Amir Geranmayeh

Heart sound reproduction based on neural network classification of cardiac valve disorders using wavelet transforms of PCG signals

Cardiac auscultatory proficiency of physicians is crucial for accurate diagnosis of many heart diseases. Plenty of diverse abnormal heart sounds with identical main specifications and different details representing the ambient noise are indispensably needed to train, assess and improve the skills of medical students in recognizing and distinguishing the primary symptoms of the cardiac diseases. This paper proposes a versatile multiresolution wavelet-based algorithm to first extract the main statistical characteristics of three well-known heart valve disorders, namely the aortic insufficiency, the aortic stenosis, and the pulmonary stenosis sounds as well as the normal ones. An artificial neural network (ANN) and statistical classifier are then applied alternatively to choose proper exclusive features. Both classification approaches suggest using Daubechies wavelet filter with four vanishing moments within five decomposition levels for the most prominent distinction of the diseases. The proffered ANN is a multilayer perceptron structure with one hidden layer trained by a back-propagation algorithm (MLP-BP) and it elevates the percentage classification accuracy to 94.42. Ultimately, the corresponding main features are manipulated in wavelet domain so as to sequentially regenerate the individual counterparts of the underlying signals.

Protein secondary structure prediction using modular reciprocal bidirectional recurrent neural networks

The supervised learning of recurrent neural networks well-suited for prediction of protein secondary structures from the underlying amino acids sequence is studied. Modular reciprocal recurrent neural networks (MRR-NN) are proposed to model the strong correlations between adjacent secondary structure elements. Besides, a multilayer bidirectional recurrent neural network (MBR-NN) is introduced to capture the long-range intramolecular interactions between amino acids in formation of the secondary structure. The final modular prediction system is devised based on the interactive integration of the MRR-NN and the MBR-NN structures to arbitrarily engage the neighboring effects of the secondary structure types concurrent with memorizing the sequential dependencies of amino acids along the protein chain. The advanced combined network augments the percentage accuracy (Q₃) to 79.36% and boosts the segment overlap (SOV) up to 70.09% when tested on the PSIPRED dataset in three-fold cross-validation.

Proper Combination of Integrators and Interpolators for Stable Marching-on-in-Time Schemes

Mathematicians have proven that few specific collocation methods provide stable numerical solution for the delay differential equations provided the accuracy order of the finite difference approximation matches to that of the temporal interpolation. To adjoin this important conclusion to the development of stable time-domain field integral equation-based solvers, this paper investigates the impact of diverse proposed interpolators over conveniently usable integrators.

Survey of Temporal Basis Functions for Integral Equation Methods

To make the implicit marching-on-in-time schemes stable for practical applications, choices of appropriate temporal basis functions are investigated. The quadratic and cubic cardinal B-spline functions are introduced as new time bases for which the numerical solution of the electric field integral equation demonstrates that they can compete with the time shifted Lagrange interpolating functions in terms of accuracy and stability. It is shown that especially for small time step sizes using the analytical closed-form derivatives of the bases tremendously enhance the extension of the stable region in comparison with the results obtained using available consistent integrator-interpolator pairs.

Toeplitz property on order indices of Laguerre expansion methods

The unconditionally stable solution of time-domain integral equations by the classical marching-on-in-order schemes demands O(N<inf>t</inf>³N<inf>s</inf>²) CPU cycles, where N<inf>t</inf> and N<inf>s</inf> are the number of temporal and spatial unknowns, respectively. Discrete fast Fourier transform (FFT)-based algorithms are proffered to expedite the recursive temporal convolution products of the Toeplitz block aggregates of the retarded interaction matrices through which the overall computational cost and memory requirements reduces to O(α(N<inf>s</inf>)N<inf>t</inf>log(N<inf>t</inf>)) and O(N<inf>t</inf>α(N<inf>s</inf>)), respectively. Simulation results for arbitrarily shaped scatterers demonstrate the accuracy and efficiency of the technique.

