We consider periodic solutions of the following nonlinear equation associated with the fractional Laplacian
\ (-\Delta)^s {u}(x)+V(x){u}(x)= {f(x,u)}, \quad x\in \mathbb{R}, \
(
−
Δ
)
s
u
(
x
)
+
V
(
...x
)
u
(
x
)
=
f
(
x
,
u
)
,
x
∈
R
,
where
$ V(x)\in C(\mathbb R) $
V
(
x
)
∈
C
(
R
)
is T-periodic and 0 belongs to a spectral gap of the operator
$ (-\Delta )^s+V $
(
−
Δ
)
s
+
V
. We obtain the existence of a periodic solution by using a generalized linking theorem.
•A novel divergent-convergent attention model (DCA) is proposed for image captioning.•Fine-grained semantic and visual components are explored in divergent observation.•Multimodal components are ...gradually converged with visual-semantic interaction.•Divergent observation and convergent attention facilitate descriptive captions.•DCA achieves state-of-the-art performance for image captioning on MS COCO.
Attention mechanism has made great progress in image captioning, where semantic words or local regions are selectively embedded into the language model. However, current attention-based image captioning methods ignore the fine-grained semantic information and their interaction with visual regions. Inspired by the activity of human in describing an image: divergent observation and convergent attention, we propose a novel divergent-convergent attention (DCA) model to tackle the problems of the current attention model in image captioning. In our DCA model, divergent observation is mainly reflected in the multi-perspective inputs: a visual collection coming from object detection and three semantic components of scene graph made of objects, attributes and relations respectively. Then the convergent attention merges these multi-perspective inputs by adaptively deciding which perspective is crucial and which element in the focused perspective dominates in the attention process through a hierarchical structure. Our model also makes use of the interaction between visual objects and semantic components to achieve complementary advantages. Above all, owing to the interaction between divergent visual and semantic components, and the gradual convergence of attention, our model can attend to the corresponding local region more precisely under the guidance of semantic components. Besides, with the assistance of the visual components, the DCA model can effectively utilize the fine-grained semantic components to generate more descriptive sentences. Experiments on the MS COCO dataset demonstrate the superiority of our proposed method.
We study the mean field equation on the flat torus Tσ:=C/(Z+Zσ)Δu+ρ(eu∫Tσeu−1|Tσ|)=0, where ρ is a real parameter. For a general flat torus, we obtain the existence of two-dimensional solutions ...bifurcating from the trivial solution at each eigenvalue (up to a multiplicative constant |Tσ|) of Laplace operator on the torus in the space of even symmetric functions. We further characterize the subset of all eigenvalues through which only one bifurcating curve passes. Finally local convexity near bifurcating points of the solution curves are obtained.
In this paper we study the structure and classification of four end solutions to a free boundary problem on the plane. These four end solutions are also characterized by having Morse index 1.
Despite the relatively small number of items in the GAD-7, fewer items are increasingly sought to shorten testing time in large-scale mental health screenings. As a result, short forms based on the ...GAD-7, the GAD-2, and GAD-mini, have become popular. However, the GAD-2 and GAD-mini have reported lower diagnostic accuracy in some cultural contexts, implying that a validated short-form version of the GAD-7 may be lacking in large-scale cross-cultural anxiety screening. Based on this, to develop an optimal short form of the GAD-7 with cross-cultural stability, we utilized seven GAD-7 datasets from six different countries, totaling 47,484 participants. Five 2 to 6 item short forms of the GAD were constructed using the Riskslim machine learning algorithm. We evaluated the diagnostic accuracy of the GAD-7 short forms in the training and test sets based on the coefficient of determination(R2) and area under the curve(AUC) metrics, and the results showed that GAD-R2 performed poorly in some cultures, and all of the 3 to 6 item short forms of the GAD performed good in cross-cultural diagnostic rates, with the GAD-R6 showing the highest diagnostic accuracy in all cultures; GAD-R3 outperformed GAD-R2, GAD-2, and GAD-mini in all cultures; GAD-R3 had higher generalizability across cultures and special populations; Given that the GAD-R3 was shorter and nearly as accurate as the GAD-R6, we recommend the use of the GAD-R3 in clinical studies and epidemiologic investigations. And we recommend the optimal actual cutoff value of 15 for GAD-R3. Overall, we recommend GAD-R3 as the short-form version of GAD-7 in cross-cultural studies. However, the 2-item GAD scale is also optimal for the short-form version in clinical practice.
