This thesis summarizes my work in systems biology as a PhD student at The Microsoft Research - University of Trento Centre for Computational and Systems Biology (COSBI) and at the University of Trento, department of Mathematics. Systems biology is an interdisciplinary field that aims at integrating biology with computational and mathematical methods to gain a better understanding of biological phenomena [5, 6]. Among these methods, mathematical and dy- namical modeling have driven the discovery of mechanistic insights from the static representations of phenomena, that is, data. As a result, mathematical and dynamical models have now become standard tools to support new discoveries in biology and in public health issues. For example, models assist governments in determining the policies to contain the spreading of the diseases and in decisions such as vaccine purchases [7]. Similarly, complex and accurate models of the cardio-vascular systems guide surgeons during many procedures on pa- tients [8]. Furthermore, dynamical models of signaling cascades help researchers in identifying new potential drug targets and therapies for many diseases [9]. We used these modeling techniques to address biological questions related to diabetes and insulin resistance. Within this framework, this thesis contains two articles I contributed to, that focus on diabetes. These works are published in the journal of Nature Scientific Reports and are included in Chapters 3 and 4. A significant contribution to the development of these models, and models in general, is given by optimization. Optimization is often used in modeling to determine certain unknown values or factors in a way that allow the model to optimally reproduce the experimental data. Moreover, the parameters of a model that correctly describe the undergoing dynamics may be used as diagnostic tools [10–13]. To this end, this thesis contains a methodological appendix that includes a review of optimization algorithms that has been submitted to the journal of Frontiers in Applied Mathematics and Statistics, special topic Optimization. The content of this article is reported in Appendix A.

Syftet med detta självständiga arbete är att undersöka förskolans måltidssituation ur ettnormkritiskt perspektiv. Studien har genomförts med hjälp av observationer för att få syn påpedagogers faktiska agerande. För att kunna besvara studiens syfte har det identifierats treolika makthandlingar som pedagoger använder sig av, samt fyra övergripande teman av deexisterande måltidsnormerna. Resultatet av studien visar hur pedagoger använder sig av subtilfysisk- , kraftfull fysisk,- och verbal makthandling i tillrättavisande av barn för att upprätthållamåltidens normer vilka i denna studie skrivs fram som normer kring att äta med bestick, sittaordentligt vid matbordet, normer kring gott uppförande vid måltiden och normer kring att ätaupp maten på tallriken. Makt existerar i olika omfattning beroende på vem som utför det ochnär det kommer till uttryck.I en framtida profession anses det relevant att det finns kunskap om maktrelationer för attmöjliggöra att barn får möjlighet till delaktighet och inflytande i sin egen utbildning. Dessakunskaper kan verka för goda relationer och en lustfylld utbildning i förskolan. Om vuxnautövar sin makt i en negativ bemärkelse är det värt att fundera på hur barns människosynkommer att utvecklas. För visst vill vi att barnen i förskolan ska utvecklas till demokratiskamedborgare i samhället? Med det sagt, hoppas vi med hjälp av denna studie kunna bidra medkunskap om hur det kan möjliggöras samt hur mer symmetriska relationer kan upprätthållasinom förskolans måltid i relation till dess dominerande normer.

In this thesis, we study the problem of reasoning and query answering over contextualized knowledge in quad format augmented with expressive forall-existential bridge rules. Such bridge rules contain conjunctions, existentially quantified variables in the head, and are strictly more expressive than the bridge rules considered so far in similar setting. A set of quads together with forall-existential bridge rules is called a quad-system. We show that query answering over quad-systems in their unrestricted form is undecidable, in general. We propose various subclasses of quad-systems, for which query answering is decidable. Context-acyclic quad-systems do not allow the context dependency graph of the bridge rules to have cycles passing through triple-generating (value-generating) contexts, and hence guarantees the chase (deductive closure) to be finite. Csafe, msafe and safe classes of quad-systems restricts the structure of descendance graph of Skolem blank nodes generated during chase process to be directed acyclic graphs (DAGs) of bounded depth, and hence has finite chases. RR and restricted RR quad-systems do not allow for the creation of Skolem blank nodes, and hence restrict the chase to be of polynomial size. Besides the undecidability result of unrestricted quad-systems, tight complexity bounds has been established for each of the classes we have introduced. We then compare the problems, (resp. classes,) we address (resp. derive) in this thesis, for quad-systems with analogous problems (resp. classes) in the realm of forall-existential rules. We show that the query answering problem over quad-systems is polynomially equivalent to the query answering problem over ternary forall-existential rules, and the technique of safety, we propose, is strictly more expressive than existing well known techniques such joint acyclicity and model maithful acyclicity, used for decidability guarantees, in the realm of forall-existential rules.

The last decade has seen an increasing interest in bio-mathematical modelling and scientific computing, resulting in new applications to relevant physiological phenomena and to a better understanding of the origin of various diseases. A topic of great interest to several degenerative diseases is filtration across microvessel walls. The role of the microvessel wall is to let oxygen and nutrients contained in the blood stream to reach the interstitium, and ultimately the surrounding cells, while blocking macromolecules. An understanding of these processes is important in preventing and curing neuro-degenerative diseases, as well as for exploring possible mechanisms to make drug delivery more efficient. This work presents a one-dimensional, time dependent mathematical model describing transport of blood plasma and macromolecules across blood vessel walls. The model takes into account the heterogeneous microvessel wall composition, in order to accurately describe trans-vascular flow. This results in a multi-layered domain, accounting for variable physical properties across the layers forming the micro-vascular wall. In particular, the glycocalyx and endothelium, accounted for in many biological studies, are represented in our model. This micro-structural, yet simplified description of the vascular wall, allows us to simulate the effect of glycocalyx damage and of other pathologies, such as hypertension, hemorrhage and hypovolemia, both in steady and time-dependent states. Due to the simplicity, and thus efficiency of the proposed model, simulations are fast and provide results which are in line with published experimental studies. Furthermore, the simulation tool may be useful for practical applications in physiological and medical studies, by evaluating the possible consequences of pathological conditions.

Many projects have dealt with mappings between classifications both in computer science and digital library communities. The adopted solutions range from fully manual to fully automatic approaches. Manual approaches are very precise, but automation becomes unavoidable when classifications contain thousands of nodes with millions of candidate correspondences. As fun-damental preliminary step towards automation, S-Match converts classifications into formal on-tologies, i.e. lightweight ontologies. Despite many solutions to the problem have been offered, with S-Match representing a state of the art matcher with good accuracy and run-time perfor-mance, there are still several open problems. In particular, the problems addressed in this thesis include: (a) Run-time performance. Due to the high number of calls to the SAT reasoning engine, semantic matching may require exponential time; (b) Maintenance. Current matching tools offer poor support to users for the process of creation, validation and maintenance of the correspond-ences; (c) Lack of background knowledge. The lack of domain specific background knowledge is one important cause of low recall. As significant progress to (a) and (b), we describe MinSMatch, a semantic matching tool we developed evolving S-Match that computes the minimal mapping between two lightweight ontologies. The minimal mapping is that minimal subset of correspondences such that all the others can be efficiently computed from them and are therefore said to be redundant. We provide a formal definition of minimal and, dually, redundant map-pings, evidence of the fact that the minimal mapping always exists and it is unique and a correct and complete algorithm for computing it. Our experiments demonstrate a substantial improve-ment in run-time. Based on this, we also developed a method to support users in the validation task that allows saving up to 99% of the time. We address problem (c) by creating and by making use of an extensible diversity-aware knowledge base providing a continuously growing quantity of properly organized knowledge. Our approach is centered on the fundamental notions of domain and context. Domains, developed by adapting the faceted approach from library science, are the main means by which diversity is captured and allow scaling as with them it is possible to add new knowledge as needed. Context allows a better disambiguation of the terms used and re-ducing the complexity of reasoning at run-time. As proof of the applicability of the approach, we developed the Space domain and applied it in the Semantic Geo-Catalogue (SGC) project.

