Linear Combination Research Articles

Predicting anti-trypanosome effect of carbazole-derived compounds by powerful SVM with novel kernel function and comprehensive learning PSO.

In order to predict the anti-trypanosome effect of carbazole-derived compounds by quantitative structure-activity relationship, five models were established by the linear method, random forest, radial basis kernel function support vector machine, linear combination mix-kernel function support vector machine, and nonlinear combination mix-kernel function support vector machine (NLMIX-SVM). The heuristic method and optimized CatBoost were used to select two different key descriptor sets for building linear and nonlinear models, respectively. Hyperparameters in all nonlinear models were optimized by comprehensive learning particle swarm optimization with low complexity and fast convergence. Furthermore, the models' robustness and reliability underwent rigorous assessment using fivefold and leave-one-out cross-validation, y-randomization, and statistics including concordance correlation coefficient (CCC), [Formula: see text] , [Formula: see text] , and [Formula: see text] . Among all the models, the NLMIX-SVM model, which was established by support vector regression using a nonlinear combination of radial basis kernel function, sigmoid kernel function, and linear kernel function as a new kernel function, demonstrated excellent learning and generalization abilities as well as robustness: [Formula: see text] = 0.9581, mean square error (MSE) = 0.0199 for the training set and [Formula: see text] = 0.9528, MSE = 0.0174 for the test set. [Formula: see text] , [Formula: see text] , CCC, [Formula: see text] , [Formula: see text], and [Formula: see text] are 0.9539, 0.8908, 0.9752, 0.9529, 0.9528, and 0.9633, respectively. The NLMIX-SVM method proved to be a promising way in quantitative structure-activity relationship research. In addition, molecular docking experiments were conducted to analyze the properties of new derivatives, and a new potential candidate drug molecule was ultimately found. In summary, this study will provide help for the design and screening of novel anti-trypanosome drugs.

Perceptual dimensions of wood materials.

Materials exhibit an extraordinary range of visual appearances. Characterizing and quantifying appearance is important not only for basic research on perceptual mechanisms but also for computer graphics and a wide range of industrial applications. Although methods exist for capturing and representing the optical properties of materials and how they vary across surfaces (Haindl & Filip, 2013), the representations are typically very high-dimensional, and how these representations relate to subjective perceptual impressions of material appearance remains poorly understood. Here, we used a data-driven approach to characterizing the perceived appearance characteristics of 30 samples of wood veneer using a "visual fingerprint" that describes each sample as a multidimensional feature vector, with each dimension capturing a different aspect of the appearance. Fifty-six crowd-sourced participants viewed triplets of movies depicting different wood samples as the sample rotated. Their task was to report which of the two match samples was subjectively most similar to the test sample. In another online experiment, 45 participants rated 10 wood-related appearance characteristics for each of the samples. The results reveal a consistent embedding of the samples across both experiments and a set of nine perceptual dimensions capturing aspects including the roughness, directionality, and spatial scale of the surface patterns. We also showed that a weighted linear combination of 11 image statistics, inspired by the rating characteristics, predicts perceptual dimensions well.

Repulsive gravity in regular black holes

We evaluate the effects of repulsive gravity using first order geometric invariants, i.e. the Ricci scalar and the eigenvalues of the Riemann curvature tensor, for three regular black holes, namely the Bardeen, Hayward, and Dymnikova spacetimes. To examine the repulsive effects, we calculate their respective onsets and regions of repulsive gravity. Afterwards, we compare the repulsive regions obtained from these metrics among themselves and then with the predictions got from the Reissner–Nordström and Schwarzschild–de Sitter. A notable characteristic, observed in all these metrics, is that the repulsive regions appear to be unaffected by the mass that generates the regular black hole. This property emerges due to the invariants employed in our analysis, which do not change sign through linear combinations of the mass and the free coefficients of the metrics. As a result, gravity can change sign independently of the specific values acquired by the mass. This conclusion suggests a potential incompleteness of regular solutions, particularly in terms of their repulsive effects. To further highlight this finding, we numerically compute, for the Reissner–Nordström and Schwarzschild–de Sitter solutions, the values of mass, M, that emulate the repulsive effects found in the Bardeen and Hayward spacetimes. These selected values of M provide evidence that regular black holes do not incorporate repulsive effects by means of the masses used to generate the solutions themselves. Implications and physical consequences of these results are then discussed in detail.

Guanidine Hydrochloride-Induced Hepatitis B Virus Capsid Disassembly Hysteresis.

