The total-variation cutoff phenomenon has been conjectured to hold for simple random walk on all transitive expanders. However, very little is actually known regarding this conjecture, and sparse graphs in general. In paper we establish Ramanujan complexes of type $\widetilde{A}_{d}$ $(d\geq1)$. As a result, obtain explicit generators the finite classical groups $\mathrm{PGL}_{n}(\mathbb{F}_{q}...

We prove the cutoff phenomenon for random walk on n-lifts of finite weighted graphs, even when base graph G lift is not reversible. The mixing time w.h.p. tmix=h−1logn, where h a constant associated to G, namely entropy its universal cover. Moreover, this smallest possible among all G. In particular case vertex with d/2 loops, d even, we obtain d-regular graph, as did Lubetzky and Sly in (Duke ...

We introduce a new type of card shuffle called one-sided transpositions. At each step is chosen uniformly from the pack and then transposed with another below it. This defines random walk on symmetric group generated by distribution which nonconstant conjugacy class Nevertheless, we provide an explicit formula for all eigenvalues demonstrating useful correspondence between standard Young tablea...

While cotinine is commonly used as a biomarker to validate self-reported smoking status, the selection of an optimal cotinine cutoff value for distinguishing true smokers from true nonsmokers shows a lack of standardization among studies. This review describes how the cutoff values have been derived, and explains the issues involved in the generalization of a cutoff value. In this study, we con...

The Strengths and Difficulties Questionnaire (SDQ) was designed to screen for behavioral problems in youths based on cutoff points that favor the instrument's diagnostic sensitivity. The present study aimed to analyze the discriminative validity of the SDQ to identify behavioral difficulties and prosocial resources in school-age children compared with the diagnostic data collected by the corres...

Objectives This study aimed to evaluate the discriminant validity of family adaptability and cohesion evaluation subscales. We investigated families referring to counseling, family courts, substance dependence treatment centers, and healthy and clinically defined cutoff scores for the breakdown of healthy Iranian families.  Methods This scale was validated by four psychologists and translated ...

Objective(s):The aim of this study was to determine whether technetium (99mTc) uptake is a relevant method for the differential diagnosis of Graves disease and subacute thyroiditis and calculate its cutoff value in case of its relevancy. Methods: A total of 69 patients, who were followed up (>3 months) in our hospital for thyrotoxi...