Relevant bibliographies by topics / Rank-one Laplacian / Journal articles
To see the other types of publications on this topic, follow the link: Rank-one Laplacian.

Journal articles on the topic 'Rank-one Laplacian'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 49 journal articles for your research on the topic 'Rank-one Laplacian.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Conejero, J. Alberto, Antonio Falcó, and María Mora–Jiménez. "A pre-processing procedure for the implementation of the greedy rank-one algorithm to solve high-dimensional linear systems." AIMS Mathematics 8, no. 11 (2023): 25633–53. http://dx.doi.org/10.3934/math.20231308.

Full text
Abstract:
<abstract><p>Algorithms that use tensor decompositions are widely used due to how well they perfor with large amounts of data. Among them, we find the algorithms that search for the solution of a linear system in separated form, where the greedy rank-one update method stands out, to be the starting point of the famous proper generalized decomposition family. When the matrices of these systems have a particular structure, called a Laplacian-like matrix which is related to the aspect of the Laplacian operator, the convergence of the previous method is faster and more accurate. The ma
APA, Harvard, Vancouver, ISO, and other styles
2

Lakaev, Sh S., O. I. Kurbonov, and V. U. Aktamova. "Threshold Analysis of the One-Rank Perturbation Non-Local Discrete Laplacian." Lobachevskii Journal of Mathematics 43, no. 8 (2022): 2187–93. http://dx.doi.org/10.1134/s1995080222110178.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

JI, LIZHEN, and ANDREAS WEBER. "The spectrum and heat dynamics of locally symmetric spaces of higher rank." Ergodic Theory and Dynamical Systems 35, no. 5 (2014): 1524–45. http://dx.doi.org/10.1017/etds.2014.3.

Full text
Abstract:
The aim of this paper is to study the spectrum of the$L^{p}$Laplacian and the dynamics of the$L^{p}$heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in the rank-one case, it turns out that the$L^{p}$heat semigroup on$M$has a certain chaotic behavior if$p\in (1,2)$, whereas for$p\geq 2$such chaotic behavior never occurs.
APA, Harvard, Vancouver, ISO, and other styles
4

Tyrtyshnikov, Eugene E. "Tensor decompositions and rank increment conjecture." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 4 (2020): 239–46. http://dx.doi.org/10.1515/rnam-2020-0020.

Full text
Abstract:
AbstractSome properties of tensor ranks and the non-closeness issue of sets with given restrictions on the rank of tensors entering those sets are studied. It is proved that the rank of the d-dimensional Laplacian equals d. The following conjecture is formulated: for any tensor of non-maximal rank there exists a nonzero decomposable tensor (tensor of rank 1) such that the rank increases by one after adding this tensor. In the general case, it is proved that this property holds algebraically almost everywhere for complex tensors of fixed size whose rank is strictly less than the generic rank.
APA, Harvard, Vancouver, ISO, and other styles
5

So, Wasin. "Rank one perturbation and its application to the laplacian spectrum of a graph∗." Linear and Multilinear Algebra 46, no. 3 (1999): 193–98. http://dx.doi.org/10.1080/03081089908818613.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Hilgert, J., A. Pasquale, and T. Przebinda. "Resonances for the Laplacian on products of two rank one Riemannian symmetric spaces." Journal of Functional Analysis 272, no. 4 (2017): 1477–523. http://dx.doi.org/10.1016/j.jfa.2016.12.009.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Xu, Zhixuan, Caikou Chen, Guojiang Han, and Jun Gao. "Robust subspace clustering based on latent low rank representation with non-negative sparse Laplacian constraints." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 12151–65. http://dx.doi.org/10.3233/jifs-210274.

Full text
Abstract:
As a successful improvement on Low Rank Representation (LRR), Latent Low Rank Representation (LatLRR) has been one of the state-of-the-art models for subspace clustering due to the capability of discovering the low dimensional subspace structures of data, especially when the data samples are insufficient and/or extremely corrupted. However, the LatLRR method does not consider the nonlinear geometric structures within data, which leads to the loss of the locality information among data in the learning phase. Moreover, the coefficients of the learnt representation matrix can be negative, which l
APA, Harvard, Vancouver, ISO, and other styles
8

Ge, Shuguang, Xuesong Wang, Yuhu Cheng, and Jian Liu. "Cancer Subtype Recognition Based on Laplacian Rank Constrained Multiview Clustering." Genes 12, no. 4 (2021): 526. http://dx.doi.org/10.3390/genes12040526.

Full text
Abstract:
Integrating multigenomic data to recognize cancer subtype is an important task in bioinformatics. In recent years, some multiview clustering algorithms have been proposed and applied to identify cancer subtype. However, these clustering algorithms ignore that each data contributes differently to the clustering results during the fusion process, and they require additional clustering steps to generate the final labels. In this paper, a new one-step method for cancer subtype recognition based on graph learning framework is designed, called Laplacian Rank Constrained Multiview Clustering (LRCMC).
APA, Harvard, Vancouver, ISO, and other styles
9

Jeyaraman, I., T. Divyadevi, and R. Azhagendran. "The Moore-Penrose inverse of the distance matrix of a helm graph." Electronic Journal of Linear Algebra 39 (March 23, 2023): 94–109. http://dx.doi.org/10.13001/ela.2023.7465.

Full text
Abstract:
In this paper, we give necessary and sufficient conditions for a real symmetric matrix and, in particular, for the distance matrix $D(H_n)$ of a helm graph $H_n$ to have their Moore-Penrose inverses as the sum of a symmetric Laplacian-like matrix and a rank-one matrix. As a consequence, we present a short proof of the inverse formula, given by Goel (Linear Algebra Appl. 621:86-104, 2021), for $D(H_n)$ when $n$ is even. Further, we derive a formula for the Moore-Penrose inverse of singular $D(H_n)$ that is analogous to the formula for $D(H_n)^{-1}$. Precisely, if $n$ is odd, we find a symmetric
APA, Harvard, Vancouver, ISO, and other styles
10

Awonusika, Richard, and Ali Taheri. "A Spectral Identity on Jacobi Polynomials and its Analytic Implications." Canadian Mathematical Bulletin 61, no. 3 (2018): 473–82. http://dx.doi.org/10.4153/cmb-2017-056-8.

Full text
Abstract:
AbstractThe Jacobi coefficientsare linked to the Maclaurin spectral expansion of the Schwartz kernel of functions of the Laplacian on a compact rank one symmetric space. It is proved that these coefficients can be computed by transforming the even derivatives of the Jacobi polynomialsinto a spectral sum associated with the Jacobi operator. The first few coefficients are explicitly computed, and a direct trace interpretation of the Maclaurin coefficients is presented.
APA, Harvard, Vancouver, ISO, and other styles
11

Khatamsi, Hafsi Afrizun, Sugiyanto Sugiyanto, and Tri Asih Budiati. "Analysis of Differences in Cystic Ovarian Neoplasm Volume on Abdomen-Pelvis MRI with Manual Measurement Technique (Linear Measurement) and Active Contour Laplacian of Gaussian (LoG) Technique." Journal of Social Research 2, no. 11 (2023): 4020–30. http://dx.doi.org/10.55324/josr.v2i11.1550.

Full text
Abstract:
MRI image evaluation of cystic ovarian neoplasms was done manually and is generally carried out by Radiologists using a manual technique called linear measurement. This technique has some weaknesses, including being considered a rough calculation estimate because measurements are made on only one largest slice and are vulnerable to subjectivity factors. This research applied a digital image processing program based on Matlab using a segmentation process and active contour Laplacian of Gaussian (LoG) in the measurement and calculation of the volume of cystic ovarian neoplasms. Analyze the diffe
APA, Harvard, Vancouver, ISO, and other styles
12

Li, Ziyue, Nurettin Dorukhan Sergin, Hao Yan, Chen Zhang, and Fugee Tsung. "Tensor Completion for Weakly-Dependent Data on Graph for Metro Passenger Flow Prediction." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 4804–10. http://dx.doi.org/10.1609/aaai.v34i04.5915.

Full text
Abstract:
Low-rank tensor decomposition and completion have attracted significant interest from academia given the ubiquity of tensor data. However, low-rank structure is a global property, which will not be fulfilled when the data presents complex and weak dependencies given specific graph structures. One particular application that motivates this study is the spatiotemporal data analysis. As shown in the preliminary study, weakly dependencies can worsen the low-rank tensor completion performance. In this paper, we propose a novel low-rank CANDECOMP / PARAFAC (CP) tensor decomposition and completion fr
APA, Harvard, Vancouver, ISO, and other styles
13

Sun, Yubao, Zhi Li, and Min Wu. "A Rank-Constrained Matrix Representation for Hypergraph-Based Subspace Clustering." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/572753.

Full text
Abstract:
This paper presents a novel, rank-constrained matrix representation combined with hypergraph spectral analysis to enable the recovery of the original subspace structures of corrupted data. Real-world data are frequently corrupted with both sparse error and noise. Our matrix decomposition model separates the low-rank, sparse error, and noise components from the data in order to enhance robustness to the corruption. In order to obtain the desired rank representation of the data within a dictionary, our model directly utilizes rank constraints by restricting the upper bound of the rank range. An
APA, Harvard, Vancouver, ISO, and other styles
14

Gao, Wenyun, Sheng Dai, Stanley Ebhohimhen Abhadiomhen, Wei He, and Xinghui Yin. "Low Rank Correlation Representation and Clustering." Scientific Programming 2021 (February 16, 2021): 1–12. http://dx.doi.org/10.1155/2021/6639582.

