Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

<p>Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.</p> <p>In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.</p> <p>The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.</p> <p>In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.</p> <p>The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.</p> <p>Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.</p>

Molecular genetic studies on voltage-gated ion channels

<p>Several different methods have been employed in the study of voltage-gated ion channels. Electrophysiological studies on excitable cells in vertebrates and molluscs have shown that many different voltage-gated potassium (K⁺) channels and sodium channels may coexist in the same organism. Parallel genetic studies in Drosophila have identified mutations in several genes that alter the properties of specific subsets of physiologically identified ion channels. Chapter 2 describes molecular studies that identify two Drosophila homologs of vertebrate sodium-channel genes. Mutations in one of these Drosophila sodium-channel genes are shown to be responsible for the temperature-dependent paralysis of a behavioural mutant para^ts. Evolutionary arguments, based on the partial sequences of the two Drosophila genes, suggest that subfamilies of voltage-gated sodium channels in vertebrates remain to be identified.</p> <p>In Drosophila, diverse voltage-gated K⁺ channels arise from alternatively spliced mRNAs generated at the Shaker locus. Chapter 3 and the Appendices describe the isolation and characterization of several human K⁺-channel genes, similar in sequence to Shaker. Each of these human genes has a highly conserved homolog in rodents; thus, this K⁺-channel gene family probably diversified prior to the mammalian radiation. Functional K⁺ channels encoded by these genes have been expressed in Xenopus oocytes and their properties have been analyzed by electrophysiological methods. These studies demonstrate that both transient and noninactivating voltage-gated K⁺ channels may be encoded by mammalian genes closely related to Shaker. In addition, results presented in Appendix 3 clearly demonstrate that independent gene products from two K⁺-channel genes may efficiently co-assemble into heterooligomeric K⁺ channels with properties distinct from either homomultimeric channel. This finding suggests yet another molecular mechanism for the generation of K⁺-channel diversity.</p>

Two topics in elementary particle physics. I. Crossing as a group and elimination of exotic channels. II. Real parts of meson-nucleon forward scattering amplitudes.

<p>I. Crossing transformations constitute a group of permutations under which the scattering amplitude is invariant. Using Mandelstem's analyticity, we decompose the amplitude into irreducible representations of this group. The usual quantum numbers, such as isospin or SU(3), are "crossing-invariant". Thus no higher symmetry is generated by crossing itself. However, elimination of certain quantum numbers in intermediate states is not crossing-invariant, and higher symmetries have to be introduced to make it possible. The current literature on exchange degeneracy is a manifestation of this statement. To exemplify application of our analysis, we show how, starting with SU(3) invariance, one can use crossing and the absence of exotic channels to derive the quark-model picture of the tensor nonet. No detailed dynamical input is used.</p> <p>II. A dispersion relation calculation of the real parts of forward ��^��p and K^��p scattering amplitudes is carried out under the assumption of constant total cross sections in the Serpukhov energy range. Comparison with existing experimental results as well as predictions for future high energy experiments are presented and discussed. Electromagnetic effects are found to be too small to account for the expected difference between the ��^-p and ��⁺p total cross sections at higher energies.</p>

Inelastic K+p reactions at incident momenta from 1.37 GeV/c to 2.17 GeV/c

<p>A number of recent experiments have suggested the possibility of a highly inelastic resonance in K⁺p scattering. To study the inelastic K⁺p reactions, a 400 K exposure has been taken at the L.R.L. 25 inch bubble chamber. The data are spread over seven K⁺ momenta between 1.37 and 2.17 GeV/c.</p> <p>Cross-sections have been measured for the reaction K⁺p ��� pK����+ which is dominated by the quasi-two body channels K��� and K*N. Both these channels are strongly peripheral, as at other momenta. The decay of the ��� is in good agreement with the predictions of the rho-photon analogy of Stodolsky and Sakurai. The data on the K*p channel show evidence of both pseudo scalar and vector exchange.</p> <p>Cross-sections for the final state pK⁺��+��- shows a strong contribution from the quasi-two body channel K*���. This reaction is also very peripheral even at threshold. The decay angular distributions indicate the reaction is dominated as at higher momenta by a pion exchange mechanism. The data are also in good agreement with the quark model predictions of Bialas and Zalewski for the K* and ��� decay.</p>

