Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error

We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting the optimal constant factors in the leading terms in a number of different models. In the randomized model, 1) we give a general technique to convert public-coin protocols to private-coin protocols by incurring a small multiplicative error, at a small additive cost. This is an improvement over Newman's theorem [Inf. Proc. Let.'91] in the dependence on the error parameter. 2) Using this we obtain a $(\log(n/\epsilon^2)+4)$-cost private-coin communication protocol that computes the $n$-bit Equality function, to error $\epsilon$. This improves upon the $\log(n/\epsilon^3)+O(1)$ upper bound implied by Newman's theorem, and matches the best known lower bound, which follows from Alon [Comb. Prob. Comput.'09], up to an additive $\log\log(1/\epsilon)+O(1)$. In the quantum model, 1) we exhibit a one-way protocol of cost $\log(n/\epsilon)+4$, that uses only pure states and computes the $n$-bit Equality function to error $\epsilon$. This bound was implicitly already shown by Nayak [PhD thesis'99]. 2) We show that any $\epsilon$-error one-way protocol for $n$-bit Equality that uses only pure states communicates at least $\log(n/\epsilon)-\log\log(1/\epsilon)-O(1)$ qubits. 3) We exhibit a one-way protocol of cost $\log(\sqrt{n}/\epsilon)+3$, that uses mixed states and computes the $n$-bit Equality function to error $\epsilon$. This is also tight up to an additive $\log\log(1/\epsilon)+O(1)$, which follows from Alon's result. Our upper bounds also yield upper bounds on the approximate rank and related measures of the Identity matrix. This also implies improved upper bounds on these measures for the distributed SINK function, which was recently used to refute the randomized and quantum versions of the log-rank conjecture.Comment: 16 page

de Sitter symmetry of Neveu-Schwarz spinors

We study the relations between Dirac fields living on the 2-dimensional Lorentzian cylinder and the ones living on the double-covering of the 2-dimensional de Sitter manifold, here identified as a certain coset space of the group $SL(2,R)$. We show that there is an extended notion of de Sitter covariance only for Dirac fields having the Neveu-Schwarz anti-periodicity and construct the relevant cocycle. Finally, we show that the de Sitter symmetry is naturally inherited by the Neveu-Schwarz massless Dirac field on the cylinder.Comment: 24 page

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Agreed Definitions and a Shared Vision for New Standards in Stroke Recovery Research: The Stroke Recovery and Rehabilitation Roundtable Taskforce

The first Stroke Recovery and Rehabilitation Roundtable established a game changing set of new standards for stroke recovery research. Common language and definitions were required to develop an agreed framework spanning the four working groups: translation of basic science, biomarkers of stroke recovery, measurement in clinical trials and intervention development and reporting. This paper outlines the working definitions established by our group and an agreed vision for accelerating progress in stroke recovery research

Health literacy, health status, and healthcare utilization of Taiwanese adults: results from a national survey

Abstract Background Low health literacy is considered a worldwide health threat. The purpose of this study is to assess the prevalence and socio-demographic covariates of low health literacy in Taiwanese adults and to investigate the relationships between health literacy and health status and health care utilization. Methods A national survey of 1493 adults was conducted in 2008. Health literacy was measured using the Mandarin Health Literacy Scale. Health status was measured based on self-rated physical and mental health. Health care utilization was measured based on self-reported outpatient clinic visits, emergency room visits, and hospitalizations. Results Approximately thirty percent of adults were found to have low (inadequate or marginal) health literacy. They tended to be older, have fewer years of schooling, lower household income, and reside in less populated areas. Inadequate health literacy was associated with poorer mental health (OR, 0.57; 95% CI, 0.35-0.91). No association was found between health literacy and health care utilization even after adjusting for other covariates. Conclusions Low (inadequate and marginal) health literacy is prevalent in Taiwan. High prevalence of low health literacy is not necessarily indicative of the need for interventions. Systematic efforts to evaluate the impact of low health literacy on health outcomes in other countries would help to illuminate features of health care delivery and financing systems that may mitigate the adverse health effects of low health literacy.http://deepblue.lib.umich.edu/bitstream/2027.42/78252/1/1471-2458-10-614.xmlhttp://deepblue.lib.umich.edu/bitstream/2027.42/78252/2/1471-2458-10-614.pdfPeer Reviewe

Validation of Self-Reported Health Literacy Questions Among Diverse English and Spanish-Speaking Populations

BackgroundLimited health literacy (HL) contributes to poor health outcomes and disparities, and direct measurement is often time-intensive. Self-reported HL questions have not been validated among Spanish-speaking and diverse English-speaking populations.ObjectiveTo evaluate three self-reported questions: 1 "How confident are you filling out medical forms?"; 2 "How often do you have problems learning about your medical condition because of difficulty understanding written information?"; and 3 "How often do you have someone help you read hospital materials?" Answers were based on a 5-point Likert scale.DesignThis was a validation study nested within a trial of diabetes self-management support in the San Francisco Department of Public Health.ParticipantsEnglish and Spanish-speaking adults with type 2 diabetes receiving primary care.MethodsUsing the Test of Functional Health Literacy in Adults (s-TOFHLA) in English and Spanish as the reference, we classified HL as inadequate, marginal, or adequate. We calculated the C-index and test characteristics of the three questions and summative scale compared to the s-TOFHLA and assessed variations in performance by language, race/ethnicity, age, and education.Key resultsOf 296 participants, 48% were Spanish-speaking; 9% were White, non-Hispanic; 47% had inadequate HL and 12% had marginal HL. Overall, 57% reported being confident with forms "somewhat" or less. The "confident with forms" question performed best for detecting inadequate (C-index = 0.82, (0.77-0.87)) and inadequate plus marginal HL (C index = 0.81, (0.76-0.86); p<0.01 for differences from other questions), and performed comparably to the summative scale. The "confident with forms" question and scale also performed best across language, race/ethnicity, educational attainment, and age.ConclusionsA single self-reported HL question about confidence with forms and a summative scale of three questions discriminated between Spanish and English speakers with adequate HL and those with inadequate and/or inadequate plus marginal HL. The "confident with forms" question or the summative scale may be useful for estimating HL in clinical research involving Spanish-speaking and English-speaking, chronically-ill, diverse populations

The dependence of dijet production on photon virtuality in ep collisions at HERA

The dependence of dijet production on the virtuality of the exchanged photon, Q^2, has been studied by measuring dijet cross sections in the range 0 < Q^2 < 2000 GeV^2 with the ZEUS detector at HERA using an integrated luminosity of 38.6 pb^-1. Dijet cross sections were measured for jets with transverse energy E_T^jet > 7.5 and 6.5 GeV and pseudorapidities in the photon-proton centre-of-mass frame in the range -3 < eta^jet <0. The variable xg^obs, a measure of the photon momentum entering the hard process, was used to enhance the sensitivity of the measurement to the photon structure. The Q^2 dependence of the ratio of low- to high-xg^obs events was measured. Next-to-leading-order QCD predictions were found to generally underestimate the low-xg^obs contribution relative to that at high xg^obs. Monte Carlo models based on leading-logarithmic parton-showers, using a partonic structure for the photon which falls smoothly with increasing Q^2, provide a qualitative description of the data.Comment: 35 pages, 6 eps figures, submitted to Eur.Phys.J.