Accurate Calculation Research Articles

GMCSpy: efficient and accurate computation of genetic minimal cut sets in Python.

The identification of minimal genetic interventions that modulate metabolic processes constitutes one of the most relevant applications of genome-scale metabolic models (GEMs). The concept of Minimal Cut Sets (MCSs) and its extension at the gene level, genetic Minimal Cut Sets (gMCSs), have attracted increasing interest in the field of Systems Biology to address this task. Different computational tools have been developed to calculate MCSs and gMCSs using both commercial and open-source software. Here, we present gMCSpy, an efficient Python package to calculate gMCSs in GEMs using both commercial and non-commercial optimization solvers. We show that gMCSpy substantially overperforms our previous computational tool GMCS, which exclusively relied on commercial software. Moreover, we compared gMCSpy with recently published competing algorithms in the literature, finding significant improvements in both accuracy and computation time. All these advances make gMCSpy an attractive tool for researchers in the field of Systems Biology for different applications in health and biotechnology. The Python package gMCSpy and the data underlying this manuscript can be accessed at: https://github.com/PlanesLab/gMCSpy.

Knudsen effusion mass spectrometry: Current and future approaches.

Knudsen effusion mass spectrometry (KEMS) has been a powerful tool in physical chemistry since 1954. There are many excellent reviews of the basic principles of KEMS in the literature. In this review, we focus on the current status and potential growth areas for this instrumental technique. We discuss (1) instrumentation, (2) measurement techniques, and (3) selected novel applications of the technique. Improved heating methods and temperature measurement allow for better control of the Knudsen cell effusive source. Accurate computer models of the effusive beam and its introduction to the ionizer allow optimization of such parameters as sensitivity and removal of background signals. Computer models of the ionizer allow for optimized sensitivity and resolution. Additionally, data acquisition systems specifically tailored to a KEMS system permit improved quantity and quality of data. KEMS is traditionally utilized for thermodynamic measurements of pure compounds and solutions. These measurements can now be strengthened using first principles and model-based computational thermochemistry. First principles can be used to calculate accurate Gibbs energy functions (gefs) for improving third law calculations. Calculated enthalpies of formation and dissociation energies from ab initio methods can be compared to those measured using KEMS. For model-based thermochemistry, solution parameters can be derived from measured thermochemical data on metallic and nonmetallic solutions. Beyond thermodynamic measurements, KEMS has been used for many specific applications. We select examples for discussion: measurements of phase changes, measurement/control of low-oxygen potential systems, thermochemistry of ultrahigh-temperature ceramics, geological applications, nuclear applications, applications to organic and organometallic compounds, and thermochemistry of functional room temperature materials, such as lithium ion batteries. We present an overview of the current status of KEMS and discuss ideas for improving KEMS instrumentation and measurements. We discuss selected KEMS studies to illustrate future directions of KEMS.

A Joint Inversion Method Algorithm for T2-Pc two Dimensional NMR based on Logistic Functions

Data processing is a key step in the analysis of nuclear magnetic resonance (NMR) experimental data, and efficient and accurate computer inversion algorithms are the core of the T2-Pc two-dimensional NMR experiment. T2-Pc two-dimensional NMR experiment is an advanced experimental method that characterizes reservoir connectivity through two dimensions: relaxation time and capillary pressure, and can obtain irreducible water saturation under different pressure differences. However, the algorithm currently used for T2-Pc two-dimensional spectrum inversion uses a mutation kernel function, resulting in low accuracy of calculation results. This paper uses the Logistic function as the two-dimensional inversion kernel function, rewrites the inversion algorithm, and obtains more accurate inversion results. Numerical simulations have proven that the T2-Pc two-dimensional map obtained by this method not only has higher resolution, but also has greater applicability in the case of low signal-to-noise ratio and a small number of centrifugal echo groups. Practice has found that the proposed method can reduce the number of centrifugations during the experiment and significantly improve the efficiency of T2-Pc two-dimensional nuclear magnetic resonance experiments.

On the computation of moments in the Super-Transition-Arrays model for radiative opacity calculations

In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the calculation of averages of products of subshell populations. In the present work, we discuss several aspects of the computation of such peculiar partition functions, insisting on the precautions that must be taken in order to avoid numerical difficulties. In a previous work, we derived a formula for supershell partition functions, which takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients for which we obtained a recursion relation and an explicit formula. We show that such an expansion can be combined with the recurrence relation for shifted partition functions. We also propose, neglecting the effect of fine structure as a first step, a positive-definite formula for the Super-Transition-Array moments of any order, providing an insight into the asymmetry and sharpness of the latter. The corresponding formulas are free of alternating sums. Several ways to speed up the calculations are also presented.

Three-dimensional numerical modeling of the temporal evolution of backward erosion piping

Backward erosion piping (BEP) is a complex degradation mechanism in geotechnical flood protection infrastructure (GFPI) that is still relatively less understood, particularly when considering its time-dependent features. This manuscript presents a novel dual random lattice modeling approach for three-dimensional simulation of BEP, with a focus on its evolution over time. The key novelty of this presented framework is twofold: (1) we propose and incorporate a novel constitutive relationship for computation of time-dependent soil erosion based on the theory of rate processes, and (2) we devise an algorithm for calculation of coupled degradation of the dual lattices for accurate computation of 3-D hydraulic gradients. The constitutive relationship was developed from fundamental granular physics, and brings the potential to provide deeper fundamental physical understanding of the phenomenon. The capabilities of the modeling framework are investigated by comparison with available laboratory experiments which illustrates good agreement in the spatial advancement of piping erosion, pipe progression speeds, as well as the evolution of local gradients. To the best knowledge of the authors, the presented model is the first to be able to capture all of the aforementioned features when simulating BEP.

High-efficiency scattering field modeling in metallic components: a machine-learning-inspired approach

We present a highly efficient method for characterizing the scattering field distribution of surface plasmon polaritons in metallic components by combining the eXtended Pseudospectral Frequency-Domain (X-PSFD) method with an iterative, machine-learning-inspired procedure. Shifting away from traditional matrix operations, we utilize the “Adam” optimizer—an effective and swift machine learning algorithm—to solve the scattering field distribution. Our method encompasses the derivation of the associated cost function and gradient differentiation of the field, leveraging spectral accuracy at Legendre collocation points in the Helmholtz equation. We refine the total-field/scattered-field (TF/SF) formulation within the X-PSFD framework for optimized incident field management and employ Chebyshev–Lagrange interpolation polynomials for rapid, accurate computation of broad-band results. To ensure global accuracy, we introduce unique physical boundary conditions at subdomain interfaces. Demonstrating our method’s robustness and computational efficiency, we model perfect electric conductors (PECs) and silver nanocylinders, and we apply our approach to analyze the excited electric field on subtly distorted metallic surfaces, particularly plasmonic structures, thereby validating its wide-ranging effectiveness.

On the accurate computation of the Newton form of the Lagrange interpolant

AbstractIn recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision, even for large ill-conditioned matrices. In this framework, the present work provides the factorization of the collocation matrices of Newton bases—of relevance when considering the Lagrange interpolation problem—together with an algorithm that allows to numerically compute it to high relative accuracy. This further allows to determine the coefficients of the interpolating polynomial and to compute the singular values and the inverse of the collocation matrix. Conditions that guarantee high relative accuracy for these methods and, in the former case, for the classical recursion formula of divided differences, are determined. Numerical errors due to imprecise computer arithmetic or perturbed input data in the computation of the factorization are analyzed. Finally, numerical experiments illustrate the accuracy and effectiveness of the proposed methods with several algebraic problems, in stark contrast with traditional approaches.

Soccer match broadcast video analysis method based on detection and tracking

AbstractWe propose a comprehensive soccer match video analysis pipeline tailored for broadcast footage, which encompasses three pivotal stages: soccer field localization, player tracking, and soccer ball detection. Firstly, we introduce sports camera calibration to seamlessly map soccer field images from match videos onto a standardized two‐dimensional soccer field template. This addresses the challenge of consistent analysis across video frames amid continuous camera angle changes. Secondly, given challenges such as occlusions, high‐speed movements, and dynamic camera perspectives, obtaining accurate position data for players and the soccer ball is non‐trivial. To mitigate this, we curate a large‐scale, high‐precision soccer ball detection dataset and devise a robust detection model, which achieved the of 80.9%. Additionally, we develop a high‐speed, efficient, and lightweight tracking model to ensure precise player tracking. Through the integration of these modules, our pipeline focuses on real‐time analysis of the current camera lens content during matches, facilitating rapid and accurate computation and analysis while offering intuitive visualizations.

Investigation and perspectives of using Graph Neural Networks to model complex systems: the simulation of the helium II bayonet heat exchanger in the LHC

Large cryogenic systems, like those installed at CERN, are complex systems relying on many diverse physical processes and phenomena that are difficult to simulate and monitor in detail. With only a limited number of properties measured and made available for monitoring and control purposes, several processes contributing to the dynamics of the systems are ignored. This lack of information can reduce the accuracy and the capability of a model to track, predict, and anticipate the behavior of the system. Accurate analytical or numerical computer modeling can be developed to simulate the non-linear dynamics of the processes but they are complex, computationally intensive, and cumbersome to test, validate, and implement with different configurations and limited measurements of the hidden properties. In this work, we present our investigation of using Graph Neural Networks (GNN) to build a model of the helium II bayonet heat exchanger operating in the LHC at CERN. We are proposing to use a hybrid machine learning approach, where the parameters of the GNN model are estimated by a combination of supervised learning algorithms trained on experimental data and bounding physics equations and parameters. The GNN model was initially trained on data from the experiments performed on the LHC prototype magnet strings and validated on data extracted during the operation of the LHC machine. We demonstrate the model’s accuracy, repeatability, and robustness in various configurations. The model is also well inspectable and explainable, providing the time evolution of all variables. We report on the results and expected applications, which include predictive control, diagnostic, and operator training.

A statistical model for estimating porosity based on various parameters of flow through porous media

ABSTRACT Flow through porous media is a process with a momentous impact on the environment. Hydraulic conductivity, which depends on the particle size, shape, and porosity of the media, has applications in different fields of science, e.g., groundwater, seepage, and soil stability. Precise estimation of porosity leads to accurate computation of the hydraulic conductivity of porous media. The present study investigates the effect of particle size on the porosity of porous media, i.e., crushed quartzite, river gravel, marble chips, and sand. The influence of the wall effect on packing and porosity of porous media based on the diameter ratio, i.e., the ratio of permeameter-to-particle size (Dp/dg) has also been investigated. The hydraulic conductivity and the porosity of porous media are observed to increase with an increase in the particle size. The study postulates a dependable relation between hydraulic conductivity and porosity. The experimentally obtained and the model-generated porosity values for crushed quartzite, river gravel, marble chips, and sand range between 0.38–0.42 and 0.37–0.43, respectively. Experimental data have been used to derive a statistical model based on the diameter ratio (5.08 ≤ (Dp/dg) ≤ 254) for estimating the porosity of media. The validation of the statistical model using experimental data establishes the efficacy of the developed model.

Analysis of Calculation of Cost of Production Using the Full Costing Method

The goal of the study is to investigate and demonstrate that, for Micro, Small, and Medium-Sized Businesses, applying the complete costing method for calculating manufacturing costs results in a more accurate computation. This study is crucial for entrepreneurs since it helps them determine the precise cost of manufacturing things and determines how much profit they should make. This study employs qualitative descriptive methods. The results of this study's comprehensive costing technique calculation of manufacturing costs for commodities are more accurate for use in micro, small, and medium-sized enterprises.

Dynamic-mode-decomposition-based gradient prediction for adjoint-based aerodynamic shape optimization

Accurate and efficient gradient computation is the key to aerodynamic shape optimization. In this paper, dynamic mode decomposition (DMD) is employed to analyze the dynamic characteristics of the early pseudo-time marching of adjoint equations and to predict the gradient. Besides the first-order zero-frequency mode, other zero-frequency modes also contribute to the pseudo iterations of the adjoint equations in the early iterations. Hence, different from existing methods, all zero-frequency modes are retained to reconstruct adjoint fields for gradient prediction. Moreover, to further improve the modeling accuracy, an improved DMD (IDMD) is proposed by omitting the initial snapshots in early iterations. The effect of pseudo-time step on modeling accuracy is also studied. By solving the adjoint equations of the transonic and subsonic flows, the accuracy of the proposed method is verified. Results indicate that the proposed method still works despite the conventional solution process diverges. Through aerodynamic shape optimization examples of transonic flow over an airfoil, the number of adjoint pseudo-time steps is remarkably reduced by 83%, which indicates the proposed IDMD-based gradient prediction method has great potential for improving the efficiency of aerodynamic shape optimization.

Improved algorithm for generating evenly-spaced streamlines from an orientation field on a triangulated surface

Background:Vector fields such as cardiac fiber orientation can be visualized on a surface using streamlines. The application of evenly-spaced streamline generation to the construction of interconnected cable structure for cardiac propagation models has more stringent requirements imperfectly fulfilled by current algorithms. Method:We developed an open-source C++/python package for the placement of evenly-spaced streamlines on a triangulated surface. The new algorithm improves upon previous works by more accurately handling streamline extremities, U-turns and limit cycles, by providing stronger geometrical guarantees on inter-streamline minimal distance, particularly when a high density of streamlines (up to 10μm spacing) is desired, and by making a more efficient parallel implementation available. The approach requires finding intersections between geometrical capsules and triangles to update an occupancy mask defined on the triangles. This enables fast streamline integration from thousands of seed points to identify optimal streamline placement. Results:The algorithm was assessed qualitatively on different left atrial models of fiber orientation with varying mesh resolutions (up to 375k triangles) and quantitatively by measuring streamline lengths and distribution of inter-streamline minimal distance. The complexity and the computational performance of the algorithm were studied as a function of streamline spacing in relation to triangular mesh resolution. Conclusion:More accurate geometrical computations, attention to details and fine-tuning led to an algorithm more amenable to applications that require precise positioning of streamlines.

Boussinesq-type equations of hydroelastic waves in shallow water

Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydroelastic waves, in which non-uniform distribution of structural stiffness and varying water depth are considered rigorously. Application of Boussinesq assumptions enables complicated three-dimensional problems to be reduced and formulated on the two-dimensional horizontal plane, therefore the proposed Boussinesq-type models are straightforward and versatile for a wide range of hydroelastic wave applications. Two configurations, a floating plate and a submerged plate, are studied. The first-order linear governing equations are solved analytically with periodic conditions assuming constant depth and uniform stiffness, and the linear dispersion relations are subsequently derived for both configurations. For flexural-gravity waves of a floating plate, unique behaviours of flexural-gravity waves different from shallow-water waves are discussed, and a generalized solitary wave solution is investigated. A nonlinear numerical solver is developed, and nonlinear flexural-gravity waves are found to have smaller wavelength and celerity than their linear counterparts. For hydroelastic waves of a submerged plate, dual-mode analytical solutions are discovered for the first time. Numerical computation has demonstrated that a plate with decreasing submerged depth is able to transfer wave energy from the deeper water to the surface layer.

A Coarsened-Shell-Based Cosserat Model for the Simulation of Hybrid Cables

The simulation of elastic slender objects like cables is essential for industrial applications in predicting elastic behaviors and life cycles. The Cosserat model and its variants are the dominant approaches due to their high efficiency and accuracy. However, these assume cables with homogeneous interiors and thus cannot simulate hybrid cables containing different materials. We address this by developing a novel coarsened-shell-based Cosserat (CSC) model. The CSC model constructs a material-aware elastic energy function along the cable’s cross-section to describe the global elastic behavior. The CSC model is specifically developed by carefully leveraging the strengths of three approaches: the Cosserat theory to model slender cables, the Kirchhoff–Love shell theory to model the cable’s cross-sectional energy, and numerical coarsening to reduce the degrees of freedom in the shell simulation via constructing a set of new types of material-aware shape/base functions. This allows the more accurate computation of the local and global deformations of hybrid cables, surpassing the classical Cosserat models in accuracy.

A personal perspective of the present status and future challenges facing thermal reaction rate theory.

Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.

Modelling permanent magnet excited uniform fields with rational approximations

PurposeA novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.Design/methodology/approachFirst, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.FindingsAAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.Research limitations/implicationsAAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.Originality/valueThe authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

Theoretical study of low-lying electronic states spectra and transition properties of BeS molecule

There are only limited theoretical results published on the transition properties of the X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ−, E1Δ, a3Π, b3Σ+, and c3Δ states of BeS, and even some of the states have no theoretical and experimental reports on the relevant aspects of these transitions. Therefore, we derived these transition properties in this study. The potential energy curves of X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ−, E1Δ, a3Π, b3Σ+, c3Δ, d3Σ−, and e3Σ− states of the BeS molecule with their Ω states and the transition dipole moments between them were calculated by the complete active space self-consistent field method, followed by the internally contracted multireference configuration interaction method. For the accurate computation of the transition properties, scalar relativistic corrections and core–valence correlation were considered. The radiative lifetimes were approximately 10−6 s for the A1Π and b3Σ+ states, 10−7 s for the E1Δ state, 10−7–10−8 s for the C1Δ and D1Σ− states, and 10−8 s for the B1Σ+, c3Δ, and e3Σ− states. The transition properties of the seven Ω states generated by the X1Σ+, A1Π, B1Σ+, and a3Π electronic states, including several electric dipole-forbidden transitions were researched. In particular, the B1Σ+ 0+–X1Σ+ 0+, B1Σ+ 0+–A1Π1, and A1Π1–X1Σ+ 0+ systems have strong transitions. In this paper, the radiative lifetimes of A1Π1, B1Σ+ 0+, a3Π0−, a3Π0+, and a3Π1 electronic states were also computed. For the A1Π1, B1Σ+ 0+, and a3Π1 states, the distribution of the radiation lifetime with the rotational angular momentum quantum number J at 0 ≤ υ ≤ 15 and J ≤ 70 was evaluated. It is expected that the outcome of the calculations in this paper can contribute some meaningful guidelines for conducting further theoretical and experimental investigations.

On development of lattice-Boltzmann method based multi phase flow solver

A numerical methodology based on lattice Boltzmann and level set function is presented to simulate the two-phase flows with stringent density and viscosity ratio. Two different strategies - single grid (SGLBLS) and dual grid (DGLBLS) are used. For accurate computation of interfacial forces in DGLBLS, the level set equations are solved on a uniform grid which is twice that for lattice-Boltzmann equations. The code validation and performance of SGLBLS and DGLBLS is carried on three different problems: Young’s Laplace law, 2D rising bubble and Rayleigh–Taylor instability. The results show that the representation of the interface is more accurate in DGLBLS with significantly less mass error - establishing it as an accurate method to handle stringent density and viscosity ratio. The comparison between DGLBLS and SGLBLS shows that the DGLBLS leads to a large improvement in the accuracy of the results with only slight increase in the computational cost.

Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method

AbstractIn this work we propose the Step Matrix Multiplication based Path Integration method (SMM-PI) for nonlinear vibro-impact oscillator systems. This method allows the efficient and accurate deterministic computation of the time-dependent response probability density function by transforming the corresponding Chapman–Kolmogorov equation to a matrix–vector multiplication using high-order numerical time-stepping and interpolation methods. Additionally, the SMM-PI approach yields the computation of the joint probability distribution for response and impact velocity, as well as the time between impacts and other important characteristics. The method is applied to a nonlinear oscillator with a pair of impact barriers, and to a linear oscillator with a single barrier, providing relevant densities and analysing energy accumulation and absorption properties. We validate the results with the help of stochastic Monte-Carlo simulations and show the superior ability of the introduced formulation to compute accurate response statistics.