Continuum Limits of ``Induced QCD": Lessons of the Gaussian Model at d=1 and Beyond

We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\rightarrow\infty$, only the conventional large-$N$ limit is relevant for its {\it continuum} limit. We also give a mean--field analysis of the $N=2$ model in {\it any} $d$ and show that a saddle point always exists in the region $m^2>m_{\rm crit}^2(=d)$. In $d=1$ it exhibits critical behaviour as $m^2\rightarrow m_{\rm crit}^2$. However when $d$$>$$1$ there is no critical behaviour unless non--Gaussian terms are added to the scalar field action. We argue that similar behaviour should occur for any finite $N$ thus providing a simple explanation of a recent result of D. Gross. We show that critical behaviour at $d$$>$$1$ and $m^2>m^2_{\rm crit}$ can be obtained by adding a $logarithmic$ term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov--Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behaviour of the Gaussian model.Comment: 31 page

A Generalised Sidelobe Canceller Architecture Based on Oversampled Subband Decompositions

Adaptive broadband beamforming can be performed in oversampled subband signals, whereby an independent beamformer is operated in each frequency band. This has been shown to result in a considerably reduced computational complexity. In this paper, we primarily investigate the convergence behaviour of the generalised sidelobe canceller (GSC) based on normalised least mean squares algorithm (NLMS) when operated in subbands. The minimum mean squared error can be limited, amongst other factors, by the aliasing present in the subbands. With regard to convergence speed, there is strong indication that the subband-GSC converges faster than a fullband counterpart of similar modelling capabilities. Simulations are presented

Magnetic Doppler imaging of the roAp star HD 24712

We present the first magnetic Doppler images of a rapidly oscillating Ap (roAp) star. We deduce information about magnetic field geometry and abundance distributions of a number of chemical elements on the surface of the hitherto best studied roAp star, HD 24712, using the magnetic Doppler imaging (MDI) code, INVERS10, which allows us to reconstruct simultaneously and consistently the magnetic field geometry and elemental abundance distributions on a stellar surface. For this purpose we analyse time series spectra obtained in Stokes I and V parameters with the SOFIN polarimeter at the Nordic Optical Telescope and recover surface abundance structures of sixteen different chemical elements, respectively ions, including Mg, Ca, Sc, Ti, Cr, Fe, Co, Ni, Y, La, Ce, Pr, Nd, Gd, Tb, and Dy. For the rare earth elements (REE) Pr and Nd separate maps were obtained using lines of the first and the second ionization stage. We find and confirm a clear dipolar structure of the surface magnetic field and an unexpected correlation of elemental abundances with respect to this field: one group of elements accumulates solely where the positive magnetic pole is visible, whereas the other group avoids this region and is enhanced where the magnetic equatorial region dominates the visible stellar surface. We also observe relative shifts of abundance enhancement- or depletion regions between the various elements exhibiting otherwise similar behaviour.Comment: 13 pages, 9 figures, to be published in Astronomy and Astrophysic

Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation

The BT of Adler's lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Backlund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter family of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit solution of the mappings within this family and hence give the solutions of Adler's equation that are 2-cycles of the BT.Comment: 10 pages, contribution to the NEEDS 2007 proceeding

Optimal Data-Dependent Hashing for Approximate Near Neighbors

We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an $n$-point data set in a $d$-dimensional space our data structure achieves query time $O(d n^{\rho+o(1)})$ and space $O(n^{1+\rho+o(1)} + dn)$, where $\rho=\tfrac{1}{2c^2-1}$ for the Euclidean space and approximation $c>1$. For the Hamming space, we obtain an exponent of $\rho=\tfrac{1}{2c-1}$. Our result completes the direction set forth in [AINR14] who gave a proof-of-concept that data-dependent hashing can outperform classical Locality Sensitive Hashing (LSH). In contrast to [AINR14], the new bound is not only optimal, but in fact improves over the best (optimal) LSH data structures [IM98,AI06] for all approximation factors $c>1$. From the technical perspective, we proceed by decomposing an arbitrary dataset into several subsets that are, in a certain sense, pseudo-random.Comment: 36 pages, 5 figures, an extended abstract appeared in the proceedings of the 47th ACM Symposium on Theory of Computing (STOC 2015

Laser Interferometric Detectors of Gravitational Waves

A laser interferometric detector of gravitational waves is studied and a complete solution (to first order in the metric perturbation) of the coupled Einstein-Maxwell equations with appropriate boundary conditions for the light beams is determined. The phase shift, the light deflection and the rotation of the polarization axis induced by gravitational waves are computed. The results are compared with previous literature, and are shown to hold also for detectors which are large in comparison with the gravitational wavelength.Comment: 13 pages, LaTe

Three Super-Earths Orbiting HD 7924

We report the discovery of two super-Earth mass planets orbiting the nearby K0.5 dwarf HD 7924 which was previously known to host one small planet. The new companions have masses of 7.9 and 6.4 M$_\oplus$, and orbital periods of 15.3 and 24.5 days. We perform a joint analysis of high-precision radial velocity data from Keck/HIRES and the new Automated Planet Finder Telescope (APF) to robustly detect three total planets in the system. We refine the ephemeris of the previously known planet using five years of new Keck data and high-cadence observations over the last 1.3 years with the APF. With this new ephemeris, we show that a previous transit search for the inner-most planet would have covered 70% of the predicted ingress or egress times. Photometric data collected over the last eight years using the Automated Photometric Telescope shows no evidence for transits of any of the planets, which would be detectable if the planets transit and their compositions are hydrogen-dominated. We detect a long-period signal that we interpret as the stellar magnetic activity cycle since it is strongly correlated with the Ca II H and K activity index. We also detect two additional short-period signals that we attribute to rotationally-modulated starspots and a one month alias. The high-cadence APF data help to distinguish between the true orbital periods and aliases caused by the window function of the Keck data. The planets orbiting HD 7924 are a local example of the compact, multi-planet systems that the Kepler Mission found in great abundance.Comment: Accepted to ApJ on 4/7/201

Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\otimes\beta$ system models the coupling of a two-level electronic system, or qubit, to a single oscillator mode, while the $E\otimes\epsilon$ models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the $E\otimes\beta$ system, the ground states of the $E\otimes\epsilon$ model always exhibit entanglement. For the $E\otimes\beta$ case we aim to clarify results from previous work, alluding to a link between the ground state entanglement characteristics and a bifurcation of a fixed point in the classical analogue. In the $E\otimes\epsilon$ case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.Comment: 11 pages, 9 figures, comments welcome; 2 references adde