EASY-GOING deconvolution: combining accurate simulation and evolutionary algorithms for fast deconvolution of solid-state quadrupolar NMR spectra

A fast and accurate fit program is presented for deconvolution of one-dimensional solid-state quadrupolar NMR spectra of powdered materials. Computational costs of the synthesis of theoretical spectra are reduced by the use of libraries containing simulated time/frequency domain data. These libraries are calculated once and with the use of second-party simulation software readily available in the NMR community, to ensure a maximum flexibility and accuracy with respect to experimental conditions. EASY-GOING deconvolution (EGdeconv) is equipped with evolutionary algorithms that provide robust many-parameter fitting and offers efficient parallellised computing. The program supports quantification of relative chemical site abundances and (dis)order in the solid-state by incorporation of (extended) Czjzek and order parameter models. To illustrate EGdeconv's current capabilities, we provide three case studies. Given the program's simple concept it allows a straightforward extension to include other NMR interactions. The program is available as is for 64-bit Linux operating systems.     

Joint data treatment for Vis–NIR reflectance imaging spectroscopy and XRF imaging acquired in the Theban Necropolis in Egypt by data fusion and t-SNE

Hyperspectral imaging allows the acquisition of representative information on cultural heritage objects. For a complete identification of the chemical compounds present, one needs instruments employing different forms of radiation, sensitive to different chemical features. Data treatment workflows are commonly developed for a single spectroscopic technique, so that data sets are evaluated separately, and the reduced representations yielded are compared during interpretation. In this publication, we describe how t-stochastic neighbor embedding (t-SNE) allows for the evaluation and interpretation of data acquired in a Ramesside tomb (13th century BC) of the Theban Necropolis in Egypt. By fusing X-ray Fluorescence (XRF) imaging and Reflectance Imaging Spectroscopy (RIS) into a single data set, we exploit the synergies between both methods to support interpretation and presentation of the results yielded.     

Exploring the chemical space of peptides for drug discovery: a focus on linear and cyclic penta-peptides

Peptide and peptide-like structures are regaining attention in drug discovery. Previous studies suggest that bioactive peptides have diverse structures and may have physicochemical properties attractive to become hit and lead compounds. However, chemoinformatic studies that characterize such diversity are limited. Herein, we report the physicochemical property profile and chemical space of four synthetic linear and cyclic combinatorial peptide libraries. As a case study, the analysis was focused on penta-peptides. The chemical space of the peptide and N-methylated peptides libraries was compared to compound data sets of pharmaceutical relevance. Results indicated that there is a major overlap in the chemical space of N-methylated cyclic peptides with inhibitors of protein–protein interactions and macrocyclic natural products available for screening. Also, there is an overlap between the chemical space of the synthetic peptides with peptides approved for clinical use (or in clinical trials), and to other approved drugs that are outside the traditional chemical space. Results further support that synthetic penta-peptides are suitable compounds to be used in drug discovery projects.     

Comparisons of wind tunnel experiments and computational fluid dynamics simulations

This paper describes the architecture of an image and data level comparative visualization system and experiences using it to study computational fluid dynamics data and experimental wind tunnel data. We illustrate how the system can be used to compare data sets from different sources, data sets with different resolutions and data sets computed by using different mathematical models of fluid flow. We include recent improvements including use of the comparison of vector fields, ability to interactively interrogate the comparisons, addition of new metrics, the latest FEL2.0 and VisTech libraries, and GUI for a calculator module.     

On the similarity of the sensitivity functions of methane combustion models

It is widely known that detailed kinetic mechanisms with identical reaction steps but with very different rate parameters may provide similar simulation results in combustion calculations. This phenomenon is related to the similarity of sensitivity functions, which arises if low-dimensional manifolds in the space of variables, and autocatalytic processes are present. We demonstrated the similarity of sensitivity functions for adiabatic explosions and burner-stabilized laminar flames of stoichiometric methane–air mixtures. The cause of similarities was investigated by calculating the dimension of the corresponding manifolds, and the pseudo-homogeneous property of the sensitivity ordinary differential equation (ODE). The methane explosion model showed global similarity, which means that different parameter sets could provide the same simulation results. This was demonstrated by numerical experiments, in which two significantly different parameter sets resulted in identical concentration profiles for all species. This phenomenon is important from a practical point of view in the fields of ‘validation’ of complex reaction mechanisms and parameter estimation of chemical kinetic systems.     

