Improving sensitivity of XANES structural fit to the bridged metal-metal coordination.

Hard X-ray absorption spectroscopy is a valuable in situ probe for non-destructive diagnostics of metal sites. The low-energy interval of a spectrum (XANES) contains information about the metal oxidation state, ligand type, symmetry and distances in the first coordination shell but shows almost no dependency on the bridged metal-metal bond length. The higher-energy interval (EXAFS), on the contrary, is more sensitive to the coordination numbers and can decouple the contribution from distances in different coordination shells. Supervised machine-learning methods can combine information from different intervals of a spectrum; however, computational approaches for the near-edge region of the spectrum and higher energies are different. This work aims to keep all benefits of XANES and extend its sensitivity towards the interatomic distances in the first and second coordination shells. Using a binuclear bridged copper complex as a case study and cross-validation analysis as a quantitative tool it is shown that the first 170 eV above the edge are already sufficient to balance the contributions of Cu-O/N scattering and Cu-Cu scattering. As a more general outcome this work highlights the trivial but often overlooked importance of using `longer' energy intervals of XANES for structural refinement and machine-learning predictions. The first 200 eV above the absorption edge still do not require parametrization of Debye-Waller damping and can be calculated within full multiple scattering or finite difference approximations with only moderately increased computational costs.

Computational study on 2D three-phase lag bioheat model during cryosurgery using RBF meshfree method.

Biological tissue has a multidimensional and non-homogeneous inner structure by nature. The temperature distribution and freezing front locations in biological tissue are crucial to optimizing the damage to tissue during cryosurgery. There is a need for a good mathematical model and effective simulation techniques to predict the effectiveness of the therapy. The present study concerns the numerical study of phase change phenomena during cryosurgery using the three-phase lag (TPL) bioheat model in arbitrary soft tissue domains, i.e., circular (Γ1), ameba-like (Γ2), and multiconnected (Γ3). We employ the effective heat capacity formulation to solve the nonlinear governing equation. The Gaussian radial basis function and Crank-Nicolson finite difference approximation are applied for spatial and time derivatives, respectively. Using the present algorithm, we study the impact of phase lag (τv) due to thermal displacement involved in the TPL model on phase change interface position and thermal distribution in all three domains. The obtained results may be beneficial in the field of oncology.

Unravelled multilevel transformation networks for predicting sparsely observed spatio-temporal dynamics.

In this paper, we address the problem of predicting complex, nonlinear spatio-temporal dynamics when available data are recorded at irregularly spaced sparse spatial locations. Most of the existing deep learning models for modelling spatio-temporal dynamics are either designed for data in a regular grid or struggle to uncover the spatial relations from sparse and irregularly spaced data sites. We propose a deep learning model that learns to predict unknown spatio-temporal dynamics using data from sparsely-distributed data sites. We base our approach on the radial basis function (RBF) collocation method which is often used for meshfree solution of partial differential equations. The RBF framework allows us to unravel the observed spatio-temporal function and learn the spatial interactions among data sites on the RBF-space. The learned spatial features are then used to compose multilevel transformations of the raw observations and predict its evolution in future time steps. We demonstrate the advantage of our approach using both synthetic and real-world climate data. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method.

This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

Estimation of Radial Basis Function Network Centers via Information Forces.

The determination of The Radial Basis Function Network centers is an open problem. This work determines the cluster centers by a proposed gradient algorithm, using the information forces acting on each data point. These centers are applied to a Radial Basis Function Network for data classification. A threshold is established based on Information Potential to classify the outliers. The proposed algorithms are analysed based on databases considering the number of clusters, overlap of clusters, noise, and unbalance of cluster sizes. Combined, the threshold, and the centers determined by information forces, show good results in comparison to a similar Network with a k-means clustering algorithm.

Assessing the Best Gap-Filling Technique for River Stage Data Suitable for Low Capacity Processors and Real-Time Application Using IoT.

Hydrometeorological data sets are usually incomplete due to different reasons (malfunctioning sensors, collected data storage problems, etc.). Missing data do not only affect the resulting decision-making process, but also the choice of a particular analysis method. Given the increase of extreme events due to climate change, it is necessary to improve the management of water resources. Due to the solution of this problem requires the development of accurate estimations and its application in real time, this work present two contributions. Firstly, different gap-filling techniques have been evaluated in order to select the most adequate one for river stage series: (i) cubic splines (CS), (ii) radial basis function (RBF) and (iii) multilayer perceptron (MLP) suitable for small processors like Arduino or Raspberry Pi. The results obtained confirmed that splines and monolayer perceptrons had the best performances. Secondly, a pre-validating Internet of Things (IoT) device was developed using a dynamic seed non-linear autoregressive neural network (NARNN). This automatic pre-validation in real time was tested satisfactorily, sending the data to the catchment basin process center (CPC) by using remote communication based on 4G technology.