Hepatitis B virus (HBV) displays remarkable self-assembly capabilities that interest the scientific community and biotechnological industries as HBV is leading to an annual mortality of up to 1 million people worldwide (especially in Africa and Southeast Asia). When the ionic strength is increased, hepatitis B virus-like particles (VLPs) can assemble from dimers of the first 149 residues of the HBV capsid protein core assembly domain (Cp149). Using solution small-angle X-ray scattering, we investigated the disassembly of the VLPs by titrating guanidine hydrochloride (GuHCl). Measurements were performed with and without 1 M NaCl, added either before or after titrating GuHCl. Fitting the scattering curves to a linear combination of atomic models of Cp149 dimer (the subunit) and T = 3 and T = 4 icosahedral capsids revealed the mass fraction of the dimer in each structure in all the titration points. Based on the mass fractions, the variation in the dimer-dimer association standard free energy was calculated as a function of added GuHCl, showing a linear relation between the interaction strength and GuHCl concentration. Using the data, we estimated the energy barriers for assembly and disassembly and the critical nucleus size for all of the assembly reactions. Extrapolating the standard free energy to [GuHCl] = 0 showed an evident hysteresis in the assembly process, manifested by differences in the dimer-dimer association standard free energy obtained for the disassembly reactions compared with the equivalent assembly reactions. Similar hysteresis was observed in the energy barriers for assembly and disassembly and the critical nucleus size. The results suggest that above 1.5 M, GuHCl disassembled the capsids by attaching to the protein and adding steric repulsion, thereby weakening the hydrophobic attraction.

A retrospective view on non-linear methods in chemometrics, and future directions

This perspective article reviews how the chemometrics community approached non-linear methods in the early years. In addition to the basic chemometric methods, some methods that fall under the term “machine learning” are also mentioned. Thereafter, types of non-linearity are briefly presented, followed by discussions on important aspects of modeling related to non-linear data. Lastly, a simulated data set with non-linear properties is analyzed for quantitative prediction and batch monitoring. The conclusion is that the latent variable methods to a large extent handle non-linearities by adding more linear combinations of the original variables. Nevertheless, with strong non-linearities between the X and Y space, non-linear methods such as Support Vector Machines might improve prediction performance at the cost of interpretability into both the sample and variable space. Applying multiple local models can improve performance compared to a single global model, of both linear and non-linear nature. When non-linear methods are applied, the need for conservative model validation is even more important. Another approach is pre-processing of the data which can make the data more linear before the actual modeling and prediction phase.

The Hill function is the universal Hopfield barrier for sharpness of input–output responses

The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Fast-Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful, non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment. This study focuses on a model-free approach, representing the NMRD profile R1 as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework. Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analyzing NMRD profiles. These include (1) MF-UPen, utilizing locally adapted L2 regularization; (2) MF-L1, based on L1 penalties; and (3) a hybrid approach combining locally adapted L2 and global L1 penalties. Each method’s regularization parameters are determined automatically according to the Balancing and Uniform Penalty principles. Our contributions include the implementation and experimental validation of the MF-UPen and MF-MUPen algorithms, and the development of a “dispersion analysis” technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios.

Epistatic Features and Machine Learning Improve Alzheimer's Disease Risk Prediction Over Polygenic Risk Scores.

Polygenic risk scores (PRS) are linear combinations of genetic markers weighted by effect size that are commonly used to predict disease risk. For complex heritable diseases such as late-onset Alzheimer's disease (LOAD), PRS models fail to capture much of the heritability. Additionally, PRS models are highly dependent on the population structure of the data on which effect sizes are assessed and have poor generalizability to new data. The goal of this study is to construct a paragenic risk score that, in addition to single genetic marker data used in PRS, incorporates epistatic interaction features and machine learning methods to predict risk for LOAD. We construct a new state-of-the-art genetic model for risk of Alzheimer's disease. Our approach innovates over PRS models in two ways: First, by directly incorporating epistatic interactions between SNP loci using an evolutionary algorithm guided by shared pathway information; and second, by estimating risk via an ensemble of non-linear machine learning models rather than a single linear model. We compare the paragenic model to several PRS models from the literature trained on the same dataset. The paragenic model is significantly more accurate than the PRS models under 10-fold cross-validation, obtaining an AUC of 83% and near-clinically significant matched sensitivity/specificity of 75%. It remains significantly more accurate when evaluated on an independent holdout dataset and maintains accuracy within APOE genotype strata. Paragenic models show potential for improving disease risk prediction for complex heritable diseases such as LOAD over PRS models.

