Generic Invertibility of Multidimensional FIR Filter Banks and MIMO Systems

We study the invertibility of M-variate Laurent polynomial N × P matrices. Such matrices represent multidimensional systems in various settings such as filter banks, multiple-input multiple-output systems, and multirate systems. Given an N × P Laurent polynomial matrix H(z1,..., zM) of degree at most k, we want to find a P × N Laurent polynomial left inverse matrix G(z) of H(z) such that G(z)H(z) = I. We provide computable conditions to test the invertibility and propose algorithms to find a particular inverse. The main result of this paper is to prove that H(z) is generically invertible when N −P ≥ M; whereas when N −P < M, then H(z) is generically noninvertible. As a result, we propose an algorithm to find a particular inverse of a Laurent polynomial matrix that is faster than current algorithms known to us

Hilbert Functions and Applications to the Estimation of Subspace Arrangements

This paper develops a new mathematical framework for studying the subspace-segmentation problem. We examine some important algebraic properties of subspace arrangements that are closely related to the subspace-segmentation problem. More specifically, we introduce an important class of invariants given by the Hilbert functions. We show that there exist rich relations between subspace arrangements and their corresponding Hilbert functions. We propose a new subspace- segmentation algorithm, and showcase two applications to demonstrate how the new theoretical revelation may solve subspace segmentation and model selection problems under less restrictive conditions with improved results.National Science Foundation / CAREER IIS-0347456, CRS-EHS-0509151, and CCF-TF-0514955ONR YIP N00014-05-1-0633Ope

A systematic review and meta-synthesis of the impact of low back pain on people's lives

Copyright @ 2014 Froud et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.Background - Low back pain (LBP) is a common and costly problem that many interpret within a biopsychosocial model. There is renewed concern that core-sets of outcome measures do not capture what is important. To inform debate about the coverage of back pain outcome measure core-sets, and to suggest areas worthy of exploration within healthcare consultations, we have synthesised the qualitative literature on the impact of low back pain on people’s lives. Methods - Two reviewers searched CINAHL, Embase, PsycINFO, PEDro, and Medline, identifying qualitative studies of people’s experiences of non-specific LBP. Abstracted data were thematic coded and synthesised using a meta-ethnographic, and a meta-narrative approach. Results - We included 49 papers describing 42 studies. Patients are concerned with engagement in meaningful activities; but they also want to be believed and have their experiences and identity, as someone ‘doing battle’ with pain, validated. Patients seek diagnosis, treatment, and cure, but also reassurance of the absence of pathology. Some struggle to meet social expectations and obligations. When these are achieved, the credibility of their pain/disability claims can be jeopardised. Others withdraw, fearful of disapproval, or unable or unwilling to accommodate social demands. Patients generally seek to regain their pre-pain levels of health, and physical and emotional stability. After time, this can be perceived to become unrealistic and some adjust their expectations accordingly. Conclusions - The social component of the biopsychosocial model is not well represented in current core-sets of outcome measures. Clinicians should appreciate that the broader impact of low back pain includes social factors; this may be crucial to improving patients’ experiences of health care. Researchers should consider social factors to help develop a portfolio of more relevant outcome measures.Arthritis Research U

Molecular Epidemiology of Methicillin-Resistant Staphylococcus aureus, Rural Southwestern Alaska1

One-sentence summary for table of contents: Epidemiology of MRSA isolates in this region differs from that in the lower 48 states

Adolescents with metabolic syndrome have a history of low aerobic fitness and physical activity levels

Abstract: Purpose: Metabolic syndrome (MS) is a clustering of cardiovascular disease risk factors that identifies individuals with the highest risk for heart disease. Two factors that may influence the MS are physical activity and aerobic fitness. This study determined if adolescent with the MS had low levels of aerobic fitness and physical activity as children. Methods: This longitudinal, exploratory study had 389 participants: 51% girls, 84% Caucasian, 12% African American, 1% Hispanic, and 3% other races, from the State of North Carolina. Habitual physical activity (PA survey), aerobic fitness (VO2max), body mass index (BMI), blood pressure, and lipids obtained at 7–10 y of age were compared to their results obtained 7 y later at ages 14–17 y. Results: Eighteen adolescents (4.6%) developed 3 or more characteristics of the MS. Logistic regression, adjusting for BMI percentile, blood pressure, and cholesterol levels, found that adolescents with the MS were 6.08 (95%CI = 1.18–60.08) times more likely to have low aerobic fitness as children and 5.16 (95%CI = 1.06–49.66) times more likely to have low PA levels. Conclusion: Low levels of childhood physical activity and aerobic fitness are associated with the presence of the metabolic syndrome in adolescents. Thus, efforts need to begin early in childhood to increase exercise