Implicit computational complexity and probabilistic classes

The thesis applies the ICC tecniques to the probabilistic polinomial complexity classes in order to get an implicit characterization of them. The main contribution lays on the implicit characterization of PP (which stands for Probabilistic Polynomial Time) class, showing a syntactical characterisation of PP and a static complexity analyser able to recognise if an imperative program computes in Probabilistic Polynomial Time. The thesis is divided in two parts. The first part focuses on solving the problem by creating a prototype of functional language (a probabilistic variation of lambda calculus with bounded recursion) that is sound and complete respect to Probabilistic Prolynomial Time. The second part, instead, reverses the problem and develops a feasible way to verify if a program, written with a prototype of imperative programming language, is running in Probabilistic polynomial time or not. This thesis would characterise itself as one of the first step for Implicit Computational Complexity over probabilistic classes. There are still open hard problem to investigate and try to solve. There are a lot of theoretical aspects strongly connected with these topics and I expect that in the future there will be wide attention to ICC and probabilistic classes.

Extending Implicit Computational Complexity and Abstract Machines to Languages with Control

The Curry-Howard isomorphism is the idea that proofs in natural deduction can be put in correspondence with lambda terms in such a way that this correspondence is preserved by normalization. The concept can be extended from Intuitionistic Logic to other systems, such as Linear Logic. One of the nice conseguences of this isomorphism is that we can reason about functional programs with formal tools which are typical of proof systems: such analysis can also include quantitative qualities of programs, such as the number of steps it takes to terminate. Another is the possiblity to describe the execution of these programs in terms of abstract machines. In 1990 Griffin proved that the correspondence can be extended to Classical Logic and control operators. That is, Classical Logic adds the possiblity to manipulate continuations. In this thesis we see how the things we described above work in this larger context.

Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability 1/2. We then prove the equi-expressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursion-theoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.

Cooperative communication and distributed detection in wireless sensor networks

Recent progress in microelectronic and wireless communications have enabled the development of low cost, low power, multifunctional sensors, which has allowed the birth of new type of networks named wireless sensor networks (WSNs). The main features of such networks are: the nodes can be positioned randomly over a given field with a high density; each node operates both like sensor (for collection of environmental data) as well as transceiver (for transmission of information to the data retrieval); the nodes have limited energy resources. The use of wireless communications and the small size of nodes, make this type of networks suitable for a large number of applications. For example, sensor nodes can be used to monitor a high risk region, as near a volcano; in a hospital they could be used to monitor physical conditions of patients. For each of these possible application scenarios, it is necessary to guarantee a trade-off between energy consumptions and communication reliability. The thesis investigates the use of WSNs in two possible scenarios and for each of them suggests a solution that permits to solve relating problems considering the trade-off introduced. The first scenario considers a network with a high number of nodes deployed in a given geographical area without detailed planning that have to transmit data toward a coordinator node, named sink, that we assume to be located onboard an unmanned aerial vehicle (UAV). This is a practical example of reachback communication, characterized by the high density of nodes that have to transmit data reliably and efficiently towards a far receiver. It is considered that each node transmits a common shared message directly to the receiver onboard the UAV whenever it receives a broadcast message (triggered for example by the vehicle). We assume that the communication channels between the local nodes and the receiver are subject to fading and noise. The receiver onboard the UAV must be able to fuse the weak and noisy signals in a coherent way to receive the data reliably. It is proposed a cooperative diversity concept as an effective solution to the reachback problem. In particular, it is considered a spread spectrum (SS) transmission scheme in conjunction with a fusion center that can exploit cooperative diversity, without requiring stringent synchronization between nodes. The idea consists of simultaneous transmission of the common message among the nodes and a Rake reception at the fusion center. The proposed solution is mainly motivated by two goals: the necessity to have simple nodes (to this aim we move the computational complexity to the receiver onboard the UAV), and the importance to guarantee high levels of energy efficiency of the network, thus increasing the network lifetime. The proposed scheme is analyzed in order to better understand the effectiveness of the approach presented. The performance metrics considered are both the theoretical limit on the maximum amount of data that can be collected by the receiver, as well as the error probability with a given modulation scheme. Since we deal with a WSN, both of these performance are evaluated taking into consideration the energy efficiency of the network. The second scenario considers the use of a chain network for the detection of fires by using nodes that have a double function of sensors and routers. The first one is relative to the monitoring of a temperature parameter that allows to take a local binary decision of target (fire) absent/present. The second one considers that each node receives a decision made by the previous node of the chain, compares this with that deriving by the observation of the phenomenon, and transmits the final result to the next node. The chain ends at the sink node that transmits the received decision to the user. In this network the goals are to limit throughput in each sensor-to-sensor link and minimize probability of error at the last stage of the chain. This is a typical scenario of distributed detection. To obtain good performance it is necessary to define some fusion rules for each node to summarize local observations and decisions of the previous nodes, to get a final decision that it is transmitted to the next node. WSNs have been studied also under a practical point of view, describing both the main characteristics of IEEE802:15:4 standard and two commercial WSN platforms. By using a commercial WSN platform it is realized an agricultural application that has been tested in a six months on-field experimentation.