Chemical-scale studies of G protein-coupled receptors and ligand-gated ion channels

<p>This dissertation describes studies of G protein-coupled receptors (GPCRs) and ligand-gated ion channels (LGICs) using unnatural amino acid mutagenesis to gain high precision insights into the function of these important membrane proteins.</p> <p>Chapter 2 considers the functional role of highly conserved proline residues within the transmembrane helices of the D2 dopamine GPCR. Through mutagenesis employing unnatural ��-hydroxy acids, proline analogs, and N-methyl amino acids, we find that lack of backbone hydrogen bond donor ability is important to proline function. At one proline site we additionally find that a substituent on the proline backbone N is important to receptor function.</p> <p>In Chapter 3, side chain conformation is probed by mutagenesis of GPCRs and the muscle-type nAChR. Specific side chain rearrangements of highly conserved residues have been proposed to accompany activation of these receptors. These rearrangements were probed using conformationally-biased ��-substituted analogs of Trp and Phe and unnatural stereoisomers of Thr and Ile. We also modeled the conformational bias of the unnatural Trp and Phe analogs employed.</p> <p>Chapters 4 and 5 examine details of ligand binding to nAChRs. Chapter 4 describes a study investigating the importance of hydrogen bonds between ligands and the complementary face of muscle-type and ��4��4 nAChRs. A hydrogen bond involving the agonist appears to be important for ligand binding in the muscle-type receptor but not the ��4��4 receptor.</p> <p>Chapter 5 describes a study characterizing the binding of varenicline, an actively prescribed smoking cessation therapeutic, to the ��7 nAChR. Additionally, binding interactions to the complementary face of the ��7 binding site were examined for a small panel of agonists. We identified side chains important for binding large agonists such as varenicline, but dispensable for binding the small agonist ACh.</p> <p>Chapter 6 describes efforts to image nAChRs site-specifically modified with a fluorophore by unnatural amino acid mutagenesis. While progress was hampered by high levels of fluorescent background, improvements to sample preparation and alternative strategies for fluorophore incorporation are described.</p> <p>Chapter 7 describes efforts toward a fluorescence assay for G protein association with a GPCR, with the ultimate goal of probing key protein-protein interactions along the G protein/receptor interface. A wide range of fluorescent protein fusions were generated, expressed in Xenopus oocytes, and evaluated for their ability to associate with each other.</p>

Theory of ozone isotopic effects and various electron transfer reactions

<p>Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.</p> <p> The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O���+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.</p> <p>Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.</p> <p>Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.</p>

Isotope shift measurements using k x-rays in Sn, Sm, and W

<p>Electronic K��l x-ray isotope shifts have been measured for Sn 116-124, Sm 148-154, W 182-184, W 184-186, and W 182-186 using a curved crystal Cauchois spectrometer. The analysis of the measurements has included the electrostatic volume effect, screening by the transition electron as well as the non-transition electrons, normal and specific mass shifts, dynamical nuclear qudrupole polarization, and a radiative correction effect of the electron magnetic moment in the nuclear charge radii are obtained. Where other experimental data are available, the agreement with the present measurements is satisfactory. Comparisons with several nuclear model predictions yield only partial agreement. </p>

Development of roll waves in open channels

<p>This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope . The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity . The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel.</p> <p>The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow . The Froude number F (F = u_n/���gh_n, u_n = normal velocity , h_n = normal depth, g =acceleration of gravity) ranged from 3. 4 to 6. 0 for channel slopes S_o of . 05 and . 12 respectively . In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile . These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h_nmax increased with distance . Once the shock waves began to overtake, the mean wave period T_av increased approximately linearly with distance.</p> <p>For a given Froude number and channel slope the observed quantities h^-_max/h_n , T' (T' = S_o T_av ���g/h_n), and the standard deviations of h^-_max/h_n and T', could be expressed as unique functions of l/h_n (l = distance from beginning of channel) for the two-fold change in h_n occurring in the observed flows . A given value of h^-_max/h_n occurred at smaller values of l/h_n as the Froude number was increased. For a given value of h /hh^-_max/h_n the growth rate of ��h^-_max/h^-_max��l of the shock waves increased as the Froude number was increased.</p> <p>A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h^-_max/h_n vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h^-_max/h_n were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent.</p> <p>For h^-_max/h_n sufficiently large (h^-_max/h_n > approximately 1.5) it was found that the h^-_max/h_n vs. T' relation for natural roll waves was practically identical to the h^-_max/h_n vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate ��h^-_max/h^-_max��l of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.</p>

Experimental study study of antiproton-proton annihilation into a pair of charged Pi-Mesons or K-Mesons for incident antiproton mementa in the range from 0.72 GeV/c to 2.62 GeV/c

<p>The cross sections for the two antiproton-proton annihilation-in-flight modes,</p> <p>��p + p ��� ��⁺ + ��^-</p> <p>��p + p ��� k⁺ + k^-</p> <p>were measured for fifteen laboratory antiproton beam momenta ranging from 0.72 to 2.62 GeV/c. No magnets were used to determine the charges in the final state. As a result, the angular distributions were obtained in the form [d��/d�� (��_C.M.) + d��/d�� (�� ��� ��_C.M.)] for 45 ��� ��_C.M. ��� 135��. </p> <p>A hodoscope-counter system was used to discriminate against events with final states having more than two particles and antiproton-proton elastic scattering events. One spark chamber was used to record the track of each of the two charged final particles. A total of about 40,000 pictures were taken. The events were analyzed by measuring the laboratory angle of the track in each chamber. The value of the square of the mass of the final particles was calculated for each event assuming the reaction</p> <p>��p + p ��� a pair of particles with equal masses.</p> <p>About 20,000 events were found to be either annihilation into �� ^��-pair or k ^��-pair events. The two different charged meson pair modes were also distinctly separated.</p> <p>The average differential cross section of ��p + p ��� ��⁺ + ��^- varied from ~ 25 ��b/sr at antiproton beam momentum 0.72 GeV/c (total energy in center-of-mass system, ���s = 2.0 GeV) to ~ 2 ��b/sr at beam momentum 2.62 GeV/c (���s = 2.64 GeV). The most striking feature in the angular distribution was a peak at ��_C.M. = 90�� (cos ��_C.M. = 0) which increased with ���s and reached a maximum at ���s ~ 2.1 GeV (beam momentum ~ 1.1 GeV/c). Then it diminished and seemed to disappear completely at ���s ~ 2.5 GeV (beam momentum ~ 2.13 GeV/c). A valley in the angular distribution occurred at cos ��_C.M. ��� 0.4. The differential cross section then increased as cos ��_C.M. approached 1.</p> <p>The average differential cross section for ��p + p ��� k⁺ + k^- was about one third of that of the ��^��-pair mode throughout the energy range of this experiment. At the lower energies, the angular distribution, unlike that of the ��^��-pair mode, was quite isotropic. However, a peak at ��_C.M. = 90�� seemed to develop at ���s ~ 2.37 GeV (antiproton beam momentum ~ 1.82 GeV/c). No observable change was seen at that energy in the ��^��-pair cross section.</p> <p>The possible connection of these features with the observed meson resonances at 2.2 GeV and 2.38 GeV, and its implications, were discussed. </p>

Thermodynamic and kinetic behavior of an argon plasma jet. Decomposition of nitric oxide between 1300 - 1750 degrees K in an argon plasma

<p>In the first part of the study, an RF coupled, atmospheric pressure, laminar plasma jet of argon was investigated for thermodynamic equilibrium and some rate processes. </p> <p>Improved values of transition probabilities for 17 lines of argon I were developed from known values for 7 lines. The effect of inhomogeneity of the source was pointed out.</p> <p>The temperatures, T, and the electron densities, n_e , were determined spectroscopically from the population densities of the higher excited states assuming the Saha-Boltzmann relationship to be valid for these states. The axial velocities, v_z, were measured by tracing the paths of particles of boron nitride using a three-dimentional mapping technique. The above quantities varied in the following ranges: 10¹² �� n_e �� 10¹⁵ particles/cm³, 3500 �� T �� 11000 ��K, and 200 �� v_z �� 1200 cm/sec.</p> <p>The absence of excitation equilibrium for the lower excitation population including the ground state under certain conditions of T and n_e was established and the departure from equilibrium was examined quantitatively. The ground state was shown to be highly underpopulated for the decaying plasma.</p> <p>Rates of recombination between electrons and ions were obtained by solving the steady-state equation of continuity for electrons. The observed rates were consistent with a dissociative-molecular ion mechanism with a steady-state assumption for the molecular ions. </p> <p>In the second part of the study, decomposition of NO was studied in the plasma at lower temperatures. The mole fractions of NO denoted by x_NO were determined gas-chromatographically and varied between 0.0012 �� x_NO �� 0.0055. The temperatures were measured pyrometrically and varied between 1300 �� T �� 1750��K. The observed rates of decomposition were orders of magnitude greater than those obtained by the previous workers under purely thermal reaction conditions. The overall activation energy was about 9 kcal/g mol which was considerably lower than the value under thermal conditions. The effect of excess nitrogen was to reduce the rate of decomposition of NO and to increase the order of the reaction with respect to NO from 1.33 to 1.85. The observed rates were consistent with a chain mechanism in which atomic nitrogen and oxygen act as chain carriers. The increased rates of decomposition and the reduced activation energy in the presence of the plasma could be explained on the basis of the observed large amount of atomic nitrogen which was probably formed as the result of reactions between excited atoms and ions of argon and the molecular nitrogen.</p>

An investigation of the reaction negative K��p ��� K������� at P_(lab) = 2 Gev/c

<p>The reaction K^-p���K^-��⁺n has been studied for incident kaon momenta of 2.0 GeV/c. A sample of 19,881 events was obtained by a measurement of film taken as part of the K-63 experiment in the Berkeley 72 inch bubble chamber. </p> <p>Based upon our analysis, we have reached four conclusions. (1) The magnitude of the extrapolated K�� cross section differs by a factor of 2 from the P-wave unitarity prediction and the K⁺n results; this is probably due to absorptive effects. (2) Fits to the moments yield precise values for the K�� S-wave which agree with other recent statistically accurate experiments. (3) An anomalous peak is present in our backward K^-p���(��+n) K^- u-distribution. (4) We find a non-linear enhancement due to interference similiar to the one found by Bland et al. (Bland 1966).</p>

The ionic basis of frequency selectivity in hair cells of the bullfrog's sacculus

