A representation of the Mathieu groupM 24 as a collineation group

Summary The Mathieu group M₂₄ can be represented as a collineation group in space of 11 dimensions over the field of two elements. This paper discusses the geometry associated with this representation. In memory of Guido Castelnuovo, in the recurrence of the first centenary of his birth.     

Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner

Acousto-optic sensing (AOS) is a dual-wave sensing technique based on the ultrasound modulation of diffuse light in a turbid medium. We experimentally demonstrate the feasibility of combining AOS and conventional ultrasound imaging by use of a commercially available pulsed-ultrasound scanner coupled with a photorefractive crystal-based optical interferometry system. Optically absorbing targets embedded in highly diffusive phantoms (mus'= 10 cm(-1)) are imaged through a thickness of 27 mm with millimeter resolution. The acousto-optic images are intrinsically coregistered with the ultrasound images.     

Modeling, measuring, and minimizing the instrument response function of a tunable diode laser spectrometer

The instrument response function (IRF) of a spectrometer limits the accuracy of measured spectroscopic parameters by broadening recorded spectral lines/features. We describe methods to model the effects of the IRF on spectral data, to minimize the IRF widths, and to measure the resulting width of the spectrometer IRF. We have modeled the IRF of our Tunable Diode Laser Spectrometer as a Voigt function. A real-time method of eliminating the effects of low-frequency spectrometer drift has been implemented and has resulted in a substantial reduction in the width of the IRF, its residual Gaussian component reduced from about to about . An accurate measurement of the IRF Gaussian width utilizes a computationally simple method making use of the spectral dependence of the RMS noise of each signal-averaged data point. Various noise sources affecting the spectrometer (preamp/detector noise, laser AM noise, and laser FM noise) are identified and separately quantified by use of the same method. The IRF Gaussian-width measurement can be automatically applied to each measured spectrum of an experimental data set. A related method is discussed which allows accurate determination of the spectral dependence of statistical noise appropriate for use in quantitative Chi-square fitting of absorption spectra. We explore simple, efficient numerical processes which can dramatically enhance the quality and usefulness of acquired spectral data, improving the ability to apply TDL spectroscopy to high-precision, quantitative measurements and the determination of detailed spectroscopic lineshape parameters. This paper provides a guide for interested readers to implement these developments in their own spectrometers.     

Acoustic radiation from a fluid-filled, subsurface vascular tube with internal turbulent flow due to a constriction

The vibration of a thin-walled cylindrical, compliant viscoelastic tube with internal turbulent flow due to an axisymmetric constriction is studied theoretically and experimentally. Vibration of the tube is considered with internal fluid coupling only, and with coupling to internal-flowing fluid and external stagnant fluid or external tissue-like viscoelastic material. The theoretical analysis includes the adaptation of a model for turbulence in the internal fluid and its vibratory excitation of and interaction with the tube wall and surrounding viscoelastic medium. Analytical predictions are compared with experimental measurements conducted on a flow model system using laser Doppler vibrometry to measure tube vibration and the vibration of the surrounding viscoelastic medium. Fluid pressure within the tube was measured with miniature hydrophones. Discrepancies between theory and experiment, as well as the coupled nature of the fluid-structure interaction, are described. This study is relevant to and may lead to further insight into the patency and mechanisms of vascular failure, as well as diagnostic techniques utilizing noninvasive acoustic measurements.     

Weak measurements are universal

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.     

Semismooth support vector machines

Support vector machines can be posed as quadratic programming problems in a variety of ways. This paper investigates a formulation using the two-norm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint under a duality construction. The quadratic term is a small rank update to a diagonal matrix with positive entries. The optimality conditions of the quadratic program are reformulated as a semismooth system of equations using the Fischer-Burmeister function and a damped Newton method is applied to solve the resulting problem. The algorithm is shown to converge from any starting point with a Q-quadratic rate of convergence. At each iteration, the Sherman-Morrison-Woodbury update formula is used to solve the key linear system. Results for a large problem with 60 million observations are presented demonstrating the scalability of the proposed method on a personal computer. Significant computational savings are realized as the inactive variables are identified and exploited during the solution process. Further results on a small problem separated by a nonlinear surface are given showing the gains in performance that can be made from restarting the algorithm as the data evolves.Accepted: December 8, 2003This work partially supported by NSF grant number CCR-9972372; AFOSR grant number F49620-01-1-0040; the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38; and Microsoft Corporation.     

Optimizing the vertebrate vestibular semicircular canal: could we balance any better?

The fluid-filled semicircular canals (SCCs) of the vestibular system are used by all vertebrates to sense angular rotation. Despite masses spanning seven decades, all mammalian SCCs are nearly the same size. We propose that the SCC represents a sensory organ that evolution has "optimally designed." Four geometric parameters characterize the SCC, and "building materials" of given physical properties are assumed. Identifying physical and physiological constraints on SCC operation, we find the most sensitive SCC has dimensions consistent with available data. Since natural selection involves optimization, this approach may find broader use in understanding biological structures.     

A rare earth-DOTA-binding antibody: probe properties and binding affinity across the lanthanide series

An antibody that binds rare earth complexes selectively could be used as a docking station for a set of probe molecules, of particular interest for medical imaging and therapy. The rare earths are rich in probe properties, such as the paramagnetism of Gd, the luminescence of Tb and Eu, and the nuclear properties of Lu and Y. We find that antibody 2D12.5, initially developed to bind analogues of Y-DOTA (1,4,7,10-tetraazacyclododecane-N,N',N' ',N' '-tetraacetic acid) for radiotherapy, binds not only Y-DOTA analogues but also analogous DOTA complexes of all of the lanthanides. Surprisingly, chelates of some metals such as Gd3+ bind more tightly than the original Y3+ complex. When the shape of the complex is perturbed by either increasing or decreasing the radius of the lanthanide ion, the thermodynamic stability of the protein-ligand complex changes in a regular fashion. The behavior of DeltaDeltaG as a function of ionic radius fits a parabola, as might be expected for a system that behaves in a thermodynamically elastic way. The broad specificity and high affinity of this antibody for all rare earth-DOTA complexes make it particularly interesting for applications that take advantage of the unique characteristics of lanthanides. For example, UV excitation of the Tb-DOTA-2D12.5 complex leads to energy transfer from aromatic side chains of the antibody to bound Tb-DOTA, enhancing green terbium luminescence >104 relative to unbound Tb-DOTA.