Modeling round-off error in the fast gradient method for predictive control

We present a method for determining the smallest precision required to have algorithmic stability of an implementation of the Fast Gradient Method (FGM) when solving a linear Model Predictive Control (MPC) problem in fixed-point arithmetic. We derive two models for the round-off error present in fixed-point arithmetic. The first is a generic model with no assumptions on the predicted system or weight matrices. The second is a parametric model that exploits the Toeplitz structure of the MPC problem for a Schur-stable system. We also propose a metric for measuring the amount of round-off error the FGM iteration can tolerate before becoming unstable. This metric is combined with the round-off error models to compute the minimum number of fractional bits needed for the fixed-point data type. Using these models, we show that exploiting the MPC problem structure nearly halves the number of fractional bits needed to implement an example problem. We show that this results in significant decreases in resource usage, computational energy and execution time for an implementation on a Field Programmable Gate Array

Horizon-independent preconditioner design for linear predictive control

First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is significantly affected by the conditioning of the problem data, with ill-conditioned problems requiring a large number of iterations. To reduce the number of iterations required, we present a simple method for computing a horizon-independent preconditioning matrix for the Hessian of the condensed problem. The preconditioner is based on the block Toeplitz structure of the Hessian. Horizon-independence allows one to use only the predicted system and cost matrices to compute the preconditioner, instead of the full Hessian. The proposed preconditioner has equivalent performance to an optimal preconditioner in numerical examples, producing speedups between 2x and 9x for the Fast Gradient Method. Additionally, we derive horizon-independent spectral bounds for the Hessian in terms of the transfer function of the predicted system, and show how these can be used to compute a novel horizon-independent bound on the condition number for the preconditioned Hessian

High-level synthesis using the Julia language

The growing proliferation of FPGAs and High-level Synthesis (HLS) tools has led to a large interest in designing hardware accelerators for complex operations and algorithms. However, existing HLS toolflows typically require a significant amount of user knowledge or training to be effective in both industrial and research applications. In this paper, we propose using the Julia language as the basis for an HLS tool. The Julia HLS tool aims to decrease the barrier to entry for hardware acceleration by taking advantage of the readability of the Julia language and by allowing the use of the existing large library of standard mathematical functions written in Julia. We present a prototype Julia HLS tool, written in Julia, that transforms Julia code to VHDL. We highlight how features of Julia and its compiler simplified the creation of this tool, and we discuss potential directions for future work

Approximate logic synthesis: a survey

Approximate computing is an emerging paradigm that, by relaxing the requirement for full accuracy, offers benefits in terms of design area and power consumption. This paradigm is particularly attractive in applications where the underlying computation has inherent resilience to small errors. Such applications are abundant in many domains, including machine learning, computer vision, and signal processing. In circuit design, a major challenge is the capability to synthesize the approximate circuits automatically without manually relying on the expertise of designers. In this work, we review methods devised to synthesize approximate circuits, given their exact functionality and an approximability threshold. We summarize strategies for evaluating the error that circuit simplification can induce on the output, which guides synthesis techniques in choosing the circuit transformations that lead to the largest benefit for a given amount of induced error. We then review circuit simplification methods that operate at the gate or Boolean level, including those that leverage classical Boolean synthesis techniques to realize the approximations. We also summarize strategies that take high-level descriptions, such as C or behavioral Verilog, and synthesize approximate circuits from these descriptions

Undiagnosed Primary Hyperparathyroidism and Recurrent Miscarriage: The First Prospective Pilot Study.

