Local Basis Research Articles

Synchrony in Learning: Investigating the Connection between Student Adjustment and Academic Performance

Adjustment is an important part of human life because it gives people the power and strength to make positive changes in the world around them. The need for adjustment extends beyond the classroom to include classmates, instructors, curriculum, any other school activities and background setting of that place. Those who possess the ability to adapt to the ever-changing conditions in their surroundings have the potential to achieve harmonious living and maintain a contented and well-rounded existence. The present study comprised 191 secondary school students of Sirmaur district, Himachal Pradesh. The method used in the current research was a descriptive survey and stratified random sampling technique was utilized in order to organize and collect data on the basis of gender and locality. The Adjustment Inventory for school students, which was established by A.K.P. Sinha and R.P. Singh and incorporates 60 items evenly split between emotional, social, and educational adjustments, was deployed to measure the level of adjustment of the students. From the previous records, academic scores were taken as academic performance of the students. There is no significant difference of adjustment scores between male and female students of secondary school but highly significant difference (t value 4.376) between urban and rural students. girls are more well-adjusted result shows that rural students are more adjusted than urban students as maximum students of rural area are in good category highly negative correlation between adjustment problems and academic achievement scores of secondary school students.

Rearrangement and breakup amplitudes from the solution of Faddeev-AGS equations by pseudo-state discretization of the two-particle continuum

The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.

A Local Radial Basis Function Method for Numerical Approximation of Multidimensional Multi-Term Time-Fractional Mixed Wave-Diffusion and Subdiffusion Equation Arising in Fluid Mechanics

This article develops a simple hybrid localized mesh-free method (LMM) for the numerical modeling of new mixed subdiffusion and wave-diffusion equation with multi-term time-fractional derivatives. Unlike conventional multi-term fractional wave-diffusion or subdiffusion equations, this equation features a unique time–space coupled derivative while simultaneously incorporating both wave-diffusion and subdiffusion terms. Our proposed method follows three basic steps: (i) The given equation is transformed into a time-independent form using the Laplace transform (LT); (ii) the LMM is then used to solve the transformed equation in the LT domain; (iii) finally, the time domain solution is obtained by inverting the LT. We use the improved Talbot method and the Stehfest method to invert the LT. The LMM is used to circumvent the shape parameter sensitivity and ill-conditioning of interpolation matrices that commonly arise in global mesh-free methods. Traditional time-stepping methods achieve accuracy only with very small time steps, significantly increasing the computational time. To overcome these shortcomings, the LT is used to provide a more powerful alternative by removing the need for fine temporal discretization. Additionally, the Ulam–Hyers stability of the considered model is analyzed. Four numerical examples are presented to illustrate the effectiveness and practical applicability of the method.

An extension of the approximate component mode synthesis method to the heterogeneous Helmholtz equation

Abstract In this work, we propose and analyze an extension of the approximate component mode synthesis (ACMS) method to the two-dimensional heterogeneous Helmholtz equation. The ACMS method has originally been introduced by Hetmaniuk and Lehoucq as a multiscale method to solve elliptic partial differential equations. The ACMS method uses a domain decomposition to separate the numerical approximation by splitting the variational problem into two independent parts: local Helmholtz problems and a global interface problem. While the former are naturally local and decoupled such that they can be easily solved in parallel, the latter requires the construction of suitable local basis functions relying on local eigenmodes and suitable extensions. We carry out a full error analysis of this approach focusing on the case where the domain decomposition is kept fixed, but the number of eigenfunctions is increased. The theoretical results in this work are supported by numerical experiments verifying algebraic convergence for the method. In certain, practically relevant cases, even super-algebraic convergence for the local Helmholtz problems can be achieved without oversampling.

NUMERICAL COMPARISON OF THREE LOCAL MULTIVARIATE GAUSSIAN-BASED INTERPOLATION SCHEMES

This study introduces the Local Explicit Radial Basis Function scheme (LE-RBF), alongside an investigation of its effectiveness compared with two other Gaussian RBF-based methods: the Modified Radial Basis Function Shepard's method (MRBFS) and the Local Radial Basis Function Karel's algorithm (KAREL), for interpolation problems. The research focuses on three challenging applications: Franke’s function in two and three dimensions, and grayscale image reconstruction. All three schemes, operating in a local interpolation manner, are assessed across multiple criteria, including accuracy, CPU time and storage, and sensitivity to parameters and node sizes. The numerical experiments conducted reveal that while all three schemes yield reasonably good results in most scenarios, the proposed LE-RBF method stands out for its higher accuracy, reduced sensitivity to nodes and shape choices, and lower CPU time and storage requirements. Notably, LE-RBF demonstrates superior performance in various node densities and shape parameter-selecting strategies, especially when combined with specific strategies like the Carlson shape at 142×142 nodes. Its efficiency in processing time further highlights its practicality for complex applications. The study concludes that LE-RBF, with its robust performance and flexibility, presents a promising avenue for future application in diverse scientific and engineering tasks.

The localized radial basis function collocation method for dendritic solidification, solid phase sintering and wetting phenomenon based on phase field

Phase-field has been effectively applied to many complex problems according to the mesh based method. However, the computational speed of the numerical method based on phase-field still needs improved. In this paper, an improved localized radial basis function collocation method (LRBFCM) based on the adaptive support domain is employed to the phase-field methods. The proposed adaptive support domain can increase the stability of the LRBFCM, and the improved LRBFCM is much more efficient than the traditional finite element method (FEM) in coupling with phase-field methods. The proposed approach is further applied to the single-phase dendrite solidification, two-phase sintering, and three-phase wetting phenomena. We compare the efficiency of the proposed LRBFCM with different numerical methods, which show that the LRBFCM combined with the Fourier spectral method can deal with the three-phase model with more than ten million nodes easily.

A New Scene Sensing Model Based on Multi-Source Data from Smartphones

Smartphones with integrated sensors play an important role in people’s lives, and in advanced multi-sensor fusion navigation systems, the use of individual sensor information is crucial. Because of the different environments, the weights of the sensors will be different, which will also affect the method and results of multi-source fusion positioning. Based on the multi-source data from smartphone sensors, this study explores five types of information—Global Navigation Satellite System (GNSS), Inertial Measurement Units (IMUs), cellular networks, optical sensors, and Wi-Fi sensors—characterizing the temporal, spatial, and mathematical statistical features of the data, and it constructs a multi-scale, multi-window, and context-connected scene sensing model to accurately detect the environmental scene in indoor, semi-indoor, outdoor, and semi-outdoor spaces, thus providing a good basis for multi-sensor positioning in a multi-sensor navigation system. Detecting environmental scenes provides an environmental positioning basis for multi-sensor fusion localization. This model is divided into four main parts: multi-sensor-based data mining, a multi-scale convolutional neural network (CNN), a bidirectional long short-term memory (BiLSTM) network combined with contextual information, and a meta-heuristic optimization algorithm.

Exploration of the structure, electronic and optical properties of AB 2(PO3)5 polyphosphates: a first-principle approach

The density functional theory method was applied using the gradient PBE, incorporating the hybrid PBE0 functional along with dispersion corrections D3(BJ). These objectives were accomplished through the utilization of the CRYSTAL package, employing a localized atomic orbital basis. Calculations encompassing crystal properties, including electronic, structural, and linear/nonlinear opto-electronic characteristics, were conducted for monoclinic AB 2(PO3)5. Specifically, the polyphosphates investigated in this study are RbPb2(PO3)5, CsPb2(PO3)5, KBa2(PO3)5, and RbBa2(PO3)5. It was demonstrated that in monoclinic phosphates, phosphorus and oxygen atoms form infinite chains [PO4]∞ based on the· ⋯ O1-P-O1 ⋯ ·structure. Alkali metal and lead (barium) atoms are surrounded by oxygen atoms O2, forming polyhedra. Infrared absorption spectra calculations confirmed the presence of chain backbone structural units. Additionally, band structure and partial density of electronic states were determined. The nature of valence and unoccupied states was also investigated. In lead-doped compounds, lead atoms contribute to the formation of upper-valence and lower-unoccupied states. Conversely, in barium-doped compounds, the upper valence states are primarily formed by O2 p-states, while the lower unoccupied states are formed by phosphorus. Also, the coefficients of second harmonic generation and birefringence were calculated, assessing the potential use of phosphates as nonlinear optical materials.

Impact of hardware impairments and BS antenna tilt on 3D drone localization and tracking

Today, GPS-free drone localization is increasingly gaining attention in various applications, but it faces significant accuracy challenges in three-dimensional (3D) space due to various impairments. This study investigates the effects of carrier frequency offset (CFO), phase noise (PN), and down-tilted base station (BS) antennas on drone positioning and tracking. Additionally, we explore the impact of inter-site distance (ISD) and BS density on drone position estimation accuracy. In our methodology, we consider a flying drone equipped with a single transmission antenna and BSs configured with 4 × 4 antennas under specific impairments. We first analyze the effects of these impairments on the signal’s covariance matrix. Then, using the MUSIC algorithm, we estimate the azimuth and elevation angles, which serve as the basis for drone localization using the Least Squares (LS) method across all BSs. Finally, the estimated positions feed into an Extended Kalman Filter (EKF) for tracking. Our results present a sequential analysis of the impact of all impairments on the off-diagonal covariance matrix, on the Angle of Arrival (AOA) estimation and 3D drone localization. We use simulations to demonstrate how hardware impairments affect 3D drone localization accuracy under varying ISD and BS densities.

The Hermite-Birkhoff Problem and Local Spline Approximation

This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff problem. The solution to a specific problem using polynomial and non-polynomial local splines of the third order of approximation is considered. Here we discuss the case when the values of the function 𝑢(𝑥) and its derivative 𝑢’(𝑥) are given at the nodes of the grid in an alternative way: … , 𝑢(𝑥𝑗), 𝑢′(𝑥𝑗+1), 𝑢(𝑥𝑗+2), … . Note that when using polynomial and non-polynomial spline approximations, it is possible to obtain acceptable solutions in several interesting cases that are impossible when we use the classical approach. In the case of using local basis splines, many previously unsolvable problems turn out to be solvable. The results of the numerical experiments are presented.

Implicit EXP-RBF techniques for modeling unsaturated flow through soils with water uptake by plant roots

Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop efficient numerical techniques for solving the Richards equation with a sink term due to plant root water uptake. The Feddes model is used for water absorption by plant roots, and the van-Genuchten model is employed for capillary pressure. We introduce a numerical approach that combines the localized exponential radial basis function (EXP-RBF) method for space and the second-order backward differentiation formula (BDF2) for temporal discretization. The localized RBF methods eliminate the need for mesh generation and avoid ill-conditioning problems. This approach yields a sparse matrix for the global system, optimizing memory usage and computational time. The proposed implicit EXP-RBF techniques have advantages in terms of accuracy and computational efficiency thanks to the use of BDF2 and the localized RBF method. Modified Picards iteration method for the mixed form of the Richards equation is employed to linearize the system. Various numerical experiments are conducted to validate the proposed numerical model of infiltration with plant root water absorption. The obtained results conclusively demonstrate the effectiveness of the proposed numerical model in accurately predicting soil moisture dynamics under water uptake by plant roots. The proposed numerical techniques can be incorporated in the numerical models where unsaturated flows and water uptake by plant roots are involved such as in hydrology, agriculture, and water management.

A POD based reduced-order local RBF collocation approach for time-dependent nonlocal diffusion problems

A fast algorithm based on reduced-order model (ROM) is proposed for unsteady nonlocal diffusion models. It combines proper orthogonal decomposition (POD) approach and collocation method with local radial basis functions (RBFs), which makes it possible for using ROM to solve nonlocal models. Several numerical experiments showed that this approach significantly reduce the computational cost of nonlocal models while keep the similar convergent behavior compared with the RBF collocation methods.

Numerical analysis of small-strain elasto-plastic deformation using local Radial Basis Function approximation with Picard iteration

In this paper, we discuss a von Mises plasticity model with nonlinear isotropic hardening assuming small strains in a plane strain example of internally pressurised thick-walled cylinder subjected to different loading conditions. The elastic deformation is modelled using the Navier-Cauchy equation. In regions where the von Mises stress exceeds the yield stress, corrections are made locally through a return mapping algorithm. We present a novel method that uses a Radial Basis Function-Finite Difference (RBF-FD) approach with Picard iteration to solve the system of nonlinear equations arising from plastic deformation. This technique eliminates the need to stabilise the divergence operator and avoids special positioning of the boundary nodes, while preserving the elegance of the meshless discretisation and avoiding the introduction of new parameters that would require tuning. The results of the proposed method are compared with analytical and Finite Element Method (FEM) solutions. The results show that the proposed method achieves comparable accuracy to FEM while offering significant advantages in the treatment of complex geometries without the need for conventional meshing or special treatment of boundary nodes or differential operators.

Locally supported, quasi-interpolatory bases for the approximation of functions on graphs

Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the approximation space is not available analytically and must be computed. We propose perturbations of Lagrange bases on graphs, where the Lagrange functions come from a class of functions analogous to classical splines. The basis functions we consider have local support, with each basis function obtained by solving a small energy minimization problem related to a differential operator on the graph. We present ℓ∞ error estimates between the local basis and the corresponding interpolatory Lagrange basis functions in cases where the underlying graph satisfies an assumption on the connections of vertices where the function is not known, and the theoretical bounds are examined further in numerical experiments. Included in our analysis is a mixed-norm inequality for positive definite matrices that is tighter than the general estimate ‖A‖∞≤n‖A‖2.

Maximum Local Density-Driven Non-overlapping Radial Basis Function Support Kernel Neural Network

The learning and optimization of kernels in the radial basis function neural network (RBFNN) are crucial. However, in existing methods, there are issues of overfitting when learning kernel parameters. The learned kernels are also sensitive to outliers. This paper proposes a general kernel learning strategy for RBFNN called non-overlapping maximum local density support kernel learning (MLD-SKL), which contains two modules, the non-overlapping maximum local density (MLD) kernel learning module and support kernel learning (SKL) module. In the MLD kernel learning stage, the candidate set of kernels is incrementally determined based on the local density of samples. Meanwhile, it is required that the coverage ranges of kernels from different classes do not overlap with each other. This module is effective in reducing the impact of outliers. In the SKL stage, kernel importance indicator is defined to measure the importance of kernels. The learned support kernels are utilized to construct a maximum local density-driven non-overlapping radial basis function support kernel neural network (MLD-RBFSKNN). The RBFNN constructed through MLD-SKL exhibits a more compact structure. The experiments demonstrate that the proposed MLD-RBFSKNN improves accuracy in recognition task. Furthermore, while achieving superior recognition performance, the final constructed network also has the minimum number of kernels.

A stable localized weak strong form radial basis function method for modelling variably saturated groundwater flow induced by pumping and injection

The unsaturated zone profoundly affects groundwater (GW) flow induced by pumping and injection due to the capillary forces. However, current radial basis function (RBF) numerical models for GW pumping and injection mostly ignore the unsaturated zone. To bridge this gap, we developed a new three-dimensional weak strong form RBF model in this study, called CCHE3D-GW-RBF. Flow processes were modelled by the mixed-form Richards equation which was iteratively solved by the modified Picard iteration. Soil-water characteristic curves were represented by the widely applicable formulas, the van Genuchten (1980) model. Differential operators were approximated by the localized Gaussian RBF, and the weighted singular value decomposition method was used to construct stable bases. The injection/pumping wells and the flux boundaries were handled by the weak formulation using Meshless Local Petrov Galerkin method, and the strong-form equation using the collocation RBF method was enforced on the other points. Good agreement was found between the simulation results from our numerical model and the well-accepted solutions in all three verification cases, demonstrating the accuracy and applicability of this model. In addition, a smaller RBF shape parameter was found to produce a more accurate modelling resulting, indicating the necessity of implementing stable bases for RBF models.

Proposal for the redesign of post COVID 19 cities in the labor field

Intercommunal Work Centers (CTI) as a solution to reconfigure urban space in response to the COVID-19 pandemic. 34 communes of Greater Santiago are examined, grouped into 5 macrocommunes, with the objective of locating at least one CTI in each macrozone. A macro simulation methodology is used that weights socio-territorial variables, including socioeconomic level, level of study, employment, overcrowding and internet connection. The results offer a solid basis for optimal localization of CTIs based on these variables.

Bulk reconstruction from generalized free fields

We propose a generalized protocol for constructing a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the Hamilton-Kabat-Liftschytz-Lowe (HKLL) construction. However, unlike the HKLL construction, our protocol relies only on boundary data with no presupposed form for the bulk equations of motion, so our reconstructed bulk is fully emergent. For a (1+1)d bulk, imposing the bulk operator algebra as well as a causal structure is sufficient to determine the bulk operators and dynamics uniquely up to an unimportant local basis choice. We study the bulk construction for several two-sided SYK models with and without coupling between the two sides, and find good agreement with known results in the low-temperature conformal limit. In particular, we find bulk features consistent with the presence of a black hole horizon for the TFD state, and characterize the infalling fermion modes. We are also able to extract bulk quantities such as the curvature and bulk state correlators in terms of boundary quantities. In the presence of coupling between the two SYK models, we are able to observe evidence of the shockwave geometry and the traversable wormhole geometry using the two-sided mutual information between the reconstructed bulk operators. Our results show evidence that features of the geometric bulk can survive away from the low temperature conformal limit. Furthermore, the generality of the protocol allows it to be applied to other boundary theories with no canonical holographic bulk.

Breakthrough inventions in China: the role of intra- and inter-regional collaboration and local knowledge base

ABSTRACT Recently, the prevalent recommendation for industrialised regions is to diversify their local knowledge base through intra- and inter-regional collaborations, to maintain a competitive advantage in dynamic regional economies. However, this has resulted in a series of policies that lean towards a ‘one-size-fits-all’ approach. Theoretically, regions with varying local knowledge bases should follow unique technological trajectories. In this context, this article intends to examine the impact of collaboration, as well as its interaction effects with the local knowledge base, on the likelihood of breakthrough inventions. Our key findings, derived from a 15-year panel dataset (2002–2016) covering 200 prefecture-level cities in China, include: (1) Intra-regional collaboration and a balanced mix of intra- and inter-regional collaboration both positively influence the likelihood of breakthrough inventions; (2) The potential for breakthrough inventions depends on the interplay between collaboration and the local knowledge base. Specifically, internal collaboration is more beneficial for diversified regions, external collaboration aids more specialised regions, and both inter-regional collaboration or balanced mix of intra- and inter-regional collaboration can enhance the probability of breakthrough inventions for cities with a complex knowledge base. Our study holds significant implications for regional development, proposing a viable technological trajectory to mitigate path dependency.

Centrocortin potentiates co-translational localization of its mRNA to the centrosome via dynein.

Centrosomes rely upon proteins within the pericentriolar material to nucleate and organize microtubules. Several mRNAs also reside at centrosomes, although less is known about how and why they accumulate there. We previously showed that local Centrocortin (Cen) mRNA supports centrosome separation, microtubule organization, and viability in Drosophila embryos. Here, using Cen mRNA as a model, we examine mechanisms of centrosomal mRNA localization. We find that while the Cen N'-terminus is sufficient for protein enrichment at centrosomes, multiple domains cooperate to concentrate Cen mRNA at this location. We further identify an N'-terminal motif within Cen that is conserved among dynein cargo adaptor proteins and test its contribution to RNA localization. Our results support a model whereby Cen protein enables the accumulation of its own mRNA to centrosomes through a mechanism requiring active translation, microtubules, and the dynein motor complex. Taken together, our data uncover the basis of translation-dependent localization of a centrosomal RNA required for mitotic integrity.