Quantum Communication Cannot Simulate a Public Coin

We study the simultaneous message passing model of communication complexity. Building on the quantum fingerprinting protocol of Buhrman et al., Yao recently showed that a large class of efficient classical public-coin protocols can be turned into efficient quantum protocols without public coin. This raises the question whether this can be done always, i.e. whether quantum communication can always replace a public coin in the SMP model. We answer this question in the negative, exhibiting a communication problem where classical communication with public coin is exponentially more efficient than quantum communication. Together with a separation in the other direction due to Bar-Yossef et al., this shows that the quantum SMP model is incomparable with the classical public-coin SMP model. In addition we give a characterization of the power of quantum fingerprinting by means of a connection to geometrical tools from machine learning, a quadratic improvement of Yao's simulation, and a nearly tight analysis of the Hamming distance problem from Yao's paper.Comment: 12 pages LaTe

Exact properties of Efron's biased coin randomization procedure

Efron [Biometrika 58 (1971) 403--417] developed a restricted randomization procedure to promote balance between two treatment groups in a sequential clinical trial. He called this the biased coin design. He also introduced the concept of accidental bias, and investigated properties of the procedure with respect to both accidental and selection bias, balance, and randomization-based inference using the steady-state properties of the induced Markov chain. In this paper we revisit this procedure, and derive closed-form expressions for the exact properties of the measures derived asymptotically in Efron's paper. In particular, we derive the exact distribution of the treatment imbalance and the variance-covariance matrix of the treatment assignments. These results have application in the design and analysis of clinical trials, by providing exact formulas to determine the role of the coin's bias probability in the context of selection and accidental bias, balancing properties and randomization-based inference.Comment: Published in at http://dx.doi.org/10.1214/09-AOS758 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fourier Growth of Regular Branching Programs

We analyze the Fourier growth, i.e. the L? Fourier weight at level k (denoted L_{1,k}), of read-once regular branching programs. We prove that every read-once regular branching program B of width w ? [1,?] with s accepting states on n-bit inputs must have its L_{1,k} bounded by min{Pr[B(U_n) = 1](w-1)^k, s ? O((n log n)/k)^{(k-1)/2}}. For any constant k, our result is tight up to constant factors for the AND function on w-1 bits, and is tight up to polylogarithmic factors for unbounded width programs. In particular, for k = 1 we have L_{1,1}(B) ? s, with no dependence on the width w of the program. Our result gives new bounds on the coin problem and new pseudorandom generators (PRGs). Furthermore, we obtain an explicit generator for unordered permutation branching programs of unbounded width with a constant factor stretch, where no PRG was previously known. Applying a composition theorem of B?asiok, Ivanov, Jin, Lee, Servedio and Viola (RANDOM 2021), we extend our results to "generalized group products," a generalization of modular sums and product tests

Flow optimization study of a batch microfluidics PET tracer synthesizing device.

We present numerical modeling and experimental studies of flow optimization inside a batch microfluidic micro-reactor used for synthesis of human-scale doses of Positron Emission Tomography (PET) tracers. Novel techniques are used for mixing within, and eluting liquid out of, the coin-shaped reaction chamber. Numerical solutions of the general incompressible Navier Stokes equations along with time-dependent elution scalar field equation for the three dimensional coin-shaped geometry were obtained and validated using fluorescence imaging analysis techniques. Utilizing the approach presented in this work, we were able to identify optimized geometrical and operational conditions for the micro-reactor in the absence of radioactive material commonly used in PET related tracer production platforms as well as evaluate the designed and fabricated micro-reactor using numerical and experimental validations

NEUROLOGICAL DISORDER AMONG PREMUTATION CARRIERS OF FRAGILE X SYNDROME AT SEMIN, GUNUNG KIDUL REGENCY

Background: Neurological disorder among male premutation carriers of Fragile X Syndrome (FXS) frequently occurs. In other hand, lacking of information results misdiagnosis of this disorder. Therefore this study is addressed to provide the data about neurological involvement of late-adult premutation carriers of FXS. Objectives: This research is to know neurological involvement of late-adult premutation carriers of FXS. Subjects and Methods: This was a descriptive study following cytogenetic, Polymerase Chain Reaction (PCR), and neurological examinations on premutation carriers of FXS. Cytogenetic and PCR results were secondary data from Central for biomedical research (CEBIOR) laboratory of Faculty of Medicine Diponegoro University during September 2009 – March 2010. Simple neurological examination techniques were done to observe neurological involment among male premutation carriers. Results: There were four males carrying premutation allele over the age of 50. Cytogenetic analysis revealed two subjects expressed fragile site. The other two subjects expressed no fragile site. PCR analysis revealed expanded allele from all subjects. Subject III.6 showed intention tremor and gait ataxia, which are two mayor clinical criterions of FXTAS. Subject III.8 showed gait ataxia which is a mayor criterion of FXTAS. Subject III.9 showed intention tremor and gait ataxia, which are two mayor criterions of FXTAS. And Subject III.10 showed gait ataxia which is a mayor criterion of FXTAS. Conclusion: Some cerebellar manifestations such as intention tremor, limb ataxia, gait ataxia, dysdiadochokinesia, and titubation have been identified in premutation carriers of FXS. Southern Blot is needed to reveal subjects’s molecular status more accurate. Simple techniques to observe mayor and minor clinical criteria in this study had been proved can be used in the future. Radiological imaging is needed to address major and minor radiological criteria of FXTAS is still needed as one of an objectives measurement. Keywords : Fragile X-associated Tremor Ataxia Syndrome, intention tremor, gait ataxia, cerebellar manifestation

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments