Distributed systems : architecture-driven specification using extended LOTOS

The thesis uses the LOTOS language (ISO International Standard ISO 8807) as a basis for the formal specification of distributed systems. Contributions are made to two key research areas: architecture-driven specification and LOTOS language extensions. The notion of architecture-driven specification is to guide the specification process by providing a reference-base of pre-defined domain-specific components. The thesis builds an infra-structure of architectural elements, and provides Extended LOTOS (XL) definitions of these elements. The thesis develops Extended LOTOS (XI.) for the specification of distributed systems. XL- is LOTOS enhanced with features for the formal specification of quantitative timing. probabilistic and priority requirements. For distributed systems, the specification of these ‘performance’ requirements, ran be as important as the specification of the associated functional requirements. To support quantitative timing features, the XL semantics define a global, discrete clock which can be used both to force events to occur at specific times, and to measure Intervals between event occurrences. XL introduces time policy operators ASAP (as soon as possible’ corresponding to “maximal progress semantics") and ALAP (late as possible'). Special internal transitions are introduced in XL semantics for the specification of probability, Conformance relations based on a notion of probabilization, together with a testing framework, are defined to support reasoning about probabilistic XL specifications. Priority within the XL semantics ensures that permitted events with the highest priority weighting of their class are allowed first. Both functional and performance specification play important roles in CIM (Computer Integrated Manufacturing) systems. The thesis uses a CIM system known as the CIM- OSA lntegrating Infrastructure as a case study of architecture-driven specification using XL. The thesis thus constitutes a step in the evolution of distributed system specification methods that have both an architectural basis and a formal basis

AKILES : An Approach to Automatic Knowledge Integration in Learning Expert Systems

Knowledge integration is defined here as a machine learning task from a practical point of view—by identifying the requirements that a real-world complex application domain poses on the expert system in relation to a changing world. We present our current approach to knowledge integration in an expert system, required when the structure of the physical system, the world on which the expert system operates changes. Our exemplar domain task is technical diagnosis. We test our approach on the particular architecture of MOLTKE/3, our workbench for technical diagnosis1- which integrates second-generation expert system techniques in a unique framework. Knowledge integration is seen as the task of elaborating and accomodating new information (due to structural changes) in the expert system's knowledge, maintaining consistency in the knowledge base. The main focus is towards improving the adaptability of the expert system to the structural changes. The approach is based on three principles from the adaptation process: incrementality, extensive and intensive use of domain knowledge, and focus on strategic knowledge. We discuss how AKILES’ knowledge integration task can be used to complete the modeling cycle, i.e., covering the model-evaluation step in the layout-elaboration-evaluation cycle, as defined in [13]

The Calder\'on Projector for Fibred Cusp Operators

A Calder\'on projector for an elliptic operator $P$ on a manifold with boundary $X$ is a projection from general boundary data to the set of boundary data of solutions $u$ of $Pu=0$. Seeley proved in 1966 that for compact $X$ and for $P$ uniformly elliptic up to the boundary there is a Calder\'on projector which is a pseudodifferential operator on $\partial X$. We generalize this result to the setting of fibred cusp operators, a class of elliptic operators on certain non-compact manifolds having a special fibred structure at infinity. This applies, for example, to the Laplacian on certain locally symmetric spaces or on particular singular spaces, such as a domain with cusp singularity or the complement of two touching smooth strictly convex domains in Euclidean space. Our main technical tool is the $\phi$-pseudodifferential calculus introduced by Mazzeo and Melrose. In our presentation we provide a setting that may be useful for doing analogous constructions for other types of singularities.Comment: 39 pages, 2 figures, 2 appendice

