Unbounded-Error Classical and Quantum Communication Complexity

Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently, \cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum} communication complexity in the {\em one-way communication} model can also be investigated using the arrangement, and showed that it is exactly (without a difference of even one qubit) half of the classical one-way communication complexity. In this paper, we extend the arrangement argument to the {\em two-way} and {\em simultaneous message passing} (SMP) models. As a result, we show similarly tight bounds of the unbounded-error two-way/one-way/SMP quantum/classical communication complexities for {\em any} partial/total Boolean function, implying that all of them are equivalent up to a multiplicative constant of four. Moreover, the arrangement argument is also used to show that the gap between {\em weakly} unbounded-error quantum and classical communication complexities is at most a factor of three.Comment: 11 pages. To appear at Proc. ISAAC 200

The Sizes of 1720 MHz OH Masers: VLBA and MERLIN Observations of the Supernova Remnants W44 and W28

We have used the NRAO Very Long Baseline Array (VLBA) to image OH(1720 MHz) masers in the supernova remnants W28 and W44 at a resolution of 40 mas. We also used MERLIN to observe the same OH(1720 MHz) masers in W44 at a resolution of 290 x 165 mas. All the masers are resolved by these VLBA and MERLIN observations. The measured sizes range from 50 to 180 mas and yield brightness temperature estimates from 0.3--20 x 10**8 K. We investigate whether these measured angular sizes are intrinsic and hence originate as a result of the physical conditions in the supernova remnant shock, or whether they are scatter broadened sizes produced by the turbulent ionized gas along the line of sight. While the current data on the temporal and angular broadening of pulsars, masers and extragalactic soures toward W44 and W28 can be understood in terms of scattering, we cannot rule out that these large sizes are intrinsic. Recent theoretical modeling by Lockett et al. suggests that the physical parameters in the shocked region are indicative of densities and OH abundances which lead to estimates of sizes as large as what we measure. If the sizes and structure are intrinsic, then the OH(1720 MHz) masrs may be more like the OH(1612 MHz) masers in circumstellar shells than OH masers associated with HII regions. At two locations in W28 we observe the classical S-shapes in the Stokes V profiles caused by Zeeman splitting and use it to infer magnetic fields of order 2 milliGauss.Comment: 24 pages, 6 figures, accepted by Ap

Domain wall mobility in nanowires: transverse versus vortex walls

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$.Comment: 5 pages, 6 figure

On the contrasting spin dynamics of La2−xSrxCuO4La_{2-x}Sr_xCuO_4, Nd2−xCexCuO4Nd_{2-x}Ce_xCuO_4 and YBa2Cu3O6+xYBa_2Cu_3O_{6+x} near half filling

We present simple calculations which show that incommensurability upon doping and the width of the magnetically ordered phase in Mott-Hubbard insulators depend strongly on the location of the hole/electron pockets in the Brillouin zone. For $LaSrCuO$ systems, we found the pockets at $(\pm \pi/2,\pm \pi/2)$, in which case the corrections to the antiferromagnetic spin stiffness grow with doping and destroy the commensurate antiferromagnetic ordering already at a very small doping. On the other hand, in $NdCeCuO$, the hole pockets are located at $(\pi,0)$ and the symmetry related points, in which case the corrections to the stiffness scale linearly with the density of carriers and do not destroy commensurate spin ordering. For $YBCuO$, systems the situation is less certain, but our results favor hole pockets at $(\pi/2,\pi/2)$. We also discuss briefly the tendency towards phase separation.Comment: 18 pages, LaTe

Polarization fluctuations in insulators and metals: New and old theories merge

The ground-state fluctuation of polarization P is finite in insulators and divergent in metals, owing to the SWM sum rule [I. Souza, T. Wilkens, and R. M. Martin, Phys. Rev. B 62, 1666 (2000)]. This is a virtue of periodic (i.e. transverse) BCs. I show that within any other boundary conditions the P fluctuation is finite even in metals, and a generalized sum rule applies. The boundary-condition dependence is a pure correlation effect, not present at the independent-particle level. In the longitudinal case div P = -rho, and one equivalently addresses charge fluctuations: the generalized sum rule reduces then to a well known result of many-body theory.Comment: 4 pages, no figur

Breakdown of Hydrodynamic Transport Theory in the Ordered Phase of Helimagnets

It is shown that strong fluctuations preclude a hydrodynamic description of transport phenomena in helimagnets, such as MnSi, at T>0. This breakdown of hydrodynamics is analogous to the one in chiral liquid crystals. Mode-mode coupling effects lead to infinite renormalizations of various transport coefficients, and the actual macroscopic description is nonlocal. At T=0 these effects are weakened due to the fluctuation-dissipation theorem, and the renormalizations remain finite. Observable consequences of these results, as manifested in the neutron scattering cross-section, are discussedComment: 4pp., 1 eps figur

Spin-Current Relaxation Time in Spin-Polarized Heisenberg Paramagnets

We study the spatial Fourier transform of the spin correlation function G_q(t) in paramagnetic quantum crystals by direct simulation of a 1d lattice of atoms interacting via a nearest-neighbor Heisenberg exchange Hamiltonian. Since it is not practical to diagonalize the s=1/2 exchange Hamiltonian for a lattice which is of sufficient size to study long-wavelength (hydrodynamic) fluctuations, we instead study the s -> infinity limit and treat each spin as a vector with a classical equation of motion. The simulations give a detailed picture of the correlation function G_q(t) and its time derivatives. At high polarization, there seems to be a hierarchy of frequency scales: the local exchange frequency, a wavelength-independent relaxation rate 1/tau that vanishes at large polarization P ->1, and a wavelength-dependent spin-wave frequency proportional to q^2. This suggests a form for the correlation function which modifies the spin diffusion coefficients obtained in a moments calculation by Cowan and Mullin, who used a standard Gaussian ansatz for the second derivative of the correlation function.Comment: 6 pages, 3 figure

The Effects of Lesions in the Dorsolateral Pons on the Coordination of Swallowing and Breathing in Awake Goats

The purpose of this retrospective study was to gain insight into the contribution of the dorsolateral pons to the coordination of swallowing and breathing in awake goats. In 4 goats, cannulas were chronically implanted bilaterally through the lateral (LPBN) and medial (MPBN) parabrachial nuclei just dorsal to the Kölliker–Fuse nucleus (KFN). After \u3e2 weeks recovery from this surgery, the goats were studied for 5½ h on a control day, and on separate days after receiving 1 and 10 μl injections of ibotenic acid (IA) separated by 1 week. The frequency of swallows did not change during the control and 1 μl IA studies, but after injection of 10 μl IA, there was a transient 65% increase in frequency of swallows (P \u3c 0.05). Under control conditions swallows occurred throughout the respiratory cycle, where late-E swallows accounted for 67.6% of swallows. The distribution of swallow occurrence throughout the respiratory cycle was unaffected by IA injections. Consistent with the concept that swallowing is dominant over breathing, we found that swallows increased inspiratory (TI) and expiratory (TE) time and decreased tidal volume (VT) of the breath of the swallow (n) and/or the subsequent (n + 1) breath. Injections of 10 μl IA attenuated the normal increases in TI and TE and further attenuated VT of the n breath. Additionally, E and I swallows reset respiratory rhythm, but injection of 1 or 10 μl IA progressively attenuated this resetting, suggesting a decreased dominance over respiratory motor output with increasing IA injections. Post mortem histological analysis revealed about 50% fewer (P \u3c 0.05) neurons remained in the KFN, LPBN, and MPBN in lesioned compared to control goats. We conclude that dorsolateral pontine nuclei have a modulatory role in a hypothesized holarchical neural network regulating swallowing and breathing particularly contributing to the normal dominance of swallowing over breathing in both rhythm and motor pattern generation

VLA OH and H I Zeeman Observations of the NGC 6334 Complex

We present OH and H I Zeeman observations of the NGC 6334 complex taken with the Very Large Array. The OH absorption profiles associated with the complex are relatively narrow (del-v_FWHM ~ 3 km s^1) and single-peaked over most of the sources. The H I absorption profiles contain several blended velocity components. One of the compact continuum sources in the complex (source A) has a bipolar morphology. The OH absorption profiles toward this source display a gradient in velocity from the northern continuum lobe to the southern continuum lobe; this velocity gradient likely indicates a bipolar outflow of molecular gas from the central regions to the northern and southern lobes. Magnetic fields of the order of 200 microG have been detected toward three discrete continuum sources in the complex. Virial estimates suggest that the detected magnetic fields in these sources are of the same order as the critical magnetic fields required to support the molecular clouds associated with the sources against gravitational collapse.Comment: 14 pages, 9 postscript figures, accepted for publication in the Astrophysical Journal (ApJ), tentatively scheduled for vol. 533, Apr. 20, 2000; also available at http://www.pa.uky.edu/~sarma/RESEARCH/aps_research.htm