On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

The focus of this paper is on the public communication required for generating a maximal-rate secret key (SK) within the multiterminal source model of Csisz{\'a}r and Narayan. Building on the prior work of Tyagi for the two-terminal scenario, we derive a lower bound on the communication complexity, $R_{\text{SK}}$, defined to be the minimum rate of public communication needed to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by $R_{\text{CO}}$, is an upper bound on $R_{\text{SK}}$. For the class of pairwise independent network (PIN) models defined on uniform hypergraphs, we show that a certain "Type $\mathcal{S}$" condition, which is verifiable in polynomial time, guarantees that our lower bound on $R_{\text{SK}}$ meets the $R_{\text{CO}}$ upper bound. Thus, PIN models satisfying our condition are $R_{\text{SK}}$-maximal, meaning that the upper bound $R_{\text{SK}} \le R_{\text{CO}}$ holds with equality. This allows us to explicitly evaluate $R_{\text{SK}}$ for such PIN models. We also give several examples of PIN models that satisfy our Type $\mathcal S$ condition. Finally, we prove that for an arbitrary multiterminal source model, a stricter version of our Type $\mathcal S$ condition implies that communication from \emph{all} terminals ("omnivocality") is needed for establishing a SK of maximum rate. For three-terminal source models, the converse is also true: omnivocality is needed for generating a maximal-rate SK only if the strict Type $\mathcal S$ condition is satisfied. Counterexamples exist that show that the converse is not true in general for source models with four or more terminals.Comment: Submitted to the IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1504.0062

ON THE GENERALIZED FRESNEL SINE INTEGRALS AND CONVOLUTION

The generalized Fresnel sine integral Sk(x) and its associated functions Sk+(x) ; Sk-(x) are de�fined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the generalized Fresnel sine integral and its associated functions are then found

Results from Super-Kamiokande

The recent results from Super-Kamiokande (SK) are reported. On atmospheric neutrino analysis, we have performed a full 3-flavor oscillation analysis with SK-I+II+III data. A CPT violation study on atmospheric neutrino is also done with SK-I+II+III data. On solar neutrino analysis, a 3-flavor oscillation analysis with SK-III data is performed.Comment: 6 pages, 8 figures, proceedings of The XXIV International Conference on Neutrino Physics and Astrophysics (Neutrino 2010

A functional role for small-conductance calcium-activated potassium channels in sensory pathways including nociceptive processes

We investigated the role of small-conductance calcium-activated potassium (SK) and intermediate-conductance calcium-activated potassium channels in modulating sensory transmission from peripheral afferents into the rat spinal cord. Subunit-specific antibodies reveal high levels of SK3 immunoreactivity in laminas I, II, and III of the spinal cord. Among dorsal root ganglion neurons, both peripherin-positive (C-type) and peripherin-negative (A-type) cells show intense SK3 immunoreactivity. Furthermore, dorsal root-stimulated sensory responses recorded in vitro are inhibited when SK channel activity is increased with 1-ethyl-2-benzimidazolinone (1-EBIO). In vivo electrophysiological recordings show that neuronal responses to naturally evoked nociceptive and nonnociceptive stimuli increase after application of the selective SK channel blocker 8,14-diaza-1,7( 1,4)-diquinolinacyclotetradecaphanedium ditrifluoroacetate (UCL 1848), indicating that SK channels are normally active in moderating afferent input. Conversely, neuronal responses evoked by mechanical stimuli are inhibited when SK channel activity is increased with 1-EBIO. These effects are reversed by the subsequent application of UCL 1848. Our data demonstrate that SK channels have an important role in controlling sensory input into the spinal cord

Solar neutrino event spectra: Tuning SNO to equalize Super-Kamiokande

The Super-Kamiokande (SK) and the Sudbury Neutrino Observatory (SNO) experiments are monitoring the flux of B solar neutrinos through the electron energy spectrum from the reactions nu_{e,mu,tau} + e --> nu_{e,mu,tau} + e and nu_e + d --> p + p + e, respectively. We show that the SK detector response to B neutrinos in each bin of the electron energy spectrum (above 8 MeV) can be approximated, with good accuracy, by the SNO detector response in an appropriate electron energy range (above 5.1 MeV). For instance, the SK response in the bin [10,10.5] MeV is reproduced (``equalized'') within 2 percent by the SNO response in the range [7.1,11.75] MeV. As a consequence, in the presence of active neutrino oscillations, the SK and SNO event rates in the corresponding energy ranges turn out to be linearly related, for any functional form of the oscillation probability. Such equalization is not spoiled by the possible contribution of hep neutrinos (within current phenomenological limits). In perspective, when the SK and the SNO spectra will both be measured with high accuracy, the SK-SNO equalization can be used to determine the absolute B neutrino flux, and to cross-check the (non)observation of spectral deviations in SK and SNO. At present, as an exercise, we use the equalization to ``predict'' the SNO energy spectrum, on the basis of the current SK data. Finally, we briefly discuss some modifications or limitations of our results in the case of sterile neutrino oscillations and of relatively large Earth matter effects.Comment: 18 pages + 6 figure