887 resultados para Computer Algebra Systems (CAS)


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A myriad of computer management systems are available for the restaurant business. The author discusses all aspects of evaluating, purchasing, and using such systems for a restaurant operation.

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7th Mediterranean Conference on Information Systems, MCIS 2012, Guimaraes, Portugal, September 8-10, 2012, Proceedings Series: Lecture Notes in Business Information Processing, Vol. 129

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Os sistemas Computer-Aided Diagnosis (CAD) auxiliam a deteção e diferenciação de lesões benignas e malignas, aumentando a performance no diagnóstico do cancro da mama. As lesões da mama estão fortemente correlacionadas com a forma do contorno: lesões benignas apresentam contornos regulares, enquanto as lesões malignas tendem a apresentar contornos irregulares. Desta forma, a utilização de medidas quantitativas, como a dimensão fractal (DF), pode ajudar na caracterização dos contornos regulares ou irregulares de uma lesão. O principal objetivo deste estudo é verificar se a utilização concomitante de 2 (ou mais) medidas de DF – uma tradicionalmente utilizada, a qual foi designada por “DF de contorno”; outra proposta por nós, designada por “DF de área” – e ainda 3 medidas obtidas a partir destas, por operações de dilatação/erosão e por normalização de uma das medidas anteriores, melhoram a capacidade de caracterização de acordo com a escala BIRADS (Breast Imaging Reporting and Data System) e o tipo de lesão. As medidas de DF (DF contorno e DF área) foram calculadas através da aplicação do método box-counting, diretamente em imagens de lesões segmentadas e após a aplicação de um algoritmo de dilatação/erosão. A última medida baseia-se na diferença normalizada entre as duas medidas DF de área antes e após a aplicação do algoritmo de dilatação/erosão. Os resultados demonstram que a medida DF de contorno é uma ferramenta útil na diferenciação de lesões, de acordo com a escala BIRADS e o tipo de lesão; no entanto, em algumas situações, ocorrem alguns erros. O uso combinado desta medida com as quatro medidas propostas pode melhorar a classificação das lesões.

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Building reliable real-time applications on top of commercial off-the-shelf (COTS) components is not a straightforward task. Thus, it is essential to provide a simple and transparent programming model, in order to abstract programmers from the low-level implementation details of distribution and replication. However, the recent trend for incorporating pre-emptive multitasking applications in reliable real-time systems inherently increases its complexity. It is therefore important to provide a transparent programming model, enabling pre-emptive multitasking applications to be implemented without resorting to simultaneously dealing with both system requirements and distribution and replication issues. The distributed embedded architecture using COTS components (DEAR-COTS) architecture has been previously proposed as an architecture to support real-time and reliable distributed computer-controlled systems (DCCS) using COTS components. Within the DEAR-COTS architecture, the hard real-time subsystem provides a framework for the development of reliable real-time applications, which are the core of DCCS applications. This paper presents the proposed framework, and demonstrates how it can be used to support the transparent replication of software components.

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The aim of this retrospective study was to compare the clinical and radiographic results after TKA (PFC, DePuy), performed either by computer assisted navigation (CAS, Brainlab, Johnson&Johnson) or by conventional means. Material and methods: Between May and December 2006 we reviewed 36 conventional TKA performed between 2002 and 2003 (group A) and 37 navigated TKA performed between 2005 and 2006 (group B) by the same experienced surgeon. The mean age in group A was 74 years (range 62-90) and 73 (range 58-85) in group B with a similar age distribution. The preoperative mechanical axes in group A ranged from -13° varus to +13° valgus (mean absolute deviation 6.83°, SD 3.86), in group B from -13° to +16° (mean absolute deviation 5.35, SD 4.29). Patients with a previous tibial osteotomy or revision arthroplasty were excluded from the study. Examination was done by an experienced orthopedic resident independent of the surgeon. All patients had pre- and postoperative long standing radiographs. The IKSS and the WOMAC were utilized to determine the clinical outcome. Patient's degree of satisfaction was assessed on a visual analogous scale (VAS). Results: 32 of the 37 navigated TKAs (86,5%) showed a postoperative mechanical axis within the limits of 3 degrees of valgus or varus deviation compared to only 24 (66%) of the 36 standard TKAs. This difference was significant (p = 0.045). The mean absolute deviation from neutral axis was 3.00° (range -5° to +9°, SD: 1.75) in group A in comparison to 1.54° (range -5° to +4°, SD: 1.41) in group B with a highly significant difference (p = 0.000). Furthermore, both groups showed a significant postoperative improvement of their mean IKSS-values (group A: 89 preoperative to 169 postoperative, group B 88 to 176) without a significant difference between the two groups. Neither the WOMAC nor the patient's degree of satisfaction - as assessed by VAS - showed significant differences. Operation time was significantly higher in group B (mean 119.9 min.) than in group A (mean 99.6 min., p <0.000). Conclusion: Our study showed consistent significant improvement of postoperative frontal alignment in TKA by computer assisted navigation (CAS) compared to standard methods, even in the hands of a surgeon well experienced in standard TKA implantation. However, the follow-up time of this study was not long enough to judge differences in clinical outcome. Thus, the relevance of computer navigation for clinical outcome and survival of TKA remains to be proved in long term studies to justify the longer operation time. References 1 Stulberg SD. Clin Orth Rel Res. 2003;(416):177-84. 2 Chauhan SK. JBJS Br. 2004;86(3):372-7. 3 Bäthis H, et al. Orthopäde. 2006;35(10):1056-65.