Size bounds for algebraic and semialgebraic proof systems

This thesis concerns the proof complexity of algebraic and semialgebraic proof systems Polynomial Calculus, Sums-of-Squares and Sherali-Adams. The most studied complexity measure for these systems is the degree of the proofs. This thesis concentrates on other possible complexity measures of interest to proof complexity, monomial-size and bit-complexity. We aim to showcase that there is a reasonably well-behaved theory for these measures also. Firstly we tie the complexity measures of degree and monomial size together by proving a size-degree trade-off for Sums-of-Squares and Sherali-Adams. We show that if there is a refutation with at most s many monomials, then there is a refutation whose degree is of order square root of n log s plus k, where k is the maximum degree of the constraints and n is the number of variables. For Polynomial Calculus similar trade-off was obtained earlier by Impagliazzo, Pudlák and Sgall. Secondly we prove a feasible interpolation property for all three systems. We show that for each system there is a polynomial time algorithm that given two sets P(x,z) and Q(y,z) of polynomial constraints in disjoint sequences x,y and z of variables, a refutation of the union of P(x,z) and Q(y,z), and an assignment a to the z-variables, finds either a refutation of P(x,a) or a refutation of Q(y,a). Finally we consider the relation between monomial-size and bit-complexity in Polynomial Calculus and Sums-of-Squares. We show that there is an unsatisfiable set of polynomial constraints that has both Polynomial Calculus and Sums-of-Squares refutations of polynomial monomial-size, but for which any Polynomial Calculus or Sums-of-Squares refutation requires exponential bit-complexity. Besides the emphasis on complexity measures other than degree, another unifying theme in all the three results is the use of semantic characterizations of resource-bounded proofs and refutations. All results make heavy use of the completeness properties of such characterizations. All in all, the work on these semantic characterizations presents itself as the fourth central contribution of this thesis.Aquesta tesi tracta de la complexitat de les proves en els sistemes de prova algebraics i semialgebraics Càlcul Polinomial (Polynomial Calculus), Sumes de Quadrats (Sums of Squares), i Sherali-Adams. La mesura de complexitat més estudiada per a aquests sistemes és el grau dels polinomis. Aquesta tesi se centra en altres possibles mesures de complexitat d'interès per a la complexitat de proves: el nombre de monomis i la longitud de representació en nombre de bits. Pretenem demostrar que aquestes mesures admeten una teoria comparable i complementària a la teoria del grau com a mesura de complexitat. En primer lloc, establim una relació entre les mesures de grau i de nombre de monomis demostrant una propietat d'intercanvi (trade-off) entre les dues mesures per als sistemes Sumes de Quadrats i Sherali-Adams. Demostrem que si hi ha una refutació amb com a màxim s monomis, aleshores hi ha una refutació el grau de la qual és d'ordre de l'arrel quadrada de n.log(s) més k, on k és el grau màxim de les restriccions i n és el nombre de variables. Per al Càlcul Polinomial, una propietat d'intercanvi similar va ser obtinguda per Impagliazzo, Pudlák i Sgall. En segon lloc, demostrem que els tres sistemes admeten la propietat d'interpolació eficient. Mostrem que, per a cadascun dels sistemes, hi ha un algorisme de temps polinomial que, donat dos conjunts P(x,z) i Q(y,z) de restriccions polinomials en successions disjuntes de variables x, y i z, donada una refutació de la unió de les restriccions de P(x,z) i Q(y,z), i donada una assignació per a les variables z, troba una refutació de P(x,a) o una refutació de Q(y,a). Finalment considerem la relació entre el nombre de monomis i la longitud de representació en bits per al Càlcul Polinomial i per a Sumes de Quadrats. Mostrem que hi ha un conjunt insatisfactible de restriccions polinomials que admet refutacions tant en Càlcul Polinomial com en Sumes de Quadrats amb un nombre polinòmic de monomis, però per a les quals qualsevol refutació en Càlcul Polinomial o en Sumes de Quadrats requereix complexitat en nombre de bits exponencial. A més de l'èmfasi en les mesures de complexitat diferents del grau, un altre tema unificador en els tres resultats és l'ús de certes caracteritzacions semàntiques de proves i refutacions limitades en recursos. Tots els resultats fan un ús clau de la propietat de completesa d'aquestes caracteritzacions. Amb tot, el treball sobre aquestes caracteritzacions semàntiques es presenta com la quarta aportació central d'aquesta tesi.Postprint (published version

