Numerical evaluation of the incomplete airy functions and their application to high frequency scattering and diffraction

The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals of such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. Here, a convergent series solution form for the incomplete Airy functions is derived. Asymptotic expansions involving several terms were also developed and serve as large argument approximations. The combination of the series solution form with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data

Home monitoring of foot skin temperatures to prevent ulceration

OBJECTIVE - To evaluate the effectiveness of at-home infrared temperature monitoring as a preventative tool in individuals at high risk for diabetes-related lower-extremity ulceration and amputation. RESEARCH DESIGN AND METHODS - Eighty-five patients who fit diabetic foot risk category 2 or 3 (neuropathy and foot deformity or previous history of ulceration or partial foot amputation) were randomized into a standard therapy group (n = 41) or an enhanced therapy group (n = 44). Standard therapy consisted of therapeutic footwear, diabetic foot education, and regular foot evaluation by a podiatrist. Enhanced therapy included the addition of a handheld infrared skin thermometer to measure temperatures on the sole of the foot in the morning and evening. Elevated temperatures (>4°F compared with the opposite foot) were considered to be "at risk" of ulceration due to inflammation at the site of measurement. When foot temperatures were elevated, subjects were instructed to reduce their activity and contact the study nurse. Study subjects were followed for 6 months. RESULTS - The enhanced therapy group had significantly fewer diabetic foot complications (enhanced therapy group 2% vs. standard therapy group 20%, P = 0.01, odds ratio 10.3, 95% CI 1.2-85.3). There were seven ulcers and two Charcot fractures among standard therapy patients and one ulcer in the enhanced therapy group. CONCLUSIONS - These results suggest that at-home patient self-monitoring with daily foot temperatures may be an effective adjunctive tool to prevent foot complications in individuals at high risk for lower-extremity ulceration and amputation

Creative tools for producing realistic 3D facial expressions and animation

Creative exploration of realistic 3D facial animation is a popular but very challenging task due to the high level knowledge and skills required. This forms a barrier for creative individuals who have limited technical skills but wish to explore their creativity in this area. This paper proposes a new technique that facilitates users’ creative exploration by hiding the technical complexities of producing facial expressions and animation. The proposed technique draws on research from psychology, anatomy and employs Autodesk Maya as a use case by developing a creative tool, which extends Maya’s Blend Shape Editor. User testing revealed that novice users in the creative media, employing the proposed tool can produce rich and realistic facial expressions that portray new interesting emotions. It reduced production time by 25% when compared to Maya and by 40% when compared to 3DS Max equivalent tools

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results

Finite Word Length FIR Filter Design Using Integer Programming Over a Discrete Coefficient Space

The article of record as published may be found at http://dx.doi.org/10.1109/TASSP.1982.1163925Published in: IEEE Transactions on Acoustics, Speech, and Signal Processing (Volume: 30 , Issue: 4 , Aug 1982)It is demonstrated that the improvement achieved by using integer programming over simple coefficient rounding in the design of finite impulse response (FIR) filters with discrete coefficients is most significant when the discrete coefficient space is the powers-of-two space or when a specification is to be met with a given coefficient word length by increasing the filter length. Both minimax and least square error criteria are considered

Fast, quantitative, murine cardiac ¹⁹F MRI/MRS of PFCE-labeled progenitor stem cells and macrophages at 9.4T

Purpose: To a) achieve cardiac ¹⁹F-Magnetic Resonance Imaging (MRI) of perfluoro-crown-ether (PFCE) labeled cardiac progenitor stem cells (CPCs) and bone-derived bone marrow macrophages, b) determine label concentration and cellular load limits, and c) achieve spectroscopic and image-based quantification. Methods: Theoretical simulations and experimental comparisons of spoiled-gradient echo (SPGR), rapid acquisition with relaxation enhancement (RARE), and steady state at free precession (SSFP) pulse sequences, and phantom validations, were conducted using ¹⁹F MRI/Magnetic Resonance Spectroscopy (MRS) at 9.4 T. Successful cell labeling was confirmed using flow cytometry and confocal microscopy. For CPC and macrophage concentration quantification, in vitro and post-mortem cardiac validations were pursued with the use of the transfection agent FuGENE. Feasibility of fast imaging is demonstrated in murine cardiac acquisitions in vivo, and in post-mortem murine skeletal and cardiac applications. Results: SPGR/SSFP proved favorable imaging sequences yielding good signal-to-noise ratio values. Confocal microscopy confirmed heterogeneity of cellular label uptake in CPCs. ¹⁹F MRI indicated lack of additional benefits upon label concentrations above 7.5–10 mg/ml/million cells. The minimum detectable CPC load was ~500k (~10k/voxel) in two-dimensional (2D) acquisitions (3–5 min) using the butterfly coil. Additionally, absolute ¹⁹F based concentration and intensity estimates (trifluoroacetic-acid solutions, macrophages, and labeled CPCs in vitro and post-CPC injections in the post-mortem state) scaled linearly with fluorine concentrations. Fast, quantitative cardiac ¹⁹F-MRI was demonstrated with SPGR/SSFP and MRS acquisitions spanning 3–5 min, using a butterfly coil. Conclusion: The developed methodologies achieved in vivo cardiac ¹⁹F of exogenously injected labeled CPCs for the first time, accelerating imaging to a total acquisition of a few minutes, providing evidence for their potential for possible translational work

In Vivo Tracking and 1H/19F Magnetic Resonance Imaging of Biodegradable Polyhydroxyalkanoate / Polycaprolactone Blend Scaffolds Seeded with Labeled Cardiac Stem Cells

Medium-chain length Polyhydroxyalkanoates (MCL-PHAs) have demonstrated exceptional properties for cardiac tissue engineering (CTE) applications. Despite prior work on MCL-PHA/Polycaprolactone (PCL) blends, optimal scaffold production and use as an alternative delivery route for controlled release of seeded cardiac progenitor cells (CPCs) in CTE applications in vivo has been lacking, We present herein applicability of MCL-PHA/PCL (95/5 wt%) blends fabricated as thin films with an improved performance compared to the neat MCL-PHA aiming to a) benefit from the material properties of natural and synthetic polymers, b) achieve controlled delivery and increase retention of delivered cells to the murine myocardium, c) extend the temporal window over which the release of labeled CPCs occurs compared to traditional direct injection techniques, and d) use 19F MRI/MRS to noninvasively detect, and longitudinally monitor the seeded scaffolds. Polymer characterization confirmed the chemical structure and composition of the synthesized scaffolds, while thermal, wettability, and mechanical properties were also investigated and compared in neat and porous counterparts. In vitro cytocompatibility studies were performed using perfluorocrown-ether (PFCE)-nanoparticle-labeled murine cardiac progenitor cells (CPC), and studied using confocal microscopy and 19F MRS/MRI. Seeded scaffolds were implanted and studied in the post-mortem murine heart in situ, and in two additional C57BL/6 mice in vivo (using single-layered and double-layered scaffolds) and imaged immediately after and at 7 days post-implantation. Superior MCL-PHA/PCL scaffold performance has been demonstrated compared to MCL-PHA through experimental comparisons of a) morphological data using scanning electron microscopy and b) contact angle measurements attesting to improved CPC adhesion, c) in vitro confocal microscopy showing increased SC proliferative capacity, d) mechanical testing that elicited good overall responses. In vitro MRI results justify the increased seeding density, increased in vitro MRI signal, and improved MRI visibility in vivo, in the double-layered compared to the single-layered scaffolds. Histological evaluations (bright-field, cytoplasmic (Atto647) and nuclear (DAPI) stains) performed in conjunction with confocal microscopy imaging attest to CPC binding within the scaffold, subsequent release and migration to the neighboring myocardium, and to increased retention in the murine myocardium in the case of the double-layered scaffold. Thus MCL-PHA/PCL blends possess tremendous potential for controlled delivery of CPCs and to maximize possible regeneration in myocardial infarction

Methodology for Jointly Assessing Myocardial Infarct Extent and Regional Contraction in 3-D CMRI

Automated extraction of quantitative parameters from Cardiac Magnetic Resonance Images (CMRI) is crucial for the management of patients with myocardial infarct. This work proposes a post-processing procedure to jointly analyze Cine and Delayed-Enhanced (DE) acquisitions in order to provide an automatic quantification of myocardial contraction and enhancement parameters and a study of their relationship. For that purpose, the following processes are performed: 1) DE/Cine temporal synchronization and 3D scan alignment, 2) 3D DE/Cine rigid registration in a region about the heart, 3) segmentation of the myocardium on Cine MRI and superimposition of the epicardial and endocardial contours on the DE images, 4) quantification of the Myocardial Infarct Extent (MIE), 5) study of the regional contractile function using a new index, the Amplitude to Time Ratio (ATR). The whole procedure was applied to 10 patients with clinically proven myocardial infarction. The comparison between the MIE and the visually assessed regional function scores demonstrated that the MIE is highly related to the severity of the wall motion abnormality. In addition, it was shown that the newly developed regional myocardial contraction parameter (ATR) decreases significantly in delayed enhanced regions. This largely automated approach enables a combined study of regional MIE and left ventricular function

Automatic generation of multi-precision multi-arithmetic CNN accelerators for FPGAs

Modern deep Convolutional Neural Networks (CNNs) are computationally demanding, yet real applications often require high throughput and low latency. To help tackle these problems, we propose Tomato, a framework designed to automate the process of generating efficient CNN accelerators. The generated design is pipelined and each convolution layer uses different arithmetics at various precisions. Using Tomato, we showcase state-of-the-art multi-precision multi-arithmetic networks, including MobileNet-V1, running on FPGAs. To our knowledge, this is the first multi-precision multi-arithmetic auto-generation framework for CNNs. In software, Tomato fine-tunes pretrained networks to use a mixture of short powers-of-2 and fixed-point weights with a minimal loss in classification accuracy. The fine-tuned parameters are combined with the templated hardware designs to automatically produce efficient inference circuits in FPGAs. We demonstrate how our approach significantly reduces model sizes and computation complexities, and permits us to pack a complete ImageNet network onto a single FPGA without accessing off-chip memories for the first time. Furthermore, we show how Tomato produces implementations of networks with various sizes running on single or multiple FPGAs. To the best of our knowledge, our automatically generated accelerators outperform closest FPGA-based competitors by at least 2-4x for lantency and throughput; the generated accelerator runs ImageNet classification at a rate of more than 3000 frames per second.EPSRC Doctoral Scholarship Peterhouse Graduate Studentshi