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

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

Quadripartite continuous-variable entanglement via quadruply concurrent downconversion

We investigate an intra-cavity coupled down-conversion scheme to generate quadripartite entanglement using concurrently resonant nonlinearities. We verify that quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of optimized inequalities of the van Loock-Furusawa type. The entanglement characteristics both above and below the oscillation threshold are considered. We also present analytic solutions for the quadrature operators and the van Loock-Furusawa correlations in the undepleted pump approximation.Comment: 9 pages, 5 figure

Dissipative dynamics of vortex arrays in trapped Bose-condensed gases: neutron stars physics on μ\muK scale

We develop a theory of dissipative dynamics of large vortex arrays in trapped Bose-condensed gases. We show that in a static trap the interaction of the vortex array with thermal excitations leads to a non-exponential decay of the vortex structure, and the characteristic lifetime depends on the initial density of vortices. Drawing an analogy with physics of pulsar glitches, we propose an experiment which employs the heating of the thermal cloud in the course of the decay of the vortex array as a tool for a non-destructive study of the vortex dynamics.Comment: 4 pages, revtex; revised versio

Mode identification of Pulsating White Dwarfs using the HST

We have obtained time-resolved ultraviolet spectroscopy for the pulsating DAV stars G226-29 and G185-32, and for the pulsating DBV star PG1351+489 with the Hubble Space Telescope Faint Object Spectrograph, to compare the ultraviolet to the optical pulsation amplitude and determine the pulsation indices. We find that for essentially all observed pulsation modes, the amplitude rises to the ultraviolet as the theoretical models predict for l=1 non-radial g-modes. We do not find any pulsation mode visible only in the ultraviolet, nor any modes whose phase flips by 180 degrees; in the ultraviolet, as would be expected if high l pulsations were excited. We find one periodicity in the light curve of G185-32, at 141 s, which does not fit theoretical models for the change of amplitude with wavelength of g-mode pulsations.Comment: Accepted for publication in the Astrophysical Journal, Aug 200

Exercise-related sensations contribute to decrease power during repeated cycle sprints with limited influence on neural drive

Purposes: We manipulated the inspired oxygen fraction (FiO2) to examine the effects of physiological perturbations on exercise-related sensations and the neural drive of the quadriceps during repeated, brief, maximal cycle sprints. Methods: Nine active males completed a repeated sprint cycle protocol (10 × 4-s maximal sprints with 30 s of passive recovery) in normoxia (NM; FiO2 0.21) and severe normobaric hypoxia (HY; FiO2 0.13). Peak power, quadriceps Root Mean Squared electromyography (RMS EMG), physiological (heart rate, arterial oxygen saturation, blood lactate concentration) and perceptual responses were recorded. Results: The 10 sprints in HY were associated with lower arterial oxygen saturation values compared to NM (80.7 ± 0.9 vs. 95.6 ± 0.6%; P0.47). Mean power for sprints 1-10 were lower (-13 ± 3%; P=0.001; ES=0.79), and sprint decrement was more pronounced in HY compared to NM (21.4 ± 3.7 vs. 13.2 ± 2.7%; P=0.003). There was a 17% decrease in RMS EMG activity from the first to the last sprint (P<0.001; ES=0.65), independent of condition (P=0.597; ES=0.04). Conclusions: Despite severe hypoxia exacerbating both physiological and perceptual perturbations, the performance decrement observed during the repeated sprint protocol did not coincide with an accentuated decline in RMS EMG activity. These data suggest that higher-than-normal exercise-related sensations or perceptions coincide with fatigue during repeated sprinting, independent of changes in neural drive, when the task characteristics are known beforehand

Supracervical Robotic-Assisted Laparoscopic Sacrocolpopexy for Pelvic Organ Prolapse

Supracervical robotic-assisted laparoscopic sacrocolpopexy was found to be an effective repair of apical vaginal defects in patients with pelvic organ prolapse who had not undergone previous hysterectomy

Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator

We examine the feasibility of generating continuous-variable multipartite entanglement in an intra-cavity quadruply concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci \textit{et al.} [Physical Review Letters \textbf{101}, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.Comment: 26 pages, 12 figure

Effect of anharmonicities in the critical number of trapped condensed atoms with attractive two-body interaction

We determine the quantitative effect, in the maximum number of particles and other static observables, due to small anharmonic terms added to the confining potential of an atomic condensed system with negative two-body interaction. As an example of how a cubic or quartic anharmonic term can affect the maximum number of particles, we consider the trap parameters and the results given by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)]. However, this study can be easily transferred to other trap geometries to estimate anharmonic effects.Comment: Total of 5 pages, 3 figures and 1 table. To appear in Phys. Rev.