5,666 research outputs found

    Decomposition of sequential and concurrent models

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    Le macchine a stati finiti (FSM), sistemi di transizioni (TS) e le reti di Petri (PN) sono importanti modelli formali per la progettazione di sistemi. Un problema fodamentale è la conversione da un modello all'altro. Questa tesi esplora il mondo delle reti di Petri e della decomposizione di sistemi di transizioni. Per quanto riguarda la decomposizione dei sistemi di transizioni, la teoria delle regioni rappresenta la colonna portante dell'intero processo di decomposizione, mirato soprattutto a decomposizioni che utilizzano due sottoclassi delle reti di Petri: macchine a stati e reti di Petri a scelta libera. Nella tesi si dimostra che una proprietà chiamata ``chiusura rispetto all'eccitazione" (excitation-closure) è sufficiente per produrre un insieme di reti di Petri la cui sincronizzazione è bisimile al sistema di transizioni (o rete di Petri di partenza, se la decomposizione parte da una rete di Petri), dimostrando costruttivamente l'esistenza di una bisimulazione. Inoltre, è stato implementato un software che esegue la decomposizione dei sistemi di transizioni, per rafforzare i risultati teorici con dati sperimentali sistematici. Nella seconda parte della dissertazione si analizza un nuovo modello chiamato MSFSM, che rappresenta un insieme di FSM sincronizzate da due primitive specifiche (Wait State - Stato d'Attesa e Transition Barrier - Barriera di Transizione). Tale modello trova un utilizzo significativo nella sintesi di circuiti sincroni a partire da reti di Petri a scelta libera. In particolare vengono identificati degli errori nell'approccio originale, fornendo delle correzioni.Finite State Machines (FSMs), transition systems (TSs) and Petri nets (PNs) are important models of computation ubiquitous in formal methods for modeling systems. Important problems involve the transition from one model to another. This thesis explores Petri nets, transition systems and Finite State Machines decomposition and optimization. The first part addresses decomposition of transition systems and Petri nets, based on the theory of regions, representing them by means of restricted PNs, e.g., State Machines (SMs) and Free-choice Petri nets (FCPNs). We show that the property called ``excitation-closure" is sufficient to produce a set of synchronized Petri nets bisimilar to the original transition system or to the initial Petri net (if the decomposition starts from a PN), proving by construction the existence of a bisimulation. Furthermore, we implemented a software performing the decomposition of transition systems, and reported extensive experiments. The second part of the dissertation discusses Multiple Synchronized Finite State Machines (MSFSMs) specifying a set of FSMs synchronized by specific primitives: Wait State and Transition Barrier. It introduces a method for converting Petri nets into synchronous circuits using MSFSM, identifies errors in the initial approach, and provides corrections

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    Covering and Separation for Permutations and Graphs

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    This is a thesis of two parts, focusing on covering and separation topics of extremal combinatorics and graph theory, two major themes in this area. They entail the existence and properties of collections of combinatorial objects which together either represent all objects (covering) or can be used to distinguish all objects from each other (separation). We will consider a range of problems which come under these areas. The first part will focus on shattering k-sets with permutations. A family of permutations is said to shatter a given k-set if the permutations cover all possible orderings of the k elements. In particular, we investigate the size of permutation families which cover t orders for every possible k-set as well as study the problem of determining the largest number of k-sets that can be shattered by a family with given size. We provide a construction for a small permutation family which shatters every k-set. We also consider constructions of large families which do not shatter any triple. The second part will be concerned with the problem of separating path systems. A separating path system for a graph is a family of paths where, for any two edges, there is a path containing one edge but not the other. The aim is to find the size of the smallest such family. We will study the size of the smallest separating path system for a range of graphs, including complete graphs, complete bipartite graphs, and lattice-type graphs. A key technique we introduce is the use of generator paths - constructed to utilise the symmetric nature of Kn. We continue this symmetric approach for bipartite graphs and study the limitations of the method. We consider lattice-type graphs as an example of the most efficient possible separating systems for any graph