Even when cooperation is clearly advantageous, attaining it is not to be taken for granted. In fact, in order to undertake a mutually beneficial joint activity, the parties must agree on the division of the gains granted by it. The self-interested nature that is supposed to characterize the same parties might then become a serious obstacle to the collectively rational choice of cooperating. Bargaining and Cooperative Game Theory are the two principal frameworks that are used by economists to investigate this puzzling but fascinating problem. In particular, if the latter proposes solutions to hypothetical bargaining problems according to normative principles such as egalitarianism and marginalism, the former examine the same problem from a positive perspective focusing on the relation between the rules of the bargaining process and its outcomes. The present Doctoral Thesis employs both these frameworks in a complementary way. Specifically, it proposes two novel solution concepts for transferable utility games in characteristic function form and a bargaining model whose outcome is exactly one of such solutions. It further compares different solution concepts with regard to their redistributive properties and their resilience to free riding. The Doctoral Thesis is composed by four standing alone, but interlinked, works forming the four chapters in which it is divided. Chapter 1 offers a literature review of bargaining models. Chapter 2 presents the two novel solution concepts: the Central Core and the Mid-central Core. Chapter 3 proposes the Burning Coalition Bargaining Model, a non cooperative bargaining model whose outcome, under a specific response strategy profile, is the Mid-central Core. Finally, Chapter 4 benchmarks different solution concepts through a numerical simulation based on an environmental game.

Reactive Search Optimization (RSO) advocates the integration of learning techniques into search heuristics for solving complex optimization problems. In the last few years, RSO has been mostly employed in self-adapting a local search method in a manner depending on the previous history of the search. The learning signals consisted of data about the structural characteristics of the instance collected while the algorithm is running. For example, data about sizes of basins of attraction, entrapment of trajectories, repetitions of previously visited configurations. In this context, the algorithm learns by interacting from a previously unknown environment given by an existing (and fixed) problem definition. This thesis considers a second interesting online learning loop, where the source of learning signals is the decision maker, who is fine-tuning her preferences (formalized as an utility function) based on a learning process triggered by the presentation of tentative solutions. The objective function and, more in general, the problem definition is not fully stated at the beginning and needs to be refined during the search for a satisfying solution. In practice, this lack of complete knowledge may occur for different reasons: insufficient or costly knowledge elicitation, soft constraints which are in the mind of the decision maker, revision of preferences after becoming aware of some possible solutions, etc. The work developed in the thesis can be classified within the well known paradigm of Interactive Decision Making (IDM). In particular, it considers interactive optimization from a machine learning perspective, where IDM is seen as a joint learning process involving the optimization component and the DM herself. During the interactive process, on one hand, the decision maker improves her knowledge about the problem in question and, on the other hand, the preference model learnt by the optimization component evolves in response to the additional information provided by the user. We believe that understanding the interplay between these two learning processes is essential to improve the design of interactive decision making systems. This thesis goes in this direction, 1) by considering a final user that may change her preferences as a result of the deeper knowledge of the problem and that may occasionally provide inconsistent feedback during the interactive process, 2) by introducing a couple of IDM techniques that can learn an arbitrary preference model in these changing and noisy conditions. The investigation is performed within two different problems settings, the traditional multi-objective optimization and a constraint-based formulation for the DM preferences. In both cases, the ultimate goal of the IDM algorithm developed is the identification of the solution preferred by the final user. This task is accomplished by alternating a learning phase generating an approximated model of the user preferences with an optimization stage identifying the optimizers of the current model. Current tentative solutions will be evaluated by the final user, in order to provide additional training data. However, the cognitive limitations of the user while analyzing the tentative solutions demands to minimize the amount of elicited information. This requires a shift of paradigm with respect to standard machine learning strategies, in order to model the relevant areas of the optimization surface rather than reconstruct it entirely. In our approach the shift is obtained both by the application of well known active learning principles during the learning phase and by the suitable trade-off among diversification and intensification of the search during the optimization stage.