Investigation of landslide detection using radial basis functions: a case study of the Taskent landslide, Turkey.

This paper investigates landslide detection over flat and steep-slope areas with large forest cover using different radial basis function interpolation methods, which can affect the quality of a digital elevation model. Unmanned aerial vehicles have been widely used in landslide detection studies. The generation of image-based point clouds is achievable with various matching algorithms from computer vision systems. Point cloud-based analysis was performed by generating multi-temporal digital elevation models to detect landslide displacement. Interpolation methodology has a crucial task to fill the gaps in insufficient areas that result from filtered areas or sensors that do not generate spatial information. Radial basis function interpolations are the most commonly used technique for estimating the unknown values in survey areas. However, the quality of the radial basis function interpolation methods for landslide studies has not been thoroughly investigated in previous studies. In this study, radial basis function interpolation methods are investigated and compared with the global navigational satellite systems, which provide high accuracy for geodetic measurement systems. The main purpose of this study was to investigate the various radial basis function models to detect landslides using a point cloud-based digital elevation model and determine the quality of detection with global navigational satellite systems. As a result of this study, each of the radial basis function-generated digital elevation models was found to be statistically compatible with global navigational satellite systems, resulting in displacements from the ground truth data.

New tools for the visualization of biological pathways.

This paper presents several geometrically motivated techniques for the visualization of high-dimensional biological data sets. The Grassmann manifold provides a robust framework for measuring data similarity in a subspace context. Sparse radial basis function classification as a visualization technique leverages recent advances in radial basis function learning via convex optimization. In the spirit of deep belief networks, supervised centroid-encoding is proposed as a way to exploit class label information. These methods are compared to linear and nonlinear principal component analysis (autoencoders) in the context of data visualization; these approaches may perform poorly for visualization when the variance of the data is spread across more than three dimensions. In contrast, the proposed methods are shown to capture significant data structure in two or three dimensions, even when the information in the data lives in higher dimensional subspaces. To illustrate these ideas, the visualization techniques are applied to gene expression data sets that capture the host immune system's response to infection by the Ebola virus in non-human primate and collaborative cross mouse.

Long-term response to recombinant human growth hormone treatment: a new predictive mathematical method.

INTRODUCTION: Recombinant GH has been offered to GH-deficient (GHD) subjects for more than 30 years, in order to improve height and growth velocity in children and to enhance metabolic effects in adults. AIM: The aim of our work is to describe the long-term effect of rhGH treatment in GHD pediatric patients, suggesting a growth prediction model. MATERIAL AND METHODS: A homogeneous database is defined for diagnosis and treatment modalities, based on GHD patients afferent to Hospital Regina Margherita in Turin (Italy). In this study, 232 GHD patients are selected (204 idiopathic GHD and 28 organic GHD). Each measure is shown in terms of mean with relative standard deviations (SD) and 95% confidence interval (95% CI). To estimate the final height of each patient on the basis of few measures, a mathematical growth prediction model [based on Gompertzian function and a mixed method based on the radial basis functions (RBFs) and the particle swarm optimization (PSO) models] was performed. RESULTS: The results seem to highlight the benefits of an early start of treatment, further confirming what is suggested by the literature. Generally, the RBF-PSO method shows a good reliability in the prediction of the final height. Indeed, RMSE is always lower than 4, i.e., in average the forecast will differ at most of 4 cm to the real value. CONCLUSIONS: In conclusion, the large and accurate database of Italian GHD patients allowed us to assess the rhGH treatment efficacy and compare the results with those obtained in other Countries. Moreover, we proposed and validated a new mathematical model forecasting the expected final height after therapy which was validated on our cohort.

Optimal interpolation approach for groundwater depth estimation.

