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

Are There Any Redshift >8 Gamma-Ray Bursts in the BATSE Catalog?

Several luminosity indicators have been found for Gamma-Ray Bursts (GRBs) wherein measurable light curve and spectral properties are well-correlated with the peak luminosity. Several papers have each applied one different luminosity relation to find redshifts for BATSE GRBs and claim to identify specific bursts with z>8. The existence of such high redshift events is not surprising, as BATSE has enough sensitivity to see them and GRBs are expected out to the redshift of the first star formation. To improve results we used five luminosity relations with updated calibrations to determine redshifts with error bars. Combining these relations, we calculated the redshifts of 36 BATSE GRBs with claimed z>8. Our results include 13 bursts with our derived best redshift z_best>8, which looks promising at first. But the calculated redshift uncertainties are significantly large in these selected cases. With only one exception, all of our bursts have z_1siglow<9. The one exception (BATSE trigger 2035) is likely a short duration burst at z>~4. Our best case for a very high redshift event is BATSE trigger 3142 with z_best>20 and z_1siglow=8.9, however we can only say z>4.1 at the two-sigma confidence level. In all, we cannot point toward any one BATSE burst as confidently having z>8. One implication is to greatly weaken prior claims that GRBs have a steeply rising rate-density out to high redshifts.Comment: ApJ in press, 18 page

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

Using an analytic network process model to incorporate qualitative factors into multi-criteria global modal choice decisions

This research develops and evaluates an Analytic Network Process (ANP) model to choose the correct mode of global transportation in the presence of complicating qualitative influences. The ANP model effectively combines important qualitative and quantitative factors into a global modal choice model. Although there is a great deal of research in the area of modal choice, the research often focuses singularly on cost or time factors. This research incorporates security, public opinion, and customer opinion into modal choice. One of the most difficult choices a transportation planner faces is deciding when qualitative factors outweigh the quantitative ones. A reliable tool to validate choice by including the important qualitative factors with the quantitative is quite valuable in military operations, humanitarian support, and disaster relief

Nonlocal Landau theory of the magnetic phase diagram of highly frustrated magnetoelectric CuFeO2_2

A nonlocal Landau-type free energy functional of the spin density is developed to model the large variety of magnetic states which occur in the magnetic field-temperature phase diagram of magnetoelectric CuFeO$_2$. Competition among long-range quadratic exchange, biquadratic anti-symmetric exchange, and trigonal anisotropy terms, consistent with the high-temperature rhombohedral R$\bar{3}$m crystal symmetry, are shown to all play important roles in stabilizing the unusual combination of commensurate and incommensurate spin structures in this highly frustrated triangular antiferromagnet. It is argued that strong magnetoelastic coupling is largely responsible for the nonlocal nature of the free energy. A key feature of the analysis is that an electric polarization is induced by a canting of the non-collinear incommensurate spin structure. Application of the model to ordered spin states in the triangular antiferromagnets MnBr$_2$ and NaFeO$_2$ is also discussed.Comment: 20 pages, 2 figure

Dimensional Changes of Upper Airway after Rapid Maxillary Expansion: A Prospective Cone-beam Computed Tomography Study

Introduction: The aim of this prospective study was to use cone-beam computed tomography to assess the dimensional changes of the upper airway in orthodontic patients with maxillary constriction treated by rapid maxillary expansion. Methods: Fourteen orthodontic patients (mean age, 12.9 years; range, 9.7-16 years) were recruited. The patients with posterior crossbite and constricted maxilla were treated with rapid maxillary expansion as the initial part of their comprehensive orthodontic treatments. Before and after rapid maxillary expansion conebeam computed tomography scans were taken to measure the retropalatal and retroglossal airway changes in terms of volume, and sagittal and cross-sectional areas. The transverse expansions by rapid maxillary expansion were assessed between the midlingual alveolar bone plates at the maxillary first molar and first premolar levels. The measurements of the before and after rapid maxillary expansion scans were compared by using paired t tests with the Bonferroni adjustment for multiple comparisons. Results: After rapid maxillary expansion, significant and equal amounts of 4.8 mm of expansion were observed at the first molar (P 5 0.0000) and the first premolar (P 5 0.0000) levels. The width increase at the first premolar level (20.0%) was significantly greater than that at the first molar level (15.0%) (P 5 0.035). As the primary outcome variable, the cross-sectional airway measured from the posterior nasal spine to basion level was the only parameter showing a significant increase of 99.4 mm2 (59.6%) after rapid maxillary expansion (P 5 0.0004). Conclusions: These results confirm the findings of previous studies of the effect of rapid maxillary expansion on the maxilla. Additionally, we found that only the cross-sectional area of the upper airway at the posterior nasal spine to basion level significantly gains a moderate increase after rapid maxillary expansion

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.

Cosmic String Formation from Correlated Fields

We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum $P(k) \propto k^n$, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over previous simulations: we include a non-zero random background field in our box to simulate the effect of long-wavelength modes, and we examine the effects of smoothing the field on small scales. The inclusion of the background field significantly reduces the fraction of length in infinite strings for $n < -2$. Our results are consistent with the possibility that infinite strings disappear at some $n = n_c$ in the range $-3 \le n_c < -2.2$, although we cannot rule out $n_c = -3$, in which case infinite strings would disappear only at the point where the mean string density goes to zero. We present an analytic argument which suggests the latter case. Smoothing on small scales eliminates closed loops on the order of the lattice cell size and leads to a ``lattice-free" estimate of the infinite string fraction. As expected, this fraction depends on the type of window function used for smoothing.Comment: 24 pages, latex, 10 figures, submitted to Phys Rev