Applicability of Process Mining Techniques in Business Environments

This thesis analyses problems related to the applicability, in business environments, of Process Mining tools and techniques. The first contribution is a presentation of the state of the art of Process Mining and a characterization of companies, in terms of their "process awareness". The work continues identifying circumstance where problems can emerge: data preparation; actual mining; and results interpretation. Other problems are the configuration of parameters by not-expert users and computational complexity. We concentrate on two possible scenarios: "batch" and "on-line" Process Mining. Concerning the batch Process Mining, we first investigated the data preparation problem and we proposed a solution for the identification of the "case-ids" whenever this field is not explicitly indicated. After that, we concentrated on problems at mining time and we propose the generalization of a well-known control-flow discovery algorithm in order to exploit non instantaneous events. The usage of interval-based recording leads to an important improvement of performance. Later on, we report our work on the parameters configuration for not-expert users. We present two approaches to select the "best" parameters configuration: one is completely autonomous; the other requires human interaction to navigate a hierarchy of candidate models. Concerning the data interpretation and results evaluation, we propose two metrics: a model-to-model and a model-to-log. Finally, we present an automatic approach for the extension of a control-flow model with social information, in order to simplify the analysis of these perspectives. The second part of this thesis deals with control-flow discovery algorithms in on-line settings. We propose a formal definition of the problem, and two baseline approaches. The actual mining algorithms proposed are two: the first is the adaptation, to the control-flow discovery problem, of a frequency counting algorithm; the second constitutes a framework of models which can be used for different kinds of streams (stationary versus evolving).

Code synchronization and interference management techniques for satellite navigation and communications

This thesis collects the outcomes of a Ph.D. course in Telecommunications engineering and it is focused on enabling techniques for Spread Spectrum (SS) navigation and communication satellite systems. It provides innovations for both interference management and code synchronization techniques. These two aspects are critical for modern navigation and communication systems and constitute the common denominator of the work. The thesis is organized in two parts: the former deals with interference management. We have proposed a novel technique for the enhancement of the sensitivity level of an advanced interference detection and localization system operating in the Global Navigation Satellite System (GNSS) bands, which allows the identification of interfering signals received with power even lower than the GNSS signals. Moreover, we have introduced an effective cancellation technique for signals transmitted by jammers, exploiting their repetitive characteristics, which strongly reduces the interference level at the receiver. The second part, deals with code synchronization. More in detail, we have designed the code synchronization circuit for a Telemetry, Tracking and Control system operating during the Launch and Early Orbit Phase; the proposed solution allows to cope with the very large frequency uncertainty and dynamics characterizing this scenario, and performs the estimation of the code epoch, of the carrier frequency and of the carrier frequency variation rate. Furthermore, considering a generic pair of circuits performing code acquisition, we have proposed a comprehensive framework for the design and the analysis of the optimal cooperation procedure, which minimizes the time required to accomplish synchronization. The study results particularly interesting since it enables the reduction of the code acquisition time without increasing the computational complexity. Finally, considering a network of collaborating navigation receivers, we have proposed an innovative cooperative code acquisition scheme, which allows exploit the shared code epoch information between neighbor nodes, according to the Peer-to-Peer paradigm.

Learning with Kernels on Graphs: DAG-based kernels, data streams and RNA function prediction.

