A gradient descent algorithm for minimizing amino acid coupling reactions when synthesizing cyclic-peptide libraries

Combinatorial chemistry has become an invaluable tool in medicinal chemistry for the identification of new drug leads. For example, libraries of predetermined sequences and head-to-tail cyclized peptides are routinely synthesized in our laboratory using the IRORI approach. Such libraries are used as molecular toolkits that enable the development of pharmacophores that define activity and specificity at receptor targets. These libraries can be quite large and difficult to handle, due to physical and chemical constraints imposed by their size. Therefore, smaller sub-libraries are often targeted for synthesis. The number of coupling reactions required can be greatly reduced if the peptides having common amino acids are grouped into the same sub-library (batching). This paper describes a schedule optimizer to minimize the number of coupling reactions by rotating and aligning sequences while simultaneously batching. The gradient descent method thereby reduces the number of coupling reactions required for synthesizing cyclic peptide libraries. We show that the algorithm results in a 75% reduction in the number of coupling reactions for a typical cyclic peptide library.

Ultra-Fast Gradient LC Method for Omeprazole Analysis Using a Monolithic Column: Assay Development, Validation, and Application to the Quality Control of Omeprazole Enteric-Coated Pellets

A method was optimized for the analysis of omeprazole (OMZ) by ultra-high speed LC with diode array detection using a monolithic Chromolith Fast Gradient RP 18 endcapped column (50 x 2.0 mm id). The analyses were performed at 30 degrees C using a mobile phase consisting of 0.15% (v/v) trifluoroacetic acid (TFA) in water (solvent A) and 0.15% (v/v) TFA in acetonitrile (solvent B) under a linear gradient of 5 to 90% B in 1 min at a flow rate of 1.0 mL/min and detection at 220 nm. Under these conditions, OMZ retention time was approximately 0.74 min. Validation parameters, such as selectivity, linearity, precision, accuracy, and robustness, showed results within the acceptable criteria. The method developed was successfully applied to OMZ enteric-coated pellets, showing that this assay can be used in the pharmaceutical industry for routine QC analysis. Moreover, the analytical conditions established allow for the simultaneous analysis of OMZ metabolites, 5-hydroxyomeprazole and omeprazole sulfone, in the same run, showing that this method can be extended to other matrixes with adequate procedures for sample preparation.

A Gradient-Type Method For Real-Time State Estimation Of Water Distribution Networks

Drinking water distribution networks risk exposure to malicious or accidental contamination. Several levels of responses are conceivable. One of them consists to install a sensor network to monitor the system on real time. Once a contamination has been detected, this is also important to take appropriate counter-measures. In the SMaRT-OnlineWDN project, this relies on modeling to predict both hydraulics and water quality. An online model use makes identification of the contaminant source and simulation of the contaminated area possible. The objective of this paper is to present SMaRT-OnlineWDN experience and research results for hydraulic state estimation with sampling frequency of few minutes. A least squares problem with bound constraints is formulated to adjust demand class coefficient to best fit the observed values at a given time. The criterion is a Huber function to limit the influence of outliers. A Tikhonov regularization is introduced for consideration of prior information on the parameter vector. Then the Levenberg-Marquardt algorithm is applied that use derivative information for limiting the number of iterations. Confidence intervals for the state prediction are also given. The results are presented and discussed on real networks in France and Germany.

Rapid determination of zinc in foods by flow injection analysis with flame AAS using gradient calibration method

A calibration method was developed using flow injection analysis (FI) with a Gradient Calibration Method (GCM). The method allows the rapid determination of zinc In foods (approximately 30 min) after treatment with concentrated sulphuric acid and 30% hydrogen peroxide, and analysis with flame atomic absorption spectrometry (FAAS). The method provides analytical results with a relative standard deviation of about 2% and requires less time than by conventional FI calibration. The electronic selection of different segments along the gradient and monitoring of the technique covers wide concentration ranges while maintaining the inherent high precision of flow injection analysis. Concentrations, flow rates, and flow times of the reagents were optimized in order to obtain best accuracy and precision. Flow rates of 10 mL/min were selected for zinc. In addition, the system enables electronic dilution and calibration where a multipoint curve can be constructed using a single sample injection.

