Improved Lower Bounds for Locally Decodable Codes and Private Information Retrieval

We prove new lower bounds for locally decodable codes and private information retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit alphabet, where the decoder only uses b bits of each queried position of the codeword, needs code length m = exp(Omega(n/(2^b Sum_{i=0}^b {l choose i}))) Similarly, a 2-server PIR scheme with an n-bit database and t-bit queries, where the user only needs b bits from each of the two l-bit answers, unknown to the servers, satisfies t = Omega(n/(2^b Sum_{i=0}^b {l choose i})). This implies that several known PIR schemes are close to optimal. Our results generalize those of Goldreich et al. who proved roughly the same bounds for linear LDCs and PIRs. Like earlier work by Kerenidis and de Wolf, our classical lower bounds are proved using quantum computational techniques. In particular, we give a tight analysis of how well a 2-input function can be computed from a quantum superposition of both inputs.Comment: 12 pages LaTeX, To appear in ICALP '0

Anaerobic consumers of monosaccharides in a moderately acidic fen

16S rRNA-based stable isotope probing identified active xylose- and glucose-fermenting Bacteria and active Archaea, including methanogens, in anoxic slurries of material obtained from a moderately acidic, CH4-emitting fen. Xylose and glucose were converted to fatty acids, CO2, H2, and CH4 under moderately acidic, anoxic conditions, indicating that the fen harbors moderately acid-tolerant xylose- and glucose-using fermenters, as well as moderately acid-tolerant methanogens. Organisms of the families Acidaminococcaceae, Aeromonadaceae, Clostridiaceae, Enterobacteriaceae, and Pseudomonadaceae and the order Actinomycetales, including hitherto unknown organisms, utilized xylose- or glucose-derived carbon, suggesting that highly diverse facultative aerobes and obligate anaerobes contribute to the flow of carbon in the fen under anoxic conditions. Uncultured Euryarchaeota (i.e., Methanosarcinaceae and Methanobacteriaceae) and Crenarchaeota species were identified by 16S rRNA analysis of anoxic slurries, demonstrating that the acidic fen harbors novel methanogens and Crenarchaeota organisms capable of anaerobiosis. Fermentation-derived molecules are conceived to be the primary drivers of methanogenesis when electron acceptors other than CO2 are absent, and the collective findings of this study indicate that fen soils harbor diverse, acid-tolerant, and novel xylose-utilizing as well as glucose-utilizing facultative aerobes and obligate anaerobes that form trophic links to novel moderately acid-tolerant methanogen

Hemoglobin-based oxygen carrier HBOC-201 provides higher and faster increase in oxygen tension in skeletal muscle of anemic dogs than do stored red blood cells

AbstractBackground: Increasing need for and potential shortage of blood products have intensified the search for alternative oxygen carriers. A solution to this problem could be use of the bovine hemoglobin-based oxygen carrier HBOC-201. While hemodynamic reactions to cell-free hemoglobin have been studied, little knowledge exists about tissue oxygenation properties of hemoglobin solutions, especially in comparison with red blood cells (RBCs). Study Design and Methods: Tissue oxygenation in skeletal muscle of 12 anesthetized dogs was examined after decrease of hemoglobin concentrations by means of hemodilution to hematocrit 10% and subsequent transfusion with either HBOC-201 or autologous banked RBCs. In addition to hemodynamic parameters, blood gas concentrations and oxygen content in arterial and muscular venous blood, tissue oxygen tension (tPo2) were measured in the gastrocnemius muscle with a polarographic needle probe. Results: Hemodilution increased muscular blood flow and oxygen extraction and decreased tPo2. Transfusion decreased muscular oxygen extraction in the RBC group but not in the HBOC-201 group (P <.01). The 10th percentile of tPo2 increased by 400% after the first dose of HBOC-201 (P <.001 vs posthemodilution) but only by 33% after equivalent RBC transfusion (P <.01 vs HBOC-201). Increases in the 50th (120%, P <.05) and 90th (31%) percentiles and all percentiles of tPo2 after the second and third HBOC-201 dose were less pronounced but higher than in the RBC group. Conclusion: Compared with RBC transfusion, infusion of low doses of HBOC-201 maintain enhanced oxygen extraction after extended hemodilution and provide faster and higher increase in muscular tissue Po2. (J Vasc Surg 2003;37:859-65.

Child Marriages and Unions in Latin America: Understanding the Roles of Agency and Social Norms

El propósito de este artículo es demostrar que los matrimonios y las uniones infantiles pueden infringir los derechos sexuales y reproductivos de adolescentes y jóvenes. Indica que las intervenciones promueven cada vez más estrategias para transformar las normas sociales. Presenta los resultados de un análisis de secundario de casos cruzados de tres estudios cualitativos: en Brasil, Guatemala y Honduras. Se trató de entender las prácticas matrimoniales. En los tres casos, la agencia como las normas sociales siempre desempeñaron un papel en el matrimonio y/o uniones de los niños

On the distinguishability of random quantum states

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi

Probability distributions consistent with a mixed state

A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, \rho = \sum_i p_i |\psi_i\ra \la \psi_i|. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a decomposition, for a fixed density matrix $\rho$. Several illustrative applications of this result to quantum mechanics and quantum information theory are given.Comment: 6 pages, submitted to Physical Review

Computational depth complexity of measurement-based quantum computation

We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a very powerful model of quantum computation. It confirms and completes previous results which have pointed out, for some specific problems, a depth separation between the one-way model and the quantum circuit model. Since one-way model has the same computational power as unbounded quantum fan-out circuits, the quantum Fourier transform can be approximated in constant depth in the one-way model, and thus the factorisation can be done by a polytime probabilistic classical algorithm which has access to a constant-depth one-way quantum computer. The extra power of the one-way model, comparing with the quantum circuit model, comes from its classical-quantum hybrid nature. We show that this extra power is reduced to the capability to perform unbounded classical parity gates in constant depth.Comment: 12 page