<p>This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L¹ functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. For Sobolev functions we study the dimension of the set of non-Lebesgue points.</p>

Patients with chronic pain are generally thought to be physically unfit and less active. Hence, physical reconditioning programs are traditionally proposed to such patients as part of their comprehensive rehabilitation program. Traditional physical fitness evaluation is often implemented in patients with low-back pain. However, most methods have not been validated in that context. We recall and discuss earliest findings in the field of physical fitness tests in patients with low-back pain. Maximal physical tests can be reliable when testing conditions are well defined, standardized and controlled. Reliability, however, does not imply validity. Maximal physical tests as applied to patients with pain should indeed be considered as multidimensional since performance to such tests is often limited by psychological factors as fear-avoidance. Hence, maximal physical tests do not allow valid evaluation of physical fitness in most patients with pain. To obtain valid unidimensional fitness assessment in such patients, submaximal testing should be preferred, which is only possible for cardiorespiratory endurance and body composition assessment. We present our personal contribution to the field. Most of this contribution can be found in 7 previously published papers that are included in our manuscript: • Nielens, H. and L. Plaghki. Evaluation of physical adaptation to exercise of chronic pain patients by a step-test procedure. The Pain Clinic. 1:21-28, 1991 • Nielens, H. and L. Plaghki. Perception of pain and exertion during exercise on a cycle ergometer in chronic pain patients. Clin J Pain. 10:204-209, 1994 • Nielens, H., V. Boisset, and E. Masquelier. Fitness and perceived exertion in patients with fibromyalgia syndrome. Clin J Pain. 16:209-213, 2000 • Nielens, H., T. M. Lejeune, A. Lalaoui, J. P. Squifflet, Y. Pirson, and E. Goffin. Increase of physical activity level after successful renal transplantation: a 5 year follow-up study. Nephrol Dial Transplant. 16:134-140, 2001 • Nielens, H. and E. Masquelier. The role of exercise in the treatment of fibromyalgia: An overview. Int Sportmed J. 2:1-8, 2001 • Nielens, H. and L. Plaghki. Cardiorespiratory fitness, physical activity level, and chronic pain: are men more affected than women? Clin J Pain. 17:129-137, 2001 • Nielens, H., D. Cornet, and F. Rigot. Maximal versus submaximal testing protocols to evaluate fitness of patients with chronic low back pain; abstract. Med Sci Sports Exerc. 34, 2002 We developed an original submaximal cycle ergometer test that allows calculation of an original Physical Working Capacity index, the PWC65%/kg and an original Rate of Perceived Exertion index, the RPE65%. We evaluated the reliability and the validity of the PWC65%/kg as a cardiorespiratory endurance index. We also present and discuss our results obtained in chronic pain patients with those indexes. Clearly, male patients with severe chronic pain are more affected than females in terms of physical fitness and activity, probably due to socio-cultural factors. Exertion perception of most patients with low-back pain and/or sciatica seems normal. However, females with fibromyalgia present with a very significant distortion of exertion perception. Physical reconditioning combined with education seems helpful in most patients with chronic pain directly through fitness improvement but also through the major cognitive change it contributes to generate.