•Lack of a short form of GAD-7 in large-scale cross-cultural anxiety screening.•Short form of the GAD were constructed using the Riskslim machine learning algorithm.•GAD-R3 exhibits high diagnostic accuracy in different cultural backgrounds.•we recommend GAD-R3 as the short form version of GAD-7 in cross-cultural studies.
The coal resources play an indispensable role in the development of heavy industry in China, and coal mining activity leads to brine wastewater drainage, causing major risks for the aquatic ...environmental system. Thus, the effective and economic treatment of coal mine wastewater is vital to mitigate the environmental burdens, and geological sequestration by deep-well injection is a promising treatment technique. This study elucidates the physical and geochemical processes of coal mine wastewater transport in deep reservoirs and proposes an optimized injection scheme to satisfy environmental and economic benefits simultaneously in the Ordos Basin, China. First, a variable density and variable parameter groundwater reactive transport model is constructed to simulate the long-term process of deep-well injection for coal mine wastewater treatment. Then, the environmental metrics, i.e., the percentage of permeability reduction, the total mass and spatial second moment of the wastewater plume, and the economic metric defined as achieving a higher concentration at a higher injection rate are proposed to evaluate the performance of the injection scheme. The simulation results show that the secondary mineral anhydrite dominates the reduction of reservoir permeability due to the precipitation reactions with SO42- in the brine wastewater, and the permeability in the reaction zone decreases by 0.66 % ~ 1.26 % after 10 years in the basic scenario. Moreover, higher concentrations negatively affect reservoir permeability and increase total dissolved solids, while higher injection rates decrease reservoir permeability and increase the brine wastewater plume. The study also identifies promising schemes that can achieve an optimal trade-off between the conflicting metrics. Based on the economic and environmental benefits demanded in this study, an injection scenario with a concentration of C4 and an injection volume of 800 m3/d is recommended to maximize environmental benefits. Overall, this numerical study offers significant implications for designing an economically and environmentally sustainable treatment injection scheme for coal mining wastewater drainage.
Compared with RGB images, hyperspectral images (HSIs) offer a distinct advantage in that they can record continuous spectral bands of light reflectance in each pixel, reflecting the physical and ...chemical characteristics of materials. This capability enables differentiation between objects that may have similar textures but different spectral characteristics. It is desirable to recover spectral information from RGB images to improve semantic segmentation accuracy. Additionally, semantic information can serve as a guide for spectral information recovery, thereby ensuring the quality of the recovered spectral information. The two tasks are mutually beneficial in this regard. In light of these considerations, we propose a multi-task framework that exploits the complementary relationship between spectral recovery and semantic segmentation tasks, comprising a complementary spectral-semantic attentive fusion model (CSSF) that enables the two tasks to mutually facilitate each other by fusing information from both branches. Specifically, the proposed CSSF incorporates a window-based spectral-semantic attentive fusion (WSSAF) module to incorporate recovered spectral information into the segmentation process effectively, and a pixel-shuffle-based fusion (PSF) module to provide semantic guidance for spectral recovery. To evaluate the effectiveness of our approach, we built the first flower hyperspectral image dataset (FHRS) with corresponding segmentation annotations and RGB images. By doing so, we have made the first attempt to explore the complementary relationship between semantic segmentation and spectral recovery. Experimental results on both the FHRS dataset and the publicly available LIB-HSI dataset demonstrate that our proposed method has the ability to enhance both tasks by utilizing their complementary relationship, indicating the generalization ability of our method.
Discovering the novel associations of biomedical entities is of great significance and can facilitate not only the identification of network biomarkers of disease but also the search for putative ...drug targets. Graph representation learning (GRL) has incredible potential to efficiently predict the interactions from biomedical networks by modeling the robust representation for each node. However, the current GRL-based methods learn the representation of nodes by aggregating the features of their neighbors with equal weights. Furthermore, they also fail to identify which features of higher-order neighbors are integrated into the representation of the central node. In this work, we propose a novel graph representation learning framework: a multi-order graph neural network based on reconstructed specific subgraphs (MGRS) for biomedical interaction prediction. In the MGRS, we apply the multi-order graph aggregation module (MOGA) to learn the wide-view representation by integrating the multi-hop neighbor features. Besides, we propose a subgraph selection module (SGSM) to reconstruct the specific subgraph with adaptive edge weights for each node. SGSM can clearly explore the dependency of the node representation on the neighbor features and learn the subgraph-based representation based on the reconstructed weighted subgraphs. Extensive experimental results on four public biomedical networks demonstrate that the MGRS performs better and is more robust than the latest baselines.
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