On Sound Relative Error Bounds for Floating-Point Arithmetic

State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the magnitude of the computed values. Relative errors, which compute errors relative to the value's magnitude, are thus preferable. While today's tools do report relative error bounds, these are merely computed via absolute errors and thus not necessarily tight or more informative. Furthermore, whenever the computed value is close to zero on part of the domain, the tools do not report any relative error estimate at all. Surprisingly, the quality of relative error bounds computed by today's tools has not been systematically studied or reported to date. In this paper, we investigate how state-of-the-art static techniques for computing sound absolute error bounds can be used, extended and combined for the computation of relative errors. Our experiments on a standard benchmark set show that computing relative errors directly, as opposed to via absolute errors, is often beneficial and can provide error estimates up to six orders of magnitude tighter, i.e. more accurate. We also show that interval subdivision, another commonly used technique to reduce over-approximations, has less benefit when computing relative errors directly, but it can help to alleviate the effects of the inherent issue of relative error estimates close to zero

Roll function in a flight simulator

Method introduces roll into the flying-spot scanner by modifying the scanning waveforms

Moduli spaces of noncommutative instantons: gauging away noncommutative parameters

Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_\theta. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.Comment: v2: 44 pages; minor changes. To appear in Quart. J. Mat

Parkinson's disease dementia: a neural networks perspective.

In the long-term, with progression of the illness, Parkinson's disease dementia affects up to 90% of patients with Parkinson's disease. With increasing life expectancy in western countries, Parkinson's disease dementia is set to become even more prevalent in the future. However, current treatments only give modest symptomatic benefit at best. New treatments are slow in development because unlike the pathological processes underlying the motor deficits of Parkinson's disease, the neural mechanisms underlying the dementing process and its associated cognitive deficits are still poorly understood. Recent insights from neuroscience research have begun to unravel the heterogeneous involvement of several distinct neural networks underlying the cognitive deficits in Parkinson's disease dementia, and their modulation by both dopaminergic and non-dopaminergic transmitter systems in the brain. In this review we collate emerging evidence regarding these distinct brain networks to give a novel perspective on the pathological mechanisms underlying Parkinson's disease dementia, and discuss how this may offer new therapeutic opportunities

A study of the means of increasing the dynamic range of visual simulation by means of a flying-spot scanner Final report

Increasing dynamic range of visual simulation for pilots using flying spot scanne

Financial Engineering and Rationality: Experimental Evidence Based on the Monty Hall Problem

Financial engineering often involves redefining existing financial assets to create new financial products. This paper investigates whether financial engineering can alter the environment so that irrational agents can quickly learn to be rational. The specific environment we investigate is based on the Monty Hall problem, a well-studied choice anomaly. Our results show that, by the end of the experiment, the majority of subjects understand the Monty Hall anomaly. Average valuation of the experimental asset is very close to the expected value based on the true probabilities.experiment, behavioral finance

Understanding the Escalation of Brain Drain in Nigeria From Poor Leadership Point of View

Migration of people from one place to another in countries of the world in search of better conditions of living predates history. It ignited western societies’ contact with Africa and the rest of the world. Prior the contact, agriculture was the main stay of Africa’s economy. Thus, the movement of farmers from one location to another in search of fertile grounds for cultivation was in vogue. After independence in Nigeria, cattle rearers are known for relocating from the North to South during dry season in search of green grass to sustain their cattle and occupation. In the present day Nigeria, the same scenario still abounds but in a new dimension. It now involves movement of highly skilled manpower from the country to developed societies. Among other things, this paper finds out if there is a relationship between poor leadership of the country and escalation of brain drain. Simple percentage and ranking method was used to analyze the study’s data. Chi-square was used to test its hypothesis. Our result revealed a relationship between poor leadership of the country and brain drain. It equally indicated that students are interested in travelling out of the country to developed societies after their study. Also from the study, twelve causes of brain drain were indentified. Some of them are: mass unemployment, poor salaries and conditions of service, mass poverty, crises-religious, communal, political, education etc. In respect of effects of brain drain on the nation’s economy, eleven factors were identified by the respondents. Some of them are: loss of human capital assets to man various institutions in the country, loss of tax of migrated manpower to foreign countries, loss of capital invested in education of migrated manpower assets etc. Finally, eleven solutions were profiled to the lingering problem of brain drain. The most important ones are: Good leadership, salary and conditions of service as well as rewarding system for diligent staff, mass employment etc

The Gysin Sequence for Quantum Lens Spaces

We define quantum lens spaces as `direct sums of line bundles' and exhibit them as `total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as `line bundles' over quantum lens spaces and generically define `torsion classes'. We work out explicit examples of these classes.Comment: 27 pages. v2: No changes in the scientific content and results. Section 5 completely re-written and a final section added; suppressed two appendices; added references; minor changes throughout the paper. To appear in the JNc

Regional Strategies of Multinational Pharmaceutical Firms

This paper examines the R&D and strategies of the world’s largest firms in the pharmaceuticals sector and finds a high degree of intra-regional sales. R&D and sales are more concentrated within North America and Europe than in Asia. In addition, the relative size of the U.S. market, compared to other parts of the triad, creates imbalances with respect to R&D, sales and international strategy.

Polymer Matrix Nanocomposites by Inkjet Printing

This paper describes work on a continuing project to form functional composites that contain ceramic nanoparticles using a Solid Freeform Fabrication (SFF) inkjet printing method. The process involves inkjet deposition of monomer/particle suspensions in layers followed by curing each layer in sequence using UV radiation. The reactive monomer is hexanediol-diacrylate (HDODA); the polymer forming reaction proceeds by a free radical mechanism. The liquid monomer containing nanoparticles is essentially a printing ink formulation. Successfully suspending the particles in the monomer is critical. We have developed a surface treatment method for forming stable suspensions of the nanoparticles so that they remain discrete throughout the processing sequence. The SFF process involves careful control of the polymer cure so that the interface between layers is seamless and residual stresses in the composites are eliminated. An immediate use for such composites is in optical applications as gradient refractive index lenses (GRIN). GRIN lenses have planar surfaces, eliminating the need for costly grinding and polishing. The planar surfaces also eliminate optical aberrations that result at the edges of spherical lenses and diminish the accuracy of focus. If the appropriate nanoparticles are fully dispersed they will modify the polymer's refractive index without interfering with light transmission. The effect is additive with volume concentration. Using 'inks' of different compositions in a multiple nozzle inkjet printer allows the formation of composites with precise composition gradients. Since an object is built one planar layer at a time, changes can be made readily both within each layer and from layer to layer. Inkjet printing with picoliter resolution is ideal for this task. Working with SiC nanoparticles in HDODA as a model system for demonstrating the inkjet deposition process, nanocomposite films with a linear concentration gradient varying from 0 to 4.5% (wt) were fabricated on Silicon wafers. These composites are 30 layer films, which total 140µm in thickness. Each layer in the composite is about 5 µm in thickness. Analytical methods for characterizing the dispersion of the nanoparticles in the composite and some of the salient optical properties of the composites also were established. The status of the program is reviewed in this paper.Mechanical Engineerin