We present a set of approximation results for several covering problems in dense graphs. These results show that for several problems, classical algorithms with constant approximation ratios can be analyzed in a finer way, and provide better constant approximation ratios under some density constraints. In particular, we show that the maximal matching heuristic approximates VERTEX COVER (VC) and MINIMUM MAXIMAL MATCHING (MMM) with a constant ratio strictly smaller than 2 when the proportion of edges present in the graph (weak density) is at least 3/4, or when the normalized minimum degree (strong density) is at least 1/2. We also show that this result can be improved by a greedy algorithm which provides a constant ratio smaller than 2 when the weak density is at least 1/2. We also provide tight families of graphs for all these approximation ratios. We then looked at several algorithms from the literature for VC and SET COVER (SC). We present a unified and critical approach to the Karpinski/Zelikovsky, Imamura/Iwama and Bar-Yehuda/Kehat algorithms, identifying the general the general scheme underlying these algorithms. Finally, we look at the CONNECTED VERTEX COVER (CVC) problem,for which we proposed new approximation results in dense graphs. We first analyze Carla Savage's algorithm, then a new variant of the Karpinski-Zelikovsky algorithm. Our results show that these algorithms provide the same approximation ratios for CVC as the maximal matching heuristic and the Karpinski-Zelikovsky algorithm did for VC. We provide tight examples for the ratios guaranteed by both algorithms. We also introduce a new invariant, the "price of connectivity of VC", defined as the ratio between the optimal solutions of CVC and VC, and showed a nearly tight upper bound on its value as a function of the weak density. Our last chapter discusses software aspects, and presents the use of the GRAPHEDRON software in the framework of approximation algorithms, as well as our contributions to the development of this system. / Nous présentons un ensemble de résultats d'approximation pour plusieurs problèmes de couverture dans les graphes denses. Ces résultats montrent que pour plusieurs problèmes, des algorithmes classiques à facteur d'approximation constant peuvent être analysés de manière plus fine, et garantissent de meilleurs facteurs d'aproximation constants sous certaines contraintes de densité. Nous montrons en particulier que l'heuristique du matching maximal approxime les problèmes VERTEX COVER (VC) et MINIMUM MAXIMAL MATCHING (MMM) avec un facteur constant inférieur à 2 quand la proportion d'arêtes présentes dans le graphe (densité faible) est supérieure à 3/4 ou quand le degré minimum normalisé (densité forte) est supérieur à 1/2. Nous montrons également que ce résultat peut être amélioré par un algorithme de type GREEDY, qui fournit un facteur constant inférieur à 2 pour des densités faibles supérieures à 1/2. Nous donnons également des familles de graphes extrémaux pour nos facteurs d'approximation. Nous nous somme ensuite intéressés à plusieurs algorithmes de la littérature pour les problèmes VC et SET COVER (SC). Nous avons présenté une approche unifiée et critique des algorithmes de Karpinski-Zelikovsky, Imamura-Iwama, et Bar-Yehuda-Kehat, identifiant un schéma général dans lequel s'intègrent ces algorithmes. Nous nous sommes finalement intéressés au problème CONNECTED VERTEX COVER (CVC), pour lequel nous avons proposé de nouveaux résultats d'approximation dans les graphes denses, au travers de l'algorithme de Carla Savage d'une part, et d'une nouvelle variante de l'algorithme de Karpinski-Zelikovsky d'autre part. Ces résultats montrent que nous pouvons obtenir pour CVC les mêmes facteurs d'approximation que ceux obtenus pour VC à l'aide de l'heuristique du matching maximal et de l'algorithme de Karpinski-Zelikovsky. Nous montrons également des familles de graphes extrémaux pour les ratios garantis par ces deux algorithmes. Nous avons également étudié un nouvel invariant, le coût de connectivité de VC, défini comme le rapport entre les solutions optimales de CVC et de VC, et montré une borne supérieure sur sa valeur en fonction de la densité faible. Notre dernier chapitre discute d'aspects logiciels, et présente l'utilisation du logiciel GRAPHEDRON dans le cadre des algorithmes d'approximation, ainsi que nos contributions au développement du logiciel.

Modern computing platforms strive to support mobile code without putting system security at stake. These platforms can be viewed as open systems, as the mobile code adds new components to the running system. Establishing that such platforms function correctly can  be divided into two steps. First, it is shown that the system functions correctly regardless of the mobile components that join it, provided that they satisfy certain assumptions. These assumptions can, for instance, restrict the behavior of the component to ensure that the security policy of the platform is not violated. Second, the mobile component is checked to satisfy its assumptions, before it is allowed to join the system. This thesis presents algorithmic verification techniques to support this methodology. In the first two parts, we present techniques for the verification of open systems relative to the given component assumptions. In the third part, a technique for the  quick certification of mobile code is presented for the case where a particular type of program rewriting is used as a means of enforcing the component assumptions.In the first part of this study, we present a framework for the verification of open systems based on explicit state space representation. We propose Extended Modal Transition Systems (EMTS) as a suitable structure for representing the state space of open systems when assumptions on components are written in the modal μ-calculus. EMTSs are based on the Modal Transition Systems (MTS) of Larsen and provide a formalism for graphical specification and facilitate a thorough understanding of the system by visualization. In interactive verification, this state space representation enables proof reuse and aids the user guiding the verification process. We present a construction of state space representations from process algebraic open system descriptions based on a maximal model construction for the modal μ-calculus. The construction is sound and complete for systems with a single unknown component and sound for those without dynamic process reation. We also suggest a tableau-based proof system for establishing temporal properties of open systems represented as EMTS. The proof system is sound in general and complete for prime formulae.The problem of open system correctness  also arises in compositional verification, where the problem of showing a global property of a system is reduced to showing local properties of components. In the second part, we extend an existing  compositional verification framework for Java bytecode programs. The framework employs control flow graphs with procedures to model component implementations and open systems for the purpose of checking control-flow properties. We generalize these models to capture exceptional and multi-threaded behavior. The resulting control flow graphs are specifically tailored to support the compositional verification principle; however, they are sufficiently intuitive and standard to be useful on their own. We describe how the models can be extracted from program code and give preliminary experimental results for our implementation of the extraction of control flow graphs with exceptions. We also discuss further tool support and practical applications of the method.In the third part of the thesis, we develop a technique for the certification of safe mobile code, by adapting the proof-carrying code scheme of Necula to the case of security policies expressed as security automata. In particular, we describe how proofs of policy compliance can  be automatically generated for  programs that include a monitor for the desired policy. A monitor is an entity that observes the execution of a program and terminates the program if a violation to the property is about to occur. One way to implement such a monitor is by rewriting the program to make it self-monitoring. Given a property, we characterize self-monitoring of Java bytecode programs for this property by an annotation scheme with annotations in the style of Floyd-Hoare logics. The annotations generated by this scheme can be extended in a straightforward way to form a correctness proof in the sense of axiomatic semantics of programs. The proof generated in this manner essentially establishes that the program satisfies the property because it contains a monitor for it. The annotations that comprise the proofs are simple and efficiently checkable, thus facilitate certification of mobile code on devices with restricted computing power such as mobile phones. / QC 20100628

Academic self-concept (ASC) refers to one's beliefs about himself or herself in academic situations. ASC has been found to be moderately correlated with academic performance when ASC and academic outcome measures are in the same domain and at the same level of specificity. It was hypothesized that differentiating between ASC under typical versus maximal environmental press may increase its predictive validity by providing further specificity to items and thus greater reliability to ASC scales. In this study, a battery of assessments was administered to Georgia Tech undergraduates in order to examine the factor structure of new measures of typical and maximal ASC, as well as their predictive and construct validities. A two-factor model fit the data better than a one-factor model, but did not meet criteria for good fit. Most hypotheses about the relationship between typical and maximal ASC and other constructs were not supported, though gender differences were found which may indicate an interesting line of future research.

The purpose of this study was to determine the validity of the Ebbeling one-stage submaximal treadmill protocol to estimate maximal oxygen uptake in overweight males and females. Forty-five male and females (36.5±10.9 years; 170.2±9.9 cm; 77.9±9.0 kg) were categorized into overweight groups using a BMI of 25-29.9 kg/m2. The subjects performed a submaximal protocol that consisted of one 4-minute stage with individualized speeds of 2.0-4.5 mph at 5% grade and subsequently performed a maximal exercise test. There were significant relationships between observed and estimated VO2max for males (r=.796), females (r=.426), and gender combined (r=.844). There was an underestimation in the estimation of VO2max in the present study when comparing males (10%), females (26%) and gender combined (17%) subjects. The results indicated that a body mass index between the values of 25-29.9 kg/m2 did create a difference in estimating VO2max in the present study when comparing that to Ebbeling et al. (1991).Ball State UniversityMuncie, IN 47306 / School of Physical Education

This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L1 functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. For Sobolev functions we study the dimension of the set of non-Lebesgue points.

The public interest in central living in today’s cities has led to an increasing effect of traffic noise pollution, and today 20% of the inhabitants in Sweden suffer from noise a level that exceeds the limits. At the same time the traffic keeps increasing, and recent researches shows that traffic noise pollution and several of today’s most common health issues are connected, for example, reduction of performance, sleeping issues and cardiovascular diseases. For this cause rules, guidelines and environmental goals has been developed, as well as software’s which calculates the levels of pollution, all this to investigate and improve the environment. The guidelines say that the average sound pressure level shouldn’t exceed 55 dBA over 24 hours of the façade, and the maximum level shouldn’t exceed 70 dBA. Today’s issue is that the guidelines isn’t legally binding and therefore they don’t have to be fully achieved which can led to confusion and unfair interpretations in the matter of a building can or cannot be built according to the limits of traffic noise pollution.   The intensions of this report are to improve the urban environment regarding traffic noise pollution and to increase the understanding and knowledge how this issue affects urban areas. The report will also investigate and compare two different calculation methods for traffic noise pollution, the Nordic propagation method and the Nord 2000.   On this basis a literature survey has been done regarding the noise pollution issues in our cities with its rules, guidelines, objective goals, measures and the two different calculation methods. Investigations of different shapes of a building has been done in combination with the software for calculation of road traffic noise Soundplan, and a case study of a site which is located in the centre of Jönköping. The workflow has been reversed from the “normal”, were the building were designed after the limits of the noise levels were investigated. This resulted in a residential proposal which is optimized from a traffic noise point of view, and uses its own body as a shield. The condoles are directed away from the source of noise and the parking space are placed towards the roads. The final result has been analysed with both of the calculation methods, were a slightly differentiation between the methods can be seen. This is causes by the way the calculation methods deal with information and the differentiation in the calculation methods.   The conclusions from this report are that the traffic noise pollution is one of our major health issues which still are increasing. The main problem in this is that there’s several unmeasurable parameters which influences the way an individual experiences the sound environment, which contributes to the difficulty to establish a proper regulations and standards. Regarding the calculation methods there is issues to use Nord 2000, because the method requires large amounts of information which can be difficult to access. At the same time the Nordic propagation method can show incorrectly results because it hasn’t the same ability to adapt to the specific conditions at each location.

In the cooperative communications, the users relay each other¡¦s signal and thus forming multiple transmission paths to the destination and therefore the system can achieve spatial diversity gain. Decode-and-forward and amplify-and-forward are the most popular relaying strategies in the literature due to their simplicity. However, in practice, cooperative users acting as relays may not always normally operated or trustworthy. When the relay misbehavior is present in the cooperative networks, the communication performance may degrade dramatically and the users may be even better off without cooperation. Therefore, it is necessary for the destination to determine the misbehaving relays and to take appropriate actions to ensure that cooperative advantages are preserved. In this thesis, we focus on developing a misbehaving relay detection method to detect whether or not the system is in the presence of some misbehaving relays. After performing misbehaving relay detection, the destination removes the signals from the un- reliable paths and then uses maximal ratio combing to achieve spatial diversity. The simulation results conducted by the thesis show that the proposed method is more robust as compared with those without employing misbehaving relay detection when the system is in the presence of some misbehaving relays.

In the cooperative communications, the users relay each other's signal and thus form multiple transmission paths to the destination and therefore the system can achieve spatial diversity gain. Most studies in the literature assumed that cooperative users acting as the relays are normally operated and trustworthy. However, this may not always be true in practice. When the relay misbehaviors are present in the cooperative communications, the communication performance may degrade dramatically and the users may be even better off without cooperation. Therefore, it is necessary for the destination to determine the misbehaving relays and to take appropriate actions to ensure that cooperative advantages are preserved. This thesis considers both models in which the cooperative communications are with direct path (WDP) and without direct path (WODP). Utilizing the proposed Kolmogorov-Smirnov test mechanism, the destination identifies the misbehaving relays within the cooperative communications and then excludes their transmitting messages when performing the diversity combining to infer the symbols of interest sent by the source. In addition, this thesis provides the bit error rate (BER) analysis of the cooperative communications employing the proposed misbehaving relay detectors. The simulation results demonstrate that the proposed methods have robust performance when the relay misbehaviors are present in the cooperative communications.