Application of higher order SVD to vibration-based system identification and damage detection

NASA Astrophysics Data System (ADS)

Chao, Shu-Hsien; Loh, Chin-Hsiung; Weng, Jian-Huang

2012-04-01

Singular value decomposition (SVD) is a powerful linear algebra tool. It is widely used in many different signal processing methods, such principal component analysis (PCA), singular spectrum analysis (SSA), frequency domain decomposition (FDD), subspace identification and stochastic subspace identification method ( SI and SSI ). In each case, the data is arranged appropriately in matrix form and SVD is used to extract the feature of the data set. In this study three different algorithms on signal processing and system identification are proposed: SSA, SSI-COV and SSI-DATA. Based on the extracted subspace and null-space from SVD of data matrix, damage detection algorithms can be developed. The proposed algorithm is used to process the shaking table test data of the 6-story steel frame. Features contained in the vibration data are extracted by the proposed method. Damage detection can then be investigated from the test data of the frame structure through subspace-based and nullspace-based damage indices.

Structural damage detection based on stochastic subspace identification and statistical pattern recognition: I. Theory

NASA Astrophysics Data System (ADS)

Ren, W. X.; Lin, Y. Q.; Fang, S. E.

2011-11-01

One of the key issues in vibration-based structural health monitoring is to extract the damage-sensitive but environment-insensitive features from sampled dynamic response measurements and to carry out the statistical analysis of these features for structural damage detection. A new damage feature is proposed in this paper by using the system matrices of the forward innovation model based on the covariance-driven stochastic subspace identification of a vibrating system. To overcome the variations of the system matrices, a non-singularity transposition matrix is introduced so that the system matrices are normalized to their standard forms. For reducing the effects of modeling errors, noise and environmental variations on measured structural responses, a statistical pattern recognition paradigm is incorporated into the proposed method. The Mahalanobis and Euclidean distance decision functions of the damage feature vector are adopted by defining a statistics-based damage index. The proposed structural damage detection method is verified against one numerical signal and two numerical beams. It is demonstrated that the proposed statistics-based damage index is sensitive to damage and shows some robustness to the noise and false estimation of the system ranks. The method is capable of locating damage of the beam structures under different types of excitations. The robustness of the proposed damage detection method to the variations in environmental temperature is further validated in a companion paper by a reinforced concrete beam tested in the laboratory and a full-scale arch bridge tested in the field.

Subspace algorithms for identifying separable-in-denominator 2D systems with deterministic-stochastic inputs

NASA Astrophysics Data System (ADS)

Ramos, José A.; Mercère, Guillaume

2016-12-01

In this paper, we present an algorithm for identifying two-dimensional (2D) causal, recursive and separable-in-denominator (CRSD) state-space models in the Roesser form with deterministic-stochastic inputs. The algorithm implements the N4SID, PO-MOESP and CCA methods, which are well known in the literature on 1D system identification, but here we do so for the 2D CRSD Roesser model. The algorithm solves the 2D system identification problem by maintaining the constraint structure imposed by the problem (i.e. Toeplitz and Hankel) and computes the horizontal and vertical system orders, system parameter matrices and covariance matrices of a 2D CRSD Roesser model. From a computational point of view, the algorithm has been presented in a unified framework, where the user can select which of the three methods to use. Furthermore, the identification task is divided into three main parts: (1) computing the deterministic horizontal model parameters, (2) computing the deterministic vertical model parameters and (3) computing the stochastic components. Specific attention has been paid to the computation of a stabilised Kalman gain matrix and a positive real solution when required. The efficiency and robustness of the unified algorithm have been demonstrated via a thorough simulation example.

