Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

The Wasteland of Random Supergravities

We show that in a general \cal{N} = 1 supergravity with N \gg 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kahler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in typical configurations, a significant fraction of the eigenvalues are negative. Building on the Tracy-Widom law governing fluctuations of extreme eigenvalues, we determine the probability P of a large fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes this extremely unlikely: we find P \propto exp(-c N^p), with c, p being constants. For generic critical points we find p \approx 1.5, while for approximately-supersymmetric critical points, p \approx 1.3. Our results have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.Comment: 39 pages, 9 figures; v2: fixed typos, added refs and clarification

Kahler-Einstein metrics emerging from free fermions and statistical mechanics

We propose a statistical mechanical derivation of Kahler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical free fermion gas on X whose one-particle states are pluricanonical holomorphic sections on X (coinciding with higher spin states in the case of a Riemann surface). A heuristic, but hopefully physically illuminating, argument for the convergence in the thermodynamical (large N) limit is given, based on a recent mathematically rigorous result about exponentially small fluctuations of Slater determinants. Relations to effective bosonization and the Yau-Tian-Donaldson program in Kahler geometry are pointed out. The precise mathematical details will be investigated elsewhere.Comment: v1: 22 pages v2: 25 pages. The relation to quantum gravity has been further developed by working over the moduli space of all complex structures. Relations to Donaldson's program pointed out. References adde

Factors associated with time delay to carotid stenting in patients with a symptomatic carotid artery stenosis

Treatment of a symptomatic stenosis is known to be most beneficial within 14 days after the presenting event but this can frequently not be achieved in daily practice. The aim of this study was the assessment of factors responsible for this time delay to treatment. A retrospective analysis of a prospective two-center CAS database was carried out to investigate the potential factors that influence a delayed CAS treatment. Of 374 patients with a symptomatic carotid stenosis, 59.1% were treated beyond ≥14 days. A retinal TIA event (OR = 3.59, 95% CI 1.47–8.74, p < 0.01) was found to be a predictor for a delayed treatment, whereas the year of the intervention (OR = 0.32, 95% CI 0.20–0.50, p < 0.01) and a contralateral carotid occlusion (OR = 0.42, 95% CI 0.21–0.86, p = 0.02) were predictive of an early treatment. Similarly, within the subgroup of patients with transient symptoms, the year of the intervention (OR = 0.28, 95% CI 0.14–0.59, p < 0.01) was associated with an early treatment, whereas a retinal TIA as the qualifying event (OR = 6.96, 95% CI 2.37–20.47, p < 0.01) was associated with a delayed treatment. Treatment delay was most pronounced in patients with an amaurosis fugax, whereas a contralateral carotid occlusion led to an early intervention. Although CAS is increasingly performed faster in the last years, there is still scope for an even more accelerated treatment strategy, which might prevent future recurrent strokes prior to treatment

Intramanual and intermanual transfer of the curvature aftereffect

The existence and transfer of a haptic curvature aftereffect was investigated to obtain a greater insight into neural representation of shape. The haptic curvature aftereffect is the phenomenon whereby a flat surface is judged concave if the preceding touched stimulus was convex and vice versa. Single fingers were used to touch the subsequently presented stimuli. A substantial aftereffect was found when the adaptation surface and the test surface were touched by the same finger. Furthermore, a partial, but significant transfer of the aftereffect was demonstrated between fingers of the same hand and between fingers of both the hands. These results provide evidence that curvature information is not only represented at a level that is directly connected to the mechanoreceptors of individual fingers but is also represented at a stage in the somatosensory cortex shared by the fingers of both the hands

Psychometric properties of Greek versions of the Modified Corah Dental Anxiety Scale (MDAS) and the Dental Fear Survey (DFS)

Background: A growing body of literature describes the performance of dental fear questionnaires in various countries. We describe the psychometric properties of Greek versions of the Modified Dental Anxiety Scale (MDAS) and the Dental Fear Survey (DFS) in adult Greek patients. Methods: Greek versions of the MDAS and DFS were administered to two samples of adult dental patients. In the first sample, 195 patients attending one of three private practice dental offices in a large city in Greece completed the questionnaires in the waiting room before dental treatment. After treatment, their dentists (who did not know how the patients had answered the questionnaire) rated their anxiety during dental treatment. In the second sample, 41 patients attending a Greek university dental school clinic completed the questionnaire twice at two separate visits, in order to provide test-retest data. Cronbach's alpha was used to compute the internal consistencies, while Spearman's rho was used to compute the testretest reliabilities. Construct validity was assessed by correlating the responses to the MDAS and DFS by Spearman's rho. Spearman's rho was also used to examine the criterion validities, by comparing the questionnaire responses with the dentists' ratings of anxiety. Results: The internal consistencies for the MDAS were 0.90 and 0.92 in the two samples; for the DFS, the internal consistencies were 0.96 in both samples. The test-retest reliabilities were 0.94 for the MDAS and 0.95 for the DFS. The correlation between the two questionnaires was 0.89. The patients' responses to both questionnaires were significantly related to the dentists' ratings of their anxiety during dental treatment (both p values less than 0.001). Conclusion: The results indicate that the Greek versions of the MDAS and DFS have good internal consistencies and test-retest reliabilities, as well as good construct and criterion validities. The psychometric properties of the Greek versions of these questionnaires appear to be similar to those previously reported in other countries.This research was supported by NIH/NIDCR grant T32DE07132

Population-Attributable Risks for Ischemic Stroke in a Community in South Brazil: A Case-Control Study

Background: Risk factors for ischemic stroke are mostly known, but it is still unclear in most countries, what are their combined population-attributable risk percent (PAR%). In a case-control study the individual odds ratios (ORs) and the individual and combined PAR%, including risk factors not addressed in previous studies were estimated. Methods: Cases and controls were selected from patients attending to an emergency department. Cases were patients aged with 45 years or more with the first episode of ischemic stroke, characterized by a focal neurological deficit or change in the mental status occurring during the previous 24 hours. Controls, matched to cases by age and gender, were selected from patients without neurological complaints. Results: 133 cases and 272 controls were studied. Odds ratios for ischemic stroke were: atrial fibrillation (27.3; CI 95 % 7.5

Rapid Growth Reduces Cold Resistance: Evidence from Latitudinal Variation in Growth Rate, Cold Resistance and Stress Proteins

Background: Physiological costs of rapid growth may contribute to the observation that organisms typically grow at submaximal rates. Although, it has been hypothesized that faster growing individuals would do worse in dealing with suboptimal temperatures, this type of cost has never been explored empirically. Furthermore, the mechanistic basis of the physiological costs of rapid growth is largely unexplored. Methodology/Principal Finding: Larvae of the damselfly Ischnura elegans from two univoltine northern and two multivoltine southern populations were reared at three temperatures and after emergence given a cold shock. Cold resistance, measured by chill coma recovery times in the adult stage, was lower in the southern populations. The faster larval growth rates in the southern populations contributed to this latitudinal pattern in cold resistance. In accordance with their assumed role in cold resistance, Hsp70 levels were lower in the southern populations, and faster growing larvae had lower Hsp70 levels. Yet, individual variation in Hsp70 levels did not explain variation in cold resistance. Conclusions/Significance: We provide evidence for a novel cost of rapid growth: reduced cold resistance. Our results indicate that the reduced cold resistance in southern populations of animals that change voltinism along the latitudinal gradient may not entirely be explained by thermal selection per se but also by the costs of time constraint-induced higher growth rates. This also illustrates that stressors imposed in the larval stage may carry over and shape fitness in the adul

Being questioned and receiving advice about alcohol and smoking in health care: Associations with patients' characteristics, health behavior, and reported stage of change

<p>Abstract</p> <p>Background</p> <p>Alcohol habits are more rarely addressed than other health behavior topics in Swedish health care. This study examined whether differences between topics could be explained by their different associations with patient characteristics or by the differences in the prevalence of the disadvantageous health behavior, i.e., excessive alcohol use and smoking. The study moreover examined whether simply being asked questions about behavior, i.e., alcohol use or smoking, was associated with reported change.</p> <p>Methods</p> <p>The study was based on a cross-sectional postal survey (n = 4 238, response rate 56.5 percent) representative of the adult population in Stockholm County in 2003. Retrospective self-reports were used to assess health care visits during the past 12 months, the questions and advice received there, patients characteristics, health behavior, and the present stage of change. Logistic regression analysis was used to estimate the associations among the 68 percent who had visited health care.</p> <p>Results</p> <p>Among the health care visitors, 23 percent reported being asked about their alcohol habits, and 3 percent reported receiving advice or/and support to modify their alcohol use - fewer than for smoking, physical exercise, or diet. When regression models adjusted for patient characteristics, the differences between health behaviors in the extent of questioning and advice remained. However, when the models also adjusted for smoking and alcohol consumption there was no difference between smoking and alcohol-related advice. In fact one-third of the present smokers and two-fifths of the persons dependent on alcohol reported having receiving advice the previous 12 months. Those who reported being asked questions or receiving advice more often reported a decreased alcohol use and similarly intended to cease smoking within 6 months. Questions about alcohol use were moreover related to a later stage of stage of change independently of advice among women but not among men.</p> <p>Conclusions</p> <p>While most patients are never addressed, many in the target groups seem to be reached anyway. Besides advice, already addressing alcohol habits appears to be associated with change. The results also indicate that gender possibly plays a role in the relationship between advice and the stage of change.</p