Transdifferential and transintegral calculus

The set of transreal numbers is a superset of the real numbers. It totalises real arithmetic by defining division by zero in terms of three def- inite, non-finite numbers: positive infinity, negative infinity and nullity. Elsewhere, in this proceedings, we extended continuity and limits from the real domain to the transreal domain, here we extended the real derivative to the transreal derivative. This continues to demonstrate that transreal analysis contains real analysis and operates at singularities where real analysis fails. Hence computer programs that rely on computing deriva- tives { such as those used in scientific, engineering and financial applica- tions { are extended to operate at singularities where they currently fail. This promises to make software, that computes derivatives, both more competent and more reliable. We also extended the integration of absolutely convergent functions from the real domain to the transreal domain.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Software evolution: a graph based model

A model based on graph isomorphisms is used to formalize software evolution. Step by step we narrow the search space by an informed selection of the attributes based on the current state-of-the-art in software engineering and generate a seed solution. We then traverse the resulting space using graph isomorphisms and other set operations over the vertex sets. The new solutions will preserve the desired attributes. The goal of defining an isomorphism based search mechanism is to construct predictors of evolution that can facilitate the automation of ’software factory’ paradigm. The model allows for automation via software tools implementing the concepts.

Transreal limits and elementary functions

We extend all elementary functions from the real to the transreal domain so that they are defined on division by zero. Our method applies to a much wider class of functions so may be of general interest.

Dual semiosis analysis model managing customer-focused service innovation

Customers will not continue to pay for a service if it is perceived to be of poor quality, and/or of no value. With a paradigm shift towards business dependence on service orientated IS solutions [1], it is critical that alignment exists between service definition, delivery, and customer expectation, businesses are to ensure customer satisfaction. Services, and micro-service development, offer businesses a flexible structure for solution innovation, however, constant changes in technology, business and societal expectations means an iterative analysis solution is required to i) determine whether provider services adequately meet customer segment needs and expectations, and ii) to help guide business service innovation and development. In this paper, by incorporating multiple models, we propose a series of steps to help identify and prioritise service gaps. Moreover, the authors propose the Dual Semiosis Analysis Model, i.e. a tool that highlights where within the symbiotic customer / provider semiosis process, requirements misinterpretation, and/or service provision deficiencies occur. This paper offers the reader a powerful customer-centric tool, designed to help business managers highlight both what services are critical to customer quality perception, and where future innovation

Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

A Survey on Graphical Methods for Classification Predictive Performance Evaluation

Predictive performance evaluation is a fundamental issue in design, development, and deployment of classification systems. As predictive performance evaluation is a multidimensional problem, single scalar summaries such as error rate, although quite convenient due to its simplicity, can seldom evaluate all the aspects that a complete and reliable evaluation must consider. Due to this, various graphical performance evaluation methods are increasingly drawing the attention of machine learning, data mining, and pattern recognition communities. The main advantage of these types of methods resides in their ability to depict the trade-offs between evaluation aspects in a multidimensional space rather than reducing these aspects to an arbitrarily chosen (and often biased) single scalar measure. Furthermore, to appropriately select a suitable graphical method for a given task, it is crucial to identify its strengths and weaknesses. This paper surveys various graphical methods often used for predictive performance evaluation. By presenting these methods in the same framework, we hope this paper may shed some light on deciding which methods are more suitable to use in different situations.

A Framework for Exploring Multidimensional Data with 3D Projections

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e. g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework`s applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

An incremental space to visualize dynamic data sets

In Information Visualization, adding and removing data elements can strongly impact the underlying visual space. We have developed an inherently incremental technique (incBoard) that maintains a coherent disposition of elements from a dynamic multidimensional data set on a 2D grid as the set changes. Here, we introduce a novel layout that uses pairwise similarity from grid neighbors, as defined in incBoard, to reposition elements on the visual space, free from constraints imposed by the grid. The board continues to be updated and can be displayed alongside the new space. As similar items are placed together, while dissimilar neighbors are moved apart, it supports users in the identification of clusters and subsets of related elements. Densely populated areas identified in the incSpace can be efficiently explored with the corresponding incBoard visualization, which is not susceptible to occlusion. The solution remains inherently incremental and maintains a coherent disposition of elements, even for fully renewed sets. The algorithm considers relative positions for the initial placement of elements, and raw dissimilarity to fine tune the visualization. It has low computational cost, with complexity depending only on the size of the currently viewed subset, V. Thus, a data set of size N can be sequentially displayed in O(N) time, reaching O(N (2)) only if the complete set is simultaneously displayed.

