Search

Crystal polymorphism of complex liquids plays a crucial role in industrial crystallization, food technology, pharmaceuticals, and materials engineering. However, the experimental identification of unknown crystal structures can be challenging, particularly for high-viscosity complex liquids, such as ionic liquids (ILs). In this study, we performed a molecular dynamics simulation coupled with metadynamics to investigate an imidazolium IL (1-alkyl-3-methylimidazolium hexafluorophosphates). The simulation employed two distinct radial-distribution functions, represented by Gaussian window functions as collective variables, and revealed at least two crystal-like phases distinct from the known α and β crystal phases typically formed by this IL. Additionally, the simulation unveiled a unique phase characterized by the ordered spatial arrangement of anion aggregations. These crystal-like and unique phases emerged regardless of the potential used. The simulation methodology presented here is broadly applicable for exploring unknown phases in complex systems and contributes to the design of functional materials, such as porous ILs for gas molecule capture and separation. [ABSTRACT FROM AUTHOR]

A synchrotron based vacuum ultraviolet absorption spectrum for γ-pyrone has been interpreted in terms of singlet excited electronic states using a variety of coupled cluster, configuration interaction, and density functional calculations. The extremely weak spectral onset at 3.557 eV shows eight vibrational peaks, which following previous analyses, are attributed to a forbidden 1A2 state. A contrasting broad peak with a maximum at 5.381 eV has a relatively high cross-section of 30 Mb; this arises from three overlapping states, where a 1A1 state dominates over progressively weaker 1B2 and 1B1 states. After fitting the second band to a polynomial Gaussian function and plotting the regular residuals over 20 vibrational peaks, we have had limited success in analyzing this fine structure. However, the small separation between these three states clearly shows that their vibrational satellites must overlap. Singlet valence and Rydberg state vibrational profiles were determined by configuration interaction using the CAM-B3LYP density functional. Vibrational analysis using both the Franck–Condon and Herzberg–Teller procedures showed that both procedures contributed to the profiles. Theoretical Rydberg states were evaluated by a highly focused CI procedure. The superposition of the lowest photoelectron spectral band on the vacuum ultraviolet spectrum near 6.4 eV shows that the 3s and 3p Rydberg states based on the 2B2 ionic state are present; those based on the other low-lying ionic state (X2B1) are destroyed by broadening; this is a dramatic extension of the broadening previously witnessed in our studies of halogenobenzenes. [ABSTRACT FROM AUTHOR]

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility. [ABSTRACT FROM AUTHOR]

We investigate, in this paper, the Gaussian (G) function with odd powers of r, rxaybzc exp(−αr2), called the r-Gaussian or simply the rG function. The reason we investigate this function here is that it is generated as the elements of the complement functions (cf's) when we apply the free complement (FC) theory for solving the Schrödinger equation to the initial functions composed of the Gaussian functions. This means that without the rG functions, the Gaussian set of functions cannot produce the exact solutions of the Schrödinger equation, showing the absolute importance of the rG functions in quantum chemistry. Actually, the rG functions drastically improve the wave function near the cusp region. This was shown by the applications of the present theory to the hydrogen and helium atoms. When we use the FC-sij theory, in which the inter-electron function rij is replaced with its square s i j = r i j 2 that is integrable, we need only one- and two-electron integrals for the G and rG functions. The one-center one- and two-electron integrals of the rG functions are always available in a closed form. To calculate the integrals of the multi-centered rG functions, we proposed the rG-NG expansion method, in which an rG function is expanded by a linear combination of the G functions. The optimal exponents and coefficients of this expansion were given for N = 2, 3, 4, 5, 6, and 9. To show the accuracy and the usefulness of the rG-NG method, we applied the FC-sij theory to the hydrogen molecule. [ABSTRACT FROM AUTHOR]

The expensive cost of computing exact exchange in periodic systems limits the application range of density functional theory with hybrid functionals. To reduce the computational cost of exact change, we present a range-separated algorithm to compute electron repulsion integrals for Gaussian-type crystal basis. The algorithm splits the full-range Coulomb interactions into short-range and long-range parts, which are, respectively, computed in real and reciprocal space. This approach significantly reduces the overall computational cost, as integrals can be efficiently computed in both regions. The algorithm can efficiently handle large numbers of k points with limited central processing unit (CPU) and memory resources. As a demonstration, we performed an all-electron k-point Hartree–Fock calculation for LiH crystal with one million Gaussian basis functions, which was completed on a desktop computer in 1400 CPU hours. [ABSTRACT FROM AUTHOR]

To improve the disadvantages of signal control and energy control, a cooperative control strategy combining signal control and energy control is proposed for manipulators driven by permanent magnet synchronous motors (PMSMs) in this article. The cooperative control strategy is achieved by way of the convex combination of signal controller and energy controller, and Gaussian function is selected as cooperative function. The energy controller applies variable damping error port Hamiltonian and the signal controller uses backstepping nonsingular terminal sliding mode control. The PMSM with loss model is applied to obtain higher efficiency. To deal with modeling errors and joint friction, a nonlinear disturbance observer is used for manipulators system. Simulation and experiment results display that the designed strategy not only increases efficiency, but also enhances dynamic and steady‐state performance of manipulators. [ABSTRACT FROM AUTHOR]

This article investigates the problem of adaptive decentralized fixed‐time tracking control for strong interconnected nonlinear systems with full‐state constraints and input quantization. During the control design process, the assumption that the strong interconnection terms are bounded is removed via an inherent feature of the Gaussian function in neural networks. Unlike presvious nonlinear state‐dependent function (NSDF) that can only handle a single constraint, a novel form of NSDF is introduced to cope with more types of state constraints in this article. Meanwhile, the introduced NSDF is still available when the system states are unconstrained. Simultaneously, quantized input is directly handled by utilizing the intrinsic characteristics of the hysteresis quantizer. Then, based on the Lyapunov stability theory, all signals in the closed‐loop systems and tracking error are guaranteed to be bounded within fixed‐time. Finally, the feasibility of the proposed control scheme is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

This study developed a method to evaluate the effective spatial resolution of sea surface temperature (SST) data produced from observations of a microwave radiometer on satellites. The method was applied to 7-year SST data from the Advanced Microwave Scanning Radiometer 2 (AMSR2) on the Japan Aerospace Exploration Agency's (JAXA) Global Change Observation Mission-Water (GCOM-W) satellite. JAXA has produced three SST products from AMSR2 observations: standard SST, 10-GHz SST, and multi-band SST. They differ in spatial resolution because the frequency used to retrieve the SST has different footprint sizes, although the resolution has not been evaluated so far. We utilized high-resolution infrared SST data from the geostationary meteorological satellite Himawari-8. The Himawari SST was spatially smoothed by a Gaussian function to identify the smoothing scale that most accurately reproduces the AMSR2 SST gradient fields in the same area and time. The similarities between the Himawari and AMSR2 SST gradient fields were assessed using three metrics. The correlation coefficient provided a stable and robust estimate against the noise included in the AMSR2 SSTs. As a result, the effective resolution was estimated at 67 km for the standard SST, 52 km for the 10-GHz SST, and 63 km for the multi-band SST. These are all larger than the nominal resolution expected from the AMSR2 footprint size. The 10-GHz and multi-band SSTs had significantly higher resolutions than the standard SST. [ABSTRACT FROM AUTHOR]

Currently, most food recognition relies on deep learning for category classification. However, these approaches struggle to effectively distinguish between visually similar food samples, highlighting the pressing need to address fine-grained issues in food recognition. To mitigate these challenges, we propose the adoption of a Gaussian and causal-attention model for fine-grained object recognition.In particular, we train to obtain Gaussian features over target regions, followed by the extraction of fine-grained features from the objects, thereby enhancing the feature mapping capabilities of the target regions. To counteract data drift resulting from uneven data distributions, we employ a counterfactual reasoning approach. By using counterfactual interventions, we analyze the impact of the learned image attention mechanism on network predictions, enabling the network to acquire more useful attention weights for fine-grained image recognition. Finally, we design a learnable loss strategy to balance training stability across various modules, ultimately improving the accuracy of the final target recognition. We validate our approach on four relevant datasets, demonstrating its excellent performance across these four datasets.We experimentally show that GCAM surpasses state-of-the-art methods on the ETH-FOOD101, UECFOOD256, and Vireo-FOOD172 datasets. Furthermore, our approach also achieves state-of-the-art performance on the CUB-200 dataset. [ABSTRACT FROM AUTHOR]

• The two-phase distribution in the header of a microchannel heat exchanger was quantified by a flexible capacitance sensor. • Distribution of local vapor quality showed that gases were concentrated upstream of the header, while liquids were concentrated in the middle and lower reaches. • Compared with the downstream, the upstream flow had less stability with more discrete capacitance signals. • The increase of mass flux caused that both the local vapor quality maximum point and the minimum point in the header were shifted back toward the downstream. The two-phase distribution has always been one of the research focuses of microchannel heat exchangers, because the maldistribution could seriously affect the heat transfer performance. This paper developed a capacitive method to quantify the two-phase distribution of vapor-liquid flow in the aluminum header of a microchannel heat exchanger. A flexible capacitance sensor was used to quantify the two-phase distribution with R134a. The inlet mass fluxes vary from 17.47 kg m−2 s−1 to 52.42 kg m−2 s−1 and inlet vapor qualities range from 0.2 to 0.6. The normalized time-averaged capacitance signal was processed by a Gaussian function to obtain the mathematical expectation and the standard deviation. The local vapor quality in the header was solved for using a correlation derived from the pre-experiments. The distribution of local vapor quality showed that gases were concentrated upstream of the header, while liquids were concentrated in the middle and lower reaches. The local vapor quality reached a minimum and remained constant at 0.1 in the middle and lower reaches, unaffected by changes in inlet conditions. As the mass flux increased, both the local vapor quality maximum point and the minimum point in the header were shifted back toward the downstream. Additionally, the increase of mass flux caused the fluctuation of the standard deviation increased, which meant the stability of the flow decreased. The two-phase flow measurement technique based on flexible capacitance sensors proposed in this study realized the extension of the capacitive method from the experimental stage to the industrial application stage. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to introduce a new definition of ( k,ℑ)$$ k,\mathfrak{\Im}\Big) $$‐incomplete Wright hypergeometric matrix functions ( k,ℑ$$ \left(k,\mathfrak{\Im}\right) $$‐IWHMFs) using the k$$ k $$‐incomplete Pochhammer matrix symbol. First, we define the k$$ k $$‐incomplete gamma matrix function and introduce the k$$ k $$‐incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these k,ℑ$$ \left(k,\mathfrak{\Im}\right) $$‐IWHMFs. We have also obtained some results regarding the k$$ k $$‐fractional calculus operators of these k,ℑ$$ \left(k,\mathfrak{\Im}\right) $$‐IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the k,ℑ$$ \left(k,\mathfrak{\Im}\right) $$‐IWHMFs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new family of the generalized k-Leonardo numbers and study their properties. We investigate the Gaussian Leonardo numbers and associated new families of these Gaussian forms. We obtain combinatorial identities like Binet formula, Cassini’s identity, partial sum, etc. in the closed form. Moreover, we give various generating and exponential generating functions. [ABSTRACT FROM AUTHOR]

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular, we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper. [ABSTRACT FROM AUTHOR]

Numerous prior publications on fractional calculus provide fascinating explanations of the theory and applications of fractional calculus operators throughout various mathematical analytic domains. In this paper, we introduce new fractional integral formulas using the Saigo-Maeda fractional integral operators and Appell’s function F3 along with the Srivastava polynomials, the (p,q)-extended Gauss hypergeometric function, and the M-Series. A few fascinating unusual cases of our main conclusions are also considered. This approach can be applied to explore a broad class of previously dispersed discoveries in the literature. [ABSTRACT FROM AUTHOR]

Two synthesized carboxamide derivatives were investigated in 1M HCl as corrosion inhibitors for carbon steel (CS): 1-benzyl-5-methyl-N-(o-tolyl)-1H-pyrazole-3-carboxamide (BPCP) and 1-benzyl-N-cyclohexyl-5-methyl-1H-pyrazole-3-carboxamide (BPCC). For a concentration of 300 ppm at room temperature 298K, the best inhibition efficiencies of BPCP and BPCC were found to be 88.2% and 84.5%, respectively. The EIS results correlated positively with parameters calculated by density functional theory, using different basis functions: Gaussian functions in Gaussian 09 software and numerical functions in Dmol3 software. In addition, calculations of the adsorption energy of each inhibitor on the CS surface, found by Monte Carlo method, confirm this correlation. [ABSTRACT FROM AUTHOR]

Padé approximations are approximations of holomorphic functions by rational functions. The application of Padé approximations to Diophantine approximations has a long history dating back to Hermite. In this paper, we use the Maier–Chudnovsky construction of Padé-type approximation to study irrationality properties about values of functions with the form f (x) = ∑ k = 0 ∞ x k k ! (b k + s) (b k + s + 1) ⋯ (b k + t) , where b , t , s are positive integers and obtain upper bounds for irrationality measures of their values at nonzero rational points. Important examples includes exponential integral, Gauss error function and Kummer's confluent hypergeometric functions. [ABSTRACT FROM AUTHOR]

We investigate the energy spectra and optical absorption of a 3D quantum dot–double quantum ring structure of GaAs/Al0.3Ga0.7As with adjustable geometrical parameters. In the effective mass approximation, we perform 3D numerical computations using as height profile a superposition of three Gaussian functions. Independent variations of height and width of the dot and of the rings and also of the dot–rings distance determine particular responses, useful in practical applications. We consider that a suitable manipulation of the geometrical parameters of this type of quantum coupling offer a variety of responses and, more important, the possibility of a fine adjusting in energy spectra and in the opportunity of choosing definite absorption domains, properties required for the improvement of the performances of optoelectronic devices. [ABSTRACT FROM AUTHOR]

Depth image has been widely involved in various tasks of 3D systems with the advancement of depth acquisition sensors in recent years. Depth images suffer from serious distortions near object boundaries due to the limitations of depth sensors or estimation methods. In this paper, a simple method is proposed to rectify the erroneous object boundaries of depth images with the guidance of reference RGB images. First, an RGB–Depth boundary inconsistency model is developed to measure whether collocated pixels in depth and RGB images belong to the same object. The model extracts the structures of RGB and depth images, respectively, by Gaussian functions. The inconsistency of two collocated pixels is then statistically determined inside large-sized local windows. In this way, pixels near object boundaries of depth images are identified to be erroneous when they are inconsistent with collocated ones in RGB images. Second, a depth image rectification method is proposed by embedding the model into a simple weighted mean filter (WMF). Experiment results on two datasets verify that the proposed method well improves the RMSE and SSIM of depth images by 2.556 and 0.028, respectively, compared with recent optimization-based and learning-based methods. [ABSTRACT FROM AUTHOR]

The accurate identification of low-voltage distribution substation topology plays a crucial role in research applications such as line loss management, fault location, imbalance correction, and intelligent operation and maintenance of substations. In response to the challenges posed by the large scale of users and the complex connection relationships in low-voltage distribution substations, which complicate the identification of their topology, a method for identifying low-voltage distribution substation topology based on user profiling technology is proposed. This method is supported by big data technology and introduces the concept of user profiling into the research of substation topology identification. Firstly, by deeply studying the theoretical knowledge of the relationship between the supply of distribution transformers and the power consumption of substation users, as well as the voltage similarity, we establish the feature labels for electricity coefficient and voltage similarity. Then, we use the continuous relaxation method and branch-and-bound method to solve the electricity coefficient matrix; and use the Gaussian kernel function to solve the voltage similarity matrix. Finally, by constructing a comprehensive attribution matrix using the electricity coefficient matrix and the voltage similarity matrix, employing a convolutional neural network to cluster and solve the comprehensive attribution matrix, outputting user-area attribution information, forming user-area attribution profiles, and completing the identification of area attribution relationships in low-voltage distribution systems. Simulation results demonstrate that the proposed method not only effectively identifies the area information to which low-voltage users belong but also discerns the connection relationships between users and area transformers. [ABSTRACT FROM AUTHOR]

Let 풦 + ⁢ ( σ ) = { ℙ ( ϑ , σ ) ⁢ ( d ⁢ ζ ) : ϑ ∈ ( 0 , ϑ + ⁢ ( σ ) ) } {{\mathcal{K}_{+}}(\sigma)=\{\mathbb{P}_{(\vartheta,\sigma)}(d\zeta):\vartheta% \in(0,\vartheta_{+}(\sigma))\}} be the Cauchy–Stieltjes Kernel (CSK) family generated by a probability measure σ which is non degenerate and has support bounded from above. Consider the concept of V a {V_{a}} -transformation of measures introduced in [A. D. Krystek and L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 2005, 3, 515–545] for a ∈ ℝ {a\in\mathbb{R}} . We prove that V a ⁢ ( ℙ ( ϑ , σ ) ) ∈ 풦 + ⁢ ( σ ) {V_{a}(\mathbb{P}_{(\vartheta,\sigma)})\in{\mathcal{K}_{+}}(\sigma)} for all a ∈ ℝ ∖ { 0 } {a\in\mathbb{R}\setminus\{0\}} if and only if the measure σ is of the free Gaussian (semicircle) type law up to affinity. [ABSTRACT FROM AUTHOR]

A growing number of industries have started to adapt to the circular economy since the concept's introduction. Therefore, in order to accurately evaluate the development level of circular economy, the circular economy prediction model based on support vector machine-Gaussian K-nearest neighbor is proposed. This model first uses the improved K-nearest neighbor algorithm based on Gaussian function to classify the index data of various levels, and then uses Support Vector Machine to make predictions based on relevant data. According to the experimental findings, the model's average prediction accuracy for each level of indicator was approximately 98.1%, 98.8%, 94.9%, and 95.9% for the levels of industrial development, resource consumption, ecological protection, and resource recycling and reuse, respectively. This prediction accuracy was higher than that of the multi-vector autoregressive model and the grey prediction model. The average prediction accuracy of the multi-vector autoregressive model, the grey prediction model, and the support vector machine-Gaussian K-nearest neighbor-based model in predicting the overall development level of the circular economy were about 94.3%, 96.2%, and 99.3%, respectively, with average recalls of about 86.6%, 87.7%, and 89.1%, and the average F1-measure was about 0.88, 0.89, and 0.92. Moreover, the average relative error based on the support vector machine-Gaussian K-nearest neighbour model was only approximately 0.6%, which was lower than the 3.7% and 2.8% for the multi-vector autoregressive model and the grey prediction model, respectively. Meanwhile, compared with the existing time series analysis techniques, the proposed SVM-Gaussian K nearest neighbor model fitted up to 0.95, which achieved good prediction performance. According to the above data, the support vector machine-Gaussian K-nearest neighbour model has the highest accuracy in predicting the amount of development of the circular economy. [ABSTRACT FROM AUTHOR]

Isotope shifts in the transition energies between several lowest $ ^3 P^{e} $ 3 P e states of the carbon atom are calculated at the nonrelativistic level of theory. We considered the $ ^{12} $ 12 C, $ ^{13} $ 13 C, and $ ^{14} $ 14 C isotopes, for which we performed variational calculations by expanding the wave functions of the atomic states in terms of all-electron explicitly correlated Gaussian functions. The Born–Oppenheimer approximation was not assumed in the calculations. By combining the computed isotope shifts with the experimentally derived Ritz wavelengths for the natural mixture of the isotopes we make predictions of the positions of the spectral lines for specific carbon isotopes. These predictions may be useful for guiding future experimental measurements of these lines using high-resolution spectroscopy. [ABSTRACT FROM AUTHOR]

As robots become increasingly common in human-populated environments, they must be perceived as social beings and behave socially. People try to preserve their own space during social interactions with others, and this space depends on a variety of factors, such as individual characteristics or their age. In real-world social spaces, there are many different types of people, and robots need to be more sensitive, especially when interacting with vulnerable subjects such as children. However, the current navigation methods do not consider these differences and apply the same avoidance strategies to everyone. Thus, we propose a new navigation framework that considers different social types and defines appropriate personal spaces for each, allowing robots to respect them. To this end, the robot needs to classify people in a real environment into social types and define the personal space for each type as a Gaussian asymmetric function to respect them. The proposed framework is validated through simulations and real-world experiments, demonstrating that the robot can improve the quality of interactions with people by providing each individual with an adaptive personal space. The proposed costmap layer is available on GitHub. [ABSTRACT FROM AUTHOR]

The article studies the dynamics of Gaussian solitary waves in nano optical fibers which are described by perturbed and improved nonlinear Schrödinger equations which have logarithmic nonlinearities with and without attenuation terms. As a result, the Gaussian solitary waves have been extracted for the logarithmic perturbed nonlinear Schrödinger equation and the logarithmic perturbed improved nonlinear Schrödinger equation. Moreover, new logarithmic improved nonlinear Schrödinger equations are presented. With the Gaussian function and symbolic computation, we obtain the Gaussian solitary waves for such equations. [ABSTRACT FROM AUTHOR]

Studies of active region (AR) lifetimes are mostly restricted to short-lived ARs. The aim of this paper is to include recurrent ARs, which should be identified unambiguously. The first step is the algorithmic listing of possible returns; then, the candidates are visually checked using the unique HTML-feature of the Debrecen sunspot database. The final step is application of an asymmetric Gaussian function, introduced in previous articles, for short-lived ARs. This function has a surprisingly good fit to the data on correctly identified recurrent sunspot groups over several rotations enabling the reconstruction of the development on the far side of the sun. The Gnevyshev–Waldmeier rule for the area–lifetime relationship is not applicable for recurrent ARs; however, as a novel approach, a linear regression analysis extended to long lifetimes made it possible to recognize two populations of sizes for which two different area–lifetime relationships can be obtained. The lifetimes exhibit weak dependencies on the heliographic latitude and solar cycle phase. If an asymmetric Gaussian cannot be fit to the data, then they presumably belong to consecutive members of an active nest. [ABSTRACT FROM AUTHOR]

SUMMARY: A major challenge in seismic tomography consists in quantifying and representing model resolution and uncertainty, particularly at global scales. This information is crucial for interpretations of tomographic images and their technical application in geodynamics. However, due to large computational costs, there have been only few attempts so far to coherently analyse the spatially varying resolving power for a complete set of model parameters. Here, we present a concept for an effective evaluation and global representation of the 3-D resolution information contained in a full set of averaging kernels. In our case, these kernels are constructed using the 'Subtractive Optimally Localized Averages' (SOLA) method, a variant of classic Backus-Gilbert inversion suitable for global tomography. Our assessment strategy incorporates the following steps: (1) a 3-D Gaussian function is fitted to each averaging kernel to measure resolution lengths in different directions and (2) we define a classification scheme for the quality of the averaging kernels based on their focus with respect to the estimated 3-D Gaussian, allowing us to reliably identify whether the inferred resolution lengths are robust. This strategy is not restricted to SOLA inversions, but can, for example, be applied in all cases where point-spread functions are computed in other tomographic frameworks. Together with model uncertainty estimates that are derived from error propagation in the SOLA method, our concept reveals at which locations, resolution lengths and interpretations of model values are actually meaningful. We finally illustrate how the complete information from our analysis can be used to calibrate the SOLA inversion parameters—locally tunable target resolution kernels and trade-off parameters—without the need for visual inspection of the individual resulting averaging kernels. Instead, our global representations provide a tool for designing tomographic models with specific resolution-uncertainty properties that are useful in geodynamic applications, especially for linking seismic inversions to models of mantle flow. [ABSTRACT FROM AUTHOR]

In the present paper, we study the shifted hypergeometric function f(z)=z_{2}F_{1}(a,b;c;z) for real parameters with 0

The article focuses on the impact of rising gold wire costs on semiconductor packaging and the advancements in gold wire bonding technology. Topics include the challenges of wire-lifting and surface degradation, the development of micro-tensile tests to assess thermomechanical properties, and the use of finite element methods combined with optimization tools to improve thermal reliability in extreme environments.

A red phosphorescent bottom-emitting organic light emitting diode (OLED) comprising host/co-host/dopant system is fabricated using vacuum thermal evaporation method. The measured characteristics of the OLED show a spectral dissimilarity between the photoluminescence and electroluminescence (EL) spectra due to the presence of a shoulder peak in the EL spectrum. This spectral discrepancy is due to the fact that the optical excitation leads mostly to singlet formation while the electrical excitation leads to the formation of both singlets and triplets. The commercial OLED device simulators that are currently available cannot reproduce this shoulder peak in electro-optical simulations. This drawback leads to a mismatch in device efficiency and color coordinates between simulation and experiment. To overcome this problem, a simulation strategy, which involves extraction of the required intrinsic luminescence spectrum for simulation using SETFOS TM 5.2.8 (Fluxim AG) and peak-deconvolution of the extracted spectrum into Gaussian functions is proposed. By considering a ± 5% variation in refractive indices n of all the layers, the electro-optical simulation results match with that of fabricated red OLED which validates our methodology. The proposed strategy will be helpful for better optimization of such device architecture. [ABSTRACT FROM AUTHOR]

The Kullback–Leibler divergence is a measure of the divergence between two probability distributions, often used in statistics and information theory. However, exact expressions for it are not known for multivariate or matrix-variate distributions apart from a few cases. In this paper, exact expressions for the Kullback–Leibler divergence are derived for over twenty multivariate and matrix-variate distributions. The expressions involve various special functions. [ABSTRACT FROM AUTHOR]

Abstract.In this article, we consider an early arrival Geo/Geo/1 queue from the statistical perspective. The estimations of parameters and system performances under Classical and Bayesian frameworks are considered. Based on queue length data, we attempt to study the uniform minimum-variance unbiased estimators (UMVUEs) and the closed Bayesian estimators for various queueing characteristics. We compare their properties using Monte Carlo (MC) simulations. As a comparison and improvement, based on arrival and departure data over a period, we use a Bivariate Beta distribution as joint prior, and solve the performance estimators using the properties of Gaussian hypergeometric function. We derive Bayesian estimators and conduct numerical simulations using Markov Chain Monte Carlo (MCMC) method. [ABSTRACT FROM AUTHOR]

The advent of single-cell RNA sequencing (scRNA-seq) technology enables researchers to gain deep insights into cellular heterogeneity. However, the high dimensionality and noise of scRNA-seq data pose significant challenges to clustering. Therefore, we propose a new single-cell type identification method, called CHLSPCA, to address these challenges. In this model, we innovatively combine correntropy with PCA to address the noise and outliers inherent in scRNA-seq data. Meanwhile, we integrate the hypergraph into the model to extract more valuable information from the local structure of the original data. Subsequently, to capture crucial similarity information not considered by the PCA model, we employ the Gaussian kernel function and the Euclidean metric to mine the similarity information between cells, and incorporate this information into the model as the similarity constraint. Furthermore, the principal components (PCs) of PCA are very dense. A new sparse constraint is introduced into the model to gain sparse PCs. Finally, based on the principal direction matrix learned from CHLSPCA, we conduct extensive downstream analyses on real scRNA-seq datasets. The experimental results show that CHLSPCA performs better than many popular clustering methods and is expected to promote the understanding of cellular heterogeneity in scRNA-seq data analysis and support biomedical research. [ABSTRACT FROM AUTHOR]

Robot navigation has transitioned from avoiding static obstacles to adopting socially aware navigation strategies for coexisting with humans. Consequently, socially aware navigation in dynamic, human-centric environments has gained prominence in the field of robotics. One of the methods for socially aware navigation, the reinforcement learning technique, has fostered its advancement. However, defining appropriate reward functions, particularly in congested environments, holds a significant challenge. These reward functions, crucial for guiding robot actions, necessitate intricate human-crafted design due to their complex nature and inability to be set automatically. The multitude of manually designed reward functions contains issues such as hyperparameter redundancy, imbalance, and inadequate representation of unique object characteristics. To address these challenges, we introduce a transformable Gaussian reward function (TGRF). The TGRF possesses two main features. First, it reduces the burden of tuning by utilizing a small number of hyperparameters that function independently. Second, it enables the application of various reward functions through its transformability. Consequently, it exhibits high performance and accelerated learning rates within the deep reinforcement learning (DRL) framework. We also validated the performance of TGRF through simulations and experiments. [ABSTRACT FROM AUTHOR]

In this study, the electronic density of states (DOSs) calculated with density functional theory (DFT) were analyzed by the machine‐learning techniques. More than 400 pure metal and bimetallic alloy systems were calculated with DFT, and obtained the surface DOSs and the CH3 adsorption energy (Ead). By fitting the Gaussian functions to the DOS, multiple descriptors, such as the Gaussian peak positions, heights, and widths were extracted. Several regression methods, such as the least absolute shrinkage of selection operator (LASSO), random‐forest, gradient‐boosting, and extra‐tree were used to find the relationship between these descriptors and the Ead. The results show that the energy position of the peaks in the d‐projected DOS is the most important descriptor, in agreement with the previously known d‐band center theory. It was also shown that the peak position in d‐projected DOS improves the regression model in addition to the d‐band center, since it reduces the regression error. [ABSTRACT FROM AUTHOR]

Summary This paper proposes a command filter‐based decentralized adaptive backstepping practical prescribed‐time (PPT) tracking control scheme for a class of non‐strict feedback interconnected systems with time varying parameters, unknown control coefficients, unmodeled dynamics, input deadzone and saturation. By the aid of the characteristics of Gaussian functions, the obstacles arising from the non‐strict feedback terms are successfully solved. By constructing a novel time‐varying scaling function and utilizing nonlinear mapping, the PPT tracking control is developed. The estimations of dynamical uncertainties resulting from unmodeled dynamics are accomplished by employing auxiliary signals, while the unknown continuous terms are characterized by the aid of radial basis function neural networks (RBFNNs). A superposition of two hyperbolic tangent functions is utilized to approximate input nonlinearity. Utilizing the compact set defined in the command filtered backstepping technique, the problem of unknown control direction is solved without using the Nussbaum gain technique. All the signals involved are proved to be semi‐global uniform ultimate bounded, and the tracking error can enter the pre‐specified convergence region within a pre‐specified time. Simulation results are used to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

Rolling bearings are essential parts for manufacturing machines. Vast quantities of features are often extracted from measured signals to comprehensively reflect the conditions of bearings, which may cause high dimensionality, information redundancy, and time consumption. In addition, it is extremely difficult, expensive, and time-consuming to collect samples with label information during the bearing fault diagnosis in real-world scenarios. In this study, a novel bearing defect diagnosis method for small sample size is proposed based on modified local joint sparse marginal embedding (MLJSME) and Wasserstein generative adversarial networks (WGANs). MLJSME can effectively extract intrinsic sparse discriminant features of high-dimensional dataset by preserving both global and local structures. Graph embedding and Gaussian kernel function are adopted to preserve the locality structure of dataset. The global structure and discriminate information are preserved by maximum margin criterion which can also avoid small sample-size problem. Moreover, joint sparsity is applied to preserve the sparse property and improve the robustness to noise and outliers. An abundance of artificial samples can be obtained with WGAN and a few labeled samples. Firstly, a high-dimensional feature dataset consisting of time-domain and frequency-domain features is extracted from original vibration signals, then MLJSME is utilized to extract sensitive low-dimensional features, and a small number of low-dimensional features are fed into WGAN to generate a large number of artificial samples that used to train the classifier, and the bearing fault types can be finally identified. The effectiveness and feasibility of the proposed method is validated by analyzing the different experimental cases. [ABSTRACT FROM AUTHOR]

Plasma bubbles represent notable ionospheric irregularities primarily observed in low latitudes, characterized by plasma depletions exhibiting large spatial scales, which can make a significant impact on the propagation of OTHR (over-the-horizon radar) waves. Firstly, we constructed a three-dimensional model of plasma bubbles, which is modulated by Gaussian function distribution in the horizontal direction, and then we analyzed the impact of EPBs (Equatorial Plasma Bubbles) on the ray path of OTHR shortwaves. When radio waves propagate through EPBs with different RMS ΔN/N, there is a significant difference in the propagation path of OTHR waves. For the EPB with an RMS ΔN/N of 75%, radio waves exhibit more pronounced refraction than those with lower RMS values, the focusing effect of radio waves is more obvious, and the focusing point is relatively lower. In terms of different seasons, OTHR shortwaves propagating through EPBs exhibit different degrees of refraction. In addition, radio waves show the effect of inward focusing in different seasons: the focusing effect is the most pronounced in spring, followed by autumn, then summer, and the weakest in winter. For different solar activities, the impact of EPBs on OTHR shortwaves is more significant in the high-solar-activity year. [ABSTRACT FROM AUTHOR]

Sea surface target detection is a key stage in a typical target detection system and directly influences the performance of the whole system. As an effective discriminator, the one-class support vector machine (OCSVM) has been widely used in target detection. In OCSCM, training samples are first mapped to the hypersphere in the kernel space with the Gaussian kernel function, and then, a linear classification hyperplane is constructed in each cluster to separate target samples from other classes of samples. However, when the distribution of the original data is complex, the transformed data in the kernel space may be nonlinearly separable. In this situation, OCSVM cannot classify the data correctly, because only a linear hyperplane is constructed in the kernel space. To solve this problem, a novel one-class classification algorithm, referred to as ensemble one-class support vector machine (En-OCSVM), is proposed in this paper. En-OCSVM is a hybrid model based on k -means clustering and OCSVM. In En-OCSVM, training samples are clustered in the kernel space with the k -means clustering algorithm, while a linear decision hyperplane is constructed in each cluster. With the combination of multiple linear classification hyperplanes, a complex nonlinear classification boundary can be achieved in the kernel space. Moreover, the joint optimization of the k -means clustering model and OCSVM model is realized in the proposed method, which ensures the linear separability of each cluster. The experimental results based on the synthetic dataset, benchmark datasets, IPIX datasets, and SAR real data demonstrate the better performance of our method over other related methods. [ABSTRACT FROM AUTHOR]

Background: Superficial targets require the use of the lowest energies within the available energy range in proton pencil‐beam scanning (PBS) technique. However, the lower efficiency of the energy selection system at these energies and the requirement of a greater number of layers may represent disadvantages for this approach. The alternative is to use a range shifter (RS) at nozzle exit. However, one of the concerns of using this beamline element is that it becomes an additional source of neutrons that could irradiate organs situated far from the target. Purpose: The purpose of this study is to assess the increase in neutron dose due to the RS in proton PBS technique. Additionally, an analytical model for the neutron production is tested. Methods: Two clinical plans, designed to achieve identical target coverage, were created for an anthropomorphic phantom. These plans consisted of a lateral field delivering an absorbed dose of 60 Gy (RBE) to the target. One of the plans employed the RS. The MCNP code was used to simulate the plans, evaluating the distribution of neutron dose equivalent (Hn) and the equivalent dose in organ. In the plan with the RS plan, neutron production from both the patient and the RS were assessed separately. Hn values were also fitted versus the distance to field edge using a Gaussian function. Results: Hn per prescription dose, in the plan using the RS, ranged between 1.4 and 3.7 mSv/Gy at the field edge, whereas doses at 40 cm from the edge ranged from 9.9 to 32 μSv/Gy. These values are 1.2 to 10 times higher compared to those obtained without the RS. Both this factor and the contribution of neutrons originating from the RS increases with the distance from field edge. A triple‐Gaussian function was able to reproduce the equivalent dose in organs within a factor of 2, although underestimating the values. Conclusions: The dose deposited in the patient by the neutrons originating from the RS predominantly affects areas away from the target (beyond approximately 25 cm from field edge), resulting in a neutron dose equivalent of the order of mSv. This indicates an overall low neutron contribution from the use of RS in PBS. [ABSTRACT FROM AUTHOR]

Using 6‐minute free‐running intracranial‐electroencephalogram (icEEG) during sleep, an optimized multilayer perceptron (MLP) neural network accurately maps the sensorimotor cortex (SM) and identifies the anterior lip of the central sulcus (CS) in intractable epilepsy patients. We calculated 6 performance metrics to evaluate the MLP's efficacy: accuracy, area under the curve (AUC), recall, precision, F1‐scores, and specificity. Each layer had 4 neurons with hyperbolic TanH activation function and 4 with Gaussian distribution function. Conventional 10‐fold cross‐validation was used. Feature extension (ε) and weighted imbalanced data (w) improved MLP performance. ANN NEUROL 2024;96:187–193 [ABSTRACT FROM AUTHOR]

The cumulative distribution functions can be used as the basis for hysteresis models. Here it is de- scribed how, using only 3 parameters, including one representing the shape, hysteresis curves can be constructed using symmetric distribution functions. The model is useful in the interpretation of magnetic Barkhausen noise data. The model also has a clear physical meaning because it represents the distribution of coercivity inside the sample. An isotropic Stoner-Wohlfarth hysteresis was partially modelled by a three-parameter cumulative distribution function of Gaussian hysteresis for the 1st and 3rd quadrants. Asymmetric distributions will provide better hysteresis adjustment, but these are four- parameter models. [ABSTRACT FROM AUTHOR]

Structures in earthquake-prone areas may suffer from accumulative damages caused by sequential shocks, including the mainshock and aftershock of an earthquake or several strong motions throughout their service lifespan. Sequential shocks lead to a decrease in the capacity of structures. Nevertheless, seismic fragility curves and their applications do not often consider the sequential effect. This study investigates the impact of sequential seismic events on seismic fragility curves of 3-, 6-, and 9-story reinforced concrete buildings constructed before and after 1982 in Japan. The research proposes analytical fragility curves based on dynamic nonlinear multi-degree-of-freedom analyses under the influence of single shock and sequential shock of recorded motions of six destructive earthquakes in Japan. The results demonstrate that the seismic sequence increases the probability of damage ratio. This increase in the fragility curve follows the Gaussian function. The study presents a regression model that can be used for other seismic areas to estimate the effect of seismic sequences on single shock seismic fragility curves. [ABSTRACT FROM AUTHOR]

In a sensor array system with the ability to design multiple sensor elements, selecting the optimal sensor elements can maximize the efficiency of the sensor array in responding to various analytes. This paper proposes the application of hard chemical modeling as a means to identify the optimal subset of indicator displacement assay (IDA)-based sensors in the array, aiming to achieve maximum performance for detection or quantification. The model governing all reactions in the IDA sensor and the model of the pure spectrum of active species are first determined. Next, by applying the model of the pure spectrum of active species (including the indicator and indicator-receptor complex) to each sensor element and taking into account the system's nonlinearity, corrected concentration profiles of active species are derived using the generalized classical least square (G-CLS) method. These corrected concentration profiles are utilized as the output signal for each sensor element. Finally, the dynamic ranges (DR) of each sensor element and subsequently the DR for all possible sensor arrays are determined. To assess the effectiveness of the sensor array through dynamic range analysis, an IDA-based sensor system comprising five different elements was designed. It was observed that sensors with a larger dynamic range, when arranged together in an array, are more efficient for the quantitative identification of analytes. However, simply increasing the number of elements in the sensor array may not necessarily enhance its effectiveness; instead, it could amplify the noise within the system. Additionally, multivariate fitting regression with Gaussian function (MFRG), a nonlinear calibration method, was applied to assess the prediction ability of all possible designed sensor arrays. [ABSTRACT FROM AUTHOR]

In this paper, we present a stochastic model that uses the Gaussian error function to change the likelihood of the Weibull distribution without changing the complexity of its parametric space. Several mathematical properties are derived for the proposed model, which has numerical examples to illustrate its usability in practice. The failure rate function of the resulting model presents non-monotonous shapes, such as the shape of a bathtub, which represents a gain concerning the base distribution. Two parameter estimation methods are presented and evaluated numerically. In addition to the unconditional model, a regression model for the quantiles of the distribution is derived. Both absolute and regression models have applications to actual data and simulation studies, corroborating their use in practical situations. [ABSTRACT FROM AUTHOR]

Yunnan-Myanmar and its surrounding areas are the areas directly affected by the collision of the Eurasian Plate and the Indian Plate. In view of the uneven distribution of GPS stations in Yunnan and Myanmar, this paper employs the method of regionally weighted interpolation. In areas with a high concentration of GPS stations, a combination of Voronoi cell weighting function and Gaussian function weighting is utilized, while in regions with sparse GPS coverage, a combination of Voronoi cell weighting function and quadratic function weighting is employed. Utilizing the rigid-body movement uniform strain model, we calculate the horizontal strain rates of the crust in Yunnan-Myanmar and adjacent areas, followed by an in-depth analysis of model performance and the activity of primary faults. The results show that: (1) We found that Yunnan Myanmar strain has obvious boundary characteristics. (2) Upon scrutinizing the model, it was ascertained that the model delineated in this study possesses an expansive search range, enabling it to yield more precise outcomes, particularly in regions characterized by the disparate distribution of GPS stations; (3) Through the analysis of the profiles of horizontal GPS velocity field and maximum shear strain rates of the main faults in the study area, we found that the direction of the maximum shear strain rate is consistent with the direction of the main faults in the study area, and that the slip and maximum shear strain rate of the major faults increase and decrease along the tectonic direction. [ABSTRACT FROM AUTHOR]

This paper deals with the well-known Becker-Stark inequality. By using variable replacement from the viewpoint of hypergeometric functions, we provide a new and general refinement of Becker-Stark inequality. As a particular case, the double inequality π² − (π² − 8) sin² x/π² − 4x² < tan x/x < π² − (4 − π²/3) sin² x/π² − 4x² for x ∈ (0, π/2) will be established. The importance of our result is not only to provide some refinements preserving the structure of Becker-Stark inequality but also that the method can be extended to the case of generalized trigonometric functions. [ABSTRACT FROM AUTHOR]

This research deals with the design problems of LED-based spectrally tunable light sources (LSTLSs). The study aims to assess the reliability of popular models for the spectral modeling of LED radiation and a typically used curve-fitting criterion (R2) in the development of high-quality multi-emitter LED retrofits for incandescent photometric illuminant. The research methodology involves modeling each LED channel using Lorentz and Gaussian functions and combining multiple channels to approximate the desired spectral power distribution (SPD). After the optimization, 20 various LED sets were designed, which allowed us to replicate the SPD of CIE illuminant A with a very high R2 value. Two sets were constructed and measured to recognize the reliability of the simulation approach. The results suggest that for planning the LSTLS for photometric applications, these models are unreliable as they do not reflect the real effect of changes in the characteristics of the components nor reveal the share of various spectral ranges. Therefore, the decisions made on these criteria may not be the best solutions in the context of specific applications. [ABSTRACT FROM AUTHOR]

Stochastic frontier models commonly assume positive skewness for the inefficiency term. However, when this assumption is violated, efficiency scores converge to unity. The potential endogeneity of model regressors introduces another empirical challenge, impeding the identification of causal relationships. This paper tackles these issues by employing an instrument-free estimation method that extends joint estimation through copulas to handle endogenous regressors and skewness issues. The method relies on the Gaussian copula function to capture dependence between endogenous regressors and composite errors with a simultaneous consideration of positively or negatively skewed inefficiency. Model parameters are estimated through maximum likelihood, and Monte Carlo simulations are employed to evaluate the performance of the proposed estimation procedures in finite samples. This research contributes to the stochastic frontier models and production economics literature by presenting a flexible and parsimonious method capable of addressing wrong skewness of inefficiency and endogenous regressors simultaneously. The applicability of the method is demonstrated through an empirical example. [ABSTRACT FROM AUTHOR]

Abstract A growing number of industries have started to adapt to the circular economy since the concept's introduction. Therefore, in order to accurately evaluate the development level of circular economy, the circular economy prediction model based on support vector machine-Gaussian K-nearest neighbor is proposed. This model first uses the improved K-nearest neighbor algorithm based on Gaussian function to classify the index data of various levels, and then uses Support Vector Machine to make predictions based on relevant data. According to the experimental findings, the model's average prediction accuracy for each level of indicator was approximately 98.1%, 98.8%, 94.9%, and 95.9% for the levels of industrial development, resource consumption, ecological protection, and resource recycling and reuse, respectively. This prediction accuracy was higher than that of the multi-vector autoregressive model and the grey prediction model. The average prediction accuracy of the multi-vector autoregressive model, the grey prediction model, and the support vector machine-Gaussian K-nearest neighbor-based model in predicting the overall development level of the circular economy were about 94.3%, 96.2%, and 99.3%, respectively, with average recalls of about 86.6%, 87.7%, and 89.1%, and the average F1-measure was about 0.88, 0.89, and 0.92. Moreover, the average relative error based on the support vector machine-Gaussian K-nearest neighbour model was only approximately 0.6%, which was lower than the 3.7% and 2.8% for the multi-vector autoregressive model and the grey prediction model, respectively. Meanwhile, compared with the existing time series analysis techniques, the proposed SVM-Gaussian K nearest neighbor model fitted up to 0.95, which achieved good prediction performance. According to the above data, the support vector machine-Gaussian K-nearest neighbour model has the highest accuracy in predicting the amount of development of the circular economy.