This paper provides the numerical investigation of two-dimensional stochastic Navier-Stokes equation driven by additive white noises. The vorticity-stream function method is presented to calculate the incompressible fluid flow. In order to solve the formulation of steam function equation, we propose a Crank-Nicolson Fourier pseudo-spectral method. Numerical results obviously show that the presence of stochastic forcing can have an impact upon the shapes of vortex in fluid flow. To a certain extent, the phenomenon of eddy shedding and the formation of some new vortex in a random medium can be observed, which make it possible for us to conduct optimal control experiments in the development of vortex structures.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences, notably lifetime, medical, and financial sciences. The Heavy tailed Nadarajah Haghighi model is introduced by compounding the heavy tailed family and Nadarajah Haghighi distribution in this paper. The so obtained model has three parameters accounting for the scale and shape of the distribution. The proposed distribution's fundamental characteristics such as probability density, cumulative distribution, hazard rate, and survival functions are provided, and several key statistical properties are established, and several entropy information measures are proposed. The estimation of model parameter is performed via the ML procedure. Further, different simulation experiments are conducted to demonstrate the performance of proposed estimator’s using some measure, like the average estimate, the average bias, and associated mean square error. Finally, we are applied our proposed model to analyze three different real datasets. In our illustration, we are compared the practicality of the recommended model with several well-known competing models.

In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra. We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications. Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.

This study employs the reflection symmetry decomposition (RSD) method to extract polarization scattering features from ground object images, aiming to determine the optimal data input scheme for deep learning networks in polarimetric synthetic aperture radar classification. Eight distinct polarizing feature combinations are designed, and the classification accuracy of various approaches is evaluated using the classic convolutional neural networks(CNNs) AlexNet and VGG16. The findings reveal that the commonly employed 6-parameter input scheme, favored by many researchers, lacks the comprehensive utilization of polarization information and warrants attention. Intriguingly, leveraging the complete 9-parameter input scheme based on the polarization coherence matrix results in improved classification accuracy. Furthermore, the input scheme incorporating all 21 parameters from the RSD and polarization coherence matrix notably enhances overall accuracy and the Kappa coefficient compared to the other 7 schemes. This comprehensive approach maximizes the utilization of polarization scattering information from ground objects, emerging as the most effective CNN input data scheme in this study. Additionally, the classification performance using the second and third component total power values (P2 and P3) from the RSD surpasses the approach utilizing surface scattering power value (PS) and secondary scattering power value (PD) from the same decomposition.

The potential of metallic lithium to become the anode material for next-generation batteries is hampered by significant challenges, chief among which is dendrite growth during battery charging. These dendritic structures not only impair battery performance but also pose safety risks. Among the non-destructive analytical techniques in battery research, Magnetic Resonance Imaging (MRI) stands out as a promising tool. However, the direct imaging of lithium by 7Li MRI is hindered by its low sensitivity and spatial resolution, making its use for of dendritic growth imaging very difficult. Instead, a recently introduced indirect imaging approach based on 1H MRI of the electrolyte was used in this study. This method was used for sequential 3D imaging to monitor the charging process of lithium metal symmetric cells in three different electrical circuits: single cell, four cells in parallel, four cells in series. The measured sequential images allowed measurement of dendrite growth in each cell using volumetric analysis. The growth results confirmed the theoretical expectation that growth across cells is uneven in a parallel circuit and even in a series circuit. The methods presented in this study can be applied also to many other dendrite-related issues in batteries.

The description of the electron-electron interactions in two-dimensional materials has a dimensional mismatch, where electrons live in (2+1)D while photons propagate in (3+1)D. In order to define an action in (2+1)D, one may perform a dimensional reduction of quantum electrodynamics in (3+1)D (QED4) into Pseudo quantum electrodynamics (PQED). The main difference between this model and QED4 is the presence of a pseudo-differential operator in the Maxwell term. However, besides the Coulomb repulsion, electrons in a material are subjected to several microscopic interactions, which are inherent in a many-body system. These are expected to reduce the range of the Coulomb potential, leading to a short-range interaction. Here, we consider the coupling to a scalar field in PQED for explaining such mechanism, which resembles the spontanoues symmetry breaking (SSB) in Abelian gauge theories. In order to do so, we consider two cases: (i) By coupling the gauge field to a Higgs field in scalar quantum electrodynamics in (3+1)D and, thereafter, performing the dimensional reduction and; (ii) By coupling a Higgs field to the gauge field in PQED and subsequently calculating its effective potential. In case (i), we obtain a model describing electrons interacting through the Yukawa potential and, in case (ii), we show that SSB does not occur at one-loop approximation. The relevance of the model for describing electronic interactions in two-dimensional materials is also adressed.

Ensuring precise segmentation of colorectal polyps holds critical importance in the early diagnosis and treatment of colorectal cancer. Nevertheless, existing deep learning-based segmentation methods are fully-supervised, requiring extensive precise manual pixel-level annotation data, which leads to high annotation costs. Additionally, it remains challenging to train large-scale segmentation models when confronted with limited colonoscopy data. To address these issues, we introduce the general segmentation foundation model—Segment Anything Model (SAM) into the field of medical image segmentation. Fine-tuning the foundation model is an effective approach to tackle sample scarcity. However, current SAM fine-tuning techniques still rely on precise annotations. To overcome this limitation, we propose WSPoly-SAM, a novel weakly-supervised approach for colonoscopy polyp segmentation. WSPoly-SAM utilizes weak annotations to guide SAM in generating segmentation masks, which are then treated as pseudo-labels to guide the fine-tuning of SAM, thereby reducing the dependence on precise annotations data. To improve the reliability and accuracy of pseudo-labels, we have designed a series of enhancement strategies to improve the quality of pseudo-labels and mitigate the negative impact of low-quality pseudo-labels. Experimental results on five medical image datasets demonstrate that WSPoly-SAM outperforms current fully-supervised mainstream polyp segmentation networks on the Kvasir-SEG, ColonDB, CVC-300, and ETIS datasets. Furthermore, by using different amounts of training data in weakly-supervised and fully-supervised experiments, it is found that weakly-supervised fine-tuning can save 70% to 73% of annotation time costs compared to fully-supervised fine-tuning. This study provides a new perspective on the combination of weakly-supervised learning and SAM models, significantly reducing annotation time and offering insights for further development in the field of colonoscopy polyp segmentation.