In many application domains data can be naturally represented as graphs. When the application of analytical solutions for a given problem is unfeasible, machine learning techniques could be a viable way to solve the problem. Classical machine learning techniques are defined for data represented in a vectorial form. Recently some of them have been extended to deal directly with structured data. Among those techniques, kernel methods have shown promising results both from the computational complexity and the predictive performance point of view. Kernel methods allow to avoid an explicit mapping in a vectorial form relying on kernel functions, which informally are functions calculating a similarity measure between two entities. However, the definition of good kernels for graphs is a challenging problem because of the difficulty to find a good tradeoff between computational complexity and expressiveness. Another problem we face is learning on data streams, where a potentially unbounded sequence of data is generated by some sources. There are three main contributions in this thesis. The first contribution is the definition of a new family of kernels for graphs based on Directed Acyclic Graphs (DAGs). We analyzed two kernels from this family, achieving state-of-the-art results from both the computational and the classification point of view on real-world datasets. The second contribution consists in making the application of learning algorithms for streams of graphs feasible. Moreover,we defined a principled way for the memory management. The third contribution is the application of machine learning techniques for structured data to non-coding RNA function prediction. In this setting, the secondary structure is thought to carry relevant information. However, existing methods considering the secondary structure have prohibitively high computational complexity. We propose to apply kernel methods on this domain, obtaining state-of-the-art results.

Specification, execution and verification of interaction protocols: an approach based on computational logic

Interaction protocols establish how different computational entities can interact with each other. The interaction can be finalized to the exchange of data, as in 'communication protocols', or can be oriented to achieve some result, as in 'application protocols'. Moreover, with the increasing complexity of modern distributed systems, protocols are used also to control such a complexity, and to ensure that the system as a whole evolves with certain features. However, the extensive use of protocols has raised some issues, from the language for specifying them to the several verification aspects. Computational Logic provides models, languages and tools that can be effectively adopted to address such issues: its declarative nature can be exploited for a protocol specification language, while its operational counterpart can be used to reason upon such specifications. In this thesis we propose a proof-theoretic framework, called SCIFF, together with its extensions. SCIFF is based on Abductive Logic Programming, and provides a formal specification language with a clear declarative semantics (based on abduction). The operational counterpart is given by a proof procedure, that allows to reason upon the specifications and to test the conformance of given interactions w.r.t. a defined protocol. Moreover, by suitably adapting the SCIFF Framework, we propose solutions for addressing (1) the protocol properties verification (g-SCIFF Framework), and (2) the a-priori conformance verification of peers w.r.t. the given protocol (AlLoWS Framework). We introduce also an agent based architecture, the SCIFF Agent Platform, where the same protocol specification can be used to program and to ease the implementation task of the interacting peers.

Computational methods for the analysis of protein structure and function

The vast majority of known proteins have not yet been experimentally characterized and little is known about their function. The design and implementation of computational tools can provide insight into the function of proteins based on their sequence, their structure, their evolutionary history and their association with other proteins. Knowledge of the three-dimensional (3D) structure of a protein can lead to a deep understanding of its mode of action and interaction, but currently the structures of <1% of sequences have been experimentally solved. For this reason, it became urgent to develop new methods that are able to computationally extract relevant information from protein sequence and structure. The starting point of my work has been the study of the properties of contacts between protein residues, since they constrain protein folding and characterize different protein structures. Prediction of residue contacts in proteins is an interesting problem whose solution may be useful in protein folding recognition and de novo design. The prediction of these contacts requires the study of the protein inter-residue distances related to the specific type of amino acid pair that are encoded in the so-called contact map. An interesting new way of analyzing those structures came out when network studies were introduced, with pivotal papers demonstrating that protein contact networks also exhibit small-world behavior. In order to highlight constraints for the prediction of protein contact maps and for applications in the field of protein structure prediction and/or reconstruction from experimentally determined contact maps, I studied to which extent the characteristic path length and clustering coefficient of the protein contacts network are values that reveal characteristic features of protein contact maps. Provided that residue contacts are known for a protein sequence, the major features of its 3D structure could be deduced by combining this knowledge with correctly predicted motifs of secondary structure. In the second part of my work I focused on a particular protein structural motif, the coiled-coil, known to mediate a variety of fundamental biological interactions. Coiled-coils are found in a variety of structural forms and in a wide range of proteins including, for example, small units such as leucine zippers that drive the dimerization of many transcription factors or more complex structures such as the family of viral proteins responsible for virus-host membrane fusion. The coiled-coil structural motif is estimated to account for 5-10% of the protein sequences in the various genomes. Given their biological importance, in my work I introduced a Hidden Markov Model (HMM) that exploits the evolutionary information derived from multiple sequence alignments, to predict coiled-coil regions and to discriminate coiled-coil sequences. The results indicate that the new HMM outperforms all the existing programs and can be adopted for the coiled-coil prediction and for large-scale genome annotation. Genome annotation is a key issue in modern computational biology, being the starting point towards the understanding of the complex processes involved in biological networks. The rapid growth in the number of protein sequences and structures available poses new fundamental problems that still deserve an interpretation. Nevertheless, these data are at the basis of the design of new strategies for tackling problems such as the prediction of protein structure and function. Experimental determination of the functions of all these proteins would be a hugely time-consuming and costly task and, in most instances, has not been carried out. As an example, currently, approximately only 20% of annotated proteins in the Homo sapiens genome have been experimentally characterized. A commonly adopted procedure for annotating protein sequences relies on the "inheritance through homology" based on the notion that similar sequences share similar functions and structures. This procedure consists in the assignment of sequences to a specific group of functionally related sequences which had been grouped through clustering techniques. The clustering procedure is based on suitable similarity rules, since predicting protein structure and function from sequence largely depends on the value of sequence identity. However, additional levels of complexity are due to multi-domain proteins, to proteins that share common domains but that do not necessarily share the same function, to the finding that different combinations of shared domains can lead to different biological roles. In the last part of this study I developed and validate a system that contributes to sequence annotation by taking advantage of a validated transfer through inheritance procedure of the molecular functions and of the structural templates. After a cross-genome comparison with the BLAST program, clusters were built on the basis of two stringent constraints on sequence identity and coverage of the alignment. The adopted measure explicity answers to the problem of multi-domain proteins annotation and allows a fine grain division of the whole set of proteomes used, that ensures cluster homogeneity in terms of sequence length. A high level of coverage of structure templates on the length of protein sequences within clusters ensures that multi-domain proteins when present can be templates for sequences of similar length. This annotation procedure includes the possibility of reliably transferring statistically validated functions and structures to sequences considering information available in the present data bases of molecular functions and structures.

