Development of a 64 channel ultrasonic high frequency linear array imaging system

In order to improve the lateral resolution and extend the field of view of a previously reported 48 element 30 MHz ultrasound linear array and 16-channel digital imaging system, the development of a 256 element 30 MHz linear array and an ultrasound imaging system with increased channel count has been undertaken. This paper reports the design and testing of a 64 channel digital imaging system which consists of an analog front-end pulser/receiver, 64 channels of Time-Gain Compensation (TGC), 64 channels of high-speed digitizer as well as a beamformer. A Personal Computer (PC) is used as the user interface to display real-time images. This system is designed as a platform for the purpose of testing the performance of high frequency linear arrays that have been developed in house. Therefore conventional approaches were taken it its implementation. Flexibility and ease of use are of primary concern whereas consideration of cost-effectiveness and novelty in design are only secondary. Even so, there are many issues at higher frequencies but do not exist at lower frequencies need to be solved. The system provides 64 channels of excitation pulsers while receiving simultaneously at a 20–120 MHz sampling rate to 12-bits. The digitized data from all channels are first fed through Field Programmable Gate Arrays (FPGAs), and then stored in memories. These raw data are accessed by the beamforming processor to re-build the image or to be downloaded to the PC for further processing. The beamformer that applies delays to the echoes of each channel is implemented with the strategy that combines coarse (8.3 ns) and fine delays (2 ns). The coarse delays are integer multiples of the sampling clock rate and are achieved by controlling the write enable pin of the First-In-First-Out (FIFO) memory to obtain valid beamforming data. The fine delays are accomplished with interpolation filters. This system is capable of achieving a maximum frame rate of 50 frames per second. Wire phantom images acquired with this system show a spatial resolution of 146 μm (lateral) and 54 μm (axial). Images with excised rabbit and pig eyeball as well as mouse embryo were also acquired to demonstrate its imaging capability.     

Anisotropy induced in a silver-chloride emulsion by two incoherent and perpendicular light vibrations

After a report on the composition of two incoherent rectilinear vibrations with perpendicular polarizations, we suggest in this paper a method of extraction of the difference between two images in incoherent and polarized light. The images, perpendicularly polarized, are simultaneously recorded on a silver chloride emulsion H where an optical anisotropy is induced only in the areas where the incident intensity distributions are not identical. After exposure, H, observed between crossed polarizers, displays the difference between the two original images in its image plane. In addition, it is shown that the sign of this difference is retrieved by means of the dichroism of the plate.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Randomised circular means of Fourier transforms of measures

We explore decay estimates for circular means of the Fourier transform of a measure on in terms of its -dimensional energy. We find new upper bounds for the decay exponent. We also prove sharp estimates for a certain family of randomised versions of this problem.

     

Irregular wakes in reaction-diffusion waves

Reaction-diffusion equations have proved to be highly successful models for a wide range of biological and chemical systems, but chaotic solutions have been very rarely documented. We present a new mechanism for generating apparently chaotic spatiotemporal irregularity in such systems, by analysing in detail the bifurcation structure of a particular set of reaction-diffusion equations on an infinite one-dimensional domain, with particular initial conditions. We show that possible solutions include travelling fronts which leave behind either regular or irregular spatiotemporal oscillations. Using a combination of analytical and numerical analysis, we show that the irregular behaviour arises from the instability of oscillations induced by the passage of the front. Finally, we discuss the generality of this mechanism as a way in which spatiotemporal irregularities can arise naturally in reaction-diffusion systems.     

Cosmology with Gravitational Waves: A Review

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3.     

The phase structure of the two-dimensionalN=2 Wess-Zumino model

We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291     

Comparison of methods for processing acoustic intensity from orthogonal multimicrophone probes

One design for three-dimensional multimicrophone probes is the four-microphone orthogonal design consisting of one microphone at an origin position with the other three microphones equally spaced along the three coordinate axes. Several distinct processing methods have been suggested for the estimation of active acoustic intensity with the orthogonal probe; however, the relative merits of each method have not been thoroughly studied. This comparative study is an investigation of the errors associated with each method. Considered are orthogonal probes consisting of matched point sensor microphones both freely suspended and embedded on the surface of a rigid sphere. Results are given for propagating plane-wave fields for all angles of incidence. It is shown that the lowest error for intensity magnitude results from having the microphones in a sphere and using just one microphone for the pressure estimate. For intensity direction, the lowest error results from having the microphones in a sphere and using Taylor approximations to estimate the particle velocity and pressure.     

Information Theories with Adversaries,Intrinsic Information,and Entanglement

There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I_M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions. It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.     

Functional MRI of working memory and selective attention in vibrotactile frequency discrimination

Background  

Focal lesions of the frontal, parietal and temporal lobe may interfere with tactile working memory and attention. To characterise the neural correlates of intact vibrotactile working memory and attention, functional MRI was conducted in 12 healthy young adults. Participants performed a forced-choice vibrotactile frequency discrimination task, comparing a cue stimulus of fixed frequency to their right thumb with a probe stimulus of identical or higher frequency. To investigate working memory, the time interval between the 2 stimuli was pseudo-randomized (either 2 or 8 s). To investigate selective attention, a distractor stimulus was occasionally presented contralaterally, simultaneous to the probe.