Algebraic lower bounds on the free distance of convolutional codes

A new module structure for convolutional codes is introduced and used to establish further links with quasi-cyclic and cyclic codes. The set of finite weight codewords of an (n,k) convolutional code over Fq is shown to be isomorphic to an Fq[x]-submodule of Fq n[x], where Fq n[x] is the ring of polynomials in indeterminate x over Fq n, an extension field of Fq. Such a module can then be associated with a quasi-cyclic code of index n and block length nL viewed as an Fq[x]-submodule of Fq n[x]/langxL-1rang, for any positive integer L. Using this new module approach algebraic lower bounds on the free distance of a convolutional code are derived which can be read directly from the choice of polynomial generators. Links between convolutional codes and cyclic codes over the field extension Fq n are also developed and Bose-Chaudhuri-Hocquenghem (BCH)-type results are easily established in this setting. Techniques to find the optimal choice of the parameter L are outline

Explicit constructions of Type-II QC LDPC codes with girth at least 6

Type-II quasi-cyclic (QC) LDPC codes are constructed from combinations of weight-0, weight-1 and weight-2 circulant matrices. The structure of cycles of length 2n are investigated, and necessary and sufficient conditions for a type-II QC LDPC parity check matrix H to have girth at least 2(n+1) are given. An explicit construction of type-II codes which guarantees girth at least 6 is presented. A necessary and sufficient condition for a QC matrix with one or more rows of circulants, to be fullrank is derived

It Isn’t Adding Up: The Gap Between the Perceptions of Engineering Mathematics Students and those Held by Lecturers in the First Year of Study of Engineering

The transition from second level to third level education offers a considerable degree of challenge for many students. One such challenge is the students’ internalized world-view and its effects on the potential of the students. The perceptions, self-efficacy, and expectancy, of the students as they move into third level education, may be significantly at variance with the beliefs held by lecturers. This research project began as an individual case study of first year engineering students in one higher education organization and was extended to include a similar organization in another EU country. Through a series of questionnaires and group interviews with students the thematic outputs of the process formed the basis for questioning of lecturers. Evidence from the data revealed many students in the initial stages of the first year of study, display low levels of confidence, do not understand the higher education assessment processes, and perceive many barriers to progress. Many lecturers do not share the outputs from the student data when individual lecturer interviews are analyzed. In an attempt to ascertain if the issues raised are localized, further research has begun to gather data from students in similar Higher Education organisations in an additional four countries. The outcomes suggest an alternative approach to assessment of engineering mathematics is required

Myths, rhetoric and opportunities surrounding new teaching technologies: engineering mathematics education

Issues of confidence and self-efficacy and expectancy relating to engineering students are not widely discussed. The transition to third level education is known to be a major stressor in the relationship between students and their prospects of completing their programmes of study. The foundations for this research project lie in a comparative study between students in Ireland and Finland; students participated in a series of questionnaires and group interviews and the thematic outputs of the process formed the basis for questioning of lecturers. Evidence from the data shows many students in the first year of study, demonstrate low levels of confidence, have poor knowledge of the assessment processes employed in Higher Education, and perceive many barriers to progress. Many lecturers do not share the outputs from the student data when individual lecturer interviews are analyzed. The research was extended to gather data from engineering students of similar educational standing in other countries to determine if evidence exists to support the findings. Initial analysis of the data suggests the findings of the initial research are not limited to the participating organisations

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units

Bone mineral content in Hawaiian, Asian, and Filipino children.

Os calcis bone mineral content (BMC) was measured by single photon absorptiometry in 86 children, ages 6 to 13 years from Hawaiian, Oriental, Caucasian, and Filipino ethnic groups. Pearson correlations indicated significant positive correlations between BMC and age, height, and weight. However, there were no significant differences in age, height or weight between ethnic groups. ANOVA revealed a significant effect of ethnic group on BMC with the Hawaiian group having a significantly higher BMC than the Asian or Caucasian groups. When age, height and weight were controlled for, ANCOVA still showed a significant effect of ethnicity on BMC. The current findings suggest that ethnic differences can develop early in life

Aggregatibacter actinomycetemcomitans leukotoxin induces cytosol acidification in LFA-1 expressing immune cells

Studies have suggested that Aggregatibacter actinomycetemcomitans leukotoxin (LtxA) kills human lymphocyte function-associated antigen 1 (LFA-1; CD11a/CD18)-bearing immune cells through a lysosomal-mediated mechanism. Lysosomes are membrane-bound cellular organelles that contain an array of acid hydrolases that are capable of breaking down biomolecules. The lysosomal membrane bilayer confines the pH-sensitive enzymes within an optimal acidic (pH 4.8) environment thereby protecting the slightly basic cytosol (pH 6.8-7.5). In the current study, we have probed the effect of LtxA-induced cytolysis on lysosomal integrity in two different K562 erythroleukemia cell lines. K562-puro/LFA-1 cells were stably transfected with CD11a and CD18 cDNA to express LFA-1 on the cell surface while K562-puro, which does not express LFA-1, served as a control. Following treatment with 100 ng ml-1 LtxA cells were analyzed by live cell imaging in conjunction with time-lapse confocal microscopy and by flow cytometry. Using a pH-sensitive indicator (pHrodo®) we demonstrated that the toxin causes a decrease in the intracellular pH in K562-puro/LFA-1 cells that is noticeable within the first 15 min of treatment. This process correlated with the disappearance of lysosomes in the cytosol as determined by both acridine orange and LysoTracker® Red DND-99 staining. These changes were not observed in K562-puro cells or when heat inactivated toxin was added to K562-puro/LFA-1. Our results suggest that LtxA induces lysosomal damage, cytosol acidification, which is followed by cell death in K562-puro/LFA-1 cells. © 2016 John Wiley & Sons A/S

Quantitative susceptibility mapping of carotid arterial tissue ex vivo: Assessing sensitivity to vessel microstructural composition

PURPOSE: To characterize microstructural contributions to the magnetic susceptibility of carotid arteries. METHOD: Arterial vessels were scanned using high-resolution quantitative susceptibility mapping (QSM) at 7 Tesla. Models of vessel degradation were generated using ex vivo porcine carotid arteries that were subjected to several different enzymatic digestion treatments that selectively removed microstructural components (smooth muscle cells, collagen, and elastin). Magnetic susceptibilities measured in these tissue models were compared to those in untreated (native) porcine arteries. Magnetic susceptibility measured in native porcine carotid arteries was further compared to the susceptibility of cadaveric human carotid arteries to investigate their similarity. RESULTS: The magnetic susceptibility of native porcine vessels was diamagnetic (χnative = -0.1820 ppm), with higher susceptibilities in all models of vessel degradation (χelastin-degraded = -0.0163 ppm; χcollagen-degraded = -0.1158 ppm; χdecellularized = -0.1379 ppm; χfixed native = -0.2199 ppm). Magnetic susceptibility was significantly higher in collagen-degraded compared to native porcine vessels (Tukey-Kramer, P .05). CONCLUSIONS: Magnetic susceptibility measured using QSM is sensitive to the microstructural composition of arterial vessels-most notably to collagen. The similarity of human and porcine arterial tissue susceptibility values provides a solid basis for translational studies. Because vessel microstructure becomes disrupted during the onset and progression of carotid atherosclerosis, QSM has the potential to provide a sensitive and specific marker of vessel disease