Results 61 to 70 of about 14,497 (259)

On the Eigenvalues and Energy of the Seidel and Seidel Laplacian Matrices of Graphs

Discrete Dynamics in Nature and Society
Let SΓ be a Seidel matrix of a graph Γ of order n and let DΓ=diagn−1−2d1,n−1−2d2,…,n−1−2dn be a diagonal matrix with di denoting the degree of a vertex vi in Γ. The Seidel Laplacian matrix of Γ is defined as SLΓ=DΓ−SΓ.
J. Askari, Kinkar Chandra Das, Yilun Shang   +2 more
doaj   +1 more source

Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph

Discussiones Mathematicae Graph Theory, 2022
Given a signed graph Ġ, let AĠ and DG˙±D_{\dot G}^ \pm denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of Ġ is defined to be NG˙=DG˙±-AG˙{N_{\dot G}} = D_{\dot G}^ \pm - {A_{\dot
Stanić Zoran
doaj   +1 more source

Permanent of the laplacian matrix of trees with a given matching

Discrete Mathematics, 1986
Let \(G=(V,E)\) be an arbitrary graph, and \(d_ i>0\) be the degree of the vertex \(v_ i\in V\). D(G) denotes the diagonal matrix whose (i,i)-entry is \(d_ i\), and A(G) denotes the adjacency matrix of the graph G. The matrix \(L(G)=D(G)-A(G)\) will be called the Laplacian matrix of the graph G.
openaire   +2 more sources

Deep Learning Prediction of Surface Roughness in Multi‐Stage Microneedle Fabrication: A Long Short‐Term Memory‐Recurrent Neural Network Approach

Advanced Intelligent Discovery, EarlyView.
A sequential deep learning framework is developed to model surface roughness progression in multi‐stage microneedle fabrication. Using real‐world experimental data from 3D printing, molding, and casting stages, an long short‐term memory‐based recurrent neural network captures the cumulative influence of geometric parameters and intermediate outputs ...
Abdollah Ahmadpour, Sara Soltanabadi Farshi, Tuanna Ozcan, Amir Mohammad Ketabchi, Alper Kiraz, Savas Tasoglu   +5 more
wiley   +1 more source

A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws

Advanced Intelligent Discovery, EarlyView.
The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows, G. Zhang, S. Anand, Z. Chen, J. Lin, A. Desai, S. Martiniani, F. Caravelli   +7 more
wiley   +1 more source

On Path Laplacian Eigenvalues and Path Laplacian Energy of Graphs

Journal of New Theory, 2018
We introduce the concept of Path Laplacian Matrix for a graph and explore the eigenvalues of this matrix. The eigenvalues of this matrix are called the path Laplacian eigenvalues of the graph.
Shridhar Chandrakant Patekar, Maruti Mukinda Shikare   +1 more
doaj  

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Composition‐Aware Cross‐Sectional Integration for Spatial Transcriptomics

Advanced Intelligent Discovery, EarlyView.
Multi‐section spatial transcriptomics demands coherent cell‐type deconvolution, domain detection, and batch correction, yet existing pipelines treat these tasks separately. FUSION unifies them within a composition‐aware latent framework, modeling reads as cell‐type–specific topics and clustering in embedding space.
Qishi Dong, Zijian Huang, Xuanwu Wang, Zhenghui Feng, Wei Liu, Bingding Huang   +5 more
wiley   +1 more source

On minors of the compound matrix of a Laplacian

Linear Algebra and its Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Toward Intelligent Multimodal Holography for Real‐Time Chemical Imaging of Dynamic Ion Separation

Advanced Intelligent Discovery, EarlyView.
Intelligent multimodal holography integrates digital off‐axis holography, spectroscopic imaging, and AI‐driven reconstruction to visualize ion transport and chemical dynamics in real time. In this perspective paper, we outline how this approach enables label‐free, chemically specific monitoring of complex environments and discuss its potential to ...
Giovanna Ricchiuti, Sarah I. Allec, Maxim Ziatdinov, Venkateshkumar Prabhakaran   +3 more
wiley   +1 more source