A computable approach to measure and integration theory

We introduce a computable framework for Lebesgue’s measure and integration theory in the spirit of domain theory. For an effectively given second countable locally compact Hausdorff space and an effectively given finite Borel measure on the space, we define a recursive measurable set, which extends the corresponding notion due to S?anin for the Lebesgue measure on the real line. We also introduce the stronger notion of a computable measurable set, where a measurable set is approximated from inside and outside by sequences of closed and open subsets, respectively. The more refined property of computable measurable sets give rise to the idea of partial measurable subsets, which naturally form a domain for measurable subsets. We then introduce interval-valued measurable functions and develop the notion of recursive and computable measurable functions using interval-valued simple functions. This leads us to the interval versions of the main results in classical measure theory. The Lebesgue integral is shown to be a continuous operator on the domain of interval-valued measurable functions and the interval-valued Lebesgue integral provides a computable framework for integration.     

Extending Spider Diagrams for policy definition

Spider Diagrams (SDs) are a well-established visual language used to specify sets, their relationships, and constraints on their cardinalities. We propose two extensions allowing their use in the definition of temporal policies. Firstly, Timed SDs (TSDs) enable the expression of temporal constraints. We adopt an interval-based model of calendar time, permitting diagram elements to be specified to exist only over some interval. We introduce basic TSDs, where time constraints refer to an entire diagram rather than individual elements, as a canonical form for TSDs, and decompose complex TSDs into comic strip-like sequences of basic TSDs. Secondly, we introduce an innovative usage of SDs by specialising and adapting them to an OO-modelling context: in type-SDs a spider represents a type, whereas in instance-SDs a spider represents a specific object of a given type. A notion of conformance of an instance-SD to a type-SD ensues and we extend the concepts to instance-TSDs and type-TSDs. Finally, we combine extensions to allow the specification of temporal policies, which define permissible states for instances of some given type over a period without temporal gaps in it, and introduce a notion of conformance to a policy for a sequence of time-annotated instances.     

Regional averaged controllability for hyperbolic parameter dependent systems

The purpose of this paper is to extend the notion of regional controllability for hyperbolic parameter dependent systems. The key idea is the characterization of the \textit{averaged regional control} with minimal energy. This control steers the state average (with respect to such a parameter) towards the desired state only on a given part of the system evolution domain. In this paper, we give the precis definition and the properties of this new concept. Then, we use an approach based on an extension of the Hilbert uniqueness method devoted to the calculation of the control in two different cases: zone control and pointwise control.     

A hybrid approach to outlier detection based on boundary region

In recent years, much attention has been given to the problem of outlier detection, whose aim is to detect outliers - objects who behave in an unexpected way or have abnormal properties. The identification of outliers is important for many applications such as intrusion detection, credit card fraud, criminal activities in electronic commerce, medical diagnosis and anti-terrorism, etc. In this paper, we propose a hybrid approach to outlier detection, which combines the opinions from boundary-based and distance-based methods for outlier detection ( [Jiang et al., 2005], [Jiang et al., 2009] and [Knorr and Ng, 1998]). We give a novel definition of outliers - BD (boundary and distance)-based outliers, by virtue of the notion of boundary region in rough set theory and the definitions of distance-based outliers. An algorithm to find such outliers is also given. And the effectiveness of our method for outlier detection is demonstrated on two publicly available databases.     

Exploiting domain knowledge to detect outliers

We present a novel definition of outlier whose aim is to embed an available domain knowledge in the process of discovering outliers. Specifically, given a background knowledge, encoded by means of a set of first-order rules, and a set of positive and negative examples, our approach aims at singling out the examples showing abnormal behavior. The technique here proposed is unsupervised, since there are no examples of normal or abnormal behavior, even if it has connections with supervised learning, since it is based on induction from examples. We provide a notion of compliance of a set of facts with respect to a background knowledge and a set of examples, which is exploited to detect the examples that prevent to improve generalization of the induced hypothesis. By testing compliance with respect to both the direct and the dual concept, we are able to distinguish among three kinds of abnormalities, that are irregular, anomalous, and outlier observations. This allows us to provide a finer characterization of the anomaly at hand and to single out subtle forms of anomalies. Moreover, we are also able to provide explanations for the abnormality of an observation which make intelligible the motivation underlying its exceptionality. We present both exact and approximate algorithms for mining abnormalities. The approximate algorithms improve execution time while guaranteeing good accuracy. Moreover, we discuss peculiarities of the novel approach, present examples of knowledge mined, analyze the scalability of the algorithms, and provide comparison with noise handling mechanisms and some alternative approaches.     

Benchmarking Hough Transform Architectures for Real-Time

This paper reviews the Hough transform hardware implementations, with a specific analysis of the architectures that explicitly address the “real-time” issue. The work presents an introduction for a critical assessment of the notion of “real-time”, especially for what concerns modern multimedia applications. The main contribution of this work is the proposal of a new metric for measuring the performance of Hough transform architectures against a given definition of “real-time”. The basic idea is that there is no single set of constraints that define “real-time” for every application domain, and that even the simplest case of Hough transform for line detection, must be properly characterized within a specific application domain. The architectures are classified and evaluated, after a proper characterization of the Hough transform complexity, in terms of dimensions of parameter space and time complexity.     

Tensor scale: An analytic approach with efficient computation and applications

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.     

A framework for the control of stable aperiodic walking in underactuated planar bipeds

This paper presents a new definition of stable walking for point-footed planar bipedal robots that is not necessarily periodic. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. Somewhat more formally, biped walking is shown to be stable if the trajectory of each step places the robot in a state at the end of the step for which a controller is known to exist that generates a trajectory for the next step with this same property. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking in the given sense. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a 5-link biped ERNIE in simulation and experiment.     

Input- and output-decoupling structural zeros of linear systems described by Rosenbrock's polynomial matrices

This paper introduces the notion of input- (output-) decoupling structural zeros for linear time-invariant systems, described by Rosenbrock's system polynomial matrices. This notion is based on the definition of polynomial system matrices having the same structure that is given in this paper. Namely the input- (output-) decoupling structural zeros are decoupling zeros that are present for every choice of the system parameters. The main results are derived using digraph theory. An example illustrates the procedure for detecting structural zeros.     

Set functors,L-fuzzy set categories,and generalized terms

In this work, we generalize previous constructions of fuzzy set categories, introduced in [1], by considering L-fuzzy sets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzy sets are used to define the L-fuzzy categories, which are proven to be rational. In the final part of the paper, the L-fuzzy functors given by the extension principles are provided with a structure of monad which is used, together with the functorial definition of the term monad, to provide monad compositions as a basis for a notion of generalised terms.     

A study of aboutness in information retrieval

This paper addresses the notion of aboutness in information retrieval. First, an exposition is given on how aboutness relates to relevance—a fundamental notion in information retrieval. A short summary is given on how aboutness is defined in more prominent information retrieval models. A model-theoretic definition of aboutness is then analyzed in an abstract setting using so called information fields. These allows properties of aboutness to be expressed independent of any given information retrieval model. As a consequence, information retrieval models can be theoretically compared according to what aboutness postulates they support. The Boolean and Coordinate retrieval models are compared in this fashion. In addition to model-theoretic aboutness, preferential entailment and conditional probabilities are employed to define aboutness between primitive information carriers. The preferential entailment approach is based on a preference semantics derived from nonmonotonic logics. The nonmonotonic behaviour of aboutness under information composition is highlighted. Rules describing how aboutness may be preserved under composition are proposed. Finally, a term aboutness definition drawn from a network-based probabilistic framework is analyzed. Conclusions regarding the implied retrieval effectiveness are drawn.     

Expressing embedded systems configurations at high abstraction levels with UML MARTE profile: Advantages,limitations and alternatives

Embedded systems have become an essential aspect of our professional and personal lives. From avionics, transport and telecommunication systems to general commercial appliances such as smart phones, high definition TVs and gaming consoles; it is difficult to find a domain where these systems have not made their mark. Moreover, Systems-on-Chips (SoCs) which are considered as an integral solution for designing embedded systems, offer advantages such as run-time reconfiguration that can change system configurations during execution, depending upon Quality-of-Service (QoS) criteria such as performance and energy levels. This article deals with aspects related to modeling of these configurations, useful for describing various states of an embedded system, from both structural and operational viewpoints. Our proposal adapts a high abstraction level approach based on the principles of Model-Driven Engineering (MDE) and takes into account the UML MARTE profile for modeling of real-time and embedded systems. Elevating the design abstraction levels help to increase design productivity and achieve execution platform independence, among other advantages. The article details the current proposition of configurations in MARTE via some examples, and points out the advantages as well as some limitations, mainly concerning the semantic aspects of the defined concepts. Finally, we report our experiences on the modeling of an alternate notion of configurations and execution modes within the MARTE compliant Gaspard2 SoC Co-Design framework that has been successful for the design as well as implementation of FPGA based SoCs.     

An Algorithmic Approach to the Identification of Rigid Domains in Proteins

Many proteins undergo conformational changes to perform their functions. A simple mechanism of conformational change in proteins is a rigid domain motion, in which two parts of a structure move rigidly with respect to each other. The identification of rigid domains is therefore useful in understanding the structure-function relationship of proteins. Many algorithms, including those in [16], [22], [13], [10], and [19], have been developed to identify rigid domains. In this paper we complement these works by proposing a mathematical definition of a rigid domain. We argue that our definition more accurately captures the intuitive notion of rigid domain in the previous work, than the quantitative definition of a rigid domain introduced by Nichols et al. [19]. Furthermore, our definition admits a practical approximation algorithm. We can prove theoretical guarantee on the quality of the output of our algorithm. We implement a randomized version of our algorithm, and demonstrate its effectiveness on several known protein complexes.     

