Spectral Thresholds in the Bipartite Stochastic Block Model

We consider a bipartite stochastic block model on vertex sets $V_1$ and $V_2$, with planted partitions in each, and ask at what densities efficient algorithms can recover the partition of the smaller vertex set. When $|V_2| \gg |V_1|$, multiple thresholds emerge. We first locate a sharp threshold for detection of the partition, in the sense of the results of \cite{mossel2012stochastic,mossel2013proof} and \cite{massoulie2014community} for the stochastic block model. We then show that at a higher edge density, the singular vectors of the rectangular biadjacency matrix exhibit a localization / delocalization phase transition, giving recovery above the threshold and no recovery below. Nevertheless, we propose a simple spectral algorithm, Diagonal Deletion SVD, which recovers the partition at a nearly optimal edge density. The bipartite stochastic block model studied here was used by \cite{feldman2014algorithm} to give a unified algorithm for recovering planted partitions and assignments in random hypergraphs and random $k$-SAT formulae respectively. Our results give the best known bounds for the clause density at which solutions can be found efficiently in these models as well as showing a barrier to further improvement via this reduction to the bipartite block model.Comment: updated version, will appear in COLT 201

Optimal control for diffusions on graphs

Starting from a unit mass on a vertex of a graph, we investigate the minimum number of "\emph{controlled diffusion}" steps needed to transport a constant mass $p$ outside of the ball of radius $n$. In a step of a controlled diffusion process we may select any vertex with positive mass and topple its mass equally to its neighbors. Our initial motivation comes from the maximum overhang question in one dimension, but the more general case arises from optimal mass transport problems. On $\mathbb{Z}^{d}$ we show that $\Theta( n^{d+2} )$ steps are necessary and sufficient to transport the mass. We also give sharp bounds on the comb graph and $d$-ary trees. Furthermore, we consider graphs where simple random walk has positive speed and entropy and which satisfy Shannon's theorem, and show that the minimum number of controlled diffusion steps is $\exp{( n \cdot h / \ell ( 1 + o(1) ))}$, where $h$ is the Avez asymptotic entropy and $\ell$ is the speed of random walk. As examples, we give precise results on Galton-Watson trees and the product of trees $\mathbb{T}_d \times \mathbb{T}_k$.Comment: 32 pages, 2 figure

Sandpiles and Dominos

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product whose factors are sums of squares of values of trigonometric functions. We provide a new derivation of the formula due to Kasteleyn and to Temperley and Fisher for counting the number of domino tilings of a 2m x 2n rectangular checkerboard and a new way of counting the number of domino tilings of a 2m x 2n checkerboard on a M\"obius strip.Comment: 35 pages, 24 figure

Behaviours, motivations and values: Validity, reliability, and utility of novice motorcyclist' self-report in road safety research

The continuing use of self-report methods demands consideration of the validity, reliability, and utility of self-report in road safety research. This thesis assesses self-report issues with respect to four key constructs in motorcycle safety research—exposure, on-road behaviours, riding motivations, and perceived value in a sample of Australian novice motorcycle riders. In Study 1 a comprehensive set of statistical analyses was performed to test the validity and reliability of various self-report measures of riding exposure. In Study 2 and Study 3 previously untested psychometric properties of stability, content validity, and predictive validity of the Motorcycle Rider Behaviour Questionnaire and the Motorcycle Rider Motivation Questionnaire in terms of police-recorded offences and crashes as well as previously assessed factor structure, internal consistency, and predictive validity in terms of self-reported crashes were examined. In Study 4 I demonstrated the utility of a contingent valuation (CV) survey in measuring, understanding, and therefore addressing the perceived value of rider training amongst novice riders. The four studies highlight that the appropriateness of self-report depends on not only the nature of the phenomenon under study but the extent to which the factors that contribute to validity and reliability are accounted for in the design of self-report measures

Initiation of fretting fatigue scar of Ti-6Al-4V alloy dependent on the influence of its surface roughness

This paper reports on the experimental studies undertaken to detect the early stage when appears the fretting wear of the Ti-6Al-4V alloy used for the hip prostheses. Wear is a critical aspect for estimating the fretting fatigue. Studies were performed on special shape samples, in order to be able to study the influence of in contact surfaces roughness on the durability to fretting. Fretting pads, with roughness Ra of the contact surface of 0.015 μm and 0.045 μm, and Ti-6Al-4V samples with roughness of 0.045 μm, 0.075 μm and 0.19 μm, were used. Testing periods of 3 seconds, 1 minute and 5 minutes were selected to capture the moment of the fretting scar appearance, long before these initiate the eventual fretting cracking. Simultaneously with the surface fretting wear, the friction coefficient was also measured. From the in-time evolution determinations of the fretting wear, it resulted that, under the experimental conditions used, the minimum wear (Vu = 7.0 × 10-6 mm3) occurs at a certain value of the roughness (0.045 μm) and not at the minimum roughness (0.015 μm). Surprisingly, the minimum friction coefficient (μ = 0.038) does not coincide with the minimum fretting wear (Vu = 7.0 × 10-6 mm3)

