Canonical basis linearity regions arising from quiver representations

In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author [Math. Z. 237 (2001) 639] arising from representations of quivers. We prove that some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large cone by linear functions arising from these monomial bases for a quantized enveloping algebra.     

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi’s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is non-conforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure.     

Sensor System for Simultaneous Measurement of Oxygen and Hydrogen Peroxide Concentration During Glucose Oxidase Activity

An amperometric sensor system, based on a repetitive double step potential method at a glassy carbon electrode, has been developed for the simultaneous measurement of hydrogen peroxide and oxygen concentrations. The current measured at a potential of –1 V (vs. Ag/AgCl/saturated Cl^–) corresponds to the sum of the reduction currents of hydrogen peroxide and dissolved oxygen. The current measured at –0.55 V (vs. Ag/AgCl/saturated Cl^–) is due to the reduction of dissolved oxygen to hydrogen peroxide. Alternatively, the concentration of dissolved oxygen can also be determined using a Clark electrode. The concentration of hydrogen peroxide and dissolved oxygen during enzymatic conversion of glucose can be followed on line and be used to control the process.     

From NGS assembly challenges to instability of fungal mitochondrial genomes: A case study in genome complexity

The presence of repetitive or non-unique DNA persisting over sizable regions of a eukaryotic genome can hinder the genome's successful de novo assembly from short reads: ambiguities in assigning genome locations to the non-unique subsequences can result in premature termination of contigs and thus overfragmented assemblies. Fungal mitochondrial (mtDNA) genomes are compact (typically less than 100 kb), yet often contain short non-unique sequences that can be shown to impede their successful de novo assembly in silico. Such repeats can also confuse processes in the cell in vivo. A well-studied example is ectopic (out-of-register, illegitimate) recombination associated with repeat pairs, which can lead to deletion of functionally important genes that are located between the repeats. Repeats that remain conserved over micro- or macroevolutionary timescales despite such risks may indicate functionally or structurally (e.g., for replication) important regions. This principle could form the basis of a mining strategy for accelerating discovery of function in genome sequences. We present here our screening of a sample of 11 fully sequenced fungal mitochondrial genomes by observing where exact k-mer repeats occurred several times; initial analyses motivated us to focus on 17-mers occurring more than three times. Based on the diverse repeats we observe, we propose that such screening may serve as an efficient expedient for gaining a rapid but representative first insight into the repeat landscapes of sparsely characterized mitochondrial chromosomes. Our matching of the flagged repeats to previously reported regions of interest supports the idea that systems of persisting, non-trivial repeats in genomes can often highlight features meriting further attention.     

Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity

We study properties of graded maximal Cohen-Macaulay modules over an \mathbb{N}-graded locally finite, Auslander Gorenstein, and Cohen-Macaulay algebra of dimension two. As a consequence, we extend a part of the McKay correspondence in dimension two to a more general setting.     

脉冲形成线放电过程中Tesla变压器锥形绕组电压分布特性

 介绍了Tesla变压器与脉冲形成线一体化结构的工作原理,实验研究了形成线放电过程中形成的冲击电压波在Tesla变压器锥形次级绕组中的分布特性;给出了输入电压脉宽分别为1 μs,500 ns和100 ns时,锥形绕组中的对地电压和匝间电压分布规律;采用首端并绕、末端并绕和在首端加入屏蔽环三种措施优化绕组结构。结果表明：形成线放电过程中,变压器锥形次级绕组不会明显影响形成线中的电场分布,绕组的对地电压呈线性分布,匝间电压曲线起伏剧烈,首端电压梯度最大;三种优化措施都能抑制电压振荡,首端并绕对降低绕组首端电压梯度最为有效,末端并绕对降低绕组末端电压梯度最有效。     

Optimizing control of simulated moving beds--experimental implementation

The operation of simulated moving beds (SMBs) at their optimal operating conditions is difficult and not robust. Therefore, it is common practice to operate SMB units far from their economic optimum in order to tolerate uncertainties in the system and minimize the effect of disturbances. Recently, we have proposed an on-line optimization based SMB control scheme that allows to exploit the full economic potential of SMB technology. The goal of this work is two-fold. Firstly, to experimentally evaluate and demonstrate the capability of the controller to optimize and operate the SMB units, thus delivering the products with maximum productivity and minimum solvent consumption. Secondly, to show the suitability of the controller even using a minimum of system information, thus making the detailed isotherm measurements redundant and saving time in the separation design phase. This paper reports and discusses the first experimental implementation of the control concept on a high purity separation of nucleosides (uridine, guanosine) with an eight-column four-section SMB where the species to be separated are retained on the source 30RPC stationary phase according to a linear isotherm.     

Quiver Quotient Varieties and Complete Intersections

In this paper, we classify all the symmetric quivers and corresponding dimension vectors whose quotient space, classifying the semisimple representation classes, is a complete intersection. The result we obtain is that such quivers can be reduced to a few number of basic quivers, using some elementary types of reduction. Presented by L. Le BruynMathematics Subject Classification (2000) 16G20.     

Grammar compressed sequences with rank/select support

Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly repetitive sequences, and classical statistical compression proves ineffective. We introduce, instead, grammar-based representations for repetitive sequences, which use up to 6% of the space needed by statistically compressed representations, and support direct access and rank/select operations within tens of microseconds. We demonstrate the impact of our structures in text indexing applications.