Particle tracking in a salinity gradient: A method for measuring sinking rate of individual phytoplankton in the laboratory

This paper presents a new method to measure the sinking rates of individual phytoplankton “particles” (cells, chains, colonies, and aggregates) in the laboratory. Conventional particle tracking and high resolution video imaging were used to measure particle sinking rates and particle size. The stabilizing force of a very mild linear salinity gradient (1 ppt over 15 cm) prevented the formation of convection currents in the laboratory settling chamber. Whereas bulk settling methods such as SETCOL provide a single value of sinking rate for a population, this method allows the measurement of sinking rate and particle size for a large number of individual particles or phytoplankton within a population. The method has applications where sinking rates vary within a population, or where sinking rate-size relationships are important. Preliminary data from experiments with both laboratory and field samples of marine phytoplankton are presented here to illustrate the use of the technique, its applications, and limitations. Whereas this paper deals only with sinking phytoplankton, the method is equally valid for positively buoyant species, as well as nonbiological particles.

Dynamics of on-line gradient descent learning for multilayer neural networks

We consider the problem of on-line gradient descent learning for general two-layer neural networks. An analytic solution is presented and used to investigate the role of the learning rate in controlling the evolution and convergence of the learning process.

Computationally efficient natural gradient descent

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Jointly multi-user detection and channel estimation with genetic algorithm

This work aims at proposing the use of the evolutionary computation methodology in order to jointly solve the multiuser channel estimation (MuChE) and detection problems at its maximum-likelihood, both related to the direct sequence code division multiple access (DS/CDMA). The effectiveness of the proposed heuristic approach is proven by comparing performance and complexity merit figures with that obtained by traditional methods found in literature. Simulation results considering genetic algorithm (GA) applied to multipath, DS/CDMA and MuChE and multi-user detection (MuD) show that the proposed genetic algorithm multi-user channel estimation (GAMuChE) yields a normalized mean square error estimation (nMSE) inferior to 11%, under slowly varying multipath fading channels, large range of Doppler frequencies and medium system load, it exhibits lower complexity when compared to both maximum likelihood multi-user channel estimation (MLMuChE) and gradient descent method (GrdDsc). A near-optimum multi-user detector (MuD) based on the genetic algorithm (GAMuD), also proposed in this work, provides a significant reduction in the computational complexity when compared to the optimum multi-user detector (OMuD). In addition, the complexity of the GAMuChE and GAMuD algorithms were (jointly) analyzed in terms of number of operations necessary to reach the convergence, and compared to other jointly MuChE and MuD strategies. The joint GAMuChE-GAMuD scheme can be regarded as a promising alternative for implementing third-generation (3G) and fourth-generation (4G) wireless systems in the near future. Copyright (C) 2010 John Wiley & Sons, Ltd.

On the determination of epsilon during discriminative GMM training

Discriminative training of Gaussian Mixture Models (GMMs) for speech or speaker recognition purposes is usually based on the gradient descent method, in which the iteration step-size, ε, uses to be defined experimentally. In this letter, we derive an equation to adaptively determine ε, by showing that the second-order Newton-Raphson iterative method to find roots of equations is equivalent to the gradient descent algorithm. © 2010 IEEE.

Reliable estimation of dense optical flow fields with large displacements

[EN] In this paper we show that a classic optical flow technique by Nagel and Enkelmann can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that avoid inconsistencies caused by centering the brightness term and the smoothness term in different images use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and create an energy functional that is invariant under linear brightness changes.  Applying a gradient descent method to the resulting energy functional leads to a system of diffusion-reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100% density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the classic optical flow methods with 100%  density that are evaluated by Barron et al. (1994). Our software is available from the Internet.

Dense disparity map estimation respecting image discontinuities

[EN] We present an energy based approach to estimate a dense disparity map from a set of two weakly calibrated stereoscopic images while preserving its discontinuities resulting from image boundaries. We first derive a simplified expression for the disparity that allows us to estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the Nagel-Enkelmann operator. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method The resulting parabolic problem has a unique solution. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scalespace. Experimental results on both synthetic and real images arere presented to illustrate the capabilities of this PDE and scale-space based method.

A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.

Registration and fusion of contrast-enhanced MRI myocardial substrate maps and X-ray angiograms

The aim of this work is to provide the necessary methods to register and fuse the endo-epicardial signal intensity (SI) maps extracted from contrast-enhanced magnetic resonance imaging (ceMRI) with X-ray coronary ngiograms using an intrinsic registrationbased algorithm to help pre-planning and guidance of catheterization procedures. Fusion of angiograms with SI maps was treated as a 2D-3D pose estimation, where each image point is projected to a Plücker line, and the screw representation for rigid motions is minimized using a gradient descent method. The resultant transformation is applied to the SI map that is then projected and fused on each angiogram. The proposed method was tested in clinical datasets from 6 patients with prior myocardial infarction. The registration procedure is optionally combined with an iterative closest point algorithm (ICP) that aligns the ventricular contours segmented from two ventriculograms.

Natural gradient matrix momentum

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.