DNA as a perfect quantum computer based on the quantum physics principles

DNA is a complex multi-resolution molecule whose theoretical study is a challenge. Its intrinsic multiscale nature requires chemistry and quantum physics to understand the structure and quantum informatics to explain its operation as a perfect quantum computer. Here, we present theoretical results of DNA that allow a better description of its structure and the operation process in the transmission, coding, and decoding of genetic information. Aromaticity is explained by the oscillatory resonant quantum state of correlated electron and hole pairs due to the quantized molecular vibrational energy acting as an attractive force. The correlated pairs form a supercurrent in the nitrogenous bases in a single band π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-molecular orbital (π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-MO). The MO wave function (Φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Phi )$$\\end{document} is assumed to be the linear combination of the n constituent atomic orbitals. The central Hydrogen bond between Adenine (A) and Thymine (T) or Guanine (G) and Cytosine (C) functions like an ideal Josephson Junction. The approach of a Josephson Effect between two superconductors is correctly described, as well as the condensation of the nitrogenous bases to obtain the two entangled quantum states that form the qubit. Combining the quantum state of the composite system with the classical information, RNA polymerase teleports one of the four Bell states. DNA is a perfect quantum computer.

Autoencoder-based composite drought indices

Abstract Depending on the type, drought events are described using different indices, such as meteorological, agricultural, and hydrological. The use of different indices often causes confusion for making water-related management decisions. One simple summarized index which can describe the different aspects of drought is desired. Several methods have therefore been proposed, especially with the linear combination method which does not adequately describe drought characteristics. Meanwhile, autoencoders, nonlinear transformation in dimensional reduction, have been applied in the deep learning literature. The objective of this study, therefore, was to derive autoencoder-based composite drought indices (ACDIs). First, a basic autoencoder was directly applied as ACDI, illustrating a negative relation with the observed drought indices which was further multiplied by a negative. Also, the hyperbolic tangent function was adopted instead of the sigmoid transfer function due to its higher sensitivity to drought conditions. For better expression of drought indices, positive and unity constraints were applied for weights, denoted as ACDI-C. Further simplification was made as sACDI by excluding the decoding module since it was not necessary. All applied weights of different sites over a country can be unified into one weight, and the same weights were made for all the sites, called as sACDI1. Overall, results indicated that the sACDI and sACDI1 outperformed other models with RMSE and MAE performance measurements as well as with less false alarm and higher alarm accuracy. The developed ACDI can summarize multiple drought aspects and provide summarized information about drought conditions.

Addition and Differentiation of ZX-diagrams

The ZX-calculus is a powerful framework for reasoning in quantum computing. It provides in particular a compact representation of matrices of interests. A peculiar property of the ZX-calculus is the absence of a formal sum allowing the linear combinations of arbitrary ZX-diagrams. The universality of the formalism guarantees however that for any two ZX-diagrams, the sum of their interpretations can be represented by a ZX-diagram. We introduce a general, inductive definition of the addition of ZX-diagrams, relying on the construction of controlled diagrams. Based on this addition technique, we provide an inductive differentiation of ZX-diagrams. Indeed, given a ZX-diagram with variables in the description of its angles, one can differentiate the diagram according to one of these variables. Differentiation is ubiquitous in quantum mechanics and quantum computing (e.g. for solving optimization problems). Technically, differentiation of ZX-diagrams is strongly related to summation as witnessed by the product rules. We also introduce an alternative, non inductive, differentiation technique rather based on the isolation of the variables. Finally, we apply our results to deduce a diagram for an Ising Hamiltonian.

Bayesian Maximal Reliability Evaluation Using Latent Variable Modeling

ABSTRACT We discuss an application of Bayesian factor analysis for estimation of the optimal linear combination and associated maximal reliability of a multi-component measuring instrument. The described procedure yields point and credibility interval estimates of this reliability coefficient, which are readily obtained in educational and behavioral measurement research. In addition, the outlined method permits evaluation of the gain in measurement consistency resulting from utilizing the maximal reliability coefficient instead of the traditionally used overall sum score reliability. The discussed Bayesian inference approach is applicable with widely available software in empirical studies, and is illustrated using a data example.