Output-only cyclo-stationary linear-parameter time-varying stochastic subspace identification method for rotating machinery and spinning structures

NASA Astrophysics Data System (ADS)

Velazquez, Antonio; Swartz, R. Andrew

2015-02-01

Economical maintenance and operation are critical issues for rotating machinery and spinning structures containing blade elements, especially large slender dynamic beams (e.g., wind turbines). Structural health monitoring systems represent promising instruments to assure reliability and good performance from the dynamics of the mechanical systems. However, such devices have not been completely perfected for spinning structures. These sensing technologies are typically informed by both mechanistic models coupled with data-driven identification techniques in the time and/or frequency domain. Frequency response functions are popular but are difficult to realize autonomously for structures of higher order, especially when overlapping frequency content is present. Instead, time-domain techniques have shown to possess powerful advantages from a practical point of view (i.e. low-order computational effort suitable for real-time or embedded algorithms) and also are more suitable to differentiate closely-related modes. Customarily, time-varying effects are often neglected or dismissed to simplify this analysis, but such cannot be the case for sinusoidally loaded structures containing spinning multi-bodies. A more complex scenario is constituted when dealing with both periodic mechanisms responsible for the vibration shaft of the rotor-blade system and the interaction of the supporting substructure. Transformations of the cyclic effects on the vibrational data can be applied to isolate inertial quantities that are different from rotation-generated forces that are typically non-stationary in nature. After applying these transformations, structural identification can be carried out by stationary techniques via data-correlated eigensystem realizations. In this paper, an exploration of a periodic stationary or cyclo-stationary subspace identification technique is presented here for spinning multi-blade systems by means of a modified Eigensystem Realization Algorithm (ERA) via stochastic subspace identification (SSI) and linear parameter time-varying (LPTV) techniques. Structural response is assumed to be stationary ambient excitation produced by a Gaussian (white) noise within the operative range bandwidth of the machinery or structure in study. ERA-OKID analysis is driven by correlation-function matrices from the stationary ambient response aiming to reduce noise effects. Singular value decomposition (SVD) and eigenvalue analysis are computed in a last stage to identify frequencies and complex-valued mode shapes. Proposed assumptions are carefully weighted to account for the uncertainty of the environment. A numerical example is carried out based a spinning finite element (SFE) model, and verified using ANSYS® Ver. 12. Finally, comments and observations are provided on how this subspace realization technique can be extended to the problem of modal-parameter identification using only ambient vibration data.

Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology

NASA Astrophysics Data System (ADS)

Parsons, Todd L.; Rogers, Tim

2017-10-01

Systems composed of large numbers of interacting agents often admit an effective coarse-grained description in terms of a multidimensional stochastic dynamical system, driven by small-amplitude intrinsic noise. In applications to biological, ecological, chemical and social dynamics it is common for these models to posses quantities that are approximately conserved on short timescales, in which case system trajectories are observed to remain close to some lower-dimensional subspace. Here, we derive explicit and general formulae for a reduced-dimension description of such processes that is exact in the limit of small noise and well-separated slow and fast dynamics. The Michaelis-Menten law of enzyme-catalysed reactions, and the link between the Lotka-Volterra and Wright-Fisher processes are explored as a simple worked examples. Extensions of the method are presented for infinite dimensional systems and processes coupled to non-Gaussian noise sources.

Method of confidence domains in the analysis of noise-induced extinction for tritrophic population system

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2017-09-01

A problem of the analysis of the noise-induced extinction in multidimensional population systems is considered. For the investigation of conditions of the extinction caused by random disturbances, a new approach based on the stochastic sensitivity function technique and confidence domains is suggested, and applied to tritrophic population model of interacting prey, predator and top predator. This approach allows us to analyze constructively the probabilistic mechanisms of the transition to the noise-induced extinction from both equilibrium and oscillatory regimes of coexistence. In this analysis, a method of principal directions for the reducing of the dimension of confidence domains is suggested. In the dispersion of random states, the principal subspace is defined by the ratio of eigenvalues of the stochastic sensitivity matrix. A detailed analysis of two scenarios of the noise-induced extinction in dependence on parameters of considered tritrophic system is carried out.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weightedmore » $$\\ell^2$$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $$\\ell^2$$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.« less

Optimizing Cubature for Efficient Integration of Subspace Deformations

PubMed Central

An, Steven S.; Kim, Theodore; James, Doug L.

2009-01-01

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation PMID:19956777

Damage detection of structures identified with deterministic-stochastic models using seismic data.

