scholarly journals On Recovery Guarantees for Angular Synchronization

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Frank Filbir ◽  
Felix Krahmer ◽  
Oleh Melnyk
Keyword(s):  
Optimization Problem ◽  
Convex Relaxation ◽  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Weighted Version ◽  
Synchronization Problem ◽  
Pairwise Differences ◽  
The Impact ◽  
Graph Laplacian Matrix

AbstractThe angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as an optimization problem on graphs involving the graph Laplacian matrix. We consider a general, weighted version of this problem, where the impact of the noise differs between different pairs of entries and some of the differences are erased completely; this version arises for example in ptychography. We study two common approaches for solving this problem, namely eigenvector relaxation and semidefinite convex relaxation. Although some recovery guarantees are available for both methods, their performance is either unsatisfying or restricted to the unweighted graphs. We close this gap, deriving recovery guarantees for the weighted problem that are completely analogous to the unweighted version.

Graph laplacian matrix learning from smooth time-vertex signal

2021 ◽  
Vol 18 (3) ◽  
pp. 187-204
Author(s):  
Ran Li ◽  
Junyi Wang ◽  
Wenjun Xu ◽  
Jiming Lin ◽  
Hongbing Qiu
Keyword(s):  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Graph Laplacian Matrix

scholarly journals Oversampled Graph Laplacian Matrix for Graph Filter Banks

2014 ◽  
Vol 62 (24) ◽  
pp. 6425-6437 ◽  
Author(s):  
Akie Sakiyama ◽  
Yuichi Tanaka
Keyword(s):  
Filter Banks ◽  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Graph Laplacian Matrix

scholarly journals Approximations of the Generalized Inverse of the Graph Laplacian Matrix

2012 ◽  
Vol 8 (4) ◽  
pp. 456-481 ◽  
Author(s):  
Enrico Bozzo ◽  
Massimo Franceschet
Keyword(s):  
Generalized Inverse ◽  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Graph Laplacian Matrix

scholarly journals Co-Simulation Framework for Optimal Allocation and Power Management of DGs in Power Distribution Networks Based on Computational Intelligence Techniques

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1648
Author(s):  
Marinko Barukčić ◽  
Toni Varga ◽  
Vedrana Jerković Jerković Štil ◽  
Tin Benšić
Keyword(s):  
Power System ◽  
Power Management ◽  
Computational Intelligence ◽  
Input Data ◽  
Optimization Problem ◽  
Optimal Allocation ◽  
Distribution Networks ◽  
Distributed Generations ◽  
Data Resolution ◽  
The Impact

The paper researches the impact of the input data resolution on the solution of optimal allocation and power management of controllable and non-controllable renewable energy sources distributed generation in the distribution power system. Computational intelligence techniques and co-simulation approach are used, aiming at more realistic system modeling and solving the complex optimization problem. The optimization problem considers the optimal allocation of all distributed generations and the optimal power control of controllable distributed generations. The co-simulation setup employs a tool for power system analysis and a metaheuristic optimizer to solve the optimization problem. Three different resolutions of input data (generation and load profiles) are used: hourly, daily, and monthly averages over one year. An artificial neural network is used to estimate the optimal output of controllable distributed generations and thus significantly decrease the dimensionality of the optimization problem. The proposed procedure is applied on a 13 node test feeder proposed by the Institute of Electrical and Electronics Engineers. The obtained results show a huge impact of the input data resolution on the optimal allocation of distributed generations. Applying the proposed approach, the energy losses are decreased by over 50–70% by the optimal allocation and control of distributed generations depending on the tested network.

scholarly journals Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

2020 ◽  
Vol 4 (3) ◽  
pp. 871-890
Author(s):  
Arseny A. Sokolov ◽  
Peter Zeidman ◽  
Adeel Razi ◽  
Michael Erb ◽  
Philippe Ryvlin ◽  
...  
Keyword(s):  
White Matter ◽  
Dynamic Range ◽  
Diffusion Processes ◽  
Brain Connectivity ◽  
Effective Connectivity ◽  
Structural Connectivity ◽  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Brain Regions ◽  
High Order

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

scholarly journals Spectral Processing for Denoising and Compression of 3D Meshes Using Dynamic Orthogonal Iterations

2020 ◽  
Vol 6 (6) ◽  
pp. 55
Author(s):  
Gerasimos Arvanitis ◽  
Aris S. Lalos ◽  
Konstantinos Moustakas
Keyword(s):  
Computational Complexity ◽  
Laplacian Matrix ◽  
3D Models ◽  
Graph Laplacian ◽  
Fixed Number ◽  
Spectral Processing ◽  
Reconstruction Quality ◽  
And Performance ◽  
Optimal Subspace

Recently, spectral methods have been extensively used in the processing of 3D meshes. They usually take advantage of some unique properties that the eigenvalues and the eigenvectors of the decomposed Laplacian matrix have. However, despite their superior behavior and performance, they suffer from computational complexity, especially while the number of vertices of the model increases. In this work, we suggest the use of a fast and efficient spectral processing approach applied to dense static and dynamic 3D meshes, which can be ideally suited for real-time denoising and compression applications. To increase the computational efficiency of the method, we exploit potential spectral coherence between adjacent parts of a mesh and then we apply an orthogonal iteration approach for the tracking of the graph Laplacian eigenspaces. Additionally, we present a dynamic version that automatically identifies the optimal subspace size that satisfies a given reconstruction quality threshold. In this way, we overcome the problem of the perceptual distortions, due to the fixed number of subspace sizes that is used for all the separated parts individually. Extensive simulations carried out using different 3D models in different use cases (i.e., compression and denoising), showed that the proposed approach is very fast, especially in comparison with the SVD based spectral processing approaches, while at the same time the quality of the reconstructed models is of similar or even better reconstruction quality. The experimental analysis also showed that the proposed approach could also be used by other denoising methods as a preprocessing step, in order to optimize the reconstruction quality of their results and decrease their computational complexity since they need fewer iterations to converge.

Quantifying the Impact of Domain Knowledge and Problem Framing on Sequential Decisions in Engineering Design

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Murtuza Shergadwala ◽  
Ilias Bilionis ◽  
Karthik N. Kannan ◽  
Jitesh H. Panchal
Keyword(s):  
Engineering Design ◽  
Information Acquisition ◽  
Design Problem ◽  
Domain Knowledge ◽  
Optimization Problem ◽  
Domain Specific ◽  
Problem Framing ◽  
Design Solutions ◽  
The Impact ◽  
Domain Independent

Many decisions within engineering systems design are typically made by humans. These decisions significantly affect the design outcomes and the resources used within design processes. While decision theory is increasingly being used from a normative standpoint to develop computational methods for engineering design, there is still a significant gap in our understanding of how humans make decisions within the design process. Particularly, there is lack of knowledge about how an individual's domain knowledge and framing of the design problem affect information acquisition decisions. To address this gap, the objective of this paper is to quantify the impact of a designer's domain knowledge and problem framing on their information acquisition decisions and the corresponding design outcomes. The objective is achieved by (i) developing a descriptive model of information acquisition decisions, based on an optimal one-step look ahead sequential strategy, utilizing expected improvement maximization, and (ii) using the model in conjunction with a controlled behavioral experiment. The domain knowledge of an individual is measured in the experiment using a concept inventory, whereas the problem framing is controlled as a treatment variable in the experiment. A design optimization problem is framed in two different ways: a domain-specific track design problem and a domain-independent function optimization problem (FOP). The results indicate that when the problem is framed as a domain-specific design task, the design solutions are better and individuals have a better state of knowledge about the problem, as compared to the domain-independent task. The design solutions are found to be better when individuals have a higher knowledge of the domain and they follow the modeled strategy closely.

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