BACKGROUND: Primary hyperparathyroidism (pHPT) in pregnancy is reported to be associated with significant maternal and foetal complications and an up to threefold increase in the risk of miscarriage. However, the true incidence of pHPT in pregnancy, complete and miscarried, is unknown and there are no data on the prevalence of undiagnosed pHPT in recurrent miscarriage (RM) (≥3 consecutive miscarriages under 24-week gestation). This is the first prospective study aiming to establish the prevalence of undiagnosed pHPT in RM. METHODS: Following UK National ethics committee approval, women who had experienced 3 or more consecutive miscarriages were recruited from a nationwide RM clinic. Serum corrected calcium, phosphate, PTH and vitamin D were evaluated. Patients with raised serum calcium and/or PTH were recalled for confirmatory tests. Power calculations suggested that a minimum of 272 patients were required to demonstrate a clinically significant incidence of pHPT. RESULTS: Three hundred women were recruited, median age 35 years (range 19-42). Eleven patients had incomplete data, leaving 289 patients suitable for analysis; 50/289 patients (17%) with abnormal tests were recalled. The prevalence of vitamin D deficiency (<25 nmol/l) and insufficiency (25-75 nmol/l) was 8.7 and 67.8%, respectively. One patient was diagnosed with pHPT (0.34%) and underwent successful parathyroidectomy. CONCLUSIONS: The prevalence of undiagnosed pHPT (0.34%) in RM in this study appears to be many times greater than the 0.05% expected in this age group. The findings of this pilot study merit follow-up with a larger-scale study. Routine serum calcium estimation is not currently undertaken in RM and should be considered

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

Multianalytical study of patina formed on archaeological metal objects from Bliesbruck-Reinheim

Patinas naturally formed on archaeological bronze alloys were characterized using light microscopy (LM), micro energy dispersive X-ray fluorescence analysis (mu-EDXRF), time of flight secondary ion mass spectrometry (TOF-SIMS) and scanning electron microscopy in combination with energy dispersive X-ray microanalysis (SEM/EDX). The examinations carried out on cross-sections of samples have shown that in all samples the copper content in the corrosion layer is lower than in the bulk, while an increase of tin and lead could be observed. Two different types of corrosion were found: first type, a corrosion formation leading to a three layer structure was observed on lead bronze. The outer layer consists mainly of Cu(II) compounds and soil material, followed by a fragmented layer of cuprous oxide and the surface layer of the alloy, where a depletion of copper and an enrichment of tin and high amounts of Cl could be detected, The second type of corrosion is characterized by a two layer structure on the tin bronze sample consisting of an outer layer with copper containing corrosion products and a layer with cracks, which reveals a depletion of copper whereas tin and lead are enriched. Also high amounts of Si were detected in this surface layer

Spinal versus General Anaesthesia in Postoperative Pain Management during Transurethral Procedures

We compared the analgesic efficacy of spinal and general anaesthesia following transurethral procedures. 97 and 47 patients underwent transurethral bladder tumour resection (TUR-B) and transurethral prostatectomy (TUR-P), respectively. Postoperative pain was recorded using an 11-point visual analogue scale (VAS). VAS score was greatest at discharge from recovery room for general anaesthesia (P = 0.027). The pattern changed significantly at 8 h and 12 h for general anaesthesia's efficacy (P = 0.017 and P = 0.007, resp.). A higher VAS score was observed in pT2 patients. Patients with resected tumour volume >10 cm3 exhibited a VAS score >3 at 8 h and 24 h (P = 0.050, P = 0.036, resp.). Multifocality of bladder tumours induced more pain overall. It seems that spinal anaesthesia is more effective during the first 2 postoperative hours, while general prevails at later stages and at larger traumatic surfaces. Finally, we incidentally found that tumour stage plays a significant role in postoperative pain, a point that requires further verification

Reliability Based Factors of Safety for VIV Fatigue Using NDP Riser High Mode VIV Tests

Understanding the level of conservatism in a riser system design for vortex-induced vibration (VIV) fatigue is an important issue for operators. This study represents a demonstration of the calibration methodology to derive consistent values for the Factor of Safety (FoS). The exercise is performed here based on medium scale VIV data and utilizing the most commonly used VIV prediction software by industry. The results emphasize the need for (i) a coherent approach to estimate the FoS to be used and (ii) monitoring/measurement of software improvements as this may increase risk of failure if the influence of such improvements on the FoS is not quantified.DeepStar (Consortium) (DeepStar Phase IX