Taking advantage of contextualized interactions while users watch TV

While watching TV, viewers use the remote control to turn the TV set on and off, change channel and volume, to adjust the image and audio settings, etc. Worldwide, research institutes collect information about audience measurement, which can also be used to provide personalization and recommendation services, among others. The interactive digital TV offers viewers the opportunity to interact with interactive applications associated with the broadcast program. Interactive TV infrastructure supports the capture of the user-TV interaction at fine-grained levels. In this paper we propose the capture of all the user interaction with a TV remote control-including short term and instant interactions: we argue that the corresponding captured information can be used to create content pervasively and automatically, and that this content can be used by a wide variety of services, such as audience measurement, personalization and recommendation services. The capture of fine grained data about instant and interval-based interactions also allows the underlying infrastructure to offer services at the same scale, such as annotation services and adaptative applications. We present the main modules of an infrastructure for TV-based services, along with a detailed example of a document used to record the user-remote control interaction. Our approach is evaluated by means of a proof-of-concept prototype which uses the Brazilian Digital TV System, the Ginga-NCL middleware.

Investigation of a new GRASP-based clustering algorithm applied to biological data

A large amount of biological data has been produced in the last years. Important knowledge can be extracted from these data by the use of data analysis techniques. Clustering plays an important role in data analysis, by organizing similar objects from a dataset into meaningful groups. Several clustering algorithms have been proposed in the literature. However, each algorithm has its bias, being more adequate for particular datasets. This paper presents a mathematical formulation to support the creation of consistent clusters for biological data. Moreover. it shows a clustering algorithm to solve this formulation that uses GRASP (Greedy Randomized Adaptive Search Procedure). We compared the proposed algorithm with three known other algorithms. The proposed algorithm presented the best clustering results confirmed statistically. (C) 2009 Elsevier Ltd. All rights reserved.

Visual analysis of image collections

Multidimensional Visualization techniques are invaluable tools for analysis of structured and unstructured data with variable dimensionality. This paper introduces PEx-Image-Projection Explorer for Images-a tool aimed at supporting analysis of image collections. The tool supports a methodology that employs interactive visualizations to aid user-driven feature detection and classification tasks, thus offering improved analysis and exploration capabilities. The visual mappings employ similarity-based multidimensional projections and point placement to layout the data on a plane for visual exploration. In addition to its application to image databases, we also illustrate how the proposed approach can be successfully employed in simultaneous analysis of different data types, such as text and images, offering a common visual representation for data expressed in different modalities.

Prediction of dynamical, nonlinear, and unstable process behavior

Process scheduling techniques consider the current load situation to allocate computing resources. Those techniques make approximations such as the average of communication, processing, and memory access to improve the process scheduling, although processes may present different behaviors during their whole execution. They may start with high communication requirements and later just processing. By discovering how processes behave over time, we believe it is possible to improve the resource allocation. This has motivated this paper which adopts chaos theory concepts and nonlinear prediction techniques in order to model and predict process behavior. Results confirm the radial basis function technique which presents good predictions and also low processing demands show what is essential in a real distributed environment.

On modeling and evaluating multicomputer transcoding architectures for live-video streams

The pervasive and ubiquitous computing has motivated researches on multimedia adaptation which aims at matching the video quality to the user needs and device restrictions. This technique has a high computational cost which needs to be studied and estimated when designing architectures and applications. This paper presents an analytical model to quantify these video transcoding costs in a hardware independent way. The model was used to analyze the impact of transcoding delays in end-to-end live-video transmissions over LANs, MANs and WANs. Experiments confirm that the proposed model helps to define the best transcoding architecture for different scenarios.

Seamlessly integrating similarity queries in SQL

Modern database applications are increasingly employing database management systems (DBMS) to store multimedia and other complex data. To adequately support the queries required to retrieve these kinds of data, the DBMS need to answer similarity queries. However, the standard structured query language (SQL) does not provide effective support for such queries. This paper proposes an extension to SQL that seamlessly integrates syntactical constructions to express similarity predicates to the existing SQL syntax and describes the implementation of a similarity retrieval engine that allows posing similarity queries using the language extension in a relational DBM. The engine allows the evaluation of every aspect of the proposed extension, including the data definition language and data manipulation language statements, and employs metric access methods to accelerate the queries. Copyright (c) 2008 John Wiley & Sons, Ltd.