Lower Bounds on Multivariate Higher Order Derivatives of Differential Entropy.

This paper studies the properties of the derivatives of differential entropy H(Xt) in Costa's entropy power inequality. For real-valued random variables, Cheng and Geng conjectured that for m≥1, (-1)m+1(dm/dtm)H(Xt)≥0, while McKean conjectured a stronger statement, whereby (-1)m+1(dm/dtm)H(Xt)≥(-1)m+1(dm/dtm)H(XGt). Here, we study the higher dimensional analogues of these conjectures. In particular, we study the veracity of the following two statements: C1(m,n):(-1)m+1(dm/dtm)H(Xt)≥0, where n denotes that Xt is a random vector taking values in Rn, and similarly, C2(m,n):(-1)m+1(dm/dtm)H(Xt)≥(-1)m+1(dm/dtm)H(XGt)≥0. In this paper, we prove some new multivariate cases: C1(3,i),i=2,3,4. Motivated by our results, we further propose a weaker version of McKean's conjecture C3(m,n):(-1)m+1(dm/dtm)H(Xt)≥(-1)m+11n(dm/dtm)H(XGt), which is implied by C2(m,n) and implies C1(m,n). We prove some multivariate cases of this conjecture under the log-concave condition: C3(3,i),i=2,3,4 and C3(4,2). A systematic procedure to prove Cl(m,n) is proposed based on symbolic computation and semidefinite programming, and all the new results mentioned above are explicitly and strictly proved using this procedure.

A Generalization of the Concavity of Rényi Entropy Power.

Recently, Savaré-Toscani proved that the Rényi entropy power of general probability densities solving the p-nonlinear heat equation in Rn is a concave function of time under certain conditions of three parameters n,p,µ, which extends Costa's concavity inequality for Shannon's entropy power to the Rényi entropy power. In this paper, we give a condition Φ(n,p,µ) of n,p,µ under which the concavity of the Rényi entropy power is valid. The condition Φ(n,p,µ) contains Savaré-Toscani's condition as a special case and much more cases. Precisely, the points (n,p,µ) satisfying Savaré-Toscani's condition consist of a two-dimensional subset of R3, and the points satisfying the condition Φ(n,p,µ) consist a three-dimensional subset of R3. Furthermore, Φ(n,p,µ) gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach.

Adaptive spline surface fitting with arbitrary topological control mesh.

Reconstructing a spline surface from a given arbitrary topological triangle mesh is a fundamental and challenging problem in computer-aided design and engineering. This paper introduces a novel surface fitting method utilizing G-NURBS capable of handling control meshes with arbitrary topologies. This method employs adaptive control point adjustment, guided by the geometric attributes of the input model, ensuring precise representation of sharp features such as edges and corners. Two primary strategies are employed: a parameter correspondence approach designed for sharp features and a control mesh iterative refinement technique that incorporates geometrical feature information. The proposed method has been tested and evaluated on various CAD models to demonstrate its effectiveness. This method can achieve higher fitting accuracy while faithfully preserving the geometrical features with fewer control points.

Patching Non-Uniform Extraordinary Points.

Smooth surfaces from an arbitrary topological control grid have been widely studied, which are mostly generalized from splines with uniform knot intervals. These methods fail to work well on extraordinary points (EPs) whose edges have varying knot intervals. This paper presents a patching solution for arbitrary topological 2-manifold control grid with non-uniform knots that defines one bi-cubic Bézier patch per control grid face except those faces with EPs. Experimental results demonstrate that the new solution can improve the surface quality for non-uniform parameterization. Applications in surface reconstruction, arbitrary sharp features on the complex surface and tool path planning for the new surface representation are also provided in the paper.

The disaster resilience trajectory of the first batch front-line nurses at fighting the Novel Coronavirus Disease 2019 in Wuhan: A qualitative study.

Aim: It is widely accepted that resilience is an essential solution to the challenges caused by disasters or crisis. The resilient individual can actively cope with challenges and maintain a good performance in facing of disastrous events. After the outbreak of Novel Coronavirus Disease 2019 (COVID-19) in Wuhan, China, numerous researchers have engaged in studying the experiences of front-line nurses in Wuhan from different perspectives. However, little is known on how the first batch front-line nurses developed their resilience trajectories during the disastrous events. The purpose of the present study is to explore the disaster resilience trajectory of the first batch front-line nurses at the early-stage of COVID-19 outbreak in Wuhan, Hubei province. Method: Qualitative research method was employed using purposive sampling. Nurses from Sichuan who had anti-epidemic experiences in Wuhan were selected to be conducted in-depth phone interviews. The interviews were transcribed verbatim, and data was analysed by adopting Colaizzi phenomenological approach. Results: Three theme categories emerged through the data analysis: (1) Challenges and difficulties; (2) Overcoming difficulties; (3) and Personal growth. Conclusion: Nurses have accumulated relevant experiences in dealing with sudden public health events after the rescue task, which can provide psychological and material supports for coping with similar situation in the future. Additionally, multiple support systems were critical elements for front-line nurses to recover from the disaster. Through uncovering front-line nurses' disaster resilience trajectories, it is significant for health care organizations and managers to establish more comprehensive system in handling with public health emergency events.

A framework from point clouds to workpieces.

Combining computer-aided design and computer numerical control (CNC) with global technical connections have become interesting topics in the manufacturing industry. A framework was implemented that includes point clouds to workpieces and consists of a mesh generation from geometric data, optimal surface segmentation for CNC, and tool path planning with a certified scallop height. The latest methods were introduced into the mesh generation with implicit geometric regularization and total generalized variation. Once the mesh model was obtained, a fast and robust optimal surface segmentation method is provided by establishing a weighted graph and searching for the minimum spanning tree of the graph for extraordinary points. This method is easy to implement, and the number of segmented patches can be controlled while preserving the sharp features of the workpiece. Finally, a contour parallel tool-path with a confined scallop height is generated on each patch based on B-spline fitting. Experimental results show that the proposed framework is effective and robust.

Regeneration pattern of primary forest species across forest-field gradients in the subtropical mountains of Southwestern China.

Evergreen broad-leaved forest is now gradually degraded and fragmented, and there is an increase in the amount of habitat edges as a result of long-term human activity. However, the role of edges in the regeneration of primary forest species is poorly understood. After 20 years of the edge creation, we analyzed primary forest species distribution and abundance, and changes in floristic composition, vegetation structure across forest-field gradients in Ailao Mountain, SW China. Our results revealed that there was a higher abundance and richness of primary species, late secondary species and thorny lianas at the distances 0-50 m than at the distances more than 50 m from the edge into the forest exterior. At the distances >50 m, no individuals of dominant canopy trees Lithocarpus xylocarpus, Castanopsis wattii, and L. jingdongensis were found, whereas the abundance of early pioneer shrub species and herbaceous cover was significantly greater. The richness of primary species showed a decrease with increasing distances from the forest edge to the exterior, particularly of medium-seeded primary species showing a drastic decrease. Moreover, no large-seeded primary species occurred at the distances >60 m. This study indicates that the forest edge as a buffer zone may be in favor of primary species regeneration. A dense shrub and herb layer, and seed dispersal may be the major factors limiting the forest regeneration farther from the forest edge. Therefore, to facilitate forest recovery processes, management should give priority to the protection of buffer zones of this forest edge.