We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions. (authors' abstract)

We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Esta tesis está dedicada a los sistemas de membranas con objetos-símbolo como marco teórico de los sistemas paralelos y distribuidos de procesamiento de multiconjuntos.Una computación de parada puede aceptar, generar o procesar un número, un vector o una palabra; por tanto el sistema define globalmente (a través de los resultados de todas sus computaciones) un conjunto de números, de vectores, de palabras (es decir, un lenguaje), o bien una función. En esta tesis estudiamos la capacidad de estos sistemas para resolver problemas particulares, así como su potencia computacional. Por ejemplo, las familias de lenguajes definidas por diversas clases de estos sistemas se comparan con las familias clásicas, esto es, lenguajes regulares, independientes del contexto, generados por sistemas 0L tabulados extendidos, generados por gramáticas matriciales sin chequeo de apariciones, recursivamente enumerables, etc. Se prestará especial atención a la comunicación de objetos entre regiones y a las distintas formas de cooperación entre ellos.Se pretende (Sección 3.4) realizar una formalización los sistemas de membranas y construir una herramienta tipo software para la variante que usa cooperación no distribuida, el navegador de configuraciones, es decir, un simulador, en el cual el usuario selecciona la siguiente configuración entre todas las posibles, estando permitido volver hacia atrás. Se considerarán diversos modelos distribuidos. En el modelo de evolución y comunicación (Capítulo 4) separamos las reglas tipo-reescritura y las reglas de transporte (llamadas symport y antiport). Los sistemas de bombeo de protones (proton pumping, Secciones 4.8, 4.9) constituyen una variante de los sistemas de evolución y comunicación con un modo restrictivo de cooperación. Un modelo especial de computación con membranas es el modelo puramente comunicativo, en el cual los objetos traspasan juntos una membrana. Estudiamos la potencia computacional de las sistemas de membranas con symport/antiport de 2 o 3 objetos (Capítulo 5) y la potencia computacional de las sistemas de membranas con alfabeto limitado (Capítulo 6).El determinismo (Secciones 4.7, 5.5, etc.) es una característica especial (restrictiva) de los sistemas computacionales. Se pondrá especial énfasis en analizar si esta restricción reduce o no la potencia computacional de los mismos. Los resultados obtenidos para sistemas de bombeo del protones están transferidos (Sección 7.3) a sistemas con catalizadores bistabiles. Unos ejemplos de aplicación concreta de los sistemas de membranas (Secciones 7.1, 7.2) son la resolución de problemas NP-completos en tiempo polinomial y la resolución de problemas de ordenación. / This thesis deals with membrane systems with symbol objects as a theoretical framework of distributed parallel multiset processing systems.A halting computation can accept, generate or process a number, a vector or a word, so the system globally defines (by the results of all its computations) a set of numbers or a set of vectors or a set of words, (i.e., a language), or a function. The ability of these systems to solve particular problems is investigated, as well as their computational power, e.g., the language families defined by different classes of these systems are compared to the classical ones, i.e., regular, context-free, languages generated by extended tabled 0L systems, languages generated by matrix grammars without appearance checking, recursively enumerable languages, etc. Special attention is paid to communication of objects between the regions and to the ways of cooperation between the objects.An attempt to formalize the membrane systems is made (Section 3.4), and a software tool is constructed for the non-distributed cooperative variant, the configuration browser, i.e., a simulator, where the user chooses the next configuration among the possible ones and can go back. Different distributed models are considered. In the evolution-communication model (Chapter 4) rewriting-like rules are separated from transport rules. Proton pumping systems (Sections 4.8, 4.9) are a variant of the evolution-communication systems with a restricted way of cooperation. A special membrane computing model is a purely communicative one: the objects are moved together through a membrane. We study the computational power of membrane systems with symport/antiport of 2 or 3 objects (Chapter 5) and the computational power of membrane systems with a limited alphabet (Chapter 6).Determinism (Sections 4.7, 5.5, etc.) is a special property of computational systems; the question of whether this restriction reduces the computational power is addressed. The results on proton pumping systems can be carried over (Section 7.3) to the systems with bi-stable catalysts. Some particular examples of membrane systems applications are solving NP-complete problems in polynomial time, and solving the sorting problem.

A universal cycle (u-cycle) is a compact listing of a collection of combinatorial objects. In this paper, we use natural encodings of these objects to show the existence of u-cycles for collections of subsets, restricted multisets, and lattice paths. For subsets, we show that a u-cycle exists for the κ-subsets of an n-set if we let κ vary in a non zero length interval. We use this result to construct a "covering" of length (1+o(1))(n/κ) for all subsets of [n] of size exactly κ with a specific formula for the o(1) term. We also show that u-cycles exist for all n-length words over some alphabet ∑, which contain all characters from R ⊂ ∑. Using this result we provide u-cycles for encodings of Sperner families of size 2 and proper chains of subsets.

Random sampling has become a crucial component of modern data management systems. Although the literature on database sampling is large, there has been relatively little work on the problem of maintaining a sample in the presence of arbitrary insertions and deletions to the underlying dataset. Most existing maintenance techniques apply either to the insert-only case or to datasets that do not contain duplicates. In this paper, we provide a scheme that maintains a Bernoulli sample of an underlying multiset in the presence of an arbitrary stream of updates, deletions, and insertions. Importantly, the scheme never needs to access the underlying multiset. Such Bernoulli samples are easy to manipulate, and are well suited to parallel processing environments. Our method can be viewed as an enhancement of the 'counting sample' scheme developed by Gibbons and Matias for estimating the frequency of highly frequent items. We show how the 'tracking counters' used by our maintenance scheme can be exploited to estimate population frequencies, sums, and averages in an unbiased manner, with lower variance than the usual estimators based on a Bernoulli sample. The number of distinct items in the multiset can also be estimated without bias. Finally, we discuss certain problems of subsampling and merging that a rise in systems with limited memory resources or distributed processing, respectively.

No description available.

Software product line engineering is a common method for designing complex software systems. Feature modeling is the most common approach to specify product lines. A feature model is a feature diagram (a special tree of features) plus some crosscutting constraints. Feature modeling languages are grouped into basic and cardinality-based models. The common understanding of the semantics of feature models is a Boolean semantics. We discuss a major deficiency of this semantics and fix it by applying, in turn, modal logic, the theory of multisets, and formal language theory. In order to adequately represent the semantics of basic models, we propose a Kripke semantics and show that basic feature modeling needs a modal rather than Boolean logic. We propose two multiset based theories for cardinality-based feature diagrams, called flat and hierarchical semantics. We show that the hierarchical semantics of a given cardinality-based diagram captures all information in the diagram. We also charac- terize sets of multisets, which can provide a hierarchical semantics of some diagrams. We provide three different reduction processes going from a cardinality-based diagram to an appropriate regular expression. As for crosscutting constraints, we propose a formal language interpretation of them. We also characterize some existing analysis operations over feature models in terms of operations on the corresponding languages and discuss the relevant decidability problems. / Thesis / Doctor of Philosophy (PhD)

No description available.