A Manifold Learning Perspective on Representation Learning: Learning Decoder and Representations without an Encoder

Autoencoders are commonly used in representation learning. They consist of an encoder and a decoder, which provide a straightforward method to map n-dimensional data in input space to a lower m-dimensional representation space and back. The decoder itself defines an m-dimensional manifold in input space. Inspired by manifold learning, we showed that the decoder can be trained on its own by learning the representations of the training samples along with the decoder weights using gradient descent. A sum-of-squares loss then corresponds to optimizing the manifold to have the smallest Euclidean distance to the training samples, and similarly for other loss functions. We derived expressions for the number of samples needed to specify the encoder and decoder and showed that the decoder generally requires much fewer training samples to be well-specified compared to the encoder. We discuss the training of autoencoders in this perspective and relate it to previous work in the field that uses noisy training examples and other types of regularization. On the natural image data sets MNIST and CIFAR10, we demonstrated that the decoder is much better suited to learn a low-dimensional representation, especially when trained on small data sets. Using simulated gene regulatory data, we further showed that the decoder alone leads to better generalization and meaningful representations. Our approach of training the decoder alone facilitates representation learning even on small data sets and can lead to improved training of autoencoders. We hope that the simple analyses presented will also contribute to an improved conceptual understanding of representation learning.     

Trends in information theory-based chemical structure codification

This report offers a chronological review of the most relevant applications of information theory in the codification of chemical structure information, through the so-called information indices. Basically, these are derived from the analysis of the statistical patterns of molecular structure representations, which include primitive global chemical formulae, chemical graphs, or matrix representations. Finally, new approaches that attempt to go “back to the roots” of information theory, in order to integrate other information-theoretic measures in chemical structure coding are discussed.     

Raynal–Revai coefficients for a general kinematic rotation

In a three-body system, transitions between different sets of normalized Jacobi coordinates are described as general kinematic transformations that include an orthogonal or a pseudoorthogonal rotation. For such rotations, the Raynal–Revai coefficients execute a unitary transformation between three-body hyperspherical functions. Recurrence relations that make it possible to calculate the Raynal–Revai coefficients for arbitrary angular momenta are derived on the basis of linearized representations of products of hyperspherical functions.     

Transition metal dichalcogenides (TMDCs) heterostructures: Optoelectric properties

Transition metal dichalcogenides (TMDCs) have suitable and adjustable band gaps, high carrier mobility and yield. Layered TMDCs have attracted great attention due to the structure diversity, stable existence in normal temperature environment and the band gap corresponding to wavelength between infrared and visible region. The ultra-thin, flat, almost defect-free surface, excellent mechanical flexibility and chemical stability provide convenient conditions for the construction of different types of TMDCs heterojunctions. The optoelectric properties of heterojunctions based on TMDCs materials are summarized in this review. Special electronic band structures of TMDCs heterojunctions lead to excellent optoelectric properties. The emitter, p-n diodes, photodetectors and photosensitive devices based on TMDCs heterojunction materials show excellent performance. These devices provide a prototype for the design and development of future high-performance optoelectric devices.     

Stages of transformation of block elements

The property to have various representations is investigated for the block elements describing the solutions of boundary-value problems for sets of partial differential equations in the regions with a boundary. These representations have various destinations. One of the representations, which is called packed, is convenient for constructing solutions in block structures on the basis of solutions in separate blocks. Another representation, which is called unpacked, is convenient for a detailed investigation of the properties of solutions in an individual block of the block structure.     

Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies

The multifractal spectrum of various three-dimensional representations of Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured, and it is determined that the curvature of the space does not alter the associated fractal structure. These results are compared to observational data and simulated models of large scale galaxy clustering, to assess the viability of the PSC as a candidate for such structure formation. It is found that the PSC dimension spectra do not match those of observation, and possible solutions to this discrepancy are offered, including accounting for potential luminosity biasing effects. Various random and uniform sets are also analyzed to provide insight into the meaning of the multifractal spectrum as it relates to the observed scaling behaviors.     

SU(2) andSU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states

We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov's generalized coherent states. On the other hand, intelligent states (which are squeezed states for a system of general symmetry) also form a subset of algebra eigenstates. We develop the general formalism and apply it to theSU(2) andSU(1,1) simple Lie groups. Complete solutions to the general eigenvalue problem are found in both cases by a method that employs analytic representations of the algebra eigenstates. This analytic method also enables us to obtain exact closed expressions for quantum statistical properties of an arbitrary algebra eigenstate. Important special cases such as standard coherent states and intelligent states are examined and relations between them are studied by using their analytic representations.     

Stabilization of RBF-generated finite difference methods for convective PDEs

Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD) methods can offer significant savings in computer resources (time and memory). This study presents a new filter mechanism, allowing such gains to be realized also for purely convective PDEs that do not naturally feature any stabilizing dissipation.     

ON THE IRREDUCIBLE REPRESENTATIONS OF THE SIMPLE LIE GROUPS I——THE TENSOR BASIS FOR THE INFINITESIMAL GENERATORS OF THE CLASSICAL SIMPLE LIE GROUPS

In this paper, we analyse the commutation relations of the infinitesimal generatorsof all simple classical Lie groups and establish a new basis for these generators, calledthe tensor basis. In tensor basis, the infinitesimal, generators can be written as somescalar operators, some sets of angular momentum operators and some sets of irreducibletensor operators. The commutation relations, of these operators are very simple andhave many regularities. By means of the method that has been used in the earlier papers, "On the irre-ducible representations of the compact simple Lie groups of rank 2, I,II,III" and thetensor basis, all the irreducible representations of the classical simple Lie groups canbe calculated systematically.     

Numerical simulation of PRESS localized MR spectroscopy

Numerical simulations of NMR spectra can provide a rapid and convenient method for optimizing acquisition sequence parameters and generating prior spectral information required for parametric spectral analysis. For spatially resolved spectroscopy, spatially dependent variables affect the resultant spectral amplitudes and phases, which must therefore be taken into account in any spectral simulation model. In this study, methods for numerical simulation of spectra obtained using the PRESS localization pulse sequence are examined. A comparison is made between three different simulation models that include different levels of detail regarding the spatial distributions of the excitation functions, and spin evolution during application of the pulses. These methods were evaluated for measurement of spectra from J-coupled spin systems that are of interest for in vivo proton spectroscopy and results compared with experimental data. It is demonstrated that for optimized refocusing pulses it is sufficient to account for chemical shift effects only, although there is some advantage to implementing a more general numerical simulation approach that includes information on RF pulse excitation profiles, which provides sufficient accuracy while maintaining moderate computational requirements and flexibility to handle different spin systems.     

Transition Dipole,Charge Transfer,and Electron-hole Coherence in Two-photon Absorption: Visualizations with Two Dimensional Site and Three Dimensional Cube Representations

采用二维和三维实空间分析方法可视化了双光子吸收特征,包括跃迁距、电荷转移和电子空穴相干性. 跃迁密度的三维实空间分析揭示了跃迁距的强度和方向,电荷差异密度显示双光子吸收过程中的电荷转移方向. 跃迁密度矩阵的二维实空间分析可视化了电子和空穴的相干性. 二维和三维实空间分析有助于清晰地理解双光子吸收的电荷转移过程和激发的分子单元对双光子吸收的贡献.     

多重表征与学习进阶整合的“库仑定律”教学探索

多重表征能够为学习者提供多样化、弹性的信息呈现方式.多重表征教学有助于学生学习进阶的顺利进行.以"库仑定律"的教学为例,探索了将多重表征与学习进阶整合的教学在物理规律知识形成中的具体应用.     

On the relation between the fractional Brownian motion and the fractional derivatives

The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.     

Interest rates hierarchical structure

We propose a general method to study the hierarchical organization of financial data by embedding the structure of their correlations in metric graphs in multi-dimensional spaces. An application to two different sets of interest rates is discussed by constructing triangular embeddings on the sphere. Three-dimensional representations of these embeddings with the correct metric geometry are constructed and visualized. The resulting graphs contain the minimum spanning tree as a sub-graph and they preserve its hierarchical structure. This produces a clear cluster differentiation and allows us to compute new local and global topological quantities.