Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states

A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on those vectors in Hilbert space whose entries belong to some chosen number field. For Mutually Unbiased Bases the relevant number field is a cyclotomic field. By including Galois unitaries we are able to remove a mismatch between the finite projective group acting on the bases on the one hand, and the set of those permutations of the bases that can be implemented as transformations in Hilbert space on the other hand. In particular we show that there exist transformations that cycle through all the bases in every dimension which is an odd power of an odd prime. (For even primes unitary MUB-cyclers exist.) These transformations have eigenvectors, which are MUB-balanced states (i.e. rotationally symmetric states in the original terminology of Wootters and Sussman) if and only if d = 3 modulo 4. We conjecture that this construction yields all such states in odd prime power dimension.Comment: 32 pages, 2 figures, AMS Latex. Version 2: minor improvements plus a few additional reference

On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class

We establish the equivalence of conjectures concerning the pair correlation of zeros of $L$-functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston & Montgomery [7] and Montgomery & Soundararajan [11] for the Riemann zeta-function to other $L$-functions in the Selberg class. Our approach is based on the statistics of the zeros because the analogue of the Hardy-Littlewood conjecture for the auto-correlation of the arithmetic functions we consider is not available in general. One of our main findings is that the variances of sums of these arithmetic functions over primes in short intervals have a different form when the degree of the associated $L$-functions is 2 or higher to that which holds when the degree is 1 (e.g. the Riemann zeta-function). Specifically, when the degree is 2 or higher there are two regimes in which the variances take qualitatively different forms, whilst in the degree-1 case there is a single regime

Model Counting for Formulas of Bounded Clique-Width

We show that #SAT is polynomial-time tractable for classes of CNF formulas whose incidence graphs have bounded symmetric clique-width (or bounded clique-width, or bounded rank-width). This result strictly generalizes polynomial-time tractability results for classes of formulas with signed incidence graphs of bounded clique-width and classes of formulas with incidence graphs of bounded modular treewidth, which were the most general results of this kind known so far.Comment: Extended version of a paper published at ISAAC 201

Evaluation of diabetic peer support in Malawi

BackgroundType 2 diabetes is a major health concern worldwide and requires urgent attention from health care providers and policy makers. Due to shortage of health care workers in low-income countries, peer support programs have been viewed as a viable option in management of diabetes and have shown to be effective in sub-Saharan Africa. ObjectiveThe aim of this study is to assess and evaluate the Kamuzu Central Hospital (KCH) diabetic peer support program’s (DPSP) impact 4 years after its establishment by assessing knowledge, self-efficacy and behaviours of DPSP members compared to non-members.Methodology This is a cross-sectional study done among diabetic patients attending clinics between 12th August and 25th September 2018 at KCH. Self and interviewer-administered questionnaires (designed based on validated survey instruments) were used. The participants (n=176) were recruited consecutively after consenting. Results Results showed DPSP members were more knowledgeable regarding the effects of skipping meals and sweet juice on blood glucose and conditions not associated with diabetes. In terms of self-efficacy and behaviour changes, DPSP members believe that they are more able to correct hypoglycaemia, to communicate their concerns to health workers and to perform daily foot exam compared to non-members.Conclusion The KCH (Lilongwe) Diabetes Peer Support program has positively impacted its members and should be scaled up to engage all diabetic patients in Malawi. Ongoing training for peer supporters is necessary to update and reinforce management, knowledge and skills, and to ensure fidelity in program implementation

Effects of Static and Dynamic Hamstring Stretching on Anaerobic Exercise Performance

Please view abstract in the attached PDF file