Investigation a unique scratching of the failure mechanisms of the coatings with TiN thin layers deposited on 316L stainless steel

Starting from the finding that the coatings with TiN of the total hip prostheses femoral heads made of Ti-6Al-4V alloy have tendencies to wear (abrasive, adhesive or bio-tribo-corrosion), the paper has proposed to establish the failure mechanisms of these thin layers coatings. For economic reasons, the studies were made on TiN coatings on 316L stainless steel (SS 316L), steel with mechanical characteristics similar to the Ti-6Al-4V alloy. Three types of TiN coatings were made on cylindrical samples of SS 316L by the Pulse Laser Deposition (PLD) method. Depending on the number of deposition pulses, coatings with different thicknesses and harnesses were obtained. Since the failure of coatings is generally due to the failure of coating's adhesion to the substrate's material, the coating's adhesion was tested by single pass single indenter (SPSI) scratch tests to completely avoid the occurrence of the fatigue phenomenon that may occur in the case of multi-pass single indenter (MPSI) scratch test or multi-pass dual indenters (MPDI). The critical failure events of the three types of coatings were highlighted and commented, concluding that PLD coatings with 10000 and 20000 pulses are the ones that offer the most favorable perspectives from the coating – substrate adhesion point of view

The bi-directional associations between psychotic experiences and DSM-IV mental disorders

OBJECTIVE: While it is now recognized that psychotic experiences are associated with an increased risk of later mental disorders, we lack a detailed understanding of the reciprocal time-lagged relationships between first onsets of psychotic experiences and mental disorders. Using data from World Health Organization World Mental Health (WMH) Surveys, the authors assessed the bidirectional temporal associations between psychotic experiences and mental disorders. METHOD: The WMH Surveys assessed lifetime prevalence and age at onset of psychotic experiences and 21 common DSM-IV mental disorders among 31,261 adult respondents from 18 countries. Discrete-time survival models were used to examine bivariate and multivariate associations between psychotic experiences and mental disorders. RESULTS: Temporally primary psychotic experiences were significantly associated with subsequent first onset of eight of the 21 mental disorders (major depressive disorder, bipolar disorder, generalized anxiety disorder, social phobia, posttraumatic stress disorder, adult separation anxiety disorder, bulimia nervosa, and alcohol abuse), with odds ratios ranging from 1.3 (95% CI=1.2-1.5) for major depressive disorder to 2.0 (95% CI=1.5-2.6) for bipolar disorder. In contrast, 18 of 21 primary mental disorders were significantly associated with subsequent first onset of psychotic experiences, with odds ratios ranging from 1.5 (95% CI=1.0-2.1) for childhood separation anxiety disorder to 2.8 (95% CI=1.0-7.8) for anorexia nervosa. CONCLUSIONS: While temporally primary psychotic experiences are associated with an elevated risk of several subsequent mental disorders, these data show that most mental disorders are associated with an elevated risk of subsequent psychotic experiences. Further investigation of the underlying factors accounting for these time-order relationships may shed light on the etiology of psychotic experiences

Comorbidity of Common Mental Disorders with Cancer and Their Treatment Gap: Findings from the World Mental Health Surveys

Objective This study aimed to study the comorbidity of common mental disorders (CMDs) and cancer, and the mental health treatment gap among community residents with active cancer, cancer survivors and cancer-free respondents in 13 high-income and 11 low-middle-income countries. Methods Data were derived from the World Mental Health Surveys (N = 66,387; n = 357 active cancer, n = 1373 cancer survivors, n = 64,657 cancer-free respondents). The World Health Organization/Composite International Diagnostic Interview was used in all surveys to estimate CMDs prevalence rates. Respondents were also asked about mental health service utilization in the preceding 12 months. Cancer status was ascertained by self-report of physician\u27s diagnosis. Results Twelve-month prevalence rates of CMDs were higher among active cancer (18.4%, SE = 2.1) than cancer-free respondents (13.3%, SE = 0.2) adjusted for sociodemographic confounders and other lifetime chronic conditions (adjusted odds ratio (AOR) = 1.44, 95% CI 1.05-1.97). CMD rates among cancer survivors (14.6%, SE = 0.9) compared with cancer-free respondents did not differ significantly (AOR = 0.95, 95% CI 0.82-1.11). Similar patterns characterized high-income and low-middle-income countries. Of respondents with active cancer who had CMD in the preceding 12 months, 59% sought services for mental health problems (SE = 5.3). The pattern of service utilization among people with CMDs by cancer status (highest among persons with active cancer, lower among survivors and lowest among cancer-free respondents) was similar in high-income (64.0%, SE = 6.0; 41.2%, SE = 3.0; 35.6%, SE = 0.6) and low-middle-income countries (46.4%, SE = 11.0; 22.5%, SE = 9.1; 17.4%, SE = 0.7). Conclusions Community respondents with active cancer have higher CMD rates and high treatment gap. Comprehensive cancer care should consider both factors