On the linear independence of spikes and sines

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof involves depends on an extrapolation argument of Bourgain and Tzafriri.Comment: 16 pages, 4 figures. Revision with new proof of major theorem

Atoms of all channels, unite! Average case analysis of multi-channel sparse recovery using greedy algorithms

This paper provides new results on computing simultaneous sparse approximations of multichannel signals over redundant dictionaries using two greedy algorithms. The first one, p-thresholding, selects the S atoms that have the largest $p$-correlation while the second one, p-simultaneous matching pursuit (p-SOMP), is a generalisation of an algorithm studied by Tropp. We first provide exact recovery conditions as well as worst case analyses of all algorithms. The results, expressed using the standard cumulative coherence, are very reminiscent of the single channel case and, in particular, impose stringent restrictions on the dictionary. We unlock the situation by performing an average case analysis of both algorithms. First, we set up a general probabilistic signal model in which the coefficients of the atoms are drawn at random from the standard gaussian distribution. Second, we show that under this model, and with mild conditions on the coherence, the probability that p-thresholding and p-SOMP fail to recover the correct components is overwhelmingly small and gets smaller as the number of channels increases. Furthermore, we analyse the influence of selecting the set of correct atoms at random. We show that, if the dictionary satisfies a uniform uncertainty principle, the probability that simultaneous OMP fails to recover any sufficiently sparse set of atoms gets increasingly smaller as the number of channels increases

On the shopfloor: exploring the impact of teacher trade unions on school-based industrial relations

Teachers are highly unionised workers and their trade unions exert an important influence on the shaping and implementation of educational policy. Despite this importance there is relatively little analysis of the impact of teacher trade unions in educational management literature. Very little empirical research has sought to establish the impact of teacher unions at school level. In an era of devolved management and quasi-markets this omission is significant. New personnel issues continue to emerge at school level and this may well generate increased trade union activity at the workplace. This article explores the extent to which devolved management is drawing school-based union representation into a more prominent role. It argues that whilst there can be significant differences between individual schools, increased school autonomy is raising the profile of trade union activity in the workplace, and this needs to be better reflected in educational management research

DOA estimation using multiple measurement vector model with sparse solutions in linear array scenarios

A novel algorithm is presented based on sparse multiple measurement vector (MMV) model for direction of arrival (DOA) estimation of far-field narrowband sources. The algorithm exploits singular value decomposition denoising to enhance the reconstruction process. The proposed multiple nature of MMV model enables the simultaneous processing of several data snapshots to obtain greater accuracy in the DOA estimation. The DOA problem is addressed in both uniform linear array (ULA) and nonuniform linear array (NLA) scenarios. Superior performance is demonstrated in terms of root mean square error and running time of the proposed method when compared with conventional compressed sensing methods such as simultaneous orthogonal matching pursuit (S-OMP), l_2,1 minimization, and root-MUISC

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

Balance in single-limb stance after surgically treated ankle fractures: a 14-month follow-up

BACKGROUND: The maintenance of postural control is fundamental for different types of physical activity. This can be measured by having subjects stand on one leg on a force plate. Many studies assessing standing balance have previously been carried out in patients with ankle ligament injuries but not in patients with ankle fractures. The aim of this study was to evaluate whether patients operated on because of an ankle fracture had impaired postural control compared to an uninjured age- and gender-matched control group. METHODS: Fifty-four individuals (patients) operated on because of an ankle fracture were examined 14 months postoperatively. Muscle strength, ankle mobility, and single-limb stance on a force-platform were measured. Average speed of centre of pressure movements and number of movements exceeding 10 mm from the mean value of centre of pressure were registered in the frontal and sagittal planes on a force-platform. Fifty-four age- and gender-matched uninjured individuals (controls) were examined in the single-limb stance test only. The paired Student t-test was used for comparisons between patients' injured and uninjured legs and between side-matched legs within the controls. The independent Student t-test was used for comparisons between patients and controls. The Chi-square test, and when applicable, Fisher's exact test were used for comparisons between groups. Multiple logistic regression was performed to identify factors associated with belonging to the group unable to complete the single-limb stance test on the force-platform. RESULTS: Fourteen of the 54 patients (26%) did not manage to complete the single-limb stance test on the force-platform, whereas all controls managed this (p < 0.001). Age over 45 years was the only factor significantly associated with not managing the test. When not adjusted for age, decreased strength in the ankle plantar flexors and dorsiflexors was significantly associated with not managing the test. In the 40 patients who managed to complete the single-limb stance test no differences were found between the results of patients' injured leg and the side-matched leg of the controls regarding average speed and the number of centre of pressure movements. CONCLUSION: One in four patients operated on because of an ankle fracture had impaired postural control compared to an age- and gender-matched control group. Age over 45 years and decreased strength in the ankle plantar flexors and dorsiflexors were found to be associated with decreased balance performance. Further, longitudinal studies are required to evaluate whether muscle and balance training in the rehabilitation phase may improve postural control

Ethnic In-Group Favoritism Among Minority and Majority Groups: Testing the Self-Esteem Hypothesis Among Preadolescents

The self-esteem hypothesis in intergroup relations, as proposed by social identity theory (SIT), states that successful intergroup discrimination enhances momentary collective self-esteem. This hypothesis is a source of continuing controversy. Furthermore, although SIT is increasingly used to account for children’s group attitudes, few studies have examined the hypothesis among children. In addition, the hypothesis’s generality makes it important to study among children from different ethnic groups. The present study, conducted among Dutch and Turkish preadolescents, examined momentary collective self-feelings as a consequence of ethnic group evaluations. The results tended to support the self-esteem hypothesis. In-group favoritism was found to have a self-enhancing effect among participants high in ethnic identification. This result was found for ethnic majority (Dutch) and minority (Turkish) participants.

Restricted Isometries for Partial Random Circulant Matrices

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling