Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging

Signals comprised of a stream of short pulses appear in many applications including bio-imaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams, and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques, and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.Comment: 14 pages, 13 figure

Multichannel Sampling of Pulse Streams at the Rate of Innovation

We consider minimal-rate sampling schemes for infinite streams of delayed and weighted versions of a known pulse shape. The minimal sampling rate for these parametric signals is referred to as the rate of innovation and is equal to the number of degrees of freedom per unit time. Although sampling of infinite pulse streams was treated in previous works, either the rate of innovation was not achieved, or the pulse shape was limited to Diracs. In this paper we propose a multichannel architecture for sampling pulse streams with arbitrary shape, operating at the rate of innovation. Our approach is based on modulating the input signal with a set of properly chosen waveforms, followed by a bank of integrators. This architecture is motivated by recent work on sub-Nyquist sampling of multiband signals. We show that the pulse stream can be recovered from the proposed minimal-rate samples using standard tools taken from spectral estimation in a stable way even at high rates of innovation. In addition, we address practical implementation issues, such as reduction of hardware complexity and immunity to failure in the sampling channels. The resulting scheme is flexible and exhibits better noise robustness than previous approaches

Radial and angular rotons in trapped dipolar gases

We study Bose-Einstein condensates with purely dipolar interactions in oblate (pancake) traps. We find that the condensate always becomes unstable to collapse when the number of particles is sufficiently large. We analyze the instability, and find that it is the trapped-gas analogue of the ``roton-maxon'' instability previously reported for a gas that is unconfined in two dimensions. In addition, we find that under certain circumstances, the condensate wave function attains a biconcave shape, with its maximum density away from the center of the gas. These biconcave condensates become unstable due to azimuthl excitation - an angular roton.Comment: 4 pages, 3 figure

Bell’s Inequalities for Particles of Arbitrary Spin in Fixed Analyzers

We propose a new set of observables for experiments on entangled particles of arbitrarily large spin that produce significant Clauser-Horne-Shimony-Holt inequality violations for fixed analyzer settings over a wider range of spins than was previously possible. These observables are better suited for experiments where analyzer orientations must be chosen before the spin of the entangled particles is known, such as experiments using polarization entangled downconverted photons

Dipolar Bose gases: Many-body versus mean-field description

We characterize zero-temperature dipolar Bose gases under external spherical confinement as a function of the dipole strength using the essentially exact many-body diffusion Monte Carlo (DMC) technique. We show that the DMC energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly. Our calculations suggest stability diagrams and collapse mechanisms of dipolar Bose gases that differ significantly from those previously proposed in the literature

N=2 Moduli Spaces and N=1 Dualities for SO(n_c) and USp(2n_c) SuperQCD

We determine the exact global structure of the moduli space of $N{=}2$ supersymmetric $SO(n)$ and \USp(2n) gauge theories with matter hypermultiplets in the fundamental representations, using the non-renormalization theorem for the Higgs branches and the exact solutions for the Coulomb branches. By adding an $(N{=}2)$--breaking mass term for the adjoint chiral field and varying the mass, the $N{=}2$ theories can be made to flow to either an ``electric'' $N{=}1$ supersymmetric QCD or its $N{=}1$ dual ``magnetic'' version. We thus obtain a derivation of the $N{=}1$ dualities of Seiberg.Comment: 20 pages, harvmac (b

A-Model Correlators from the Coulomb Branch

We compute the contribution of discrete Coulomb vacua to A-Model correlators in toric Gauged Linear Sigma Models. For models corresponding to a compact variety, this determines the correlators at arbitrary genus. For non-compact examples, our results imply the surprising conclusion that the quantum cohomology relations break down for a subset of the correlators.Comment: 27 pages, 1 xy-pic figur

Dipolar Bose-Einstein condensates with dipole-dependent scattering length

We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in non-isotropic traps

SPREADSHEET ANALYSIS AND DESIGN

Spreadsheet programs and microcomputers have revolutionized information processing in organizations. Users have adopted spreadsheets to solve problems and circumvent the long delays encountered in dealing with the traditional information services department. A significant number of serious errors have been reported through the misuse of spreadsheet technology. This paper discusses several different contexts for the development of spreadsheet models and presents structured design techniques for these models. The recommended approach to spreadsheet analysis and design encourages the use of a block structure format for the worksheet and introduces Spreadsheet Flow Diagrams as a systems design tool. The objective of this design approach is to reduce the probability and severity of spreadsheet errors, improve auditability and promote greater longevity for spreadsheet models.Information Systems Working Papers Serie

How Does a Dipolar Bose-Einstein Condensate Collapse?

We emphasize that the macroscopic collapse of a dipolar Bose-Einstein condensate in a pancake-shaped trap occurs through local density fluctuations, rather than through a global collapse to the trap center. This hypothesis is supported by a recent experiment in a chromium condensate.Comment: Proceedings of 17th International Laser Physics Worksho