Η ραγδαία ανάπτυξη που παρουσιάστηκε τα τελευταία χρόνια σε διάφορους τομείς της πληροφορικής με την αύξηση της ισχύος επεξεργασίας και της δυνατότητας αποθήκευσης ενός τεράστιου όγκου δεδομένων έδωσε νέα ώθηση στον τομέα διαχείρισης, αναζήτησης, σύνοψης και εξαγωγής της πληροφορίας από ένα βίντεο. Για την διαχείριση αυτής της πληροφορίας αναπτύχθηκαν τεχνικές περίληψης βίντεο. Η περίληψη ενός βίντεο υπό μορφή μιας στατικής ακολουθίας χαρακτηριστικών καρέ, μειώνει τον απαραίτητο όγκο της πληροφορίας που απαιτείται σε συστήματα αναζήτησης, ενώ διαμορφώνει την βάση για την αντιμετώπιση του σημασιολογικού περιεχομένου του σε εφαρμογές ανάκτησης. Το ερευνητικό αντικείμενο της παρούσας διδακτορικής διατριβής αναφέρεται σε τεχνικές αυτόματης περίληψης βίντεο με χρήση της θεωρίας γράφων, για την ανάπτυξη μη επιβλεπόμενων αλγόριθμων ομαδοποίησης. Κάθε καρέ της ακολουθίας του βίντεο δεν αντιμετωπίζεται ως ένα διακριτό στοιχείο, αλλά λαμβάνεται υπόψη ο βαθμός συσχέτισης μεταξύ τους. Με αυτόν τον τρόπο το πρόβλημα της ομαδοποίησης ανάγεται από μια τυπική διαδικασία αναγνώρισης ομάδων σε ένα σύστημα ανάλυσης της δομής που περιέχεται στο σύνολο των δεδομένων. Ακόμη παρουσιάζεται μια νέα τεχνική βελτίωσης του βαθμού ομοιότητας των καρέ, η οποία βασίζεται στο θεωρητικό φορμαλισμό τεχνικών ημί-επιβλεπόμενης εκμάθησης, με χρήση όμως αλγόριθμων δυναμικής συμπίεσης, για την αναπαράσταση του οπτικού περιεχομένου τους. Τα αναλυτικά πειραματικά αποτελέσματα που παρατίθενται, αποδεικνύουν την βελτίωση της απόδοσης των προτεινόμενων μεθόδων σε σχέση με γνωστές τεχνικές περίληψης. Τέλος, προτείνονται κάποιες μελλοντικές κατευθύνσεις έρευνας στο αντικείμενο που πραγματεύεται η παρούσα διατριβή, με άμεσες επεκτάσεις στο πεδίο ανάκτησης εικόνας και βίντεο. / The rapid development witnessed in the recent years enabling the storage and processing of a huge amount of data, in various fields of computer technology and image/video understanding, has given new impetus to the field of video manipulation, browsing, indexing, and retrieval. Video summarization, as a static sequence of key frames, reduces the amount of information required for video searching, while provides the basis for understanding the semantic content in video retrieval applications. The research subject of this doctoral thesis is the incorporation of graph theory and unsupervised clustering algorithms in Automatic Video Summarization applications of large video sequences. In this context, every frame from a video sequence is not processed as a discrete element, but the relations between the frames are considered. Thus, the clustering problem is transformed from a typical computation procedure, to the problem of data structure analysis. Detailed experimental results demonstrate the performance improvement provided by the proposed methods in comparison with well-known video summarization techniques from the literature. Finally, future research directions are proposed, directly applicable to the fields of image and video retrieval.

Perhaps the most flexible synopsis of a database is a uniform random sample of the data; such samples are widely used to speed up the processing of analytic queries and data-mining tasks, to enhance query optimization, and to facilitate information integration. Most of the existing work on database sampling focuses on how to create or exploit a random sample of a static database, that is, a database that does not change over time. The assumption of a static database, however, severely limits the applicability of these techniques in practice, where data is often not static but continuously evolving. In order to maintain the statistical validity of the sample, any changes to the database have to be appropriately reflected in the sample. In this thesis, we study efficient methods for incrementally maintaining a uniform random sample of the items in a dataset in the presence of an arbitrary sequence of insertions, updates, and deletions. We consider instances of the maintenance problem that arise when sampling from an evolving set, from an evolving multiset, from the distinct items in an evolving multiset, or from a sliding window over a data stream. Our algorithms completely avoid any accesses to the base data and can be several orders of magnitude faster than algorithms that do rely on such expensive accesses. The improved efficiency of our algorithms comes at virtually no cost: the resulting samples are provably uniform and only a small amount of auxiliary information is associated with the sample. We show that the auxiliary information not only facilitates efficient maintenance, but it can also be exploited to derive unbiased, low-variance estimators for counts, sums, averages, and the number of distinct items in the underlying dataset. In addition to sample maintenance, we discuss methods that greatly improve the flexibility of random sampling from a system's point of view. More specifically, we initiate the study of algorithms that resize a random sample upwards or downwards. Our resizing algorithms can be exploited to dynamically control the size of the sample when the dataset grows or shrinks; they facilitate resource management and help to avoid under- or oversized samples. Furthermore, in large-scale databases with data being distributed across several remote locations, it is usually infeasible to reconstruct the entire dataset for the purpose of sampling. To address this problem, we provide efficient algorithms that directly combine the local samples maintained at each location into a sample of the global dataset. We also consider a more general problem, where the global dataset is defined as an arbitrary set or multiset expression involving the local datasets, and provide efficient solutions based on hashing.