In arid and semi-arid regions where surface water resources are scarce, groundwater is crucial. Accurate mapping of groundwater depth is vital for sustainable management practices. This study evaluated the performance of three spatial interpolation techniques - inverse distance weighting (IDW), ordinary kriging (OK), and radial basis functions (RBF) - in predicting groundwater depth distribution across Dire Dawa City, Ethiopia. The results demonstrated the superiority of the RBF method, exhibiting the lowest RMSE (3.21 m), MAE (0.16 m), and the highest R2 (0.99) compared to IDW and OK. The IDW method emerged as the next best performer (RMSE = 4.68 m, MAE = 0.16 m, R2= 0.97), followed by OK (RMSE = 5.32 m, MAE = 0.42 m, R2= 0.95). The RBF's superior accuracy aligns with findings from other semi-arid regions, underscoring its suitability for data-scarce areas like Dire Dawa. This comparative evaluation provides valuable insights for selecting the optimal interpolation method for groundwater depth mapping, supporting informed decision-making in local water resource management. The methodological approach comprised:•Implementation of three interpolation techniques, namely, inverse distance weighting (IDW), ordinary kriging (OK), and radial basis functions (RBF), utilizing 56 groundwater depth measurements from locations dispersed throughout the study area.•Cross-validation through randomly withholding 20 % of the data for validation purposes.•Comparison of the techniques based on statistical measures of accuracy, including root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2).

A method for detecting spatiotemporal patterns of cancer biomarkers-evoked activity using radial basis function network extracted time-domain features from calcium imaging data.

BACKGROUND: Two-photon calcium imaging is widely used to study the odor-evoked glomerular activity in the dorsal olfactory bulb of macrosmatic animals. The nonstationary character of activated patterns sets a limit on the use of a traditional image processing approaches. NEW METHOD: The developed method makes it possible to automatically map cancer biomarkers-activated glomeruli in the rat dorsal olfactory bulb. We interpolated fluorescence intensity of calcium dynamics based on the Gaussian RBF network and synthesized the physiological fluorescence model of the receptive glomerular field. RESULTS: The experiments on 5 rats confirmed the correctness of the developed approach. Patterns evoked by the 6-methyl-5-hepten-2-one (stomach cancer biomarker) and benzene (lung cancer biomarker) were correctly identified. COMPARISON WITH EXISTING METHODS: The proposed method was compared with the nonnegative matrix factorization method and with the method based on computer vision algorithms. The developed approach showed better accuracy in experiments and provided the mathematical models of the odor-evoked patterns synthesis. These models can be used to generate synthetic images of odor-evoked glomerular activity and thus to overcome the problem of small experimental data collected in calcium imaging. CONCLUSIONS: The proposed method should be considered part of the toolkit for fully automatic analysis of calcium imaging-based studies. Currently available methodology is not able to use breath biomarkers to reliably discriminate between cancer patients and healthy controls. Nevertheless, the effective identification of the spatial patterns of cancer biomarkers-evoked glomerular activity can serve as the foundation for highly sensitive biohybrid systems for cancer screening.

A study of different modeling choices for simulating platelets within the immersed boundary method.

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations - radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations - for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations.

A Radial Basis Function Neural Network for Stochastic Frontier Analyses of General Multivariate Production and Cost Functions.

Production function techniques often impose functional form and other restrictions that limit their applicability. One common limitation in popular production function techniques is the requirement that all inputs and outputs must be positive numbers. There is a need to develop a production function analysis technique that is less restrictive in the assumptions it makes, and inputs it can process. This paper proposes such a general technique by linking fields of neural networks and econometrics. Specifically, two radial basis function (RBF) neural networks are proposed for stochastic production and cost frontier analyses. The functional forms of production and cost functions are considered unknown except that they are multivariate. Using simulated and real-world datasets, experiments are performed, and results are provided. The results illustrate that the proposed technique has broad applicability and performs equal to or better than the traditional stochastic frontier analysis technique.

Structural optimisation of the DEMO alternative divertor configurations based on FE and RBF mesh morphing.

