Discriminative clustering on manifold for adaptive transductive classification.

Science.gov (United States)

Zhang, Zhao; Jia, Lei; Zhang, Min; Li, Bing; Zhang, Li; Li, Fanzhang

2017-10-01

In this paper, we mainly propose a novel adaptive transductive label propagation approach by joint discriminative clustering on manifolds for representing and classifying high-dimensional data. Our framework seamlessly combines the unsupervised manifold learning, discriminative clustering and adaptive classification into a unified model. Also, our method incorporates the adaptive graph weight construction with label propagation. Specifically, our method is capable of propagating label information using adaptive weights over low-dimensional manifold features, which is different from most existing studies that usually predict the labels and construct the weights in the original Euclidean space. For transductive classification by our formulation, we first perform the joint discriminative K-means clustering and manifold learning to capture the low-dimensional nonlinear manifolds. Then, we construct the adaptive weights over the learnt manifold features, where the adaptive weights are calculated through performing the joint minimization of the reconstruction errors over features and soft labels so that the graph weights can be joint-optimal for data representation and classification. Using the adaptive weights, we can easily estimate the unknown labels of samples. After that, our method returns the updated weights for further updating the manifold features. Extensive simulations on image classification and segmentation show that our proposed algorithm can deliver the state-of-the-art performance on several public datasets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Image reconstruction by domain-transform manifold learning

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Zhu, Bo; Liu, Jeremiah Z.; Cauley, Stephen F.; Rosen, Bruce R.; Rosen, Matthew S.

2018-03-01

Image reconstruction is essential for imaging applications across the physical and life sciences, including optical and radar systems, magnetic resonance imaging, X-ray computed tomography, positron emission tomography, ultrasound imaging and radio astronomy. During image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the exact inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain, the composition of which depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. Here we present a unified framework for image reconstruction—automated transform by manifold approximation (AUTOMAP)—which recasts image reconstruction as a data-driven supervised learning task that allows a mapping between the sensor and the image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for various magnetic resonance imaging acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate that manifold learning during training results in sparse representations of domain transforms along low-dimensional data manifolds, and observe superior immunity to noise and a reduction in reconstruction artefacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate that AUTOMAP and other learned reconstruction approaches will accelerate the development

Resonance-Based Time-Frequency Manifold for Feature Extraction of Ship-Radiated Noise

Science.gov (United States)

Yan, Jiaquan; Sun, Haixin; Chen, Hailan; Junejo, Naveed Ur Rehman; Cheng, En

2018-01-01

In this paper, a novel time-frequency signature using resonance-based sparse signal decomposition (RSSD), phase space reconstruction (PSR), time-frequency distribution (TFD) and manifold learning is proposed for feature extraction of ship-radiated noise, which is called resonance-based time-frequency manifold (RTFM). This is suitable for analyzing signals with oscillatory, non-stationary and non-linear characteristics in a situation of serious noise pollution. Unlike the traditional methods which are sensitive to noise and just consider one side of oscillatory, non-stationary and non-linear characteristics, the proposed RTFM can provide the intact feature signature of all these characteristics in the form of a time-frequency signature by the following steps: first, RSSD is employed on the raw signal to extract the high-oscillatory component and abandon the low-oscillatory component. Second, PSR is performed on the high-oscillatory component to map the one-dimensional signal to the high-dimensional phase space. Third, TFD is employed to reveal non-stationary information in the phase space. Finally, manifold learning is applied to the TFDs to fetch the intrinsic non-linear manifold. A proportional addition of the top two RTFMs is adopted to produce the improved RTFM signature. All of the case studies are validated on real audio recordings of ship-radiated noise. Case studies of ship-radiated noise on different datasets and various degrees of noise pollution manifest the effectiveness and robustness of the proposed method. PMID:29565288

Ensemble manifold regularization.

Science.gov (United States)

Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng

2012-06-01

We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.

Manifold learning in machine vision and robotics

Science.gov (United States)

Bernstein, Alexander

2017-02-01

Smart algorithms are used in Machine vision and Robotics to organize or extract high-level information from the available data. Nowadays, Machine learning is an essential and ubiquitous tool to automate extraction patterns or regularities from data (images in Machine vision; camera, laser, and sonar sensors data in Robotics) in order to solve various subject-oriented tasks such as understanding and classification of images content, navigation of mobile autonomous robot in uncertain environments, robot manipulation in medical robotics and computer-assisted surgery, and other. Usually such data have high dimensionality, however, due to various dependencies between their components and constraints caused by physical reasons, all "feasible and usable data" occupy only a very small part in high dimensional "observation space" with smaller intrinsic dimensionality. Generally accepted model of such data is manifold model in accordance with which the data lie on or near an unknown manifold (surface) of lower dimensionality embedded in an ambient high dimensional observation space; real-world high-dimensional data obtained from "natural" sources meet, as a rule, this model. The use of Manifold learning technique in Machine vision and Robotics, which discovers a low-dimensional structure of high dimensional data and results in effective algorithms for solving of a large number of various subject-oriented tasks, is the content of the conference plenary speech some topics of which are in the paper.

Support Vector Machines with Manifold Learning and Probabilistic Space Projection for Tourist Expenditure Analysis

Directory of Open Access Journals (Sweden)

Xin Xu

2009-03-01

Full Text Available The significant economic contributions of the tourism industry in recent years impose an unprecedented force for data mining and machine learning methods to analyze tourism data. The intrinsic problems of raw data in tourism are largely related to the complexity, noise and nonlinearity in the data that may introduce many challenges for the existing data mining techniques such as rough sets and neural networks. In this paper, a novel method using SVM- based classification with two nonlinear feature projection techniques is proposed for tourism data analysis. The first feature projection method is based on ISOMAP (Isometric Feature Mapping, which is a class of manifold learning approaches for dimension reduction. By making use of ISOMAP, part of the noisy data can be identified and the classification accuracy of SVMs can be improved by appropriately discarding the noisy training data. The second feature projection method is a probabilistic space mapping technique for scale transformation. Experimental results on expenditure data of business travelers show that the proposed method can improve prediction performance both in terms of testing accuracy and statistical coincidence. In addition, both of the feature projection methods are helpful to reduce the training time of SVMs.

Quantum filter reduction for measurement-feedback control via unsupervised manifold learning

DEFF Research Database (Denmark)

Nielsen, Anne E. B.; Hopkins, Asa S .; Mabuchi, Hideo

2009-01-01

We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space ...

A framework for optimal kernel-based manifold embedding of medical image data.

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Zimmer, Veronika A; Lekadir, Karim; Hoogendoorn, Corné; Frangi, Alejandro F; Piella, Gemma

2015-04-01

Kernel-based dimensionality reduction is a widely used technique in medical image analysis. To fully unravel the underlying nonlinear manifold the selection of an adequate kernel function and of its free parameters is critical. In practice, however, the kernel function is generally chosen as Gaussian or polynomial and such standard kernels might not always be optimal for a given image dataset or application. In this paper, we present a study on the effect of the kernel functions in nonlinear manifold embedding of medical image data. To this end, we first carry out a literature review on existing advanced kernels developed in the statistics, machine learning, and signal processing communities. In addition, we implement kernel-based formulations of well-known nonlinear dimensional reduction techniques such as Isomap and Locally Linear Embedding, thus obtaining a unified framework for manifold embedding using kernels. Subsequently, we present a method to automatically choose a kernel function and its associated parameters from a pool of kernel candidates, with the aim to generate the most optimal manifold embeddings. Furthermore, we show how the calculated selection measures can be extended to take into account the spatial relationships in images, or used to combine several kernels to further improve the embedding results. Experiments are then carried out on various synthetic and phantom datasets for numerical assessment of the methods. Furthermore, the workflow is applied to real data that include brain manifolds and multispectral images to demonstrate the importance of the kernel selection in the analysis of high-dimensional medical images. Copyright © 2014 Elsevier Ltd. All rights reserved.

Parts-based stereoscopic image assessment by learning binocular manifold color visual properties

Science.gov (United States)

Xu, Haiyong; Yu, Mei; Luo, Ting; Zhang, Yun; Jiang, Gangyi

2016-11-01

Existing stereoscopic image quality assessment (SIQA) methods are mostly based on the luminance information, in which color information is not sufficiently considered. Actually, color is part of the important factors that affect human visual perception, and nonnegative matrix factorization (NMF) and manifold learning are in line with human visual perception. We propose an SIQA method based on learning binocular manifold color visual properties. To be more specific, in the training phase, a feature detector is created based on NMF with manifold regularization by considering color information, which not only allows parts-based manifold representation of an image, but also manifests localized color visual properties. In the quality estimation phase, visually important regions are selected by considering different human visual attention, and feature vectors are extracted by using the feature detector. Then the feature similarity index is calculated and the parts-based manifold color feature energy (PMCFE) for each view is defined based on the color feature vectors. The final quality score is obtained by considering a binocular combination based on PMCFE. The experimental results on LIVE I and LIVE Π 3-D IQA databases demonstrate that the proposed method can achieve much higher consistency with subjective evaluations than the state-of-the-art SIQA methods.

Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction.

Science.gov (United States)

Nie, Feiping; Xu, Dong; Tsang, Ivor Wai-Hung; Zhang, Changshui

2010-07-01

We propose a unified manifold learning framework for semi-supervised and unsupervised dimension reduction by employing a simple but effective linear regression function to map the new data points. For semi-supervised dimension reduction, we aim to find the optimal prediction labels F for all the training samples X, the linear regression function h(X) and the regression residue F(0) = F - h(X) simultaneously. Our new objective function integrates two terms related to label fitness and manifold smoothness as well as a flexible penalty term defined on the residue F(0). Our Semi-Supervised learning framework, referred to as flexible manifold embedding (FME), can effectively utilize label information from labeled data as well as a manifold structure from both labeled and unlabeled data. By modeling the mismatch between h(X) and F, we show that FME relaxes the hard linear constraint F = h(X) in manifold regularization (MR), making it better cope with the data sampled from a nonlinear manifold. In addition, we propose a simplified version (referred to as FME/U) for unsupervised dimension reduction. We also show that our proposed framework provides a unified view to explain and understand many semi-supervised, supervised and unsupervised dimension reduction techniques. Comprehensive experiments on several benchmark databases demonstrate the significant improvement over existing dimension reduction algorithms.

Reconstructing spatial organizations of chromosomes through manifold learning.

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Zhu, Guangxiang; Deng, Wenxuan; Hu, Hailin; Ma, Rui; Zhang, Sai; Yang, Jinglin; Peng, Jian; Kaplan, Tommy; Zeng, Jianyang

2018-02-02

Decoding the spatial organizations of chromosomes has crucial implications for studying eukaryotic gene regulation. Recently, chromosomal conformation capture based technologies, such as Hi-C, have been widely used to uncover the interaction frequencies of genomic loci in a high-throughput and genome-wide manner and provide new insights into the folding of three-dimensional (3D) genome structure. In this paper, we develop a novel manifold learning based framework, called GEM (Genomic organization reconstructor based on conformational Energy and Manifold learning), to reconstruct the three-dimensional organizations of chromosomes by integrating Hi-C data with biophysical feasibility. Unlike previous methods, which explicitly assume specific relationships between Hi-C interaction frequencies and spatial distances, our model directly embeds the neighboring affinities from Hi-C space into 3D Euclidean space. Extensive validations demonstrated that GEM not only greatly outperformed other state-of-art modeling methods but also provided a physically and physiologically valid 3D representations of the organizations of chromosomes. Furthermore, we for the first time apply the modeled chromatin structures to recover long-range genomic interactions missing from original Hi-C data. © The Author(s) 2018. Published by Oxford University Press on behalf of Nucleic Acids Research.

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin

2013-01-01

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.

2013-09-26

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Dimensionality reduction of collective motion by principal manifolds

Science.gov (United States)

Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.

2015-01-01

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.

Echocardiogram enhancement using supervised manifold denoising.

Science.gov (United States)

Wu, Hui; Huynh, Toan T; Souvenir, Richard

2015-08-01

This paper presents data-driven methods for echocardiogram enhancement. Existing denoising algorithms typically rely on a single noise model, and do not generalize to the composite noise sources typically found in real-world echocardiograms. Our methods leverage the low-dimensional intrinsic structure of echocardiogram videos. We assume that echocardiogram images are noisy samples from an underlying manifold parametrized by cardiac motion and denoise images via back-projection onto a learned (non-linear) manifold. Our methods incorporate synchronized side information (e.g., electrocardiography), which is often collected alongside the visual data. We evaluate the proposed methods on a synthetic data set and real-world echocardiograms. Quantitative results show improved performance of our methods over recent image despeckling methods and video denoising methods, and a visual analysis of real-world data shows noticeable image enhancement, even in the challenging case of noise due to dropout artifacts. Copyright © 2015 Elsevier B.V. All rights reserved.

Quasi-Newton Exploration of Implicitly Constrained Manifolds

KAUST Repository

Tang, Chengcheng

2011-08-01

A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.

Manifold Regularized Correlation Object Tracking.

Science.gov (United States)

Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling

2018-05-01

In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.

Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Volovich, I.V.

1985-08-01

The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)

Dictionary Pair Learning on Grassmann Manifolds for Image Denoising.

Science.gov (United States)

Zeng, Xianhua; Bian, Wei; Liu, Wei; Shen, Jialie; Tao, Dacheng

2015-11-01

Image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real-world applications. The traditional patch-based and sparse coding-driven image denoising methods convert 2D image patches into 1D vectors for further processing. Thus, these methods inevitably break down the inherent 2D geometric structure of natural images. To overcome this limitation pertaining to the previous image denoising methods, we propose a 2D image denoising model, namely, the dictionary pair learning (DPL) model, and we design a corresponding algorithm called the DPL on the Grassmann-manifold (DPLG) algorithm. The DPLG algorithm first learns an initial dictionary pair (i.e., the left and right dictionaries) by employing a subspace partition technique on the Grassmann manifold, wherein the refined dictionary pair is obtained through a sub-dictionary pair merging. The DPLG obtains a sparse representation by encoding each image patch only with the selected sub-dictionary pair. The non-zero elements of the sparse representation are further smoothed by the graph Laplacian operator to remove the noise. Consequently, the DPLG algorithm not only preserves the inherent 2D geometric structure of natural images but also performs manifold smoothing in the 2D sparse coding space. We demonstrate that the DPLG algorithm also improves the structural SIMilarity values of the perceptual visual quality for denoised images using the experimental evaluations on the benchmark images and Berkeley segmentation data sets. Moreover, the DPLG also produces the competitive peak signal-to-noise ratio values from popular image denoising algorithms.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.

Science.gov (United States)

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L 2 -metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.

3-manifolds

CERN Document Server

Hempel, John

2004-01-01

A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. -Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The t

Dictionary Learning on the Manifold of Square Root Densities and Application to Reconstruction of Diffusion Propagator Fields*

Science.gov (United States)

Sun, Jiaqi; Xie, Yuchen; Ye, Wenxing; Ho, Jeffrey; Entezari, Alireza; Blackband, Stephen J.

2013-01-01

In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are vectors in some Euclidean space, our dictionary learning algorithm is designed to incorporate the intrinsic geometric structure of manifolds and performs better than traditional dictionary learning approaches when applied to data lying on the manifold of square root densities. Non-negativity as well as smoothness across the whole field of the reconstructed DPs is guaranteed in our approach. We demonstrate the advantage of our approach by comparing it with an existing dictionary based reconstruction method on synthetic and real multi-shell MRI data. PMID:24684004

TH-CD-207A-07: Prediction of High Dimensional State Subject to Respiratory Motion: A Manifold Learning Approach

International Nuclear Information System (INIS)

Liu, W; Sawant, A; Ruan, D

2016-01-01

Purpose: The development of high dimensional imaging systems (e.g. volumetric MRI, CBCT, photogrammetry systems) in image-guided radiotherapy provides important pathways to the ultimate goal of real-time volumetric/surface motion monitoring. This study aims to develop a prediction method for the high dimensional state subject to respiratory motion. Compared to conventional linear dimension reduction based approaches, our method utilizes manifold learning to construct a descriptive feature submanifold, where more efficient and accurate prediction can be performed. Methods: We developed a prediction framework for high-dimensional state subject to respiratory motion. The proposed method performs dimension reduction in a nonlinear setting to permit more descriptive features compared to its linear counterparts (e.g., classic PCA). Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where low-dimensional prediction is performed. A fixed-point iterative pre-image estimation method is applied subsequently to recover the predicted value in the original state space. We evaluated and compared the proposed method with PCA-based method on 200 level-set surfaces reconstructed from surface point clouds captured by the VisionRT system. The prediction accuracy was evaluated with respect to root-mean-squared-error (RMSE) for both 200ms and 600ms lookahead lengths. Results: The proposed method outperformed PCA-based approach with statistically higher prediction accuracy. In one-dimensional feature subspace, our method achieved mean prediction accuracy of 0.86mm and 0.89mm for 200ms and 600ms lookahead lengths respectively, compared to 0.95mm and 1.04mm from PCA-based method. The paired t-tests further demonstrated the statistical significance of the superiority of our method, with p-values of 6.33e-3 and 5.78e-5, respectively. Conclusion: The proposed approach benefits from the descriptiveness of a nonlinear manifold and the prediction

Morphological appearance manifolds for group-wise morphometric analysis.

Science.gov (United States)

Lian, Nai-Xiang; Davatzikos, Christos

2011-12-01

Computational anatomy quantifies anatomical shape based on diffeomorphic transformations of a template. However, different templates warping algorithms, regularization parameters, or templates, lead to different representations of the same exact anatomy, raising a uniqueness issue: variations of these parameters are confounding factors as they give rise to non-unique representations. Recently, it has been shown that learning the equivalence class derived from the multitude of representations of a given anatomy can lead to improved and more stable morphological descriptors. Herein, we follow that approach, by approximating this equivalence class of morphological descriptors by a (nonlinear) morphological appearance manifold fitting to the data via a locally linear model. Our approach parallels work in the computer vision field, in which variations lighting, pose and other parameters lead to image appearance manifolds representing the exact same figure in different ways. The proposed framework is then used for group-wise registration and statistical analysis of biomedical images, by employing a minimum variance criterion to perform manifold-constrained optimization, i.e. to traverse each individual's morphological appearance manifold until group variance is minimal. The hypothesis is that this process is likely to reduce aforementioned confounding effects and potentially lead to morphological representations reflecting purely biological variations, instead of variations introduced by modeling assumptions and parameter settings. Copyright © 2011 Elsevier B.V. All rights reserved.

Postoperative 3D spine reconstruction by navigating partitioning manifolds

Energy Technology Data Exchange (ETDEWEB)

Kadoury, Samuel, E-mail: samuel.kadoury@polymtl.ca [Department of Computer and Software Engineering, Ecole Polytechnique Montreal, Montréal, Québec H3C 3A7 (Canada); Labelle, Hubert, E-mail: hubert.labelle@recherche-ste-justine.qc.ca; Parent, Stefan, E-mail: stefan.parent@umontreal.ca [CHU Sainte-Justine Hospital Research Center, Montréal, Québec H3T 1C5 (Canada)

2016-03-15

Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities.

Postoperative 3D spine reconstruction by navigating partitioning manifolds

International Nuclear Information System (INIS)

Kadoury, Samuel; Labelle, Hubert; Parent, Stefan

2016-01-01

Purpose: The postoperative evaluation of scoliosis patients undergoing corrective treatment is an important task to assess the strategy of the spinal surgery. Using accurate 3D geometric models of the patient’s spine is essential to measure longitudinal changes in the patient’s anatomy. On the other hand, reconstructing the spine in 3D from postoperative radiographs is a challenging problem due to the presence of instrumentation (metallic rods and screws) occluding vertebrae on the spine. Methods: This paper describes the reconstruction problem by searching for the optimal model within a manifold space of articulated spines learned from a training dataset of pathological cases who underwent surgery. The manifold structure is implemented based on a multilevel manifold ensemble to structure the data, incorporating connections between nodes within a single manifold, in addition to connections between different multilevel manifolds, representing subregions with similar characteristics. Results: The reconstruction pipeline was evaluated on x-ray datasets from both preoperative patients and patients with spinal surgery. By comparing the method to ground-truth models, a 3D reconstruction accuracy of 2.24 ± 0.90 mm was obtained from 30 postoperative scoliotic patients, while handling patients with highly deformed spines. Conclusions: This paper illustrates how this manifold model can accurately identify similar spine models by navigating in the low-dimensional space, as well as computing nonlinear charts within local neighborhoods of the embedded space during the testing phase. This technique allows postoperative follow-ups of spinal surgery using personalized 3D spine models and assess surgical strategies for spinal deformities

Manifold Regularized Experimental Design for Active Learning.

Science.gov (United States)

Zhang, Lining; Shum, Hubert P H; Shao, Ling

2016-12-02

Various machine learning and data mining tasks in classification require abundant data samples to be labeled for training. Conventional active learning methods aim at labeling the most informative samples for alleviating the labor of the user. Many previous studies in active learning select one sample after another in a greedy manner. However, this is not very effective because the classification models has to be retrained for each newly labeled sample. Moreover, many popular active learning approaches utilize the most uncertain samples by leveraging the classification hyperplane of the classifier, which is not appropriate since the classification hyperplane is inaccurate when the training data are small-sized. The problem of insufficient training data in real-world systems limits the potential applications of these approaches. This paper presents a novel method of active learning called manifold regularized experimental design (MRED), which can label multiple informative samples at one time for training. In addition, MRED gives an explicit geometric explanation for the selected samples to be labeled by the user. Different from existing active learning methods, our method avoids the intrinsic problems caused by insufficiently labeled samples in real-world applications. Various experiments on synthetic datasets, the Yale face database and the Corel image database have been carried out to show how MRED outperforms existing methods.

An empirical study on the performance of spectral manifold learning techniques

DEFF Research Database (Denmark)

Mysling, Peter; Hauberg, Søren; Pedersen, Kim Steenstrup

2011-01-01

In recent years, there has been a surge of interest in spectral manifold learning techniques. Despite the interest, only little work has focused on the empirical behavior of these techniques. We construct synthetic data of variable complexity and observe the performance of the techniques as they ...

On a program manifold's stability of one contour automatic control systems

Science.gov (United States)

Zumatov, S. S.

2017-12-01

Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold's absolute stability of one contour automatic control systems are obtained. The Hurwitz's angle of absolute stability was determined. The sufficient conditions of program manifold's absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov's second method.

Manifold Regularized Correlation Object Tracking

OpenAIRE

Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling

2017-01-01

In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...

Manifold learning to interpret JET high-dimensional operational space

International Nuclear Information System (INIS)

Cannas, B; Fanni, A; Pau, A; Sias, G; Murari, A

2013-01-01

In this paper, the problem of visualization and exploration of JET high-dimensional operational space is considered. The data come from plasma discharges selected from JET campaigns from C15 (year 2005) up to C27 (year 2009). The aim is to learn the possible manifold structure embedded in the data and to create some representations of the plasma parameters on low-dimensional maps, which are understandable and which preserve the essential properties owned by the original data. A crucial issue for the design of such mappings is the quality of the dataset. This paper reports the details of the criteria used to properly select suitable signals downloaded from JET databases in order to obtain a dataset of reliable observations. Moreover, a statistical analysis is performed to recognize the presence of outliers. Finally data reduction, based on clustering methods, is performed to select a limited and representative number of samples for the operational space mapping. The high-dimensional operational space of JET is mapped using a widely used manifold learning method, the self-organizing maps. The results are compared with other data visualization methods. The obtained maps can be used to identify characteristic regions of the plasma scenario, allowing to discriminate between regions with high risk of disruption and those with low risk of disruption. (paper)

Principal Curves on Riemannian Manifolds.

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Hauberg, Soren

2016-09-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

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Sun, Shiliang; Xie, Xijiong

2016-09-01

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash

2012-03-09

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

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Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Introduction to global analysis minimal surfaces in Riemannian manifolds

CERN Document Server

Moore, John Douglas

2017-01-01

During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...

A nonlinear multi-proxy model based on manifold learning to reconstruct water temperature from high resolution trace element profiles in biogenic carbonates

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M. Bauwens

2010-11-01

Full Text Available A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ¹⁸O carbonate. It is problematic in the case of freshwater influenced environments because the δ¹⁸O isotopic composition of the ambient water (related to salinity needs to be known. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization (WDMR to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information for other trace elements in multi-proxy models. Although the models presented here are black-box models that do not use any prior knowledge about the proxies, the comparison of model reconstruction performances based on different proxy combinations do yield useful information about proxy characteristics. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enables a temperature reconstruction with a root mean squared error of ± 2.19 °C for a salinity range between 15 and 32.

Smooth manifolds for certain dynamical systems and periodic solitons for nonlinear Klein-Gordon equations on R2

International Nuclear Information System (INIS)

Vuillermot, P.A.

1988-01-01

We present and discuss three new theorems concerning the existence of smooth manifolds associated with certain infinite-dimensional dynamical systems defined from nonlinear Klein-Gordon equations of the form u tt (x, t) = u xx (x, t)-g(u(x, t)), where g: R → R is analytic and where (x, t) ε R 2 . In particular, we prove the nonexistence of small amplitude soliton bound state solutions in the classical Φ 4 -theory, a fact recently brought about by the perturbative analysis of Kruskal and Segur [fr

Manifold regularized multitask feature learning for multimodality disease classification.

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Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang

2015-02-01

Multimodality based methods have shown great advantages in classification of Alzheimer's disease (AD) and its prodromal stage, that is, mild cognitive impairment (MCI). Recently, multitask feature selection methods are typically used for joint selection of common features across multiple modalities. However, one disadvantage of existing multimodality based methods is that they ignore the useful data distribution information in each modality, which is essential for subsequent classification. Accordingly, in this paper we propose a manifold regularized multitask feature learning method to preserve both the intrinsic relatedness among multiple modalities of data and the data distribution information in each modality. Specifically, we denote the feature learning on each modality as a single task, and use group-sparsity regularizer to capture the intrinsic relatedness among multiple tasks (i.e., modalities) and jointly select the common features from multiple tasks. Furthermore, we introduce a new manifold-based Laplacian regularizer to preserve the data distribution information from each task. Finally, we use the multikernel support vector machine method to fuse multimodality data for eventual classification. Conversely, we also extend our method to the semisupervised setting, where only partial data are labeled. We evaluate our method using the baseline magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET), and cerebrospinal fluid (CSF) data of subjects from AD neuroimaging initiative database. The experimental results demonstrate that our proposed method can not only achieve improved classification performance, but also help to discover the disease-related brain regions useful for disease diagnosis. © 2014 Wiley Periodicals, Inc.

Stochastic parameterizing manifolds and non-Markovian reduced equations stochastic manifolds for nonlinear SPDEs II

CERN Document Server

Chekroun, Mickaël D; Wang, Shouhong

2015-01-01

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.

Alzheimer's Disease Early Diagnosis Using Manifold-Based Semi-Supervised Learning.

Science.gov (United States)

Khajehnejad, Moein; Saatlou, Forough Habibollahi; Mohammadzade, Hoda

2017-08-20

Alzheimer's disease (AD) is currently ranked as the sixth leading cause of death in the United States and recent estimates indicate that the disorder may rank third, just behind heart disease and cancer, as a cause of death for older people. Clearly, predicting this disease in the early stages and preventing it from progressing is of great importance. The diagnosis of Alzheimer's disease (AD) requires a variety of medical tests, which leads to huge amounts of multivariate heterogeneous data. It can be difficult and exhausting to manually compare, visualize, and analyze this data due to the heterogeneous nature of medical tests; therefore, an efficient approach for accurate prediction of the condition of the brain through the classification of magnetic resonance imaging (MRI) images is greatly beneficial and yet very challenging. In this paper, a novel approach is proposed for the diagnosis of very early stages of AD through an efficient classification of brain MRI images, which uses label propagation in a manifold-based semi-supervised learning framework. We first apply voxel morphometry analysis to extract some of the most critical AD-related features of brain images from the original MRI volumes and also gray matter (GM) segmentation volumes. The features must capture the most discriminative properties that vary between a healthy and Alzheimer-affected brain. Next, we perform a principal component analysis (PCA)-based dimension reduction on the extracted features for faster yet sufficiently accurate analysis. To make the best use of the captured features, we present a hybrid manifold learning framework which embeds the feature vectors in a subspace. Next, using a small set of labeled training data, we apply a label propagation method in the created manifold space to predict the labels of the remaining images and classify them in the two groups of mild Alzheimer's and normal condition (MCI/NC). The accuracy of the classification using the proposed method is 93

Gauge equivalence of σ models with non-compact Grassmannian manifolds

International Nuclear Information System (INIS)

Kundu, A.

1986-01-01

The gauge equivalence (GE) of σ models associated with non-compact Grassmannian manifolds is investigated with emphasis on the necessary restrictions for the choice of gauge elements in such cases. The importance of GE in solving a non-linear system with the help of inverse scattering data of its gauge related counterpart is demonstrated. The gauge relations between generalised Landau-Lifshitz (LL) and non-linear Schroedinger (NLS) type equations and also between non-linear σ models and generalised 'sine-sinh-Gordon' equations for non-compact SU(p,q)/S(U(u,v) x U(s,t)) manifolds are established. Using H-gauge invariance of LL the GE is extended to some higher-order specific non-linear systems. The gauge connection among various LL and NLS equations are schematically represented. Along with the recovery of earlier results important new results, some with significant non-compact structures, are discovered. (author)

Nonlinear machine learning and design of reconfigurable digital colloids.

Science.gov (United States)

Long, Andrew W; Phillips, Carolyn L; Jankowksi, Eric; Ferguson, Andrew L

2016-09-14

Digital colloids, a cluster of freely rotating "halo" particles tethered to the surface of a central particle, were recently proposed as ultra-high density memory elements for information storage. Rational design of these digital colloids for memory storage applications requires a quantitative understanding of the thermodynamic and kinetic stability of the configurational states within which information is stored. We apply nonlinear machine learning to Brownian dynamics simulations of these digital colloids to extract the low-dimensional intrinsic manifold governing digital colloid morphology, thermodynamics, and kinetics. By modulating the relative size ratio between halo particles and central particles, we investigate the size-dependent configurational stability and transition kinetics for the 2-state tetrahedral (N = 4) and 30-state octahedral (N = 6) digital colloids. We demonstrate the use of this framework to guide the rational design of a memory storage element to hold a block of text that trades off the competing design criteria of memory addressability and volatility.

