A multiplicative Gauss-Newton minimization algorithm:Theory and application to exponential functions

Multiplicative calculus(MUC) measures the rate of change of function in terms of ratios, which makes the exponential functions significantly linear in the framework of MUC.Therefore, a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC. Taking this as motivation, this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM) algorithm in the framework of MUC. This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM) method along with its convergence properties.The proposed method is generalized for n number of variables, and all its theoretical concepts are authenticated by simulation results. Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions. From simulation results, it has been observed that proposed MGNM method converges for 12972 points, out of 19600 points considered while optimizing multiplicatively-linear exponential function, whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points, respectively. Furthermore, for a given set of initial value, the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods. A similar pattern is observed for multiplicatively-non-linear exponential function. Therefore, it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.     

DAMQT 2.1.0: A new version of the DAMQT package enabled with the topographical analysis of electron density and electrostatic potential in molecules

DAMQT‐2.1.0 is a new version of DAMQT package which includes topographical analysis of molecular electron density (MED) and molecular electrostatic potential (MESP), such as mapping of critical points (CPs), creating molecular graphs, and atomic basins. Mapping of CPs is assisted with algorithmic determination of Euler characteristic in order to provide a necessary condition for locating all possible CPs. Apart from the mapping of CPs and determination of molecular graphs, the construction of MESP‐based atomic basin is a new and exclusive feature introduced in DAMQT‐2.1.0. The GUI in DAMQT provides a user‐friendly interface to run the code and visualize the final outputs. MPI libraries have been implemented for all the tasks to develop the parallel version of the software. Almost linear scaling of computational time is achieved with the increasing number of processors while performing various aspects of topography. A brief discussion of molecular graph and atomic basin is provided in the current article highlighting their chemical importance. Appropriate example sets have been presented for demonstrating the functions and efficiency of the code. © 2015 Wiley Periodicals, Inc.     

FFParam: Standalone package for CHARMM additive and Drude polarizable force field parametrization of small molecules

Accurate force-field (FF) parameters are key to reliable prediction of properties obtained from molecular modeling (MM) and molecular dynamics (MD) simulations. With ever-widening applicability of MD simulations, robust parameters need to be generated for a wider range of chemical species. The CHARMM General Force Field program (CGenFF, https://cgenff.umaryland.edu/ ) is a tool for obtaining initial parameters for a given small molecule based on analogy with the available CGenFF parameters. However, improvement of these parameters is often required and performing their optimization remains tedious and time consuming. In addition, tools for optimization of small molecule parameters in the context of the Drude polarizable FF are not yet available. To overcome these issues, the FFParam package has been designed to facilitate the parametrization process. The package includes a graphical user interface (GUI) created using Qt libraries. FFParam supports Gaussian and Psi4 for performing quantum mechanical calculations and CHARMM and OpenMM for MM calculations. A Monte Carlo simulated annealing (MCSA) algorithm has been implemented for automated fitting of partial atomic charge, atomic polarizabilities and Thole scale parameters. The LSFITPAR program is called for automated fitting of bonded parameters. Accordingly, FFParam provides all the features required for generation and analysis of CHARMM and Drude FF parameters for small molecules. FFParam-GUI includes a text editor, graph plotter, molecular visualization, and text to table converter to meet various requirements of the parametrization process. It is anticipated that FFParam will facilitate wider use of CGenFF as well as promote future use of the Drude polarizable FF.     

Genetically encoded pH sensor for tracking surface proteins through endocytosis

Traffic cam: a tandem dye prepared from a FRET acceptor and a fluorogenic donor functions as a cell surface ratiometric pH indicator, which upon internalization serves to follow protein trafficking during endocytosis. This sensor was used to analyze agonist-dependent internalization of β(2)-adrenergic receptors. It was also used as a surrogate antigen to reveal direct surface-to-endosome antigen transfer between dendritic cells (not shown).     

Discriminant Analysis under f-Divergence Measures

In statistical inference, the information-theoretic performance limits can often be expressed in terms of a statistical divergence between the underlying statistical models (e.g., in binary hypothesis testing, the error probability is related to the total variation distance between the statistical models). As the data dimension grows, computing the statistics involved in decision-making and the attendant performance limits (divergence measures) face complexity and stability challenges. Dimensionality reduction addresses these challenges at the expense of compromising the performance (the divergence reduces by the data-processing inequality). This paper considers linear dimensionality reduction such that the divergence between the models is maximally preserved. Specifically, this paper focuses on Gaussian models where we investigate discriminant analysis under five f-divergence measures (Kullback–Leibler, symmetrized Kullback–Leibler, Hellinger, total variation, and χ2). We characterize the optimal design of the linear transformation of the data onto a lower-dimensional subspace for zero-mean Gaussian models and employ numerical algorithms to find the design for general Gaussian models with non-zero means. There are two key observations for zero-mean Gaussian models. First, projections are not necessarily along the largest modes of the covariance matrix of the data, and, in some situations, they can even be along the smallest modes. Secondly, under specific regimes, the optimal design of subspace projection is identical under all the f-divergence measures considered, rendering a degree of universality to the design, independent of the inference problem of interest.     

Insecticidal Activity of Extracts,Fractions, and Pure Molecules of Cissampelos pareira Linnaeus against Aphid,Aphis craccivora Koch

Aphis craccivora Koch is a polyphagous and major pest of leguminous crops causing significant damage by reducing the yield. Repeated application of synthetic insecticides for the control of aphids has led to development of resistance. Therefore, the present study aimed to screen the insecticidal activity of root/stem extracts/fractions, and pure molecules from Cissampelos pareira Linnaeus against A. craccivora for identification of lead(s). Among root extract/fractions, the n-hexane fraction was found most effective (LC₅₀ = 1828.19 mg/L) against A. craccivora, followed by parent extract (LC₅₀ = 2211.54 mg/L). Among stem extract/fractions, the n-hexane fraction (LC₅₀ = 1246.92 mg/L) was more effective than the water and n-butanol fractions. Based on GC and GC-MS analysis, among different compounds identified in the n-hexane fraction of root and stem, ethyl palmitate (known to possess insecticidal activity) was present in the highest concentration (24.94 to 52.95%) in both the fractions. Among pure molecules, pareirarineformate was found most effective (LC₅₀ = 1491.93 mg/L) against A. craccivora, followed by cissamine (LC₅₀ = 1556.31 mg/L). Parent extract and fractions of C. pareira possess promising activity against aphid. Further, field bio-efficacy studies are necessary to validate the current findings for the development of botanical formulation.     

Constructing Potential Energy Surface with Correlated Theory for Dipeptides Using Molecular Tailoring Approach

We demonstrate a cost-effective alternative employing the fragment-based molecular tailoring approach (MTA) for building the potential energy surface (PES) for two dipeptides viz. alanine-alanine and alanine-proline employing correlated theory, with augmented Dunning basis sets. About 1369 geometries are generated for each test dipeptide by systematically varying the dihedral angles and . These conformational geometries are partially optimized by relaxing all the other Z-matrix parameters, fixing the values of and . The MP2 level PES is constructed from the MTA-energies of chemically intact geometries using minimal hardware. The fidelity of MP2/aug-cc-pVDZ level PES is brought out by comparing it with its full calculation counterpart. Further, we bring out the power of the method by reporting the MTA-based CCSD/aug-cc-pVDZ level PES for these two dipeptides containing 498 and 562 basis functions respectively.