Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt)

Given a knot K we may construct a group G_n(K) from the fundamental group of K by adjoining an nth root of the meridian that commutes with the corresponding longitude. These "generalised knot groups" were introduced independently by Wada and Kelly, and contain the fundamental group as a subgroup. The square knot SK and the granny knot GK are a well known example of a pair of distinct knots with isomorphic fundamental groups. We show that G_n(SK) and G_n(GK) are non-isomorphic for all n>1. This confirms a conjecture of Lin and Nelson, and shows that the isomorphism type of G_n(K), n>1, carries more information about K than the isomorphism type of the fundamental group. An appendix by David Savitt contains some results on representations of the trefoil group in PSL(2,p) that are needed for the proof.Comment: 25 pages, 5 figures, to appear in JKTR. v3: example of the target groups added; slight correction to the construction of the target groups; references updated; some changes to notation. v2: section 4.2 expanded to give overview of proo

Equity of Inpatient Health Care in Rural Tanzania:\ud A Population- and Facility-Based Survey

To explore the equity of utilization of inpatient health care at rural Tanzanian health centers through the use of a short wealth questionnaire.Methods: Patients admitted to four rural health centers in the Kigoma Region of Tanzania from May 2008 to May 2009 were surveyed about their illness, asset ownership and demographics. Principal component analysis was used to compare the wealth of the inpatients to the wealth of the region’s general population, using data from a previous population-based survey. Among inpatients, 15.3% were characterized as the most poor, 19.6% were characterized as very poor, 16.5% were characterized as poor, 18.9% were characterized as less poor, and 29.7% were characterized as the least poor. The wealth distribution of all inpatients (p < 0.0001), obstetric inpatients (p < 0.0001), other inpatients (p < 0.0001), and fee-exempt inpatients (p < 0.001) were significantly different than the wealth distribution in the community population, with poorer patients underrepresented among inpatients. The wealth distribution of pediatric inpatients (p = 0.2242) did not significantly differ from the population at large. The findings indicated that while current Tanzanian health financing policies may have improved access to health care for children under five, additional policies are needed to further close the equity gap, especially for obstetric inpatients.\u

Study of perturbed periodic systems of differential equations - The Stroboscopic method

Stroboscopic method for solving perturbed periodic systems of differential equation

Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic Matrices

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list seven axioms that we might want such a theory to satisfy, and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we construct a new hidden-variable theory that is both robust to small perturbations and indifferent to the identity operation, by exploiting an unexpected connection between unitary matrices and network flows. We also analyze previous hidden-variable theories of Dieks and Schrodinger in terms of our axioms. In a companion paper, we will show that actually sampling the history of a hidden variable under reasonable axioms is at least as hard as solving the Graph Isomorphism problem; and indeed is probably intractable even for quantum computers.Comment: 19 pages, 1 figure. Together with a companion paper to appear, subsumes the earlier paper "Quantum Computing and Dynamical Quantum Models" (quant-ph/0205059

Maximally symmetric stabilizer MUBs in even prime-power dimensions

One way to construct a maximal set of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of all affine symplectic phase-space transformations. However, this construction is not canonical: as a consequence, many different choices of covariance sugroups are possible. In particular, when the Hilbert space is $2^n$ dimensional, it is known that covariance with respect to the full group of affine symplectic phase-space transformations can never be achieved. Here we show that in this case there exist two essentially different choices of maximal subgroups admitting covariant MUBs. For both of them, we explicitly construct a family of $2^n$ covariant MUBs. We thus prove that, contrary to the odd dimensional case, maximally covariant MUBs are very far from being unique.Comment: 22 page

Identification of a surrogate to validate irradiation processing of selected spices

Onion powder and talc were inoculated with one of three groups of Salmonella enterica or a putative surrogate, Enterococcus faecium NRRL B-2354, and the radiation sensitivity of S. enterica was compared to E. faecium. For both inoculated onion powder and inoculated talc, D10-values were greater for E. faecium than any of the three groups of S. enterica. The survival of E. faecium in irradiated talc was used to estimate the potential survival of S. enterica in irradiated spices. Onion powder, dried oregano, whole cumin seeds or peppercorns were mixed with talc inoculated with either S. enterica (previously associated with a foodborne disease outbreak) or E. faecium and irradiated. The D10-values were calculated for each bacterial group and compared between E. faecium and S. enterica within each spice. For each spice, the D10-value for E. faecium was either not statistically different from (P \u3c 0.05) S. entericaor greater than that of S. enterica (onion powder). Quadratic and linear models were developed to allow the estimation of potential surviving populations, and potential decimal reductions of S. enterica, based on surviving populations and decimal reductions determined with E. faecium. The use of E. faecium and these mathematical models would allow a processor to validate an irradiation process by estimating the reduction in S. enterica, based on the population reductions of E. faecium

Algebro-Geometric Solutions of the Boussinesq Hierarchy

We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function representation of all algebro-geometric quasi-periodic solutions and related quantities of the Bsq hierarchy.Comment: LaTeX, 48 page

Neuropathologic basis of frontotemporal dementia in progressive supranuclear palsy.

BackgroundProgressive supranuclear palsy (PSP) is a neurodegenerative disorder characterized by neuronal loss in the extrapyramidal system with pathologic accumulation of tau in neurons and glia. The most common clinical presentation of PSP, referred to as Richardson syndrome, is that of atypical parkinsonism with vertical gaze palsy, axial rigidity, and frequent falls. Although cognitive deficits in PSP are often ascribed to subcortical dysfunction, a subset of patients has dementia with behavioral features similar to the behavioral variant of frontotemporal dementia. In this study we aimed to identify the clinical and pathological characteristics of PSP presenting with frontotemporal dementia.MethodsIn this study, we compared clinical and pathologic characteristics of 31 patients with PSP with Richardson syndrome with 15 patients with PSP with frontotemporal dementia. For pathological analysis, we used semiquantitative methods to assess neuronal and glial lesions with tau immunohistochemistry, as well image analysis of tau burden using digital microscopic methods.ResultsWe found greater frontal and temporal neocortical neuronal tau pathology in PSP with frontotemporal dementia compared with PSP with Richardson syndrome. White matter tau pathology was also greater in PSP with frontotemporal dementia than PSP with Richardson syndrome. Genetic and demographic factors were not associated with atypical distribution of tau pathology in PSP with frontotemporal dementia.ConclusionsThe results confirm the subset of cognitive-predominant PSP mimicking frontotemporal dementia in PSP. PSP with frontotemporal dementia has distinct clinical features that differ from PSP with Richardson syndrome, as well as differences in distribution and density of tau pathology. © 2019 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society