Full text
Abstract:
Correlation learning is a technique utilized to find a common representation in cross-domain and multiview datasets. However, most existing methods are not robust enough to handle noisy data. As such, the common representation matrix learned could be influenced easily by noisy samples inherent in different instances of the data. In this paper, we propose a novel correlation learning method based on a low-rank representation, which learns a common representation between two instances of data in a latent subspace. Specifically, we begin by learning a low-rank representation matrix and an orthogo
APA, Harvard, Vancouver, ISO, and other styles
15

Rasulov, T. Kh, A. M. Khalkhuzhaev, M. A. Pardabaev, and Kh G. Khayitova. "Expansions of eigenvalues of a discrete bilaplacian with two-dimensional perturbation." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 10 (November 9, 2024): 77–89. http://dx.doi.org/10.26907/0021-3446-2024-10-77-89.

Full text
Abstract:
In this paper we consider the family of operators μH:= ΔΔ— Vμ, μ > 0, that is, a bilaplacian with a finite-dimensional perturbation on a one-dimensional lattice Z , where Δ is a discrete Laplacian, and Vμ is an operator of rank two. It is proved that for any μ > 0 the discrete spectrum μH is two-element e1(μ ) < 0 and e2(μ ) < 0. We find convergent expansions of the eigenvalues ei(μ ), i = 1, 2 in a small neighborhood of zero for small μ > 0.
APA, Harvard, Vancouver, ISO, and other styles
16

Das, Joyentanuj, and Sumit Mohanty. "Inverse of the squared distance matrix of a complete multipartite graph." Electronic Journal of Linear Algebra 40 (July 15, 2024): 475–90. http://dx.doi.org/10.13001/ela.2024.8283.

Full text
Abstract:
Let $G$ be a connected graph on $n$ vertices and $d_{ij}$ be the length of the shortest path between vertices $i$ and $j$ in $G$. We set $d_{ii}=0$ for every vertex $i$ in $G$. The squared distance matrix $\Delta(G)$ of $G$ is the $n\times n$ matrix with $(i,j)^{th}$ entry equal to $0$ if $i = j$ and equal to $d_{ij}^2$ if $i \neq j$. For a given complete $t$-partite graph $K_{n_1,n_2,\cdots,n_t}$ on $n=\sum_{i=1}^t n_i$ vertices, under some condition we find the inverse $\Delta(K_{n_1,n_2,\cdots,n_t})^{-1}$ as a rank-one perturbation of a symmetric Laplacian-like matrix $\mathcal{L}$ with $\t
APA, Harvard, Vancouver, ISO, and other styles
17

Engliš, Miroslav, and Jaak Peetre. "Green's Functions for Powers of the Invariant Laplacian." Canadian Journal of Mathematics 50, no. 1 (1998): 40–73. http://dx.doi.org/10.4153/cjm-1998-004-8.

Full text
Abstract:
AbstractThe aim of the present paper is the computation of Green's functions for the powers Δm of the invariant Laplace operator on rank-one Hermitian symmetric spaces. Starting with the noncompact case, the unit ball in ℂd, we obtain a complete result for m= 1, 2 in all dimensions. For m≥ 3 the formulas grow quite complicated so we restrict ourselves to the case of the unit disc (d= 1) where we develop a method, possibly applicable also in other situations, for reducing the number of integrations by half, and use it to give a description of the boundary behaviour of these Green functions and
APA, Harvard, Vancouver, ISO, and other styles
18

Zhang, Wenjuan, Xiangchu Feng, Feng Xiao, and Yunmei Chen. "A Folded Concave Penalty Regularized Subspace Clustering Method to Integrate Affinity and Clustering." Mathematical Problems in Engineering 2021 (May 17, 2021): 1–13. http://dx.doi.org/10.1155/2021/6641180.

Full text
Abstract:
Most sparse or low-rank-based subspace clustering methods divide the processes of getting the affinity matrix and the final clustering result into two independent steps. We propose to integrate the affinity matrix and the data labels into a minimization model. Thus, they can interact and promote each other and finally improve clustering performance. Furthermore, the block diagonal structure of the representation matrix is most preferred for subspace clustering. We define a folded concave penalty (FCP) based norm to approximate rank function and apply it to the combination of label matrix and r
APA, Harvard, Vancouver, ISO, and other styles
19

Peng, Yong, Wanzeng Kong, Feiwei Qin, and Feiping Nie. "Manifold Adaptive Kernelized Low-Rank Representation for Semisupervised Image Classification." Complexity 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/2857594.

