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Computation, Volume 5, Issue 4 (December 2017)

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Research

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Open AccessFeature PaperArticle A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation
Computation 2017, 5(4), 42; doi:10.3390/computation5040042
Received: 31 August 2017 / Revised: 22 September 2017 / Accepted: 23 September 2017 / Published: 26 September 2017
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Abstract
We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages
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We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations. Full article
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Open AccessArticle Multiresolution Modeling of Semidilute Polymer Solutions: Coarse-Graining Using Wavelet-Accelerated Monte Carlo
Computation 2017, 5(4), 44; doi:10.3390/computation5040044
Received: 21 August 2017 / Revised: 20 September 2017 / Accepted: 25 September 2017 / Published: 28 September 2017
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Abstract
We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations.
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We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC) method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations. Previously, it was applied to simulations examining the structure of individual polymer chains in solution using up to four levels of coarse-graining (Ismail et al., J. Chem. Phys., 2005, 122, 234901 and Ismail et al., J. Chem. Phys., 2005, 122, 234902), recovering the correct scaling behavior in the coarse-grained representation. In the present work, we extend this method to the study of polymer solutions, deriving the bonded and non-bonded potentials between coarse-grained superatoms from the single chain statistics. A universal scaling function is obtained, which does not require recalculation of the potentials as the scale of the system is changed. To model semi-dilute polymer solutions, we assume the intermolecular potential between the coarse-grained beads to be equal to the non-bonded potential, which is a reasonable approximation in the case of semidilute systems. Thus, a minimal input of microscopic data is required for simulating the systems at the mesoscopic scale. We show that coarse-grained polymer solutions can reproduce results obtained from the more detailed atomistic system without a significant loss of accuracy. Full article
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Open AccessArticle Deformable Cell Model of Tissue Growth
Computation 2017, 5(4), 45; doi:10.3390/computation5040045
Received: 30 September 2017 / Revised: 24 October 2017 / Accepted: 24 October 2017 / Published: 30 October 2017
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Abstract
This paper is devoted to modelling tissue growth with a deformable cell model. Each cell represents a polygon with particles located at its vertices. Stretching, bending and pressure forces act on particles and determine their displacement. Pressure-dependent cell proliferation is considered. Various patterns
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This paper is devoted to modelling tissue growth with a deformable cell model. Each cell represents a polygon with particles located at its vertices. Stretching, bending and pressure forces act on particles and determine their displacement. Pressure-dependent cell proliferation is considered. Various patterns of growing tissue are observed. An application of the model to tissue regeneration is illustrated. Approximate analytical models of tissue growth are developed. Full article
(This article belongs to the Section Computational Biology)
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Review

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Open AccessReview Self-Organizing Map for Characterizing Heterogeneous Nucleotide and Amino Acid Sequence Motifs
Computation 2017, 5(4), 43; doi:10.3390/computation5040043
Received: 19 July 2017 / Revised: 18 September 2017 / Accepted: 25 September 2017 / Published: 26 September 2017
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Abstract
A self-organizing map (SOM) is an artificial neural network algorithm that can learn from the training data consisting of objects expressed as vectors and perform non-hierarchical clustering to represent input vectors into discretized clusters, with vectors assigned to the same cluster sharing similar
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A self-organizing map (SOM) is an artificial neural network algorithm that can learn from the training data consisting of objects expressed as vectors and perform non-hierarchical clustering to represent input vectors into discretized clusters, with vectors assigned to the same cluster sharing similar numeric or alphanumeric features. SOM has been used widely in transcriptomics to identify co-expressed genes as candidates for co-regulated genes. I envision SOM to have great potential in characterizing heterogeneous sequence motifs, and aim to illustrate this potential by a parallel presentation of SOM with a set of numerical vectors and a set of equal-length sequence motifs. While there are numerous biological applications of SOM involving numerical vectors, few studies have used SOM for heterogeneous sequence motif characterization. This paper is intended to encourage (1) researchers to study SOM in this new domain and (2) computer programmers to develop user-friendly motif-characterization SOM tools for biologists. Full article
(This article belongs to the Section Computational Biology)
Open AccessFeature PaperReview Dynamic Data-Driven Modeling for Ex Vivo Data Analysis: Insights into Liver Transplantation and Pathobiology
Computation 2017, 5(4), 46; doi:10.3390/computation5040046
Received: 15 October 2017 / Revised: 12 November 2017 / Accepted: 16 November 2017 / Published: 23 November 2017
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Abstract
Extracorporeal organ perfusion, in which organs are preserved in an isolated, ex vivo environment over an extended time-span, is a concept that has led to the development of numerous alternative preservation protocols designed to better maintain organ viability prior to transplantation. These protocols
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Extracorporeal organ perfusion, in which organs are preserved in an isolated, ex vivo environment over an extended time-span, is a concept that has led to the development of numerous alternative preservation protocols designed to better maintain organ viability prior to transplantation. These protocols offer researchers a novel opportunity to obtain extensive sampling of isolated organs, free from systemic influences. Data-driven computational modeling is a primary means of integrating the extensive and multivariate data obtained in this fashion. In this review, we focus on the application of dynamic data-driven computational modeling to liver pathophysiology and transplantation based on data obtained from ex vivo organ perfusion. Full article
(This article belongs to the Section Computational Biology)
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