    Statistical analysis of grouped text documents

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    L'argomento di questa tesi sono i modelli statistici per l'analisi dei dati testuali, con particolare attenzione ai contesti in cui i campioni di testo sono raggruppati. Quando si ha a che fare con dati testuali, il primo problema è quello di elaborarli, per renderli compatibili dal punto di vista computazionale e metodologico con i metodi matematici e statistici prodotti e continuamente sviluppati dalla comunità scientifica. Per questo motivo, la tesi passa in rassegna i metodi esistenti per la rappresentazione analitica e l'elaborazione di campioni di dati testuali, compresi i "Vector Space Models", le "rappresentazioni distribuite" di parole e documenti e i "contextualized embeddings". Questa rassegna comporta la standardizzazione di una notazione che, anche all'interno dello stesso approccio di rappresentazione, appare molto eterogenea in letteratura. Vengono poi esplorati due domini di applicazione: i social media e il turismo culturale. Per quanto riguarda il primo, viene proposto uno studio sull'autodescrizione di gruppi diversi di individui sulla piattaforma StockTwits, dove i mercati finanziari sono gli argomenti dominanti. La metodologia proposta ha integrato diversi tipi di dati, sia testuali che variabili categoriche. Questo studio ha agevolato la comprensione sul modo in cui le persone si presentano online e ha trovato stutture di comportamento ricorrenti all'interno di gruppi di utenti. Per quanto riguarda il turismo culturale, la tesi approfondisce uno studio condotto nell'ambito del progetto "Data Science for Brescia - Arts and Cultural Places", in cui è stato addestrato un modello linguistico per classificare le recensioni online scritte in italiano in quattro aree semantiche distinte relative alle attrazioni culturali della città di Brescia. Il modello proposto permette di identificare le attrazioni nei documenti di testo, anche quando non sono esplicitamente menzionate nei metadati del documento, aprendo così la possibilità di espandere il database relativo a queste attrazioni culturali con nuove fonti, come piattaforme di social media, forum e altri spazi online. Infine, la tesi presenta uno studio metodologico che esamina la specificità di gruppo delle parole, analizzando diversi stimatori di specificità di gruppo proposti in letteratura. Lo studio ha preso in considerazione documenti testuali raggruppati con variabile di "outcome" e variabile di gruppo. Il suo contributo consiste nella proposta di modellare il corpus di documenti come una distribuzione multivariata, consentendo la simulazione di corpora di documenti di testo con caratteristiche predefinite. La simulazione ha fornito preziose indicazioni sulla relazione tra gruppi di documenti e parole. Inoltre, tutti i risultati possono essere liberamente esplorati attraverso un'applicazione web, i cui componenti sono altresì descritti in questo manoscritto. In conclusione, questa tesi è stata concepita come una raccolta di studi, ognuno dei quali suggerisce percorsi di ricerca futuri per affrontare le sfide dell'analisi dei dati testuali raggruppati.The topic of this thesis is statistical models for the analysis of textual data, emphasizing contexts in which text samples are grouped. When dealing with text data, the first issue is to process it, making it computationally and methodologically compatible with the existing mathematical and statistical methods produced and continually developed by the scientific community. Therefore, the thesis firstly reviews existing methods for analytically representing and processing textual datasets, including Vector Space Models, distributed representations of words and documents, and contextualized embeddings. It realizes this review by standardizing a notation that, even within the same representation approach, appears highly heterogeneous in the literature. Then, two domains of application are explored: social media and cultural tourism. About the former, a study is proposed about self-presentation among diverse groups of individuals on the StockTwits platform, where finance and stock markets are the dominant topics. The methodology proposed integrated various types of data, including textual and categorical data. This study revealed insights into how people present themselves online and found recurring patterns within groups of users. About the latter, the thesis delves into a study conducted as part of the "Data Science for Brescia - Arts and Cultural Places" Project, where a language model was trained to classify Italian-written online reviews into four distinct semantic areas related to cultural attractions in the Italian city of Brescia. The model proposed allows for the identification of attractions in text documents, even when not explicitly mentioned in document metadata, thus opening possibilities for expanding the database related to these cultural attractions with new sources, such as social media platforms, forums, and other online spaces. Lastly, the thesis presents a methodological study examining the group-specificity of words, analyzing various group-specificity estimators proposed in the literature. The study considered grouped text documents with both outcome and group variables. Its contribution consists of the proposal of modeling the corpus of documents as a multivariate distribution, enabling the simulation of corpora of text documents with predefined characteristics. The simulation provided valuable insights into the relationship between groups of documents and words. Furthermore, all its results can be freely explored through a web application, whose components are also described in this manuscript. In conclusion, this thesis has been conceived as a collection of papers. It aimed to contribute to the field with both applications and methodological proposals, and each study presented here suggests paths for future research to address the challenges in the analysis of grouped textual data

    Quantum-Classical hybrid systems and their quasifree transformations

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    The focus of this work is the description of a framework for quantum-classical hybrid systems. The main emphasis lies on continuous variable systems described by canonical commutation relations and, more precisely, the quasifree case. Here, we are going to solve two main tasks: The first is to rigorously define spaces of states and observables, which are naturally connected within the general structure. Secondly, we want to describe quasifree channels for which both the Schrödinger picture and the Heisenberg picture are well defined. We start with a general introduction to operator algebras and algebraic quantum theory. Thereby, we highlight some of the mathematical details that are often taken for granted while working with purely quantum systems. Consequently, we discuss several possibilities and their advantages respectively disadvantages in describing classical systems analogously to the quantum formalism. The key takeaway is that there is no candidate for a classical state space or observable algebra that can be put easily alongside a quantum system to form a hybrid and simultaneously fulfills all of our requirements for such a partially quantum and partially classical system. Although these straightforward hybrid systems are not sufficient enough to represent a general approach, we use one of the candidates to prove an intermediate result, which showcases the advantages of a consequent hybrid ansatz: We provide a hybrid generalization of classical diffusion generators where the exchange of information between the classical and the quantum side is controlled by the induced noise on the quantum system. Then, we present solutions for our initial tasks. We start with a CCR-algebra where some variables may commute with all others and hence generate a classical subsystem. After clarifying the necessary representations, our hybrid states are given by continuous characteristic functions, and the according state space is equal to the state space of a non-unital C*-algebra. While this C*-algebra is not a suitable candidate for an observable algebra itself, we describe several possible subsets in its bidual which can serve this purpose. They can be more easily characterized and will also allow for a straightforward definition of a proper Heisenberg picture. The subsets are given by operator-valued functions on the classical phase space with varying degrees of regularity, such as universal measurability or strong*-continuity. We describe quasifree channels and their properties, including a state-channel correspondence, a factorization theorem, and some basic physical operations. All this works solely on the assumption of a quasifree system, but we also show that the more famous subclass of Gaussian systems fits well within this formulation and behaves as expected

