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BackgroundSentinel lymph node metastasis (SLNM) is a critical factor in the prognosis and treatment planning for breast cancer (BC), as it indicates the potential spread of cancer to other parts of the body. The accurate prediction and diagnosis of SLNM are essential for improving clinical outcomes and guiding treatment decisions.ObjectiveThis study aimed to construct a Lasso regression model by integrating multimodal ultrasound (US) techniques, including US, shear wave elastography (SWE), and contrast-enhanced ultrasound (CEUS), to improve the predictive accuracy of sentinel lymph node metastasis in breast cancer and provide more precise guidance for clinical treatment.ResultsA total of 253 eligible samples were screened, of which 148 were group benign and 105 were group malignant. There were statistically significant differences (p < 0.05) between group malignant patients in terms of age, palpable mass, body mass index, distance to nipple, maximum diameter, blood flow, microcalcification, 2D border, 2D morphology, and 2D uniformity and group benign. The Lasso regression model was useful in the diagnosis of benign and malignant nodules with an AUC of 0.966 and in diagnosing SLNM with an AUC of 0.832.ConclusionIn this study, we successfully constructed and validated a Lasso regression model based on the multimodal ultrasound technique for predicting whether SLNM occurs in BCs, showing high diagnostic accuracy.

Identifying the optimal cabin layout is an important way to improve the efficiency of ship systems and ensure the efficient circulation of personnel and materials. The ship task state refers to the state maintained by the joint actions of ship machinery and equipment, cargo, and personnel when facing different jobs and tasks during operation. A cabin layout that facilitates multitasking states can improve the efficiency of collaboration between systems and ensure the operation of the ship. The demand for human flow and logistics is different in multitasking states. To express the demand in mathematical form, there is a certain random uncertainty in the numerical quantification of the demand. Thus, to better meet the needs of different states, the coefficient values of each state can be integrated using special methods. Ensuring values’ initial preference to the greatest extent inevitably produces a degree of cognitive uncertainty. Therefore, uncertainty analysis is necessary for cabin layout design to be used for multitasking states. In this paper, a deterministic optimization platform of cabin layout in multitasking states is obtained. Adjacent and circulating strength coefficients are obtained through numerical quantization of the demand for human flow and logistics. The random uncertainty in the input values of two coefficients was represented by random variables, and the cognitive uncertainty was represented by interval variables. In order to solve the problem of two types of variables, a random-interval hybrid uncertainty model was established. Through random intervalization and interval randomization, three cases, of random variables, interval variables, and random variables and interval variables, were studied. The probability distribution of the model function was used to evaluate the influence of different compositions of uncertainty parameters on the robustness of the cabin layout scheme. The necessity and effectiveness of uncertainty analysis in multitasking cabin layout are discussed below.

In [16], using Rudin sets, Miao, Li and Zhao introduced a new concept of weakly well-filtered spaces—$ k $-bounded well-filtered spaces. Now, also using Rudin sets, we introduce another type of $ T_0 $ spaces—weakly bounded well-filtered spaces, which are strictly stronger than $ k $-bounded well-filtered spaces. Some basic properties of $ k $-bounded well-filtered spaces and weakly bounded well-filtered spaces are investigated and the relationships among some kinds of weakly sober spaces and weakly well-filtered spaces are posed. It is proved that the category $ {\bf KBWF} $ is not reflective in the category $ {\bf Top}_{0} $.

In this paper, we mainly study function spaces related to some kinds of weakly sober spaces, such as bounded sober spaces, $ k $-bounded sober spaces and weakly sober spaces. For $ T_{0} $ spaces $ X $ and $ Y $, it is proved that $ Y $ is bounded sober iff the function space $ {\bf{Top}}(X, Y) $ of all continuous functions $ f : X\longrightarrow Y $ equipped with the pointwise convergence topology is bounded sober iff $ {\bf{Top}}(X, Y) $ equipped with the Isbell topology is bounded sober. But for a $ k $-bounded sober space $ X $, the function space $ {\bf{Top}}(X, Y) $ equipped with the pointwise convergence topology or the Isbell topology may not be $ k $-bounded sober. It is shown that if the function space $ {\bf{Top}}(X, Y) $ equipped with the pointwise convergence topology or the Isbell topology is weakly sober (resp., a cut space), then $ Y $ is weakly sober (resp., a cut space). Relationships among some kinds of (weakly) sober spaces are also investigated.