Full text
Abstract:
Constructing a powerful graph that can effectively depict the intrinsic connection of data points is the critical step to make the graph-based semisupervised learning algorithms achieve promising performance. Among popular graph construction algorithms, low-rank representation (LRR) is a very competitive one that can simultaneously explore the global structure of data and recover the data from noisy environments. Therefore, the learned low-rank coefficient matrix in LRR can be used to construct the data affinity matrix. Consider the existing problems such as the following: (1) the essentially
APA, Harvard, Vancouver, ISO, and other styles
20

Chorwadwala, Anisa M. H., and M. K. Vemuri. "Two functionals connected to the Laplacian in a class of doubly connected domains on rank one symmetric spaces of non-compact type." Geometriae Dedicata 167, no. 1 (2012): 11–21. http://dx.doi.org/10.1007/s10711-012-9800-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
21

Athira, V. S., Vijayakumar S. Muni, Kallu Vetty Muhammed Rafeek, and Gudala Janardhana Reddy. "Controllability of consensus heterogeneous multi-agent networks over continuous time scale." Control and Cybernetics 52, no. 2 (2023): 199–245. http://dx.doi.org/10.2478/candc-2023-0037.

Full text
Abstract:
Abstract The research, presented in this paper, concernes the controllability of a multi-agent network with a directed, unweighted, cooperative, and time-invariant communication topology. The network’s agents follow linear and heterogeneous dynamics, encompassing first-order, second-order, and third-order differential equations over continuous time. Two classes of neighbour-based linear distributed control protocols are considered: the first one utilises average feedback from relative velocities/relative accelerations, and the second one utilises feedback from absolute velocities/absolute acce
APA, Harvard, Vancouver, ISO, and other styles
22

Abhadiomhen, Stanley Ebhohimhen, Zhiyang Wang, Xiangjun Shen, and Jianping Fan. "Multiview Common Subspace Clustering via Coupled Low Rank Representation." ACM Transactions on Intelligent Systems and Technology 12, no. 4 (2021): 1–25. http://dx.doi.org/10.1145/3465056.

Full text
Abstract:
Multi-view subspace clustering (MVSC) finds a shared structure in latent low-dimensional subspaces of multi-view data to enhance clustering performance. Nonetheless, we observe that most existing MVSC methods neglect the diversity in multi-view data by considering only the common knowledge to find a shared structure either directly or by merging different similarity matrices learned for each view. In the presence of noise, this predefined shared structure becomes a biased representation of the different views. Thus, in this article, we propose a MVSC method based on coupled low-rank representa
APA, Harvard, Vancouver, ISO, and other styles
23

Saha, Aadirupa, Rakesh Shivanna, and Chiranjib Bhattacharyya. "How Many Pairwise Preferences Do We Need to Rank a Graph Consistently?" Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4830–37. http://dx.doi.org/10.1609/aaai.v33i01.33014830.

Full text
Abstract:
We consider the problem of optimal recovery of true ranking of n items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of Ω(n2) for the purpose. We analyze the problem with an additional structure of relational graph G([n],E) over the n items added with an assumption of locality: Neighboring items are similar in their rankings. Noting the preferential nature of the data, we choose to embed not the graph, but, its strong product to capture the pairwise node relationships. Furthermore, unlike existing l
APA, Harvard, Vancouver, ISO, and other styles
24

Das, Joyentanuj, Sachindranath Jayaraman, and Sumit Mohanty. "Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse." Special Matrices 8, no. 1 (2020): 160–71. http://dx.doi.org/10.1515/spma-2020-0109.

Full text
Abstract:
AbstractA real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both nonnegative and positive semidefinite is a completely positive matrix. Our aim in this manuscript is to compute the determinant and inverse (when it exists) of the distance matrix of a class of completely positive graphs. We compute a matrix 𝒭 such that the inverse of the distance matrix of a class of completely positive graphs is expressed a li
APA, Harvard, Vancouver, ISO, and other styles
25

Song, Shangzhen, Yixin Yang, Huixin Zhou, and Jonathan Cheung-Wai Chan. "Hyperspectral Anomaly Detection via Graph Dictionary-Based Low Rank Decomposition with Texture Feature Extraction." Remote Sensing 12, no. 23 (2020): 3966. http://dx.doi.org/10.3390/rs12233966.

Full text
Abstract:
The accuracy of anomaly detection in hyperspectral images (HSIs) faces great challenges due to the high dimensionality, redundancy of data, and correlation of spectral bands. In this paper, to further improve the detection accuracy, we propose a novel anomaly detection method based on texture feature extraction and a graph dictionary-based low rank decomposition (LRD). First, instead of using traditional clustering methods for the dictionary, the proposed method employs the graph theory and designs a graph Laplacian matrix-based dictionary for LRD. The robust information of the background matr
APA, Harvard, Vancouver, ISO, and other styles
26

Bunke, Ulrich, Martin Olbrich, and Andreas Juhl. "The wave kernel for the Laplacian on the classical locally symmetric spaces of rank one, theta functions, trace formulas and the Selberg zeta function." Annals of Global Analysis and Geometry 12, no. 1 (1994): 357–405. http://dx.doi.org/10.1007/bf02108307.

Full text
APA, Harvard, Vancouver, ISO, and other styles
27

Wang, Heyong, and Ming Hong. "Distance Variance Score: An Efficient Feature Selection Method in Text Classification." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/695720.

Full text
Abstract:
With the rapid development of web applications such as social network, a large amount of electric text data is accumulated and available on the Internet, which causes increasing interests in text mining. Text classification is one of the most important subfields of text mining. In fact, text documents are often represented as a high-dimensional sparse document term matrix (DTM) before classification. Feature selection is essential and vital for text classification due to high dimensionality and sparsity of DTM. An efficient feature selection method is capable of both reducing dimensions of DTM
APA, Harvard, Vancouver, ISO, and other styles
28

Obbu Ramesh,. "A Study on Signless Laplacian Energy of an Intuitionistic Fuzzy Graphs with Applications to Group Decision Making." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 185–98. https://doi.org/10.52783/cana.v32.3847.

Full text
Abstract:
Abstract:Introduction: Group decision-making shows a critical job while designating with dynamic issues of quick development of society. Decision make is the manner about discovering the beneficial option among the possible alternatives. In first-rate multiple-criteria choice construction methods, the rankings or the weights of the standards are recognized precisely. However, if selection makers are now not capable in conformity with involve doubt within the defining on linguistic variables based concerning fuzzy sets (FSs) and the intuitionistic fuzzy set (IFS) theory is useful to this job we
APA, Harvard, Vancouver, ISO, and other styles
29

Xiao, Yun, Pengzhen Ren, Zhihui Li, Xiaojiang Chen, Xin Wang, and Dingyi Fang. "RS3CIS: Robust Single-Step Spectral Clustering with Intrinsic Subspace." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5482–89. http://dx.doi.org/10.1609/aaai.v33i01.33015482.

Full text
Abstract:
Spectral clustering has been widely adopted because it can mine structures between data clusters. The clustering performance of spectral clustering depends largely on the quality of the constructed affinity graph, especially when the data has noise. Subspace learning can transform the original input features to a low-dimensional subspace and help to produce a robust method. Therefore, how to learn an intrinsic subspace and construct a pure affinity graph on a dataset with noise is a challenge in spectral clustering. In order to deal with this challenge, a new Robust Single-Step Spectral Cluste
APA, Harvard, Vancouver, ISO, and other styles
30

Kholmatov, Shokhrukh Yu, Ahmad Khalkhuzhaev, and Mardon Pardabaev. "Expansion of eigenvalues of the perturbed discrete bilaplacian." Monatshefte für Mathematik 197, no. 4 (2022): 607–33. http://dx.doi.org/10.1007/s00605-022-01678-1.

Full text
Abstract:
AbstractWe consider the family $$\begin{aligned} {\widehat{{ H}}}_\mu := {\widehat{\varDelta }} {\widehat{\varDelta }} - \mu {\widehat{{ V}}},\qquad \mu \in {\mathbb {R}}, \end{aligned}$$ H ^ μ : = Δ ^ Δ ^ - μ V ^ , μ ∈ R , of discrete Schrödinger-type operators in d-dimensional lattice $${\mathbb {Z}}^d$$ Z d , where $${\widehat{\varDelta }}$$ Δ ^ is the discrete Laplacian and $${\widehat{{ V}}}$$ V ^ is of rank-one. We prove that there exist coupling constant thresholds $$\mu _o,\mu ^o\ge 0$$ μ o , μ o ≥ 0 such that for any $$\mu \in [-\mu ^o,\mu _o]$$ μ ∈ [ - μ o , μ o ] the discrete spectr
APA, Harvard, Vancouver, ISO, and other styles
31

Ludwig, J., and D. Müller. "Sub-Laplacians of Holomorphic Lp-type on Rank One AN-Groups and Related Solvable Groups." Journal of Functional Analysis 170, no. 2 (2000): 366–427. http://dx.doi.org/10.1006/jfan.1999.3517.

Full text
APA, Harvard, Vancouver, ISO, and other styles
32

Matsumoto, Hiroyuki. "Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one." Bulletin des Sciences Mathématiques 125, no. 6-7 (2001): 553–81. http://dx.doi.org/10.1016/s0007-4497(01)01099-5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
33

Kluitenberg, Martijn. "On the Cheeger Inequality in Carnot-Carathéodory Spaces." Journal of Geometric Analysis 35, no. 3 (2025). https://doi.org/10.1007/s12220-025-01912-w.

Full text
Abstract:
Abstract We generalize the Cheeger inequality, a lower bound on the first nontrivial eigenvalue of a Laplacian, to the case of geometric sub-Laplacians on rank-varying Carnot-Carathéodory spaces and we describe a concrete method to lower bound the Cheeger constant. The proof is geometric, and works for Dirichlet, Neumann and mixed boundary conditions. One of the main technical tools in the proof is a generalization of Courant’s nodal domain theorem, which is proven from scratch for Neumann and mixed boundary conditions. Carnot groups and the Baouendi-Grushin cylinder are treated as examples.
APA, Harvard, Vancouver, ISO, and other styles
34

Acosta, Joel, Alan Garbarz, Andrés Goya, and Mauricio Leston. "One-loop partition function, gauge accessibility and spectra in AdS3 gravity." Journal of High Energy Physics 2021, no. 12 (2021). http://dx.doi.org/10.1007/jhep12(2021)097.

Full text
Abstract:
Abstract We continue the study of the one-loop partition function of AdS3 gravity with focus on the square-integrability condition on the fluctuating fields. In a previous work we found that the Brown-Henneaux boundary conditions follow directly from the L2 condition. Here we rederive the partition function as a ratio of Laplacian determinants by performing a suitable decomposition of the metric fluctuations. We pay special attention to the asymptotics of the fields appearing in the partition function. We also show that in the usual computation using ghost fields for the de Donder gauge, such
APA, Harvard, Vancouver, ISO, and other styles
35

Azimi, Ali, Rakesh Jana, Mukesh Nagar, and Sivaramakrishnan Sivasubramanian. "On the Min4PC Matrix of a Tree." American Journal of Combinatorics 3 (February 14, 2024). https://doi.org/10.63151/amjc.v3i.16.

Full text
Abstract:
The Four point condition (abbreviated as 4PC) is a condition used to test if a given distance matrix arises from shortest path distances on trees. From a tree \(T\), Bapat and Sivasubramanian defined a matrix \(\operatorname{Min4PC}_T\) based on this condition. They also gave a basis \(B\) for the row space of \(\operatorname{Min4PC}_T\) and determined its Smith Normal Form. In this paper, we consider the matrix \(\operatorname{Min4PC}_T[B,B]\) restricted to a basis \(B\) and give an explicit inverse for it. It is known that the distance matrix \(D_T\) of a tree \(T\), is invertible and that i
APA, Harvard, Vancouver, ISO, and other styles
36

Benzi, Michele, and Igor Simunec. "Rational Krylov methods for fractional diffusion problems on graphs." BIT Numerical Mathematics, July 1, 2021. http://dx.doi.org/10.1007/s10543-021-00881-0.

Full text
Abstract:
AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of
APA, Harvard, Vancouver, ISO, and other styles
37

Silini, Lauro. "Quantitative C 1-stability of spheres in rank one symmetric spaces of non-compact type." Advances in Calculus of Variations, November 17, 2024. http://dx.doi.org/10.1515/acv-2023-0062.

Full text
Abstract:
Abstract We prove that in any rank one symmetric space of non-compact type M ∈ { ℝ ⁢ H n , ℂ ⁢ H m , ℍ ⁢ H m , 𝕆 ⁢ H 2 } {M\in\{\mathbb{R}H^{n},\mathbb{C}H^{m},\mathbb{H}H^{m},\mathbb{O}H^{2}\}} , geodesic spheres are uniformly quantitatively stable with respect to small C 1 {C^{1}} -volume preserving perturbations. We quantify the gain of perimeter in terms of the W 1 , 2 {W^{1,2}} -norm of the perturbation, taking advantage of the explicit spectral gap of the Laplacian on geodesic spheres in M. As a consequence, we give a quantitative proof that for small volumes, geodesic spheres are isoper
APA, Harvard, Vancouver, ISO, and other styles
38

Conejero, J. Alberto, Antonio Falcó, and María Mora-Jiménez. "Structure and Approximation Properties of Laplacian-Like Matrices." Results in Mathematics 78, no. 5 (2023). http://dx.doi.org/10.1007/s00025-023-01960-0.

Full text
Abstract:
AbstractMany of today’s problems require techniques that involve the solution of arbitrarily large systems $$A\textbf{x}=\textbf{b}$$ A x = b . A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor decomposition. The numerical experiments support the fact that this algorithm converges especially fast when the matrix of the linear system is Laplacian-Like. These matrices that follow the tensor structure of the Laplacian operator are formed by sums of Kronecker product of matrices following a particular pattern. Moreover, this set of matrice
APA, Harvard, Vancouver, ISO, and other styles
39

Ahmed, Hamza, and Fabian Ruehle. "Level crossings, attractor points and complex multiplication." Journal of High Energy Physics 2023, no. 6 (2023). http://dx.doi.org/10.1007/jhep06(2023)164.

Full text
Abstract:
Abstract We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau n-folds in ℙn+1. It was previously observed that some eigenmodes get lighter while others get heavier as a function of these moduli, which leads to eigenvalue crossing. We identify the cause for this behavior for the torus. We then show that at points in a sublocus of complex structure moduli space where Laplacian eigenmodes cross, the torus has complex multiplication. We speculate that the generalization to arbitrary Calabi-Yau manifolds could be that level cro
APA, Harvard, Vancouver, ISO, and other styles
40

Graczyk, P., T. Luks, and P. Sawyer. "Potential kernels for radial Dunkl Laplacians." Canadian Journal of Mathematics, April 20, 2021, 1–29. http://dx.doi.org/10.4153/s0008414x21000195.

Full text
Abstract:
Abstract We derive two-sided bounds for the Newton and Poisson kernels of the W-invariant Dunkl Laplacian in the geometric complex case when the multiplicity $k(\alpha )=1$ i.e., for flat complex symmetric spaces. For the invariant Dunkl–Poisson kernel $P^{W}(x,y)$ , the estimates are $$ \begin{align*} P^{W}(x,y)\asymp \frac{P^{\mathbf{R}^{d}}(x,y)}{\prod_{\alpha> 0 \ }|x-\sigma_{\alpha} y|^{2k(\alpha)}}, \end{align*} $$ where the $\alpha $ ’s are the positive roots of a root system acting in $\mathbf {R}^{d}$ , the $\sigma _{\alpha }$ ’s are the corresponding symmetries and $P^{\mathbf {R}
APA, Harvard, Vancouver, ISO, and other styles
41

Papageorgiou, Effie. "Large-Time Behavior of Two Families of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds." Potential Analysis, December 20, 2023. http://dx.doi.org/10.1007/s11118-023-10109-1.

Full text
Abstract:
AbstractThis note is concerned with two families of operators related to the fractional Laplacian, the first arising from the Caffarelli-Silvestre extension problem and the second from the fractional heat equation. They both include the Poisson semigroup. We show that on a complete, connected, and non-compact Riemannian manifold of non-negative Ricci curvature, in both cases, the solution with $$L^1$$ L 1 initial data behaves asymptotically as the mass times the fundamental solution. Similar long-time convergence results remain valid on more general manifolds satisfying the Li-Yau two-sided es
APA, Harvard, Vancouver, ISO, and other styles
42

Niedermaier, Ralph Max, and Rudrajit Banerjee. "Wick rotation in the lapse, admissible complex metrics, and foliation changing diffeomorphisms." Classical and Quantum Gravity, April 7, 2025. https://doi.org/10.1088/1361-6382/adc9ef.

Full text
Abstract:
Abstract A Wick rotation in the lapse (not in time) is introduced that interpolates between Riemannian and Lorentzian metrics on real
 manifolds admitting a codimension-one foliation. The definition refers to a fiducial foliation but covariance under foliation
 changing diffeomorphisms can be rendered explicit in a reformulation as a rank one perturbation. Applied to scalar field
 theories a Lorentzian signature action develops a positive imaginary part thereby identifying the underlying complex metric
 as `admissible'. This admissibility is ensured in non-fiduc
APA, Harvard, Vancouver, ISO, and other styles
43

Moutuou, Elkaïoum M., Obaï B. K. Ali, and Habib Benali. "Topology and spectral interconnectivities of higher-order multilayer networks." Frontiers in Complex Systems 1 (November 20, 2023). http://dx.doi.org/10.3389/fcpxs.2023.1281714.

Full text
Abstract:
Multilayer networks have permeated all areas of science as an abstraction for interdependent heterogeneous complex systems. However, describing such systems through a purely graph-theoretic formalism presupposes that the interactions that define the underlying infrastructures are only pairwise-based, a strong assumption likely leading to oversimplification. Most interdependent systems intrinsically involve higher-order intra- and inter-layer interactions. For instance, ecological systems involve interactions among groups within and in-between species, collaborations and citations link teams of
APA, Harvard, Vancouver, ISO, and other styles
44

Rusho, Rushdi Zahid, Abdul Haseeb Ahmed, Stanley Kruger, et al. "Prospectively accelerated dynamic speech magnetic resonance imaging at 3 T using a self‐navigated spiral‐based manifold regularized scheme." NMR in Biomedicine, March 5, 2024. http://dx.doi.org/10.1002/nbm.5135.

