An FPGA Architecture for Extracting Real-Time Zernike Coefficients from Measured Phase Gradients

Zernike modes are commonly used in adaptive optics systems to represent optical wavefronts. However, real-time calculation of Zernike modes is time consuming due to two factors: the large factorial components in the radial polynomials used to define them and the large inverse matrix calculation needed for the linear fit. This paper presents an efficient parallel method for calculating Zernike coefficients from phase gradients produced by a Shack-Hartman sensor and its real-time implementation using an FPGA by pre-calculation and storage of subsections of the large inverse matrix. The architecture exploits symmetries within the Zernike modes to achieve a significant reduction in memory requirements and a speed-up of 2.9 when compared to published results utilising a 2D-FFT method for a grid size of 8×8. Analysis of processor element internal word length requirements show that 24-bit precision in precalculated values of the Zernike mode partial derivatives ensures less than 0.5% error per Zernike coefficient and an overall error of <1%. The design has been synthesized on a Xilinx Spartan-6 XC6SLX45 FPGA. The resource utilisation on this device is <3% of slice registers, <15% of slice LUTs, and approximately 48% of available DSP blocks independent of the Shack-Hartmann grid size. Block RAM usage is <16% for Shack-Hartmann grid sizes up to 32×32

Non-topological solitons in brane world models

We examine some general properties of a certain class of scalar filed theory models containing non-topological soliton solutions in the context of brane world models with compact large extra dimensions. If a scalar field is allowed to propagate in extra space, then, beside standard Kaluza-Klein type excitations, a whole new class of very massive soliton-type states can exist. Depending on their abundance, they can be important dark matter candidates or give significant contribution to entropy and energy density in our universe. .Comment: version accepted for publication in Physical Review

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

The Fokker-Planck equation for bistable potential in the optimized expansion

The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to agree well with the exact solution of the Fokker-Planck equation. Even for a bistable system the whole period of evolution to equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an

A phospholipase D2 inhibitor, CAY10594, ameliorates acetaminophen-induced acute liver injury by regulating the phosphorylated-GSK-3 beta/JNK axis

We examined the role of phospholipase D2 (PLD2) on acetaminophen (APAP)-induced acute liver injury using a PLD2 inhibitor (CAY10594). 500 mg/kg of APAP challenge caused acute liver damage. CAY10594 administration markedly blocked the acute liver injury in a dose-dependent manner, showing almost complete inhibition with 8 mg/kg of CAY10594. During the pathological progress of acute liver injury, GSH levels are decreased, and this is significantly recovered upon the administration of CAY10594 at 6 hours post APAP challenge. GSK-3 beta (Serine 9)/JNK phosphorylation is mainly involved in APAPinduced liver injury. CAY10594 administration strongly blocked GSK-3 beta (Serine 9)/JNK phosphorylation in the APAP-induced acute liver injury model. Consistently, sustained JNK activation in the cytosol and mitochondria from hepatocytes were also decreased in CAY10594-treated mice. Many types of immune cells are also implicated in APAP-induced liver injury. However, neutrophil and monocyte populations were not different between vehicle- and CAY10594-administered mice which are challenged with APAP. Therapeutic administration of CAY10594 also significantly attenuated liver damage caused by the APAP challenge, eliciting an enhanced survival rate. Taken together, these results indicate that PLD2 is involved in the intrinsic response pathway of hepatocytes driving the pathogenesis of APAP-induced acute liver injury, and PLD2 may therefore represent an important therapeutic target for patients with drug-induced liver injury.11Ysciescopu