PubMed

Huang, Ming-Chih; Wang, Yen-Po; Chang, Ming-Lian

2014-01-01

A deterministic-stochastic subspace identification method is adopted and experimentally verified in this study to identify the equivalent single-input-multiple-output system parameters of the discrete-time state equation. The method of damage locating vector (DLV) is then considered for damage detection. A series of shaking table tests using a five-storey steel frame has been conducted. Both single and multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged counterpart has also been studied. This study gives further insights into the scheme in terms of effectiveness, robustness, and limitation for damage localization of frame systems.

Evaluating the utility of mid-infrared spectral subspaces for predicting soil properties.

PubMed

Sila, Andrew M; Shepherd, Keith D; Pokhariyal, Ganesh P

2016-04-15

We propose four methods for finding local subspaces in large spectral libraries. The proposed four methods include (a) cosine angle spectral matching; (b) hit quality index spectral matching; (c) self-organizing maps and (d) archetypal analysis methods. Then evaluate prediction accuracies for global and subspaces calibration models. These methods were tested on a mid-infrared spectral library containing 1907 soil samples collected from 19 different countries under the Africa Soil Information Service project. Calibration models for pH, Mehlich-3 Ca, Mehlich-3 Al, total carbon and clay soil properties were developed for the whole library and for the subspace. Root mean square error of prediction was used to evaluate predictive performance of subspace and global models. The root mean square error of prediction was computed using a one-third-holdout validation set. Effect of pretreating spectra with different methods was tested for 1st and 2nd derivative Savitzky-Golay algorithm, multiplicative scatter correction, standard normal variate and standard normal variate followed by detrending methods. In summary, the results show that global models outperformed the subspace models. We, therefore, conclude that global models are more accurate than the local models except in few cases. For instance, sand and clay root mean square error values from local models from archetypal analysis method were 50% poorer than the global models except for subspace models obtained using multiplicative scatter corrected spectra with which were 12% better. However, the subspace approach provides novel methods for discovering data pattern that may exist in large spectral libraries.

A Model Comparison for Characterizing Protein Motions from Structure

NASA Astrophysics Data System (ADS)

David, Charles; Jacobs, Donald

2011-10-01

A comparative study is made using three computational models that characterize native state dynamics starting from known protein structures taken from four distinct SCOP classifications. A geometrical simulation is performed, and the results are compared to the elastic network model and molecular dynamics. The essential dynamics is quantified by a direct analysis of a mode subspace constructed from ANM and a principal component analysis on both the FRODA and MD trajectories using root mean square inner product and principal angles. Relative subspace sizes and overlaps are visualized using the projection of displacement vectors on the model modes. Additionally, a mode subspace is constructed from PCA on an exemplar set of X-ray crystal structures in order to determine similarly with respect to the generated ensembles. Quantitative analysis reveals there is significant overlap across the three model subspaces and the model independent subspace. These results indicate that structure is the key determinant for native state dynamics.

Active Subspaces for Wind Plant Surrogate Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

King, Ryan N; Quick, Julian; Dykes, Katherine L

Understanding the uncertainty in wind plant performance is crucial to their cost-effective design and operation. However, conventional approaches to uncertainty quantification (UQ), such as Monte Carlo techniques or surrogate modeling, are often computationally intractable for utility-scale wind plants because of poor congergence rates or the curse of dimensionality. In this paper we demonstrate that wind plant power uncertainty can be well represented with a low-dimensional active subspace, thereby achieving a significant reduction in the dimension of the surrogate modeling problem. We apply the active sub-spaces technique to UQ of plant power output with respect to uncertainty in turbine axial inductionmore » factors, and find a single active subspace direction dominates the sensitivity in power output. When this single active subspace direction is used to construct a quadratic surrogate model, the number of model unknowns can be reduced by up to 3 orders of magnitude without compromising performance on unseen test data. We conclude that the dimension reduction achieved with active subspaces makes surrogate-based UQ approaches tractable for utility-scale wind plants.« less

Data-driven monitoring for stochastic systems and its application on batch process

