scholarly journals Lelong–Jensen formula, Demailly–Lelong numbers and weighted degree of positive supercurrents

2020 ◽  
pp. 1-35
Author(s):  
Fredj Elkhadhra ◽  
Khalil Zahmoul
Keyword(s):  
Weighted Degree ◽  
Lelong Numbers

scholarly journals Relative non-pluripolar product of currents

2021 ◽  
Author(s):  
Duc-Viet Vu
Keyword(s):  
Kähler Manifold ◽  
Monotonicity Property ◽  
Necessary Condition ◽  
Positive Current ◽  
Lelong Numbers ◽  
Kahler Manifold ◽  
Closed Positive Current ◽  
Positive Currents ◽  
Compact Kähler Manifold

AbstractLet X be a compact Kähler manifold. Let $$T_1, \ldots , T_m$$ T 1 , … , T m be closed positive currents of bi-degree (1, 1) on X and T an arbitrary closed positive current on X. We introduce the non-pluripolar product relative to T of $$T_1, \ldots , T_m$$ T 1 , … , T m . We recover the well-known non-pluripolar product of $$T_1, \ldots , T_m$$ T 1 , … , T m when T is the current of integration along X. Our main results are a monotonicity property of relative non-pluripolar products, a necessary condition for currents to be of relative full mass intersection in terms of Lelong numbers, and the convexity of weighted classes of currents of relative full mass intersection. The former two results are new even when T is the current of integration along X.

scholarly journals Variation of singular Kähler–Einstein metrics: Positive Kodaira dimension

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Junyan Cao ◽  
Henri Guenancia ◽  
Mihai Păun
Keyword(s):  
General Type ◽  
Einstein Metrics ◽  
Kodaira Dimension ◽  
Einstein Metric ◽  
Canonical Bundle ◽  
Fiber Space ◽  
Generic Fiber ◽  
Lelong Numbers ◽  
Kähler Einstein Metrics

Abstract Given a Kähler fiber space p : X → Y {p:X\to Y} whose generic fiber is of general type, we prove that the fiberwise singular Kähler–Einstein metric induces a semipositively curved metric on the relative canonical bundle K X / Y {K_{X/Y}} of p. We also propose a conjectural generalization of this result for relative twisted Kähler–Einstein metrics. Then we show that our conjecture holds true if the Lelong numbers of the twisting current are zero. Finally, we explain the relevance of our conjecture for the study of fiberwise Song–Tian metrics (which represent the analogue of KE metrics for fiber spaces whose generic fiber has positive but not necessarily maximal Kodaira dimension).

EM Algorithm Based on Fuzzification and its Application

2012 ◽  
Vol 532-533 ◽  
pp. 1445-1449
Author(s):  
Ting Ting Tong ◽  
Zhen Hua Wu
Keyword(s):  
Em Algorithm ◽  
Mixed Model ◽  
Image Data ◽  
Training Sample ◽  
Model Parameters ◽  
Parameter Learning ◽  
Weighted Degree ◽  
The Em Algorithm ◽  
The Impact

EM algorithm is a common method to solve mixed model parameters in statistical classification of remote sensing image. The EM algorithm based on fuzzification is presented in this paper to use a fuzzy set to represent each training sample. Via the weighted degree of membership, different samples will be of different effect during iteration to decrease the impact of noise on parameter learning and to increase the convergence rate of algorithm. The function and accuracy of classification of image data can be completed preferably.

Improved influential nodes identification in complex networks

2021 ◽  
pp. 1-9
Author(s):  
Shi Dong ◽  
Wengang Zhou
Keyword(s):  
Theoretical Analysis ◽  
Complex Networks ◽  
Network Structure ◽  
Information Entropy ◽  
Network System ◽  
Weighted Degree ◽  
Identification Methods ◽  
Hybrid Mechanism ◽  
Influential Nodes ◽  
Influential Node

Influential node identification plays an important role in optimizing network structure. Many measures and identification methods are proposed for this purpose. However, the current network system is more complex, the existing methods are difficult to deal with these networks. In this paper, several basic measures are introduced and discussed and we propose an improved influential nodes identification method that adopts the hybrid mechanism of information entropy and weighted degree of edge to improve the accuracy of identification (Hm-shell). Our proposed method is evaluated by comparing with nine algorithms in nine datasets. Theoretical analysis and experimental results on real datasets show that our method outperforms other methods on performance.

scholarly journals Peripheral inflammation is associated with micro-structural and functional connectivity changes in depression-related brain networks

2021 ◽  
Author(s):  
Manfred G. Kitzbichler ◽  
Athina R. Aruldass ◽  
Gareth J. Barker ◽  
Tobias C. Wood ◽  
Nicholas G. Dowell ◽  
...  
Keyword(s):  
Functional Connectivity ◽  
Venous Blood ◽  
Regional Analysis ◽  
Brain Magnetic Resonance Imaging ◽  
Structural Mri ◽  
Posterior Cingulate Cortex ◽  
Proton Density ◽  
Peripheral Inflammation ◽  
Tissue Water ◽  
Weighted Degree

AbstractInflammation is associated with depressive symptoms and innate immune mechanisms are likely causal in some cases of major depression. Systemic inflammation also perturbs brain function and microstructure, though how these are related remains unclear. We recruited N = 46 healthy controls, and N = 83 depressed cases stratified by CRP (> 3 mg/L: N = 33; < 3 mg/L: N = 50). All completed clinical assessment, venous blood sampling for C-reactive protein (CRP) assay, and brain magnetic resonance imaging (MRI). Micro-structural MRI parameters including proton density (PD), a measure of tissue water content, were measured at 360 cortical and 16 subcortical regions. Resting-state fMRI time series were correlated to estimate functional connectivity between individual regions, as well as the sum of connectivity (weighted degree) of each region. Multiple tests for regional analysis were controlled by the false discovery rate (FDR = 5%). We found that CRP was significantly associated with PD in precuneus, posterior cingulate cortex (pC/pCC) and medial prefrontal cortex (mPFC); and with functional connectivity between pC/pCC, mPFC and hippocampus. Depression was associated with reduced weighted degree of pC/pCC, mPFC, and other nodes of the default mode network (DMN). Thus CRP-related increases in proton density—a plausible marker of extracellular oedema—and changes in functional connectivity were anatomically co-localised with DMN nodes that also demonstrated significantly reduced hubness in depression. We suggest that effects of peripheral inflammation on DMN node micro-structure and connectivity may mediate inflammatory effects on depression.

scholarly journals Identifying the most influential roads based on traffic correlation networks

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Shengmin Guo ◽  
Dong Zhou ◽  
Jingfang Fan ◽  
Qingfeng Tong ◽  
Tongyu Zhu ◽  
...  
Keyword(s):  
Traffic Congestion ◽  
Temporal Correlation ◽  
Correlation Network ◽  
Traffic Flows ◽  
Weighted Degree ◽  
Correlation Networks ◽  
Spatio Temporal ◽  
Smart Traffic ◽  
The Impact ◽  
Impact Distance

Abstract Prediction of traffic congestion is one of the core issues in the realization of smart traffic. Accurate prediction depends on understanding of interactions and correlations between different city locations. While many methods merely consider the spatio-temporal correlation between two locations, here we propose a new approach of capturing the correlation network in a city based on realtime traffic data. We use the weighted degree and the impact distance as the two major measures to identify the most influential locations. A road segment with larger weighted degree or larger impact distance suggests that its traffic flow can strongly influence neighboring road sections driven by the congestion propagation. Using these indices, we find that the statistical properties of the identified correlation network is stable in different time periods during a day, including morning rush hours, evening rush hours, and the afternoon normal time respectively. Our work provides a new framework for assessing interactions between different local traffic flows. The captured correlation network between different locations might facilitate future studies on predicting and controlling the traffic flows.

scholarly journals Network design with weighted degree constraints

2010 ◽  
Vol 7 (4) ◽  
pp. 246-255 ◽  
Author(s):  
Takuro Fukunaga ◽  
Hiroshi Nagamochi
Keyword(s):  
Network Design ◽  
Weighted Degree
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