Nanoscale capacitance spectroscopy based on multifrequency electrostatic force microscopy by Pascal N. Rohrbeck, Lukas D. Cavar, Franjo Weber, Peter G. Reichel, Mara Niebling, Stefan A. L. Weber

“…Besides a high spatial resolution, the key advantage of the multifrequency approach of MFH-EFM is that it measures the second-order capacitance gradient at almost arbitrary frequencies, enabling the measurement of the local dielectric function over a wide range of frequencies. …”
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Solving Fractional Differential Equations by Using Triangle Neural Network by Feng Gao, Yumin Dong, Chunmei Chi

“…Then, based on the technique of minimizing the loss function of the neural network, the proposed numerical methods reduce the fractional differential equation into a gradient descent problem or the quadratic optimization problem. …”
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Barrier Solutions of Elliptic Differential Equations in Musielak-Orlicz-Sobolev Spaces by Ge Dong, Xiaochun Fang

“…In this paper, we study the solution set of the following Dirichlet boundary equation: −diva1x,u,Du+a0x,u=fx,u,Du in Musielak-Orlicz-Sobolev spaces, where a1:Ω×ℝ×ℝN⟶ℝN, a0:Ω×ℝ⟶ℝ, and f:Ω×ℝ×ℝN⟶ℝ are all Carathéodory functions. Both a1 and f depend on the solution u and its gradient Du. …”
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Next-Generation Biomaterials for Load-Bearing Tissue Interfaces: Sensor-Integrated Scaffolds and Mechanoadaptive Constructs for Skeletal Regeneration by Rahul Kumar, Kyle Sporn, Pranay Prabhakar, Phani Paladugu, Akshay Khanna, Alex Ngo, Chirag Gowda, Ethan Waisberg, Ram Jagadeesan, Nasif Zaman, Alireza Tavakkoli

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A dictionary learning approach with overlap for the low dose computed tomography reconstruction and its vectorial application to differential phase tomography. by Alessandro Mirone, Emmanuel Brun, Paola Coan

“…In this scenario, we implemented a dictionary learning method with a new form of convex functional. This functional contains in addition to the usual sparsity inducing and fidelity terms, a new term which forces similarity between overlapping patches in the superimposed regions. …”
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High afterload rather than myocardial fibrosis predicts reduced ejection fraction in severe aortic stenosis with afterload mismatch by Anton Doubell, Philip Herbst, Megan Rian Rajah

“…The extent, pattern and functional impact of myocardial fibrosis (MF), which is associated with systolic impairment, is poorly understood in the context of AM.Methods High-gradient severe AS patients with (n=25; low ejection fraction high-gradient, LEF-HG) and without (n=33; normal ejection fraction high-gradient (NEF-HG)) reduced LVEF underwent cardiovascular MRI. …”
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Solution of the Inverse Problem of Subsurface Electric Exploration for Horizontally Stratified Medium by A. L. Karchevsky, Zh. O. Oralbekova, K. T. Iskakov

“…In this paper, we offer the generalization of the known technique of the construction of the gradient of the residual functional based on the statement of the conjugate problem for the case when the unknown function is complex valued. …”
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Suppression of the surface roughness by adjusting the temperature distribution in the top-seeded solution growth of SiC crystal by Mengyu Li, Yuhui Liu, Xiaofang Qi, Wencheng Ma, Yongkuan Xu, Zhanggui Hu, Yicheng Wu

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A Study on Contact Metric Manifolds Admitting a Type of Solitons by Tarak Mandal, Uday Chand De, Meraj Ali Khan, Mohammad Nazrul Islam Khan

“…In this regard, it is shown that if a K-contact manifold admits a gradient η-Ricci–Bourguignon soliton, then the scalar curvature is a constant and either the soliton reduces to gradient Ricci–Bourguignon soliton, or the potential function is a constant. …”
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Scaling of hardware-compatible perturbative training algorithms by B. G. Oripov, A. Dienstfrey, A. N. McCaughan, S. M. Buckley

“…In this work, we explore the capabilities of multiplexed gradient descent (MGD), a scalable and efficient perturbative zeroth-order training method for estimating the gradient of a loss function in hardware and training it via stochastic gradient descent. …”
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Dung beetles (Coleoptera: Scarabaeidae, Scarabaeinae) and dung removal in Mexican livestock pastures by Carmen Huerta, Lucrecia Arellano, Magdalena Cruz

“…Nocturnal tunnelers reincorporated the largest quantity of dung over the first 24 hours; in contrast, rollers only removed dung at the lowest areas of the gradient (< 250 m asl). However, much more information is still required regarding the capacity of the different functional groups and dung beetle species for dung burial in the livestock production zones of Mexico.…”
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Clinical relevance of transperineal ultrasound compared with anorectal manometry for the evaluation of female patients with obstructive defecation syndrome by Jingjing Li, Yahong Xue, Qian Chen, Yan Ling, Huifen Zhou, Min Li, Xinyi Xu, Yusha Zeng

“…We assert that combined imaging and functional testing is essential for comprehensive assessment of pelvic floor structural and functional characteristics in refractory ODS.…”
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Decoding cortical chronotopy—Comparing the influence of different cortical organizational schemes by Falko Mecklenbrauck, Jorge Sepulcre, Jana Fehring, Ricarda I. Schubotz

“…Based on this data, we extracted six organizational schemes: (1) the structural Rich Club (RC) architecture, shown to synchronize the connectome; (2) the structural Diverse Club architecture, as an alternative to the RC based on the network's module structure; (3) the functional uni-to-multimodal gradient, reflected in a wide range of structural and functional features; and (4) the spatial posterior/lateral-to-anterior/medial gradient, established for hierarchical levels of cognitive control. …”
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Recurrent neural network consisting of FitzHugh–Nagumo systems: characteristics required for training by Semenova, Nadezhda Igorevna

“…It was clearly shown what features should be taken into account during loss function calculation and how the gradient descent should be realized. …”
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Underwater sound absorption characteristics of the acoustic metamaterials with multiple coupling substructure by Kangkang Shi, Dongsheng Li, Dongsen Hu, Xiaoli Yu, Canlong Ding, Guoyong Jin

“…Therefore, a composite acoustic structure is designed by inserting regularly distributed lateral plates into the viscoelastic rubber, and then, the AMs with multiple coupling substructure (AMs-MCS) can be obtained through combining the local resonance structure and functional gradient structure. Based on underwater acoustic calculation model for the functional gradient acoustic structure established by grade finite element method (G-FEM), the underwater sound absorption characteristics of the AMs-MCS are studied, and the influence of each substructure on the acoustic performance of the AMs-MCS is explored. …”
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Expectation-maximization alternating least squares for tensor network logistic regression by Naoya Yamauchi, Hidekata Hontani, Tatsuya Yokota, Tatsuya Yokota

“…When constructing a classification function for high-dimensional data using a basis function model, a huge number of basis functions and coefficients are generally required, but the TN model makes it possible to avoid the curse of dimensionality by representing the huge coefficients using TNs. …”
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Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions by Yuchen Luo, Xiaoqun Cao, Kecheng Peng, Mengge Zhou, Yanan Guo

“…Traditional 4-dimensional variational data assimilation methods have limitations due to the Gaussian distribution assumption of observation errors, and the gradient of the objective functional is vulnerable to observation noise and outliers. …”
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Mechanical performance of graded lattice structures with periodic density variations fabricated by selective laser melting by Gangxian Zhu, Fangyuan Xu, Xulei Wang, Xing Zhang, Jiaqiang Li

“…Functionally graded lattice structures (GLSs) represent a novel class of non-uniform structures that leverage density gradients to optimize mechanical responses based on specific functional requirements. …”
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Adaptive Whole-Brain Dynamics Predictive Method: Relevancy to Mental Disorders by Qian-Yun Zhang, Chun-Wang Su, Qiang Luo, Celso Grebogi, Zi-Gang Huang, Junjie Jiang

“…We also developed an approximate loss function and gradient adjustment mechanism, enhancing parameter fitting accuracy and stability. …”
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