NASA Astrophysics Data System (ADS)

Yin, Shen; Ding, Steven X.; Haghani Abandan Sari, Adel; Hao, Haiyang

2013-07-01

Batch processes are characterised by a prescribed processing of raw materials into final products for a finite duration and play an important role in many industrial sectors due to the low-volume and high-value products. Process dynamics and stochastic disturbances are inherent characteristics of batch processes, which cause monitoring of batch processes a challenging problem in practice. To solve this problem, a subspace-aided data-driven approach is presented in this article for batch process monitoring. The advantages of the proposed approach lie in its simple form and its abilities to deal with stochastic disturbances and process dynamics existing in the process. The kernel density estimation, which serves as a non-parametric way of estimating the probability density function, is utilised for threshold calculation. An industrial benchmark of fed-batch penicillin production is finally utilised to verify the effectiveness of the proposed approach.

Improving the Fitness of High-Dimensional Biomechanical Models via Data-Driven Stochastic Exploration

PubMed Central

Bustamante, Carlos D.; Valero-Cuevas, Francisco J.

2010-01-01

The field of complex biomechanical modeling has begun to rely on Monte Carlo techniques to investigate the effects of parameter variability and measurement uncertainty on model outputs, search for optimal parameter combinations, and define model limitations. However, advanced stochastic methods to perform data-driven explorations, such as Markov chain Monte Carlo (MCMC), become necessary as the number of model parameters increases. Here, we demonstrate the feasibility and, what to our knowledge is, the first use of an MCMC approach to improve the fitness of realistically large biomechanical models. We used a Metropolis–Hastings algorithm to search increasingly complex parameter landscapes (3, 8, 24, and 36 dimensions) to uncover underlying distributions of anatomical parameters of a “truth model” of the human thumb on the basis of simulated kinematic data (thumbnail location, orientation, and linear and angular velocities) polluted by zero-mean, uncorrelated multivariate Gaussian “measurement noise.” Driven by these data, ten Markov chains searched each model parameter space for the subspace that best fit the data (posterior distribution). As expected, the convergence time increased, more local minima were found, and marginal distributions broadened as the parameter space complexity increased. In the 36-D scenario, some chains found local minima but the majority of chains converged to the true posterior distribution (confirmed using a cross-validation dataset), thus demonstrating the feasibility and utility of these methods for realistically large biomechanical problems. PMID:19272906

Ambient Vibration Testing for Story Stiffness Estimation of a Heritage Timber Building

PubMed Central

Min, Kyung-Won; Kim, Junhee; Park, Sung-Ah; Park, Chan-Soo

2013-01-01

This paper investigates dynamic characteristics of a historic wooden structure by ambient vibration testing, presenting a novel estimation methodology of story stiffness for the purpose of vibration-based structural health monitoring. As for the ambient vibration testing, measured structural responses are analyzed by two output-only system identification methods (i.e., frequency domain decomposition and stochastic subspace identification) to estimate modal parameters. The proposed methodology of story stiffness is estimation based on an eigenvalue problem derived from a vibratory rigid body model. Using the identified natural frequencies, the eigenvalue problem is efficiently solved and uniquely yields story stiffness. It is noteworthy that application of the proposed methodology is not necessarily confined to the wooden structure exampled in the paper. PMID:24227999

Adaptiveness in monotone pseudo-Boolean optimization and stochastic neural computation.

PubMed

Grossi, Giuliano

2009-08-01

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance. In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process. The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize. We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin; Forstall, Virginia; Tuminaro, Ray

This paper presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we proposemore » specific goal-oriented POD `ingredients' that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting 'augmented' POD subspace, we propose a hybrid direct/iterative three-stage method that leverages 1) the optimal ordering of POD basis vectors, and 2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.« less

Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method

DOE PAGES

Carlberg, Kevin; Forstall, Virginia; Tuminaro, Ray

2016-01-01

This paper presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we proposemore » specific goal-oriented POD `ingredients' that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting 'augmented' POD subspace, we propose a hybrid direct/iterative three-stage method that leverages 1) the optimal ordering of POD basis vectors, and 2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.« less

General subspace learning with corrupted training data via graph embedding.

PubMed

Bao, Bing-Kun; Liu, Guangcan; Hong, Richang; Yan, Shuicheng; Xu, Changsheng

2013-11-01

We address the following subspace learning problem: supposing we are given a set of labeled, corrupted training data points, how to learn the underlying subspace, which contains three components: an intrinsic subspace that captures certain desired properties of a data set, a penalty subspace that fits the undesired properties of the data, and an error container that models the gross corruptions possibly existing in the data. Given a set of data points, these three components can be learned by solving a nuclear norm regularized optimization problem, which is convex and can be efficiently solved in polynomial time. Using the method as a tool, we propose a new discriminant analysis (i.e., supervised subspace learning) algorithm called Corruptions Tolerant Discriminant Analysis (CTDA), in which the intrinsic subspace is used to capture the features with high within-class similarity, the penalty subspace takes the role of modeling the undesired features with high between-class similarity, and the error container takes charge of fitting the possible corruptions in the data. We show that CTDA can well handle the gross corruptions possibly existing in the training data, whereas previous linear discriminant analysis algorithms arguably fail in such a setting. Extensive experiments conducted on two benchmark human face data sets and one object recognition data set show that CTDA outperforms the related algorithms.

ASCS online fault detection and isolation based on an improved MPCA

NASA Astrophysics Data System (ADS)

Peng, Jianxin; Liu, Haiou; Hu, Yuhui; Xi, Junqiang; Chen, Huiyan

2014-09-01

Multi-way principal component analysis (MPCA) has received considerable attention and been widely used in process monitoring. A traditional MPCA algorithm unfolds multiple batches of historical data into a two-dimensional matrix and cut the matrix along the time axis to form subspaces. However, low efficiency of subspaces and difficult fault isolation are the common disadvantages for the principal component model. This paper presents a new subspace construction method based on kernel density estimation function that can effectively reduce the storage amount of the subspace information. The MPCA model and the knowledge base are built based on the new subspace. Then, fault detection and isolation with the squared prediction error (SPE) statistic and the Hotelling ( T 2) statistic are also realized in process monitoring. When a fault occurs, fault isolation based on the SPE statistic is achieved by residual contribution analysis of different variables. For fault isolation of subspace based on the T 2 statistic, the relationship between the statistic indicator and state variables is constructed, and the constraint conditions are presented to check the validity of fault isolation. Then, to improve the robustness of fault isolation to unexpected disturbances, the statistic method is adopted to set the relation between single subspace and multiple subspaces to increase the corrective rate of fault isolation. Finally fault detection and isolation based on the improved MPCA is used to monitor the automatic shift control system (ASCS) to prove the correctness and effectiveness of the algorithm. The research proposes a new subspace construction method to reduce the required storage capacity and to prove the robustness of the principal component model, and sets the relationship between the state variables and fault detection indicators for fault isolation.

MODAL TRACKING of A Structural Device: A Subspace Identification Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Candy, J. V.; Franco, S. N.; Ruggiero, E. L.

Mechanical devices operating in an environment contaminated by noise, uncertainties, and extraneous disturbances lead to low signal-to-noise-ratios creating an extremely challenging processing problem. To detect/classify a device subsystem from noisy data, it is necessary to identify unique signatures or particular features. An obvious feature would be resonant (modal) frequencies emitted during its normal operation. In this report, we discuss a model-based approach to incorporate these physical features into a dynamic structure that can be used for such an identification. The approach we take after pre-processing the raw vibration data and removing any extraneous disturbances is to obtain a representation ofmore » the structurally unknown device along with its subsystems that capture these salient features. One approach is to recognize that unique modal frequencies (sinusoidal lines) appear in the estimated power spectrum that are solely characteristic of the device under investigation. Therefore, the objective of this effort is based on constructing a black box model of the device that captures these physical features that can be exploited to “diagnose” whether or not the particular device subsystem (track/detect/classify) is operating normally from noisy vibrational data. Here we discuss the application of a modern system identification approach based on stochastic subspace realization techniques capable of both (1) identifying the underlying black-box structure thereby enabling the extraction of structural modes that can be used for analysis and modal tracking as well as (2) indicators of condition and possible changes from normal operation.« less

Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

NASA Astrophysics Data System (ADS)

Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

2017-12-01

The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

Globally convergent techniques in nonlinear Newton-Krylov

NASA Technical Reports Server (NTRS)

Brown, Peter N.; Saad, Youcef

1989-01-01

Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.

