Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$

Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding

In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper bound, we obtain the Hoeffding bound, which are identical with the classical counter part if the hypotheses, composed of two density operators, are mutually commutative. Our upper bound improves the bound by Ogawa-Hayashi, and also provides a simpler proof of the direct part of the quantum Stein's lemma. Further, using this bound, we obtain a better exponential upper bound of the average error probability of classical-quantum channel coding

Formation of a disk-structure and jets in the symbiotic prototype Z And during its 2006-2010 active phase

We present an analysis of spectrophotometric observations of the latest cycle of activity of the symbiotic binary Z And from 2006 to 2010. We estimate the temperature of the hot component of Z And to be \approx 150000 - 170000 K at minimum brightness, decreasing to \approx 90000 K at the brightness maximum. Our estimate of the electron density in the gaseous nebula is N_{e}=10^{10}-10^{12} cm^{-3} in the region of formation of lines of neutral helium and 10^6-10^7 cm^{-3} in the region of formation of the [OIII] and [NeIII] nebular lines. A trend for the gas density derived from helium lines to increase and the gas density derived from [OIII] and [NeIII] lines to simultaneously decrease with increasing brightness of the system was observed. Our estimates show that the ratios of the theoretical and observed fluxes in the [OIII] and [NeIII] lines agree best when the O/Ne ratio is similar to its value for planetary nebulae. The model spectral energy distribution showed that, in addition to a cool component and gaseous nebula, a relatively cool pseudophotosphere (5250-11 500 K) is present in the system. The simultaneous presence of a relatively cool pseudophotosphere and high-ionization spectral lines is probably related to a disk-like structure of the pseudophotosphere. The pseudophotosphere formed very rapidly, over several weeks, during a period of increasing brightness of Z And. We infer that in 2009, as in 2006, the activity of the system was accompanied by a collimated bipolar ejection of matter. In contrast to the situation in 2006, the jets were detected even before the system reached its maximum brightness. Moreover, components with velocities close to 1200 km/s disappeared at the maximum, while those with velocities close to 1800 km/s appeared.Comment: 18 pages, 19 figures, Accepted for publication in Astronomy Report

Capacity of optical reading, Part 1: Reading boundless error-free bits using a single photon

We show that nature imposes no fundamental upper limit to the number of information bits per expended photon that can, in principle, be read reliably when classical data is encoded in a medium that can only passively modulate the amplitude and phase of the probe light. We show that with a coherent-state (laser) source, an on-off (amplitude-modulation) pixel encoding, and shot-noise-limited direct detection (an overly-optimistic model for commercial CD/DVD drives), the highest photon information efficiency achievable in principle is about 0.5 bit per transmitted photon. We then show that a coherent-state probe can read unlimited bits per photon when the receiver is allowed to make joint (inseparable) measurements on the reflected light from a large block of phase-modulated memory pixels. Finally, we show an example of a spatially-entangled non-classical light probe and a receiver design---constructable using a single-photon source, beam splitters, and single-photon detectors---that can in principle read any number of error-free bits of information. The probe is a single photon prepared in a uniform coherent superposition of multiple orthogonal spatial modes, i.e., a W-state. The code, target, and joint-detection receiver complexity required by a coherent-state transmitter to achieve comparable photon efficiency performance is shown to be much higher in comparison to that required by the W-state transceiver.Comment: 11 pages, 12 figures, v3 includes a new plot characterizing the photon efficiency vs. encoding efficiency tradeoff for optical reading. The main technical body of the paper remains unaltere

Stable, synthetic analogs of diadenosine tetraphosphate inhibit rat and human P2X3 receptors and inflammatory pain

© 2016, © The Author(s) 2016.Background: A growing body of evidence suggests that ATP-gated P2X3 receptors (P2X3Rs) are implicated in chronic pain. We address the possibility that stable, synthetic analogs of diadenosine tetraphosphate (Ap4A) might induce antinociceptive effects by inhibiting P2X3Rs in peripheral sensory neurons. Results: The effects of two stable, synthetic Ap4A analogs (AppNHppA and AppCH2ppA) are studied firstly in vitro on HEK293 cells expressing recombinant rat P2XRs (P2X2Rs, P2X3Rs, P2X4Rs, and P2X7Rs) and then using native rat brain cells (cultured trigeminal, nodose, or dorsal root ganglion neurons). Thereafter, the action of these stable, synthetic Ap4A analogs on inflammatory pain and thermal hyperalgesia is studied through the measurement of antinociceptive effects in formalin and Hargreaves plantar tests in rats in vivo. In vitro inhibition of rat P2X3Rs (not P2X2Rs, P2X4Rs nor P2X7Rs) is shown to take place mediated by high-affinity desensitization (at low concentrations; IC50 values 100–250 nM) giving way to only weak partial agonism at much higher concentrations (EC50 values ≥ 10 µM). Similar inhibitory activity is observed with human recombinant P2X3Rs. The inhibitory effects of AppNHppA on nodose, dorsal root, and trigeminal neuron whole cell currents suggest that stable, synthetic Ap4A analogs inhibit homomeric P2X3Rs in preference to heteromeric P2X2/3Rs. Both Ap4A analogs mediate clear inhibition of pain responses in both in vivo inflammation models. Conclusions: Stable, synthetic Ap4A analogs (AppNHppA and AppCH2ppA) being weak partial agonist provoke potent high-affinity desensitization-mediated inhibition of homomeric P2X3Rs at low concentrations. Therefore, both analogs demonstrate clear potential as potent analgesic agents for use in the management of chronic pain associated with heightened P2X3R activation

