Fast algorithm for border bases of Artinian Gorenstein algebras

Given a multi-index sequence $$\sigma$$, we present a new efficient algorithm to compute generators of the linear recurrence relations between the terms of $$\sigma$$. We transform this problem into an algebraic one, by identifying multi-index sequences, multivariate formal power series and linear functionals on the ring of multivariate polynomials. In this setting, the recurrence relations are the elements of the kerne l$I$\sigma of the Hankel operator $H$\sigma associated to $$\sigma$$. We describe the correspondence between multi-index sequences with a Hankel operator of finite rank and Artinian Gorenstein Algebras. We show how the algebraic structure of the Artinian Gorenstein algebra $A$\sigma$$associated to the sequence$$\sigma yields the structure of the terms $\sigma\alpha$for all$$\alpha$ $\in$ N n$. This structure is explicitly given by a border basis of$A$\sigma$$, which is presented as a quotient of the polynomial ring$K[x 1 ,. .. , xn$] by the kernel$I$\sigma$$of the Hankel operator$H$\sigma$$. The algorithm provides generators of$I$\sigma$$constituting a border basis, pairwise orthogonal bases of$A$\sigma$$ and the tables of multiplication by the variables in these bases. It is an extension of Berlekamp-Massey-Sakata (BMS) algorithm, with improved complexity bounds. We present applications of the method to different problems such as the decomposition of functions into weighted sums of exponential functions, sparse interpolation, fast decoding of algebraic codes, computing the vanishing ideal of points, and tensor decomposition. Some benchmarks illustrate the practical behavior of the algorithm

Persuading consumers to reduce their consumption of electricity in the home

Previous work has identified that providing real time feedback or interventions to consumers can persuade consumers to change behaviour and reduce domestic electricity consumption. However, little work has investigated what exactly those feedback mechanisms should be. Most past work is based on an in-home display unit, possibly complemented by lower tariffs and delayed use of non-essential home appliances such as washing machines. In this paper we focus on four methods for real time feedback on domestic energy use, developed to gauge the impact on energy consumption in homes. Their feasibility had been tested using an experimental setup of 24 households collecting minute-by-minute electricity consumption data readings over a period of 18 months. Initial results are mixed, and point to the difficulties of sustaining a reduction in energy consumption, i.e. persuading consumers to change their behaviour. Some of the methods we used exploit small group social dynamics whereby people want to conform to social norms within groups they identify with. It may be that a variety of feedback mechanisms and interventions are needed in order to sustain user interest

Potential impact of multiple interventions on HIV incidence in a hyperendemic region in Western Kenya : a modelling study

Background: Multiple prevention interventions, including early antiretroviral therapy initiation, may reduce HIV incidence in hyperendemic settings. Our aim was to predict the short-term impact of various single and combined interventions on HIV spreading in the adult population of Ndhiwa subcounty (Nyanza Province, Kenya). Methods: A mathematical model was used with data on adults (15-59 years) from the Ndhiwa HIV Impact in Population Survey to compare the impacts on HIV prevalence, HIV incidence rate, and population viral load suppression of various interventions. These interventions included: improving the cascade of care (use of three guidelines), increasing voluntary medical male circumcision (VMMC), and implementing pre-exposure prophylaxis (PrEP) use among HIV-uninfected women. Results: After four years, improving separately the cascade of care under the WHO 2013 guidelines and under the treat-all strategy would reduce the overall HIV incidence rate by 46 and 58 %, respectively, vs. the baseline rate, and by 35 and 49 %, respectively, vs. the implementation of the current Kenyan guidelines. With conservative and optimistic scenarios, VMMC and PrEP would reduce the HIV incidence rate by 15-25 % and 22-28 % vs. the baseline, respectively. Combining the WHO 2013 guidelines with VMMC would reduce the HIV incidence rate by 35-56 % and combining the treat-all strategy with VMMC would reduce it by 49-65 %. Combining the WHO 2013 guidelines, VMMC, and PrEP would reduce the HIV incidence rate by 46-67 %. Conclusions: The impacts of the WHO 2013 guidelines and the treat-all strategy were relatively close; their implementation is desirable to reduce HIV spread. Combining several strategies is promising in adult populations of hyperendemic areas but requires regular, reliable, and costly monitoring

On Embeddability of Buses in Point Sets

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the \emph{bus embeddability problem} (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.Comment: 19 pages, 9 figures, conference version at GD 201

A new method of RF power generation for two-beam linear colliders

In this paper we discuss a new approach to two-beam acceleration. The energy for RF production is initially stored in a long-pulse electron beam which is efficiently accelerated to about 1.2 GeV by a fully loaded, conventional, low frequency (~1 GHz) linac. The beam pulse length is twice the length of the high-gradient linac. Segments of this long pulse beam are compressed using combiner rings to create a sequence of higher peak power drive beams with gaps in between. This train of drive beams is distributed from the end of the linac against the main beam direction down a common transport line so that each drive beam can power a section of the main linac. After a 180-degree turn, each high-current, low-energy drive beam is decelerated in low-impedance decelerator structures, and the resulti ng power is used to accelerate the low-current, high-energy beam in the main linac. The method discussed here seems relatively inexpensive is very flexible and can be used to accelerate beams for lin ear colliders over the entire frequency and energy range