The DEMO tokamak exhibits extraordinary complexity due to the constraints and requirements pertaining to different fields of physics and engineering. The multidisciplinary nature of the DEMO system makes its design phase extremely challenging since different and often opposite requirements need to be accounted for. Toroidal field (TF) coils generate the toroidal magnetic field required to magnetically confine the plasma particles and support at the same time the poloidal field coils. They must bear tremendous loads deriving from electromagnetic interactions between the coil currents and the generated magnetic field. An efficient tokamak design aims at minimizing the energy stored in its magnetic field and hence at reducing the toroidal volume within the TF coils whose shape would hence ideally mimic co-centrically the shape of the plasma. In order to bear the enormous forces a D-shape is most suitable for the TF coils as it allows them to resist the very large compression on the inner side and to carry the electro-magnetic (EM) pressure mainly by membrane stresses preventing large bending to occur on the outer side. At the same time the divertor structures must fit within the TF coils and this requires adaptations of the TF coil shape in the case of so-called advanced divertor configurations (ADCs), which require larger divertor structures. This article shows the TF coils adapted to ADCs using a structural optimisation procedure applied to the reference shape. The introduced strategy takes as structural optimum the iso-stress profile associated to each coil. A continuous transformation, based on radial basis functions mesh morphing, turns the baseline finite element (FE) model into its iso-stress counterpart, with a series of intermediate configurations available for electromagnetic and structural investigations as output. The adopted strategy allowed to determine, for each of the ADC cases, a candidate shape. Static membrane stress levels during magnetization could be reduced significantly from more than 700 MPa to below 450 MPa.

Increasing frame rate of echocardiography based on a novel 2D spatio-temporal meshless interpolation.

BACKGROUND: Increasing temporal resolution through numerical methods aids clinicians to evaluate fast moving structures of the heart with more confidence. METHODOLOGY: In this study, a spatio-temporal numerical method is proposed to increase the frame rate based on two-dimensional (2D) interpolation. More specifically, we propose a novel intensity variation time surface (IVTS) strategy to incorporate both temporal and spatial information in the reconstruction. In this regard, we exploit radial basis functions (RBFs) for 2D interpolation. The reason for choosing RBFs for this task is manifold. First, RBFs are able to interpolate on large-scale datasets. Moreover, their mathematical implementation is simple. Another important property of this interpolation technique, which is addressed in this study, is its meshless nature. The meshless property enables higher up-sampling (UpS) rates for echocardiography to improve temporal resolution without noticeably degrading image quality. To evaluate the proposed approach, we tested the RBF interpolation on 2D/3D echocardiography datasets. The reconstructed frames were analyzed using different image quality metrics, and the results were compared with two popular techniques from the literature. RESULTS: The findings demonstrated that, with a down-sampling rate of 3, the proposed technique outperformed the best existing method by 42%, 87%, 8%, and 11%, respectively, in terms of mean square error (MSE), contrast to noise ratio (CNR), peak signal-to-noise ratio (PSNR), and figure of merit (FOM). It should be noted that the proposed method is comparable to the best available method in terms of structural similarity (SSIM) index. Furthermore, when compared to the original images, the results of employing our technique on radio-frequency (RF) level analysis demonstrated that the reconstruction accuracy is satisfactory in terms of image quality criterion. CONCLUSION: Finally, it is worthwhile noting that the proposed method is better than (or comparable to) the other methods in terms of reconstruction performance and processing time. Therefore, the RBF interpolation can be a promising alternative to the existing methods.

Fast strain mapping in abdominal aortic aneurysm wall reveals heterogeneous patterns.

Abdominal aortic aneurysm patients are regularly monitored to assess aneurysm development and risk of rupture. A preventive surgical procedure is recommended when the maximum aortic antero-posterior diameter, periodically assessed on two-dimensional abdominal ultrasound scans, reaches 5.5 mm. Although the maximum diameter criterion has limited ability to predict aneurysm rupture, no clinically relevant tool that could complement the current guidelines has emerged so far. In vivo cyclic strains in the aneurysm wall are related to the wall response to blood pressure pulse, and therefore, they can be linked to wall mechanical properties, which in turn contribute to determining the risk of rupture. This work aimed to enable biomechanical estimations in the aneurysm wall by providing a fast and semi-automatic method to post-process dynamic clinical ultrasound sequences and by mapping the cross-sectional strains on the B-mode image. Specifically, the Sparse Demons algorithm was employed to track the wall motion throughout multiple cardiac cycles. Then, the cyclic strains were mapped by means of radial basis function interpolation and differentiation. We applied our method to two-dimensional sequences from eight patients. The automatic part of the analysis took under 1.5 min per cardiac cycle. The tracking method was validated against simulated ultrasound sequences, and a maximum root mean square error of 0.22 mm was found. The strain was calculated both with our method and with the established finite-element method, and a very good agreement was found, with mean differences of one order of magnitude smaller than the image spatial resolution. Most patients exhibited a strain pattern that suggests interaction with the spine. To conclude, our method is a promising tool for investigating abdominal aortic aneurysm wall biomechanics as it can provide a fast and accurate measurement of the cyclic wall strains from clinical ultrasound sequences.

Tunable superconducting neurons for networks based on radial basis functions.

The hardware implementation of signal microprocessors based on superconducting technologies seems relevant for a number of niche tasks where performance and energy efficiency are critically important. In this paper, we consider the basic elements for superconducting neural networks on radial basis functions. We examine the static and dynamic activation functions of the proposed neuron. Special attention is paid to tuning the activation functions to a Gaussian form with relatively large amplitude. For the practical implementation of the required tunability, we proposed and investigated heterostructures designed for the implementation of adjustable inductors that consist of superconducting, ferromagnetic, and normal layers.

An RBF Meshless Approach to Evaluate Strain Due to Large Displacements in Flexible Printed Circuit Boards.

Thin plates are very often employed in a context of large displacements and rotations, for example, whenever the extreme flexibility of a body can replace the use of complicated kinematic pairs. This is the case of the flexible Printed Circuit Boards (PCBs) used, for example, within last-generation foldable laptops and consumer electronics products. In these applications, the range of motion is generally known in advance, and a simple strategy of stress assessment leaving out nonlinear numerical calculations appears feasible other than desirable. In this paper, Radial Basis Functions (RBFs) are used to represent a generic transformation of a bi-dimensional plate, with all the derivate fields being analytically achieved without the need for a numerical grid for large-displacement applications. Strains due to bending are easily retrieved with this method and satisfactorily compared to analytical and shell-based Finite Element Method (FEM) benchmarks. On the other hand, the computational costs of the juxtaposed methods appear far different; with the machine being equal, the orders of magnitude of the time elapsed in computation are seconds for the RBF-based strategy versus minutes for the FEM approach.

Intelligent Control with Artificial Neural Networks for Automated Insulin Delivery Systems.

Type 1 diabetes mellitus is a disease that affects millions of people around the world. Recent progress in embedded devices has allowed the development of artificial pancreas that can pump insulin subcutaneously to automatically regulate blood glucose levels in diabetic patients. In this work, a Lyapunov-based intelligent controller using artificial neural networks is proposed for application in automated insulin delivery systems. The adoption of an adaptive radial basis function network within the control scheme allows regulation of blood glucose levels without the need for a dynamic model of the system. The proposed model-free approach does not require the patient to inform when they are going to have a meal and is able to deal with inter- and intrapatient variability. To ensure safe operating conditions, the stability of the control law is rigorously addressed through a Lyapunov-like analysis. In silico analysis using virtual patients are provided to demonstrate the effectiveness of the proposed control scheme, showing its ability to maintain normoglycemia in patients with type 1 diabetes mellitus. Three different scenarios were considered: one long- and two short-term simulation studies. In the short-term analyses, 20 virtual patients were simulated for a period of 7 days, with and without prior basal therapy, while in the long-term simulation, 1 virtual patient was assessed over 63 days. The results show that the proposed approach was able to guarantee a time in the range above 95% for the target glycemia in all scenarios studied, which is in fact well above the desirable 70%. Even in the long-term analysis, the intelligent control scheme was able to keep blood glucose metrics within clinical care standards: mean blood glucose of 119.59 mg/dL with standard deviation of 32.02 mg/dL and coefficient of variation of 26.78%, all below the respective reference values.

Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing.

The production of thin-walled beams with various cross-sections is increasingly automated and digitized. This allows producing complicated cross-section shapes with a very high precision. Thus, a new opportunity has appeared to optimize these types of products. The optimized parameters are not only the lengths of the individual sections of the cross section, but also the bending angles and openings along the beam length. The simultaneous maximization of the compressive, bending and shear stiffness as well as the minimization of the production cost or the weight of the element makes the problem a multi-criteria issue. The paper proposes a complete procedure for optimizing various open sections of thin-walled beam with different openings along its length. The procedure is based on the developed algorithms for traditional and soft computing optimization as well as the original numerical homogenization method. Although the work uses the finite element method (FEM), no computational stress analyses are required, i.e., solving the system of equations, except for building a full stiffness matrix of the optimized element. The shell-to-beam homogenization procedure used is based on equivalence strain energy between the full 3D representative volume element (RVE) and its beam representation. The proposed procedure allows for quick optimization of any open sections of thin-walled beams in a few simple steps. The procedure can be easily implemented in any development environment, for instance in MATLAB, as it was done in this paper.