Bi Sparsity Pursuit: A Paradigm for Robust Subspace Recovery

DTIC Science & Technology

2016-09-27

16. SECURITY CLASSIFICATION OF: The success of sparse models in computer vision and machine learning is due to the fact that, high dimensional data...Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 Signal recovery, Sparse learning , Subspace modeling REPORT DOCUMENTATION PAGE 11...vision and machine learning is due to the fact that, high dimensional data is distributed in a union of low dimensional subspaces in many real-world

EEG and MEG source localization using recursively applied (RAP) MUSIC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mosher, J.C.; Leahy, R.M.

1996-12-31

The multiple signal characterization (MUSIC) algorithm locates multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetoencephalography (MEG) data. A signal subspace is estimated from the data, then the algorithm scans a single dipole model through a three-dimensional head volume and computes projections onto this subspace. To locate the sources, the user must search the head volume for local peaks in the projection metric. Here we describe a novel extension of this approach which we refer to as RAP (Recursively APplied) MUSIC. This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections, which usesmore » the metric of principal correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace. The dipolar orientations, a form of `diverse polarization,` are easily extracted using the associated principal vectors.« less

Interpretation of the MEG-MUSIC scan in biomagnetic source localization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mosher, J.C.; Lewis, P.S.; Leahy, R.M.

1993-09-01

MEG-Music is a new approach to MEG source localization. MEG-Music is based on a spatio-temporal source model in which the observed biomagnetic fields are generated by a small number of current dipole sources with fixed positions/orientations and varying strengths. From the spatial covariance matrix of the observed fields, a signal subspace can be identified. The rank of this subspace is equal to the number of elemental sources present. This signal sub-space is used in a projection metric that scans the three dimensional head volume. Given a perfect signal subspace estimate and a perfect forward model, the metric will peak atmore » unity at each dipole location. In practice, the signal subspace estimate is contaminated by noise, which in turn yields MUSIC peaks which are less than unity. Previously we examined the lower bounds on localization error, independent of the choice of localization procedure. In this paper, we analyzed the effects of noise and temporal coherence on the signal subspace estimate and the resulting effects on the MEG-MUSIC peaks.« less

Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric

NASA Astrophysics Data System (ADS)

Suzuki, Akito

2008-04-01

We study a model of the quantized electromagnetic field interacting with an external static source ρ in the Feynman (Lorentz) gauge and construct the quantized radiation field Aμ (μ=0,1,2,3) as an operator-valued distribution acting on the Fock space F with an indefinite metric. By using the Gupta subsidiary condition ∂μAμ(x)(+)Ψ=0, one can select the physical subspace Vphys. According to the Gupta-Bleuler formalism, Vphys is a non-negative subspace so that elements of Vphys, called physical states, can be probabilistically interpretable. Indeed, assuming that the external source ρ is infrared regular, i.e., ρ̂/∣k∣3/2ɛL2(R3), we can characterize the physical subspace Vphys and show that Vphys is non-negative. In addition, we find that the Hamiltonian of the model is reduced to the Hamiltonian of the transverse photons with the Coulomb interaction. We, however, prove that the physical subspace is trivial, i.e., Vphys={0}, if and only if the external source ρ is infrared singular, i.e., ρ̂/∣k∣3/2∉L2(R3). We also discuss a representation different from the above representation such that the physical subspace is not trivial under the infrared singular condition.

Continuity properties of the semi-group and its integral kernel in non-relativistic QED

NASA Astrophysics Data System (ADS)

Matte, Oliver

2016-07-01

Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J. S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued Lp-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostatic potentials and the actual assumptions on the model are general enough to cover the Nelson model as well. As a corollary, we obtain some new pointwise exponential decay and continuity results on elements of low-energetic spectral subspaces of atoms or molecules that also take spin into account. In a simpler situation where spin is neglected, we explain how to verify the joint continuity of positive ground state eigenvectors with respect to spatial coordinates and model parameters. There are no smallness assumptions imposed on any model parameter.

Learning Robust and Discriminative Subspace With Low-Rank Constraints.

PubMed

Li, Sheng; Fu, Yun

2016-11-01

In this paper, we aim at learning robust and discriminative subspaces from noisy data. Subspace learning is widely used in extracting discriminative features for classification. However, when data are contaminated with severe noise, the performance of most existing subspace learning methods would be limited. Recent advances in low-rank modeling provide effective solutions for removing noise or outliers contained in sample sets, which motivates us to take advantage of low-rank constraints in order to exploit robust and discriminative subspace for classification. In particular, we present a discriminative subspace learning method called the supervised regularization-based robust subspace (SRRS) approach, by incorporating the low-rank constraint. SRRS seeks low-rank representations from the noisy data, and learns a discriminative subspace from the recovered clean data jointly. A supervised regularization function is designed to make use of the class label information, and therefore to enhance the discriminability of subspace. Our approach is formulated as a constrained rank-minimization problem. We design an inexact augmented Lagrange multiplier optimization algorithm to solve it. Unlike the existing sparse representation and low-rank learning methods, our approach learns a low-dimensional subspace from recovered data, and explicitly incorporates the supervised information. Our approach and some baselines are evaluated on the COIL-100, ALOI, Extended YaleB, FERET, AR, and KinFace databases. The experimental results demonstrate the effectiveness of our approach, especially when the data contain considerable noise or variations.

Active subspace uncertainty quantification for a polydomain ferroelectric phase-field model

NASA Astrophysics Data System (ADS)

Leon, Lider S.; Smith, Ralph C.; Miles, Paul; Oates, William S.

2018-03-01

Quantum-informed ferroelectric phase field models capable of predicting material behavior, are necessary for facilitating the development and production of many adaptive structures and intelligent systems. Uncertainty is present in these models, given the quantum scale at which calculations take place. A necessary analysis is to determine how the uncertainty in the response can be attributed to the uncertainty in the model inputs or parameters. A second analysis is to identify active subspaces within the original parameter space, which quantify directions in which the model response varies most dominantly, thus reducing sampling effort and computational cost. In this investigation, we identify an active subspace for a poly-domain ferroelectric phase-field model. Using the active variables as our independent variables, we then construct a surrogate model and perform Bayesian inference. Once we quantify the uncertainties in the active variables, we obtain uncertainties for the original parameters via an inverse mapping. The analysis provides insight into how active subspace methodologies can be used to reduce computational power needed to perform Bayesian inference on model parameters informed by experimental or simulated data.

Data-driven modeling and predictive control for boiler-turbine unit using fuzzy clustering and subspace methods.

PubMed

Wu, Xiao; Shen, Jiong; Li, Yiguo; Lee, Kwang Y

2014-05-01

This paper develops a novel data-driven fuzzy modeling strategy and predictive controller for boiler-turbine unit using fuzzy clustering and subspace identification (SID) methods. To deal with the nonlinear behavior of boiler-turbine unit, fuzzy clustering is used to provide an appropriate division of the operation region and develop the structure of the fuzzy model. Then by combining the input data with the corresponding fuzzy membership functions, the SID method is extended to extract the local state-space model parameters. Owing to the advantages of the both methods, the resulting fuzzy model can represent the boiler-turbine unit very closely, and a fuzzy model predictive controller is designed based on this model. As an alternative approach, a direct data-driven fuzzy predictive control is also developed following the same clustering and subspace methods, where intermediate subspace matrices developed during the identification procedure are utilized directly as the predictor. Simulation results show the advantages and effectiveness of the proposed approach. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

NASA Astrophysics Data System (ADS)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Analytical minimization of synchronicity errors in stochastic identification

NASA Astrophysics Data System (ADS)

Bernal, D.

