On Binary Matroid Minors and Applications to Data Storage over Small Fields

Locally repairable codes for distributed storage systems have gained a lot of interest recently, and various constructions can be found in the literature. However, most of the constructions result in either large field sizes and hence too high computational complexity for practical implementation, or in low rates translating into waste of the available storage space. In this paper we address this issue by developing theory towards code existence and design over a given field. This is done via exploiting recently established connections between linear locally repairable codes and matroids, and using matroid-theoretic characterisations of linearity over small fields. In particular, nonexistence can be shown by finding certain forbidden uniform minors within the lattice of cyclic flats. It is shown that the lattice of cyclic flats of binary matroids have additional structure that significantly restricts the possible locality properties of $\mathbb{F}_{2}$-linear storage codes. Moreover, a collection of criteria for detecting uniform minors from the lattice of cyclic flats of a given matroid is given, which is interesting in its own right.Comment: 14 pages, 2 figure

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

A Survey of Kansas Physicians' Perceptions of Physician Assistant Education and Qualifications

BACKGROUND: Effective physician-physician assistant (PA) teams improve patient access and satisfaction, and increase productivity and revenue while reducing physician workload. This survey assessed perceptions of Kansas primary care physicians regarding educational requirements and qualifications of PAs, professional and legal regulations, and the most important skills and competencies for PAs to possess. Understanding these perceptions may lead to improved communication and refined expectations of physician-physician assistant teams, thereby increasing their utilization and effectiveness. METHODS: A 20-question survey was emailed to all 1,551 primary care physicians registered with the Kansas Board of Healing Arts in 2012. Descriptive data were reported as frequencies; comparisons between groups were analyzed using Chi-square. RESULTS: The response rate was 9.2% (n = 143). Physicians were highly accurate regarding the program’s generalist/primary care educational model and moderately accurate regarding the degree awarded, average pre-program grade point average, lock-step full-time curriculum, weeks of clinical rotations, recertification and continuing medical education hours, and Medicare PA fee schedule. Physicians had low accuracy regarding program and pharmacology credit hours, strict dismissal policy, pre-program healthcare experience, and co-signatory regulations. Physicians with PA supervisory experience had higher knowledge than those without (p = 0.001). Physicians most commonly selected history taking and performing physical exam as the most important skill (49%) and providing patient care that is patient-centered, efficient, and equitable as the most important competency (42%). CONCLUSIONS: Physicians often underestimated the average PA applicant qualifications, program rigor and intensity, professional regulatory standards, and co-signatory requirements. Correcting misperceptions and improving understanding of which PA skills and competencies are most valued by physicians may optimize PAs as part of the healthcare team

Western privacy and/or Ubuntu? Some critical comments on the influences in the forthcoming data privacy bill in South Africa

There is a worldwide concern growing regarding the increasing potential threats to the personal privacy of individuals caused by technologies and governments. The international response of governments has been to draught comprehensive privacy legislation in order to protect their citizen's personal information and to enable their citizens to have control over their personal information. In South Africa, the right to privacy is protected by both Section 14 of the Constitution and the provisions of the Common Law, but at this stage no formal privacy legislation is in place to enforce fair data protection principles. A new Data Privacy Bill is in the process of being draughted by the South African Law Commission and it is taking into account South Africa's unique political and social context as well as international demands made by the global economy. The prime influences acting upon the new Data Privacy Bill are the mandate in the Constitution, the EU Data Protection Directive and the Ubuntu worldview. Ubuntu can be described as a community-based mindset in which the welfare of the group is greater than the welfare of a single individual in the group. In this article, we argue that the EU Data Protection Directive is one of the best articulated privacy laws in existence today and the Ubuntu philosophy has been pressed into service very successfully in diverse arenas in South Africa. This paper argues that both influences will be seen in the future Data Privacy Act, but that the EU Data Protection Directive's influence will be pre-eminent

On character generators for simple Lie algebras

We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is first reviewed. A new general formula is then found. It makes clear the distinct roles of ``outside'' and ``inside'' elements of the integrity basis, and helps determine their quadratic incompatibilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We find that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure

Towards a fullerene-based quantum computer

Molecular structures appear to be natural candidates for a quantum technology: individual atoms can support quantum superpositions for long periods, and such atoms can in principle be embedded in a permanent molecular scaffolding to form an array. This would be true nanotechnology, with dimensions of order of a nanometre. However, the challenges of realising such a vision are immense. One must identify a suitable elementary unit and demonstrate its merits for qubit storage and manipulation, including input / output. These units must then be formed into large arrays corresponding to an functional quantum architecture, including a mechanism for gate operations. Here we report our efforts, both experimental and theoretical, to create such a technology based on endohedral fullerenes or 'buckyballs'. We describe our successes with respect to these criteria, along with the obstacles we are currently facing and the questions that remain to be addressed.Comment: 20 pages, 13 figs, single column forma

Calculated corrections to superallowed Fermi beta decay: New evaluation of the nuclear-structure-dependent terms

The measured $ft$-values for superallowed $0^{+} \to 0^{+}$ nuclear $\beta$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -- it still fails by more than two standard deviations -- but they provide calculated corrections for eleven new superallowed transitions that are likely to become accessible to precise measurements in the future. The reliability of all calculated corrections is explored and an experimental method indicated by which the structure-dependent corrections can be tested and, if necessary, improved.Comment: Revtex4, one figur

Fractionation of parietal function in bistable perception probed with concurrent TMS-EEG

When visual input has conflicting interpretations, conscious perception can alternate spontaneously between these possible interpretations. This is called bistable perception. Previous neuroimaging studies have indicated the involvement of two right parietal areas in resolving perceptual ambiguity (ant-SPLr and post-SPLr). Transcranial magnetic stimulation (TMS) studies that selectively interfered with the normal function of these regions suggest that they play opposing roles in this type of perceptual switch. In the present study, we investigated this fractionation of parietal function by use of combined TMS with electroencephalography (EEG). Specifically, while participants viewed either a bistable stimulus, a replay stimulus, or resting-state fixation, we applied single pulse TMS to either location independently while simultaneously recording EEG. Combined with participant’s individual structural magnetic resonance imaging (MRI) scans, this dataset allows for complex analyses of the effect of TMS on neural time series data, which may further elucidate the causal role of the parietal cortex in ambiguous perception