Random matrices with equispaced external source

We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends to infinity. We obtain strong asymptotics for the multiple orthogonal polynomials associated to these models, and as a consequence for the average characteristic polynomials. One feature of the multiple orthogonal polynomials analyzed in this paper is that the number of orthogonality weights of the polynomials grows with the degree. Nevertheless we are able to characterize them in terms of a pair of 2 x 1 vector-valued Riemann-Hilbert problems, and to perform an asymptotic analysis of the Riemann-Hilbert problems.Comment: 53 pages, 9 figures; textual changes and minor typos correcte

VHDL-AMS based genetic optimisation of fuzzy logic controllers

Purpose – This paper presents a VHDL-AMS based genetic optimisation methodology for fuzzy logic controllers (FLCs) used in complex automotive systems and modelled in mixed physical domains. A case study applying this novel method to an active suspension system has been investigated to obtain a new type of fuzzy logic membership function with irregular shapes optimised for best performance. Design/methodology/approach – The geometrical shapes of the fuzzy logic membership functions are irregular and optimised using a genetic algorithm (GA). In this optimisation technique, VHDL-AMS is used not only for the modelling and simulation of the FLC and its underlying active suspension system but also for the implementation of a parallel GA directly in the system testbench. Findings – Simulation results show that the proposed FLC has superior performance in all test cases to that of existing FLCs that use regular-shape, triangular or trapezoidal membership functions. Research limitations – The test of the FLC has only been done in the simulation stage, no physical prototype has been made. Originality/value – This paper proposes a novel way of improving the FLC’s performance and a new application area for VHDL-AMS

VHDL-AMS based genetic optimization of a fuzzy logic controller for automotive active suspension systems

This paper presents a new type of fuzzy logic controller (FLC) membership functions for automotive active suspension systems. The shapes of the membership functions are irregular and optimized using a genetic algorithm (GA). In this optimization technique, VHDL-AMS is used not only for the modeling and simulation of the fuzzy logic controller and its underlying active suspension system but also for the implementation of a parallel GA. Simulation results show that the proposed FLC has superior performance to that of existing FLCs that use triangular or trapezoidal membership functions

VHDL-AMS modeling of an automotive vibration isolation seating system

This paper presents VHDL-AMS model of an automotive vibration isolation seating system with an active electromechanical actuator. Five control algorithms for the actuator are implemented and their efficiencies are investigated by subjecting the system to a number of stimuli, such as a single jolt or noisy harmonic excitations. Simulations were carried out using the SystemVision simulator and results are shown to compare the relative performance merits of the control methods

Adaptive Mesh Fluid Simulations on GPU

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.Comment: Submitted to New Astronom

Effect of influent nutrient ratios and hydraulic retention time (HRT) on simultaneous phosphorus and nitrogen removal in a two-sludge sequencing batch reactor process

A laboratory-scale anaerobic–anoxic/nitrification sequencing batch reactor (A2N- SBR) fed with domestic wastewater was operated to examine the effect of varying ratios of influent COD/P, COD/TN and TN/P on the nutrient removal. With the increased COD/P, the phosphorus removals exhibited an upward trend. The influent TN/P ratios had a positive linear correlation with the phosphorus removal efficiencies, mainly because nitrates act as electron acceptors for the phosphorus uptake in the A2N-SBR. Moreover, it was found that lower COD/TN ratio, e.g. 3.5, did not significantly weaken the phosphorus removal, though the nitrogen removal first decreased greatly. The optimal phosphorus and nitrogen removals of 94% and 91%, respectively were achieved with influent COD/P and COD/ TN ratios of 19.9 and 9.9, respectively. Additionally, a real-time control strategy for A2N-SBR can be undertaken based on some characteristic points of pH, redox potential (ORP) and dissolved oxygen (DO) profiles in order to obtain the optimum hydraulic retention time (HRT) and improve the operating reliabili

SystemC-A modeling of an automotive seating vibration isolation system

A modeling methodology for mixed physical domains system in a new modelling Language is presented. The system is automotive seating vibration isolation system with electronic control. It is described and simulated in SystemCA, an extended version of SystemC which provides analogue, mixed-signal and mixed-domain modeling capabilities. Results show that SystemC-A provides efficient means to model and investigate performance of complex mixed-domain systems for automotive applications

Automatic Brain Tumor Segmentation using Cascaded Anisotropic Convolutional Neural Networks

A cascade of fully convolutional neural networks is proposed to segment multi-modal Magnetic Resonance (MR) images with brain tumor into background and three hierarchical regions: whole tumor, tumor core and enhancing tumor core. The cascade is designed to decompose the multi-class segmentation problem into a sequence of three binary segmentation problems according to the subregion hierarchy. The whole tumor is segmented in the first step and the bounding box of the result is used for the tumor core segmentation in the second step. The enhancing tumor core is then segmented based on the bounding box of the tumor core segmentation result. Our networks consist of multiple layers of anisotropic and dilated convolution filters, and they are combined with multi-view fusion to reduce false positives. Residual connections and multi-scale predictions are employed in these networks to boost the segmentation performance. Experiments with BraTS 2017 validation set show that the proposed method achieved average Dice scores of 0.7859, 0.9050, 0.8378 for enhancing tumor core, whole tumor and tumor core, respectively. The corresponding values for BraTS 2017 testing set were 0.7831, 0.8739, and 0.7748, respectively.Comment: 12 pages, 5 figures. MICCAI Brats Challenge 201

Correlation kernels for sums and products of random matrices

Let $X$ be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared singular values of $GX$ and $TX$, where $G$ is a complex Ginibre matrix and $T$ is a truncated unitary matrix. We also consider the product of $X$ and several complex Ginibre/truncated unitary matrices. As an application, we derive the precise condition for the squared singular values of the product of several truncated unitary matrices to follow a polynomial ensemble. We also consider the sum $H + M$ where $H$ is a GUE matrix and $M$ is a random matrix whose eigenvalue density is a polynomial ensemble. We show that the eigenvalues of $H + M$ follow a polynomial ensemble whose correlation kernel can be expressed as a double contour integral. As an application, we point out a connection to the two-matrix model.Comment: 33 pages, some changes suggested by the referee is made and some references are adde