An efficient scheme for the evaluation of coding performance of high speed links incorporating joint error behaviour based on Monte Carlo Method

While channel coding is a standard method of improving a system’s energy efficiency in digital communications, its practice does not extend to high-speed links. Increasing demands in network speeds are placing a large burden on the energy efficiency of high-speed links and render the benefit of channel coding for these systems a timely subject. The low error rates of interest and the presence of residual intersymbol interference (ISI) caused by hardware constraints impede the analysis and simulation of coded high-speed links. Focusing on the residual ISI and combined noise as the dominant error mechanisms, this paper analyses error correlation through concepts of error region, channel signature, and correlation distance. This framework provides a deeper insight into joint error behaviours in high-speed links, extends the range of statistical simulation for coded high-speed links, and provides a case against the use of biased Monte Carlo methods in this setting

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education

Bayesian Analysis of Simple Step-stress Model under Weibull Lifetimes

Department of Statistics, Cochin University of Science & Technology, Part of this work has been supported by grants from DST and CSIR, Government of India. 2Department of Mathematics and Statistics, IIT Kanpur

Model Diagnostics in the presence of measurement error

The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.

Error estimates for approximate approximations on compact intervals

The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in- tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.

An approximation method using approximate approximations

The aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

Difference and equality: A critical theorist analysis of post-modern philosophy

The following paper is a critical theorist analysis of post-structuralist philosophy. It examines the omission of an economic critique in post-structuralism and describes this omission as the result of a particular flaw in Nietzsche's epistemological work, an error which has persisted all the way down through deconstruction, post-colonialism, and cultural studies. The paper seeks to reintroduce an economic critique of capitalism back into the social critique of post-structuralism, with the promise that the combination of the two will prove stronger than either critical theory or post-structuralism alone. To achieve this it reinterprets Marx' concept of metabolism as a critical economic category that mirrors post-structuralism's concept of differance.

Statistical Analysis of Diabetes Mellitus

Diabetes mellitus is a disease where the glucosis-content of the blood does not automatically decrease to a ”normal” value between 70 mg/dl and 120 mg/dl (3,89 mmol/l and 6,67 mmol/l) between perhaps one hour (or two hours) after eating. Several instruments can be used to arrive at a relative low increase of the glucosis-content. Besides drugs (oral antidiabetica, insulin) the blood-sugar content can mainly be influenced by (i) eating, i.e., consumption of the right amount of food at the right time (ii) physical training (walking, cycling, swimming). In a recent paper the author has performed a regression analysis on the influence of eating during the night. The result was that one ”bread-unit” (12g carbon-hydrats) increases the blood-sugar by about 50 mg/dl, while one hour after eating the blood-sugar decreases by about 10 mg/dl per hour. By applying this result-assuming its correctness - it is easy to eat the right amount during the night and to arrive at a fastening blood-sugar (glucosis-content) in the morning of about 100 mg/dl (5,56 mmol/l). In this paper we try to incorporate some physical exercise into the model.

A Modeling Analysis of Changing Global Land Use as affected by Changing Demands for Wood Products

The 21st century has brought new challenges for forest management at a time when globalization in world trade is increasing and global climate change is becoming increasingly apparent. In addition to various goods and services like food, feed, timber or biofuels being provided to humans, forest ecosystems are a large store of terrestrial carbon and account for a major part of the carbon exchange between the atmosphere and the land surface. Depending on the stage of the ecosystems and/or management regimes, forests can be either sinks, or sources of carbon. At the global scale, rapid economic development and a growing world population have raised much concern over the use of natural resources, especially forest resources. The challenging question is how can the global demands for forest commodities be satisfied in an increasingly globalised economy, and where could they potentially be produced? For this purpose, wood demand estimates need to be integrated in a framework, which is able to adequately handle the competition for land between major land-use options such as residential land or agricultural land. This thesis is organised in accordance with the requirements to integrate the simulation of forest changes based on wood extraction in an existing framework for global land-use modelling called LandSHIFT. Accordingly, the following neuralgic points for research have been identified: (1) a review of existing global-scale economic forest sector models (2) simulation of global wood production under selected scenarios (3) simulation of global vegetation carbon yields and (4) the implementation of a land-use allocation procedure to simulate the impact of wood extraction on forest land-cover. Modelling the spatial dynamics of forests on the global scale requires two important inputs: (1) simulated long-term wood demand data to determine future roundwood harvests in each country and (2) the changes in the spatial distribution of woody biomass stocks to determine how much of the resource is available to satisfy the simulated wood demands. First, three global timber market models are reviewed and compared in order to select a suitable economic model to generate wood demand scenario data for the forest sector in LandSHIFT. The comparison indicates that the ‘Global Forest Products Model’ (GFPM) is most suitable for obtaining projections on future roundwood harvests for further study with the LandSHIFT forest sector. Accordingly, the GFPM is adapted and applied to simulate wood demands for the global forestry sector conditional on selected scenarios from the Millennium Ecosystem Assessment and the Global Environmental Outlook until 2050. Secondly, the Lund-Potsdam-Jena (LPJ) dynamic global vegetation model is utilized to simulate the change in potential vegetation carbon stocks for the forested locations in LandSHIFT. The LPJ data is used in collaboration with spatially explicit forest inventory data on aboveground biomass to allocate the demands for raw forest products and identify locations of deforestation. Using the previous results as an input, a methodology to simulate the spatial dynamics of forests based on wood extraction is developed within the LandSHIFT framework. The land-use allocation procedure specified in the module translates the country level demands for forest products into woody biomass requirements for forest areas, and allocates these on a five arc minute grid. In a first version, the model assumes only actual conditions through the entire study period and does not explicitly address forest age structure. Although the module is in a very preliminary stage of development, it already captures the effects of important drivers of land-use change like cropland and urban expansion. As a first plausibility test, the module performance is tested under three forest management scenarios. The module succeeds in responding to changing inputs in an expected and consistent manner. The entire methodology is applied in an exemplary scenario analysis for India. A couple of future research priorities need to be addressed, particularly the incorporation of plantation establishments; issue of age structure dynamics; as well as the implementation of a new technology change factor in the GFPM which can allow the specification of substituting raw wood products (especially fuelwood) by other non-wood products.