Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur

The mass of the neutron star in Vela X-1 and tidally induced non-radial oscillations in GP Vel

We report new radial velocity observations of GP Vel/HD77581, the optical companion to the eclipsing X-ray pulsar Vela X-1. Using data spanning more than two complete orbits of the system, we detect evidence for tidally induced non-radial oscillations on the surface of GP Vel, apparent as peaks in the power spectrum of the residuals to the radial velocity curve fit. By removing the effect of these oscillations (to first order) and binning the radial velocities, we have determined the semi-amplitude of the radial velocity curve of GP Vel to be K_o=22.6+/-1.5 km/s. Given the accurately measured semi-amplitude of the pulsar's orbit, the mass ratio of the system is 0.081+/-0.005. We are able to set upper and lower limits on the masses of the component stars as follows. Assuming GP Vel fills its Roche lobe then the inclination angle of the system, i=70.1+/-2.6 deg. In this case we obtain the masses of the two stars as M_x=2.27 +/-0.17 M_sun for the neutron star and M_o=27.9+/-1.3 M_sun for GP Vel. Conversely, assuming the inclination angle is i=90 deg, the ratio of the radius of GP Vel to the radius of its Roche lobe is beta=0.89+/-0.03 and the masses of the two stars are M_x=1.88+/-0.13 M_sun and M_o=23.1+/-0.2 M_sun. A range of solutions between these two sets of limits is also possible, corresponding to other combinations of i and beta. In addition, we note that if the zero phase of the radial velocity curve is allowed as a free parameter, rather than constrained by the X-ray ephemeris, a significantly improved fit is obtained with an amplitude of 21.2+/-0.7 km/s and a phase shift of 0.033+/-0.007 in true anomaly. The apparent shift in the zero phase of the radial velocity curve may indicate the presence of an additional radial velocity component at the orbital period.Comment: Accepted for publication in Astronomy & Astrophysic

Thermodynamic efficiency of information and heat flow

A basic task of information processing is information transfer (flow). Here we study a pair of Brownian particles each coupled to a thermal bath at temperature $T_1$ and $T_2$, respectively. The information flow in such a system is defined via the time-shifted mutual information. The information flow nullifies at equilibrium, and its efficiency is defined as the ratio of flow over the total entropy production in the system. For a stationary state the information flows from higher to lower temperatures, and its the efficiency is bound from above by $\frac{{\rm max}[T_1,T_2]}{|T_1-T_2|}$. This upper bound is imposed by the second law and it quantifies the thermodynamic cost for information flow in the present class of systems. It can be reached in the adiabatic situation, where the particles have widely different characteristic times. The efficiency of heat flow|defined as the heat flow over the total amount of dissipated heat|is limited from above by the same factor. There is a complementarity between heat- and information-flow: the setup which is most efficient for the former is the least efficient for the latter and {\it vice versa}. The above bound for the efficiency can be [transiently] overcome in certain non-stationary situations, but the efficiency is still limited from above. We study yet another measure of information-processing [transfer entropy] proposed in literature. Though this measure does not require any thermodynamic cost, the information flow and transfer entropy are shown to be intimately related for stationary states.Comment: 19 pages, 1 figur

Entropic bounds on coding for noisy quantum channels

In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if the loss is zero, quantum information can be perfectly transmitted at a rate measured by the quantum source entropy. By using block coding based on sequences of n entangled symbols, the average loss (defined as the overall loss of the joint n-symbol channel divided by n, when n tends to infinity) can be made lower than the loss for a single use of the channel. In this context, we examine several upper bounds on the rate at which quantum information can be transmitted reliably via a noisy channel, that is, with an asymptotically vanishing average loss while the one-symbol loss of the channel is non-zero. These bounds on the channel capacity rely on the entropic Singleton bound on quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we analyze the Singleton bounds when the noisy quantum channel is supplemented with a classical auxiliary channel.Comment: 20 pages RevTeX, 10 Postscript figures. Expanded Section II, added 1 figure, changed title. To appear in Phys. Rev. A (May 98

The photometric properties of a vast stellar substructure in the outskirts of M33