Manifold optimization-based analysis dictionary learning with an ℓ1∕2-norm regularizer.

Science.gov (United States)

Li, Zhenni; Ding, Shuxue; Li, Yujie; Yang, Zuyuan; Xie, Shengli; Chen, Wuhui

2018-02-01

Recently there has been increasing attention towards analysis dictionary learning. In analysis dictionary learning, it is an open problem to obtain the strong sparsity-promoting solutions efficiently while simultaneously avoiding the trivial solutions of the dictionary. In this paper, to obtain the strong sparsity-promoting solutions, we employ the ℓ 1∕2 norm as a regularizer. The very recent study on ℓ 1∕2 norm regularization theory in compressive sensing shows that its solutions can give sparser results than using the ℓ 1 norm. We transform a complex nonconvex optimization into a number of one-dimensional minimization problems. Then the closed-form solutions can be obtained efficiently. To avoid trivial solutions, we apply manifold optimization to update the dictionary directly on the manifold satisfying the orthonormality constraint, so that the dictionary can avoid the trivial solutions well while simultaneously capturing the intrinsic properties of the dictionary. The experiments with synthetic and real-world data verify that the proposed algorithm for analysis dictionary learning can not only obtain strong sparsity-promoting solutions efficiently, but also learn more accurate dictionary in terms of dictionary recovery and image processing than the state-of-the-art algorithms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Semi-supervised manifold learning with affinity regularization for Alzheimer's disease identification using positron emission tomography imaging.

Science.gov (United States)

Lu, Shen; Xia, Yong; Cai, Tom Weidong; Feng, David Dagan

2015-01-01

Dementia, Alzheimer's disease (AD) in particular is a global problem and big threat to the aging population. An image based computer-aided dementia diagnosis method is needed to providing doctors help during medical image examination. Many machine learning based dementia classification methods using medical imaging have been proposed and most of them achieve accurate results. However, most of these methods make use of supervised learning requiring fully labeled image dataset, which usually is not practical in real clinical environment. Using large amount of unlabeled images can improve the dementia classification performance. In this study we propose a new semi-supervised dementia classification method based on random manifold learning with affinity regularization. Three groups of spatial features are extracted from positron emission tomography (PET) images to construct an unsupervised random forest which is then used to regularize the manifold learning objective function. The proposed method, stat-of-the-art Laplacian support vector machine (LapSVM) and supervised SVM are applied to classify AD and normal controls (NC). The experiment results show that learning with unlabeled images indeed improves the classification performance. And our method outperforms LapSVM on the same dataset.

Reconstructing 3D Face Model with Associated Expression Deformation from a Single Face Image via Constructing a Low-Dimensional Expression Deformation Manifold.

Science.gov (United States)

Wang, Shu-Fan; Lai, Shang-Hong

2011-10-01

Facial expression modeling is central to facial expression recognition and expression synthesis for facial animation. In this work, we propose a manifold-based 3D face reconstruction approach to estimating the 3D face model and the associated expression deformation from a single face image. With the proposed robust weighted feature map (RWF), we can obtain the dense correspondences between 3D face models and build a nonlinear 3D expression manifold from a large set of 3D facial expression models. Then a Gaussian mixture model in this manifold is learned to represent the distribution of expression deformation. By combining the merits of morphable neutral face model and the low-dimensional expression manifold, a novel algorithm is developed to reconstruct the 3D face geometry as well as the facial deformation from a single face image in an energy minimization framework. Experimental results on simulated and real images are shown to validate the effectiveness and accuracy of the proposed algorithm.

Distributed Extreme Learning Machine for Nonlinear Learning over Network

Directory of Open Access Journals (Sweden)

Songyan Huang

2015-02-01

Full Text Available Distributed data collection and analysis over a network are ubiquitous, especially over a wireless sensor network (WSN. To our knowledge, the data model used in most of the distributed algorithms is linear. However, in real applications, the linearity of systems is not always guaranteed. In nonlinear cases, the single hidden layer feedforward neural network (SLFN with radial basis function (RBF hidden neurons has the ability to approximate any continuous functions and, thus, may be used as the nonlinear learning system. However, confined by the communication cost, using the distributed version of the conventional algorithms to train the neural network directly is usually prohibited. Fortunately, based on the theorems provided in the extreme learning machine (ELM literature, we only need to compute the output weights of the SLFN. Computing the output weights itself is a linear learning problem, although the input-output mapping of the overall SLFN is still nonlinear. Using the distributed algorithmto cooperatively compute the output weights of the SLFN, we obtain a distributed extreme learning machine (dELM for nonlinear learning in this paper. This dELM is applied to the regression problem and classification problem to demonstrate its effectiveness and advantages.

A manifold learning approach to data-driven computational materials and processes

Science.gov (United States)

Ibañez, Ruben; Abisset-Chavanne, Emmanuelle; Aguado, Jose Vicente; Gonzalez, David; Cueto, Elias; Duval, Jean Louis; Chinesta, Francisco

2017-10-01

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, …), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ universal laws while minimizing the need of explicit, often phenomenological, models. They are based on manifold learning methodologies.

Statistical Shape Model for Manifold Regularization: Gleason grading of prostate histology.

Science.gov (United States)

Sparks, Rachel; Madabhushi, Anant

2013-09-01

Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides subtle morphologic and architectural differences of histological attributes, in addition to other factors, may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a

Moving Manifolds in Electromagnetic Fields

Directory of Open Access Journals (Sweden)

David V. Svintradze

2017-08-01

Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.

Enhanced manifold regularization for semi-supervised classification.

Science.gov (United States)

Gan, Haitao; Luo, Zhizeng; Fan, Yingle; Sang, Nong

2016-06-01

Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervised learning field. It has shown superiority by exploiting the local manifold structure of both labeled and unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and then incorporated in learning through a smoothness regularization term. Hence the labels of labeled and unlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminative ability of the labeled and unlabeled data. To address the problem, we propose an enhanced MR framework for semi-supervised classification in which the local discriminative information of the labeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ a semi-supervised clustering method to discover the underlying data space structure of the whole dataset. Then we construct a local discrimination graph to model the discriminative information of labeled and unlabeled data according to the discovered intrinsic structure. Therefore, the data points that may be from different clusters, though similar on the manifold, are enforced far away from each other. Finally, the discrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervised fuzzy c-means and Laplacian regularized Kernel minimum squared error for semi-supervised clustering and classification, respectively. Experimental results on several benchmark datasets and face recognition demonstrate the effectiveness of our proposed method.

Discriminative Structured Dictionary Learning on Grassmann Manifolds and Its Application on Image Restoration.

Science.gov (United States)

Pan, Han; Jing, Zhongliang; Qiao, Lingfeng; Li, Minzhe

2017-09-25

Image restoration is a difficult and challenging problem in various imaging applications. However, despite of the benefits of a single overcomplete dictionary, there are still several challenges for capturing the geometric structure of image of interest. To more accurately represent the local structures of the underlying signals, we propose a new problem formulation for sparse representation with block-orthogonal constraint. There are three contributions. First, a framework for discriminative structured dictionary learning is proposed, which leads to a smooth manifold structure and quotient search spaces. Second, an alternating minimization scheme is proposed after taking both the cost function and the constraints into account. This is achieved by iteratively alternating between updating the block structure of the dictionary defined on Grassmann manifold and sparsifying the dictionary atoms automatically. Third, Riemannian conjugate gradient is considered to track local subspaces efficiently with a convergence guarantee. Extensive experiments on various datasets demonstrate that the proposed method outperforms the state-of-the-art methods on the removal of mixed Gaussian-impulse noise.

Dynamic MRI Using SmooThness Regularization on Manifolds (SToRM).

Science.gov (United States)

Poddar, Sunrita; Jacob, Mathews

2016-04-01

We introduce a novel algorithm to recover real time dynamic MR images from highly under-sampled k- t space measurements. The proposed scheme models the images in the dynamic dataset as points on a smooth, low dimensional manifold in high dimensional space. We propose to exploit the non-linear and non-local redundancies in the dataset by posing its recovery as a manifold smoothness regularized optimization problem. A navigator acquisition scheme is used to determine the structure of the manifold, or equivalently the associated graph Laplacian matrix. The estimated Laplacian matrix is used to recover the dataset from undersampled measurements. The utility of the proposed scheme is demonstrated by comparisons with state of the art methods in multi-slice real-time cardiac and speech imaging applications.

[Multi-Target Recognition of Internal and External Defects of Potato by Semi-Transmission Hyperspectral Imaging and Manifold Learning Algorithm].

Science.gov (United States)

Huang, Tao; Li, Xiao-yu; Jin, Rui; Ku, Jing; Xu, Sen-miao; Xu, Meng-ling; Wu, Zhen-zhong; Kong, De-guo

2015-04-01

The present paper put forward a non-destructive detection method which combines semi-transmission hyperspectral imaging technology with manifold learning dimension reduction algorithm and least squares support vector machine (LSSVM) to recognize internal and external defects in potatoes simultaneously. Three hundred fifteen potatoes were bought in farmers market as research object, and semi-transmission hyperspectral image acquisition system was constructed to acquire the hyperspectral images of normal external defects (bud and green rind) and internal defect (hollow heart) potatoes. In order to conform to the actual production, defect part is randomly put right, side and back to the acquisition probe when the hyperspectral images of external defects potatoes are acquired. The average spectrums (390-1,040 nm) were extracted from the region of interests for spectral preprocessing. Then three kinds of manifold learning algorithm were respectively utilized to reduce the dimension of spectrum data, including supervised locally linear embedding (SLLE), locally linear embedding (LLE) and isometric mapping (ISOMAP), the low-dimensional data gotten by manifold learning algorithms is used as model input, Error Correcting Output Code (ECOC) and LSSVM were combined to develop the multi-target classification model. By comparing and analyzing results of the three models, we concluded that SLLE is the optimal manifold learning dimension reduction algorithm, and the SLLE-LSSVM model is determined to get the best recognition rate for recognizing internal and external defects potatoes. For test set data, the single recognition rate of normal, bud, green rind and hollow heart potato reached 96.83%, 86.96%, 86.96% and 95% respectively, and he hybrid recognition rate was 93.02%. The results indicate that combining the semi-transmission hyperspectral imaging technology with SLLE-LSSVM is a feasible qualitative analytical method which can simultaneously recognize the internal and

Person-Independent Head Pose Estimation Using Biased Manifold Embedding

Directory of Open Access Journals (Sweden)

Sethuraman Panchanathan

2008-02-01

Full Text Available Head pose estimation has been an integral problem in the study of face recognition systems and human-computer interfaces, as part of biometric applications. A fine estimate of the head pose angle is necessary and useful for several face analysis applications. To determine the head pose, face images with varying pose angles can be considered to be lying on a smooth low-dimensional manifold in high-dimensional image feature space. However, when there are face images of multiple individuals with varying pose angles, manifold learning techniques often do not give accurate results. In this work, we propose a framework for a supervised form of manifold learning called Biased Manifold Embedding to obtain improved performance in head pose angle estimation. This framework goes beyond pose estimation, and can be applied to all regression applications. This framework, although formulated for a regression scenario, unifies other supervised approaches to manifold learning that have been proposed so far. Detailed studies of the proposed method are carried out on the FacePix database, which contains 181 face images each of 30 individuals with pose angle variations at a granularity of 1∘. Since biometric applications in the real world may not contain this level of granularity in training data, an analysis of the methodology is performed on sparsely sampled data to validate its effectiveness. We obtained up to 2∘ average pose angle estimation error in the results from our experiments, which matched the best results obtained for head pose estimation using related approaches.

Manifold regularized matrix completion for multi-label learning with ADMM.

Science.gov (United States)

Liu, Bin; Li, Yingming; Xu, Zenglin

2018-05-01

Multi-label learning is a common machine learning problem arising from numerous real-world applications in diverse fields, e.g, natural language processing, bioinformatics, information retrieval and so on. Among various multi-label learning methods, the matrix completion approach has been regarded as a promising approach to transductive multi-label learning. By constructing a joint matrix comprising the feature matrix and the label matrix, the missing labels of test samples are regarded as missing values of the joint matrix. With the low-rank assumption of the constructed joint matrix, the missing labels can be recovered by minimizing its rank. Despite its success, most matrix completion based approaches ignore the smoothness assumption of unlabeled data, i.e., neighboring instances should also share a similar set of labels. Thus they may under exploit the intrinsic structures of data. In addition, the matrix completion problem can be less efficient. To this end, we propose to efficiently solve the multi-label learning problem as an enhanced matrix completion model with manifold regularization, where the graph Laplacian is used to ensure the label smoothness over it. To speed up the convergence of our model, we develop an efficient iterative algorithm, which solves the resulted nuclear norm minimization problem with the alternating direction method of multipliers (ADMM). Experiments on both synthetic and real-world data have shown the promising results of the proposed approach. Copyright © 2018 Elsevier Ltd. All rights reserved.

Hyperspin manifolds

International Nuclear Information System (INIS)

Finkelstein, D.; Finkelstein, S.R.; Holm, C.

1986-01-01

Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d 2 (Minkowski time space) and 2 (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N 2 . In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash; Goriely, Alain

2012-01-01

but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed

Indirect learning control for nonlinear dynamical systems

Science.gov (United States)

Ryu, Yeong Soon; Longman, Richard W.

1993-01-01

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Toric Vaisman manifolds

Science.gov (United States)

Pilca, Mihaela

2016-09-01

Vaisman manifolds are strongly related to Kähler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose Kähler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding Kähler quotient is toric.

Multimodal manifold-regularized transfer learning for MCI conversion prediction.

Science.gov (United States)

Cheng, Bo; Liu, Mingxia; Suk, Heung-Il; Shen, Dinggang; Zhang, Daoqiang

2015-12-01

As the early stage of Alzheimer's disease (AD), mild cognitive impairment (MCI) has high chance to convert to AD. Effective prediction of such conversion from MCI to AD is of great importance for early diagnosis of AD and also for evaluating AD risk pre-symptomatically. Unlike most previous methods that used only the samples from a target domain to train a classifier, in this paper, we propose a novel multimodal manifold-regularized transfer learning (M2TL) method that jointly utilizes samples from another domain (e.g., AD vs. normal controls (NC)) as well as unlabeled samples to boost the performance of the MCI conversion prediction. Specifically, the proposed M2TL method includes two key components. The first one is a kernel-based maximum mean discrepancy criterion, which helps eliminate the potential negative effect induced by the distributional difference between the auxiliary domain (i.e., AD and NC) and the target domain (i.e., MCI converters (MCI-C) and MCI non-converters (MCI-NC)). The second one is a semi-supervised multimodal manifold-regularized least squares classification method, where the target-domain samples, the auxiliary-domain samples, and the unlabeled samples can be jointly used for training our classifier. Furthermore, with the integration of a group sparsity constraint into our objective function, the proposed M2TL has a capability of selecting the informative samples to build a robust classifier. Experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database validate the effectiveness of the proposed method by significantly improving the classification accuracy of 80.1 % for MCI conversion prediction, and also outperforming the state-of-the-art methods.

Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds

OpenAIRE

Barreto, Yadira; Verjovsky, Alberto

2013-01-01

We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

Riemannian multi-manifold modeling and clustering in brain networks

Science.gov (United States)

Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.

2017-08-01

This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.

Gene selection for microarray data classification via subspace learning and manifold regularization.

Science.gov (United States)

Tang, Chang; Cao, Lijuan; Zheng, Xiao; Wang, Minhui

2017-12-19

With the rapid development of DNA microarray technology, large amount of genomic data has been generated. Classification of these microarray data is a challenge task since gene expression data are often with thousands of genes but a small number of samples. In this paper, an effective gene selection method is proposed to select the best subset of genes for microarray data with the irrelevant and redundant genes removed. Compared with original data, the selected gene subset can benefit the classification task. We formulate the gene selection task as a manifold regularized subspace learning problem. In detail, a projection matrix is used to project the original high dimensional microarray data into a lower dimensional subspace, with the constraint that the original genes can be well represented by the selected genes. Meanwhile, the local manifold structure of original data is preserved by a Laplacian graph regularization term on the low-dimensional data space. The projection matrix can serve as an importance indicator of different genes. An iterative update algorithm is developed for solving the problem. Experimental results on six publicly available microarray datasets and one clinical dataset demonstrate that the proposed method performs better when compared with other state-of-the-art methods in terms of microarray data classification. Graphical Abstract The graphical abstract of this work.

Tensor manifold-based extreme learning machine for 2.5-D face recognition

Science.gov (United States)

Chong, Lee Ying; Ong, Thian Song; Teoh, Andrew Beng Jin

2018-01-01

We explore the use of the Gabor regional covariance matrix (GRCM), a flexible matrix-based descriptor that embeds the Gabor features in the covariance matrix, as a 2.5-D facial descriptor and an effective means of feature fusion for 2.5-D face recognition problems. Despite its promise, matching is not a trivial problem for GRCM since it is a special instance of a symmetric positive definite (SPD) matrix that resides in non-Euclidean space as a tensor manifold. This implies that GRCM is incompatible with the existing vector-based classifiers and distance matchers. Therefore, we bridge the gap of the GRCM and extreme learning machine (ELM), a vector-based classifier for the 2.5-D face recognition problem. We put forward a tensor manifold-compliant ELM and its two variants by embedding the SPD matrix randomly into reproducing kernel Hilbert space (RKHS) via tensor kernel functions. To preserve the pair-wise distance of the embedded data, we orthogonalize the random-embedded SPD matrix. Hence, classification can be done using a simple ridge regressor, an integrated component of ELM, on the random orthogonal RKHS. Experimental results show that our proposed method is able to improve the recognition performance and further enhance the computational efficiency.

Predicting CT Image From MRI Data Through Feature Matching With Learned Nonlinear Local Descriptors.

Science.gov (United States)

Yang, Wei; Zhong, Liming; Chen, Yang; Lin, Liyan; Lu, Zhentai; Liu, Shupeng; Wu, Yao; Feng, Qianjin; Chen, Wufan

2018-04-01

Attenuation correction for positron-emission tomography (PET)/magnetic resonance (MR) hybrid imaging systems and dose planning for MR-based radiation therapy remain challenging due to insufficient high-energy photon attenuation information. We present a novel approach that uses the learned nonlinear local descriptors and feature matching to predict pseudo computed tomography (pCT) images from T1-weighted and T2-weighted magnetic resonance imaging (MRI) data. The nonlinear local descriptors are obtained by projecting the linear descriptors into the nonlinear high-dimensional space using an explicit feature map and low-rank approximation with supervised manifold regularization. The nearest neighbors of each local descriptor in the input MR images are searched in a constrained spatial range of the MR images among the training dataset. Then the pCT patches are estimated through k-nearest neighbor regression. The proposed method for pCT prediction is quantitatively analyzed on a dataset consisting of paired brain MRI and CT images from 13 subjects. Our method generates pCT images with a mean absolute error (MAE) of 75.25 ± 18.05 Hounsfield units, a peak signal-to-noise ratio of 30.87 ± 1.15 dB, a relative MAE of 1.56 ± 0.5% in PET attenuation correction, and a dose relative structure volume difference of 0.055 ± 0.107% in , as compared with true CT. The experimental results also show that our method outperforms four state-of-the-art methods.

On some properties of the superposition operator on topological manifolds

Directory of Open Access Journals (Sweden)

Janusz Dronka

2010-01-01

Full Text Available In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.

M-Isomap: Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction.

Science.gov (United States)

Zhang, Zhao; Chow, Tommy W S; Zhao, Mingbo

2013-02-01

Isomap is a well-known nonlinear dimensionality reduction (DR) method, aiming at preserving geodesic distances of all similarity pairs for delivering highly nonlinear manifolds. Isomap is efficient in visualizing synthetic data sets, but it usually delivers unsatisfactory results in benchmark cases. This paper incorporates the pairwise constraints into Isomap and proposes a marginal Isomap (M-Isomap) for manifold learning. The pairwise Cannot-Link and Must-Link constraints are used to specify the types of neighborhoods. M-Isomap computes the shortest path distances over constrained neighborhood graphs and guides the nonlinear DR through separating the interclass neighbors. As a result, large margins between both interand intraclass clusters are delivered and enhanced compactness of intracluster points is achieved at the same time. The validity of M-Isomap is examined by extensive simulations over synthetic, University of California, Irvine, and benchmark real Olivetti Research Library, YALE, and CMU Pose, Illumination, and Expression databases. The data visualization and clustering power of M-Isomap are compared with those of six related DR methods. The visualization results show that M-Isomap is able to deliver more separate clusters. Clustering evaluations also demonstrate that M-Isomap delivers comparable or even better results than some state-of-the-art DR algorithms.

Smooth manifolds

CERN Document Server

Sinha, Rajnikant

2014-01-01

This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book ...

A non-linear manifold alignment approach to robot learning from demonstrations

CSIR Research Space (South Africa)

Makondo, Ndivhuwo

2018-04-01

Full Text Available with potentially different, but unknown, kinematics from humans. This paper proposes a method that enables robots with unknown kinematics to learn skills from demonstrations. Our proposed method requires a motion trajectory obtained from human demonstrations via a...

Feature extraction for SAR target recognition based on supervised manifold learning

International Nuclear Information System (INIS)

Du, C; Zhou, S; Sun, J; Zhao, J

2014-01-01

On the basis of manifold learning theory, a new feature extraction method for Synthetic aperture radar (SAR) target recognition is proposed. First, the proposed algorithm estimates the within-class and between-class local neighbourhood surrounding each SAR sample. After computing the local tangent space for each neighbourhood, the proposed algorithm seeks for the optimal projecting matrix by preserving the local within-class property and simultaneously maximizing the local between-class separability. The use of uncorrelated constraint can also enhance the discriminating power of the optimal projecting matrix. Finally, the nearest neighbour classifier is applied to recognize SAR targets in the projected feature subspace. Experimental results on MSTAR datasets demonstrate that the proposed method can provide a higher recognition rate than traditional feature extraction algorithms in SAR target recognition

A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference

KAUST Repository

Tegner, Jesper; Zenil, Hector; Kiani, Narsis A.; Ball, Gordon; Gomez-Cabrero, David

2016-01-01

Systems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems.

A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference

KAUST Repository

Tegner, Jesper

2016-10-04

Systems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems.

Laplacian embedded regression for scalable manifold regularization.

Science.gov (United States)

Chen, Lin; Tsang, Ivor W; Xu, Dong

2012-06-01

Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real

Toward Optimal Manifold Hashing via Discrete Locally Linear Embedding.

Science.gov (United States)

Rongrong Ji; Hong Liu; Liujuan Cao; Di Liu; Yongjian Wu; Feiyue Huang

2017-11-01

Binary code learning, also known as hashing, has received increasing attention in large-scale visual search. By transforming high-dimensional features to binary codes, the original Euclidean distance is approximated via Hamming distance. More recently, it is advocated that it is the manifold distance, rather than the Euclidean distance, that should be preserved in the Hamming space. However, it retains as an open problem to directly preserve the manifold structure by hashing. In particular, it first needs to build the local linear embedding in the original feature space, and then quantize such embedding to binary codes. Such a two-step coding is problematic and less optimized. Besides, the off-line learning is extremely time and memory consuming, which needs to calculate the similarity matrix of the original data. In this paper, we propose a novel hashing algorithm, termed discrete locality linear embedding hashing (DLLH), which well addresses the above challenges. The DLLH directly reconstructs the manifold structure in the Hamming space, which learns optimal hash codes to maintain the local linear relationship of data points. To learn discrete locally linear embeddingcodes, we further propose a discrete optimization algorithm with an iterative parameters updating scheme. Moreover, an anchor-based acceleration scheme, termed Anchor-DLLH, is further introduced, which approximates the large similarity matrix by the product of two low-rank matrices. Experimental results on three widely used benchmark data sets, i.e., CIFAR10, NUS-WIDE, and YouTube Face, have shown superior performance of the proposed DLLH over the state-of-the-art approaches.

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

Rigid Body Energy Minimization on Manifolds for Molecular Docking.

Science.gov (United States)

Mirzaei, Hanieh; Beglov, Dmitri; Paschalidis, Ioannis Ch; Vajda, Sandor; Vakili, Pirooz; Kozakov, Dima

2012-11-13

Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space. We use a canonical parametrization of the manifold, called the exponential parametrization, to map the Euclidean tangent space of the manifold onto the manifold itself. Thus, we locally transform the rigid body optimization to an optimization over a Euclidean space where basic optimization algorithms are applicable. Compared to commonly used methods, this formulation substantially reduces the dimension of the search space. As a result, it requires far fewer costly function and gradient evaluations and leads to a more efficient algorithm. We have selected the LBFGS quasi-Newton method for local optimization since it uses only gradient information to obtain second order information about the energy function and avoids the far more costly direct Hessian evaluations. Two applications, one in protein-protein docking, and the other in protein-small molecular interactions, as part of macromolecular docking protocols are presented. The code is available to the community under open source license, and with minimal effort can be incorporated into any molecular modeling package.

Manifold-Based Visual Object Counting.

Science.gov (United States)

Wang, Yi; Zou, Yuexian; Wang, Wenwu

2018-07-01

Visual object counting (VOC) is an emerging area in computer vision which aims to estimate the number of objects of interest in a given image or video. Recently, object density based estimation method is shown to be promising for object counting as well as rough instance localization. However, the performance of this method tends to degrade when dealing with new objects and scenes. To address this limitation, we propose a manifold-based method for visual object counting (M-VOC), based on the manifold assumption that similar image patches share similar object densities. Firstly, the local geometry of a given image patch is represented linearly by its neighbors using a predefined patch training set, and the object density of this given image patch is reconstructed by preserving the local geometry using locally linear embedding. To improve the characterization of local geometry, additional constraints such as sparsity and non-negativity are also considered via regularization, nonlinear mapping, and kernel trick. Compared with the state-of-the-art VOC methods, our proposed M-VOC methods achieve competitive performance on seven benchmark datasets. Experiments verify that the proposed M-VOC methods have several favorable properties, such as robustness to the variation in the size of training dataset and image resolution, as often encountered in real-world VOC applications.

Multiscale singular value manifold for rotating machinery fault diagnosis

Energy Technology Data Exchange (ETDEWEB)

Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)

2017-01-15

Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.

Dual manifold heat pipe evaporator

Science.gov (United States)

Adkins, D.R.; Rawlinson, K.S.

1994-01-04

An improved evaporator section is described for a dual manifold heat pipe. Both the upper and lower manifolds can have surfaces exposed to the heat source which evaporate the working fluid. The tubes in the tube bank between the manifolds have openings in their lower extensions into the lower manifold to provide for the transport of evaporated working fluid from the lower manifold into the tubes and from there on into the upper manifold and on to the condenser portion of the heat pipe. A wick structure lining the inner walls of the evaporator tubes extends into both the upper and lower manifolds. At least some of the tubes also have overflow tubes contained within them to carry condensed working fluid from the upper manifold to pass to the lower without spilling down the inside walls of the tubes. 1 figure.

Manifolds, Tensors, and Forms

Science.gov (United States)

Renteln, Paul

2013-11-01

Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.

Facial Expression Recognition of Various Internal States via Manifold Learning

Institute of Scientific and Technical Information of China (English)

Young-Suk Shin

2009-01-01

Emotions are becoming increasingly important in human-centered interaction architectures. Recognition of facial expressions, which are central to human-computer interactions, seems natural and desirable. However, facial expressions include mixed emotions, continuous rather than discrete, which vary from moment to moment. This paper represents a novel method of recognizing facial expressions of various internal states via manifold learning, to achieve the aim of humancentered interaction studies. A critical review of widely used emotion models is described, then, facial expression features of various internal states via the locally linear embedding (LLE) are extracted. The recognition of facial expressions is created with the pleasure-displeasure and arousal-sleep dimensions in a two-dimensional model of emotion. The recognition result of various internal state expressions that mapped to the embedding space via the LLE algorithm can effectively represent the structural nature of the two-dimensional model of emotion. Therefore our research has established that the relationship between facial expressions of various internal states can be elaborated in the two-dimensional model of emotion, via the locally linear embedding algorithm.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation.

Science.gov (United States)

Brito, Carlos S N; Gerstner, Wulfram

2016-09-01

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems

CERN Document Server

Mielke, Alexander

1991-01-01

The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists,...

Diffeomorphisms of elliptic 3-manifolds

CERN Document Server

Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam

2012-01-01

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...

Introduction to differentiable manifolds

CERN Document Server

Auslander, Louis

2009-01-01

The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation.

Directory of Open Access Journals (Sweden)

Carlos S N Brito

2016-09-01

Full Text Available The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

Multi-task Vector Field Learning.

Science.gov (United States)

Lin, Binbin; Yang, Sen; Zhang, Chiyuan; Ye, Jieping; He, Xiaofei

2012-01-01

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously and identifying the shared information among tasks. Most of existing MTL methods focus on learning linear models under the supervised setting. We propose a novel semi-supervised and nonlinear approach for MTL using vector fields. A vector field is a smooth mapping from the manifold to the tangent spaces which can be viewed as a directional derivative of functions on the manifold. We argue that vector fields provide a natural way to exploit the geometric structure of data as well as the shared differential structure of tasks, both of which are crucial for semi-supervised multi-task learning. In this paper, we develop multi-task vector field learning (MTVFL) which learns the predictor functions and the vector fields simultaneously. MTVFL has the following key properties. (1) The vector fields MTVFL learns are close to the gradient fields of the predictor functions. (2) Within each task, the vector field is required to be as parallel as possible which is expected to span a low dimensional subspace. (3) The vector fields from all tasks share a low dimensional subspace. We formalize our idea in a regularization framework and also provide a convex relaxation method to solve the original non-convex problem. The experimental results on synthetic and real data demonstrate the effectiveness of our proposed approach.

Geometry of mirror manifolds

International Nuclear Information System (INIS)

Aspinwall, P.S.; Luetken, C.A.

1991-01-01

We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.)

A study of Para-Sasakian manifold

International Nuclear Information System (INIS)

Rahman, M.S.