Chapter Nabladot Analysis of Hybrid Theories in International Relations

Scientific research in International Relations has produced a growing corpus of empirically grounded formal theoretical models of phenomena ranging from deterrence to systemic polarity, from conditions of peace to the onset of war. Many of these important theories contain a mix of continuous and discrete dimensions, causal variables, and parameters. Analysis and understanding of this fundamental and intriguing class of theories containing functions with a mix of continuous and discrete variables has puzzled generations of social scientists and applied mathematicians. This challenging and longstanding puzzle now has a solution. Here we demonstrate how the recently created calculus with nabladot operators is beginning to uncover previously unknown properties of hybrid international phenomena. Results include new concepts and precise principles on causal relationships, previously unknown political features, and fundamental properties of probabilistic causality, demonstrated through nabladot analysis of international events, crisis dynamics, and warfare

Analysing the familiar : reasoning about space and time in the everyday world

The development of suitable explicit representations of knowledge that can be manipulated by general purpose inference mechanisms has always been central to Artificial Intelligence (AI). However, there has been a distinct lack of rigorous formalisms in the literature that can be used to model domain knowledge associated with the everyday physical world. If AI is to succeed in building automata that can function reasonably well in unstructured physical domains, the development and utility of such formalisms must be secured. This thesis describes a first order axiomatic theory that can be used to encode much topological and metrical information that arises in our everyday dealings with the physical world. The formalism is notable for the minimal assumptions required in order to lift up a very general framework that can cover the representation of much intuitive spatial and temporal knowledge. The basic ontology assumes regions that can be either spatial or temporal and over which a set of relations and functions are defined. The resulting partitioning of these abstract spaces, allow complex relationships between objects and the description of processes to be formally represented. This also provides a useful foundation to control the proliferation of inference commonly associated with mechanised logics. Empirical information extracted from the domain is added and mapped to these basic structures showing how further control of inference can be secured. The representational power of the formalism and computational tractability of the general methodology proposed is substantiated using two non-trivial domain problems - modelling phagocytosis and exocytosis of uni-cellular organisms, and modelling processes arising during the cycle of operations of a force pump

3D CNN methods in biomedical image segmentation

A definite trend in Biomedical Imaging is the one towards the integration of increasingly complex interpretative layers to the pure data acquisition process. One of the most interesting and looked-forward goals in the field is the automatic segmentation of objects of interest in extensive acquisition data, target that would allow Biomedical Imaging to look beyond its use as a purely assistive tool to become a cornerstone in ambitious large-scale challenges like the extensive quantitative study of the Human Brain. In 2019 Convolutional Neural Networks represent the state of the art in Biomedical Image segmentation and scientific interests from a variety of fields, spacing from automotive to natural resource exploration, converge to their development. While most of the applications of CNNs are focused on single-image segmentation, biomedical image data -being it MRI, CT-scans, Microscopy, etc- often benefits from three-dimensional volumetric expression. This work explores a reformulation of the CNN segmentation problem that is native to the 3D nature of the data, with particular interest to the applications to Fluorescence Microscopy volumetric data produced at the European Laboratories for Nonlinear Spectroscopy in the context of two different large international human brain study projects: the Human Brain Project and the White House BRAIN Initiative

Optimization of Photonic Band Structures

In this work we study mathematical optimization problems that arise in the design of photonic crystals, whose band structures should exhibit specific properties. To this end we develop a mathematical model for time-harmonic wave propagation in three-dimensional, periodic media. We investigate the dependency of band structures on the medium structure and develop two types of optimization algorithms. The performance of these algorithms is demonstrated through several of numerical experiments