We have surveyed $\sim40$sq.degrees surrounding M33 with CFHT MegaCam in the g and i filters, as part of the Pan-Andromeda Archaeological Survey. Our observations are deep enough to resolve the top 4mags of the red giant branch population in this galaxy. We have previously shown that the disk of M33 is surrounded by a large, irregular, low-surface brightness substructure. Here, we quantify the stellar populations and structure of this feature using the PAndAS data. We show that the stellar populations of this feature are consistent with an old population with $<[Fe/H]>\sim-1.6$dex and an interquartile range in metallicity of $\sim0.5$dex. We construct a surface brightness map of M33 that traces this feature to $\mu_V\simeq33$mags\,arcsec$^{-2}$. At these low surface brightness levels, the structure extends to projected radii of $\sim40$kpc from the center of M33 in both the north-west and south-east quadrants of the galaxy. Overall, the structure has an "S-shaped" appearance that broadly aligns with the orientation of the HI disk warp. We calculate a lower limit to the integrated luminosity of the structure of $-12.7\pm0.5$mags, comparable to a bright dwarf galaxy such as Fornax or AndII and slightly less than $1\$ of the total luminosity of M33. Further, we show that there is tentative evidence for a distortion in the distribution of young stars near the edge of the HI disk that occurs at similar azimuth to the warp in HI. The data also hint at a low-level, extended stellar component at larger radius that may be a M33 halo component. We revisit studies of M33 and its stellar populations in light of these new results, and we discuss possible formation scenarios for the vast stellar structure. Our favored model is that of the tidal disruption of M33 in its orbit around M31.Comment: Accepted for publication in ApJ. 17 figures. ApJ preprint forma

A Comprehensive Study of Leptoquark Bounds

We make a comprehensive study of indirect bounds on scalar leptoquarks that couple chirally and diagonally to the first generation by examining available data from low energy experiments as well as from high energy e+ e- and p pbar accelerators. The strongest bounds turn out to arise from low energy data: For leptoquarks that couple to right--handed quarks, the most stringent bound comes from atomic parity violation. For leptoquarks that couple to left--handed quarks, there are two mass regions: At low masses the bounds arise from atomic parity violation or from universality in leptonic pi decays. At masses above a few hundred GeV's, the dominant bounds come from the FCNC processes that are unavoidable in these leptoquarks: The FCNC bound of the up sector, that arises from D-Dbar mixing, combines with the FCNC bounds from the down sector, that arise from rare K decays and K-Kbar mixing, to a bound on the flavour CONSERVING coupling to the first generation. The bounds restrict leptoquarks that couple with electromagnetic strength to lie above 600 GeV or 630 GeV for leptoquarks that couple to RH quarks, and above 1040 GeV, 440 GeV, and 750 GeV for the SU(2)_W scalar, doublet and triplet leptoquarks that couple to LH quarks. These bounds are considerably stronger than the first results from the direct searches at HERA. Our bounds also already exclude large regions in the parameter space that could be examined by various methods proposed for indirect leptoquark searches.Comment: 23 Pages (LaTeX), including 3 uufiled postscript figures. WIS--93/90/Sept--PH. To appear in PRD. Changes: updated numbers ---> stronger bound

Information Tradeoff Relations for Finite-Strength Quantum Measurements

In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a two-state quantum system. The question we address is to what extent one observer can, by measurement, increase the purity of his density operator without affecting the purity of the other observer's. If there were no restrictions on the first observer's measurements, then he could carry this out trivially by measuring the initial density operator's eigenbasis. If, however, the allowed measurements are those of finite strength---i.e., those measurements strictly within the interior of the convex set of all measurements---then the issue becomes significantly more complex. We find that for a large class of such measurements the first observer's purity increases the most precisely when there is some loss of purity for the second observer. More generally the tradeoff between the two purities, when it exists, forms a monotonic relation. This tradeoff has potential application to quantum state control and feedback.Comment: 15 pages, revtex3, 3 eps figure

Modular symbols in Iwasawa theory

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous conjecture and result for $d = 2$ over $\mathbb{F}_q(t)$. In the third, we pose questions for general $d$ over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page

Bounds on Vector Leptoquarks

We derive bounds on vector leptoquarks coupling to the first generation, using data from low energy experiments as well as from high energy accelerators. Similarly to the case of scalar leptoquarks, we find that the strongest indirect bounds arise from atomic parity violation and universality in leptonic pi decays. These bounds are considerably stronger than the first direct bounds of HERA, restricting vector leptoquarks that couple with electromagnetic strength to right-handed quarks to lie above 430 GeV or 460 GeV, and leptoquarks that couple with electromagnetic strength to left-handed quarks to lie above 1.3 TeV, 1.2 TeV and 1.5 TeV for the SU(2)_W singlet, doublet and triplet respectively.Comment: 14 Pages (LaTeX), including 1 uufiled postscript figure. WIS-93/119/Dec-P