1995-08-01

A Para-Sasakian manifold M is viewed in the light of an almost paracontact manifold. The fundamental concepts of M in spirit to Recurrent, Ricci-recurrent, 2-Recurrent and 2-Ricci-recurrent manifolds are presented. An η-Einstein manifold modelled on P-Sasakian manifold is then treated with simplified proofs of some results. (author). 7 refs

Splitting Parabolic Manifolds

OpenAIRE

Kalka, Morris; Patrizio, Giorgio

2014-01-01

We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\\C^{N}$ viewed as a product of lower dimensional complex euclidean spaces.

Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential

Directory of Open Access Journals (Sweden)

Runzhang Xu

2012-11-01

Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].

TU-F-BRF-06: 3D Pancreas MRI Segmentation Using Dictionary Learning and Manifold Clustering

International Nuclear Information System (INIS)

Gou, S; Rapacchi, S; Hu, P; Sheng, K

2014-01-01

Purpose: The recent advent of MRI guided radiotherapy machines has lent an exciting platform for soft tissue target localization during treatment. However, tools to efficiently utilize MRI images for such purpose have not been developed. Specifically, to efficiently quantify the organ motion, we develop an automated segmentation method using dictionary learning and manifold clustering (DLMC). Methods: Fast 3D HASTE and VIBE MR images of 2 healthy volunteers and 3 patients were acquired. A bounding box was defined to include pancreas and surrounding normal organs including the liver, duodenum and stomach. The first slice of the MRI was used for dictionary learning based on mean-shift clustering and K-SVD sparse representation. Subsequent images were iteratively reconstructed until the error is less than a preset threshold. The preliminarily segmentation was subject to the constraints of manifold clustering. The segmentation results were compared with the mean shift merging (MSM), level set (LS) and manual segmentation methods. Results: DLMC resulted in consistently higher accuracy and robustness than comparing methods. Using manual contours as the ground truth, the mean Dices indices for all subjects are 0.54, 0.56 and 0.67 for MSM, LS and DLMC, respectively based on the HASTE image. The mean Dices indices are 0.70, 0.77 and 0.79 for the three methods based on VIBE images. DLMC is clearly more robust on the patients with the diseased pancreas while LS and MSM tend to over-segment the pancreas. DLMC also achieved higher sensitivity (0.80) and specificity (0.99) combining both imaging techniques. LS achieved equivalent sensitivity on VIBE images but was more computationally inefficient. Conclusion: We showed that pancreas and surrounding normal organs can be reliably segmented based on fast MRI using DLMC. This method will facilitate both planning volume definition and imaging guidance during treatment

TU-F-BRF-06: 3D Pancreas MRI Segmentation Using Dictionary Learning and Manifold Clustering

Energy Technology Data Exchange (ETDEWEB)

Gou, S; Rapacchi, S; Hu, P; Sheng, K [UCLA School of Medicine, Los Angeles, CA (United States)

2014-06-15

Purpose: The recent advent of MRI guided radiotherapy machines has lent an exciting platform for soft tissue target localization during treatment. However, tools to efficiently utilize MRI images for such purpose have not been developed. Specifically, to efficiently quantify the organ motion, we develop an automated segmentation method using dictionary learning and manifold clustering (DLMC). Methods: Fast 3D HASTE and VIBE MR images of 2 healthy volunteers and 3 patients were acquired. A bounding box was defined to include pancreas and surrounding normal organs including the liver, duodenum and stomach. The first slice of the MRI was used for dictionary learning based on mean-shift clustering and K-SVD sparse representation. Subsequent images were iteratively reconstructed until the error is less than a preset threshold. The preliminarily segmentation was subject to the constraints of manifold clustering. The segmentation results were compared with the mean shift merging (MSM), level set (LS) and manual segmentation methods. Results: DLMC resulted in consistently higher accuracy and robustness than comparing methods. Using manual contours as the ground truth, the mean Dices indices for all subjects are 0.54, 0.56 and 0.67 for MSM, LS and DLMC, respectively based on the HASTE image. The mean Dices indices are 0.70, 0.77 and 0.79 for the three methods based on VIBE images. DLMC is clearly more robust on the patients with the diseased pancreas while LS and MSM tend to over-segment the pancreas. DLMC also achieved higher sensitivity (0.80) and specificity (0.99) combining both imaging techniques. LS achieved equivalent sensitivity on VIBE images but was more computationally inefficient. Conclusion: We showed that pancreas and surrounding normal organs can be reliably segmented based on fast MRI using DLMC. This method will facilitate both planning volume definition and imaging guidance during treatment.

Machine learning control taming nonlinear dynamics and turbulence

CERN Document Server

Duriez, Thomas; Noack, Bernd R

2017-01-01

This is the first book on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. In Chapter 3, methods of linear control theory are reviewed. In Chapter 4, MLC is shown to reproduce known optimal control laws for linear dynamics (LQR, LQG). In Chapter 5, MLC detects and exploits a strongly nonlinear actuation mechanism of a low-dimensional dynamical system when linear control methods are shown to fail. Experimental control demonstrations from a laminar shear-layer to turbulent boundary-layers are reviewed in Chapter 6, followed by general good practices for experiments in Chapter 7. The book concludes with an outlook on the vast future applications of MLC in Chapter 8. Matlab codes are provided for easy reproducibility of the presented results. The book includes interviews with leading r...

Holonomy of Einstein Lorentzian manifolds

International Nuclear Information System (INIS)

Galaev, Anton S

2010-01-01

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp. vacuum Einstein) Lorentzian manifold; the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.

Eigenvalue pinching on spinc manifolds

Science.gov (United States)

Roos, Saskia

2017-02-01

We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.

Improving head and body pose estimation through semi-supervised manifold alignment

KAUST Repository

Heili, Alexandre

2014-10-27

In this paper, we explore the use of a semi-supervised manifold alignment method for domain adaptation in the context of human body and head pose estimation in videos. We build upon an existing state-of-the-art system that leverages on external labelled datasets for the body and head features, and on the unlabelled test data with weak velocity labels to do a coupled estimation of the body and head pose. While this previous approach showed promising results, the learning of the underlying manifold structure of the features in the train and target data and the need to align them were not explored despite the fact that the pose features between two datasets may vary according to the scene, e.g. due to different camera point of view or perspective. In this paper, we propose to use a semi-supervised manifold alignment method to bring the train and target samples closer within the resulting embedded space. To this end, we consider an adaptation set from the target data and rely on (weak) labels, given for example by the velocity direction whenever they are reliable. These labels, along with the training labels are used to bias the manifold distance within each manifold and to establish correspondences for alignment.

Oscillations in nonlinear systems

CERN Document Server

Hale, Jack K

2015-01-01

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

Harmonic maps of V-manifolds

International Nuclear Information System (INIS)

Chiang, Yuan-Jen.

1989-01-01

Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S

Descriptor Learning via Supervised Manifold Regularization for Multioutput Regression.

Science.gov (United States)

Zhen, Xiantong; Yu, Mengyang; Islam, Ali; Bhaduri, Mousumi; Chan, Ian; Li, Shuo

2017-09-01

Multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis. However, due to the huge image variability and ambiguity, it is fundamentally challenging to handle the highly complex input-target relationship of multioutput regression, especially with indiscriminate high-dimensional representations. In this paper, we propose a novel supervised descriptor learning (SDL) algorithm for multioutput regression, which can establish discriminative and compact feature representations to improve the multivariate estimation performance. The SDL is formulated as generalized low-rank approximations of matrices with a supervised manifold regularization. The SDL is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low-dimensional space aligned to targets. The achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression, which enables more accurate and efficient multivariate estimation. We conduct extensive evaluation of the proposed SDL on both synthetic data and real-world multioutput regression tasks for both computer vision and medical image analysis. Experimental results have shown that the proposed SDL can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts. Our method establishes a novel SDL framework for multioutput regression, which can be widely used to boost the performance in different applications.

The topology of toric origami manifolds

OpenAIRE

Holm, Tara; Pires, Ana Rita

2012-01-01

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co-orientable folding hypersurface. We prove that the cohomology i...

Smooth Maps of a Foliated Manifold in a Symplectic Manifold

Indian Academy of Sciences (India)

Let be a smooth manifold with a regular foliation F and a 2-form which induces closed forms on the leaves of F in the leaf topology. A smooth map f : ( M , F ) ⟶ ( N , ) in a symplectic manifold ( N , ) is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the ...

Constructions of Calabi-Yau manifolds

International Nuclear Information System (INIS)

Hubsch, T.

1987-01-01

Among possible compactifications of Superstring Theories (defined in 9+1 dimensional space-time) it is argued that only those in Calabi-Yau manifolds may lead to phenomenologically acceptable models. Thus, constructions of such manifolds are studied and a huge sequence is presented, giving rise to many possibly applicable manifolds

Individualized Learning Through Non-Linear use of Learning Objects: With Examples From Math and Stat

DEFF Research Database (Denmark)

Rootzén, Helle

2015-01-01

Our aim is to ensure individualized learning that is fun, inspiring and innovative. We believe that when you enjoy, your brain will open up and learning will be easier and more effective. The methods use a non-linear learning environment based on self-contained learning objects which are pieced t...

Smooth maps of a foliated manifold in a symplectic manifold

Indian Academy of Sciences (India)

Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.

Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing.

Science.gov (United States)

Elmoataz, Abderrahim; Lezoray, Olivier; Bougleux, Sébastien

2008-07-01

We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists of minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2-D and 3-D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds, and data represented as graphs.

Graded manifolds and supermanifolds

International Nuclear Information System (INIS)

Batchelor, M.

1984-01-01

In this paper, a review is presented on graded manifolds and supermanifolds. Many theorems, propositions, corrollaries, etc. are given with proofs or sketch proofs. Graded manifolds, supereuclidian space, Lie supergroups, etc. are dealt with

Hazy spaces, tangent spaces, manifolds and groups

International Nuclear Information System (INIS)

Dodson, C.T.J.

1977-03-01

The results on hazy spaces and the developments leading to hazy manifolds and groups are summarized. Proofs have appeared elsewhere so here examples are considered and some motivation for definitions and constructions in the theorems is analyzed. It is shown that quite simple ideas, intuitively acceptable, lead to remarkable similarity with the theory of differentiable manifolds. Hazy n manifolds have tangent bundles that are hazy 2n manifolds and there are hazy manifold structures for groups. Products and submanifolds are easily constructed and in particular the hazy n-sphere manifolds as submanifolds of the standard hazy manifold Zsup(n+1)

Flexible fuel cell gas manifold system

Science.gov (United States)

Cramer, Michael; Shah, Jagdish; Hayes, Richard P.; Kelley, Dana A.

2005-05-03

A fuel cell stack manifold system in which a flexible manifold body includes a pan having a central area, sidewall extending outward from the periphery of the central area, and at least one compound fold comprising a central area fold connecting adjacent portions of the central area and extending between opposite sides of the central area, and a sidewall fold connecting adjacent portions of the sidewall. The manifold system further includes a rail assembly for attachment to the manifold body and adapted to receive pins by which dielectric insulators are joined to the manifold assembly.

Differential manifolds

CERN Document Server

Kosinski, Antoni A

2007-01-01

The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho

Right-angled polyhedra and hyperbolic 3-manifolds

Science.gov (United States)

Vesnin, A. Yu.

2017-04-01

Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.

Topology of high-dimensional manifolds

Energy Technology Data Exchange (ETDEWEB)

Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)

2002-08-15

The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.

A novel approach for fire recognition using hybrid features and manifold learning-based classifier

Science.gov (United States)

Zhu, Rong; Hu, Xueying; Tang, Jiajun; Hu, Sheng

2018-03-01

Although image/video based fire recognition has received growing attention, an efficient and robust fire detection strategy is rarely explored. In this paper, we propose a novel approach to automatically identify the flame or smoke regions in an image. It is composed to three stages: (1) a block processing is applied to divide an image into several nonoverlapping image blocks, and these image blocks are identified as suspicious fire regions or not by using two color models and a color histogram-based similarity matching method in the HSV color space, (2) considering that compared to other information, the flame and smoke regions have significant visual characteristics, so that two kinds of image features are extracted for fire recognition, where local features are obtained based on the Scale Invariant Feature Transform (SIFT) descriptor and the Bags of Keypoints (BOK) technique, and texture features are extracted based on the Gray Level Co-occurrence Matrices (GLCM) and the Wavelet-based Analysis (WA) methods, and (3) a manifold learning-based classifier is constructed based on two image manifolds, which is designed via an improve Globular Neighborhood Locally Linear Embedding (GNLLE) algorithm, and the extracted hybrid features are used as input feature vectors to train the classifier, which is used to make decision for fire images or non fire images. Experiments and comparative analyses with four approaches are conducted on the collected image sets. The results show that the proposed approach is superior to the other ones in detecting fire and achieving a high recognition accuracy and a low error rate.

Nonlinear Motion Tracking by Deep Learning Architecture

Science.gov (United States)

Verma, Arnav; Samaiya, Devesh; Gupta, Karunesh K.

2018-03-01

In the world of Artificial Intelligence, object motion tracking is one of the major problems. The extensive research is being carried out to track people in crowd. This paper presents a unique technique for nonlinear motion tracking in the absence of prior knowledge of nature of nonlinear path that the object being tracked may follow. We achieve this by first obtaining the centroid of the object and then using the centroid as the current example for a recurrent neural network trained using real-time recurrent learning. We have tweaked the standard algorithm slightly and have accumulated the gradient for few previous iterations instead of using just the current iteration as is the norm. We show that for a single object, such a recurrent neural network is highly capable of approximating the nonlinearity of its path.

Connections and curvatures on complex Riemannian manifolds

International Nuclear Information System (INIS)

Ganchev, G.; Ivanov, S.

1991-05-01

Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs

Convex nonnegative matrix factorization with manifold regularization.

Science.gov (United States)

Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong

2015-03-01

Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Background field method for nonlinear σ-model in stochastic quantization

International Nuclear Information System (INIS)

Nakazawa, Naohito; Ennyu, Daiji

1988-01-01

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model. (orig.)

Canonical action-angle formalism for quantized nonlinear fields

International Nuclear Information System (INIS)

Garbaczewki, P.

1987-01-01

The canonical quantizations of field and action-angle coordinates which (locally) parameterize the phase manifold for the same nonlinear field theory model (e.g. sine-Gordon and nonlinear Schrodinger with the attractive coupling) are reconciled on the common for both cases state space. The classical-quantum relationship is maintained in the mean: coherent state expectation values of operators give rise to classical objects

Strongly not relatives Kähler manifolds

Directory of Open Access Journals (Sweden)

Zedda Michela

2017-02-01

Full Text Available In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.

Differential geometry of quasi-Sasakian manifolds

International Nuclear Information System (INIS)

Kirichenko, V F; Rustanov, A R

2002-01-01

The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of CR 1 quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the B-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind

Manifold seal structure for fuel cell stack

Science.gov (United States)

Collins, William P.

1988-01-01

The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.

Formation Learning Control of Multiple Autonomous Underwater Vehicles With Heterogeneous Nonlinear Uncertain Dynamics.

Science.gov (United States)

Yuan, Chengzhi; Licht, Stephen; He, Haibo

2017-09-26

In this paper, a new concept of formation learning control is introduced to the field of formation control of multiple autonomous underwater vehicles (AUVs), which specifies a joint objective of distributed formation tracking control and learning/identification of nonlinear uncertain AUV dynamics. A novel two-layer distributed formation learning control scheme is proposed, which consists of an upper-layer distributed adaptive observer and a lower-layer decentralized deterministic learning controller. This new formation learning control scheme advances existing techniques in three important ways: 1) the multi-AUV system under consideration has heterogeneous nonlinear uncertain dynamics; 2) the formation learning control protocol can be designed and implemented by each local AUV agent in a fully distributed fashion without using any global information; and 3) in addition to the formation control performance, the distributed control protocol is also capable of accurately identifying the AUVs' heterogeneous nonlinear uncertain dynamics and utilizing experiences to improve formation control performance. Extensive simulations have been conducted to demonstrate the effectiveness of the proposed results.

Generalized graph manifolds and their effective recognition

International Nuclear Information System (INIS)

Matveev, S V

1998-01-01

A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented

On some classes of super quasi-Einstein manifolds

International Nuclear Information System (INIS)

Ozguer, Cihan

2009-01-01

Quasi-Einstein and generalized quasi-Einstein manifolds are the generalizations of Einstein manifolds. In this study, we consider a super quasi-Einstein manifold, which is another generalization of an Einstein manifold. We find the curvature characterizations of a Ricci-pseudosymmetric and a quasi-conformally flat super quasi-Einstein manifolds. We also consider the condition C ∼ .S=0 on a super quasi-Einstein manifold, where C ∼ and S denote the quasi-conformal curvature tensor and Ricci tensor of the manifold, respectively.

Natural Connections on Riemannian Product Manifolds

OpenAIRE

Gribacheva, Dobrinka

2011-01-01

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

The manifold model for space-time

International Nuclear Information System (INIS)

Heller, M.

1981-01-01

Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)

Visual words assignment via information-theoretic manifold embedding.

Science.gov (United States)

Deng, Yue; Li, Yipeng; Qian, Yanjun; Ji, Xiangyang; Dai, Qionghai

2014-10-01

Codebook-based learning provides a flexible way to extract the contents of an image in a data-driven manner for visual recognition. One central task in such frameworks is codeword assignment, which allocates local image descriptors to the most similar codewords in the dictionary to generate histogram for categorization. Nevertheless, existing assignment approaches, e.g., nearest neighbors strategy (hard assignment) and Gaussian similarity (soft assignment), suffer from two problems: 1) too strong Euclidean assumption and 2) neglecting the label information of the local descriptors. To address the aforementioned two challenges, we propose a graph assignment method with maximal mutual information (GAMI) regularization. GAMI takes the power of manifold structure to better reveal the relationship of massive number of local features by nonlinear graph metric. Meanwhile, the mutual information of descriptor-label pairs is ultimately optimized in the embedding space for the sake of enhancing the discriminant property of the selected codewords. According to such objective, two optimization models, i.e., inexact-GAMI and exact-GAMI, are respectively proposed in this paper. The inexact model can be efficiently solved with a closed-from solution. The stricter exact-GAMI nonparametrically estimates the entropy of descriptor-label pairs in the embedding space and thus leads to a relatively complicated but still trackable optimization. The effectiveness of GAMI models are verified on both the public and our own datasets.

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

Science.gov (United States)

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

Seismic Target Classification Using a Wavelet Packet Manifold in Unattended Ground Sensors Systems

Directory of Open Access Journals (Sweden)

Enliang Song

2013-07-01

Full Text Available One of the most challenging problems in target classification is the extraction of a robust feature, which can effectively represent a specific type of targets. The use of seismic signals in unattended ground sensor (UGS systems makes this problem more complicated, because the seismic target signal is non-stationary, geology-dependent and with high-dimensional feature space. This paper proposes a new feature extraction algorithm, called wavelet packet manifold (WPM, by addressing the neighborhood preserving embedding (NPE algorithm of manifold learning on the wavelet packet node energy (WPNE of seismic signals. By combining non-stationary information and low-dimensional manifold information, WPM provides a more robust representation for seismic target classification. By using a K nearest neighbors classifier on the WPM signature, the algorithm of wavelet packet manifold classification (WPMC is proposed. Experimental results show that the proposed WPMC can not only reduce feature dimensionality, but also improve the classification accuracy up to 95.03%. Moreover, compared with state-of-the-art methods, WPMC is more suitable for UGS in terms of recognition ratio and computational complexity.

Analysis of mixed mode microwave distribution manifolds

International Nuclear Information System (INIS)

White, T.L.

1982-09-01

The 28-GHz microwave distribution manifold used in the ELMO Bumpy Torus-Scale (EBT-S) experiments consists of a toroidal metallic cavity, whose dimensions are much greater than a wavelength, fed by a source of microwave power. Equalization of the mixed mode power distribution ot the 24 cavities of EBT-S is accomplished by empirically adjusting the coupling irises which are equally spaced around the manifold. The performance of the manifold to date has been very good, yet no analytical models exist for optimizing manifold transmission efficiency or for scaling this technology to the EBT-P manifold design. The present report develops a general model for mixed mode microwave distribution manifolds based on isotropic plane wave sources of varying amplitudes that are distributed toroidally around the manifold. The calculated manifold transmission efficiency for the most recent EBT-S coupling iris modification is 90%. This agrees with the average measured transmission efficiency. Also, the model predicts the coupling iris areas required to balance the distribution of microwave power while maximizing transmission efficiency, and losses in waveguide feeds connecting the irises to the cavities of EBT are calculated using an approach similar to the calculation of mainfold losses. The model will be used to evaluate EBT-P manifold designs

The simplex method for nonlinear sliding mode control

Directory of Open Access Journals (Sweden)

Bartolini G.

1998-01-01

Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.

Solution path for manifold regularized semisupervised classification.

Science.gov (United States)

Wang, Gang; Wang, Fei; Chen, Tao; Yeung, Dit-Yan; Lochovsky, Frederick H

2012-04-01

Traditional learning algorithms use only labeled data for training. However, labeled examples are often difficult or time consuming to obtain since they require substantial human labeling efforts. On the other hand, unlabeled data are often relatively easy to collect. Semisupervised learning addresses this problem by using large quantities of unlabeled data with labeled data to build better learning algorithms. In this paper, we use the manifold regularization approach to formulate the semisupervised learning problem where a regularization framework which balances a tradeoff between loss and penalty is established. We investigate different implementations of the loss function and identify the methods which have the least computational expense. The regularization hyperparameter, which determines the balance between loss and penalty, is crucial to model selection. Accordingly, we derive an algorithm that can fit the entire path of solutions for every value of the hyperparameter. Its computational complexity after preprocessing is quadratic only in the number of labeled examples rather than the total number of labeled and unlabeled examples.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

Science.gov (United States)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process

Directory of Open Access Journals (Sweden)

Dazi Li

2015-01-01

Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.

Heterotic model building: 16 special manifolds

International Nuclear Information System (INIS)

He, Yang-Hui; Lee, Seung-Joo; Lukas, Andre; Sun, Chuang

2014-01-01

We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.

On the trace-manifold generated by the deformations of a body-manifold

Directory of Open Access Journals (Sweden)

Boja Nicolae

2003-01-01

Full Text Available In this paper, concerned to the study of continuous deformations of material media using some tools of modem differential geometry, a moving frame of Frenet type along the orbits of an one-parameter group acting on a so-called "trace-manifold", M, associated to the deformations, is constructed. The manifold M is defined as an infinite union of non-disjoint compact manifolds, generated by the consecutive positions in the Euclidean affine 3-space of a body-manifold under deformations in a closed time interval. We put in evidence a skew-symmetric band tensor of second order, ω, which describes the deformation in a small neighborhood of any point along the orbits. The non-null components ωi,i+i, (i =1,2, of ω are assimilated as like curvatures at each point of an orbit in the planes generated by the pairs of vectors (ĕi,ĕi+i of a moving frame in M associated to the orbit in a similar way as the Frenet's frame is. Also a formula for the energy of the orbits is given and its relationship with some stiffness matrices is established.

Robinson manifolds and Cauchy-Riemann spaces

CERN Document Server

Trautman, A

2002-01-01

A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...

Understanding 3D human torso shape via manifold clustering

Science.gov (United States)

Li, Sheng; Li, Peng; Fu, Yun

2013-05-01

Discovering the variations in human torso shape plays a key role in many design-oriented applications, such as suit designing. With recent advances in 3D surface imaging technologies, people can obtain 3D human torso data that provide more information than traditional measurements. However, how to find different human shapes from 3D torso data is still an open problem. In this paper, we propose to use spectral clustering approach on torso manifold to address this problem. We first represent high-dimensional torso data in a low-dimensional space using manifold learning algorithm. Then the spectral clustering method is performed to get several disjoint clusters. Experimental results show that the clusters discovered by our approach can describe the discrepancies in both genders and human shapes, and our approach achieves better performance than the compared clustering method.

Adaptive nodes enrich nonlinear cooperative learning beyond traditional adaptation by links.

Science.gov (United States)

Sardi, Shira; Vardi, Roni; Goldental, Amir; Sheinin, Anton; Uzan, Herut; Kanter, Ido

2018-03-23

Physical models typically assume time-independent interactions, whereas neural networks and machine learning incorporate interactions that function as adjustable parameters. Here we demonstrate a new type of abundant cooperative nonlinear dynamics where learning is attributed solely to the nodes, instead of the network links which their number is significantly larger. The nodal, neuronal, fast adaptation follows its relative anisotropic (dendritic) input timings, as indicated experimentally, similarly to the slow learning mechanism currently attributed to the links, synapses. It represents a non-local learning rule, where effectively many incoming links to a node concurrently undergo the same adaptation. The network dynamics is now counterintuitively governed by the weak links, which previously were assumed to be insignificant. This cooperative nonlinear dynamic adaptation presents a self-controlled mechanism to prevent divergence or vanishing of the learning parameters, as opposed to learning by links, and also supports self-oscillations of the effective learning parameters. It hints on a hierarchical computational complexity of nodes, following their number of anisotropic inputs and opens new horizons for advanced deep learning algorithms and artificial intelligence based applications, as well as a new mechanism for enhanced and fast learning by neural networks.

On Kähler–Norden manifolds

Indian Academy of Sciences (India)

Abstract. This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.

Analytic manifolds in uniform algebras

International Nuclear Information System (INIS)

Tonev, T.V.

1988-12-01

Here we extend Bear-Hile's result concerning the version of famous Bishop's theorem for one-dimensional analytic structures in two directions: for n-dimensional complex analytic manifolds, n>1, and for generalized analytic manifolds. 14 refs

Hamiltonian PDEs and Frobenius manifolds

International Nuclear Information System (INIS)

Dubrovin, Boris A

2008-01-01

In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

Hamiltonian PDEs and Frobenius manifolds

Energy Technology Data Exchange (ETDEWEB)

Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2008-12-31

In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.

S-matrix regularities of two-dimensional sigma-models of Stiefel manifolds

International Nuclear Information System (INIS)

Flume-Gorczyca, B.

1980-01-01

The S-matrices of the two-dimensional nonlinear O(n + m)/O(n) and O(n + m)/O(n) x O(m) sigma-models corresponding to Stiefel and Grassmann manifolds, respectively, are compared in leading order in 1/n. It is shown, that after averaging over O(m) labels of the incoming and outgoing particles, the S-matrices of both models become identical. This result explains why commonly expected regularities of the Grassmann models, in particular absence of particle production, are found, modulo an O(m) average, also in Stiefel models. (orig.)

Slow manifolds in chemical kinetics

International Nuclear Information System (INIS)

Shahzad, M.; Haq, I. U.; Sultan, F.; Wahab, A.; Faizullah, F.; Rahman, G. U.

2016-01-01

Modelling the chemical system, especially for complex and higher dimensional problems, gives an easy way to handle the ongoing reaction process with respect to time. Here, we will consider some of the newly developed computational methods commonly used for model reductions in a chemical reaction. An effective (simple) method is planned to measure the low dimensional manifold, which reduces the higher dimensional system in such a way that it may not affect the precision of the whole mechanism. The phase flow of the solution trajectories near the equilibrium point is observed while the initial approximation is measured with the spectral quasi equilibrium manifold, which starts from the equilibrium point. To make it an invariant curve, the approximated curve is first refined a certain number of times using the method of invariant grids. The other way of getting the reduced data in the low dimensional manifold is possible through the intrinsic low dimensional manifold. Then, we compare these two invariant curves given by both the methods. Finally, the idea is extended to the higher dimensional manifold, where more number of progress variables will be added. (author)

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

Science.gov (United States)

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Hirzebruch genera of manifolds with torus action

International Nuclear Information System (INIS)

Panov, T E

2001-01-01

A quasitoric manifold is a smooth 2n-manifold M 2n with an action of the compact torus T n such that the action is locally isomorphic to the standard action of T n on C n and the orbit space is diffeomorphic, as a manifold with corners, to a simple polytope P n . The name refers to the fact that topological and combinatorial properties of quasitoric manifolds are similar to those of non-singular algebraic toric varieties (or toric manifolds). Unlike toric varieties, quasitoric manifolds may fail to be complex. However, they always admit a stably (or weakly almost) complex structure, and their cobordism classes generate the complex cobordism ring. Buchstaber and Ray have recently shown that the stably complex structure on a quasitoric manifold is determined in purely combinatorial terms, namely, by an orientation of the polytope and a function from the set of codimension-one faces of the polytope to primitive vectors of the integer lattice. We calculate the χ y -genus of a quasitoric manifold with a fixed stably complex structure in terms of the corresponding combinatorial data. In particular, this gives explicit formulae for the classical Todd genus and the signature. We also compare our results with well-known facts in the theory of toric varieties

Non-Kaehler attracting manifolds

International Nuclear Information System (INIS)

Dall'Agata, Gianguido

2006-01-01

We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski 'attractor points' for 3-form fluxes are special-hermitian manifolds

Rigorous high-precision enclosures of fixed points and their invariant manifolds

Science.gov (United States)

Wittig, Alexander N.

The well established concept of Taylor Models is introduced, which offer highly accurate C0 enclosures of functional dependencies, combining high-order polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly non-linear dynamical systems. A method is proposed to extend the existing implementation of Taylor Models in COSY INFINITY from double precision coefficients to arbitrary precision coefficients. Great care is taken to maintain the highest efficiency possible by adaptively adjusting the precision of higher order coefficients in the polynomial expansion. High precision operations are based on clever combinations of elementary floating point operations yielding exact values for round-off errors. An experimental high precision interval data type is developed and implemented. Algorithms for the verified computation of intrinsic functions based on the High Precision Interval datatype are developed and described in detail. The application of these operations in the implementation of High Precision Taylor Models is discussed. An application of Taylor Model methods to the verification of fixed points is presented by verifying the existence of a period 15 fixed point in a near standard Henon map. Verification is performed using different verified methods such as double precision Taylor Models, High Precision intervals and High Precision Taylor Models. Results and performance of each method are compared. An automated rigorous fixed point finder is implemented, allowing the fully automated search for all fixed points of a function within a given domain. It returns a list of verified enclosures of each fixed point, optionally verifying uniqueness within these enclosures. An application of the fixed point finder to the rigorous analysis of beam transfer maps in accelerator physics is presented. Previous work done by

Controllability of non-linear systems: generic singularities and their stability

International Nuclear Information System (INIS)

Davydov, Alexey A; Zakalyukin, Vladimir M

2012-01-01

This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.

Engineering high-order nonlinear dissipation for quantum superconducting circuits

Science.gov (United States)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

Machinery fault diagnosis using joint global and local/nonlocal discriminant analysis with selective ensemble learning

Science.gov (United States)

Yu, Jianbo

2016-11-01

The vibration signals of faulty machine are generally non-stationary and nonlinear under those complicated working conditions. Thus, it is a big challenge to extract and select the effective features from vibration signals for machinery fault diagnosis. This paper proposes a new manifold learning algorithm, joint global and local/nonlocal discriminant analysis (GLNDA), which aims to extract effective intrinsic geometrical information from the given vibration data. Comparisons with other regular methods, principal component analysis (PCA), local preserving projection (LPP), linear discriminant analysis (LDA) and local LDA (LLDA), illustrate the superiority of GLNDA in machinery fault diagnosis. Based on the extracted information by GLNDA, a GLNDA-based Fisher discriminant rule (FDR) is put forward and applied to machinery fault diagnosis without additional recognizer construction procedure. By importing Bagging into GLNDA score-based feature selection and FDR, a novel manifold ensemble method (selective GLNDA ensemble, SE-GLNDA) is investigated for machinery fault diagnosis. The motivation for developing ensemble of manifold learning components is that it can achieve higher accuracy and applicability than single component in machinery fault diagnosis. The effectiveness of the SE-GLNDA-based fault diagnosis method has been verified by experimental results from bearing full life testers.

Kernel and wavelet density estimators on manifolds and more general metric spaces

DEFF Research Database (Denmark)

Cleanthous, G.; Georgiadis, Athanasios; Kerkyacharian, G.

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the development of smooth functional calculus with well localized...... spectral kernels, Besov regularity spaces, and wavelet type systems. Kernel and both linear and nonlinear wavelet density estimators are introduced and studied. Convergence rates for these estimators are established, which are analogous to the existing results in the classical setting of real...

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects

Four-manifolds, geometries and knots

CERN Document Server

Hillman, Jonathan A

2007-01-01

The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...

An introduction to differential manifolds

CERN Document Server

Lafontaine, Jacques

2015-01-01

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...

Function approximation using combined unsupervised and supervised learning.

Science.gov (United States)

Andras, Peter

2014-03-01

Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

Pluripotential theory on quaternionic manifolds

Science.gov (United States)

Alesker, Semyon

2012-05-01

On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003) [1] for the flat quaternionic space Hn and in Alesker and Verbitsky (2006) [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.

Manifolds of positive scalar curvature

Energy Technology Data Exchange (ETDEWEB)

Stolz, S [Department of Mathematics, University of Notre Dame, Notre Dame (United States)

2002-08-15

This lecture gives an survey on the problem of finding a positive scalar curvature metric on a closed manifold. The Gromov-Lawson-Rosenberg conjecture and its relation to the Baum-Connes conjecture are discussed and the problem of finding a positive Ricci curvature metric on a closed manifold is explained.

Approaches to analysis of data that concentrate near higher-dimensional manifolds

International Nuclear Information System (INIS)

Friedman, J.H.; Tukey, J.W.; Tukey, P.A.

1979-01-01

The need to explore structure in high-dimensional clouds of data points that may concentrate near (possibly nonlinear) manifolds of lower dimension led to the current development of three new approaches. The first is a computer-graphic system (PRIM'79) that facilitates interactive viewing and manipulation of an ensemble of points. The other two are automatic procedures for separating a cloud into more manageable pieces. One of these (BIDEC) performs successive partitioning of the cloud by use of hyperplanes; the other (Cake Maker) explores expanding sequences of neighborhoods. Both procedures provide facilities for examining the resulting pieces and the relationships among them

Some theorems on a class of harmonic manifolds

International Nuclear Information System (INIS)

Rahman, M.S.; Chen Weihuan.

1993-08-01

A class of harmonic n-manifold, denoted by HM n , is, in fact, focussed on a Riemannian manifold with harmonic curvature. A variety of results, with properties, on HM n is presented in a fair order. Harmonic manifolds are then touched upon manifolds with recurrent Ricci curvature, biRicci-recurrent curvature and recurrent conformal curvature, and, in consequence, a sequence of theorems are deduced. (author). 21 refs

On Riemannian manifolds (Mn, g) of quasi-constant curvature

International Nuclear Information System (INIS)

Rahman, M.S.

1995-07-01

A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs

Reduced order models inertial manifold and global bifurcations: searching instability boundaries in nuclear power systems

International Nuclear Information System (INIS)

Suarez Antola, R.

2009-01-01

In the framework of an analytic or numerical model of a BWR power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behaviour of this nonlinear system, and then a classification of the different solution types concerning their relation with the operational safety of the power plant, by distributing the different solution types in relation with the exclusion region of the power-flow map. Then the goal is to obtain the best attainable qualitative and quantitative global picture of plant dynamics. To do this, the construction and the analysis of the so called reduced order models (Rom) seems a necessary step. A reduced order model results after the full system of coupled nonlinear partial differential equations of the plant is reduced to a system of coupled nonlinear ordinary differential equations

Minimal genera of open 4-manifolds

OpenAIRE

Gompf, Robert E.

2013-01-01

We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with much more control of these genus functions than the compact setting seems to allow. As an application, we expand the range of 4-manifolds known to have exotic smoothings (up to ...

Higher-order Jordan Osserman pseudo-Riemannian manifolds

International Nuclear Information System (INIS)

Gilkey, Peter B; Ivanova, Raina; Zhang Tan

2002-01-01

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds

Higher-order Jordan Osserman pseudo-Riemannian manifolds

Energy Technology Data Exchange (ETDEWEB)

Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)

2002-09-07

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.

A viewpoint on nearly conformally symmetric manifold

International Nuclear Information System (INIS)

Rahman, M.S.

1990-06-01

Some observations, with definition, on Nearly Conformally Symmetric (NCS) manifold are made. A number of theorems concerning conformal change of metric and parallel tensors on NCS manifolds are presented. It is illustrated that a manifold M = R n-1 x R + 1 , endowed with a special metric, is NCS but not of harmonic curvature. (author). 8 refs

Nonlinear Semi-Supervised Metric Learning Via Multiple Kernels and Local Topology.

Science.gov (United States)

Li, Xin; Bai, Yanqin; Peng, Yaxin; Du, Shaoyi; Ying, Shihui

2018-03-01

Changing the metric on the data may change the data distribution, hence a good distance metric can promote the performance of learning algorithm. In this paper, we address the semi-supervised distance metric learning (ML) problem to obtain the best nonlinear metric for the data. First, we describe the nonlinear metric by the multiple kernel representation. By this approach, we project the data into a high dimensional space, where the data can be well represented by linear ML. Then, we reformulate the linear ML by a minimization problem on the positive definite matrix group. Finally, we develop a two-step algorithm for solving this model and design an intrinsic steepest descent algorithm to learn the positive definite metric matrix. Experimental results validate that our proposed method is effective and outperforms several state-of-the-art ML methods.

The Hodge theory of projective manifolds

CERN Document Server

de Cataldo, Mark Andrea

2007-01-01

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.

Transition Manifolds of Complex Metastable Systems

Science.gov (United States)

Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof

2018-04-01

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Learning on probabilistic manifolds in massive fusion databases: Application to confinement regime identification

International Nuclear Information System (INIS)

Verdoolaege, Geert; Van Oost, Guido

2012-01-01

Highlights: ► We present an integrated framework for pattern recognition in fusion data. ► We model measurement uncertainty through an appropriate probability distribution. ► We use the geodesic distance on probabilistic manifolds as a similarity measure. ► We apply the framework to confinement mode classification. ► The classification accuracy benefits from uncertainty information and its geometry. - Abstract: We present an integrated framework for (real-time) pattern recognition in fusion data. The main premise is the inherent probabilistic nature of measurements of plasma quantities. We propose the geodesic distance on probabilistic manifolds as a similarity measure between data points. Substructure induced by data dependencies may further reduce the dimensionality and redundancy of the data set. We present an application to confinement mode classification, showing the distinct advantage obtained by considering the measurement uncertainty and its geometry.

Current algebra of classical non-linear sigma models

International Nuclear Information System (INIS)

Forger, M.; Laartz, J.; Schaeper, U.

1992-01-01

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)

New complete noncompact Spin(7) manifolds

International Nuclear Information System (INIS)

Cvetic, M.; Gibbons, G.W.; Lue, H.; Pope, C.N.

2002-01-01

We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by (A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4 . Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4 , our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2 -normalisable harmonic 4-form for the (A)) 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 - similar to B 8

Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

Directory of Open Access Journals (Sweden)

Fan Yang

2015-07-01

Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.

Learning Inverse Rig Mappings by Nonlinear Regression.

Science.gov (United States)

Holden, Daniel; Saito, Jun; Komura, Taku

2017-03-01

We present a framework to design inverse rig-functions-functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.

Spectral gaps, inertial manifolds and kinematic dynamos

Energy Technology Data Exchange (ETDEWEB)

Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es

2005-10-17

Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.

Space time manifolds and contact structures

Directory of Open Access Journals (Sweden)

K. L. Duggal

1990-01-01

Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.

On complete manifolds supporting a weighted Sobolev type inequality

International Nuclear Information System (INIS)

Adriano, Levi; Xia Changyu

2011-01-01

Highlights: → We study manifolds supporting a weighted Sobolev or log-Sobolev inequality. → We investigate manifolds of asymptotically non-negative Ricci curvature. → The constant in the weighted Sobolev inequality on complete manifolds is studied. - Abstract: This paper studies the geometric and topological properties of complete open Riemannian manifolds which support a weighted Sobolev or log-Sobolev inequality. We show that the constant in the weighted Sobolev inequality on a complete open Riemannian manifold should be bigger than or equal to the optimal one on the Euclidean space of the same dimension and that a complete open manifold of asymptotically non-negative Ricci curvature supporting a weighted Sobolev inequality must have large volume growth. We also show that a complete manifold of non-negative Ricci curvature on which the log-Sobolev inequality holds is not very far from the Euclidean space.

Sasakian manifolds and M-theory

International Nuclear Information System (INIS)

Figueroa-O’Farrill, José; Santi, Andrea

2016-01-01

We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of η-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterizing them in terms of generalized Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a new class of such backgrounds, extending previous work of Haupt, Lukas and Stelle. (paper)

Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Lauze, Francois Bernard; Hauberg, Søren

2010-01-01

, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations...... and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking...

Total Generalized Variation for Manifold-valued Data

OpenAIRE

Bredies, K.; Holler, M.; Storath, M.; Weinmann, A.

2017-01-01

In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the manifold setting and present two possible concrete instances that fulfill the proposed axioms. We provide well-posedness results and present algorithms for a numerical realization of these generalizations to the manifold setup. Further, we provide experimental results for syntheti...

Moduli space of Calabi-Yau manifolds

International Nuclear Information System (INIS)

Candelas, P.; De la Ossa, X.C.

1991-01-01

We present an accessible account of the local geometry of the parameter space of Calabi-Yau manifolds. It is shown that the parameter space decomposes, at least locally, into a product with the space of parameters of the complex structure as one factor and a complex extension of the parameter space of the Kaehler class as the other. It is also shown that each of these spaces is itself a Kaehler manifold and is moreover a Kaehler manifold of restricted type. There is a remarkable symmetry in the intrinsic structures of the two parameter spaces and the relevance of this to the conjectured existence of mirror manifolds is discussed. The two parameter spaces behave differently with respect to modular transformations and it is argued that the role of quantum corrections is to restore the symmetry between the two types of parameters so as to enforce modular invariance. (orig.)

Nonassociative geometry of manifold with trajectories

International Nuclear Information System (INIS)

Bouetou, T.B.; Matveev, O.A.

2004-12-01

We give some properties of solution of second order differential or system of differential equations on the manifold. It turns out that such manifolds can be seen as quasigroups or loop under certain circumstances. Output of the operations are given and the connection defined. (author)

A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds

OpenAIRE

Baker, Mark; Cooper, Daryl

2005-01-01

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...

Characteristic manifolds in relativistic hypoelasticity

Energy Technology Data Exchange (ETDEWEB)

Giambo, S [Messina Univ. (Italy). Istituto di Matematica

1978-10-02

The relativistic hypoelasticity is considered and the characteristic manifolds are determined by using the Cauchy-Kovalevski theorem for the Cauchy problem with analytic initial conditions. Taking into account that the characteristic manifold represents the image of the front-wave in the space-time, it is possible to determine the velocities of propagation. Three wave-species are obtained: material waves, longitudinal waves and transverse waves.

Vector Fields on Product Manifolds

OpenAIRE

Kurz, Stefan

2011-01-01

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.

The structure of some classes of K-contact manifolds

Indian Academy of Sciences (India)

Abstract. We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi ...

Discriminative Nonlinear Analysis Operator Learning: When Cosparse Model Meets Image Classification.

Science.gov (United States)

Wen, Zaidao; Hou, Biao; Jiao, Licheng

2017-05-03

Linear synthesis model based dictionary learning framework has achieved remarkable performances in image classification in the last decade. Behaved as a generative feature model, it however suffers from some intrinsic deficiencies. In this paper, we propose a novel parametric nonlinear analysis cosparse model (NACM) with which a unique feature vector will be much more efficiently extracted. Additionally, we derive a deep insight to demonstrate that NACM is capable of simultaneously learning the task adapted feature transformation and regularization to encode our preferences, domain prior knowledge and task oriented supervised information into the features. The proposed NACM is devoted to the classification task as a discriminative feature model and yield a novel discriminative nonlinear analysis operator learning framework (DNAOL). The theoretical analysis and experimental performances clearly demonstrate that DNAOL will not only achieve the better or at least competitive classification accuracies than the state-of-the-art algorithms but it can also dramatically reduce the time complexities in both training and testing phases.

Submanifolds of a Finsler manifold - I

International Nuclear Information System (INIS)

Rastogi, S.C.

1986-06-01

In 1981, Hojo defined a scalar function φ (p) (x,y), where p is a real number (not= 1). He used this function to define a tensor φ ij (p) (x,y) and a c P Γ-connection which reduce to g ij (x,y) and cΓ-connection for p=2. The aim of this paper is to study submanifolds of a Finsler manifold admitting a c P Γ-connection. In this paper I have obtained four kinds of Gauss-Codazzi equations based on various derivatives in a Finsler manifold admitting a c P Γ-connection. The method used in this paper is similar to the one used by the author in obtaining generalized Gauss-Codazzi equations based on congruences of curves in a Finsler manifold. Besides considering some special cases we have also studied the relationship between the Riemannian curvatures and Ricci tensors of the submanifold and the enveloping manifold. (author)

Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds

Indian Academy of Sciences (India)

We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...

Unsupervised image matching based on manifold alignment.

Science.gov (United States)

Pei, Yuru; Huang, Fengchun; Shi, Fuhao; Zha, Hongbin

2012-08-01

This paper challenges the issue of automatic matching between two image sets with similar intrinsic structures and different appearances, especially when there is no prior correspondence. An unsupervised manifold alignment framework is proposed to establish correspondence between data sets by a mapping function in the mutual embedding space. We introduce a local similarity metric based on parameterized distance curves to represent the connection of one point with the rest of the manifold. A small set of valid feature pairs can be found without manual interactions by matching the distance curve of one manifold with the curve cluster of the other manifold. To avoid potential confusions in image matching, we propose an extended affine transformation to solve the nonrigid alignment in the embedding space. The comparatively tight alignments and the structure preservation can be obtained simultaneously. The point pairs with the minimum distance after alignment are viewed as the matchings. We apply manifold alignment to image set matching problems. The correspondence between image sets of different poses, illuminations, and identities can be established effectively by our approach.

Markerless gating for lung cancer radiotherapy based on machine learning techniques

International Nuclear Information System (INIS)

Lin Tong; Li Ruijiang; Tang Xiaoli; Jiang, Steve B; Dy, Jennifer G

2009-01-01

In lung cancer radiotherapy, radiation to a mobile target can be delivered by respiratory gating, for which we need to know whether the target is inside or outside a predefined gating window at any time point during the treatment. This can be achieved by tracking one or more fiducial markers implanted inside or near the target, either fluoroscopically or electromagnetically. However, the clinical implementation of marker tracking is limited for lung cancer radiotherapy mainly due to the risk of pneumothorax. Therefore, gating without implanted fiducial markers is a promising clinical direction. We have developed several template-matching methods for fluoroscopic marker-less gating. Recently, we have modeled the gating problem as a binary pattern classification problem, in which principal component analysis (PCA) and support vector machine (SVM) are combined to perform the classification task. Following the same framework, we investigated different combinations of dimensionality reduction techniques (PCA and four nonlinear manifold learning methods) and two machine learning classification methods (artificial neural networks-ANN and SVM). Performance was evaluated on ten fluoroscopic image sequences of nine lung cancer patients. We found that among all combinations of dimensionality reduction techniques and classification methods, PCA combined with either ANN or SVM achieved a better performance than the other nonlinear manifold learning methods. ANN when combined with PCA achieves a better performance than SVM in terms of classification accuracy and recall rate, although the target coverage is similar for the two classification methods. Furthermore, the running time for both ANN and SVM with PCA is within tolerance for real-time applications. Overall, ANN combined with PCA is a better candidate than other combinations we investigated in this work for real-time gated radiotherapy.

Non-linear realization of the Virasoro-Kac-Moody algebra and the anomalies

International Nuclear Information System (INIS)

Aoyama, S.

1988-01-01

The non-linear realization of the Virasoro algebra x Kac-Moody algebra will be studied. We will calculate the Ricci tensor of the relevant Kaehler manifold to show a new vacuum structure for this coupled algebra. (orig.)

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

Science.gov (United States)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Global dynamics and control of a comprehensive nonlinear beam equation

International Nuclear Information System (INIS)

You Yuncheng; Taboada, M.

1994-01-01

A nonlinear hinged extensible elastic beam equation with the structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures. It is proved that there exists an absorbing set in the energy space and that there exist inertial manifolds whose exponential attracting rates however are nonuniform. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite-dimensional feedback control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to uncertainty in the structural parameters. (author). 5 refs

PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.

Science.gov (United States)

Xia, Jing; Wang, Michelle Yongmei

Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.

Massively parallel unsupervised single-particle cryo-EM data clustering via statistical manifold learning.

Directory of Open Access Journals (Sweden)

Jiayi Wu

Full Text Available Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the assessment of structural heterogeneity. However, traditional algorithms for unsupervised classification, such as K-means clustering and maximum likelihood optimization, may classify images into wrong classes with decreasing signal-to-noise-ratio (SNR in the image data, yet demand increased computational costs. Overcoming these limitations requires further development of clustering algorithms for high-performance cryo-EM data processing. Here we introduce an unsupervised single-particle clustering algorithm derived from a statistical manifold learning framework called generative topographic mapping (GTM. We show that unsupervised GTM clustering improves classification accuracy by about 40% in the absence of input references for data with lower SNRs. Applications to several experimental datasets suggest that our algorithm can detect subtle structural differences among classes via a hierarchical clustering strategy. After code optimization over a high-performance computing (HPC environment, our software implementation was able to generate thousands of reference-free class averages within hours in a massively parallel fashion, which allows a significant improvement on ab initio 3D reconstruction and assists in the computational purification of homogeneous datasets for high-resolution visualization.

Massively parallel unsupervised single-particle cryo-EM data clustering via statistical manifold learning.

Science.gov (United States)

Wu, Jiayi; Ma, Yong-Bei; Congdon, Charles; Brett, Bevin; Chen, Shuobing; Xu, Yaofang; Ouyang, Qi; Mao, Youdong

2017-01-01

Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM) data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the assessment of structural heterogeneity. However, traditional algorithms for unsupervised classification, such as K-means clustering and maximum likelihood optimization, may classify images into wrong classes with decreasing signal-to-noise-ratio (SNR) in the image data, yet demand increased computational costs. Overcoming these limitations requires further development of clustering algorithms for high-performance cryo-EM data processing. Here we introduce an unsupervised single-particle clustering algorithm derived from a statistical manifold learning framework called generative topographic mapping (GTM). We show that unsupervised GTM clustering improves classification accuracy by about 40% in the absence of input references for data with lower SNRs. Applications to several experimental datasets suggest that our algorithm can detect subtle structural differences among classes via a hierarchical clustering strategy. After code optimization over a high-performance computing (HPC) environment, our software implementation was able to generate thousands of reference-free class averages within hours in a massively parallel fashion, which allows a significant improvement on ab initio 3D reconstruction and assists in the computational purification of homogeneous datasets for high-resolution visualization.

Moduli space of torsional manifolds

International Nuclear Information System (INIS)

Becker, Melanie; Tseng, L.-S.; Yau, S.-T.

2007-01-01

We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian Yang-Mills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over K3

Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network.

Science.gov (United States)

Gilra, Aditya; Gerstner, Wulfram

2017-11-27

The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically.

Wave equations on anti self dual (ASD) manifolds

Science.gov (United States)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

Lectures on nonlinear sigma-models in projective superspace

Energy Technology Data Exchange (ETDEWEB)

Kuzenko, Sergei M, E-mail: kuzenko@cyllene.uwa.edu.a [School of Physics M013, University of Western Australia, 35 Stirling Highway, Crawley WA 6009 (Australia)

2010-11-05

N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkaehler and quaternionic Kaehler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkaehler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kaehler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N= 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkaehler and quaternionic Kaehler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach. (topical review)

Lectures on nonlinear sigma-models in projective superspace

International Nuclear Information System (INIS)

Kuzenko, Sergei M

2010-01-01

N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkaehler and quaternionic Kaehler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkaehler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kaehler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N= 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkaehler and quaternionic Kaehler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach. (topical review)

The use of machine learning and nonlinear statistical tools for ADME prediction.

Science.gov (United States)

Sakiyama, Yojiro

2009-02-01

Absorption, distribution, metabolism and excretion (ADME)-related failure of drug candidates is a major issue for the pharmaceutical industry today. Prediction of ADME by in silico tools has now become an inevitable paradigm to reduce cost and enhance efficiency in pharmaceutical research. Recently, machine learning as well as nonlinear statistical tools has been widely applied to predict routine ADME end points. To achieve accurate and reliable predictions, it would be a prerequisite to understand the concepts, mechanisms and limitations of these tools. Here, we have devised a small synthetic nonlinear data set to help understand the mechanism of machine learning by 2D-visualisation. We applied six new machine learning methods to four different data sets. The methods include Naive Bayes classifier, classification and regression tree, random forest, Gaussian process, support vector machine and k nearest neighbour. The results demonstrated that ensemble learning and kernel machine displayed greater accuracy of prediction than classical methods irrespective of the data set size. The importance of interaction with the engineering field is also addressed. The results described here provide insights into the mechanism of machine learning, which will enable appropriate usage in the future.

Fluid manifold design for a solar energy storage tank

Science.gov (United States)

Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.

1975-01-01

A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

Nonlinear analysis and synthesis of video images using deep dynamic bottleneck neural networks for face recognition.

Science.gov (United States)

Moghadam, Saeed Montazeri; Seyyedsalehi, Seyyed Ali

2018-05-31

Nonlinear components extracted from deep structures of bottleneck neural networks exhibit a great ability to express input space in a low-dimensional manifold. Sharing and combining the components boost the capability of the neural networks to synthesize and interpolate new and imaginary data. This synthesis is possibly a simple model of imaginations in human brain where the components are expressed in a nonlinear low dimensional manifold. The current paper introduces a novel Dynamic Deep Bottleneck Neural Network to analyze and extract three main features of videos regarding the expression of emotions on the face. These main features are identity, emotion and expression intensity that are laid in three different sub-manifolds of one nonlinear general manifold. The proposed model enjoying the advantages of recurrent networks was used to analyze the sequence and dynamics of information in videos. It is noteworthy to mention that this model also has also the potential to synthesize new videos showing variations of one specific emotion on the face of unknown subjects. Experiments on discrimination and recognition ability of extracted components showed that the proposed model has an average of 97.77% accuracy in recognition of six prominent emotions (Fear, Surprise, Sadness, Anger, Disgust, and Happiness), and 78.17% accuracy in the recognition of intensity. The produced videos revealed variations from neutral to the apex of an emotion on the face of the unfamiliar test subject which is on average 0.8 similar to reference videos in the scale of the SSIM method. Copyright © 2018 Elsevier Ltd. All rights reserved.

Convex functions and optimization methods on Riemannian manifolds

CERN Document Server

Udrişte, Constantin

1994-01-01

This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...

System light-loading technology for mHealth: Manifold-learning-based medical data cleansing and clinical trials in WE-CARE Project.

Science.gov (United States)

Huang, Anpeng; Xu, Wenyao; Li, Zhinan; Xie, Linzhen; Sarrafzadeh, Majid; Li, Xiaoming; Cong, Jason

2014-09-01

Cardiovascular disease (CVD) is a major issue to public health. It contributes 41% to the Chinese death rate each year. This huge loss encouraged us to develop a Wearable Efficient teleCARdiology systEm (WE-CARE) for early warning and prevention of CVD risks in real time. WE-CARE is expected to work 24/7 online for mobile health (mHealth) applications. Unfortunately, this purpose is often disrupted in system experiments and clinical trials, even if related enabling technologies work properly. This phenomenon is rooted in the overload issue of complex Electrocardiogram (ECG) data in terms of system integration. In this study, our main objective is to get a system light-loading technology to enable mHealth with a benchmarked ECG anomaly recognition rate. To achieve this objective, we propose an approach to purify clinical features from ECG raw data based on manifold learning, called the Manifold-based ECG-feature Purification algorithm. Our clinical trials verify that our proposal can detect anomalies with a recognition rate of up to 94% which is highly valuable in daily public health-risk alert applications based on clinical criteria. Most importantly, the experiment results demonstrate that the WE-CARE system enabled by our proposal can enhance system reliability by at least two times and reduce false negative rates to 0.76%, and extend the battery life by 40.54%, in the system integration level.

Variable area manifolds for ring mirror heat exchangers

Science.gov (United States)

Eng, Albert; Senterfitt, Donald R.

1988-05-01

A laser ring mirror assembly is disclosed which supports and cools an annular ring mirror of a high powered laser with a cooling manifold which has a coolant flow design which is intended to reduce thermal distortions of the ring mirror by minimizing azimuthal variations in temperature around its circumference. The cooling manifold has complementary pairs of cooling passages each of which conduct coolant in opposite flow directions. The manifold also houses adjusters which vary the depth between the annular ring mirror and each cooling, and which vary the flow area of the cooling passage to produce a control over the cooling characteristics of the cooling manifold.

Cohomological rigidity of manifolds defined by 3-dimensional polytopes

Science.gov (United States)

Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.

2017-04-01

A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.

Polynomial chaos representation of databases on manifolds

Energy Technology Data Exchange (ETDEWEB)

Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

Example-driven manifold priors for image deconvolution.

Science.gov (United States)

Ni, Jie; Turaga, Pavan; Patel, Vishal M; Chellappa, Rama

2011-11-01

Image restoration methods that exploit prior information about images to be estimated have been extensively studied, typically using the Bayesian framework. In this paper, we consider the role of prior knowledge of the object class in the form of a patch manifold to address the deconvolution problem. Specifically, we incorporate unlabeled image data of the object class, say natural images, in the form of a patch-manifold prior for the object class. The manifold prior is implicitly estimated from the given unlabeled data. We show how the patch-manifold prior effectively exploits the available sample class data for regularizing the deblurring problem. Furthermore, we derive a generalized cross-validation (GCV) function to automatically determine the regularization parameter at each iteration without explicitly knowing the noise variance. Extensive experiments show that this method performs better than many competitive image deconvolution methods.

Rank Two Affine Manifolds in Genus 3

OpenAIRE

Aulicino, David; Nguyen, Duc-Manh

2016-01-01

We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.

Nonlinear analysis on power reactor dynamics

International Nuclear Information System (INIS)

Konno, H.; Hayashi, K.

1997-01-01

We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)

Dynamics on Lorentz manifolds

CERN Document Server

Adams, Scot

2001-01-01

Within the general framework of the dynamics of "large" groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of the

CT Image Reconstruction in a Low Dimensional Manifold

OpenAIRE

Cong, Wenxiang; Wang, Ge; Yang, Qingsong; Hsieh, Jiang; Li, Jia; Lai, Rongjie

2017-01-01

Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionality characterizes structural information of an image. In this paper, we propose a CT image reconstruc...

Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions

Science.gov (United States)

Holmes, Philip J.

1981-06-01

We study the instabilities known to aeronautical engineers as flutter and divergence. Mathematically, these states correspond to bifurcations to limit cycles and multiple equilibrium points in a differential equation. Making use of the center manifold and normal form theorems, we concentrate on the situation in which flutter and divergence become coupled, and show that there are essentially two ways in which this is likely to occur. In the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator. This system, which may be analyzed by conventional phase-plane techniques, captures all the qualitative features of the full system. We discuss the reduction and show how the nonlinear terms may be simplified and put into normal form. Invariant manifold theory and the normal form theorem play a major role in this work and this paper serves as an introduction to their application in mechanics. Repeating the approach in the second case, we show that the essential model is now three dimensional and that far more complex behavior is possible, including nonperiodic and ‘chaotic’ motions. Throughout, we take a two degree of freedom system as an example, but the general methods are applicable to multi- and even infinite degree of freedom problems.

Reflections on the nature of non-linear responses of the climate to forcing

Science.gov (United States)

Ditlevsen, Peter

2017-04-01

On centennial to multi-millennial time scales the paleoclimatic record shows that climate responds in a very non-linear way to the external forcing. Perhaps most puzzling is the change in glacial period duration at the Middle Pleistocene Transition. From a dynamical systems perspective, this could be a change in frequency locking between the orbital forcing and the climatic response or it could be a non-linear resonance phenomenon. In both cases the climate system shows a non-trivial oscillatory behaviour. From the records it seems that this behaviour can be described by an effective dynamics on a low-dimensional slow manifold. These different possible dynamical behaviours will be discussed. References: Arianna Marchionne, Peter Ditlevsen, and Sebastian Wieczorek, "Three types of nonlinear resonances", arXiv:1605.00858 Peter Ashwin and Peter Ditlevsen, "The middle Pleistocene transition as a generic bifurcation on a slow manifold", Climate Dynamics, 45, 2683, 2015. Peter D. Ditlevsen, "The bifurcation structure and noise assisted transitions in the Pleistocene glacial cycles", Paleoceanography, 24, PA3204, 2009

On the dynamical mass generation in gauge-invariant non-linear σ-models

International Nuclear Information System (INIS)

Diaz, A.; Helayel-Neto, J.A.; Smith, A.W.

1987-12-01

We argue that external gauge fields coupled in a gauge-invariant way to both the bosonic and supersymmetric two-dimensional non-linear σ-models acquire a dynamical mass term whenever the target space is restricted to be a group manifold. (author). 11 refs

Piping structural design for the ITER thermal shield manifold

Energy Technology Data Exchange (ETDEWEB)

Noh, Chang Hyun, E-mail: chnoh@nfri.re.kr [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Chung, Wooho, E-mail: whchung@nfri.re.kr [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Nam, Kwanwoo; Kang, Kyoung-O. [ITER Korea, National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Bae, Jing Do; Cha, Jong Kook [Korea Marine Equipment Research Institute, Busan 606-806 (Korea, Republic of); Kim, Kyoung-Kyu [Mecha T& S, Jinju-si 660-843 (Korea, Republic of); Hamlyn-Harris, Craig; Hicks, Robby; Her, Namil; Jun, Chang-Hoon [ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex (France)

2015-10-15

Highlights: • We finalized piping design of ITER thermal shield manifold for procurement. • Support span is determined by stress and deflection limitation. • SQP, which is design optimization method, is used for the pipe design. • Benchmark analysis is performed to verify the analysis software. • Pipe design is verified by structural analyses. - Abstract: The thermal shield (TS) provides the thermal barrier in the ITER tokamak to minimize heat load transferred by thermal radiation from the hot components to the superconducting magnets operating at 4.2 K. The TS is actively cooled by 80 K pressurized helium gas which flows from the cold valve box to the cooling tubes on the TS panels via manifold piping. This paper describes the manifold piping design and analysis for the ITER thermal shield. First, maximum allowable span for the manifold support is calculated based on the simple beam theory. In order to accommodate the thermal contraction in the manifold feeder, a contraction loop is designed and applied. Sequential Quadratic Programming (SQP) method is used to determine the optimized dimensions of the contraction loop to ensure adequate flexibility of manifold pipe. Global structural behavior of the manifold is investigated when the thermal movement of the redundant (un-cooled) pipe is large.

Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

Directory of Open Access Journals (Sweden)

Saeed Mahmoudkhani

Full Text Available Abstract The nonlinear vibration and normal mode shapes of FG cylindrical shells are investigated using an efficient analytical method. The equations of motion of the shell are based on the Donnell’s non-linear shallow-shell, and the material is assumed to be gradually changed across the thickness according to the simple power law. The solution is provided by first discretizing the equations of motion using the multi-mode Galerkin’s method. The nonlinear normal mode of the system is then extracted using the invariant manifold approach and employed to decouple the discretized equations. The homotopy analysis method is finally used to determine the nonlinear frequency. Numerical results are presented for the backbone curves of FG cylindrical shells, nonlinear mode shapes and also the nonlinear invariant modal surfaces. The volume fraction index and the geometric properties of the shell are found to be effective on the type of nonlinear behavior and also the nonlinear mode shapes of the shell. The circumferential half-wave numbers of the nonlinear mode shapes are found to change with time especially in a thinner cylinder.

Blowup for flat slow manifolds

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall

2017-01-01

In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a......) the regularization of piecewise smooth systems by tanh, (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b)....

Blowup for flat slow manifolds

Science.gov (United States)

Kristiansen, K. U.

2017-05-01

In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a) the regularization of piecewise smooth systems by \\tanh , (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b).

Investigating performance of microchannel evaporators with different manifold structures

Energy Technology Data Exchange (ETDEWEB)

Shi, Junye; Qu, Xiaohua; Qi, Zhaogang; Chen, Jiangping [Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, No. 800, Dongchuan Rd, Shanghai 200240 (China)

2011-01-15

In this paper, the performances of microchannel evaporators with different manifold structures are experimentally investigated. Eight evaporator samples with 7 different designs of the I/O manifold and 5 different designs of the return manifold are made for this study. The performances of the evaporator samples are tested on a psychometric calorimeter test bench with the refrigerant 134A at a real automotive AC condition. The results on the variations of the cooling capacity and air temperature distribution of the evaporator due to the deflector designs in the I/O manifold and flow hole arrangements in the return manifold are presented and analyzed. By studying the KPI's for the performance of an evaporator, the design trade-off for an evaporator designer is summarized and discussed. (author)

Noncommutative gauge theory for Poisson manifolds

Energy Technology Data Exchange (ETDEWEB)

Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

2000-09-25

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Noncommutative gauge theory for Poisson manifolds

International Nuclear Information System (INIS)

Jurco, Branislav; Schupp, Peter; Wess, Julius

2000-01-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

On the construction of inertial manifolds under symmetry constraints II: O(2) constraint and inertial manifolds on thin domains

International Nuclear Information System (INIS)

Rodriguez-Bernal, A.

1993-01-01

On a model example, the Kuramoto-Velarde equation, which includes the Kuramoto-Sivashin-sky and the Cahn-Hilliard models, and under suitable and reasonable hypothesis, we show the dimension and determining modes of inertial manifolds for several classes of solutions. We also give bounds for the dimensions of inertial manifolds of the full system as a parameter is varied. The results are pointed out to be almost model-independent. The same ideas are also applied to a class of parabolic equations in higher space dimension, obtaining results about inertial manifolds on thin and small domains. (Author). 30 refs

Dissipative quantum dynamics and nonlinear sigma-model

International Nuclear Information System (INIS)

Tarasov, V.E.

1992-01-01

Sedov variational principle which is the generalization of the least action principle for the dissipative and irreversible processes and the classical dissipative mechanics in the phase space is considered. Quantum dynamics for the dissipative and irreversible processes is constructed. As an example of the dissipative quantum theory the nonlinear two-dimensional sigma-model is considered. The conformal anomaly of the energy momentum tensor trace for closed bosonic string on the affine-metric manifold is investigated. The two-loop metric beta-function for nonlinear dissipative sigma-model was calculated. The results are compared with the ultraviolet two-loop conterterms for affine-metric sigma model. 71 refs

Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds

OpenAIRE

Weeks, Jeffrey R.

2005-01-01

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D...

On generalized de Rham-Hodge complexes, the related characteristic Chern classes and some applications to integrable multi-dimensional differential systems on Riemannian manifolds

International Nuclear Information System (INIS)

Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.

2006-12-01

The differential-geometric aspects of generalized de Rham-Hodge complexes naturally related with integrable multi-dimensional differential systems of M. Gromov type, as well as the geometric structure of Chern characteristic classes are studied. Special differential invariants of the Chern type are constructed, their importance for the integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson type nonlinear strongly integrable differential system is considered, its Cartan type connection mapping and related Chern type differential invariants are analyzed. (author)

Algebras and manifolds: Differential, difference, simplicial and quantum

International Nuclear Information System (INIS)

Finkelstein, D.; Rodriguez, E.

1986-01-01

Generalized manifolds and Clifford algebras depict the world at levels of resolution ranging from the classical macroscopic to the quantum microscopic. The coarsest picture is a differential manifold and algebra (dm), direct integral of familiar local Clifford algebras of spin operators in curved time-space. Next is a finite difference manifold (Δm) of Regge calculus. This is a subalgebra of the third, a Minkowskian simplicial manifold (Σm). The most detailed description is the quantum manifold (Qm), whose algebra is the free Clifford algebra S of quantum set theory. We surmise that each Σm is a classical 'condensation' of a Qm. Quantum simplices have both integer and half-integer spins in their spectrum. A quantum set theory of nature requires a series of reductions leading from the Qm and a world descriptor W up through the intermediate Σm and Δm to a dm and an action principle. What may be a new algebraic language for topology, classical or quantum, is a by-product of the work. (orig.)

A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems

Science.gov (United States)

Stavrou, D.; Duit, R.; Komorek, M.

2008-01-01

A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…

Stein Manifolds and Holomorphic Mappings

CERN Document Server

Forstneric, Franc

2011-01-01

The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. This book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applicat

Matrix regularization of 4-manifolds

OpenAIRE

Trzetrzelewski, M.

2012-01-01

We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...

Birkhoff’s theorem in Lovelock gravity for general base manifolds

Science.gov (United States)

Ray, Sourya

2015-10-01

We extend the Birkhoff’s theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.

Singular reduction of Nambu-Poisson manifolds

Science.gov (United States)

Das, Apurba

The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.

Holomorphic curves in exploded manifolds: Kuranishi structure

OpenAIRE

Parker, Brett

2013-01-01

This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside a moduli stack of curves. The construction also works for the moduli stack of holomorphic curves in any compact symplectic manifold.

Nonlinear programming for classification problems in machine learning

Science.gov (United States)

Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio

2016-10-01

We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.

Compactifications of heterotic strings on non-Kaehler complex manifolds II

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Dasgupta, Keshav; Green, Paul S.; Sharpe, Eric

2004-01-01

We continue our study of heterotic compactifications on non-Kaehler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kaehler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We construct new examples of non-Kaehler complex manifolds with torsion in lower dimensions, that have nonzero Euler characteristics. Some of these examples are constructed from consistent backgrounds in F-theory and therefore are solutions to the string equations of motion. We discuss consistency conditions for compactifications of the heterotic string on smooth non-Kaehler manifolds and illustrate how some results well known for Calabi-Yau compactifications, including counting the number of generations, apply to the non-Kaehler case. We briefly address various issues regarding possible phenomenological applications

Enhancement of ELM by Clustering Discrimination Manifold Regularization and Multiobjective FOA for Semisupervised Classification

OpenAIRE

Qing Ye; Hao Pan; Changhua Liu

2015-01-01

A novel semisupervised extreme learning machine (ELM) with clustering discrimination manifold regularization (CDMR) framework named CDMR-ELM is proposed for semisupervised classification. By using unsupervised fuzzy clustering method, CDMR framework integrates clustering discrimination of both labeled and unlabeled data with twinning constraints regularization. Aiming at further improving the classification accuracy and efficiency, a new multiobjective fruit fly optimization algorithm (MOFOA)...

Duality constructions from quantum state manifolds

Science.gov (United States)

Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.

2015-11-01

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

Harmonic manifolds with minimal horospheres are flat

Indian Academy of Sciences (India)

Abstract. In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting ...

Harmonic Manifolds with Minimal Horospheres are Flat

Indian Academy of Sciences (India)

In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.

A relation connecting scale transformation, Galilean transformation and Baecklund transformation for the nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Steudel, H.

1980-01-01

It is shown that the two-parameter manifold of Baecklund transformations known for the nonlinear Schroedinger equation can be generated from one Baecklund transformation with specified parameters by use of scale transformation and Galilean transformation. (orig.)

Para-Hermitian and para-quaternionic manifolds

International Nuclear Information System (INIS)

Ivanov, S.; Zamkovoy, S.

2003-10-01

A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S 1 x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)

Para-Hermitian and para-quaternionic manifolds

Energy Technology Data Exchange (ETDEWEB)

Ivanov, S [University of Sofia ' St. Kl. Ohridski' , Faculty of Mathematics and Informatics, Sofia (Bulgaria) and Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Zamkovoy, S [University of Sofia ' St. Kl. Ohridski' , Faculty of Mathematics and Informatics, Sofia (Bulgaria)

2003-10-01

A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S{sup 1} x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)

On the de Rham–Wu decomposition for Riemannian and Lorentzian manifolds

International Nuclear Information System (INIS)

Galaev, Anton S

2014-01-01

It is explained how to find the de Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold. (paper)

Natural differential operations on manifolds: an algebraic approach

International Nuclear Information System (INIS)

Katsylo, P I; Timashev, D A

2008-01-01

Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles V,W→M all the natural differential operations D:Γ(V)→Γ(W) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds. Bibliography: 21 titles.

Slow Invariant Manifolds in Chemically Reactive Systems

Science.gov (United States)

Paolucci, Samuel; Powers, Joseph M.

2006-11-01

The scientific design of practical gas phase combustion devices has come to rely on the use of mathematical models which include detailed chemical kinetics. Such models intrinsically admit a wide range of scales which renders their accurate numerical approximation difficult. Over the past decade, rational strategies, such as Intrinsic Low Dimensional Manifolds (ILDM) or Computational Singular Perturbations (CSP), for equilibrating fast time scale events have been successfully developed, though their computation can be challenging and their accuracy in most cases uncertain. Both are approximations to the preferable slow invariant manifold which best describes how the system evolves in the long time limit. Strategies for computing the slow invariant manifold are examined, and results are presented for practical combustion systems.

Strictly convex functions on complete Finsler manifolds

Indian Academy of Sciences (India)

convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...

Finiteness of Ricci flat supersymmetric non-linear sigma-models

International Nuclear Information System (INIS)

Alvarez-Gaume, L.; Ginsparg, P.

1985-01-01

Combining the constraints of Kaehler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear sigma-models with target space an arbitrary riemannian manifold M. We show that the constraint of N=2 supersymmetry requires that all counterterms to the metric beyond one-loop order are cohomologically trivial. It follows that such supersymmetric non-linear sigma-models defined on locally symmetric spaces are super-renormalizable and that N=4 models are on-shell ultraviolet finite to all orders of perturbation theory. (orig.)

Generalized Transversal Lightlike Submanifolds of Indefinite Sasakian Manifolds

OpenAIRE

Yaning Wang; Ximin Liu

2012-01-01

We introduce and study generalized transversal lightlike submanifold of indefinite Sasakian manifolds which includes radical and transversal lightlike submanifolds of indefinite Sasakian manifolds as its trivial subcases. A characteristic theorem and a classification theorem of generalized transversal lightlike submanifolds are obtained.

Some problems of dynamical systems on three dimensional manifolds

International Nuclear Information System (INIS)

Dong Zhenxie.

1985-08-01

It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)

Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

Science.gov (United States)

Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

2017-09-01

Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

International Nuclear Information System (INIS)

Suarez-Antola, Roberto; Ministerio de Industria, Energia y Mineria, Montevideo

2011-01-01

One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)

Multiscale asymmetric orthogonal wavelet kernel for linear programming support vector learning and nonlinear dynamic systems identification.

Science.gov (United States)

Lu, Zhao; Sun, Jing; Butts, Kenneth

2014-05-01

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

Classification problem for exactly integrable embeddings of two-dimensional manifolds and coefficients of the third fundametal forms

International Nuclear Information System (INIS)

Saveliev, M.V.

1983-01-01

A method is proposed for classification of exactly and completely integrable embeddings of two dimensional manifoilds into Riemann or non-Riemann enveloping space, which are based on the algebraic approach to the integration of nonlinear dynamical systems.Here the grading conditions and spectral structure of the Lax-pair operators taking the values in a graded Lie algebra that pick out the integrable class of nonlinear systems are formulated 1n terms of a structure of the 3-d fundamental form tensors. Corresponding to every embedding of three-dimensional subalgebra sb(2) into a simple finite-dimensional (infinite-dimensional of finite growth) Lie algebra L is a definite class of exactly (completely) integrable embeddings of two dimensional manifold into the corresponding enveloping space supplied with the structure of L

Quaternionic Kaehler and hyperkaehler manifolds with torsion and twistor spaces

International Nuclear Information System (INIS)

Ivanov, Stefan; Minchev, Ivan

2001-12-01

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(l) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only if the twistor space of the QKT manifold admits an almost hermitian structure with totally skew-symmetric Nijenhuis tensor, thus connecting two structures arising from quantum field theories and supersymmetric sigma models with Wess- Zumino term. We discovered that a HKT manifold has always co-closed Lee form. Applying this property to compact HKT manifold we get information about the plurigenera. (author)

Online Manifold Regularization by Dual Ascending Procedure

Directory of Open Access Journals (Sweden)

Boliang Sun

2013-01-01

Full Text Available We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approaches. An important conclusion is that our online MR algorithms can handle the settings where the target hypothesis is not fixed but drifts with the sequence of examples. We also recap and draw connections to earlier works. This paper paves a way to the design and analysis of online manifold regularization algorithms.

Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent.

Science.gov (United States)

Guan, Naiyang; Tao, Dacheng; Luo, Zhigang; Yuan, Bo

2011-07-01

Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R(1600), FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.

Topological field theory and surgery on three-manifolds

International Nuclear Information System (INIS)

Guadagnini, E.; Panicucci, S.

1992-01-01

The solution of the SU(2) quantum Chern-Simons field theory defined on a closed, connected and orientable three-manifold is presented. The vacuum expectation values of Wilson line operators, associated with framed links in a generic manifold, are computed in terms of the expectation values of the three-sphere. The method consists of using an operator realization of Dehn surgery. The rules, corresponding to the surgery instructions in the three-sphere, are derived and the three-manifold invariant defined by the Chern-Simons theory is constructed. Several examples are considered and explicit results are reported. (orig.)

Data-driven non-linear elasticity: constitutive manifold construction and problem discretization

Science.gov (United States)

Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco

2017-11-01

The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.

Group manifold approach to gravity and supergravity theories

International Nuclear Information System (INIS)

d'Auria, R.; Fre, P.; Regge, T.

1981-05-01

Gravity theories are presented from the point of view of group manifold formulation. The differential geometry of groups and supergroups is discussed first; the notion of connection and related Yang-Mills potentials is introduced. Then ordinary Einstein gravity is discussed in the Cartan formulation. This discussion provides a first example which will then be generalized to more complicated theories, in particular supergravity. The distinction between ''pure'' and ''impure' theories is also set forth. Next, the authors develop an axiomatic approach to rheonomic theories related to the concept of Chevalley cohomology on group manifolds, and apply these principles to N = 1 supergravity. Then the panorama of so far constructed pure and impure group manifold supergravities is presented. The pure d = 5 N = 2 case is discussed in some detail, and N = 2 and N = 3 in d = 4 are considered as examples of the impure theories. The way a pure theory becomes impure after dimensional reduction is illustrated. Next, the role of kinematical superspace constraints as a subset of the group-manifold equations of motion is discussed, and the use of this approach to obtain the auxiliary fields is demonstrated. Finally, the application of the group manifold method to supersymmetric Super Yang-Mills theories is addressed

Nonlinear Denoising and Analysis of Neuroimages With Kernel Principal Component Analysis and Pre-Image Estimation

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup; Abrahamsen, Trine Julie; Madsen, Kristoffer Hougaard

2012-01-01

We investigate the use of kernel principal component analysis (PCA) and the inverse problem known as pre-image estimation in neuroimaging: i) We explore kernel PCA and pre-image estimation as a means for image denoising as part of the image preprocessing pipeline. Evaluation of the denoising...... procedure is performed within a data-driven split-half evaluation framework. ii) We introduce manifold navigation for exploration of a nonlinear data manifold, and illustrate how pre-image estimation can be used to generate brain maps in the continuum between experimentally defined brain states/classes. We...

Differential geometry curves, surfaces, manifolds

CERN Document Server

Kohnel, Wolfgang

2002-01-01

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

A Symbiotic Framework for coupling Machine Learning and Geosciences in Prediction and Predictability

Science.gov (United States)

Ravela, S.

2017-12-01

In this presentation we review the two directions of a symbiotic relationship between machine learning and the geosciences in relation to prediction and predictability. In the first direction, we develop ensemble, information theoretic and manifold learning framework to adaptively improve state and parameter estimates in nonlinear high-dimensional non-Gaussian problems, showing in particular that tractable variational approaches can be produced. We demonstrate these applications in the context of autonomous mapping of environmental coherent structures and other idealized problems. In the reverse direction, we show that data assimilation, particularly probabilistic approaches for filtering and smoothing offer a novel and useful way to train neural networks, and serve as a better basis than gradient based approaches when we must quantify uncertainty in association with nonlinear, chaotic processes. In many inference problems in geosciences we seek to build reduced models to characterize local sensitivies, adjoints or other mechanisms that propagate innovations and errors. Here, the particular use of neural approaches for such propagation trained using ensemble data assimilation provides a novel framework. Through these two examples of inference problems in the earth sciences, we show that not only is learning useful to broaden existing methodology, but in reverse, geophysical methodology can be used to influence paradigms in learning.

Folding-retraction of chaotic dynamical manifold and the VAK of vacuum fluctuation

International Nuclear Information System (INIS)

El-Ghoul, M.; El-Ahmady, A.E.; Rafat, H.

2004-01-01

In this paper we introduce the retraction of chaos dynamical manifold. Some properties of chaos dynamical manifold will be deduced. Theorems governing the relation between the folding and retraction of chaos dynamical manifold will be discussed. Some applications of chaos dynamical manifolds and their retractions are achieved in particular high energy particle physics

Gauge theory and the topology of four-manifolds

CERN Document Server

Friedman, Robert Marc

1998-01-01

The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying SU(2)-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the SU(2)-moduli spaces may one day be important for purposes beyond the algebraic invariants that ...

Enhancing Low-Rank Subspace Clustering by Manifold Regularization.

Science.gov (United States)

Liu, Junmin; Chen, Yijun; Zhang, JiangShe; Xu, Zongben

2014-07-25

Recently, low-rank representation (LRR) method has achieved great success in subspace clustering (SC), which aims to cluster the data points that lie in a union of low-dimensional subspace. Given a set of data points, LRR seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself. However, LRR only considers the global Euclidean structure, while the local manifold structure, which is often important for many real applications, is ignored. In this paper, to exploit the local manifold structure of the data, a manifold regularization characterized by a Laplacian graph has been incorporated into LRR, leading to our proposed Laplacian regularized LRR (LapLRR). An efficient optimization procedure, which is based on alternating direction method of multipliers (ADMM), is developed for LapLRR. Experimental results on synthetic and real data sets are presented to demonstrate that the performance of LRR has been enhanced by using the manifold regularization.

Transversal lightlike submanifolds of indefinite sasakian manifolds

OpenAIRE

YILDIRIM, Cumali; Yıldırım, Cumali; Şahin, Bayram

2014-01-01

We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical tr...

Transversal lightlike submanifolds of indefinite sasakian manifolds

OpenAIRE

YILDIRIM, Cumali

2010-01-01

We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical tr...

Ground state solutions for diffusion system with superlinear nonlinearity

Directory of Open Access Journals (Sweden)

Zhiming Luo

2015-03-01

where $z=(u,v\\colon\\mathbb{R}\\times\\mathbb{R}^{N}\\rightarrow\\mathbb{R}^{2}$, $b\\in C^{1}(\\mathbb{R}\\times\\mathbb{R}^{N}, \\mathbb{R}^{N}$ and $V(x\\in C(\\mathbb{R}^{N},\\mathbb{R}$. Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.

Asymptotic stabilization of nonlinear systems using state feedback

International Nuclear Information System (INIS)

D'Attellis, Carlos

1990-01-01

This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

Strong Proximities on Smooth Manifolds and Vorono\\" i Diagrams

OpenAIRE

Peters, J. F.; Guadagni, C.

2015-01-01

This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family $\\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to which singletons are added, (ii) manifold strong proximity, (iii) strong proximity of charts in manifold atlases implies that the charts have nonempty intersection. The application of these results is given in terms of the nearness of atlases and charts of proxim...

On a method for constructing the Lax pairs for nonlinear integrable equations

International Nuclear Information System (INIS)

Habibullin, I T; Poptsova, M N; Khakimova, A R

2016-01-01

We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found immediately, coinciding with the linearization of the considered nonlinear equation. The second one is obtained as an invariant manifold to the linearized equation. A surprisingly simple relation between the second operator of the Lax pair and the recursion operator is discussed: the recursion operator can immediately be found from the Lax pair. Examples considered in the article are convincing evidence that the found Lax pairs differ from the classical ones. The examples also show that the suggested objects are true Lax pairs which allow the construction of infinite series of conservation laws and hierarchies of higher symmetries. In the case of the hyperbolic type partial differential equation our algorithm is slightly modified; in order to construct the Lax pairs from the invariant manifolds we use the cutting off conditions for the corresponding infinite Laplace sequence. The efficiency of the method is illustrated by application to some equations given in the Svinolupov–Sokolov classification list for which the Lax pairs and the recursion operators have not been found earlier. (paper)

Scientific data interpolation with low dimensional manifold model

Science.gov (United States)

Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley

2018-01-01

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Scientific data interpolation with low dimensional manifold model

International Nuclear Information System (INIS)

Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.

2017-01-01

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Geometric transitions, flops and non-Kahler manifolds: I

International Nuclear Information System (INIS)

Becker, Melanie; Dasgupta, Keshav; Knauf, Anke; Tatar, Radu

2004-01-01

We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G2 manifolds that are circle fibrations over non-Kahler manifolds is presented

A regularized approach for geodesic-based semisupervised multimanifold learning.

Science.gov (United States)

Fan, Mingyu; Zhang, Xiaoqin; Lin, Zhouchen; Zhang, Zhongfei; Bao, Hujun

2014-05-01

Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learning. However, most geodesic distance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semisupervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL face versus nonface data set, and an intelligent traffic data set show the effectiveness of the proposed algorithm.

A teaching and learning sequence about the interplay of chance and determinism in nonlinear systems

International Nuclear Information System (INIS)

Stavrou, D; Duit, R; Komorek, M

2008-01-01

A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper secondary students' capabilities and difficulties in understanding the scientific point of view were investigated, using a teaching experiment design. The results show that most students were capable of sound explanations concerning the interplay of chance and determinism in nonlinear systems

IMPROVED INTAKE MANIFOLD DESIGN FOR I.C. ENGINE EMISSION CONTROL

Directory of Open Access Journals (Sweden)

R. K. TYAGI

2015-09-01

Full Text Available The Spark Ignition engine has been extensively used in multifaceted sectors, viz. Automobiles, Industry engineering, etc. due to their exceptional driveability, performance and minimal maintenance. However, gasoline engines have their share of complications as they release a variety of air pollutants, viz. CO, NOx, HC and CO2 etc. and other harmful emissions. In this paper a comparison of these gases with the Government policies or norms have been studied and the parameters which are responsible for increasing the more Air pollution have been minimised using innovative engineering solutions. This paper depicts research done on inlet manifolds and their modifications to achieve exemplary fuel-air swirl. During subsequent analysis at idle condition (1300 rpm, it has been concluded that the venturi-based intake manifold has shown remarkable results in decreasing the HC levels from 180 ppm to 60 ppm (66.6 % at Idle Range. The work is also complementary to the various other designs of inlet manifolds, viz. Inlet manifold Modified 1 and Inlet Manifold Modified 2 out of which it is concluded that the Inlet manifold Modified 2 results in better reduction of pollutants.

A TQFT associated to the LMO invariant of three-dimensional manifolds

DEFF Research Database (Denmark)

Cheptea, Dorin; Le, Thang

2007-01-01

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is ......We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category...

Computer calculation of Witten's 3-manifold invariant

International Nuclear Information System (INIS)

Freed, D.S.; Gompf, R.E.

1991-01-01

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)

A stable-manifold-based method for chaos control and synchronization

International Nuclear Information System (INIS)

Chen Shihua; Zhang Qunjiao; Xie Jin; Wang Changping

2004-01-01

A stable-manifold-based method is proposed for chaos control and synchronization. The novelty of this new and effective method lies in that, once the suitable stable manifold according to the desired dynamic properties is constructed, the goal of control is only to force the system state to lie on the selected stable manifold because once the stable manifold is reached, the chaotic system will be guided towards the desired target. The effectiveness of the approach and idea is tested by stabilizing the Newton-Leipnik chaotic system which possesses more than one strange attractor and by synchronizing the unified chaotic system which unifies both the Lorenz system and the Chen system

Efficient non-linear two-photon effects from the Cesium 6D manifold

Science.gov (United States)

Haluska, Nathan D.; Perram, Glen P.; Rice, Christopher A.

2018-02-01

We report several non-linear process that occur when two-photon pumping the cesium 6D states. Cesium vapor possess some of the largest two-photon pump cross sections in nature. Pumping these cross sections leads to strong amplified spontaneous emission that we observe on over 17 lasing lines. These new fields are strong enough to couple with the pump to create additional tunable lines. We use a heat pipe with cesium densities of 1014 to 1016 cm-3 and 0 to 5 Torr of helium buffer gas. The cesium 6D States are interrogated by both high energy pulses and low power CW sources. We observe four-wave mixing, six-wave mixing, potential two-photon lasing, other unknown nonlinear processes, and the persistence of some processes at low thresholds. This system is also uniquely qualified to support two-photon lasing under the proper conditions.

Sparse alignment for robust tensor learning.

Science.gov (United States)

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

Experimental Analysis of Exhaust Manifold with Ceramic Coating for Reduction of Heat Dissipation

Science.gov (United States)

Saravanan, J.; Valarmathi, T. N.; Nathc, Rajdeep; Kumar, Prasanth

2017-05-01

Exhaust manifold plays an important role in the exhaust system, the manifold delivers the waste toxic gases to a safe distance and it is used to reduce the sound pollution and air pollution. Exhaust manifold suffers with lot of thermal stress, due to this blow holes occurs in the surface of the exhaust manifold and also more noise is developed. The waste toxic gases from the multiple cylinders are collected into a single pipe by the exhaust manifold. The waste toxic gases can damage the material of the manifold. In this study, to prevent the damage zirconia powder has been coated in the inner surface and alumina (60%) combined with titania (40%) has been used for coating the outer surface of the exhaust manifold. After coating experiments have been performed using a multiple-cylinder four stroke stationary petrol engine. The test results of hardness, emission, corrosion and temperature of the coated and uncoated manifolds have been compared. The result shows that the performance is improved and also emission is reduced in the coated exhaust manifold.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

Science.gov (United States)

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Anomalies, conformal manifolds, and spheres

Energy Technology Data Exchange (ETDEWEB)

Gomis, Jaume [Perimeter Institute for Theoretical Physics,Waterloo, Ontario, N2L 2Y5 (Canada); Hsin, Po-Shen [Department of Physics, Princeton University,Princeton, NJ 08544 (United States); Komargodski, Zohar; Schwimmer, Adam [Weizmann Institute of Science,Rehovot 76100 (Israel); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Theisen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,14476 Golm (Germany)

2016-03-04

The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space M is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail N=(2,2) and N=(0,2) supersymmetric theories in d=2 and N=2 supersymmetric theories in d=4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kähler-Hodge and we further argue that it has vanishing Kähler class. For N=(2,2) theories in d=2 and N=2 theories in d=4 we also show that the relation between the sphere partition function and the Kähler potential of M follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.

Compactifications of IIA supergravity on SU(2)-structure manifolds

Energy Technology Data Exchange (ETDEWEB)

Spanjaard, B.

2008-07-15

In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)

Pseudo-differential operators on manifolds with singularities

CERN Document Server

Schulze, B-W

1991-01-01

The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

Energy Technology Data Exchange (ETDEWEB)

Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.u, E-mail: rsuarez@ucu.edu.u [Universidad Catolica del Uruguay, Montevideo (Uruguay). Fac. de Ingenieria y Tecnologias. Dept. de Matematica; Ministerio de Industria, Energia y Mineria, Montevideo (Uruguay). Direccion General de Secretaria

2011-07-01

One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)

Manifold regularization for sparse unmixing of hyperspectral images.

Science.gov (United States)

Liu, Junmin; Zhang, Chunxia; Zhang, Jiangshe; Li, Huirong; Gao, Yuelin

2016-01-01

Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression , ignore the intrinsic geometric structure in the hyperspectral data. In this paper, we propose a novel model, called manifold regularized collaborative sparse regression , by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.

Online Manifold Regularization by Dual Ascending Procedure

OpenAIRE

Sun, Boliang; Li, Guohui; Jia, Li; Zhang, Hui

2013-01-01

We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approache...

Sasaki-Einstein Manifolds and Volume Minimisation

CERN Document Server

Martelli, D; Yau, S T; Martelli, Dario; Sparks, James; Yau, Shing-Tung

2006-01-01

We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theo...

Unimodularity criteria for Poisson structures on foliated manifolds

Science.gov (United States)

Pedroza, Andrés; Velasco-Barreras, Eduardo; Vorobiev, Yury

2018-03-01

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for regular Poisson manifolds related to the notion of the Reeb class. In particular, we show that the unimodularity of the transverse Poisson structure of the leaf is a necessary condition for the semilocal unimodular property. Our main tool is an explicit formula for a bigraded decomposition of modular vector fields of a coupling Poisson structure on a foliated manifold. Moreover, we also exploit the notion of the modular class of a Poisson foliation and its relationship with the Reeb class.

Deep Transfer Metric Learning.

Science.gov (United States)

Junlin Hu; Jiwen Lu; Yap-Peng Tan; Jie Zhou

2016-12-01

Conventional metric learning methods usually assume that the training and test samples are captured in similar scenarios so that their distributions are assumed to be the same. This assumption does not hold in many real visual recognition applications, especially when samples are captured across different data sets. In this paper, we propose a new deep transfer metric learning (DTML) method to learn a set of hierarchical nonlinear transformations for cross-domain visual recognition by transferring discriminative knowledge from the labeled source domain to the unlabeled target domain. Specifically, our DTML learns a deep metric network by maximizing the inter-class variations and minimizing the intra-class variations, and minimizing the distribution divergence between the source domain and the target domain at the top layer of the network. To better exploit the discriminative information from the source domain, we further develop a deeply supervised transfer metric learning (DSTML) method by including an additional objective on DTML, where the output of both the hidden layers and the top layer are optimized jointly. To preserve the local manifold of input data points in the metric space, we present two new methods, DTML with autoencoder regularization and DSTML with autoencoder regularization. Experimental results on face verification, person re-identification, and handwritten digit recognition validate the effectiveness of the proposed methods.

Action-angle variables and a KAM theorem for b-Poisson manifolds

OpenAIRE

Kiesenhofer, Anna; Miranda Galcerán, Eva; Scott, Geoffrey

2015-01-01

In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [14] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds. (C) 2015 Elsevier Masson SAS. All rights reserved.

Variable volume combustor with nested fuel manifold system

Science.gov (United States)

McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael

2016-09-13

The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.

Semisupervised kernel marginal Fisher analysis for face recognition.

Science.gov (United States)

Wang, Ziqiang; Sun, Xia; Sun, Lijun; Huang, Yuchun

2013-01-01

Dimensionality reduction is a key problem in face recognition due to the high-dimensionality of face image. To effectively cope with this problem, a novel dimensionality reduction algorithm called semisupervised kernel marginal Fisher analysis (SKMFA) for face recognition is proposed in this paper. SKMFA can make use of both labelled and unlabeled samples to learn the projection matrix for nonlinear dimensionality reduction. Meanwhile, it can successfully avoid the singularity problem by not calculating the matrix inverse. In addition, in order to make the nonlinear structure captured by the data-dependent kernel consistent with the intrinsic manifold structure, a manifold adaptive nonparameter kernel is incorporated into the learning process of SKMFA. Experimental results on three face image databases demonstrate the effectiveness of our proposed algorithm.

The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold

Directory of Open Access Journals (Sweden)

J. A. Helayël-Neto

2017-01-01

Full Text Available It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

CFD simulations for engine intake manifolds

International Nuclear Information System (INIS)

Witry, A.; Zhao, A.

2002-01-01

This paper attempts to explain a procedure for using Computational Fluid Dynamics (CFD) for product development of engine intake manifolds. The paper uses the development of an intake manifold as an example of such a process. Using the commercial FLUENT solver, its standard wall functions and k-ε model, a four runner intake manifold with an average mesh size of 300, 000 hexa elements created in ICEM-CFD with a maximum skewness of 0.85 produces rapid results for quick product turn-around times. The setup used allows for compressibility and viscous heating effects to be modeled whilst ignoring wall heat transfer due to the high speeds of the air/foil mixture and low residence times. Eight consecutive models were modeled here whilst carrying out continuous enhancements. For every iteration, four different so called 'static' runs with only one runner open at any one time using a steady state assumption were calculated further assuming that only one intake valve is open at any one time. Even flow distributions between the runner are deemed to be 'dynamically' obtained once the pressure drops between the manifold's inlet and runner outlets are equalized. Furthermore, different modifications were attempted to ensure that the fluid's particle tracks show very little particle return tendencies along with excellent nonuniformity indexes at the runners outlets. Confirmation of these results were obtained from test data showing CFD pressure drop predictions to be within 4% error with 67% of any runner's pressure losses being caused in the runner itself due to the small cross sectional area(s). (author)

Lattices in group manifolds

International Nuclear Information System (INIS)

Lisboa, P.; Michael, C.

1982-01-01

We address the question of designing optimum discrete sets of points to represent numerically a continuous group manifold. We consider subsets which are extensions of the regular discrete subgroups. Applications to Monte Carlo simulation of SU(2) and SU(3) gauge theory are discussed. (orig.)

Harmonic mappings into manifolds with boundary

International Nuclear Information System (INIS)

Chen Yunmei; Musina, R.

1989-08-01

In this paper we deal with harmonic maps from a compact Riemannian manifold into a manifold with boundary. In this case, a weak harmonic map is by definition a solution to a differential inclusion. In the first part of the paper we investigate the general properties of weak harmonic maps, which can be seen as solutions to a system of elliptic differential equations. In the second part we concentrate our attention on the heat flow method for harmonic maps. The result we achieve in this context extends a result by Chen and Struwe. (author). 21 refs

Matrix regularization of embedded 4-manifolds

International Nuclear Information System (INIS)

Trzetrzelewski, Maciej

2012-01-01

We consider products of two 2-manifolds such as S 2 ×S 2 , embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N 2 ×N 2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S 3 also possible).

Bound state solution of the Grassmannian nonlinear sigma model with fermions

International Nuclear Information System (INIS)

Abdalla, E.; Lima-Santos, A.

1987-11-01

We construct the s matrix for bound state (gauge-invariant) scattering for nonlinear sigma models defined on the manifold SU(N)/S(U(p)x (lower casex)U(n-p)) with fermions. It is not possible to compute gauge non-singlet matrix elements. In the present language they are not submitted to sufficiently many constraints derived from higher conservation laws. (author) [pt

Manifold learning based ECG-free free-breathing cardiac CINE MRI.

Science.gov (United States)

Usman, Muhammad; Atkinson, David; Kolbitsch, Christoph; Schaeffter, Tobias; Prieto, Claudia

2015-06-01

To present and validate a manifold learning (ML)-based method that can estimate both cardiac and respiratory navigator signals from electrocardiogram (ECG)-free free-breathing cardiac magnetic resonance imaging (MRI) data to achieve self-gated retrospective CINE reconstruction. In this work the use of the ML method is demonstrated for 2D cardiac CINE to achieve both cardiac and respiratory self-gating without the need of an external navigator or ECG signal. This is achieved by sequentially applying ML to two sets of retrospectively reconstructed real-time images with differing temporal resolutions. A 1D cardiac signal is estimated by applying ML to high temporal resolution real-time images reconstructed from the acquired data. Using the estimated cardiac signal, a 1D respiratory signal was obtained by applying the ML method to low temporal resolution images reconstructed from the same acquired data for each cardiac cycle. Data were acquired in five volunteers with a 2D golden angle radial trajectory in a balanced steady-state free precession (b-SSFP) acquisition. The accuracy of the estimated cardiac signal was calculated as the standard deviation of the temporal difference between the estimated signal and the recorded ECG. The correlation between the estimated respiratory signal and standard pencil beam navigator signal was evaluated. Gated CINE reconstructions (20 cardiac phases per cycle, temporal resolution ∼30 msec) using the estimated cardiac and respiratory signals were qualitatively compared against conventional ECG-gated breath-hold CINE acquisitions. Accurate cardiac signals were estimated with the proposed method, with an error standard deviation in comparison to ECG lower than 20 msec. Respiratory signals estimated with the proposed method achieved a mean cross-correlation of 94% with respect to standard pencil beam navigator signals. Good quality visual scores of 2.80 ± 0.45 (scores from 0, bad, to 4, excellent quality) were observed for the

Mechanical systems with closed orbits on manifolds of revolution

International Nuclear Information System (INIS)

Kudryavtseva, E A; Fedoseev, D A

2015-01-01

We study natural mechanical systems describing the motion of a particle on a two-dimensional Riemannian manifold of revolution in the field of a central smooth potential. We obtain a classification of Riemannian manifolds of revolution and central potentials on them that have the strong Bertrand property: any nonsingular (that is, not contained in a meridian) orbit is closed. We also obtain a classification of manifolds of revolution and central potentials on them that have the 'stable' Bertrand property: every parallel is an 'almost stable' circular orbit, and any nonsingular bounded orbit is closed. Bibliography: 14 titles

Rigidity of complete noncompact bach-flat n-manifolds

Science.gov (United States)

Chu, Yawei; Feng, Pinghua

2012-11-01

Let (Mn,g) be a complete noncompact Bach-flat n-manifold with the positive Yamabe constant and constant scalar curvature. Assume that the L2-norm of the trace-free Riemannian curvature tensor R∘m is finite. In this paper, we prove that (Mn,g) is a constant curvature space if the L-norm of R∘m is sufficiently small. Moreover, we get a gap theorem for (Mn,g) with positive scalar curvature. This can be viewed as a generalization of our earlier results of 4-dimensional Bach-flat manifolds with constant scalar curvature R≥0 [Y.W. Chu, A rigidity theorem for complete noncompact Bach-flat manifolds, J. Geom. Phys. 61 (2011) 516-521]. Furthermore, when n>9, we derive a rigidity result for R<0.

Homotopy L-infinity spaces and Kuranishi manifolds, I: categorical structures

OpenAIRE

Tu, Junwu

2016-01-01

Motivated by the definition of homotopy $L_\\infty$ spaces, we develop a new theory of Kuranishi manifolds, closely related to Joyce's recent theory. We prove that Kuranishi manifolds form a $2$-category with invertible $2$-morphisms, and that certain fiber product property holds in this $2$-category. In a subsequent paper, we construct the virtual fundamental cycle of a compact oriented Kuranishi manifold, and prove some of its basic properties. Manifest from this new formulation is the fact ...

Multi-view clustering via multi-manifold regularized non-negative matrix factorization.

Science.gov (United States)

Zong, Linlin; Zhang, Xianchao; Zhao, Long; Yu, Hong; Zhao, Qianli

2017-04-01

Non-negative matrix factorization based multi-view clustering algorithms have shown their competitiveness among different multi-view clustering algorithms. However, non-negative matrix factorization fails to preserve the locally geometrical structure of the data space. In this paper, we propose a multi-manifold regularized non-negative matrix factorization framework (MMNMF) which can preserve the locally geometrical structure of the manifolds for multi-view clustering. MMNMF incorporates consensus manifold and consensus coefficient matrix with multi-manifold regularization to preserve the locally geometrical structure of the multi-view data space. We use two methods to construct the consensus manifold and two methods to find the consensus coefficient matrix, which leads to four instances of the framework. Experimental results show that the proposed algorithms outperform existing non-negative matrix factorization based algorithms for multi-view clustering. Copyright © 2017 Elsevier Ltd. All rights reserved.

Quivers, YBE and 3-manifolds

Science.gov (United States)

Yamazaki, Masahito

2012-05-01

We study 4d superconformal indices for a large class of {N} = 1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T 2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T 2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in {{H}^3} , each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1].

Two-dimensional manifolds with metrics of revolution

International Nuclear Information System (INIS)

Sabitov, I Kh

2000-01-01

This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)

Nonparametric Bayes Classification and Hypothesis Testing on Manifolds

Science.gov (United States)

Bhattacharya, Abhishek; Dunson, David

2012-01-01

Our first focus is prediction of a categorical response variable using features that lie on a general manifold. For example, the manifold may correspond to the surface of a hypersphere. We propose a general kernel mixture model for the joint distribution of the response and predictors, with the kernel expressed in product form and dependence induced through the unknown mixing measure. We provide simple sufficient conditions for large support and weak and strong posterior consistency in estimating both the joint distribution of the response and predictors and the conditional distribution of the response. Focusing on a Dirichlet process prior for the mixing measure, these conditions hold using von Mises-Fisher kernels when the manifold is the unit hypersphere. In this case, Bayesian methods are developed for efficient posterior computation using slice sampling. Next we develop Bayesian nonparametric methods for testing whether there is a difference in distributions between groups of observations on the manifold having unknown densities. We prove consistency of the Bayes factor and develop efficient computational methods for its calculation. The proposed classification and testing methods are evaluated using simulation examples and applied to spherical data applications. PMID:22754028

Teaching and Learning the Interplay between Chance and Determinism in Nonlinear Systems

Science.gov (United States)

Stavrou, Dimitrios; Duit, Reinders

2014-01-01

That the interplay of random and deterministic processes may result in both the limited predictability of nonlinear systems and the formation of structures seems to be a most valuable general insight into the nature of science. This study investigates the possibility of teaching and learning the interplay of chance and determinism in nonlinear…

Nonlinear Bayesian filtering and learning: a neuronal dynamics for perception.

Science.gov (United States)

Kutschireiter, Anna; Surace, Simone Carlo; Sprekeler, Henning; Pfister, Jean-Pascal

2017-08-18

The robust estimation of dynamical hidden features, such as the position of prey, based on sensory inputs is one of the hallmarks of perception. This dynamical estimation can be rigorously formulated by nonlinear Bayesian filtering theory. Recent experimental and behavioral studies have shown that animals' performance in many tasks is consistent with such a Bayesian statistical interpretation. However, it is presently unclear how a nonlinear Bayesian filter can be efficiently implemented in a network of neurons that satisfies some minimum constraints of biological plausibility. Here, we propose the Neural Particle Filter (NPF), a sampling-based nonlinear Bayesian filter, which does not rely on importance weights. We show that this filter can be interpreted as the neuronal dynamics of a recurrently connected rate-based neural network receiving feed-forward input from sensory neurons. Further, it captures properties of temporal and multi-sensory integration that are crucial for perception, and it allows for online parameter learning with a maximum likelihood approach. The NPF holds the promise to avoid the 'curse of dimensionality', and we demonstrate numerically its capability to outperform weighted particle filters in higher dimensions and when the number of particles is limited.

Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases

International Nuclear Information System (INIS)

Sobolev, Vladimir

2016-01-01

We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples. (paper)

Pseudo-Reimannian manifolds endowed with an almost para f-structure

Directory of Open Access Journals (Sweden)

Vladislav V. Goldberg

1985-01-01

Full Text Available Let M˜(U,Ω˜,η˜,ξ,g˜ be a pseudo-Riemannian manifold of signature (n+1,n. One defines on M˜ an almost cosymplectic para f-structure and proves that a manifold M˜ endowed with such a structure is ξ-Ricci flat and is foliated by minimal hypersurfaces normal to ξ, which are of Otsuki's type. Further one considers on M˜ a 2(n−1-dimensional involutive distribution P⊥ and a recurrent vector field V˜. It is proved that the maximal integral manifold M⊥ of P⊥ has V as the mean curvature vector (up to 1/2(n−1. If the complimentary orthogonal distribution P of P⊥ is also involutive, then the whole manifold M˜ is foliate. Different other properties regarding the vector field V˜ are discussed.

Conservation laws in quantum mechanics on a Riemannian manifold

International Nuclear Information System (INIS)

Chepilko, N.M.

1992-01-01

In Refs. 1-5 the quantum dynamics of a particle on a Riemannian manifold V n is considered. The advantage of Ref. 5, in comparison with Refs. 1-4, is the fact that in it the differential-geometric character of the theory and the covariant definition (via the known Lagrangian of the particle) of the algebra of quantum-mechanical operators on V n are mutually consistent. However, in Ref. 5 the procedure for calculating the expectation values of operators from the known wave function of the particle is not discussed. In the authors view, this question is problematical and requires special study. The essence of the problem is that integration on a Riemannian manifold V n , unlike that of a Euclidean manifold R n , is uniquely defined only for scalars. For this reason, the calculation of the expectation value of, e.g., the operator of the momentum or angular momentum of a particle on V n is not defined in the usual sense. However, this circumstance was not taken into account by the authors of Refs. 1-4, in which quantum mechanics on a Riemannian manifold V n was studied. In this paper the author considers the conservation laws and a procedure for calculating observable quantities in the classical mechanics (Sec. 2) and quantum mechanics (Sec. 3) of a particle on V n . It is found that a key role here is played by the Killing vectors of the Riemannian manifold V n . It is shown that the proposed approach to the problem satisfies the correspondence principle for both the classical and the quantum mechanics of a particle on a Euclidean manifold R n

Discrete-time online learning control for a class of unknown nonaffine nonlinear systems using reinforcement learning.

Science.gov (United States)

Yang, Xiong; Liu, Derong; Wang, Ding; Wei, Qinglai

2014-07-01

In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input-multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov's direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach. Copyright © 2014 Elsevier Ltd. All rights reserved.

A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

Science.gov (United States)

Haddout, Soufiane

2018-01-01

The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

Maps between Grassmann manifolds

Indian Academy of Sciences (India)

Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in Indian Academy of Sciences Platinum Jubilee Meeting Hyderabad

2009-07-02

Jul 2, 2009 ... Classification of all manifolds (or maps between them) is an impossible task. The coarser, homotopical classification, is relatively easier–but only relatively! Homotopy is, roughly speaking, the study of properties of spaces and maps invariant under continuous deformations. Denote by [X, Y ] the set of all ...

On nonlinear equations associated with Lie algebras of diffeomorphism groups of two-dimensional manifolds

International Nuclear Information System (INIS)

Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.

1990-01-01

Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs

Global Linear Representations of Nonlinear Systems and the Adjoint Map

OpenAIRE

Banks, S.P.

1988-01-01

In this paper we shall study the global linearization of nonlinear systems on a manifold by two methods. The first consists of an expansion of the vector field in the space of square integrable vector fields. In the second method we use the adjoint representation of the Lie algebra vector fields to obtain an infinite-dimensional matrix representation of the system. A connection between the two approaches will be developed.

Nonlinear elastic inclusions in isotropic solids

KAUST Repository

Yavari, A.

2013-10-16

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.

Sensitive periods in affective development: nonlinear maturation of fear learning.

Science.gov (United States)

Hartley, Catherine A; Lee, Francis S

2015-01-01

At specific maturational stages, neural circuits enter sensitive periods of heightened plasticity, during which the development of both brain and behavior are highly receptive to particular experiential information. A relatively advanced understanding of the regulatory mechanisms governing the initiation, closure, and reinstatement of sensitive period plasticity has emerged from extensive research examining the development of the visual system. In this article, we discuss a large body of work characterizing the pronounced nonlinear changes in fear learning and extinction that occur from childhood through adulthood, and their underlying neural substrates. We draw upon the model of sensitive period regulation within the visual system, and present burgeoning evidence suggesting that parallel mechanisms may regulate the qualitative changes in fear learning across development.

Classification of fMRI resting-state maps using machine learning techniques: A comparative study

Science.gov (United States)

Gallos, Ioannis; Siettos, Constantinos

2017-11-01

We compare the efficiency of Principal Component Analysis (PCA) and nonlinear learning manifold algorithms (ISOMAP and Diffusion maps) for classifying brain maps between groups of schizophrenia patients and healthy from fMRI scans during a resting-state experiment. After a standard pre-processing pipeline, we applied spatial Independent component analysis (ICA) to reduce (a) noise and (b) spatial-temporal dimensionality of fMRI maps. On the cross-correlation matrix of the ICA components, we applied PCA, ISOMAP and Diffusion Maps to find an embedded low-dimensional space. Finally, support-vector-machines (SVM) and k-NN algorithms were used to evaluate the performance of the algorithms in classifying between the two groups.

On Kähler–Norden manifolds

Indian Academy of Sciences (India)

Kähler–Norden manifolds using the theory of Tachibana operators is presented. ... arguments is subject to the action of the affinor structure ϕ. ..... [20] Vishnevskii V V, Integrable affinor structures and their plural interpretations, J. Math. Sci.

LCD OF AIR INTAKE MANIFOLDS PHASE 2: FORD F250 AIR INTAKE MANIFOLD

Science.gov (United States)

The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...

Estimating Turaev-Viro three-manifold invariants is universal for quantum computation

International Nuclear Information System (INIS)

Alagic, Gorjan; Reichardt, Ben W.; Jordan, Stephen P.; Koenig, Robert

2010-01-01

The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-dimensional topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a relation between the task of distinguishing nonhomeomorphic 3-manifolds and the power of a general quantum computer.

Minimal Webs in Riemannian Manifolds

DEFF Research Database (Denmark)

Markvorsen, Steen

2008-01-01

For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence...

The quantum equivariant cohomology of toric manifolds through mirror symmetry

NARCIS (Netherlands)

Baptista, J.M.

2009-01-01

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.

The quantum equivariant cohomology of toric manifolds through mirror symmetry

OpenAIRE

Baptista, J. M.

2008-01-01

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.

A vacuum manifold for rapid world-to-chip connectivity of complex PDMS microdevices.

Science.gov (United States)

Cooksey, Gregory A; Plant, Anne L; Atencia, Javier

2009-05-07

The lack of simple interfaces for microfluidic devices with a large number of inlets significantly limits production and utilization of these devices. In this article, we describe the fabrication of a reusable manifold that provides rapid world-to-chip connectivity. A vacuum network milled into a rigid manifold holds microdevices and prevents leakage of fluids injected into the device from ports in the manifold. A number of different manifold designs were explored, and all performed similarly, yielding an average of 100 kPa (15 psi) fluid holding pressure. The wide applicability of this manifold concept is demonstrated by interfacing with a 51-inlet microfluidic chip containing 144 chambers and hundreds of embedded pneumatic valves. Due to the speed of connectivity, the manifolds are ideal for rapid prototyping and are well suited to serve as "universal" interfaces.

Causal relationship: a new tool for the causal characterization of Lorentzian manifolds

International Nuclear Information System (INIS)

Garcia-Parrado, Alfonso; Senovilla, Jose M M

2003-01-01

We define and study a new kind of relation between two diffeomorphic Lorentzian manifolds called a causal relation, which is any diffeomorphism characterized by mapping every causal vector of the first manifold onto a causal vector of the second. We perform a thorough study of the mathematical properties of causal relations and prove in particular that two given Lorentzian manifolds (say V and W) may be causally related only in one direction (say from V to W, but not from W to V). This leads us to the concept of causally equivalent (or isocausal in short) Lorentzian manifolds as those mutually causally related and to a definition of causal structure over a differentiable manifold as the equivalence class formed by isocausal Lorentzian metrics upon it. Isocausality is a more general concept than the conformal relationship, because we prove the remarkable result that a conformal relation φ is characterized by the fact of being a causal relation of the particular kind in which both φ and φ -1 are causal relations. Isocausal Lorentzian manifolds are mutually causally compatible, they share some important causal properties, and there are one-to-one correspondences, which are sometimes non-trivial, between several classes of their respective future (and past) objects. A more important feature is that they satisfy the same standard causality constraints. We also introduce a partial order for the equivalence classes of isocausal Lorentzian manifolds providing a classification of all the causal structures that a given fixed manifold can have. By introducing the concept of causal extension we put forward a new definition of causal boundary for Lorentzian manifolds based on the concept of isocausality, and thereby we generalize the traditional Penrose constructions of conformal infinity, diagrams and embeddings. In particular, the concept of causal diagram is given. Many explicit clarifying examples are presented throughout the paper

T4 fibrations over Calabi–Yau two-folds and non-Kähler manifolds in string theory

Directory of Open Access Journals (Sweden)

Hai Lin

2016-08-01

Full Text Available We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial T4 fibrations over Calabi–Yau two-folds. These give rise to eight-dimensional non-Kähler Hermitian manifolds with SU(4 structure. The eight-manifold is also a circle fibration over a seven-dimensional G2 manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with SU(4 structure in type IIB string theory with F3 and F7 fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.

Reduction of Nambu-Poisson Manifolds by Regular Distributions

Science.gov (United States)

Das, Apurba

2018-03-01

The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibáñez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduction theorem for Nambu-Poisson manifolds. Finally, we define gauge transformations of Nambu-Poisson structures and show that these transformations commute with the reduction procedure.

Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

KAUST Repository

Abdelkefi, Abdessattar

2013-06-18

In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

Complex manifolds

CERN Document Server

Morrow, James

2006-01-01

This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965-66, is an excellent, well-written introduction to the study of abstract complex (analytic) manifolds-a subject that began in the late 1940's and early 1950's. It is largely self-contained, except for some standard results about elliptic partial differential equations, for which complete references are given. -D. C. Spencer, MathSciNet The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic

Predicting the bounds of large chaotic systems using low-dimensional manifolds.

Directory of Open Access Journals (Sweden)

Asger M Haugaard

Full Text Available Predicting extrema of chaotic systems in high-dimensional phase space remains a challenge. Methods, which give extrema that are valid in the long term, have thus far been restricted to models of only a few variables. Here, a method is presented which treats extrema of chaotic systems as belonging to discretised manifolds of low dimension (low-D embedded in high-dimensional (high-D phase space. As a central feature, the method exploits that strange attractor dimension is generally much smaller than parent system phase space dimension. This is important, since the computational cost associated with discretised manifolds depends exponentially on their dimension. Thus, systems that would otherwise be associated with tremendous computational challenges, can be tackled on a laptop. As a test, bounding manifolds are calculated for high-D modifications of the canonical Duffing system. Parameters can be set such that the bounding manifold displays harmonic behaviour even if the underlying system is chaotic. Thus, solving for one post-transient forcing cycle of the bounding manifold predicts the extrema of the underlying chaotic problem indefinitely.

Collective coordinates on symplectic manifolds

International Nuclear Information System (INIS)

Razumov, A.V.; Taranov, A.Yu.

1981-01-01

For an arbitrary Lie group of canonical transformations on a symplectic manifold collective coordinates are introduced. They describe a motion of the dynamical system as a whole under the group transformations. Some properties of Lie group of canonical transformations are considered [ru

Principal Curves on Riemannian Manifolds

DEFF Research Database (Denmark)

Hauberg, Søren

2015-01-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Eucl...

Invariance for Single Curved Manifold

KAUST Repository

Castro, Pedro Machado Manhaes de

2012-01-01

Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.

Invariance for Single Curved Manifold

KAUST Repository

Castro, Pedro Machado Manhaes de

2012-08-01

Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

Directory of Open Access Journals (Sweden)

Zeki Kasap

2015-01-01

Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

Modular categories and 3-manifold invariants

International Nuclear Information System (INIS)

Tureav, V.G.

1992-01-01

The aim of this paper is to give a concise introduction to the theory of knot invariants and 3-manifold invariants which generalize the Jones polynomial and which may be considered as a mathematical version of the Witten invariants. Such a theory was introduced by N. Reshetikhin and the author on the ground of the theory of quantum groups. here we use more general algebraic objects, specifically, ribbon and modular categories. Such categories in particular arise as the categories of representations of quantum groups. The notion of modular category, interesting in itself, is closely related to the notion of modular tensor category in the sense of G. Moore and N. Seiberg. For simplicity we restrict ourselves in this paper to the case of closed 3-manifolds

On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature

Science.gov (United States)

Hu, Xue

2018-06-01

In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove that the trace-free part of the mass aspect tensor of an APE 4-manifold with harmonic curvature and normalized Einstein conformal infinity is zero. As to the rigidity, we first show that a complete noncompact Riemannian 4-manifold with harmonic curvature and positive Yamabe constant as well as a L2-pinching condition is Einstein. As an application, we then obtain that an APE 4-manifold with harmonic curvature and positive Yamabe constant is isometric to the hyperbolic space provided that the L2-norm of the traceless Ricci tensor or the Weyl tensor is small enough and the conformal infinity is a standard round 3-sphere.

Cayley transform on Stiefel manifolds

Science.gov (United States)

Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel

2018-01-01

The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.

An imbedding of Lorentzian manifolds

International Nuclear Information System (INIS)

Kim, Do-Hyung

2009-01-01

A new method for imbedding a Lorentzian manifold with a non-compact Cauchy surface is presented. As an application, it is shown that any two-dimensional globally hyperbolic spacetime with a non-compact Cauchy surface can be causally isomorphically imbedded into two-dimensional Minkowski spacetime.

Integral reinforcement learning for continuous-time input-affine nonlinear systems with simultaneous invariant explorations.

Science.gov (United States)

Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2015-05-01

This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.

Radical Transversal Lightlike Submanifolds of Indefinite Para-Sasakian Manifolds

OpenAIRE

Shukla S.S.; Yadav Akhilesh

2014-01-01

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transvers...

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

Science.gov (United States)

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

Obstruction theory on 8-manifolds

Czech Academy of Sciences Publication Activity Database

Čadek, M.; Crabb, M.; Vanžura, Jiří

2008-01-01

Roč. 127, č. 2 (2008), s. 167-186 ISSN 0025-2611 R&D Projects: GA ČR GA201/05/2117 Institutional research plan: CEZ:AV0Z10190503 Keywords : 8-manifolds * obstruction theory Subject RIV: BA - General Mathematics Impact factor: 0.509, year: 2008

Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mickael D. Chekroun

2017-07-01

Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

Ultrasonic defect characterization using parametric-manifold mapping

Science.gov (United States)

Velichko, A.; Bai, L.; Drinkwater, B. W.

2017-06-01

The aim of ultrasonic non-destructive evaluation includes the detection and characterization of defects, and an understanding of the nature of defects is essential for the assessment of structural integrity in safety critical systems. In general, the defect characterization challenge involves an estimation of defect parameters from measured data. In this paper, we explore the extent to which defects can be characterized by their ultrasonic scattering behaviour. Given a number of ultrasonic measurements, we show that characterization information can be extracted by projecting the measurement onto a parametric manifold in principal component space. We show that this manifold represents the entirety of the characterization information available from far-field harmonic ultrasound. We seek to understand the nature of this information and hence provide definitive statements on the defect characterization performance that is, in principle, extractable from typical measurement scenarios. In experiments, the characterization problem of surface-breaking cracks and the more general problem of elliptical voids are studied, and a good agreement is achieved between the actual parameter values and the characterization results. The nature of the parametric manifold enables us to explain and quantify why some defects are relatively easy to characterize, whereas others are inherently challenging.

Manifolds for pose tracking from monocular video

Science.gov (United States)

Basu, Saurav; Poulin, Joshua; Acton, Scott T.

2015-03-01

We formulate a simple human-pose tracking theory from monocular video based on the fundamental relationship between changes in pose and image motion vectors. We investigate the natural embedding of the low-dimensional body pose space into a high-dimensional space of body configurations that behaves locally in a linear manner. The embedded manifold facilitates the decomposition of the image motion vectors into basis motion vector fields of the tangent space to the manifold. This approach benefits from the style invariance of image motion flow vectors, and experiments to validate the fundamental theory show reasonable accuracy (within 4.9 deg of the ground truth).

Effective Field Theory on Manifolds with Boundary

Science.gov (United States)

Albert, Benjamin I.

In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.

Brazing retort manifold design concept may minimize air contamination and enhance uniform gas flow

Science.gov (United States)

Ruppe, E. P.

1966-01-01

Brazing retort manifold minimizes air contamination, prevents gas entrapment during purging, and provides uniform gas flow into the retort bell. The manifold is easily cleaned and turbulence within the bell is minimized because all manifold construction lies outside the main enclosure.

Nonlinear sigma-models and their gauging in and out of superspace

International Nuclear Information System (INIS)

Hull, C.M.; California Univ., Santa Barbara; Karlhede, A.; Lindstroem, U.; Rocek, M.

1986-01-01

We analyze and generalize bosonic nonlinear sigma-models and their N=1,2 supersymmetric extensions in (4 spacetime-dimensional) N=1 superspace. We give a general construction of nonminimal kinetic terms for gauge fields and of N=1,2 gauging of isometries on Kaehler and hyper-Kaehler manifolds. In particular, we study the gauging of noncompact groups. We derive the complete component action and supertrace formula. For N=2 models, the supertrace always vanishes. (orig.)

Partial Synchronization Manifolds for Linearly Time-Delay Coupled Systems

OpenAIRE

Steur, Erik; van Leeuwen, Cees; Michiels, Wim

2014-01-01

Sometimes a network of dynamical systems shows a form of incomplete synchronization characterized by synchronization of some but not all of its systems. This type of incomplete synchronization is called partial synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of C, the state space of the network of systems. We focus on partial synchronization manifolds in networks of system...

Linear and Non-Linear Dose-Response Functions Reveal a Hormetic Relationship Between Stress and Learning

OpenAIRE

Zoladz, Phillip R.; Diamond, David M.

2008-01-01

Over a century of behavioral research has shown that stress can enhance or impair learning and memory. In the present review, we have explored the complex effects of stress on cognition and propose that they are characterized by linear and non-linear dose-response functions, which together reveal a hormetic relationship between stress and learning. We suggest that stress initially enhances hippocampal function, resulting from amygdala-induced excitation of hippocampal synaptic plasticity, as ...

Spherical stochastic neighbor embedding of hyperspectral data

CSIR Research Space (South Africa)

Lunga, D

2012-07-01

Full Text Available and manifold learning in Euclidean spaces, very few attempts have focused on non-Euclidean spaces. Here, we propose a novel approach that embeds hyperspectral data, transformed into bilateral probability similarities, onto a nonlinear unit norm coordinate...

Higher dimensional maximally symmetric stationary manifold with pure gauge condition and codimension one flat submanifold

International Nuclear Information System (INIS)

Wiliardy, Abednego; Gunara, Bobby Eka

2016-01-01

An n dimensional flat manifold N is embedded into an n +1 dimensional stationary manifold M. The metric of M is derived from a general form of stationary manifold. By taking several assumption, such as 1) the ambient manifold M to be maximally symmetric space and satisfying a pure gauge condition, and 2) the submanifold is taken to be flat, then we find the solution that satisfies Ricci scalar of N . Moreover, we determine whether the solution is compatible with the Ricci and Riemann tensor of manifold N depending on the dimension. (paper)

Heat shield manifold system for a midframe case of a gas turbine engine

Energy Technology Data Exchange (ETDEWEB)

Mayer, Clinton A.; Eng, Jesse; Schopf, Cheryl A.

2017-07-25

A heat shield manifold system for an inner casing between a compressor and turbine assembly is disclosed. The heat shield manifold system protects the outer case from high temperature compressor discharge air, thereby enabling the outer case extending between a compressor and a turbine assembly to be formed from less expensive materials than otherwise would be required. In addition, the heat shield manifold system may be configured such that compressor bleed air is passed from the compressor into the heat shield manifold system without passing through a conventional flange to flange joint that is susceptible to leakage.

Hidden physics models: Machine learning of nonlinear partial differential equations

Science.gov (United States)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Active learning for semi-supervised clustering based on locally linear propagation reconstruction.

Science.gov (United States)

Chang, Chin-Chun; Lin, Po-Yi

2015-03-01

The success of semi-supervised clustering relies on the effectiveness of side information. To get effective side information, a new active learner learning pairwise constraints known as must-link and cannot-link constraints is proposed in this paper. Three novel techniques are developed for learning effective pairwise constraints. The first technique is used to identify samples less important to cluster structures. This technique makes use of a kernel version of locally linear embedding for manifold learning. Samples neither important to locally linear propagation reconstructions of other samples nor on flat patches in the learned manifold are regarded as unimportant samples. The second is a novel criterion for query selection. This criterion considers not only the importance of a sample to expanding the space coverage of the learned samples but also the expected number of queries needed to learn the sample. To facilitate semi-supervised clustering, the third technique yields inferred must-links for passing information about flat patches in the learned manifold to semi-supervised clustering algorithms. Experimental results have shown that the learned pairwise constraints can capture the underlying cluster structures and proven the feasibility of the proposed approach. Copyright © 2014 Elsevier Ltd. All rights reserved.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

Science.gov (United States)

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

Tops as building blocks for G 2 manifolds

Science.gov (United States)

Braun, Andreas P.

2017-10-01

A large number of examples of compact G 2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.

Gauge groups and topological invariants of vacuum manifolds

International Nuclear Information System (INIS)

Golo, V.L.; Monastyrsky, M.I.

1978-01-01

The paper is concerned with topological properties of the vacuum manifolds in the theories with the broken gauge symmetry for the groups of the type SO(k) x U(n), SO(k) x SO(p) x U(r). For the Ginsburg-Landau theory of the superfluid 3 He the gauge transformations are discussed. They provide the means to indicate all possible types of the vacuum manifolds, which are likely to correspond to distinct phases of the superfluid 3 He. Conditions on the existence of the minimums of the Ginsburg-Landau functional are discussed

Markov's theorem and algorithmically non-recognizable combinatorial manifolds

International Nuclear Information System (INIS)

Shtan'ko, M A

2004-01-01

We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem

Spontaneous compactification and Ricci-flat manifolds with torsion

International Nuclear Information System (INIS)

McInnes, B.

1985-06-01

The Freund-Rubin mechanism is based on the equation Rsub(ik)=lambdagsub(ik) (where lambda>0), which, via Myers' Theorem, implies ''spontaneous'' compactification. The difficulties connected with the cosmological constant in this approach can be resolved if torsion is introduced and lambda set equal to zero, but then compactification ''by hand'' is necessary, since the equation Rsub(ik)=0 can be satisfied both on compact and on non-compact manifolds. In this paper we discuss the global geometry of Ricci-flat manifolds with torsion, and suggest ways of restoring the ''spontaneity'' of the compactification. (author)

Hermitian-Einstein metrics on holomorphic vector bundles over Hermitian manifolds

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we prove the long-time existence of the Hermitian-Einstein flow on a holomorphic vector bundle over a compact Hermitian (non-kaehler) manifold, and solve the Dirichlet problem for the Hermitian-Einstein equations. We also prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete noncompact Hermitian manifolds. (author)

Brain Emotional Learning Based Intelligent Decoupler for Nonlinear Multi-Input Multi-Output Distillation Columns

Directory of Open Access Journals (Sweden)

M. H. El-Saify

2017-01-01

Full Text Available The distillation process is vital in many fields of chemical industries, such as the two-coupled distillation columns that are usually highly nonlinear Multi-Input Multi-Output (MIMO coupled processes. The control of MIMO process is usually implemented via a decentralized approach using a set of Single-Input Single-Output (SISO loop controllers. Decoupling the MIMO process into group of single loops requires proper input-output pairing and development of decoupling compensator unit. This paper proposes a novel intelligent decoupling approach for MIMO processes based on new MIMO brain emotional learning architecture. A MIMO architecture of Brain Emotional Learning Based Intelligent Controller (BELBIC is developed and applied as a decoupler for 4 input/4 output highly nonlinear coupled distillation columns process. Moreover, the performance of the proposed Brain Emotional Learning Based Intelligent Decoupler (BELBID is enhanced using Particle Swarm Optimization (PSO technique. The performance is compared with the PSO optimized steady state decoupling compensation matrix. Mathematical models of the distillation columns and the decouplers are built and tested in simulation environment by applying the same inputs. The results prove remarkable success of the BELBID in minimizing the loops interactions without degrading the output that every input has been paired with.

ON A FAIR MANIFOLD FARE RATING ON A LONG TRAFFIC LINE

Directory of Open Access Journals (Sweden)

Stanislav PALÚCH

2017-06-01

Full Text Available The paper studies the possibilities to design a fair manifold tariff on a long traffic line. If a single tariff is used on a long bus or railway line, passengers travelling long distances are favoured at the expense of those travelling short distances. The fairest approach to tariff is setting an individual tariff for every origin–destination relation of line stops that expresses real travel costs. However, sometimes the individual tariff is too complicated and is therefore replaced by double-, triple- or manifold tariff. This paper shows how to design a manifold tariff in order to minimize unfairness to passengers.

Decompositions of manifolds

CERN Document Server

Daverman, Robert J

2007-01-01

Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve

A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry

OpenAIRE

Wang, Xu-Jia

2006-01-01

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.

Topological anomalies for Seifert 3-manifolds

Energy Technology Data Exchange (ETDEWEB)

Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)

2015-07-14

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.

Hyperspherical Manifold for EEG Signals of Epileptic Seizures

Directory of Open Access Journals (Sweden)

Tahir Ahmad

2012-01-01

Full Text Available The mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst minimizing the loss of signal data due to smoothing. This paper utilizes measure theory to design a discrete probability measure that reformats EEG data without altering its geometric structure. An analysis of EEG data from three patients experiencing epileptic seizures is made using the developed measure, resulting in successful identification of increased potential difference in portions of the brain that correspond to physical symptoms demonstrated by the patients. A mapping then is devised to transport the measure data onto the surface of a high-dimensional manifold, enabling the analysis of seizures using directional statistics and manifold theory. The subset of seizure signals on the manifold is shown to be a topological space, verifying Ahmad's approach to use topological modelling.

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

Science.gov (United States)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Conformal Vector Fields on Doubly Warped Product Manifolds and Applications

Directory of Open Access Journals (Sweden)

H. K. El-Sayied

2016-01-01

Full Text Available This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.

Pseudo-Kaehler quantization on flag manifolds

International Nuclear Information System (INIS)

Karabegov, A.V.

1997-07-01

A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols. (author). 16 refs

Stable harmonic maps from complete manifolds

International Nuclear Information System (INIS)

Xin, Y.L.

1986-01-01

By choosing distinguished cross-sections in the second variational formula for harmonic maps from manifolds with not too fast volume growth into certain submanifolds in the Euclidean space some Liouville type theorems have been proved in this article. (author)

Stein manifolds and holomorphic mappings the homotopy principle in complex analysis

CERN Document Server

Forstnerič, Franc

2017-01-01

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka t...

Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

International Nuclear Information System (INIS)

Suarez Antola, R.

2011-01-01

One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems, during steady operation and during transients, to remain inside a certain bounded set of admissible states and state variations. Also, during transients, certain restrictions must be imposed on the time scale of evolution of the critical subsystem's state. A classification of the different solution types concerning their relation with the operational safety of the power plant is done by distributing the different solution types in relation with the exclusion region of the power-flow map. In the framework of an analytic or numerical modeling process of a boiling water reactor (BWR) power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behavior of this nonlinear system, and then a classification of the different solution types concerning their relation with the operational safety of the power plant, by distributing the different solution types in relation with the exclusion region of the power-flow map. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is used to exemplify the analytical approach developed here. The equation for excess void reactivity of this ROM is generalized. A nonlinear integral-differential equation in the logarithmic power is derived, including the generalized thermal-hydraulics feedback on the reactivity. Introducing a Krilov- Bogoliubov-Mitropolsky (KBM) ansatz with both amplitude and phase being slowly varying functions of time relative to the center period of oscillation, a coupled set of nonlinear ordinary differential equations for amplitude and phase

A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning

DEFF Research Database (Denmark)

Fraccaro, Marco; Kamronn, Simon Due; Paquet, Ulrich

2017-01-01

This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce the Kalman variational auto-encoder, a framework...... for unsupervised learning of sequential data that disentangles two latent representations: an object’s representation, coming from a recognition model, and a latent state describing its dynamics. As a result, the evolution of the world can be imagined and missing data imputed, both without the need to generate...

Selecting protein families for environmental features based on manifold regularization.

Science.gov (United States)

Jiang, Xingpeng; Xu, Weiwei; Park, E K; Li, Guangrong

2014-06-01

Recently, statistics and machine learning have been developed to identify functional or taxonomic features of environmental features or physiological status. Important proteins (or other functional and taxonomic entities) to environmental features can be potentially used as biosensors. A major challenge is how the distribution of protein and gene functions embodies the adaption of microbial communities across environments and host habitats. In this paper, we propose a novel regularization method for linear regression to adapt the challenge. The approach is inspired by local linear embedding (LLE) and we call it a manifold-constrained regularization for linear regression (McRe). The novel regularization procedure also has potential to be used in solving other linear systems. We demonstrate the efficiency and the performance of the approach in both simulation and real data.

Geometry of superconformal manifolds. Part 1

International Nuclear Information System (INIS)

Roslyi, A.A.; Schwarz, A.S.; Voronov, A.A.

1987-01-01

The main facts about complex curves are generalized to superconformal manifolds. The results thus obtained are relevant to the dermion string theory and, in particular, they are useful for computation of determinants of superlaplacians which enter the string partition function

Beyond Nonlinear (Organisational) Learning. The impact of Sustainable Structure to Teach Sustainability.

OpenAIRE

Cardoso-Castro, P; Medina, L

2016-01-01

Though a case study in which the researchers participated and collected information in the conception - involving the design of the infrastructure, implementation and current operation of a K-12 and High School education project in Colombia. In this study, based on the work previously reported by Medina (2015) the authors used linear analysis, action reach, and defined (organizational) learning as a nonlinear and Complex Adaptive System phenomena. The theoretical framework proposes that when ...

Camera-pose estimation via projective Newton optimization on the manifold.

Science.gov (United States)

Sarkis, Michel; Diepold, Klaus

2012-04-01

Determining the pose of a moving camera is an important task in computer vision. In this paper, we derive a projective Newton algorithm on the manifold to refine the pose estimate of a camera. The main idea is to benefit from the fact that the 3-D rigid motion is described by the special Euclidean group, which is a Riemannian manifold. The latter is equipped with a tangent space defined by the corresponding Lie algebra. This enables us to compute the optimization direction, i.e., the gradient and the Hessian, at each iteration of the projective Newton scheme on the tangent space of the manifold. Then, the motion is updated by projecting back the variables on the manifold itself. We also derive another version of the algorithm that employs homeomorphic parameterization to the special Euclidean group. We test the algorithm on several simulated and real image data sets. Compared with the standard Newton minimization scheme, we are now able to obtain the full numerical formula of the Hessian with a 60% decrease in computational complexity. Compared with Levenberg-Marquardt, the results obtained are more accurate while having a rather similar complexity.

Prescribed curvature tensor in locally conformally flat manifolds

Science.gov (United States)

Pina, Romildo; Pieterzack, Mauricio

2018-01-01

A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.

Discrete method for design of flow distribution in manifolds

International Nuclear Information System (INIS)

Wang, Junye; Wang, Hualin

2015-01-01

Flow in manifold systems is encountered in designs of various industrial processes, such as fuel cells, microreactors, microchannels, plate heat exchanger, and radial flow reactors. The uniformity of flow distribution in manifold is a key indicator for performance of the process equipment. In this paper, a discrete method for a U-type arrangement was developed to evaluate the uniformity of the flow distribution and the pressure drop and then was used for direct comparisons between the U-type and the Z-type. The uniformity of the U-type is generally better than that of the Z-type in most of cases for small ζ and large M. The U-type and the Z-type approach each other as ζ increases or M decreases. However, the Z-type is more sensitive to structures than the U-type and approaches uniform flow distribution faster than the U-type as M decreases or ζ increases. This provides a simple yet powerful tool for the designers to evaluate and select a flow arrangement and offers practical measures for industrial applications. - Highlights: • Discrete methodology of flow field designs in manifolds with U-type arrangements. • Quantitative comparison between U-type and Z-type arrangements. • Discrete solution of flow distribution with varying flow coefficients. • Practical measures and guideline to design of manifold systems.

Online transfer learning with extreme learning machine

Science.gov (United States)

Yin, Haibo; Yang, Yun-an

2017-05-01

In this paper, we propose a new transfer learning algorithm for online training. The proposed algorithm, which is called Online Transfer Extreme Learning Machine (OTELM), is based on Online Sequential Extreme Learning Machine (OSELM) while it introduces Semi-Supervised Extreme Learning Machine (SSELM) to transfer knowledge from the source to the target domain. With the manifold regularization, SSELM picks out instances from the source domain that are less relevant to those in the target domain to initialize the online training, so as to improve the classification performance. Experimental results demonstrate that the proposed OTELM can effectively use instances in the source domain to enhance the learning performance.

Encoding quantum information in a stabilized manifold of a superconducting cavity

Science.gov (United States)

Touzard, S.; Leghtas, Z.; Mundhada, S. O.; Axline, C.; Reagor, M.; Chou, K.; Blumoff, J.; Sliwa, K. M.; Shankar, S.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.

In a superconducting Josephson circuit architecture, we activate a multi-photon process between two modes by applying microwave drives at specific frequencies. This creates a pairwise exchange of photons between a high-Q cavity and the environment. The resulting open dynamical system develops a two-dimensional quasi-energy ground state manifold. Can we encode, protect and manipulate quantum information in this manifold? We experimentally investigate the convergence and escape rates in and out of this confined subspace. Finally, using quantum Zeno dynamics, we aim to perform gates which maintain the state in the protected manifold at all times. Work supported by: ARO, ONR, AFOSR and YINQE.

Nonlinear dynamics of rotating shallow water methods and advances

CERN Document Server

Zeitlin, Vladimir

2007-01-01

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa

Osserman and conformally Osserman manifolds with warped and twisted product structure

OpenAIRE

Brozos-Vazquez, M.; Garcia-Rio, E.; Vazquez-Lorenzo, R.

2008-01-01

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature.

Renormalization, unstable manifolds, and the fractal structure of mode locking

International Nuclear Information System (INIS)

Cvitanovic, P.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.

1985-01-01

The apparent universality of the fractal dimension of the set of quasiperiodic windings at the onset of chaos in a wide class of circle maps is described by construction of a universal one-parameter family of maps which lies along the unstable manifold of the renormalization group. The manifold generates a universal ''devil's staircase'' whose dimension agrees with direct numerical calculations. Applications to experiments are discussed

LIFE CYCLE DESIGN OF AIR INTAKE MANIFOLDS; PHASE I: 2.0 L FORD CONTOUR AIR INTAKE MANIFOLD

Science.gov (United States)

The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...

A self-organized learning strategy for object recognition by an embedded line of attraction

Science.gov (United States)

Seow, Ming-Jung; Alex, Ann T.; Asari, Vijayan K.

2012-04-01

on this observation we developed a self- organizing line attractor, which is capable of generating new lines in the feature space to learn unrecognized patterns. Experiments performed on UMIST pose database and CMU face expression variant database for face recognition have shown that the proposed nonlinear line attractor is able to successfully identify the individuals and it provided better recognition rate when compared to the state of the art face recognition techniques. Experiments on FRGC version 2 database has also provided excellent recognition rate in images captured in complex lighting environments. Experiments performed on the Japanese female face expression database and Essex Grimace database using the self organizing line attractor have also shown successful expression invariant face recognition. These results show that the proposed model is able to create nonlinear manifolds in a multidimensional feature space to distinguish complex patterns.

Manifold regularized multi-task feature selection for multi-modality classification in Alzheimer's disease.

Science.gov (United States)

Jie, Biao; Zhang, Daoqiang; Cheng, Bo; Shen, Dinggang

2013-01-01

Accurate diagnosis of Alzheimer's disease (AD), as well as its prodromal stage (i.e., mild cognitive impairment, MCI), is very important for possible delay and early treatment of the disease. Recently, multi-modality methods have been used for fusing information from multiple different and complementary imaging and non-imaging modalities. Although there are a number of existing multi-modality methods, few of them have addressed the problem of joint identification of disease-related brain regions from multi-modality data for classification. In this paper, we proposed a manifold regularized multi-task learning framework to jointly select features from multi-modality data. Specifically, we formulate the multi-modality classification as a multi-task learning framework, where each task focuses on the classification based on each modality. In order to capture the intrinsic relatedness among multiple tasks (i.e., modalities), we adopted a group sparsity regularizer, which ensures only a small number of features to be selected jointly. In addition, we introduced a new manifold based Laplacian regularization term to preserve the geometric distribution of original data from each task, which can lead to the selection of more discriminative features. Furthermore, we extend our method to the semi-supervised setting, which is very important since the acquisition of a large set of labeled data (i.e., diagnosis of disease) is usually expensive and time-consuming, while the collection of unlabeled data is relatively much easier. To validate our method, we have performed extensive evaluations on the baseline Magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (FDG-PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our experimental results demonstrate the effectiveness of the proposed method.

Adaptive Shape Kernel-Based Mean Shift Tracker in Robot Vision System

Directory of Open Access Journals (Sweden)

Chunmei Liu

2016-01-01

Full Text Available This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour.

Adaptive Shape Kernel-Based Mean Shift Tracker in Robot Vision System

Science.gov (United States)

2016-01-01

This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour. PMID:27379165

From Stein to Weinstein and back symplectic geometry of affine complex manifolds

CERN Document Server

Cieliebak, Kai

2013-01-01

A beautiful and comprehensive introduction to this important field. -Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment of the interplay between the world of Stein manifolds and the more topological and flexible world of Weinstein manifolds. Devoted to this subject with a long history, the book serves as a superb introduction to this area and also contains the authors' new results. -Tomasz Mrowka, MIT This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine co

Total Variation Regularization for Functions with Values in a Manifold

KAUST Repository

Lellmann, Jan

2013-12-01

While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.

Total Variation Regularization for Functions with Values in a Manifold

KAUST Repository

Lellmann, Jan; Strekalovskiy, Evgeny; Koetter, Sabrina; Cremers, Daniel

2013-01-01

While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.

GPU accelerated manifold correction method for spinning compact binaries

Science.gov (United States)

Ran, Chong-xi; Liu, Song; Zhong, Shuang-ying

2018-04-01

The graphics processing unit (GPU) acceleration of the manifold correction algorithm based on the compute unified device architecture (CUDA) technology is designed to simulate the dynamic evolution of the Post-Newtonian (PN) Hamiltonian formulation of spinning compact binaries. The feasibility and the efficiency of parallel computation on GPU have been confirmed by various numerical experiments. The numerical comparisons show that the accuracy on GPU execution of manifold corrections method has a good agreement with the execution of codes on merely central processing unit (CPU-based) method. The acceleration ability when the codes are implemented on GPU can increase enormously through the use of shared memory and register optimization techniques without additional hardware costs, implying that the speedup is nearly 13 times as compared with the codes executed on CPU for phase space scan (including 314 × 314 orbits). In addition, GPU-accelerated manifold correction method is used to numerically study how dynamics are affected by the spin-induced quadrupole-monopole interaction for black hole binary system.

Schoen manifold with line bundles as resolved magnetized orbifolds

Energy Technology Data Exchange (ETDEWEB)

Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-12-15

We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.

Fault Detection for Nonlinear Process With Deterministic Disturbances: A Just-In-Time Learning Based Data Driven Method.

Science.gov (United States)

Yin, Shen; Gao, Huijun; Qiu, Jianbin; Kaynak, Okyay

2017-11-01

Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.

Nonlinear machine learning in soft materials engineering and design

Science.gov (United States)

Ferguson, Andrew

The inherently many-body nature of molecular folding and colloidal self-assembly makes it challenging to identify the underlying collective mechanisms and pathways governing system behavior, and has hindered rational design of soft materials with desired structure and function. Fundamentally, there exists a predictive gulf between the architecture and chemistry of individual molecules or colloids and the collective many-body thermodynamics and kinetics. Integrating machine learning techniques with statistical thermodynamics provides a means to bridge this divide and identify emergent folding pathways and self-assembly mechanisms from computer simulations or experimental particle tracking data. We will survey a few of our applications of this framework that illustrate the value of nonlinear machine learning in understanding and engineering soft materials: the non-equilibrium self-assembly of Janus colloids into pinwheels, clusters, and archipelagos; engineering reconfigurable ''digital colloids'' as a novel high-density information storage substrate; probing hierarchically self-assembling onjugated asphaltenes in crude oil; and determining macromolecular folding funnels from measurements of single experimental observables. We close with an outlook on the future of machine learning in soft materials engineering, and share some personal perspectives on working at this disciplinary intersection. We acknowledge support for this work from a National Science Foundation CAREER Award (Grant No. DMR-1350008) and the Donors of the American Chemical Society Petroleum Research Fund (ACS PRF #54240-DNI6).

Molecular nonlinear dynamics and protein thermal uncertainty quantification

Science.gov (United States)

Xia, Kelin; Wei, Guo-Wei

2014-01-01

This work introduces molecular nonlinear dynamics (MND) as a new approach for describing protein folding and aggregation. By using a mode system, we show that the MND of disordered proteins is chaotic while that of folded proteins exhibits intrinsically low dimensional manifolds (ILDMs). The stability of ILDMs is found to strongly correlate with protein energies. We propose a novel method for protein thermal uncertainty quantification based on persistently invariant ILDMs. Extensive comparison with experimental data and the state-of-the-art methods in the field validate the proposed new method for protein B-factor prediction. PMID:24697365

Definability and stability of multiscale decompositions for manifold-valued data

KAUST Repository

Grohs, Philipp

2012-06-01

We discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold analogs of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midpoint-interpolating. For definable multiscale decompositions we obtain a stability result. © 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Towards generalized mirror symmetry for twisted connected sum G 2 manifolds

Science.gov (United States)

Braun, Andreas P.; Del Zotto, Michele

2018-03-01

We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G 2 manifolds. For a given G 2 manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of G 2 manifolds, the other is a duality between Type II strings with different chiralities for another pair of mirror manifolds. We clarify the role of the B-field in the construction, and check that the corresponding massless spectra are respected by the generalized mirror maps. We discuss hints towards a homological version based on BPS spectroscopy. We provide several novel examples of smooth, as well as singular, mirror G 2 backgrounds via pairs of dual projecting tops. We test our conjectures against a Joyce orbifold example, where we reproduce, using our geometrical methods, the known mirror maps that arise from the SCFT worldsheet perspective. Along the way, we discuss non-Abelian gauge symmetries, and argue for the generation of the Affleck-Harvey-Witten superpotential in the pure SYM case.

Integral manifolding structure for fuel cell core having parallel gas flow

Science.gov (United States)

Herceg, Joseph E.

1984-01-01

Disclosed herein are manifolding means for directing the fuel and oxidant gases to parallel flow passageways in a fuel cell core. Each core passageway is defined by electrolyte and interconnect walls. Each electrolyte and interconnect wall consists respectively of anode and cathode materials layered on the opposite sides of electrolyte material, or on the opposite sides of interconnect material. A core wall projects beyond the open ends of the defined core passageways and is disposed approximately midway between and parallel to the adjacent overlaying and underlying interconnect walls to define manifold chambers therebetween on opposite sides of the wall. Each electrolyte wall defining the flow passageways is shaped to blend into and be connected to this wall in order to redirect the corresponding fuel and oxidant passageways to the respective manifold chambers either above or below this intermediate wall. Inlet and outlet connections are made to these separate manifold chambers respectively, for carrying the fuel and oxidant gases to the core, and for carrying their reaction products away from the core.

Quantization of a symplectic manifold associated to a manifold with projective structure

International Nuclear Information System (INIS)

Biswas, Indranil

2009-01-01

Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L P ' over X associated with P. We show that the holomorphic cotangent bundle of the total space of L P ' equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim C X=1.

