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Nonseparating Independent Sets and Maximum Genus of Graphs

Acta Mathematicae Applicatae Sinica 2022年第3期38卷 719-728页

作者： Chao YANG Han REN Er-ling WEI Center of Intelligent Computing and Applied Statistics School of MathematicsPhysics and StatisticsShanghai University of Engineering ScienceShanghai 201620China School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of PMMP Shanghai 200241China School of Mathematics Renmin University of ChinaBeijing 100872China

A subset I of vertices of an undirected connected graph G is a nonseparating independent set(NSIS)if no two vertices of I are adjacent and G􀀀I is *** Z(G)denote the cardinality of a maximum NSIS of G.A nonseparating independent set containing Z(G)vertices is called the maximum nonseparating independent *** this paper,we firstly give an upper bound for Z(G)of regular graphs and determine Z(G)for some types of circular ***,we show a relationship between Z(G)and the maximum genus M(G)of a general ***,an important formula is provided to compute Z(G),i.e.,Z(G)=Σx∈I dI(x)+2(M(G-I)-γM(G))+(ξ(G-I)-ξ(G));where I is the maximum nonseparating independent set and ξ(G)is the Betti deficiency(Xuong,1979)of G.

关键词： nonseparating independent sets maximum genus graph embedding decycling set

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Operational Effectiveness Evaluation of UAV Cluster Based on Bayesian Networks

Operational Effectiveness Evaluation of UAV Cluster Based on...

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2022 International Conference on applied mathematics and Physics, ICAMP 2022

作者： Wang, J.J. Zhang, Y.Y. Ma, J. Hou, J. Wang, F.M. Li, N. Beijing Jinghang Research Institute of Computing and Communication Beijing China Applied Mathematics Research Center of China Aerospace Science and Industry Group Beijing China

This paper focuses on the requirements of operational efficiency evaluation for UAV cluster, and establishes an evaluation index system for UAV cluster operations, and establishes evaluation index system from the aspects of cooperative attack capability, autonomous reconnaissance capability, instant messaging capability, rapid planning capability and autonomous formation capability. The evaluation network model is built by using Bayesian network, and the corresponding prior and conditional probabilities are calculated. The effectiveness values of each capability are calculated and verified by experiments. This paper provides an applicable quantitative evaluation method for UAV cluster operational effectiveness evaluation. © Published under licence by IOP Publishing Ltd.

关键词： Unmanned aerial vehicles (UAV)

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Shape of my heart: Cardiac models through learned signed distance functions 7

Shape of my heart: Cardiac models through learned signed dis...

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7th International Conference on Medical Imaging with Deep Learning, MIDL 2024

作者： Verhülsdonk, Jan Grandits, Thomas Costabal, Francisco Sahli Pinetz, Thomas Krause, Rolf Auricchio, Angelo Haase, Gundolf Pezzuto, Simone Effland, Alexander Institute for Applied Mathematics University of Bonn Germany Department of Mathematics and Scientific Computing University of Graz Austria Institute for Biological and Medical Engineering Pontificia Universidad Católica de Chile Chile Center for Computational Medicine in Cardiology Università della Svizzera Italiana Switzerland FernUni Schweiz Brig Switzerland Instituto Cardiocentro Ticino EOC Switzerland Department of Mathematics University of Trento Italy

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM). © 2024 CC-BY 4.0, J. Verhülsdonk et al.

关键词： Image segmentation

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Evaluation method of equipment system contribution rate based on machine learning

Evaluation method of equipment system contribution rate base...

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2022 International Conference on applied Statistics, Computational mathematics, and Software Engineering, ASCMSE 2022

作者： Wang, Jiajia Hu, Huabo Hou, Jian Ma, Jing Li, Na Beijing Jinghang Research Institute of Computing and Communication Beijing China Applied Mathematics Research Center of China Aerospace Science and Industry Group Beijing China

ISBN: (纸本)9781510657625

This paper mainly provides a method to evaluate the contribution rate of equipment system based on machine learning. Firstly, the index system of contribution rate evaluation of equipment system is established, the requirements of evaluation are clarified, and the normalized data is used as input. The evaluation model based on Principal Component Analysis (PCA) is built, and the contribution rate of the system is sorted by weight calculation. This paper uses experiments to verify the validity of our method. © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.

关键词： Principal component analysis

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SURREAL-GAN:SEMI-SUPERVISED REPRESENTATION LEARNING VIA GAN FOR UNCOVERING HETEROGENEOUS DISEASE-RELATED IMAGING PATTERNS 10

SURREAL-GAN:SEMI-SUPERVISED REPRESENTATION LEARNING VIA GAN ...

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10th International Conference on Learning Representations, ICLR 2022

作者： Yang, Zhijian Wen, Junhao Davatzikos, Christos Center for Biomedical Image Computing and Analytics University of Pennsylvania United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States

A plethora of machine learning methods have been applied to imaging data, enabling the construction of clinically relevant imaging signatures of neurological and neuropsychiatric diseases. Oftentimes, such methods do not explicitly model the heterogeneity of disease effects, or approach it via nonlinear models that are not interpretable. Moreover, unsupervised methods may parse heterogeneity that is driven by nuisance confounding factors that affect global brain structure or function, rather than heterogeneity relevant to a pathology of interest. On the other hand, semi-supervised clustering methods seek to derive a pathology-related dichotomous subtypes, ignoring the truth that disease heterogeneity spatially and temporally extends along a continuum. To address the aforementioned limitations, herein, we propose a novel method, termed Surreal-GAN (Semi-SUpeRvised ReprEsentAtion Learning via GAN). Using cross-sectional imaging data, Surreal-GAN dissects underlying disease-related heterogeneity under the principle of semi-supervised clustering [cluster mappings from the normal control (CN) to patient (PT) domain], proposes a continuously dimensional representation, and infers the disease severity of patients at individual level along each dimension. The model first learns a transformation function from the CN domain to the PT domain with latent variables controlling transformation directions. An inverse mapping function together with regularization on function continuity, pattern orthogonality and monotonicity was also imposed to make sure that the transformation function captures necessarily meaningful imaging patterns with clinical significance. We first validated the model through semi-synthetic experiments, and then demonstrated its potential in capturing biologically plausible imaging patterns in Alzheimer's disease (AD). © 2022 ICLR 2022 - 10th International Conference on Learning Representationss. All rights reserved.

关键词： Pathology

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Algebraic algorithms for betweenness and percolation centrality

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Journal of Graph Algorithms and Applications 2021年第1期25卷 241-261页

作者： Tumurbaatar, Altansuren Sottile, Matthew J. Department of Mathematics and Statistics Washington State University United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States

In this paper, we explored different ways to write the algebraic version of betweenness centrality algorithm. Particularly, we focused on Brandes’ algorithm [8]. We aimed for algebraic betweenness centrality that can be parallelized easily. We proposed 3-tuple geodetic semiring as an extension to the usual geodetic semiring with 2-tuples [6]. Using the 3-tuple geodetic semiring, Dijkstra’s and Brandes’ algorithm, we wrote more concise and general algebraic betweenness centrality (ABC) algorithm which is valid for weighted and directed graphs. We also proposed an alternative version of ABC using the usual geodetic semiring with 2-tuple where we used a simple way to construct shortest path tree after computing shortest path distances in the usual geodetic semiring. This allows us to avoid computational complexity of ABC implementation using 3-tuple geodetic semiring. We used numba [18] to optimize and parallelize ABC. We evaluated the performance of ABC using 2-tuple geodetic semiring as compared to NetworkX [16], a common python package for graph algorithms. We did scalability experiments on parallel ABC and showed its total speedup. We also showed that with small modification, ABC can be adapted to algebraicly compute other centrality measures such as percolation centrality. © 2021, Brown University. All rights reserved.

关键词： Directed graphs

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Efficient Quantum Counting and Quantum Content-Addressable Memory for DNA Similarity 4

Efficient Quantum Counting and Quantum Content-Addressable M...

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4th IEEE International Conference on Quantum computing and Engineering, QCE 2023

作者： Balewski, Jan Camps, Daan Klymko, Katherine Tritt, Andrew National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States

ISBN: (纸本)9798350343236

We present QCAM, a quantum analogue of Content-Addressable Memory (CAM), useful for finding matches in two sequences of bit-strings. Our QCAM implementation takes advantage of Grover's search algorithm and proposes a highly-optimized quantum circuit implementation of the QCAM oracle. Our circuit construction uses the parallel uniformly controlled rotation gates, which were used in previous work to generate QBArt encodings. These circuits have a high degree of quantum parallelism which reduces their critical depth. The optimal number of repetitions of the Grover iterator used in QCAM depends on the number of true matches and hence is input dependent. We additionally propose a hardware-efficient implementation of the quantum counting algorithm (HEQC) that can infer the optimal number of Grover iterations from the measurement of a single observable. We demonstrate the QCAM application for computing the Jaccard similarity between two sets of k-mers obtained from two DNA sequences. © 2023 IEEE.