Description Logics (DLs) are a family of logic-based knowledge representation formalisms aimed at representing the knowledge of an application domain in a structured way one of whose main characteristic is the emphasis on reasoning. Since the last two decades Description logics have been widely studied and applied to numerous areas of computer science (including artificial intelligence, formal verification, database theory, natural language processing and distributed computing). In recent years, however, the interest in the problem of automated reasoning in Description Logics has seen a tremendous growth because of the explosion of new notable applications in the domains of Semantic Web and of bio-medical ontologies. The more real-world problems are represented through DL-based ontologies the more these new applications represents a challenge due to the required efficiency in handling complex logical constructors (e.g. numerical constraints) and in handling the huge dimensions of this kind of ontologies. For these reasons the development of efficient algorithms and procedures for reasoning in Description Logic has become crucial. SAT-based technologies, in the meanwhile, proved to be mature and largely successful in many other automated reasoning fields, first of all on many very hard practical applications of formal verification, often huge characterized by problems of huge dimension. In the last twenty years, in fact, we have witnessed an impressive advance in the efficiency of SAT techniques, which has brought problems of hundreds of millions of clauses and variables to be at the reach of the freely-available state-of-the-art solvers. As a consequence, many problems have been successfully solved by mean of SAT-based techniques and these approaches are currently state-of-the-art in the respective communities (among all Model Checking). Furthermore, the progress in SAT-solving techniques, together with the concrete needs from real applications, have inspired significant research on richer and more expressive Boolean formalism, like Satisfiability Modulo Theories (SMT), and on the use of the SAT formalism to solve problems with a wider extent (e.g. to compute interpolants, unsatisfiable cores, all-SAT). The research trends in Description Logic, its manifold practical applications, the quest of efficient and scalable procedures, on one hand, the wide variety of mature and efficient techniques offered by the SAT research area, on the other hand, motivated our research. In this thesis dissertation we explore the idea of exploiting the power and efficiency of state-of-the-art SAT-based techniques for automated reasoning and ontology manipulation in Description Logics, proposing a convenient alternative to the traditional tableau based algorithms. With this aim we propose and develop novel and complete approaches able to solve Description Logic problems as SAT and SMT ones, by mean of sound and complete encodings. On these encodings we develop new procedures and optimizations techniques based on a variety of existing SAT-based formalisms and technologies. In this work, in particular, we focus on three gradually harder reasoning problems in Description Logics which tackle increasingly more expressive languages or increasingly harder reasoning services, among which we face also non-standard services supporting the debugging of ontologies like modularization and axiom pinpointing. We implemented our approaches in tools which integrate with the available SAT/SMT-solvers; finally, we show the effectiveness of our novel approaches through very extensive empirical evaluations on benchmarks and ontologies from real application, in which we compare our performance against the other state-of-the-art available systems. Notice that any advance in the exploited Boolean reasoning techniques/tools will be freely inherited from our proposed approaches extending also to Description Logics/ontologies the benefits of the observable great and fast advance in the efficiency of SAT-based techniques.

Gröbner bases are special sets of polynomials, which are useful to solve problems in many fields such as computer vision, geometric modeling, geometric theorem proving, optimization, control theory, statistics, communications, biology, robotics, coding theory, and cryptography. The major disadvantage of algorithms to compute Gröbner bases is that computations can use a lot of computer power. One of the reasons is the amount of useless critical pairs that the algorithm has to compute. Hence, a lot of effort has been put into developing new criteria to detect such pairs in advance. This thesis is devoted to describe efficient algorithms for the computation of Gröbner bases, with particular emphasis to those based on polynomial signatures. The idea of associating each polynomial with a signature on which the criteria and reduction steps depend, has become extremely popular in part due to its good performance. Our main result combines the criteria from Gao-Volny-Wang's algorithm with the knowledge of Hilbert Series. A parallel implementation of the algorithm is also investigated to improve the computational efficiency. Our algorithm is implemented in CoCoALib, a C++ free library for computations in commutative algebra.

Assuring safety and reliability is fundamental when developing a safety critical system. Road, naval and avionic transportation; water and gas distribution; nuclear, eolic, and photovoltaic energy production are only some examples where it is mandatory to guarantee those properties. The continuous increasing in the design complexity of safety critical system calls for a never ending sought of new and more advanced analytical techniques. In fact, they are required to assure that undesired consequences are highly improbable. In this Thesis we introduce a novel methodology able to raise the bar in the area of automated safety and reliability analysis. The proposed approach integrates a series of techniques, based on symbolic model checking, into the current development process of safety critical systems. Moreover, our methodology and the resulting techniques are thereafter applied to a series of real-world case studies, developed in collaboration with authoritative entities such as NASA and the Boeing Company.