1,246 research outputs found

    Shift invariant preduals of &#8467;<sub>1</sub>(&#8484;)

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    The Banach space &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) weak&lt;sup&gt;*&lt;/sup&gt;-continuous. This is equivalent to making the natural convolution multiplication on &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) separately weak*-continuous and so turning &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) into a dual Banach algebra. We call such preduals &lt;i&gt;shift-invariant&lt;/i&gt;. It is known that the only shift-invariant predual arising from the standard duality between C&lt;sub&gt;0&lt;/sub&gt;(K) (for countable locally compact K) and &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) is c&lt;sub&gt;0&lt;/sub&gt;(&#8484;). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak&lt;sup&gt;*&lt;/sup&gt;-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c&lt;sub&gt;0&lt;/sub&gt;. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of &#8484;. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c&lt;sub&gt;0&lt;/sub&gt;

    Geographic constraints on social network groups

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    Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social group structure. We construct a social network of individuals whose most frequent geographical locations are also known. We also classify the individuals into groups according to a community detection algorithm. We study the variation of geographical span for social groups of varying sizes, and explore the relationship between topological positions and geographic positions of their members. We find that small social groups are geographically very tight, but become much more clumped when the group size exceeds about 30 members. Also, we find no correlation between the topological positions and geographic positions of individuals within network communities. These results suggest that spreading processes face distinct structural and spatial constraints.Comment: 10 pages, 5 figure

    UK experience of liver transplantation for erythropoietic protoporphyria

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    Erythropoietic protoporphyria (EPP) is characterised by excess production of free protoporphyrin from the bone marrow, most commonly due to deficiency of the enzyme ferrochelatase. Excess protoporphyrin gives rise to the cutaneous photosensitivity characteristic of the disease, and in a minority of patients leads to end-stage liver disease necessitating liver transplantation (LT). There is limited information regarding the timing, impact and long-term outcome of LT in such patients, thus we aimed to identify the indications and outcomes of all transplants performed for EPP in the UK using data from the UK Transplant Registry. Between 1987 and 2009, five patients underwent LT for EPP liver disease. Median follow-up was 60 months, and there were two deaths at 44 and 95 months from causes unrelated to liver disease. The remaining recipients are alive at 22.4 years, 61 months and 55 months after transplant. A high rate of postoperative biliary stricturing requiring multiple biliary interventions was observed. Recurrent EPP-liver disease occurred in 4/5 (80%) of patients but graft failure has not been observed. Given the role of biliary obstruction in inducing EPP-mediated liver damage, we suggest that consideration should be given for construction of a Roux loop at the time of transplant. Thus we demonstrate that although EPP liver transplant recipients have a good long-term survival, comparable to patients undergoing LT for other indications, biliary complications and disease recurrence are almost universal, and bone marrow transplantation should be considered where possible

    Cerebral activations related to ballistic, stepwise interrupted and gradually modulated movements in parkinson patients

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    Patients with Parkinson's disease (PD) experience impaired initiation and inhibition of movements such as difficulty to start/stop walking. At single-joint level this is accompanied by reduced inhibition of antagonist muscle activity. While normal basal ganglia (BG) contributions to motor control include selecting appropriate muscles by inhibiting others, it is unclear how PD-related changes in BG function cause impaired movement initiation and inhibition at single-joint level. To further elucidate these changes we studied 4 right-hand movement tasks with fMRI, by dissociating activations related to abrupt movement initiation, inhibition and gradual movement modulation. Initiation and inhibition were inferred from ballistic and stepwise interrupted movement, respectively, while smooth wrist circumduction enabled the assessment of gradually modulated movement. Task-related activations were compared between PD patients (N = 12) and healthy subjects (N = 18). In healthy subjects, movement initiation was characterized by antero-ventral striatum, substantia nigra (SN) and premotor activations while inhibition was dominated by subthalamic nucleus (STN) and pallidal activations, in line with the known role of these areas in simple movement. Gradual movement mainly involved antero-dorsal putamen and pallidum. Compared to healthy subjects, patients showed reduced striatal/SN and increased pallidal activation for initiation, whereas for inhibition STN activation was reduced and striatal-thalamo-cortical activation increased. For gradual movement patients showed reduced pallidal and increased thalamo-cortical activation. We conclude that PD-related changes during movement initiation fit the (rather static) model of alterations in direct and indirect BG pathways. Reduced STN activation and regional cortical increased activation in PD during inhibition and gradual movement modulation are better explained by a dynamic model that also takes into account enhanced responsiveness to external stimuli in this disease and the effects of hyper-fluctuating cortical inputs to the striatum and STN in particular

    Private Sector Union Density and the Wage Premium: Past, Present, and Future

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    The rise and decline of private sector unionization were among the more important features of the U.S. labor market during the twentieth century. Following a dramatic spurt in unionization after passage of the depression-era National Labor Relations Act (NLRA) of 1935, union density peaked in the mid-1950s, and then began a continuous decline. At the end of the century, the percentage of private wage and salary workers who were union members was less than 10 percent, not greatly different from union density prior to the NLRA

    Modern microwave methods in solid state inorganic materials chemistry: from fundamentals to manufacturing

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