关键词： DNA

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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

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Advances in applied mathematics and Mechanics 2023年第6期15卷 1631-1654页

作者： Jiaqi Zhang Yin Yang Zhaojie Zhou School of Mathematics and Computational Science Xiangtan UniversityHunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan 411105HunanChina School of Mathematics and Computational Science Xiangtan UniversityNational Center for Applied Mathematics in HunanHunan International Scientific and Technological Innovation Cooperation Base of Computational ScienceXiangtan 411105HunanChina School of Mathematics and Statistics Shandong Normal UniversityJinan 250014ShandongChina

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is *** deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is *** first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is *** experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

关键词： Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials

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A Scalable Interior-Point Gauss-Newton Method for PDE-Constrained Optimization with Bound Constraints

arXiv

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arXiv 2024年

作者： Hartland, Tucker Petra, Cosmin G. Petra, Noémi Wang, Jingyi Center for Applied Scientific Computing Lawrence Livermore National Laboratory CA United States Department of Applied Mathematics University of California MercedCA United States

We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton optimization method. To cope with the poorly-conditioned IP-Gauss-Newton saddle-point linear systems that need to be solved, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE-constrained optimization problems. A block Gauss-Seidel preconditioner is proposed for the GMRES-based solution of the IP-Gauss-Newton linear systems. It is shown, for a large-class of PDE- and bound-constrained optimization problems, that the spectrum of the block Gauss-Seidel preconditioned IP-Gauss-Newton matrix is asymptotically independent of discretization and is not impacted by the ill-conditioning that notoriously plagues interior-point methods. We exploit symmetry of the IP-Gauss-Newton linear systems and propose a regularization and log-barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)based solution of the related IP-Gauss-Newton-Schur complement linear systems. The eigenvalues of the block Gauss-Seidel preconditioned IP-Gauss-Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log-barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on an example problem with bound and nonlinear elliptic PDE constraints. The numerical solution of the optimization problem is shown to require a discretization independent number of IP-Gauss-Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill-conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of preconditioner and linear system matrix applies, achieved with algebraic multigrid based solvers, and

关键词： Constrained optimization

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Pose Estimation of Spacecraft Using Dual Transformers and Efficient Bayesian Hyperparameter Optimization

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International Journal of Advanced Computer Science and Applications 2025年第4期16卷 629-644页

作者： Raja, N. Kannaiya Ramesh, Janjhyam Venkata Naga El-Ebiary, Yousef A. Baker Muniyandy, Elangovan Reddy, N. Konda Kumar, Vanipenta Ravi Devarasetty, Prasad School of Computing Science and Engineering VIT Bhopal University Madhya Pradesh Bhopal466114 India Department of CSE Graphic Era Hill University Dehradun248002 India Department of CSE Graphic Era Deemed To Be University Uttarakhand Dehradun248002 India Faculty of Informatics and Computing UniSZA University Malaysia Department of Biosciences Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai602 105 India Applied Science Research Center Applied Science Private University Amman Jordan Department of Engineering Mathematics K L University Greenfields Guntur Dist Andhra Pradesh Vaddeswaram522302 India Department of Mathematics Annamacharya University New Boyanapalli Rajampet India Department of Computer Science and Engineering DVR & Dr HS MIC College of Technology Andhra Pradesh Kanchikacherla India

Spacecraft pose estimation is an essential contribution to facilitating central space mission activities like autonomous navigation, rendezvous, docking, and on-orbit servicing. Nonetheless, methods like Convolutional Neural Networks (CNNs), Simultaneous Localization and Mapping (SLAM), and Particle Filtering suffer significant drawbacks when implemented in space. Such techniques tend to have high computational complexity, low domain generalization capacity for varied or unknown conditions (domain generalization problem), and accuracy loss with noise from the space environment causes such as fluctuating lighting, sensor limitations, and background interference. In order to overcome these challenges, this study suggests a new solution through the combination of a Dual-Channel Transformer Network with Bayesian Optimization methods. The innovation is at the center with the utilization of EfficientNet, augmented with squeeze-and-excitation attention modules, to extract feature-rich representations without sacrificing computational efficiency. The dual-channel architecture dissects satellite pose estimation into two dedicated streams—translational data prediction and orientation estimation via quaternion-based activation functions for rotational precision. Activation maps are transformed into transformer-compatible sequences via 1×1 convolutions, allowing successful learning in the transformer's encoder-decoder system. To maximize model performance, Bayesian Optimization with Gaussian Process Regression and the Upper Confidence Bound (UCB) acquisition function makes the optimal hyperparameter selection with fewer queries, conserving time and resources. This entire framework, used here in Python and verified with the SLAB Satellite Pose Estimation Challenge dataset, had an outstanding Mean IOU of 0.9610, reflecting higher accuracy compared to standard models. In total, this research sets a new standard for spacecraft pose estimation, by marrying the versatility of deep le

关键词： Convolutional neural networks

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