Multifunctional analysis of CaX2Bi2O9 (X = Nb, V, Ta, and Pa) compound by first principles framework for photovoltaic applications by Nawishta Jabeen, Ahmad Hussain, Ameer Hamza, Omer Musa, Nagappan Beemkumar, Jajneswar Nanda

“…This investigation highlights the use of energy approximations based on the generalized gradient approximation in conjunction with the Perdew–Burke–Ernzerhof functional to analyze these complex compounds. …”
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Micro-screw extrusion 3D printing of multiscale ternary nanocomposite absorbers – Part II: Design and process simulation of the extrusion system by Jiahang Zhang, Dongsheng Li, Mingming Wang

“…Optimizing extrusion die geometry significantly improves melt flow performance, enabling the efficient production of functional structural components. 3D printing experiments have proved that the process can achieve stable extrusion of polymer materials with an extremely wide viscosity range, and thanks to the effective pressure gradient and high shear rate, the ternary nanometer composite material finally achieves nanoscale mixing. …”
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Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks by Qian Yin, Hongwen Jing, Richeng Liu, Guowei Ma, Liyuan Yu, Haijian Su

“…The transmissivity of fracture networks decreases with the hydraulic gradient, and the variation process can be estimated using an exponential function. …”
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CASTEP investigation of FeS and FeSe: Structural, electronic, optical, and mechanical properties using the HSE03 hybrid by Geoffrey Tse

“…The dielectric function was calculated using the Ambroxol–Sofos and Kramers–Kronig theory for optical properties. …”
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Efficacy and safety of myectomy and radiofrequency septal ablation for treating hypertrophic obstructive cardiomyopathy by Larissa Ventura Ribeiro Bruscky, Bruno Pereira Valdigem, Edileide de Barros Correia, Paulo Chaccur, Andrea de Andrade Vilela, Antônio Tito Paladino Filho, Ibraim Pinto, Rui Fernando Ramos, Jorge Eduardo Assef

“…Procedural success, defined as a reduction in the LVOT gradient to <50 mm Hg or an improvement to functional class I or II, showed no significant difference between the groups (HR: −3.5; 95% CI: −20.2 to 13.12; p=0.673). …”
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Eddy Viscosity in Accelerated and Retarded Cascade-Wake Flows by J.W. Elsner

“…For x1 -> 11 it appears to be the increasing function of the longitudinal pressure gradient. …”
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Lightweight and rapid adaptive super-resolution interpolation reconstruction algorithm for super-pixel segmentation of super-wide field-of-view long-wave infrared images by Dongdong Shi, Xia Cai, Limin Liu, Fuyu Huang, Kangli Xu, Yuanbo Wang, Yudan Chen

“…Notably, the “sinc” function is employed to construct the interpolation weighting function, particularly for high-gradient regions. …”
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Microcrack feature extraction method for chaotic optical surface of silicon nitride ceramic bearing roller based on multi-scale wavelet transform enhancement and optimized PSO-FCM... by Yi Jiang, Mengtao Tang, Wenjie Dong, Guoxing Tang, Weiwen Hu, Jiao Li

“…Through the db4 basis function of multi-scale decomposition of microcrack features, the soft threshold function is constructed to deeply denoise the image. …”
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Towards Achilles Tendon Injury Prevention in Athletes with Structural MRI Biomarkers: A Machine Learning Approach by Norbert Kapinski, Karol Jaskulski, Justyna Witkowska, Adam Kozlowski, Pawel Adamczyk, Bartosz Wysoczanski, Agnieszka Zdrodowska, Adam Niemaszyk, Beata Ciszkowska-Lyson, Michal Starczewski

“…Aiming to identify relationships between the structured assessment of the Achilles tendon and its function that could support injury prevention. We examined 72 athletes to investigate the link between Achilles tendon structure, as visualised in magnetic resonance images using a precise T2*-weighted gradient echo sequence with very short echo times, and its functional attributes. …”
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Optimal design of vertical slot fishways by using shallow water equations by Mostafa Kadiri, Mohammed Louaked, Houari Mechkour

“…The work involves modeling, mathematical analysis and numerical approximation of a coupled problem between a primal hyperbolic system and adjoint problem of shallow water for the cost function of the optimal structure. We express the shape gradient of the cost function by introducing the associated adjoint state system. …”
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ClusterEmbed: Lightweight Protein Structure Prediction on PCs by Yuan Chuxin

“…Biological sequence design seeks to generate novel sequences, such as proteins, with optimized functional properties, a task complicated by vast combinatorial spaces and complex sequence-function relationships. …”
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Symmetric and Positive Definite Broyden Update for Unconstrained Optimization by Saad et al.

“…In this paper the guarantee of positive definite and symmetric property for the Hessian matrix will be established by updating the vector  which represents the difference between the next gradient and the current gradient of the objective function assumed to be twice continuous and differentiable .Numerical results are reported to compare the proposed method with the Broyden method under standard problems.…”
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Variational quantum algorithm for enhanced continuous variable optical phase sensing by Jens A. H. Nielsen, Mateusz J. Kicinski, Tummas N. Arge, Kannan Vijayadharan, Jonathan Foldager, Johannes Borregaard, Johannes Jakob Meyer, Jonas S. Neergaard-Nielsen, Tobias Gehring, Ulrik L. Andersen

“…The second strategy involves a gradient-free Bayesian optimizer, fine-tuning the system using the same cost function and trained on the data acquired through the gradient-dependent algorithm. …”
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On Training Of Feed Forward Neural Networks by Baghdad Science Journal

“…In all of these algorithms we use the gradient of the performance function, energy function, to determine how to adjust the weights such that the performance function is minimized, where the back propagation algorithm has been used to increase the speed of training. …”
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Barlow Twins deep neural network for advanced 1D drug–target interaction prediction by Maximilian G. Schuh, Davide Boldini, Annkathrin I. Bohne, Stephan A. Sieber

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Research on distributed economic dispatching algorithm for information security and privacy protection in smart grid by ZHANG Yanjun, SONG Mingshu, MA Xiaolei

“…The algorithm estimates the real gradient information based on one-point feedback to guide the updating of decision variables, avoids accurate gradient calculation, and is suitable for the scenario where gradient information is unavailable. …”
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Computational and experimental insights into the spectroscopy, electronic states, and molecular docking of (2S)-2,6-diaminohexanoic acid [DAHA] by T. Amna Sherin, P. V. Abdul Nazar, Sandhya Savita, Mudassar Shahid, Nazia Siddiqui, Saleem Javed

“…The electron localization function and reduced density gradient were determined to understand bonding and electronic structure. …”
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Modification and Patterning of Thiolate‐Anchored Self‐Assembled Monolayers with UV Light by Michael Zharnikov, Andreas Terfort

“…Since the extent of the substitution can be controlled by the irradiation dose, the final chemical composition can be flexibly tuned, allowing the preparation of functional binary SAMs and the creation of complex gradient‐like patterns. …”
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STUDY ON THE EQUIVALENT PROPERTIES AND ENERGY ABSORPTION PROPERTIES OF A NOVEL MATERIAL WITH NEGATIVE POISSON′S RATIO (MT) by WU XiaoLi, LI ZhaoKai

“…Through the finite element simulation method, the response difference of different structural parameters（inclined wall angle, width ratio, aspect ratio） to the equivalent elastic mechanical performance parameters of the cell is compared, and the influence of these structural parameters on the energy absorption performance is explored, and the research is further extended to the structure under four common functional gradient arrays. The energy absorption effect of the structure is evaluated by three indexes: energy absorption, energy absorption efficiency and platform stress. …”
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Alpha-defensin-dependent enhancement of enteric viral infection. by Sarah S Wilson, Beth A Bromme, Mayumi K Holly, Mayim E Wiens, Anshu P Gounder, Youngmee Sul, Jason G Smith

“…Although they most commonly function as potent antivirals in cell culture, enteric α-defensins have also been shown to enhance some viral infections in vitro. …”
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