Suslin’s algorithms for reduction of unimodular rows

A well-known lemma of Suslin says that for a commutative ring $A$ if $(v_1\left(X\right),\dots ,v_n\left(X\right))\in {\left(A\left[X\right]\right)}^n$ is unimodular where $v_1$ is monic and $n\ge 3$, then there exist ${\gamma }_1,\dots ,{\gamma }_{\ell }\in E_{n-1}\left(A\left[X\right]\right)$ such that the ideal generated by $\mathrm{Res}(v_1,e_1.{\gamma }_1{}^t(v_2,\dots ,v_n)),\dots ,\mathrm{Res}(v_1,e_1.{\gamma }_{\ell }{}^t(v_2,\dots ,v_n))$ equals $A$. This lemma played a central role in the resolution of Serre’s Conjecture. In the case where $A$ contains a set $E$ of cardinality greater than $deg{v}_1+1$ such that $y-y^{\prime }$ is invertible for each $y\ne y^{\prime }$ in $E$, we prove that the ${\gamma }_i$ can simply correspond to the elementary operations $L_1\to L_1+y_i{\sum }_{j=2}^{n-1}{u}_{j+1}{L}_j$, $1\le i\le \ell =deg{v}_1+1$, where $u_1{v}_1+\cdots +u_n{v}_n=1$. These efficient elementary operations enable us to give new and simple algorithms for reducing unimodular rows with entries in $K[X_1,\dots ,X_k]$ to ${}^t(1,0,\dots ,0)$ using elementary operations in the case where $K$ is an infinite field. Another feature of this paper is that it shows that the concrete local–global principles can produce competitive complexity bounds.     

Statistical analysis of some second-order methods for blind channelidentification/equalization with respect to channel undermodeling

Many second-order approaches have been proposed for blind FIR channel identification in single-input/multi-output context. In practical conditions, the measured impulse responses usually possess “small” leading and trailing terms, the second-order statistics are estimated from finite sample size, and there is additive white noise. This paper, based on a functional methodology, develops a statistical performance analysis of any second-order approach under these practical conditions. We study two channel models. In the first model, the channel tails are considered to be deterministic. We derive expressions for the asymptotic bias and covariance matrix (when the sample size tends to ∞) of the mth-order estimated significant part of the impulse response. In the second model, the tails are treated as zero mean Gaussian random variables. Expressions for the asymptotic covariance matrix of the estimated significant part of the impulse response are then derived when the sample size tends to ∞, and the variance of the tails tends to 0. Furthermore, some asymptotic statistics are given for the estimated zero-forcing equalizer, the combined channel-equalizer impulse response, and some byproducts, such as the open eye measure. This allows one to assess the influence of the limited sample size and the size of the tails, respectively, on the performance of identification and equalization of the algorithms under study. Closed-form expressions of these statistics are given for the least-squares, the subspace, the linear prediction, and the outer-product decomposition (OPD) methods, as examples. Finally, the accuracy of the asymptotic analysis is checked by numerical simulations; the results are found to be valid in a very large domain of the sample size and the size of the tails     

Crossing roads safely: an experimental study of age differences in gap selection by pedestrians

The over-representation of older pedestrians in serious injury and fatal crashes compared to younger adults may be due, in part, to age-related diminished ability to select gaps in oncoming traffic for safe road-crossing. Two experiments are described that examine age differences in gap selection decisions in a simulated road-crossing environment. Three groups of participants were tested, younger (30-45 years), young-old (60-69 years) and old-old (>75 years). The results showed that, for all age groups, gap selection was primarily based on vehicle distance and less so on time-of-arrival. Despite the apparent ability to process the distance and speed of oncoming traffic when given enough time to do so, many of the old-old adults appeared to select insufficiently large gaps. These results are discussed in terms of age-related physical, perceptual and cognitive limitations and the ability to compensate for these limitations. Practical implications for road safety countermeasures are also highlighted, particularly the provision of safe road environments and development of behavioural and training packages.     