<p>Hair cells from the bull frog's sacculus, a vestibular organ responding to substrate-borne vibration, possess electrically resonant membrane properties which maximize the sensitivity of each cell to a particular frequency of mechanical input. The electrical resonance of these cells and its underlying ionic basis were studied by applying gigohm-seal recording techniques to solitary hair cells enzymatically dissociated from the sacculus. The contribution of electrical resonance to frequency selectivity was assessed from microelectrode recordings from hair cells in an excised preparation of the sacculus.</p> <p>Electrical resonance in the hair cell is demonstrated by damped membrane-potential oscillations in response to extrinsic current pulses applied through the recording pipette. This response is analyzed as that of a damped harmonic oscillator. Oscillation frequency rises with membrane depolarization, from 80-160 Hz at resting potential to asymptotic values of 200-250 Hz. The sharpness of electrical tuning, denoted by the electrical quality factor, Q_e, is a bell-shaped function of membrane voltage, reaching a maximum value around eight at a membrane potential slightly positive to the resting potential.</p> <p>In whole cells, three time-variant ionic currents are activated at voltages more positive than -60 to -50 mV; these are identified as a voltage-dependent, non-inactivating Ca current (I_ca), a voltage-dependent, transient K current (I_a), and a Ca-dependent K current (I_c). The C channel is identified in excised, inside-out membrane patches on the basis of its large conductance (130-200 pS), its selective permeability to Kover Na or Cl, and its activation by internal Ca ions and membrane depolarization. Analysis of open- and closed-lifetime distributions suggests that the C channel can assume at least two open and three closed kinetic states.</p> <p>Exposing hair cells to external solutions that inhibit the Ca or C conductances degrades the electrical resonance properties measured under current-clamp conditions, while blocking the A conductance has no significant effect, providing evidence that only the Ca and C conductances participate in the resonance mechanism. To test the sufficiency of these two conductances to account for electrical resonance, a mathematical model is developed that describes I_ca, I_c, and intracellular Ca concentration during voltage-clamp steps. I_ca activation is approximated by a third-order Hodgkin-Huxley kinetic scheme. Ca entering the cell is assumed to be confined to a small submembrane compartment which contains an excess of Ca buffer; Ca leaves this space with first-order kinetics. The Ca- and voltage-dependent activation of C channels is described by a five-state kinetic scheme suggested by the results of single-channel observations. Parameter values in the model are adjusted to fit the waveforms of I_ca and I_c evoked by a series of voltage-clamp steps in a single cell. Having been thus constrained, the model correctly predicts the character of voltage oscillations produced by current-clamp steps, including the dependencies of oscillation frequency and Q_e on membrane voltage. The model shows quantitatively how the Ca and C conductances interact, via changes in intracellular Ca concentration, to produce electrical resonance in a vertebrate hair cell.</p>

CP and the three pion decay of the K��

<p>The time distribution of the decays of an initially pure K�� beam into ��+��-���� has been analyzed to determine the complex parameter W (also known as ��^+-�� and (x + iy)). The K�� beam was produced in a brass target by the interactions of a 2.85 GeV/c ��- beam which was generated on an internal target in the Lawrence Radiation Laboratory (LRL) Bevatron. The counters and hodoscopes in the apparatus selected for events with a neutral (K��) produced in the brass target, two charged secondaries passing through a magnet spectrometer and a ��-ray shower in a shower hodoscope. </p> <p>From the 275K apparatus triggers, 148 K ��� ��+��-���� events were isolated. The presence of a ��-ray shower in the optical shower chambers and a two-prong vee in the optical spark chambers were devices used to isolate the events. The backgrounds were further reduced by reconstructing the momenta of the two charged secondaries and applying kinematic constraints.</p> <p>The best fit to the final sample of 148 events distributed between .3 and 7.0 K_S lifetimes gives: </p> <p>ReW = -.05 ��.17</p> <p>ImW = +.39 +.35/-.37</p> <p>This result is consistent with both CPT invariance (ReW = 0) and CP invariance (W = 0). Backgrounds are estimated to be less than 10% and systematic effects have also been estimated to be negligible.</p> <p>An analysis of the present data on CP violation in this decay mode and other K�� decay modes has estimated the phase of �� to be 45.3 �� 2.3 degrees. This result is consistent with the super weak theories of CP violation which predicts the phase of �� to be 43��. This estimate is in turn used to predict the phase of ������ to be 48.0 �� 7.9 degrees. This is a substantial improvement on presently available measurements. The largest error in this analysis comes from the present limits on W from the world average of recent experiments. The K ��� ��u�� mode produces the next largest error. Therefore further experimentation in these modes would be useful.</p>