Pruning neural networks for protein secondary structure prediction

Secondary structure prediction is an effective approach in deducing the three dimensional structure and functions of proteins. Although the multilayer neural network is currently used for the prediction, appropriate determination of the network size is yet an important factor in improving the performance of the network. In this work, two systematic approaches for pruning the oversized multilayer perceptron neural networks (MLP-NN) are proposed to determine the optimum size of the hidden layer. Using the RS126 dataset in seven-fold cross-validation, the percentage accuracy of the prediction reaches to 75.38.

Finite difference delay modeling of potential time integrals

The temporal discretization of the time-domain integral equations (TDIE) is commonly accomplished by either the implicit marching-on-in-time (MOT) schemes using subdomain Lagrange polynomial interpolations or the always-stable marching-on-in-order/degrees (MOD) of the entire-domain weighted Laguerre basis functions [1]. An alternative approach for discretizing the time convolution integrals in the TDIE, competitive to the time basis expansion in the MOT or MOD recipes, is the Lubichs convolution quadrature methods (CQM), using the (first or) second order backward finite difference (BFD) approximations in the Laplace domain [2]. The underlying physics describing the wave scattering process is time invariant, as the material properties do not change over time. The CQM are utilized to transform continuous-time representation of the time-invariant integral kernel (system transfer function) to discrete-time domain. The CQM are called finite difference delay modeling (FDDM) when the scattering analysis of arbitrarily shaped three-dimensional (3D) structures is carried out in a marching style [3].

Symplectic time integration methods for retarded potential integral equations

The numerical accuracy and energy conservation are of great importance in real-life electromagnetic (EM) problems, such as tracing the influence of excited wake fields inside accelerator structures on moving charge particles over long time periods. In practice, the essential property needed for accurate time-domain simulations is the fulfillment of the energy conservation law implied by Maxwell equations. Time-domain integral equations (TDIE) are commonly solved by the marching-on-intime (MOT) or marching-on-in-degree (MOD) methods [1]. Both discretization schemes employ the Galerkin method in space whereas only the MOT applies the point-matching for time testing. The Greens function is a reciprocal function of observation and source points distance |r − r′|, and hence, the Galerkin method clearly preserves the symmetry of a scattering operator and inherently can satisfy conservation of energy [2]. Due to the use of the Galerkin technique at the core stage of the TDIE formulations, similar to the frequency-domain method of moments, the evaluation of mutual interactions of subdomains demands computation of double surface integrals. The inner integrals over source subdomains have been calculated either analytically or numerically whereas to lessen the matrix fill-in costs, the outer surface integrals has been widely replaced by the centroid value of the integrand or approximated by a few fixed collocation points. Consequently, the equivalent resulting lossless scattering matrices are asymmetric for which the conservation of energy has been violated [2].

FFT Accelerated Marching-on-in-Order Methods

A fast, yet unconditionally stable, solution of time-domain electric field integral equations (EFIE) pertinent to the scattering analysis of uniformly meshed conducting structures is introduced. A discrete fast Fourier transform (FFT)-based algorithm is proffered to expedite the recursive spatial convolution products of the Toeplitz-block-Toeplitz retarded interaction matrices in a new marching-without-time-variable scheme. The total computational cost and storage requirements of the proposed method scales as O(N_t ² N_slog(N_s)) and O(N_tN_s), respectively, as opposed to O(N_t ² N_s ²) and O(N_tN² _s) for classical marching-on-in-order methods, where N_t and N_s are the number of temporal and spatial unknowns, respectively. Simulation results for long strip, platelike, and cylindrical scatterers demonstrate the accuracy and efficiency of the technique.

1/R 2 -Kernel cancelation in classical marching-on-in-time schemes

Cancelation of 1/R2-associated integrals in the numerical solution procedure of the time-domain magnetic field integral equations are explained to halve the computational costs of the classical marching-on-in-time (MOT) schemes in which the delay time is approximated by the barycentric electric distance of the subdomain patches. The new technique improves the accuracy of the MOT as the resulting interpolation coefficients for the calculation of the impedance matrices became independent of the electrical distance of surface elements. Additionally, the analytical closed-form expressions for the evaluation of the remaining 1/R3-associated integrals allow the fast computation of the retarded matrices on demand. The applicability of the scheme to large-scale wave scattering problems is investigated.