Interferon β-1a in relapsing multiple sclerosis: four-year extension of the European IFNβ-1a Dose-C omparison Study

Background: Multiple sclerosis (MS) is a chronic disease requiring long-term monitoring of treatment. Objective: To assess the four-year clinical efficacy of intramuscular (IM) IFNb-1a in patients with relapsing MS from the European IFNb-1a Dose-C omparison Study. Methods: Patients who completed 36 months of treatment (Part 1) of the European IFNb-1a Dose-C omparison Study were given the option to continue double-blind treatment with IFNb-1a 30 mcg or 60 mcg IM once weekly (Part 2). Analyses of 48-month data were performed on sustained disability progression, relapses, and neutralizing antibody (NA b) formation. Results: O f 608/802 subjects who completed 36 months of treatment, 493 subjects continued treatment and 446 completed 48 months of treatment and follow-up. IFNb-1a 30 mcg and 60 mcg IM once weekly were equally effective for up to 48 months. There were no significant differences between doses over 48 months on any of the clinical endpoints, including rate of disability progression, cumulative percentage of patients who progressed (48 and 43, respectively), and annual relapse rates; relapses tended to decrease over 48 months. The incidence of patients who were positive for NAbs at any time during the study was low in both treatment groups. Conclusion: C ompared with 60-mcg IM IFNb-1a once weekly, a dose of 30 mcg IM IFNb-1a once weekly maintains the same clinical efficacy over four years

CLIC: a Two-Beam Multi-TeV e±e\pm Linear Collider

The CLIC study of a high-energy (0.5 - 5 TeV), high-luminosity (1034 - 1035 cm-2 sec-1) e+e- linear collider is presented. Beam acceleration using high frequency (30 GHz) normal-conducting structures operating at high accelerating fields (150 MV/m) significantly reduces the length and, in consequence, the cost of the linac. Using parameters derived from general scaling laws for linear colliders, the beam stability is shown to be similar to lower frequency designs in spite of the strong wake-field dependency on frequency. A new cost-effective and efficient drive beam generation scheme for RF power production by the so-called "Two-Beam Acceleration" method is described. It uses a thermionic gun and a fully-loaded normal-conducting linac operating at low frequency (937 MHz) to generate and accelerate the drive beam bunches, and RF multiplication by funnelling in compressor rings to produce the desired bunch structure. Recent 30 GHz hardware developments and CLIC Test Facility (CTF) results are described

Influence of arrays errors on the performances of radar adaptive antenna processing

The purpose of ibis chapter is to present some results concerning the impact of array errors residuals, after calibration of the antenna, on the performances of adoptive array processing in radar applications . Adoptive array processing is a means for detecting targets in presence of jammers, e.g. in presence of spatially coloured noise. The processing concept is recalled, and indexes of performance examined. Some models of array errors are presented concerning for instance, complex gains différences, or transfert function différences, from channel to channel . Two examples illustrate the influence of the various types of error on the processing performancesL'objet de ce chapitre est de présenter quelques élements d'analyse relatifs à l'influence des imperfections de calibration d'antenne sur les performances de traitements de formation de voies adaptives en radar. Ce type de traitement est mis en place pour détecter les cibles en présence de brouillage, ce qui se traduit par une coloration spatiale du bruit de réception. On rappelle dans un premier temps les caractéristiques générales des traitements considérés et les critères de performances examiné

Hyperspectral imaging for phenotyping plant drought stress and nitrogen interactions using multivariate modelling and machine learning techniques in wh

Accurate detection of drought stress in plants is essential for water use efficiency and agricultural output. Hyperspectral imaging (HSI) provides a non-invasive method in plant phenotyping, allowing the long-term monitoring of plant health due to sensitivity to subtle changes in leaf constituents. The broad spectral range of HSI enables the development of different vegetation indices (VIs) to analyze plant trait responses to multiple stresses, such as the combination of nutrient and drought stresses. However, known VIs may underperform when subjected to multiple stresses. This study presents new VIs in tandem with machine learning models to identify drought stress in wheat plants under varying nitrogen (N) levels. A pot wheat experiment was set up in the glasshouse with four treatments: well-watered high-N (WWHN), well-watered low-N (WWLN), drought-stress high-N (DSHN) and drought-stress low-N (DSLN). In addition to ensuring that plants were watered according to the experiment design, photosynthetic rate (Pn) and stomatal conductance (gs) (which are used to assess plant drought stress) were taken regularly, serving as the ground truth data for this study. The proposed VIs, together with known VIs, were used to train three classification models: support vector machines (SVM), random forest (RF), and deep neural networks (DNN) to classify plants based on their drought status. The proposed VIs achieved more than 0.94 accuracy across all models, and their performance further increased when combined with known VIs. The combined VIs were used to train three regression models to predict the stomatal conductance and photosynthetic rates of plants. The random forest regression model performed best, suggesting that it could be used as a stand-alone tool to forecast gs and Pn and track drought stress in wheat. This study shows that combining hyperspectral data with machine learning can effectively monitor and predict drought stress in crops, especially in varying nitrogen condition