Robust visual odometry using uncertainty models

In dense, urban environments, GPS by itself cannot be relied on to provide accurate positioning information. Signal reception issues (e.g. occlusion, multi-path effects) often prevent the GPS receiver from getting a positional lock, causing holes in the absolute positioning data. In order to keep assisting the driver, other sensors are required to track the vehicle motion during these periods of GPS disturbance. In this paper, we propose a novel method to use a single on-board consumer-grade camera to estimate the relative vehicle motion. The method is based on the tracking of ground plane features, taking into account the uncertainty on their backprojection as well as the uncertainty on the vehicle motion. A Hough-like parameter space vote is employed to extract motion parameters from the uncertainty models. The method is easy to calibrate and designed to be robust to outliers and bad feature quality. Preliminary testing shows good accuracy and reliability, with a positional estimate within 2 metres for a 400 metre elapsed distance. The effects of inaccurate calibration are examined using artificial datasets, suggesting a self-calibrating system may be possible in future work

Exact fuzzy sphere thermodynamics in matrix quantum mechanics

We study thermodynamical properties of a fuzzy sphere in matrix quantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of the effective action in the large-N limit. The fuzzy sphere becomes unstable at sufficiently strong coupling, and the critical point is obtained explicitly as a function of the temperature. The whole phase diagram is investigated by Monte Carlo simulation. Above the critical point, we obtain perfect agreement with the all order results. In the region below the critical point, which is not accessible by perturbation theory, we observe the Hagedorn transition. In the high temperature limit our model is equivalent to a totally reduced model, and the relationship to previously known results is clarified.Comment: 22 pages, 14 figures, (v2) some typos correcte

Spin wave dispersion softening in the ferromagnetic Kondo lattice model for manganites

Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice model taking into account strong on-site correlations between e_g electrons and antiferromagnetic (AFM) exchange among t_{2g} spins. Our study suggests that competing FM double-exchange and AFM super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional Dq^2 spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of our results to the experimental data are discussed.Comment: 6 RevTex pages, 3 embedded PostScript figure

Phases of a two dimensional large N gauge theory on a torus

We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2 dimensional pure Yang-Mills theory on T^{D+2} with D small radii. The two dimensional model has various phases characterized by the holonomy of the gauge field around non-contractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method, developed in an earlier work (arxiv:0910.4526), which is nonperturbative in the 'tHooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2 dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations (arxiv:0710.0098). We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation.Comment: 28 pages (+ 17 pages of appendix + 6 pages of ref.); 8 figures; (v2) LaTeX Showkeys command deleted; (v3) refs and minor clarifications added; emphasized the new proposal for applying holography to nonsupersymmetric gauge theory; (v4) modified the arguments about holography; (v5) minor corrections, version appeared in PR

NMR characterization of spin-1/2 alternating antiferromagnetic chains in the high-pressure phase of (VO)2P2O7

Local-susceptibility measurements via the NMR shifts of $^{31}$P and $^{51}$V nuclei in the high-pressure phase of (VO)$_{2}$P$_{2}$O$_{7}$ confirmed the existence of a unique alternating antiferromagnetic chain with a zero-field spin gap of 34 K. The $^{31}$P nuclear spin-lattice relaxation rate scales with the uniform spin susceptibility below about 15 K which shows that the temperature dependence of both the static and dynamical spin susceptibilities becomes identical at temperatures not far below the spin-gap energy.Comment: 6 pages, 5 figures; To be published in J. Phys. Condens. Matte

Dynamical aspects of the fuzzy CP2^{2} in the large NN reduced model with a cubic term

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of the well-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S^2, which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP^2, Monte Carlo simulation shows that the fuzzy CP^2 is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term ($\alpha$) is sufficiently large. As \alpha is decreased, both the fuzzy CP$^2$ and the fuzzy S^2 collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (\alpha = 0). The corresponding transitions are of first order and the critical points can be understood analytically. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP^2 and S^2 cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N=\infty, we find excellent agreement with the all order results.Comment: 27 pages, 7 figures, (v2) References added (v3) all order analyses added, some typos correcte

Strong Coupling Expansions for Antiferromagnetic Heisenberg S=1/2 Ladders

The properties of antiferromagnetic Heisenberg $S=\frac{1}{2}$ ladders with 2, 3, and 4 chains are expanded in the ratio of the intra- and interchain coupling constants. A simple mapping procedure is introduced to relate the 4 and 2-chain ladders which holds down to moderate values of the expansion parameters. A second order calculation of the spin gap to the lowest triplet excitation in the 2- and 4-chain ladders is found to be quite accurate even at the isotropic point where the couplings are equal. Similar expansions and mapping procedures are presented for the 3-chain ladders which are in the same universality class as single chains.Comment: 10 physical pages, uuencoded compressed PostScript file including 12 figures, ETH-TH/942

63Cu NQR evidence of dimensional crossover to anisotropic 2d regime in S= 1/2 three-leg ladder Sr2Cu3O5

We probed spin-spin correlations up to 725 K with 63Cu NQR in the S= 1/2 three-leg ladder Sr2Cu3O5. We present experimental evidence that below 300 K, weak inter-ladder coupling causes dimensional crossover of the spin-spin correlation length \xi from quasi-1d (\xi ~ 1/T) to anisotropic 2d regime (\xi \~ exp[2\pi\rho_{s}/T], where 2\pi\rho_{s} = 290 +/- 30 K is the effective spin stiffness). This is the first experimental verification of the renormalized classical behavior of the anisotropic non-linear sigma model in 2d, which has been recently proposed for the striped phase in high T_{c} cuprates.Comment: 4 pages, 3 figure

Matrix geometries and Matrix Models

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.Comment: 20 page

Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.Comment: 31 pages. V2: minor corrections, references adde