On trivariate blending sums of univariate and bivariate quadratic spline quasi-interpolants on bounded domains

The aim of this paper is to investigate, in a bounded domain of R³, two blending sums of univariate and bivariate C¹ quadratic spline quasi-interpolants.The main problem consists in constructing the coefficient functionals associated with boundary generators, i.e. generators with supports not entirely inside the domain. In their definition, these functionals involve data points lying inside or on the boundary of the domain. Moreover, the weights of these functionals must be chosen so that the quasi-interpolants have the best approximation order and a reasonable infinite norm.We give their explicit constructions, infinite norms and error estimates. In order to illustrate the approximation properties of the proposed quasi-interpolants, some numerical examples are presented and compared with those obtained by some other trivariate quasi-interpolants given recently in the literature.     

Practical L2 disturbance attenuation for nonlinear systems

In this work, a notion of generalized L₂-gain for nonlinear systems, where the gain is considered as a function of the state instead of a (global) constant, is presented. This new notion seems to be adequate to characterize the gain properties of several nonlinear systems which do not possess a uniform L₂-gain property (i.e. the L₂-gain depends on the operating point). Moreover, a notion of practical L₂-gain attenuation, which extends the standard definition and parallels (mutatae mutandis) the concepts of practical stability, is also proposed.     

A Note on Formal Iterated Function Systems

Edalat has introduced the notion of weakly hyperbolic iterated function systems [3] and showed that it allows for natural domain theoretic proofs (also for the probabilistic case). This note tries to analyse some of these arguments from the point of view of formal (or point-free) topology [4]. Given a suitable definition of weakly hyperbolic, we show the existence and uniqueness of an attractor, and of an invariant measure.     

On the equivalence of data base schemas—a semantic approach to data translation

A notion of the equivalence of data is the basis for deriving a correct translation of data bases. The equivalence of data base states and data base schemas is defined. Since this definition can only be given with respect to the semantics of data, a short discussion of data base semantics is given. It is shown, how a semantic data model and data definition language (LDDL) can be used to construct a correct specification of a translation function. Finally, an example of the translation of a CODASYL data base schema to a relational data base schema is given.     

Efficient Discovery of Unusual Patterns in Time Series

The problem of finding a specified pattern in a time series database (i.e., query by content) has received much attention and is now a relatively mature field. In contrast, the important problem of enumerating all surprising or interesting patterns has received far less attention. This problem requires a meaningful definition of “surprise”, and an efficient search technique. All previous attempts at finding surprising patterns in time series use a very limited notion of surprise, and/or do not scale to massive datasets. To overcome these limitations we propose a novel technique that defines a pattern surprising if the frequency of its occurrence differs substantially from that expected by chance, given some previously seen data. This notion has the advantage of not requiring the user to explicitly define what is a surprising pattern, which may be hard, or perhaps impossible, to elicit from a domain expert. Instead, the user gives the algorithm a collection of previously observed “normal” data. Our algorithm uses a suffix tree to efficiently encode the frequency of all observed patterns and allows a Markov model to predict the expected frequency of previously unobserved patterns. Once the suffix tree has been constructed, a measure of surprise for all the patterns in a new database can be determined in time and space linear in the size of the database. We demonstrate the utility of our approach with an extensive experimental evaluation.     

A parametric similarity method: Comparative experiments based on semantically annotated large datasets

We present the parametric method SemSim^p aimed at measuring semantic similarity of digital resources. SemSim^p is based on the notion of information content, and it leverages a reference ontology and taxonomic reasoning, encompassing different approaches for weighting the concepts of the ontology. In particular, weights can be computed by considering either the available digital resources or the structure of the reference ontology of a given domain. SemSim^p is assessed against six representative semantic similarity methods for comparing sets of concepts proposed in the literature, by carrying out an experimentation that includes both a statistical analysis and an expert judgment evaluation. To the purpose of achieving a reliable assessment, we used a real-world large dataset based on the Digital Library of the Association for Computing Machinery (ACM), and a reference ontology derived from the ACM Computing Classification System (ACM-CCS). For each method, we considered two indicators. The first concerns the degree of confidence to identify the similarity among the papers belonging to some special issues selected from the ACM Transactions on Information Systems journal, the second the Pearson correlation with human judgment. The results reveal that one of the configurations of SemSim^p outperforms the other assessed methods. An additional experiment performed in the domain of physics shows that, in general, SemSim^p provides better results than the other similarity methods.     

Degenerate problems of optimal control. I

Considered is the practically important and theoretically challenging class of optimal control problems which can be integrated within the common notion of “degenerate problems.” The general definition of such problems is given, which arises from the connection between the degeneracy and the presence of hidden passive differential constraints or discrete chains in the problem. This definition is analyzed with the focus on its relation with the classical notion of degeneracy in the variational calculus and the notion of singular and sliding modes well known in the control theory. This paper is the first one in the series of three, which are aimed at presenting a survey of the main facts and applications of the special theory of such problems, which is essentially based on finding and eliminating passive constraints. New results and generalizations are also reported.