New Scale Factor Measure

The computation of probabilities in an eternally inflating universe requires a regulator or "measure". The scale factor time measure truncates the universe when a congruence of timelike geodesics has expanded by a fixed volume factor. This definition breaks down if the generating congruence is contracting---a serious limitation that excludes from consideration gravitationally bound regions such as our own. Here we propose a closely related regulator which is well-defined in the entire spacetime. The New Scale Factor Cutoff restricts to events with scale factor below a given value. Since the scale factor vanishes at caustics and crunches, this cutoff always includes an infinite number of disconnected future regions. We show that this does not lead to divergences. The resulting measure combines desirable features of the old scale factor cutoff and of the light-cone time cutoff, while eliminating some of the disadvantages of each.Comment: 20 pages, 1 figure; v2: references adde

New Local Duals in Eternal Inflation

Global-local duality is the equivalence of seemingly different regulators in eternal inflation. For example, the light-cone time cutoff (a global measure, which regulates time) makes the same predictions as the causal patch (a local measure that cuts off space). We show that global-local duality is far more general. It rests on a redundancy inherent in any global cutoff: at late times, an attractor regime is reached, characterized by the unlimited exponential self-reproduction of a certain fundamental region of spacetime. An equivalent local cutoff can be obtained by restricting to this fundamental region. We derive local duals to several global cutoffs of interest. The New Scale Factor Cutoff is dual to the Short Fat Geodesic, a geodesic of fixed infinitesimal proper width. Vilenkin's CAH Cutoff is equivalent to the Hubbletube, whose width is proportional to the local Hubble volume. The famous youngness problem of the Proper Time Cutoff can be readily understood by considering its local dual, the Incredible Shrinking Geodesic.Comment: 30 pages, 3 figure

Light-sheets and Bekenstein's bound

From the covariant bound on the entropy of partial light-sheets, we derive a version of Bekenstein's bound: S/M \leq pi x/hbar, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light-sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.Comment: 5 pages, 1 figure; v2: published version, improved discussion of weak gravity condition, final paragraph adde

Eternal inflation predicts that time will end

Present treatments of eternal inflation regulate infinities by imposing a geometric cutoff. We point out that some matter systems reach the cutoff in finite time. This implies a nonzero probability for a novel type of catastrophe. According to the most successful measure proposals, our galaxy is likely to encounter the cutoff within the next 5 billion years.Comment: 22 pages, 1 figur

On a class of pseudocompact spaces derived from ring epimorphisms

AbstractA Tychonoff space X is RG if the embedding of C(X)→C(Xδ) is an epimorphism of rings. Compact RG-spaces are known and easily described. We study the pseudocompact RG-spaces. These must be scattered of finite Cantor Bendixon degree but need not be locally compact. However, under strong hypotheses, (countable compactness, or small cardinality) these spaces must, indeed, be compact. The main theorems shows, how to construct a suitable maximal almost disjoint family, and apply it to obtain examples of RG-spaces that are almost compact, locally compact, non-compact, almost-P, and of Cantor Bendixon degree 2. More complicated examples of pseudocompact non-compact RG-spaces ensue

Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects

We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains' penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high grafting density modify the friction force by grafted chain. We develop here a simple model that takes into account those interactions and gives a limit grafting density beyond which the friction no longer increases with the grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter

Prevalence and clinical characteristics of left ventricular dysfunction among elderly patients in general practice setting: cross sectional survey

Objective: To assess the prevalence and clinical characteristics of left ventricular dysfunction among elderly patients in the general practice setting by echocardiographic assessment of ventricular function. Design: Cross sectional survey. Setting: Four centre general practice in Poole, Dorset. Subjects: 817 elderly patients aged 70-84 years. Main outcomes: Echocardiographic assessment of left ventricular systolic function including measurement of ejection fraction by biplane summation method where possible, clinical symptoms, and signs of left ventricular dysfunction. Results: The overall prevalence of left ventricular systolic dysfunction was 7.5% (95% confidence interval 5.8% to 9.5%); mild dysfunction (5.0%) was considerably more prevalent than moderate (1.6%) or severe dysfunction (0.7%). Measurement of ejection fraction was possible in 82% of patients (n=667): in patients categorised as having mild, moderate, or severe dysfunction, the mean ejection fraction was 48% (SD 12.0), 38% (8.1), and 26% (7.9) respectively. At all ages the prevalence was much higher in men than in women (odds ratio 5.1, 95% confidence interval 2.6 to 10.1). No clinical symptom or sign was both sensitive and specific. In around half the patients with ventricular dysfunction (52%, 32/61) heart failure had not been previously diagnosed. Conclusions: Unrecognised left ventricular dysfunction is a common problem in elderly patients in the general practice setting. Appropriate treatment with angiotensin converting enzyme inhibitors has the potential to reduce hospitalisation and mortality in these patients, but diagnosis should not be based on clinical history and examination alone. Screening is feasible in general practice, but it should not be implemented until the optimum method of identifying left ventricular dysfunction is clarified, and the cost effectiveness of screening has been shown

VAMP: semantic validation for MPEG-7 profile descriptions

MPEG-7 can be used to create complex and comprehensive metadata descriptions of multimedia content. Since MPEG-7 is defined in terms of an XML schema, the semantics of its elements has no formal grounding. In addition, certain features can be described in multiple ways. MPEG-7 profiles are subsets of the standard that apply to specific application areas and that aim to reduce this syntactic variability, but they still lack formal semantics. We propose an approach for expressing the semantics explicitly

A Minimal Regular Ring Extension of C(X)

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,Τ). We investigate when G(X) coincides with the ring C(X,Τδ) of continuous real-valued functions on the space (X,Τδ), where Τδ is the smallest Tikhonov topology on X for which tau subset of or equal to tau(delta) and C(X,Τδ) is von Neumann regular. The compact and metric spaces for which G(X) = C(X,Τδ) are characterized. Necessary, and different sufficient, conditions for the equality to hold more generally are found