Tracklet style transfer and part-level feature description for person reidentification in a camera network

Pattern Analysis and Applications - Reidentifying multiple objects in a camera network are a difficult problem, especially when determining whether the same object appears in a different place at a...     

Optimum Ambiguity-Free Directional and Omnidirectional Planar Antenna Arrays for DOA Estimation

This paper studies the antenna array geometry impact on both direction of arrival (DOA) estimation accuracy and array rank ambiguity. Some restrictions are imposed on the array geometry that guarantee first-order ambiguity-free arrays and, at the same time, reduce the cost of a global systematic optimization. The subsequently derived Cramer-Rao bound (CRB) on the DOA estimates shows to be attractive for numerical evaluation. Depending on whether the DOA estimation accuracy is desired to be uniform in all possible directions or is to be enhanced in a given aperture around some privileged direction, two optimization problems are formulated and solved by exhaustive search to compute the optimal array geometries. The obtained optimal arrays significantly outperform their circular counterparts and tend to have a form close to the V shape. We study in details V-shaped arrays and derive asymptotic performance measures that apply for large sized arrays where exhaustive search is unaffordable.     

Dynamic and scalar turbulent fluctuation in a diffusion flame of an-axisymmetric methane jet into air

 A study of turbulence/combustion interactions in a relatively large turbulent diffusion flame of an axisymmetric methane jet into air is presented. A first order k–ɛ turbulence closure model is used along with two different models (equal scales and non-equal scales) for the submodel describing the scalar dissipation rate. The flamelet concept is used to model the turbulent combustion along with a joint mixture fraction/strain rate probability density function (PDF) for the prediction of the average parameters of the turbulent diffusion flame. The numerical approach is that of Patankar and Spalding, while the flamelet simulations are obtained from the RUN-1DL code of Rogg and co-workers based on a 17 species detailed reaction mechanism. The chosen configuration is that of the experimentally studied turbulent diffusion flame of Streb [1]. A comparison between these experimental results and the obtained numerical ones is thus presented. Relatively good agreements are obtained which show the usefulness of the two-scale model compared to the classical one-scale model for predicting turbulent diffusion flames. Nonetheless some discrepancies are obtained in the outer and downstream regions of the jet, especially in comparison with the experimental data. These are attributed to short coming of the considered turbulence model and soot radiation which is not accounted for. Received: 2 May 2002 / Accepted: 31 January 2003     

Fatty acid methyl and ethyl esters obtained from rare seeds from Tunisia: Ammi visnaga,Citrullus colocynthis,Datura stramonium,Ecballium elaterium,and Silybum marianum

This work aims to study the properties of fatty acid methyl and ethyl esters from Tunisian oils in order to assess their potential use as biofuel sources. The oils chosen for this study have been scarcely researched by other authors and are very interesting for a possible exploitation as fuels. Most of them are nonedible sources and all of them can be grown in arid places with no need of supplementary water: the bishop’s weed Ammi visnaga, the bitter apple Citrullus colocynthis, the stramonium Datura stramonium, the devil pickle Ecballium elaterium, and the milk thistle Silybum marianum.     

Differences in traffic judgements between young and old adult pedestrians

Older pedestrians have been shown to be over-involved in casualty crashes, compared to younger pedestrians, in recent reports. This study set out to investigate whether older pedestrians' road crossing behaviour might render them more vulnerable to crashes because of declines in their physical, sensory, perceptual or cognitive abilities. An initial ‘blackspot’ accident analysis highlighted the types of crashes in which older (and younger) adult pedestrians were involved and likely crossing actions. Road crossing behaviour was then systematically measured from unobtrusive video recordings of individual road crossings for a sample of younger and older pedestrians at several urban locations. On two-way undivided roads, older pedestrians crossed more frequently when there was closer moving traffic and generally adopted less safe road crossing strategies than their younger counterparts. On one-way divided roads, their crossing behaviour was considerably more safe and similar to that of younger pedestrians. The findings suggest that age-related perceptual and cognitive deficits may play a substantial role in many of the crashes involving older pedestrians.