Periodic 2-graphs arising from subshifts

Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz-Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whose $C^*$-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we call \emph{domino graphs}. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the $C^*$-algebras of domino graphs.Comment: 17 page

Extremal Quantum Correlations and Cryptographic Security

We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that probability distributions that are secure in this sense are exactly the extremal quantum probability distributions. This allows us to give a characterization of security in algebraic terms. We apply the method to common examples for two-party as well as multi-party setups and present a scheme for verifying security of probability distributions with two parties, two measurement settings, and two outcomes.Comment: 7 pages, 2 figures, revised version, accepted for publication in Phys. Rev. Let

A family of 2-graphs arising from two-dimensional subshifts

Higher-rank graphs (or $k$-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz-Krieger $C^*$-algebras of Robertson and Steger. Here we consider a family of finite 2-graphs whose path spaces are dynamical systems of algebraic origin, as studied by Schmidt and others. We analyse the $C^*$-algebras of these 2-graphs, find criteria under which they are simple and purely infinite, and compute their $K$-theory. We find examples whose $C^*$-algebras satisfy the hypotheses of the classification theorem of Kirchberg and Phillips, but are not isomorphic to the $C^*$-algebras of ordinary directed graphs.Comment: 28 pages, 3 figures, 1 tabl

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic

Active management in Serious Genetic Disorders

Twenty years ago we were taught to classify the cause of any medical condition into those that were 'genetic' and those that were 'acquired'.  Subsequently the acquired group could be subdivided according to aetiology. Either directly or by implication we were told that genetic disorders were untreatable and that they were always rare, making up an insignificant proportion of medical practice. This article gives a personal view of the field of medical genetics and is based on two established facts, firstly that genetic diseases are now so frequent that every doctor should be conversant with basic genetic principles. Secondly many genetic conditions if not amenable to curative treatment, are at least responsive to careful management which can prolong and increase the quality of life. At this stage we should emphasise one other aspect, which concerns the philosophy behind genetic counselling. Such counselling is not just the calculation of empiric or theoretical risks that a disease will recur, followed by telling the family and then leaving them to come to terms with unpleasant probabilities. In genetic counselling the range of options open to different members of a family can be fully explained in the light of their risks. At the same time counselling of a wider nature can be offered providing emotional support to many members of the family. By allowing individuals within a family to come to terms with the emotional aspects of an inherited condition, counselling, not necessarily provided by a genetic counsellor alone can be actively therapeutic. Let us now select some severe disorders with a major genetic component and examine the therapeutic approaches available

NS Fivebrane and Tachyon Condensation

We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of as a gerbe.Comment: 20 pages, harvma

National Health Service – Some Achievements

The National Health Service has now been in existence for over fifteen years, and is firmly established as one of the features of Twentieth Century Britain. There are many criticisms of it and many defects and deficiencies; one has only to read the newspapers—particularly the correspondence columns — to have them pointed out. However, it is good to look at the service’s successes and achievements, not in any sense of complacency, but rather in the spirit of Sir Winston Churchill’s famous minute, written in 1942, on the possibility of establishing artificial harbours on the Invasion Beaches of Europe:— “Let me have the best solution worked out. Don’t argue the matter; the difficulties will argue for themselves.

The Status of Antibiotics

From a dissertation read before the Royal Medical Society on Friday, 1st November, 1963.Many attribute the earliest recognition of an antibiotic effect to Sir Alexander Fleming. However, in 1877, 50 years before Fleming’s discovery, Pasteur and Joubert described the phenomenon of bacterial antagonism; the process whereby the growth of certain species is inhibited in the presence of others. In the particular case of the anthrax bacillus they found that growth was inhibited in cultures contaminated with ‘common bacteria’ (those types now known as the Enterobacteriaciae). Shortly afterwards the term “antibiosis” was introduced for such antagonism

Gut dysfunction in patients with multiple sclerosis and the role of spinal cord involvement in the disease.

Bowel and bladder symptoms are highly prevalent in patients with multiple sclerosis (MS). Bladder dysfunction (affecting 75% of these patients) is caused by disease in the spinal cord, whilst the pathophysiology of bowel dysfunction is unknown. Pathways regulating both the organs lie in close proximity to the spinal cord, and coexistence of their dysfunction might be the result of a common pathophysiology. If so, the prevalence of bladder symptoms should be greater in patients with MS and bowel symptoms. This hypothesis is tested in the study. We also evaluated how patient-reported symptoms quantify bowel dysfunction

Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space \H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function $m$ which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space \H is $L^2(\mathbb R^n)$, the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function $m$ satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function $m$.Comment: 16 pages including bibliograph