Computing resultants on Graphics Processing Units: Towards GPU-accelerated computer algebra

In this article we report on our experience in computing resultants of bivariate polynomials on Graphics Processing Units (GPU). Following the outline of Collins’ modular approach [6], our algorithm starts by mapping the input polynomials to a finite field for sufficiently many primes m$m$. Next, the GPU algorithm evaluates the polynomials at a number of fixed points x∈_Zm$x\in {\mathbb{Z}}_m$, and computes a set of univariate resultants for each modular image. Afterwards, the resultant is reconstructed using polynomial interpolation and Chinese remaindering. The GPU returns resultant coefficients in the form of Mixed Radix (MR) digits. Finally, large integer coefficients are recovered from the MR representation on the CPU. All computations performed by the algorithm (except for, partly, Chinese remaindering) are outsourced to the graphics processor thereby minimizing the amount of work to be done on the host machine. The main theoretical contribution of this work is the modification of Collins’ modular algorithm using the methods of matrix algebra to make an efficient realization on the GPU feasible. According to the benchmarks, our algorithm outperforms a CPU-based resultant algorithm from 64-bit Maple 14 by a factor of 100.     

Automatic learners with feedback queries

Automatic classes are classes of languages for which a finite automaton can decide whether a given element is in a set given by its index. The present work studies the learnability of automatic families by automatic learners which, in each round, output a hypothesis and update a long-term memory, depending on the input datum, via an automatic function. Many variants of automatic learners are investigated: where the long-term memory is restricted to be the current hypothesis whenever this exists, cannot be of length larger than the length of the longest datum seen, or has to consist of a constant number of examples seen so far. Learnability is also studied with respect to queries which reveal information about past data or past computation history; the number of queries per round is bounded by a constant.     

Decay of end effects in graphite/epoxy bolted joints

Almost all analyses of large structures neglect local effects due to the application of loads and due to the transfer of loads between structural elements. In recent years, however, the use in aircraft structures of highly anisotropic materials, such as graphite/epoxy, has motivated more detailed studies of the applicability of Saint-Venant's principle.

In this paper in graphite/epoxy is analysed using the finite element method (FEM). The influence of anisotropy and transition from a thicker to a thinner laminate cross-section (ply-drop) is investigated. The characteristic decay length which is large for highly anisotropic materials is lessened by a change in thickness.     

Chemical Markers of Human Tendon Health Identified Using Raman Spectroscopy: Potential for In Vivo Assessment

The purpose of this study is to determine whether age-related changes to tendon matrix molecules can be detected using Raman spectroscopy. Raman spectra were collected from human Achilles (n = 8) and tibialis anterior (n = 8) tendon tissue excised from young (17 ± 3 years) and old (72 ± 7 years) age groups. Normalised Raman spectra underwent principal component analysis (PCA), to objectively identify differences between age groups and tendon types. Certain Raman band intensities were correlated with levels of advanced glycation end-product (AGE) collagen crosslinks, quantified using conventional destructive biochemistry techniques. Achilles and tibialis anterior tendons in the old age group demonstrated significantly higher overall Raman intensities and fluorescence levels compared to young tendons. PCA was able to distinguish young and old age groups and different tendon types. Raman intensities differed significantly for several bands, including those previously associated with AGE crosslinks, where a significant positive correlation with biochemical measures was demonstrated. Differences in Raman spectra between old and young tendon tissue and correlation with AGE crosslinks provides the basis for quantifying age-related chemical modifications to tendon matrix molecules in intact tissue. Our results suggest that Raman spectroscopy may provide a powerful tool to assess tendon health and vitality in the future.     

Fabrication of buried microfluidic channels with observation windows using femtosecond laser photoablation and parylene-C coating

We developed an advanced method for fabricating microfluidic structures comprising channels and inputs/outputs buried within a silicon wafer based on single level lithography. We etched trenches into a silicon substrate, covered these trenches with parylene-C, and selectively opened their bottoms using femtosecond laser photoablation, forming channels and inputs/outputs by isotropic etching of silicon by xenon difluoride vapors. We subsequently sealed the channels with a second parylene-C layer. Unlike in previously published works, this entire process is conducted at ambient temperature to allow for integration with complementary metal oxide semiconductor devices for smart readout electronics. We also demonstrated a method of chip cryo-cleaving with parylene presence that allows for monitoring of the process development. We also created an observation window for in situ visualization inside the opaque silicon substrate by forming a hole in the parylene layer at the silicon backside and with local silicon removal by xenon difluoride vapor etching. We verified the microfluidic chip performance by forming a segmented flow of a fluorescein solution in an oil stream. This proposed technique provides opportunities for forming simple microfluidic systems with buried channels at ambient temperature.     

The effect of ripening and storage conditions on the distribution of tyramine,putrescine and cadaverine in Edam-cheese

The aim of the work was to describe the development of selected biogenic amines (histamine, tyramine, putrescine and cadaverine) in 4 layers of Dutch-type cheese (Edam-cheese) depending on 3 ripening/storage regimes during a 98-day period. Biogenic amines were analysed by means of ion-exchange chromatography. A further goal was to identify microbial sources of biogenic amines in the material analysed. Phenotype characterization and repetitive sequence-based PCR fingerprinting were used to identify the isolated bacteria. The highest content of tyramine, putrescine and cadaverine was determined in cheeses stored in a ripening cellar at a temperature of 10 °C during the whole observation period. Lower biogenic amines content was determined in samples which were moved into a cold storage device (5 °C) after 38 days of storage in a ripening cellar (10 °C). The lowest concentrations of biogenic amines were detected in cheeses which were moved into a cold storage device (5 °C) after 23 days of storage in a ripening cellar (10 °C). During the 98-day period, histamine was not detected in any of the regimes. Within the cheeses analysed, non-starter lactic acid bacteria Lactobacillus curvatus, Lactobacillus casei/paracasei and Lactobacillus plantarum were detected as the main producers of the biogenic amines tested. In starter bacteria Lactococcus lactis subsp. lactis and Lactococcus lactis subsp. cremoris the decarboxylase activity tested was not detected.     

Selective catalytic transformations of methanol to C2-C3 hydrocarbons over the new zeolite type LZ 132

The small pore zeolite HLZ 132 exhibits, in comparison with other zeolites, an increased selectivity for the transformation of methanol to ethylene in the reaction temperature range 350–500 °C: the weight ratio of C₂H₄ to C₃H₆ in the products ranges between 1 and 4 at WHSV=2 h^–1. Besides the effect of the reactant shape selectivity this fact may be interpreted by the participation of the asymmetrical methoxy groups in the surface as well as by proton-donor centres of lower acidity which do not catalyze the oligomerization of ethylene but which do the more basic molecule of propylene, thereby generating polyene-type coke.     

Characteristics of planar diodes based on heavily doped GaAs/AlAs superlattices in the terahertz frequency region

Characteristics of ohmic InGaAs contacts in planar diodes based on semiconductor superlattices with a small-area active region (1–10 μm²) are studied. The diodes were formed on the basis of short (18 or 30 periods) heavily doped (10¹⁸ cm⁻³) GaAs/AlAs superlattices with a miniband width of 24.4 meV. The reduced resistance of the ohmic contact was equal to 2×10⁻⁷ Ω cm² at room temperature. It is shown that the properties of fabricated planar diodes make it possible to use these diodes later on in semiconductor devices that operate in the terahertz frequency region in a wide temperature range (4–300 K). __________ Translated from Fizika i Tekhnika Poluprovodnikov, Vol. 38, No. 9, 2004, pp. 1141–1146. Original Russian Text Copyright ? 2004 by Pavel’ev, Demarina, Koshurinov, Vasil’ev, Semenova, Zhukov, Ustinov.     

Electrode position scaling in realistic laplacian computation

This note discusses the effects of the electrode position scaling on the realistic Laplacian (RL) computation. It is shown that when the RL is estimated with the help of Tikhonov regularization and the generalized cross-validation (GCV) criterion, improper electrode position scaling may influence the GCV criterion, which results in the decrease of RL precision. We identify what the proper scaling should be, and we provide a closer examination of how the GCV criterion is affected by the electrode position scaling.