Physical Orbit for Lambda Virginis and a Test of Stellar Evolution Models

Lambda Virginis (LamVir) is a well-known double-lined spectroscopic Am binary with the interesting property that both stars are very similar in abundance but one is sharp-lined and the other is broad-lined. We present combined interferometric and spectroscopic studies of LamVir. The small scale of the LamVir orbit (~20 mas) is well resolved by the Infrared Optical Telescope Array (IOTA), allowing us to determine its elements as well as the physical properties of the components to high accuracy. The masses of the two stars are determined to be 1.897 Msun and 1.721 Msun, with 0.7% and 1.5% errors respectively, and the two stars are found to have the same temperature of 8280 +/- 200 K. The accurately determined properties of LamVir allow comparisons between observations and current stellar evolution models, and reasonable matches are found. The best-fit stellar model gives LamVir a subsolar metallicity of Z=0.0097, and an age of 935 Myr. The orbital and physical parameters of LamVir also allow us to study its tidal evolution time scales and status. Although currently atomic diffusion is considered to be the most plausible cause of the Am phenomenon, the issue is still being actively debated in the literature. With the present study of the properties and evolutionary status of LamVir, this system is an ideal candidate for further detailed abundance analyses that might shed more light on the source of the chemical anomalies in these A stars.Comment: 43 Pages, 13 figures. Accepted for publication in Ap

Multimode Pulsations of the λ Bootis Star 29 Cygni: The 1995 and 1996 Multisite Campaigns

In this paper we present the results of multisite photometric and spectroscopic campaigns, carried out during the years 1995 and 1996, to study the pulsations of a typical λ Bootis star, 29 Cyg. During the 1995 campaign we found well-defined multiperiodicity in 29 Cyg, which was studied in detail during a multilongitude campaign covering a 65 day time interval in 1996. The frequency analysis of the 1996 campaign's data easily revealed 11 excited low ℓ degree modes with frequencies of oscillation ranging from 20.3 to 37.4 cycles day-1 and mean photometric amplitudes ranging from 10.65 to 0.96 mmag in the V filter. After removing the well-identified frequencies, the discrete Fourier transform of the residuals showed excess power in the 20-40 cycle day-1 domain, which indicates the probable existence of unresolved rich p-mode spectra with photometric V amplitudes below 0.5 mmag. We found a regular spacing of 2.41 cycles day-1 within the modes of 29 Cyg, which was interpreted as the spacing of consecutive even and odd ℓ-values. The asteroseismic luminosity log L/L⊙ = 1.12, calculated from the frequency spacing, is in good agreement with the Hipparcos luminosity log L/L⊙ = 1.16 and with luminosities from photometric and spectroscopic calibrations. Using our multicolor photometry we tentatively identified the dominant f1 = 37.425 cycle day -1 mode as an ℓ= 2, n = 5 mode, and made radial overtone identification for all frequencies. These ranged from n = 2 to 5. Analysis of the photometric data shows the long-term (years) and probable short-term (days) variability of amplitudes for all of these modes in 29 Cyg. Using our multicolor WBVR filter photometry, we found the wavelength dependence of the pulsation amplitudes for the five highest amplitude modes. Based on the Hα line radial velocity observations of 29 Cyg, we detected multiperiodic radial velocity variations with frequencies of 38.36 and 29.99 cycles day-1 and semiamplitudes of 1.0 and 0.8 km s-1, respectively. These frequencies coincide within the errors with the photometric frequencies of the two highest amplitude modes, 37.425 and 29.775 cycles day-1. For the highest amplitude ℓ = 2, n = 5 mode (37.425 cycles day-1), the radial velocity-to-light amplitude ratio and velocity-to-light phase shift are equal to 2K(Hα)/ Δ V = 94 km mag-1 s-1 and Φf1 = φVr - φV = +0.08 ± 0.01, respectively, and are in good agreement with values for δ Scuti stars. The rich multiperiodic spectrum makes 29 Cyg a promising target for future multisite campaigns. © 2007. The American Astronomical Society. All rights reserved.M. D. E. and K. Y. W. acknowledge their work as part of the research activity of the Astrophysical Research Center for the Structure and Evolution of the Cosmos, which is supported by the Korean Science and Engineering Foundation. The participation of G. H., E. P., and W. W. was supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung under grant S-7303. The spectroscopic observations described in this publication were made possible in part by grants R2Q000 and U1C000 from the International Science Foundation and by grant A-05-067 from the ESO C&EE programme. This work was supported in part by US Civilian and Research Development Foundation grant UP2-317.Peer reviewe

TARP γ-7 selectively enhances synaptic expression of calcium-permeable AMPARs

Regulation of calcium-permeable AMPA receptors (CP-AMPARs) is crucial in normal synaptic function and neurological disease states. Although transmembrane AMPAR regulatory proteins (TARPs) such as stargazin (γ-2) modulate the properties of calcium-impermeable AMPARs (CI-AMPARs) and promote their synaptic targeting, the TARP-specific rules governing CP-AMPAR synaptic trafficking remain unclear. We used RNA interference to manipulate AMPAR-subunit and TARP expression in γ-2–lacking stargazer cerebellar granule cells—the classic model of TARP deficiency. We found that TARP γ-7 selectively enhanced the synaptic expression of CP-AMPARs and suppressed CI-AMPARs, identifying a pivotal role of γ-7 in regulating the prevalence of CP-AMPARs. In the absence of associated TARPs, both CP-AMPARs and CI-AMPARs were able to localize to synapses and mediate transmission, although their properties were altered. Our results also establish that TARPed synaptic receptors in granule cells require both γ-2 and γ-7 and reveal an unexpected basis for the loss of AMPAR-mediated transmission in stargazer mice