of pminimizers. Then we consider two-valued real functions of two variables which are stationarywith respect to both domain and range transformations. We prove their local Lipschitzcontinuity and use it to establish strong convergence in W1,2 to their unique blow-up at anypoint. We claim that the branch set of any such function consists of finitely many real analyticcurves meeting at nod points with equal angles. We also provide an example showing thatstationarity with respect to domain transformations only does not imply continuity.In a second part, we prove that there does not exist a uniformly continuous retractionfrom the space of continuous vector fields onto the subspace of vector fields whose divergencevanishes in the distributional sense. We then generalise this result using the concept of mcharges on any subset X _ Rn satisfying a mild geometric condition, there is no uniformlycontinuous representation operator for mcharges in X.