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Markkinasegmentointi nousi esiin ensi kerran jo 50-luvulla ja se on ollut siitä lähtien yksi markkinoinnin peruskäsitteistä. Suuri osa segmentointia käsittelevästä tutkimuksesta on kuitenkin keskittynyt kuluttajamarkkinoiden segmentointiin yritys- ja teollisuusmarkkinoiden segmentoinnin jäädessä vähemmälle huomiolle. Tämän tutkimuksen tavoitteena on luoda segmentointimalli teollismarkkinoille tietotekniikan tuotteiden ja palveluiden tarjoajan näkökulmasta. Tarkoituksena on selvittää mahdollistavatko case-yrityksen nykyiset asiakastietokannat tehokkaan segmentoinnin, selvittää sopivat segmentointikriteerit sekä arvioida tulisiko tietokantoja kehittää ja kuinka niitä tulisi kehittää tehokkaamman segmentoinnin mahdollistamiseksi. Tarkoitus on luoda yksi malli eri liiketoimintayksiköille yhteisesti. Näin ollen eri yksiköiden tavoitteet tulee ottaa huomioon eturistiriitojen välttämiseksi. Tutkimusmetodologia on tapaustutkimus. Lähteinä tutkimuksessa käytettiin sekundäärisiä lähteitä sekä primäärejä lähteitä kuten case-yrityksen omia tietokantoja sekä haastatteluita. Tutkimuksen lähtökohtana oli tutkimusongelma: Voiko tietokantoihin perustuvaa segmentointia käyttää kannattavaan asiakassuhdejohtamiseen PK-yritys sektorilla? Tavoitteena on luoda segmentointimalli, joka hyödyntää tietokannoissa olevia tietoja tinkimättä kuitenkaan tehokkaan ja kannattavan segmentoinnin ehdoista. Teoriaosa tutkii segmentointia yleensä painottuen kuitenkin teolliseen markkinasegmentointiin. Tarkoituksena on luoda selkeä kuva erilaisista lähestymistavoista aiheeseen ja syventää näkemystä tärkeimpien teorioiden osalta. Tietokantojen analysointi osoitti selviä puutteita asiakastiedoissa. Peruskontaktitiedot löytyvät mutta segmentointia varten tietoa on erittäin rajoitetusti. Tietojen saantia jälleenmyyjiltä ja tukkureilta tulisi parantaa loppuasiakastietojen saannin takia. Segmentointi nykyisten tietojen varassa perustuu lähinnä sekundäärisiin tietoihin kuten toimialaan ja yrityskokoon. Näitäkään tietoja ei ole saatavilla kaikkien tietokannassa olevien yritysten kohdalta.

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Whenever a spacecraft is launched it is essential that the algorithms in the on-board software systems and at ground control are efficient and reliable over extended periods of time. Geometric numerical integrators, and in particular variational integrators, have both these characteristics. In "Numerics of Spacecraft Dynamics" new numerical integrators are presented and analysed in depth. These algorithms have been designed specifically for the dynamics of spacecraft and artificial satellites in Earth orbits. Full analytical solutions to a class of integrable deformations of the two-body problem in classical mechanics are derived, and a systematic method to compute variational integrators to arbitrary order with a computer algebra system is introduced.

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Nowadays, computer-based systems tend to become more complex and control increasingly critical functions affecting different areas of human activities. Failures of such systems might result in loss of human lives as well as significant damage to the environment. Therefore, their safety needs to be ensured. However, the development of safety-critical systems is not a trivial exercise. Hence, to preclude design faults and guarantee the desired behaviour, different industrial standards prescribe the use of rigorous techniques for development and verification of such systems. The more critical the system is, the more rigorous approach should be undertaken. To ensure safety of a critical computer-based system, satisfaction of the safety requirements imposed on this system should be demonstrated. This task involves a number of activities. In particular, a set of the safety requirements is usually derived by conducting various safety analysis techniques. Strong assurance that the system satisfies the safety requirements can be provided by formal methods, i.e., mathematically-based techniques. At the same time, the evidence that the system under consideration meets the imposed safety requirements might be demonstrated by constructing safety cases. However, the overall safety assurance process of critical computerbased systems remains insufficiently defined due to the following reasons. Firstly, there are semantic differences between safety requirements and formal models. Informally represented safety requirements should be translated into the underlying formal language to enable further veri cation. Secondly, the development of formal models of complex systems can be labour-intensive and time consuming. Thirdly, there are only a few well-defined methods for integration of formal verification results into safety cases. This thesis proposes an integrated approach to the rigorous development and verification of safety-critical systems that (1) facilitates elicitation of safety requirements and their incorporation into formal models, (2) simplifies formal modelling and verification by proposing specification and refinement patterns, and (3) assists in the construction of safety cases from the artefacts generated by formal reasoning. Our chosen formal framework is Event-B. It allows us to tackle the complexity of safety-critical systems as well as to structure safety requirements by applying abstraction and stepwise refinement. The Rodin platform, a tool supporting Event-B, assists in automatic model transformations and proof-based verification of the desired system properties. The proposed approach has been validated by several case studies from different application domains.

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The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [Bieberbach1916]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [deBranges1985] when some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [AskeyGasper1976] about certain hypergeometric functions played a crucial role in de Branges' proof. In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [Weinstein1991] follows, and it is shown how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.

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This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

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This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

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The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

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During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

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In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.