Bioimaging of animal embryogenesis: mathematical methods and computational algorithms

Some fundamental biological processes such as embryonic development have been preserved during evolution and are common to species belonging to different phylogenetic positions, but are nowadays largely unknown. The understanding of cell morphodynamics leading to the formation of organized spatial distribution of cells such as tissues and organs can be achieved through the reconstruction of cells shape and position during the development of a live animal embryo. We design in this work a chain of image processing methods to automatically segment and track cells nuclei and membranes during the development of a zebrafish embryo, which has been largely validates as model organism to understand vertebrate development, gene function and healingrepair mechanisms in vertebrates. The embryo is previously labeled through the ubiquitous expression of fluorescent proteins addressed to cells nuclei and membranes, and temporal sequences of volumetric images are acquired with laser scanning microscopy. Cells position is detected by processing nuclei images either through the generalized form of the Hough transform or identifying nuclei position with local maxima after a smoothing preprocessing step. Membranes and nuclei shapes are reconstructed by using PDEs based variational techniques such as the Subjective Surfaces and the Chan Vese method. Cells tracking is performed by combining informations previously detected on cells shape and position with biological regularization constraints. Our results are manually validated and reconstruct the formation of zebrafish brain at 7-8 somite stage with all the cells tracked starting from late sphere stage with less than 2% error for at least 6 hours. Our reconstruction opens the way to a systematic investigation of cellular behaviors, of clonal origin and clonal complexity of brain organs, as well as the contribution of cell proliferation modes and cell movements to the formation of local patterns and morphogenetic fields.

Engineering Complex Computational Ecosystems

Self-organising pervasive ecosystems of devices are set to become a major vehicle for delivering infrastructure and end-user services. The inherent complexity of such systems poses new challenges to those who want to dominate it by applying the principles of engineering. The recent growth in number and distribution of devices with decent computational and communicational abilities, that suddenly accelerated with the massive diffusion of smartphones and tablets, is delivering a world with a much higher density of devices in space. Also, communication technologies seem to be focussing on short-range device-to-device (P2P) interactions, with technologies such as Bluetooth and Near-Field Communication gaining greater adoption. Locality and situatedness become key to providing the best possible experience to users, and the classic model of a centralised, enormously powerful server gathering and processing data becomes less and less efficient with device density. Accomplishing complex global tasks without a centralised controller responsible of aggregating data, however, is a challenging task. In particular, there is a local-to-global issue that makes the application of engineering principles challenging at least: designing device-local programs that, through interaction, guarantee a certain global service level. In this thesis, we first analyse the state of the art in coordination systems, then motivate the work by describing the main issues of pre-existing tools and practices and identifying the improvements that would benefit the design of such complex software ecosystems. The contribution can be divided in three main branches. First, we introduce a novel simulation toolchain for pervasive ecosystems, designed for allowing good expressiveness still retaining high performance. Second, we leverage existing coordination models and patterns in order to create new spatial structures. Third, we introduce a novel language, based on the existing ``Field Calculus'' and integrated with the aforementioned toolchain, designed to be usable for practical aggregate programming.