    Language integrated relational lenses

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    Relational databases are ubiquitous. Such monolithic databases accumulate large amounts of data, yet applications typically only work on small portions of the data at a time. A subset of the database defined as a computation on the underlying tables is called a view. Querying views is helpful, but it is also desirable to update them and have these changes be applied to the underlying database. This view update problem has been the subject of much previous work before, but support by database servers is limited and only rarely available. Lenses are a popular approach to bidirectional transformations, a generalization of the view update problem in databases to arbitrary data. However, perhaps surprisingly, lenses have seldom actually been used to implement updatable views in databases. Bohannon, Pierce and Vaughan propose an approach to updatable views called relational lenses. However, to the best of our knowledge this proposal has not been implemented or evaluated prior to the work reported in this thesis. This thesis proposes programming language support for relational lenses. Language integrated relational lenses support expressive and efficient view updates, without relying on updatable view support from the database server. By integrating relational lenses into the programming language, application development becomes easier and less error-prone, avoiding the impedance mismatch of having two programming languages. Integrating relational lenses into the language poses additional challenges. As defined by Bohannon et al. relational lenses completely recompute the database, making them inefficient as the database scales. The other challenge is that some parts of the well-formedness conditions are too general for implementation. Bohannon et al. specify predicates using possibly infinite abstract sets and define the type checking rules using relational algebra. Incremental relational lenses equip relational lenses with change-propagating semantics that map small changes to the view into (potentially) small changes to the source tables. We prove that our incremental semantics are functionally equivalent to the non-incremental semantics, and our experimental results show orders of magnitude improvement over the non-incremental approach. This thesis introduces a concrete predicate syntax and shows how the required checks are performed on these predicates and show that they satisfy the abstract predicate specifications. We discuss trade-offs between static predicates that are fully known at compile time vs dynamic predicates that are only known during execution and introduce hybrid predicates taking inspiration from both approaches. This thesis adapts the typing rules for relational lenses from sequential composition to a functional style of sub-expressions. We prove that any well-typed functional relational lens expression can derive a well-typed sequential lens. We use these additions to relational lenses as the foundation for two practical implementations: an extension of the Links functional language and a library written in Haskell. The second implementation demonstrates how type-level computation can be used to implement relational lenses without changes to the compiler. These two implementations attest to the possibility of turning relational lenses into a practical language feature

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Machine learning applications in search algorithms for gravitational waves from compact binary mergers

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    Gravitational waves from compact binary mergers are now routinely observed by Earth-bound detectors. These observations enable exciting new science, as they have opened a new window to the Universe. However, extracting gravitational-wave signals from the noisy detector data is a challenging problem. The most sensitive search algorithms for compact binary mergers use matched filtering, an algorithm that compares the data with a set of expected template signals. As detectors are upgraded and more sophisticated signal models become available, the number of required templates will increase, which can make some sources computationally prohibitive to search for. The computational cost is of particular concern when low-latency alerts should be issued to maximize the time for electromagnetic follow-up observations. One potential solution to reduce computational requirements that has started to be explored in the last decade is machine learning. However, different proposed deep learning searches target varying parameter spaces and use metrics that are not always comparable to existing literature. Consequently, a clear picture of the capabilities of machine learning searches has been sorely missing. In this thesis, we closely examine the sensitivity of various deep learning gravitational-wave search algorithms and introduce new methods to detect signals from binary black hole and binary neutron star mergers at previously untested statistical confidence levels. By using the sensitive distance as our core metric, we allow for a direct comparison of our algorithms to state-of-the-art search pipelines. As part of this thesis, we organized a global mock data challenge to create a benchmark for machine learning search algorithms targeting compact binaries. This way, the tools developed in this thesis are made available to the greater community by publishing them as open source software. Our studies show that, depending on the parameter space, deep learning gravitational-wave search algorithms are already competitive with current production search pipelines. We also find that strategies developed for traditional searches can be effectively adapted to their machine learning counterparts. In regions where matched filtering becomes computationally expensive, available deep learning algorithms are also limited in their capability. We find reduced sensitivity to long duration signals compared to the excellent results for short-duration binary black hole signals
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