Type GQS-1 high pressure steam manifold water level monitoring system

International Nuclear Information System (INIS)

Li Nianzu; Li Beicheng; Jia Shengming

1993-10-01

The GQS-1 high pressure steam manifold water level monitoring system is an advanced nuclear gauge that is suitable for on-line detecting and monitor in high pressure steam manifold water level. The physical variable of water level is transformed into electrical pulses by the nuclear sensor. A computer is equipped for data acquisition, analysis and processing and the results are displayed on a 14 inch color monitor. In addition, a 4 ∼ 20 mA output current is used for the recording and regulation of water level. The main application of this gauge is for on-line measurement of high pressure steam manifold water level in fossil-fired power plant and other industries

Semi-Supervised Multitask Learning for Scene Recognition.

Science.gov (United States)

Lu, Xiaoqiang; Li, Xuelong; Mou, Lichao

2015-09-01

Scene recognition has been widely studied to understand visual information from the level of objects and their relationships. Toward scene recognition, many methods have been proposed. They, however, encounter difficulty to improve the accuracy, mainly due to two limitations: 1) lack of analysis of intrinsic relationships across different scales, say, the initial input and its down-sampled versions and 2) existence of redundant features. This paper develops a semi-supervised learning mechanism to reduce the above two limitations. To address the first limitation, we propose a multitask model to integrate scene images of different resolutions. For the second limitation, we build a model of sparse feature selection-based manifold regularization (SFSMR) to select the optimal information and preserve the underlying manifold structure of data. SFSMR coordinates the advantages of sparse feature selection and manifold regulation. Finally, we link the multitask model and SFSMR, and propose the semi-supervised learning method to reduce the two limitations. Experimental results report the improvements of the accuracy in scene recognition.

Hopf bifurcation in love dynamical models with nonlinear couples and time delays

International Nuclear Information System (INIS)

Liao Xiaofeng; Ran Jiouhong

2007-01-01

A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results

The index of Fourier integral operators on manifolds with conical singularities

International Nuclear Information System (INIS)

Nazaikinskii, Vladimir E; Sternin, B Yu; Schulze, B-W

2001-01-01

We describe homogeneous canonical transformations of the cotangent bundle of a manifold with conical singular points and compute the index of an elliptic Fourier integral operator obtained by the quantization of such a transformation. The answer involves the index of an elliptic Fourier integral operator on a smooth manifold and the residues of the conormal symbol

L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature

Directory of Open Access Journals (Sweden)

Junya Takahashi

2018-05-01

Full Text Available We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L 2 -harmonic forms and on which the L 2 -Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.

Nonlinear dynamical system approaches towards neural prosthesis

International Nuclear Information System (INIS)

Torikai, Hiroyuki; Hashimoto, Sho

2011-01-01

An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

Rotation vectors for homeomorphisms of non-positively curved manifolds

International Nuclear Information System (INIS)

Lessa, Pablo

2011-01-01

Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation vectors are shown to exist for almost every orbit of such a dynamical system with respect to any invariant measure with compact support. The concept is then extended to flows and, as an application, it is shown how non-null rotation vectors can be used to construct a measurable semi-conjugacy between a given flow and the geodesic flow of a manifold

Objected constrained registration and manifold learning: A new patient setup approach in image guided radiation therapy of thoracic cancer

Energy Technology Data Exchange (ETDEWEB)

Chen Ting; Jabbour, Salma K.; Haffty, Bruce G.; Yue, Ning [Radiation Oncology Department, Cancer Institute of New Jersey, University of Medicine and Dentistry of New Jersey, 195 Little Albany Street, New Brunswick, New Jersey 08901 (United States); Qin Songbing [Department of Radiation Oncology, The First Affiliated Hospital of Soochow University, Suzhou 215006 (China)

2013-04-15

Purpose: The management of thoracic malignancies with radiation therapy is complicated by continuous target motion. In this study, a real time motion analysis approach is proposed to improve the accuracy of patient setup. Methods: For 11 lung cancer patients a long training fluoroscopy was acquired before the first treatment, and multiple short testing fluoroscopies were acquired weekly at the pretreatment patient setup of image guided radiotherapy (IGRT). The data analysis consisted of three steps: first a 4D target motion model was constructed from 4DCT and projected to the training fluoroscopy through deformable registration. Then the manifold learning method was used to construct a 2D subspace based on the target motion (kinetic) and location (static) information in the training fluoroscopy. Thereafter the respiratory phase in the testing fluoroscopy was determined by finding its location in the subspace. Finally, the phase determined testing fluoroscopy was registered to the corresponding 4DCT to derive the pretreatment patient position adjustment for the IGRT. The method was tested on clinical image sets and numerical phantoms. Results: The registration successfully reconstructed the 4D motion model with over 98% volume similarity in 4DCT, and over 95% area similarity in the training fluoroscopy. The machine learning method derived the phase values in over 98% and 93% test images of the phantom and patient images, respectively, with less than 3% phase error. The setup approach achieved an average accumulated setup error less than 1.7 mm in the cranial-caudal direction and less than 1 mm in the transverse plane. All results were validated against the ground truth of manual delineations by an experienced radiation oncologist. The expected total time for the pretreatment setup analysis was less than 10 s. Conclusions: By combining the registration and machine learning, the proposed approach has the potential to improve the accuracy of pretreatment setup for

Objected constrained registration and manifold learning: A new patient setup approach in image guided radiation therapy of thoracic cancer

International Nuclear Information System (INIS)

Chen Ting; Jabbour, Salma K.; Haffty, Bruce G.; Yue, Ning; Qin Songbing

2013-01-01

Purpose: The management of thoracic malignancies with radiation therapy is complicated by continuous target motion. In this study, a real time motion analysis approach is proposed to improve the accuracy of patient setup. Methods: For 11 lung cancer patients a long training fluoroscopy was acquired before the first treatment, and multiple short testing fluoroscopies were acquired weekly at the pretreatment patient setup of image guided radiotherapy (IGRT). The data analysis consisted of three steps: first a 4D target motion model was constructed from 4DCT and projected to the training fluoroscopy through deformable registration. Then the manifold learning method was used to construct a 2D subspace based on the target motion (kinetic) and location (static) information in the training fluoroscopy. Thereafter the respiratory phase in the testing fluoroscopy was determined by finding its location in the subspace. Finally, the phase determined testing fluoroscopy was registered to the corresponding 4DCT to derive the pretreatment patient position adjustment for the IGRT. The method was tested on clinical image sets and numerical phantoms. Results: The registration successfully reconstructed the 4D motion model with over 98% volume similarity in 4DCT, and over 95% area similarity in the training fluoroscopy. The machine learning method derived the phase values in over 98% and 93% test images of the phantom and patient images, respectively, with less than 3% phase error. The setup approach achieved an average accumulated setup error less than 1.7 mm in the cranial-caudal direction and less than 1 mm in the transverse plane. All results were validated against the ground truth of manual delineations by an experienced radiation oncologist. The expected total time for the pretreatment setup analysis was less than 10 s. Conclusions: By combining the registration and machine learning, the proposed approach has the potential to improve the accuracy of pretreatment setup for

Generalized regular genus for manifolds with boundary

Directory of Open Access Journals (Sweden)

Paola Cristofori

2003-05-01

Full Text Available We introduce a generalization of the regular genus, a combinatorial invariant of PL manifolds ([10], which is proved to be strictly related, in dimension three, to generalized Heegaard splittings defined in [12].

Stability of Kinesthetic Perception in Efferent-Afferent Spaces: The Concept of Iso-perceptual Manifold.

Science.gov (United States)

Latash, Mark L

2018-02-21

The main goal of this paper is to introduce the concept of iso-perceptual manifold for perception of body configuration and related variables (kinesthetic perception) and to discuss its relation to the equilibrium-point hypothesis and the concepts of reference coordinate and uncontrolled manifold. Hierarchical control of action is postulated with abundant transformations between sets of spatial reference coordinates for salient effectors at different levels. Iso-perceptual manifold is defined in the combined space of afferent and efferent variables as the subspace corresponding to a stable percept. Examples of motion along an iso-perceptual manifold (perceptually equivalent motion) are considered during various natural actions. Some combinations of afferent and efferent signals, in particular those implying a violation of body's integrity, give rise to variable percepts by artificial projection onto iso-perceptual manifolds. This framework is used to interpret unusual features of vibration-induced kinesthetic illusions and to predict new illusions not yet reported in the literature. Copyright © 2017 IBRO. Published by Elsevier Ltd. All rights reserved.

The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

International Nuclear Information System (INIS)

Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

2007-05-01

The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

Pseudo-Kähler Quantization on Flag Manifolds

Science.gov (United States)

Karabegov, Alexander V.

A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kähler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols.

Group actions, non-Kähler complex manifolds and SKT structures

Directory of Open Access Journals (Sweden)

Poddar Mainak

2018-02-01

Full Text Available We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler complex structures on tangential frame bundles of complex orbifolds.

Quantum invariants of knots and 3-manifolds. 2. rev. ed.

International Nuclear Information System (INIS)

Turaev, Vladimir G.

2010-01-01

Due to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. From the contents: - Invariants of graphs in Euclidean 3-space and of closed 3-manifolds - Foundations of topological quantum field theory - Three-dimensional topological quantum field theory - Two-dimensional modular functors - 6j-symbols - Simplicial state sums on 3-manifolds - Shadows of manifolds and state sums on shadows - Constructions of modular categories. (orig.)

On the scalar curvature of self-dual manifolds

International Nuclear Information System (INIS)

Kim, J.

1992-08-01

We generalize LeBrun's explicit ''hyperbolic ansatz'' construction of self-dual metrics on connected sums of conformally flat manifolds and CP 2 's through a systematic use of the theory of hyperbolic geometry and Kleinian groups. (This construction produces, for example, all self-dual manifolds with semi-free S 1 -action and with either nonnegative scalar curvature or positive-definite intersection form.) We then point out a simple criterion for determining the sign of the scalar curvature of these conformal metrics. Exploiting this, we then show that the sign of the scalar curvature can change on connected components of the moduli space of self-dual metrics, thereby answering a question raised by King and Kotschick. (author). Refs

Laplacian manifold regularization method for fluorescence molecular tomography

Science.gov (United States)

He, Xuelei; Wang, Xiaodong; Yi, Huangjian; Chen, Yanrong; Zhang, Xu; Yu, Jingjing; He, Xiaowei

2017-04-01

Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ℓ1-regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ℓ1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai-Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ℓ1 minimization method in both spatial aggregation and location accuracy.

M-theory and G2 manifolds

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Robbins, Daniel

2015-01-01

In this talk we report on recent progress in describing compactifications of string theory and M-theory on G 2 and Spin(7) manifolds. We include the infinite set of α’-corrections and describe the entire tower of massless and massive Kaluza–Klein modes resulting from such compactifications. (invited comment)

On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

Science.gov (United States)

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

Manifold Regularized Multi-Task Feature Selection for Multi-Modality Classification in Alzheimer’s Disease

Science.gov (United States)

Jie, Biao; Cheng, Bo

2014-01-01

Accurate diagnosis of Alzheimer’s disease (AD), as well as its pro-dromal stage (i.e., mild cognitive impairment, MCI), is very important for possible delay and early treatment of the disease. Recently, multi-modality methods have been used for fusing information from multiple different and complementary imaging and non-imaging modalities. Although there are a number of existing multi-modality methods, few of them have addressed the problem of joint identification of disease-related brain regions from multi-modality data for classification. In this paper, we proposed a manifold regularized multi-task learning framework to jointly select features from multi-modality data. Specifically, we formulate the multi-modality classification as a multi-task learning framework, where each task focuses on the classification based on each modality. In order to capture the intrinsic relatedness among multiple tasks (i.e., modalities), we adopted a group sparsity regularizer, which ensures only a small number of features to be selected jointly. In addition, we introduced a new manifold based Laplacian regularization term to preserve the geometric distribution of original data from each task, which can lead to the selection of more discriminative features. Furthermore, we extend our method to the semi-supervised setting, which is very important since the acquisition of a large set of labeled data (i.e., diagnosis of disease) is usually expensive and time-consuming, while the collection of unlabeled data is relatively much easier. To validate our method, we have performed extensive evaluations on the baseline Magnetic resonance imaging (MRI) and fluorodeoxyglucose positron emission tomography (FDG-PET) data of Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Our experimental results demonstrate the effectiveness of the proposed method. PMID:24505676

L1-norm locally linear representation regularization multi-source adaptation learning.

Science.gov (United States)

Tao, Jianwen; Wen, Shiting; Hu, Wenjun

2015-09-01

In most supervised domain adaptation learning (DAL) tasks, one has access only to a small number of labeled examples from target domain. Therefore the success of supervised DAL in this "small sample" regime needs the effective utilization of the large amounts of unlabeled data to extract information that is useful for generalization. Toward this end, we here use the geometric intuition of manifold assumption to extend the established frameworks in existing model-based DAL methods for function learning by incorporating additional information about the target geometric structure of the marginal distribution. We would like to ensure that the solution is smooth with respect to both the ambient space and the target marginal distribution. In doing this, we propose a novel L1-norm locally linear representation regularization multi-source adaptation learning framework which exploits the geometry of the probability distribution, which has two techniques. Firstly, an L1-norm locally linear representation method is presented for robust graph construction by replacing the L2-norm reconstruction measure in LLE with L1-norm one, which is termed as L1-LLR for short. Secondly, considering the robust graph regularization, we replace traditional graph Laplacian regularization with our new L1-LLR graph Laplacian regularization and therefore construct new graph-based semi-supervised learning framework with multi-source adaptation constraint, which is coined as L1-MSAL method. Moreover, to deal with the nonlinear learning problem, we also generalize the L1-MSAL method by mapping the input data points from the input space to a high-dimensional reproducing kernel Hilbert space (RKHS) via a nonlinear mapping. Promising experimental results have been obtained on several real-world datasets such as face, visual video and object. Copyright © 2015 Elsevier Ltd. All rights reserved.

Microwave transport in EBT distribution manifolds using Monte Carlo ray-tracing techniques

International Nuclear Information System (INIS)

Lillie, R.A.; White, T.L.; Gabriel, T.A.; Alsmiller, R.G. Jr.

1983-01-01

Ray tracing Monte Carlo calculations have been carried out using an existing Monte Carlo radiation transport code to obtain estimates of the microsave power exiting the torus coupling links in EPT microwave manifolds. The microwave power loss and polarization at surface reflections were accounted for by treating the microwaves as plane waves reflecting off plane surfaces. Agreement on the order of 10% was obtained between the measured and calculated output power distribution for an existing EBT-S toroidal manifold. A cost effective iterative procedure utilizing the Monte Carlo history data was implemented to predict design changes which could produce increased manifold efficiency and improved output power uniformity

Totally Contact Umbilical Lightlike Hypersurfaces of Indefinite -Manifolds

Directory of Open Access Journals (Sweden)

Rachna Rani

2013-01-01

Full Text Available We study totally contact umbilical lightlike hypersurfaces of indefinite -manifolds and prove the nonexistence of totally contact umbilical lightlike hypersurface in indefinite -space form.

Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes

DEFF Research Database (Denmark)

Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo

2012-01-01

In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...... our algorithm on the same data that was used in [5], where the authors use motion capture devices to record the demonstrations. As further validation we test our approach on novel data acquired on our iCub in a different demonstration scenario in which the robot is physically driven by the human...

Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary

International Nuclear Information System (INIS)

Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.

2005-08-01

We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)

Multidimensional flamelet-generated manifolds for partially premixed combustion

Energy Technology Data Exchange (ETDEWEB)

Nguyen, Phuc-Danh; Vervisch, Luc; Subramanian, Vallinayagam; Domingo, Pascale [CORIA - CNRS and INSA de Rouen, Technopole du Madrillet, BP 8, 76801 Saint-Etienne-du-Rouvray (France)

2010-01-15

Flamelet-generated manifolds have been restricted so far to premixed or diffusion flame archetypes, even though the resulting tables have been applied to nonpremixed and partially premixed flame simulations. By using a projection of the full set of mass conservation species balance equations into a restricted subset of the composition space, unsteady multidimensional flamelet governing equations are derived from first principles, under given hypotheses. During the projection, as in usual one-dimensional flamelets, the tangential strain rate of scalar isosurfaces is expressed in the form of the scalar dissipation rates of the control parameters of the multidimensional flamelet-generated manifold (MFM), which is tested in its five-dimensional form for partially premixed combustion, with two composition space directions and three scalar dissipation rates. It is shown that strain-rate-induced effects can hardly be fully neglected in chemistry tabulation of partially premixed combustion, because of fluxes across iso-equivalence-ratio and iso-progress-of-reaction surfaces. This is illustrated by comparing the 5D flamelet-generated manifold with one-dimensional premixed flame and unsteady strained diffusion flame composition space trajectories. The formal links between the asymptotic behavior of MFM and stratified flame, weakly varying partially premixed front, triple-flame, premixed and nonpremixed edge flames are also evidenced. (author)

The Hantzsche-Wendt manifold in cosmic topology

Science.gov (United States)

Aurich, R.; Lustig, S.

2014-08-01

The Hantzsche-Wendt space is one of the 17 multiply connected spaces of the three-dimensional Euclidean space {{{E}}^{3}}. It is a compact and orientable manifold which can serve as a model for a spatial finite universe. Since it possesses much fewer matched back-to-back circle pairs on the cosmic microwave background (CMB) sky than the other compact flat spaces, it can escape the detection by a search for matched circle pairs. The suppression of temperature correlations C(\\vartheta ) on large angular scales on the CMB sky is studied. It is shown that the large-scale correlations are of the same order as for the three-torus topology but express a much larger variability. The Hantzsche-Wendt manifold provides a topological possibility with reduced large-angle correlations that can hide from searches for matched back-to-back circle pairs.

Higher efficiency with cylinder-bank comprehensive exhaust manifold; Effizienzsteigerung durch Zylinderbank-uebergreifenden Kruemmer

Energy Technology Data Exchange (ETDEWEB)

Diez, Rainer; Kornherr, Heinz; Pirntke, Frank; Schmidt, Juergen [Friedrich Boysen GmbH und Co. KG, Altensteig (Germany)

2010-05-15

In close interdisciplinary cooperation with BMW Group, Boysen has developed an air-gap-insulated exhaust manifold that encompasses both banks of the 4.4 l V8 spark-ignition twin turbo engine of the BMW X5 M and BMW X6 M. The manifold merges the exhaust gas flow from the cylinders of the left-hand and right-hand cylinder banks in opposing pairs, thus optimising gas exchange. Due to improvements in response, torque and power characteristics of the engine, the cylinder-bank comprehensive exhaust manifold helps achieve high fuel efficiency. (orig.)

Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds

Science.gov (United States)

Chikin, V. M.

2017-07-01

In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular n-gons with n≥ 7 their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles.

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

Science.gov (United States)

Wang, W.; Wang, D.; Peng, Z. H.

2017-09-01

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.

Frobenius splitting of thick flag manifolds of Kac-Moody algebras

OpenAIRE

Kato, Syu

2017-01-01

We explain that the Pl\\"ucker relations provide the defining equations of the thick flag manifold associated to a Kac-Moody algebra. This naturally transplant the result of Kumar-Mathieu-Schwede about the Frobenius splitting of thin flag manifolds to the thick case. As a consequence, we provide a description of the global sections of line bundles of a thick Schubert variety as conjectured in Kashiwara-Shimozono [Duke Math. J. 148 (2009)]. This also yields the existence of a compatible basis o...

A model reference and sensitivity model-based self-learning fuzzy logic controller as a solution for control of nonlinear servo systems

NARCIS (Netherlands)

Kovacic, Z.; Bogdan, S.; Balenovic, M.

1999-01-01

In this paper, the design, simulation and experimental verification of a self-learning fuzzy logic controller (SLFLC) suitable for the control of nonlinear servo systems are described. The SLFLC contains a learning algorithm that utilizes a second-order reference model and a sensitivity model

Torsions of 3-dimensional manifolds

CERN Document Server

Wurzbacher, T

2002-01-01

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews

Project Development Specification for Valve Pit Manifold

International Nuclear Information System (INIS)

MCGREW, D.L.

2000-01-01

Establishes the performance, design development, and test requirements for the valve pit manifolds. The system engineering approach was used to develop this document in accordance with the guidelines laid out in the Systems Engineering Management Plan for Project W-314

Foliations and the geometry of 3-manifolds

CERN Document Server

Calegari, Danny

2014-01-01

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.

Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds

International Nuclear Information System (INIS)

Rusokov, B.Y.

1990-01-01

Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including non-orientable one. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities' point of view, non-orientability of the manifold is equivalent to its non-compactness

The heat flows and harmonic maps from complete manifolds into generalized regular balls

International Nuclear Information System (INIS)

Li Jiayu.

1993-01-01

Let M be a complete Riemannian manifold (compact (with or without boundary) or noncompact). Let N be a complete Riemannian manifold. We generalize the existence result for harmonic maps obtained by Hildebrandt-Kaul-Widman using the heat flow method. (author). 21 refs

Chebyshev-Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

Science.gov (United States)

Mireles James, J. D.; Murray, Maxime

2017-12-01

This paper develops a Chebyshev-Taylor spectral method for studying stable/unstable manifolds attached to periodic solutions of differential equations. The work exploits the parameterization method — a general functional analytic framework for studying invariant manifolds. Useful features of the parameterization method include the fact that it can follow folds in the embedding, recovers the dynamics on the manifold through a simple conjugacy, and admits a natural notion of a posteriori error analysis. Our approach begins by deriving a recursive system of linear differential equations describing the Taylor coefficients of the invariant manifold. We represent periodic solutions of these equations as solutions of coupled systems of boundary value problems. We discuss the implementation and performance of the method for the Lorenz system, and for the planar circular restricted three- and four-body problems. We also illustrate the use of the method as a tool for computing cycle-to-cycle connecting orbits.

Toric geometry of G2-manifolds

DEFF Research Database (Denmark)

Madsen, Thomas Bruun; Swann, Andrew Francis

We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz...

M theory and singularities of exceptional holonomy manifolds

International Nuclear Information System (INIS)

Acharya, Bobby S.; Gukov, Sergei

2004-12-01

M theory compactifications on G 2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory. (author)

Harmonic spinors on a family of Einstein manifolds

Science.gov (United States)

Franchetti, Guido

2018-06-01

The purpose of this paper is to study harmonic spinors defined on a 1-parameter family of Einstein manifolds which includes Taub–NUT, Eguchi–Hanson and with the Fubini–Study metric as particular cases. We discuss the existence of and explicitly solve for spinors harmonic with respect to the Dirac operator twisted by a geometrically preferred connection. The metrics examined are defined, for generic values of the parameter, on a non-compact manifold with the topology of and extend to as edge-cone metrics. As a consequence, the subtle boundary conditions of the Atiyah–Patodi–Singer index theorem need to be carefully considered in order to show agreement between the index of the twisted Dirac operator and the result obtained by counting the explicit solutions.

Solving variational problems and partial differential equations that map between manifolds via the closest point method

Science.gov (United States)

King, Nathan D.; Ruuth, Steven J.

2017-05-01

Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.

Preliminary Experimental Study on Pressure Loss Coefficients of Exhaust Manifold Junction

Directory of Open Access Journals (Sweden)

Xiao-lu Lu

2014-01-01

Full Text Available The flow characteristic of exhaust system has an important impact on inlet boundary of the turbine. In this paper, high speed flow in a diesel exhaust manifold junction was tested and simulated. The pressure loss coefficient of the junction flow was analyzed. The steady experimental results indicated that both of static pressure loss coefficients L13 and L23 first increased and then decreased with the increase of mass flow ratio of lateral branch and public manifold. The total pressure loss coefficient K13 always increased with the increase of mass flow ratio of junctions 1 and 3. The total pressure loss coefficient K23 first increased and then decreased with the increase of mass flow ratio of junctions 2 and 3. These pressure loss coefficients of the exhaust pipe junctions can be used in exhaust flow and turbine inlet boundary conditions analysis. In addition, simulating calculation was conducted to analyze the effect of branch angle on total pressure loss coefficient. According to the calculation results, total pressure loss coefficient was almost the same at low mass flow rate of branch manifold 1 but increased with lateral branch angle at high mass flow rate of branch manifold 1.

A generalized construction of mirror manifolds

International Nuclear Information System (INIS)

Berglund, P.; Huebsch, T.

1993-01-01

We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known. (orig.)

Point interactions in two- and three-dimensional Riemannian manifolds

International Nuclear Information System (INIS)

Erman, Fatih; Turgut, O Teoman

2010-01-01

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac-delta interactions on two- and three-dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator Φ(E). In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for a general class of manifolds, e.g. for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by the Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the β function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by Rajeev.

Cobordism independence of Grassmann manifolds

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

ν(m) divides m. Given a positive integer d, let G(d) denote the set of bordism classes of all non-bounding. Grassmannian manifolds Gk(Fn+k) having real dimension d such that k < n. The restric- tion k

Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

International Nuclear Information System (INIS)

Czachor, M.

1996-01-01

Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

Exactly and completely integrable nonlinear dynamical systems

International Nuclear Information System (INIS)

Leznov, A.N.; Savel'ev, M.V.

1987-01-01

The survey is devoted to a consitent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including generalized (periodic and finite nonperiodic Toda lattice, nonlinear Schroedinger, Korteweg-de Vries, Lotka-Volterra equations, etc.) For exactly integrable systems the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed. Application of the developed methods to a differential geometry problem of classification of the integrable manifolds embeddings is discussed. For exactly integrable systems the supersymmetric extensions are constructed. By the example of the generalized Toda lattice a quantization scheme is developed. It includes an explicit derivation of the corresponding Heisenberg operators and their desription in terms of the quantum algebras of the Hopf type. Among multidimensional systems the four-dimensional self-dual Yang-Mills equations are investigated most attentively with a goal of constructing their general solutions

M Theory, G2-manifolds and four dimensional physics

International Nuclear Information System (INIS)

Acharya, B.S.

2003-01-01

M theory on a manifold of G 2 -holonomy is a natural framework for obtaining vacua with four large spacetime dimensions and N = 1 supersymmetry. In order to obtain, within this framework, the standard features of particle physics, namely non-Abelian gauge groups and chiral fermions, we consider G 2 -manifolds with certain kinds of singularities at which these features reside. The aim of these lectures is to describe in detail how the above picture emerges. Along the way we will see how interesting aspects of strongly coupled gauge theories, such as confinement, receive relatively simple explanations within the context of M theory. (author)

Holomorphic Yukawa couplings for complete intersection Calabi-Yau manifolds

Energy Technology Data Exchange (ETDEWEB)

Blesneag, Stefan [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom); Buchbinder, Evgeny I. [The University of Western Australia,35 Stirling Highway, Crawley WA 6009 (Australia); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)

2017-01-27

We develop methods to compute holomorphic Yukawa couplings for heterotic compactifications on complete intersection Calabi-Yau manifolds, generalising results of an earlier paper for Calabi-Yau hypersurfaces. Our methods are based on constructing the required bundle-valued forms explicitly and evaluating the relevant integrals over the projective ambient space. We also show how our approach relates to an earlier, algebraic one to calculate the holomorphic Yukawa couplings. A vanishing theorem, which we prove, implies that certain Yukawa couplings allowed by low-energy symmetries are zero due to topological reasons. To illustrate our methods, we calculate Yukawa couplings for SU(5)-based standard models on a co-dimension two complete intersection manifold.

Holomorphic two-spheres in complex Grassmann manifold

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 3. Holomorphic Two-Spheres in Complex Grassmann Manifold (2, 4). Xiaowei Xu ... Author Affiliations. Xiaowei Xu1 Xiaoxiang Jiao1. School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China ...

Conservative systems with ports on contact manifolds

NARCIS (Netherlands)

Eberard, D.; Maschke, B.M.; van der Schaft, Arjan; Piztek, P.

In this paper we propose an extension of port Hamiltonian systems, called conservative systems with ports, which encompass systems arising from the Irreversible Thermodynamics. Firstly we lift a port Hamiltonian system from its state space manifold to the thermodynamic phase space to a contact

Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.

Science.gov (United States)

Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof

2018-01-01

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Hamilton's gradient estimate for the heat kernel on complete manifolds

OpenAIRE

Kotschwar, Brett

2007-01-01

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \\geq -Kg$. We accomplish this extension via a maximum principle of L. Karp and P. Li and a Bernstein-type estimate on the gradient of the solution. An application of our result, together with the bounds of P. Li and S.T. Yau, yields an estimate on the gradient of the heat kernel for complete manifol...

Information-theoretic semi-supervised metric learning via entropy regularization.

Science.gov (United States)

Niu, Gang; Dai, Bo; Yamada, Makoto; Sugiyama, Masashi

2014-08-01

We propose a general information-theoretic approach to semi-supervised metric learning called SERAPH (SEmi-supervised metRic leArning Paradigm with Hypersparsity) that does not rely on the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize its entropy on labeled data and minimize its entropy on unlabeled data following entropy regularization. For metric learning, entropy regularization improves manifold regularization by considering the dissimilarity information of unlabeled data in the unsupervised part, and hence it allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Moreover, we regularize SERAPH by trace-norm regularization to encourage low-dimensional projections associated with the distance metric. The nonconvex optimization problem of SERAPH could be solved efficiently and stably by either a gradient projection algorithm or an EM-like iterative algorithm whose M-step is convex. Experiments demonstrate that SERAPH compares favorably with many well-known metric learning methods, and the learned Mahalanobis distance possesses high discriminability even under noisy environments.

Flipped SU(5) from manifold compactification of the ten-dimensional heterotic string

Energy Technology Data Exchange (ETDEWEB)

Campbell, B.A.; Ellis, J.; Hagelin, J.S.; Ticciati, R.; Nanopoulos, D.V.

1987-11-19

We show that a recently proposed flipped SU(5) x U(1) GUT cannot be obtained from a conventional SO(10) GUT, nor from the heterotic string by Hosotani gauge symmetry breaking of E/sub 6/ on a manifold with (2,2) world-sheet supersymmetry. It can in principle be obtained by Hosotani gauge symmetry breaking of SO(10) on a manifold with (1,2) world-sheet supersymmetry. We identify the topological conditions under which the required chiral matter generations, Higgs multiplets, and gauge singlet fields can be light. In particular we show that non-perturbative world-sheet instanton effects neither destabilize the manifold nor give masses to the gauge singlets. The required Yukawa couplings are not forbidden by any known selection rules.