Full text
Abstract:
AbstractThis work develops and evaluates a self‐navigated variable density spiral (VDS)‐based manifold regularization scheme to prospectively improve dynamic speech magnetic resonance imaging (MRI) at 3 T. Short readout duration spirals (1.3‐ms long) were used to minimize sensitivity to off‐resonance. A custom 16‐channel speech coil was used for improved parallel imaging of vocal tract structures. The manifold model leveraged similarities between frames sharing similar vocal tract postures without explicit motion binning. The self‐navigating capability of VDS was leveraged to learn the Laplaci
APA, Harvard, Vancouver, ISO, and other styles
45

Ma, Jiani, Hui Liu, Yumeng Mao, and Lin Zhang. "LRTCLS: low-rank tensor completion with Laplacian smoothing regularization for unveiling the post-transcriptional machinery of N6-methylation (m6A)-mediated diseases." Briefings in Bioinformatics, August 21, 2022. http://dx.doi.org/10.1093/bib/bbac325.

Full text
Abstract:
Abstract Recently, N6-methylation (m6A) has recently become a hot topic due to its key role in disease pathogenesis. Identifying disease-related m6A sites aids in the understanding of the molecular mechanisms and biosynthetic pathways underlying m6A-mediated diseases. Existing methods treat it primarily as a binary classification issue, focusing solely on whether an m6A–disease association exists or not. Although they achieved good results, they all shared one common flaw: they ignored the post-transcriptional regulation events during disease pathogenesis, which makes biological interpretation
APA, Harvard, Vancouver, ISO, and other styles
46

Loc, Tran. "Application of three graph Laplacian based semisupervised learning methods to protein function prediction problem." August 25, 2018. https://doi.org/10.5121/ijbb.2013.3202.

Full text
Abstract:
International Journal on Bioinformatics & Biosciences (IJBB) Vol.3, No.2, June 2013 DOI: 10.5121/ijbb.2013.3202 11 Application of three graph Laplacian based semisupervised learning methods to protein function prediction problem Loc Tran University of Minnesota tran0398@umn.edu Abstract: Protein function prediction is the important problem in modern biology. In this paper, the un-normalized, symmetric normalized, and random walk graph Laplacian based semi-supervised learning methods will be applied to the integrated network combined from multiple networks to predict the functions of all ye
APA, Harvard, Vancouver, ISO, and other styles
47

Liu, Jian, Shuguang Ge, Yuhu Cheng, and Xuesong Wang. "Multi-View Spectral Clustering Based on Multi-Smooth Representation Fusion for Cancer Subtype Prediction." Frontiers in Genetics 12 (September 6, 2021). http://dx.doi.org/10.3389/fgene.2021.718915.

Full text
Abstract:
It is a vital task to design an integrated machine learning model to discover cancer subtypes and understand the heterogeneity of cancer based on multiple omics data. In recent years, some multi-view clustering algorithms have been proposed and applied to the prediction of cancer subtypes. Among them, the multi-view clustering methods based on graph learning are widely concerned. These multi-view approaches usually have one or more of the following problems. Many multi-view algorithms use the original omics data matrix to construct the similarity matrix and ignore the learning of the similarit
APA, Harvard, Vancouver, ISO, and other styles
48

Ebisu, Hiromi, and Bo Han. "Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs." SciPost Physics 14, no. 5 (2023). http://dx.doi.org/10.21468/scipostphys.14.5.106.

Full text
Abstract:
We study unusual gapped topological phases where they admit \mathbb{Z}_NℤN fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by \bigl
APA, Harvard, Vancouver, ISO, and other styles
49

Emmerson, Parker Yaohushuason. "Geometry of Phenomenological Velocity: Energy Numbers, Curvature and Fukaya-Type Categories." May 27, 2025. https://doi.org/10.5281/zenodo.15523017.

Full text
Abstract:
Thank you, Yaohushua for letting me continue to distribute these mathematical gesturing forms so interesting. The paper constructs an algebraic–geometric framework around the “phenomenological ve-locity” expression v = pN/D that arose in previous informal work. We introduce (i) theenergy-number field E, (ii) a non-commutative velocity-string algebra V, (iii) a curvature scalarKPV defined from a “PV–Hessian”, and (iv) a curved A∞ category Fukv (M ) obtained from anordinary Fukaya category by multiplication with v. Basic structural results are proved; se
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography