Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

A frontier functions approach to optimal scales of sustainable production

This paper translates the concepts of sustainable production to three dimensions of economic, environmental and ecological sustainability to analyze optimal production scales by solving optimizing problems. Economic optimization seeks input-output combinations to maximize profits. Environmental optimization searches for input-output combinations that minimize the polluting effects of materials balance on the surrounding environment. Ecological optimization looks for input-output combinations that minimize the cumulative destruction of the entire ecosystem. Using an aggregate space, the framework illustrates that these optimal scales are often not identical because markets fail to account for all negative externalities. Profit-maximizing firms normally operate at the scales which are larger than optimal scales from the viewpoints of environmental and ecological sustainability; hence policy interventions are favoured. The framework offers a useful tool for efficiency studies and policy implication analysis. The paper provides an empirical investigation using a data set of rice farms in South Korea.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Augustine and the functions of concupiscence

This study analyses Augustine s concept of concupiscentia, or evil desire (together with two cognate terms, libido and cupiditas) in the context of his entire oeuvre. By the aid of systematic analysis, the concept and its development is explored in four distinct ways. It is claimed that Augustine used the concept of concupiscentia for several theological purposes, and the task of the study is to represent these distinct functions, and their connections to Augustine s general theological and philosophical convictions. The study opens with a survey on terminology. A general overview of the occurrences of the negatively connoted words for desire in Latin literature precedes a corresponding examination of Augustine s own works. In this introductory chapter it is shown that, despite certain preferences in the uses of the words, a sufficient degree of synonymy reigns so as to allow an analysis of the concept without tightly discriminating between the terms. The theological functions of concupiscentia with its distinct contexts are analysed in separate chapters. The function of concupiscentia as a divine punishment is explored first (Ch 3). It is seen how Augustine links together concupiscentia and ideas about divine justice, and finally suggests that in the inordinate, psychologically experienced sexual desire, the original theological disobedience of Adam and Eve can be perceived. Augustine was criticized for this solution already in his own times, and the analysis of the function of concupiscentia as a divine punishment ends in a discussion on the critical response of punitive concupiscentia by Julian of Aeclanum. Augustine also attached to concupiscentia another central theological function by viewing evil desire as an inward originating cause for all external evil actions. In the study, this function is analysed by surveying two formally distinct images of evil desire, i.e. as the root (radix) of all evil, and as a threefold (triplex) matrix of evil actions (Ch 4). Both of these images were based on a single verse of the Bible (1 Jn 2, 16 and 1 Tim 6, 10). This function of concupiscentia was formed both parallel to, and in answer to, Manichaean insights into concupiscentia. Being familiar with the traditional philosophical discussions on the nature and therapy of emotions, Augustine situated concupiscentia also into this context. It is acknowledged that these philosophical traditions had an obvious impact into his way of explaining psychological processes in connection with concupiscentia. Not only did Augustine implicitly receive and exploit these traditions, but he also explicitly moulded and criticized them in connection with concupiscentia. Eventually, Augustine conceives the philosophical traditions of emotions as partly useful but also partly inadequate to deal with concupiscentia (Ch 5). The role of concupiscentia in connection to divine grace and Christian renewal is analysed in the final chapter of the study. Augustine s gradual development in internalizing the effects of concupiscentia also into the life of a baptized Christian are elucidated, as are the strong limitations and mitigations Augustine makes to the concept when attaching it into the life under grace (sub gratia). A crucial part in the development of this function is played by Augustine s changing interpretation of Rom 7, and the way concupiscentia appears in Augustine s readings of this text is therefore also analysed. As a result of the analysis of these four distinct functions and contexts of concupiscentia, it is concluded that Augustine s concept of concupiscentia is fairly tightly and coherently connected to his views of central theological importance. Especially the functions of concupiscentia as a punishment and the function of concupiscentia in Christian renewal were both tightly interwoven into Augustine s view of God s being and God s grace. The study shows the importance of reading Augustine s discussions on evil desire with a constant awareness of their role in their larger context, that is, of their function in each situation. The study warns against too simplistic and unifying readings of Augustine s concupiscentia, emphasizing the need to acknowledge both the necessitating, sinful aspects of concupiscentia, and the domesticated features of concupiscentia during Christian renewal.

Novel hardware and software combination for automotive motorsport vehicles based on direct processing of graphical functions

The main motivation for the work presented here began with previously conducted experiments with a programming concept at the time named "Macro". These experiments led to the conviction that it would be possible to build a system of engine control from scratch, which could eliminate many of the current problems of engine management systems in a direct and intrinsic way. It was also hoped that it would minimize the full range of software and hardware needed to make a final and fully functional system. Initially, this paper proposes to make a comprehensive survey of the state of the art in the specific area of software and corresponding hardware of automotive tools and automotive ECUs. Problems arising from such software will be identified, and it will be clear that practically all of these problems stem directly or indirectly from the fact that we continue to make comprehensive use of extremely long and complex "tool chains". Similarly, in the hardware, it will be argued that the problems stem from the extreme complexity and inter-dependency inside processor architectures. The conclusions are presented through an extensive list of "pitfalls" which will be thoroughly enumerated, identified and characterized. Solutions will also be proposed for the various current issues and for the implementation of these same solutions. All this final work will be part of a "proof-of-concept" system called "ECU2010". The central element of this system is the before mentioned "Macro" concept, which is an graphical block representing one of many operations required in a automotive system having arithmetic, logic, filtering, integration, multiplexing functions among others. The end result of the proposed work is a single tool, fully integrated, enabling the development and management of the entire system in one simple visual interface. Part of the presented result relies on a hardware platform fully adapted to the software, as well as enabling high flexibility and scalability in addition to using exactly the same technology for ECU, data logger and peripherals alike. Current systems rely on a mostly evolutionary path, only allowing online calibration of parameters, but never the online alteration of their own automotive functionality algorithms. By contrast, the system developed and described in this thesis had the advantage of following a "clean-slate" approach, whereby everything could be rethought globally. In the end, out of all the system characteristics, "LIVE-Prototyping" is the most relevant feature, allowing the adjustment of automotive algorithms (eg. Injection, ignition, lambda control, etc.) 100% online, keeping the engine constantly working, without ever having to stop or reboot to make such changes. This consequently eliminates any "turnaround delay" typically present in current automotive systems, thereby enhancing the efficiency and handling of such systems.

Empirical Orthogonal Functions: The Medium is the Message

Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

Natural compounds Camptothecin and Triptolide: highly specific enzyme inhibitors and tools to dissect transcriptional functions

With this work I elucidated new and unexpected mechanisms of two strong and highly specific transcription inhibitors: Triptolide and Campthotecin. Triptolide (TPL) is a diterpene epoxide derived from the Chinese plant Trypterigium Wilfoordii Hook F. TPL inhibits the ATPase activity of XPB, a subunit of the general transcription factor TFIIH. In this thesis I found that degradation of Rbp1 (the largest subunit of RNA Polymerase II) caused by TPL treatments, is preceded by an hyperphosphorylation event at serine 5 of the carboxy-terminal domain (CTD) of Rbp1. This event is concomitant with a block of RNA Polymerase II at promoters of active genes. The enzyme responsible for Ser5 hyperphosphorylation event is CDK7. Notably, CDK7 downregulation rescued both Ser5 hyperphosphorylation and Rbp1 degradation triggered by TPL. Camptothecin (CPT), derived from the plant Camptotheca acuminata, specifically inhibits topoisomerase 1 (Top1). We first found that CPT induced antisense transcription at divergent CpG islands promoter. Interestingly, by immunofluorescence experiments, CPT was found to induce a burst of R loop structures (DNA/RNA hybrids) at nucleoli and mitochondria. We then decided to investigate the role of Top1 in R loop homeostasis through a short interfering RNA approach (RNAi). Using DNA/RNA immunoprecipitation techniques coupled to NGS I found that Top1 depletion induces an increase of R loops at a genome-wide level. We found that such increase occurs on the entire gene body. At a subset of loci R loops resulted particularly stressed after Top1 depletion: some of these genes showed the formation of new R loops structures, whereas other loci showed a reduction of R loops. Interestingly we found that new peaks usually appear at tandem or divergent genes in the entire gene body, while losses of R loop peaks seems to be a feature specific of 3’ end regions of convergent genes.

The 3′ untranslated region of a rice α-amylase gene functions as a sugar-dependent mRNA stability determinant

In plants, sugar feedback regulation provides a mechanism for control of carbohydrate allocation and utilization among tissues and organs. The sugar repression of α-amylase gene expression in rice provides an ideal model for studying the mechanism of sugar feedback regulation. We have shown previously that sugar repression of α-amylase gene expression in rice suspension cells involves control of both transcription rate and mRNA stability. The α-amylase mRNA is significantly more stable in sucrose-starved cells than in sucrose-provided cells. To elucidate the mechanism of sugar-dependent mRNA turnover, we have examined the effect of αAmy3 3′ untranslated region (UTR) on mRNA stability by functional analyses in transformed rice suspension cells. We found that the entire αAmy3 3′ UTR and two of its subdomains can independently mediate sugar-dependent repression of reporter mRNA accumulation. Analysis of reporter mRNA half-lives demonstrated that the entire αAmy3 3′ UTR and the two subdomains each functioned as a sugar-dependent destabilizing determinant in the turnover of mRNA. Nuclear run-on transcription analysis further confirmed that the αAmy3 3′ UTR and the two subdomains did not affect the transcription rate of promoter. The identification of sequence elements in the α-amylase mRNA that dictate the differential stability has very important implications for the study of sugar-dependent mRNA decay mechanisms.

Estimation of the Crustal Bulk Properties Beneath Mainland Portugal from P-Wave Teleseismic Receiver Functions

In this work, we present results from teleseismic P-wave receiver functions (PRFs) obtained in Portugal, Western Iberia. A dense seismic station deployment conducted between 2010 and 2012, in the scope of the WILAS project and covering the entire country, allowed the most spatially extensive probing on the bulk crustal seismic properties of Portugal up to date. The application of the H-kappa stacking algorithm to the PRFs enabled us to estimate the crustal thickness (H) and the average crustal ratio of the P- and S-waves velocities V (p)/V (s) (kappa) for the region. Observations of Moho conversions indicate that this interface is relatively smooth with the crustal thickness ranging between 24 and 34 km, with an average of 30 km. The highest V (p)/V (s) values are found on the Mesozoic-Cenozoic crust beneath the western and southern coastal domain of Portugal, whereas the lowest values correspond to Palaeozoic crust underlying the remaining part of the subject area. An average V (p)/V (s) is found to be 1.72, ranging 1.63-1.86 across the study area, indicating a predominantly felsic composition. Overall, we systematically observe a decrease of V (p)/V (s) with increasing crustal thickness. Taken as a whole, our results indicate a clear distinction between the geological zones of the Variscan Iberian Massif in Portugal, the overall shape of the anomalies conditioned by the shape of the Ibero-Armorican Arc, and associated Late Paleozoic suture zones, and the Meso-Cenozoic basin associated with Atlantic rifting stages. Thickened crust (30-34 km) across the studied region may be inherited from continental collision during the Paleozoic Variscan orogeny. An anomalous crustal thinning to around 28 km is observed beneath the central part of the Central Iberian Zone and the eastern part of South Portuguese Zone.

The Expanded Human Kallikrein (KLK) gene family : genomic organisation, tissue specific expression and potential functions

The tissue kallikreins are serine proteases encoded by highly conserved multigene families. The rodent kallikrein (KLK) families are particularly large, consisting of 13 26 genes clustered in one chromosomal locus. It has been recently recognised that the human KLK gene family is of a similar size (15 genes) with the identification of another 12 related genes (KLK4-KLK15) within and adjacent to the original human KLK locus (KLK1-3) on chromosome 19q13.4. The structural organisation and size of these new genes is similar to that of other KLK genes except for additional exons encoding 5 or 3 untranslated regions. Moreover, many of these genes have multiple mRNA transcripts, a trait not observed with rodent genes. Unlike all other kallikreins, the KLK4-KLK15 encoded proteases are less related (25–44%) and do not contain a conventional kallikrein loop. Clusters of genes exhibit high prostatic (KLK2-4, KLK15) or pancreatic (KLK6-13) expression, suggesting evolutionary conservation of elements conferring tissue specificity. These genes are also expressed, to varying degrees, in a wider range of tissues suggesting a functional involvement of these newer human kallikrein proteases in a diverse range of physiological processes.