Tailoring data assimilation to discontinuous Galerkin models

AbstractIn recent years discontinuous Galerkin (DG) methods have received increased interest from the geophysical community. In these methods the solution in each grid cell is approximated as a linear combination of basis functions. Ensemble data assimilation (DA) aims to approximate the true state by combining model outputs with observations using error statistics estimated from an ensemble of model runs. Ensemble data assimilation in geophysical models faces several well‐documented issues. In this work we exploit the expansion of the solution in DG basis functions to address some of these issues. Specifically, it is investigated whether a DA–DG combination (a) mitigates the need for observation thinning, (b) reduces errors in the field's gradients, and (c) can be used to set up scale‐dependent localisation. Numerical experiments are carried out using stochastically generated ensembles of model states, with different noise properties, and with Legendre polynomials as basis functions. It is found that strong reduction in the analysis error is achieved by using DA–DG and that the benefit increases with increasing DG order. This is especially the case when small scales dominate the background error. The DA improvement in the first derivative is, on the other hand, marginal. We think this to be a counter‐effect of the power of DG to fit the observations closely, which can deteriorate the estimates of the derivatives. Applying optimal localisation to the different polynomial orders, thus exploiting their different spatial length, is beneficial: it results in a covariance matrix closer to the true covariance than the matrix obtained using traditional optimal localisation in state space.

Fragment Orbitals Extracted from First-Principles Plane-Wave Calculations.

Decomposing extended structures into smaller, molecular, even functional groups or simple fragments has a long tradition in chemistry because it allows for understanding certain electronic peculiarities in truly chemical terms. By doing so, invaluable property information is chemically accessible, for example, needed to rationalize catalytic or magnetic or optical nature. In order to also follow that train of thought for periodic materials, we have developed a tool which in a straightforward manner derives fragment molecular orbitals from plane-wave electronic-structure data of whatever kind of solid-state material. We here report on the mathematical apparatus of the method dubbed linear combination of fragment orbitals (LCFO) used for that purpose, implemented within the LOBSTER code. The method is illustrated from various sorts of molecular entities contained in such crystalline materials, together with an assessment of both accuracy and robustness of the new tool.

An efficient viscoelastic multiscale model for investigation on the cure‐induced microscopic residual stresses of composite laminates

AbstractThe cure‐induced residual stresses have a significant influence on the deformation and mechanical properties of composites. Moreover, the cure‐induced residual stresses exhibit multi‐level and multiscale distributions due to the complexity of micro‐structure of composites and anisotropic characteristics. In this paper, a computationally efficient multiscale procedure is proposed to predict the microscopic residual stresses induced by cure temperature, cure shrinkage and macroscopic residual stresses, which is based to the linear viscoelastic theory combined with the micro‐mechanics method. The instantaneous microscopic residual stresses are expressed as a linear combination of the instantaneous temperature increment, degree of cure increment and macroscopic strain increment at all times of the cure process until to the current time. The proposed method is verified in comparison with the published results in literature and the microscale FEA at different length scales, respectively. The results show that the proposed method is about a thousand times faster than directly using FEA in the microscale RVE model once the influence coefficient matrices are determined. At length, the microscale stresses of all nodes of the entire macroscale model are examined by using the proposed method. It is found that the thermal‐chemical‐mechanical loads lead to serious microscopic stresses for the matrix and interphase constituents, especially for those due to the macroscopic residual stresses.Highlights Microscale residual stress is written as a linear combination of macroscale loads. Applying macroscale loads on microscale FEA model to obtain influence matrices. The presented model avoids repeatedly FEA microscopic to improve the efficiency. The online time required for the proposed model is much less than microscale FEA. The microscale stress increases the risk of matrix cracking and interface bonding.

Centrality measures-based sensitivity analysis and entropy of nonzero component graphs

The nonzero component graph of a finite-dimensional vector space over a finite field is a graph whose vertices are the nonzero vectors in the vector space, and any two vertices are adjacent if the corresponding linear combination contains a common basis vector. In this paper, we discuss the centrality measures and entropy of the nonzero component graph and also analyze the sensitivity of the graph using the centrality measures.

Proper orthogonal descriptors for multi-element chemical systems

We introduce the proper orthogonal descriptors for efficient and accurate interatomic potentials of multi-element chemical systems. The potential energy surface of a multi-element system is represented as a many-body expansion of parametrized potentials which are functions of atom positions, atom types, and parameters. The proper orthogonal decomposition is employed to decompose the parametrized potentials as a linear combination of orthogonal basis functions. The orthogonal basis functions are used to construct proper orthogonal descriptors based on the elements of atoms, thus leading to multi-element descriptors. We compose the multi-element proper orthogonal descriptors to develop linear and quadratic interatomic potentials. We devise an algorithm to efficiently compute the total energy and forces of the interatomic potentials constructed from the proper orthogonal descriptors. The potentials are demonstrated for indium phosphide and titanium dioxide in comparison with the spectral neighbor analysis potential (SNAP) and atomic cluster expansion (ACE) potentials.

