A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Vibration limiting of rotors by feedback control

Experimental findings of a three mass rotor with four channels of feedback control are reported. The channels are independently controllable with force being proportional to the velocity and/or instantaneous displacement from equilibrium of the shaft at the noncontacting probe locations (arranged in the vertical and horizontal attitudes near the support bearings). The findings suggest that automatic feedback control of rotors is feasible for limiting certain vibration levels. Control of one end of a rotor does afford some predictable vibration limiting of the rotor at the other end

Evolutionary Timescale of the DAV G117-B15A: The Most Stable Optical Clock Known

We observe G117-B15A, the most precise optical clock known, to measure the rate of change of the main pulsation period of this blue-edge DAV white dwarf. Even though the obtained value is only within 1 sigma, Pdot = (2.3 +/- 1.4) x 10^{-15} s/s, it is already constraining the evolutionary timescale of this cooling white dwarf star.Comment: Accepted for publication in ApJ

Redshifts and Luminosities for 112 Gamma Ray Bursts

Two different luminosity indicators have recently been proposed for Gamma Ray Bursts that use gamma-ray observations alone. They relate the burst luminosity (L) with the time lag between peaks in hard and soft energies, and the spikiness or variability of the burst's light curve (V). These relations are currently justified and calibrated with only 6 or 7 bursts with known red shifts. We have examined BATSE data for the lag and V for 112 bursts. (1) A strong correlation between the lag and V exists, and it is exactly as predicted from the two proposed relations. This is proof that both luminosity indicators are reliable. (2) GRB830801 is the all-time brightest burst, yet with a small V and a large lag, and hence is likely the closest known event being perhaps as close as 3.2 Mpc. (3) We have combined the luminosities as derived from both indicators as a means to improve the statistical and systematic accuracy when compared with the accuracy from either method alone. The result is a list of 112 bursts with good luminosities and hence red shifts. (4) The burst averaged hardness ratio rises strongly with the luminosity of the burst. (5) The burst luminosity function is a broken power law, with the break at L = 2x10^{52} erg/s. The luminosity function has power law indices of -2.8+-0.2 above the break and -1.7+-0.1 below the break. (6) The number density of GRBs varies with red shift roughly as (1+z)^(2.5+-0.3) between 0.2<z<5. Excitingly, this result also provides a measure of the star formation rate out to z~5 with no effects from reddening, and the rate is rising uniformly for red shifts above 2.Comment: 13 pages, 4 figures, submitted to ApJLet

A Dusty Disk Around WD1150-153: Explaining the Metals in White Dwarfs by Accretion from the Interstellar Medium versus Debris Disks

We report the discovery of excess K-band radiation from a metal-rich DAV white dwarf star, WD1150-153. Our near infrared spectroscopic observations show that the excess radiation cannot be explained by a (sub)stellar companion, and is likely to be caused by a debris disk similar to the other DAZ white dwarfs with circumstellar debris disks. We find that the fraction of DAZ white dwarfs with detectable debris disks is at least 14%. We also revisit the problem of explaining the metals in white dwarf photospheres by accretion from the interstellar medium (ISM). We use the observed interstellar column densities toward stars in close angular proximity and similar distance as DAZ white dwarfs to constrain the contribution of accretion from the ISM. We find no correlation between the accretion density required to supply metals observed in DAZs with the densities observed in their interstellar environment, indicating that ISM accretion alone cannot explain the presence of metals in nearby DAZ white dwarfs. Although ISM accretion will certainly contribute, our analysis indicates that it is not the dominant source of metals for most DAZ white dwarfs. Instead, the growing number of circumstellar debris disks around DAZs suggests that circumstellar material may play a more dominant role in polluting the white dwarf atmospheres.Comment: ApJ, in pres

Odd Parity and Line Nodes in Non-Symmorphic Superconductors

Group theory arguments have been invoked to argue that odd parity order parameters cannot have line nodes in the presence of spin-orbit coupling. In this paper we show that these arguments do not hold for certain non-symmorphic superconductors. Specifically, we demonstrate that when the underlying crystal has a twofold screw axis, half of the odd parity representations vanish on the Brillouin zone face perpendicular to this axis. Many unconventional superconductors have non-symmorphic space groups, and we discuss implications for several materials, including UPt3, UBe13, Li2Pt3B and Na4Ir3O8.Comment: 4 page

Bank Competition: Measurement, Decision-Making, and Risk Profiles

This paper investigates how competition impacts the future operating decisions and risk profile of banks. We construct a comprehensive, time-varying, bank-specific measure of a bank’s competitive environment (BCE) using textual analysis of banks’ 10-K filings. Using U.S. branch banking deregulation to capture exogenous changes in threats of entry, we provide evidence that BCE is a timely measure of real competitive pressures by showing that it significantly increases following decreases in barriers to entry. Measuring competition with BCE, we find that higher competition is associated with lower underwriting standards, less timely loan loss recognition and a shift towards non-interest revenue. Further, we find that higher competition is associated with higher stand-alone risk of individual banks, greater sensitivity of a bank’s downside equity risk to system-wide distress, and a greater contribution by individual banks to downside risk of the banking sector. We then show that these results using BCE are largely robust to replacing BCE with branch bank deregulation. Finally, we show that our BCE results hold in a post-deregulation analysis restricted to time periods following the final deregulation event in each state. These results combine to suggest that competition increases the risk profile of banks and that BCE can be of value to researchers and analysts for measuring competitive pressure at any point in time, regardless of the existence of a regulatory event.http://deepblue.lib.umich.edu/bitstream/2027.42/107866/1/1243_Williams.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/107866/4/1243_Williams_Jan2015.pdfDescription of 1243_Williams_Jan2015.pdf : January 2015 revision (new title