Quantum Weakly Nondeterministic Communication Complexity

We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this model of quantum nondeterministic communication complexity for a total function. This separation is quadratic.Comment: 12 pages. v3: minor correction

Maps of zeroes of the grand canonical partition function in a statistical model of high energy collisions

Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.Comment: 17 pages, figures (ps included); added references, some figures enlarged. To appear in J. Phys.

Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change

{Improved Bounds on Fourier Entropy and Min-entropy}

Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that $H(\hat{f}^2)\leq C Inf(f)$, where $H(\hat{f}^2)$ is the Shannon entropy of the Fourier distribution of $f$ and $Inf(f)$ is the total influence of $f$. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if $H_{\infty}(\hat{f}^2)\leq C Inf(f)$, where $H_{\infty}(\hat{f}^2)$ is the min-entropy of the Fourier distribution. We show $H_{\infty}(\hat{f}^2)\leq 2C_{\min}^\oplus(f)$, where $C_{\min}^\oplus(f)$ is the minimum parity certificate complexity of $f$. We also show that for every $\epsilon\geq 0$, we have $H_{\infty}(\hat{f}^2)\leq 2\log (\|\hat{f}\|_{1,\epsilon}/(1-\epsilon))$, where $\|\hat{f}\|_{1,\epsilon}$ is the approximate spectral norm of $f$. As a corollary, we verify the FMEI conjecture for the class of read-$k$ $DNF$s (for constant $k$). 2) We show that $H(\hat{f}^2)\leq 2 aUC^\oplus(f)$, where $aUC^\oplus(f)$ is the average unambiguous parity certificate complexity of $f$. This improves upon Chakraborty et al. An important consequence of the FEI conjecture is the long-standing Mansour's conjecture. We show that a weaker version of FEI already implies Mansour's conjecture: is $H(\hat{f}^2)\leq C \min\{C^0(f),C^1(f)\}$?, where $C^0(f), C^1(f)$ are the 0- and 1-certificate complexities of $f$, respectively. 3) We study what FEI implies about the structure of polynomials that 1/3-approximate a Boolean function. We pose a conjecture (which is implied by FEI): no "flat" degree-$d$ polynomial of sparsity $2^{\omega(d)}$ can 1/3-approximate a Boolean function. We prove this conjecture unconditionally for a particular class of polynomials

Finite element analysis of thermo-elastical modal damping of mems vibrations

The paper deals with finite element analysis of damped modal vibrations Q-factor values determined by thermal-elastic damping in micro-electrical-mechanical systems (MEMS). Mathematically the problem is formulated as a complex eigenvalue problem. Verification problems have been solved by using several computational environments and different presentations of model equations in order to comprehend and reduce the influence of rounding errors. The analysis of damped modal properties of selected real MEMS resonator revealed the main features of thermal-elastic damping by taking into account 3D geometry of the resonator and anchoring (clamping) structur

Significant differences in incubation times in sheep infected with bovine spongiform encephalopathy result from variation at codon 141 in the PRNP gene

The susceptibility of sheep to prion infection is linked to variation in the PRNP gene, which encodes the prion protein. Common polymorphisms occur at codons 136, 154 and 171. Sheep which are homozygous for the A<sub>136</sub>R<sub>154</sub>Q<sub>171</sub> allele are the most susceptible to bovine spongiform encephalopathy (BSE). The effect of other polymorphisms on BSE susceptibility is unknown. We orally infected ARQ/ARQ Cheviot sheep with equal amounts of BSE brain homogenate and a range of incubation periods was observed. When we segregated sheep according to the amino acid (L or F) encoded at codon 141 of the PRNP gene, the shortest incubation period was observed in LL141 sheep, whilst incubation periods in FF<sub>141</sub> and LF<sub>141</sub> sheep were significantly longer. No statistically significant differences existed in the expression of total prion protein or the disease-associated isoform in BSE-infected sheep within each genotype subgroup. This suggested that the amino acid encoded at codon 141 probably affects incubation times through direct effects on protein misfolding rates

Step-wedge cluster-randomised community-based trials: An application to the study of the impact of community health insurance

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.BACKGROUND: We describe a step-wedge cluster-randomised community-based trial which has been conducted since 2003 to accompany the implementation of a community health insurance (CHI) scheme in West Africa. The trial aims at overcoming the paucity of evidence-based information on the impact of CHI. Impact is defined in terms of changes in health service utilisation and household protection against the cost of illness. Our exclusive focus on the description and discussion of the methods is justified by the fact that the study relies on a methodology previously applied in the field of disease control, but never in the field of health financing. METHODS: First, we clarify how clusters were defined both in respect of statistical considerations and of local geographical and socio-cultural concerns. Second, we illustrate how households within clusters were sampled. Third, we expound the data collection process and the survey instruments. Finally, we outline the statistical tools to be applied to estimate the impact of CHI. CONCLUSION: We discuss all design choices both in relation to methodological considerations and to specific ethical and organisational concerns faced in the field. On the basis of the appraisal of our experience, we postulate that conducting relatively sophisticated trials (such as our step-wedge cluster-randomised community-based trial) aimed at generating sound public health evidence, is both feasible and valuable also in low income settings. Our work shows that if accurately designed in conjunction with local health authorities, such trials have the potential to generate sound scientific evidence and do not hinder, but at times even facilitate, the implementation of complex health interventions such as CHI