Biomechanical Integrity Score of the Female Pelvic Floor for Stress Urinary Incontinence.

This study is aimed at developing and validating a new integral parameter, the Biomechanical Integrity score (BI-score) of the female pelvic floor for stress urinary incontinence conditions. A total of 130 subjects were included in the observational cohort study; 70 subjects had normal pelvic floor conditions, and 60 subjects had stress urinary incontinence (SUI). A Vaginal Tactile Imager (VTI) was used to acquire and automatically calculate 52 biomechanical parameters for eight VTI test procedures (probe insertion, elevation, rotation, Valsalva maneuver, voluntary muscle contractions in two planes, relaxation, and reflex contraction). Statistical methods were applied (t test, correlation) to identify the VTI parameters sensitive to the pelvic SUI conditions. Twenty-seven parameters were identified as statistically sensitive to SUI development. They were subdivided into five groups to characterize tissue elasticity (group 1), pelvic support (group 2), pelvic muscle contraction (group 3), involuntary muscle relaxation (group 4), and pelvic muscle mobility (group 5). Every parameter was transformed to its standard deviation units using the dataset for normal pelvic conditions, similar to the T-score for bone density. Linear combinations with specified weights led to the composition of five component parameters for groups 1-5 and to the BI-score in standard deviation units. The p value for the BI-score has p = 4.0 × 10-28 for SUI versus normal conditions. Quantitative transformations of the pelvic tissues, support structures, and functions under diseased conditions may be studied with the SUI BI-score in future research and clinical applications.

Optimal permeance ratio, flux direction and layer distribution in composite asymmetric membranes composed of sequences of layers obeying real-power flux laws

In this study, the optimal permeance ratio and layers distribution in multilayer membranes and thin films in which each layer obeys the following real-power law: Flux=πi(P1,ini−P2,ini) are determined for any positive real values of ni. Such an exponent has a physical meaning in several cases, such as: diffusion-controlled permeation of hydrogen in metal membranes i) under infinite-dilution conditions (n = 0.5), and ii) under higher-concentration ones (0.5 < n < 1.5), iii) desorption-limited permeation (n = 1) in the same type of membranes, Knudsen-type diffusional mechanism (n = 1) and viscous flow (n = 2) in microporous membranes. Furthermore, n is equal to 4 in radiation-driven thermal flux. The work considers two generic layers of different thicknesses and exponents, for which it is proven the existence of a general optimal permeance ratio π1/π2 maximising the flux ratio, which is found to be equal to the inverse of the ratio between the respective maximum theoretical driving forces that can be established in each layer. Such an optimal permeance ratio is also proven to be a global optimum. Afterwards, we provide a theoretical generalisation of this optimality to whatever types of driving forces. Then, we provide a demonstration that the highest species permeating flux is always established when feeding it from the layer side with the highest exponent independently of the permeance ratio. As an important consequence, to maximise flux, a multilayer membrane/thin film should be fabricated by depositing the layers in cascade according to the ascending or descending exponents, and should be used in a configuration in which the flux flows from the layer with the highest pressure exponent to the layer with the lowest one. It is also shown that there exists an optimal value of the lower exponent n1 that maximizes the flux ratio keeping constant the other parameters. Finally, we showed that a virial-type linear combination of polynomial driving forces can be approximated by the empirical flux law investigated. Overall, our results are valid not only for whatever type of composite membranes and thin films (metallic, ceramic, polymeric and hybrid ones), but also for any sequential system involving a flux of whatever physical entity obeying the aforementioned law, such as heat transfer in the presence of radiation, non-linear electrical resistances and possible others.

Double-virtual NNLO QCD corrections for five-parton scattering. I. The gluon channel

We compute the two-loop helicity amplitudes for the scattering of five gluons, including all contributions beyond the leading-color approximation. The analytic expressions are represented as linear combinations of transcendental functions with rational coefficients, which we reconstruct from finite-field samples obtained with the numerical unitarity method. Guided by the requirement of removing unphysical singularities, we find a remarkably compact generating set of rational coefficients, which we display entirely in the manuscript. We implement our results in a public code, which provides efficient and reliable numerical evaluations for phenomenological applications. Published by the American Physical Society 2024