2018-01-01

An approach to minimize error due to synchronicity faults in stochastic system identification is presented. The scheme is based on shifting the time domain signals so the phases of the fundamental eigenvector estimated from the spectral density are zero. A threshold on the mean of the amplitude-weighted absolute value of these phases, above which signal shifting is deemed justified, is derived and found to be proportional to the first mode damping ratio. It is shown that synchronicity faults do not map precisely to phasor multiplications in subspace identification and that the accuracy of spectral density estimated eigenvectors, for inputs with arbitrary spectral density, decrease with increasing mode number. Selection of a corrective strategy based on signal alignment, instead of eigenvector adjustment using phasors, is shown to be the product of the foregoing observations. Simulations that include noise and non-classical damping suggest that the scheme can provide sufficient accuracy to be of practical value.

Generation of skeletal mechanism by means of projected entropy participation indices

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Valorani, Mauro; Ciottoli, Pietro Paolo; Galassi, Riccardo Malpica

2017-11-01

When the dynamics of reactive systems develop very-slow and very-fast time scales separated by a range of active time scales, with gaps in the fast/active and slow/active time scales, then it is possible to achieve multi-scale adaptive model reduction along-with the integration of the ODEs using the G-Scheme. The scheme assumes that the dynamics is decomposed into active, slow, fast, and invariant subspaces. We derive expressions that establish a direct link between time scales and entropy production by using estimates provided by the G-Scheme. To calculate the contribution to entropy production, we resort to a standard model of a constant pressure, adiabatic, batch reactor, where the mixture temperature of the reactants is initially set above the auto-ignition temperature. Numerical experiments show that the contribution to entropy production of the fast subspace is of the same magnitude as the error threshold chosen for the identification of the decomposition of the tangent space, and the contribution of the slow subspace is generally much smaller than that of the active subspace. The information on entropy production associated with reactions within each subspace is used to define an entropy participation index that is subsequently utilized for model reduction.

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

NASA Astrophysics Data System (ADS)

Constable, George W. A.; McKane, Alan J.

2018-07-01

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.

Entanglement dynamics in a non-Markovian environment: An exactly solvable model

NASA Astrophysics Data System (ADS)

Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.

2012-05-01

We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

NASA Astrophysics Data System (ADS)

Constable, George W. A.; McKane, Alan J.

2017-11-01

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.

Array magnetics modal analysis for the DIII-D tokamak based on localized time-series modelling

DOE PAGES

Olofsson, K. Erik J.; Hanson, Jeremy M.; Shiraki, Daisuke; ...

2014-07-14

Here, time-series analysis of magnetics data in tokamaks is typically done using block-based fast Fourier transform methods. This work presents the development and deployment of a new set of algorithms for magnetic probe array analysis. The method is based on an estimation technique known as stochastic subspace identification (SSI). Compared with the standard coherence approach or the direct singular value decomposition approach, the new technique exhibits several beneficial properties. For example, the SSI method does not require that frequencies are orthogonal with respect to the timeframe used in the analysis. Frequencies are obtained directly as parameters of localized time-series models.more » The parameters are extracted by solving small-scale eigenvalue problems. Applications include maximum-likelihood regularized eigenmode pattern estimation, detection of neoclassical tearing modes, including locked mode precursors, and automatic clustering of modes, and magnetics-pattern characterization of sawtooth pre- and postcursors, edge harmonic oscillations and fishbones.« less

Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation

DOE PAGES

Shen, Xinyue; Krim, Hamid; Gu, Yuantao

2016-03-01

Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. Here in this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints onmore » the Grassmann manifold, as well as the bilinearity in the penalty caused by the subspace bases and coefficients. Nevertheless, numerical experiments verify that the proposed algorithm, which provides elegant solutions to the sub-problems in each step, is able to de-couple the subspaces and pursue each of them under time-efficient parallel computation.« less

Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering.

PubMed

Peng, Xi; Yu, Zhiding; Yi, Zhang; Tang, Huajin

2017-04-01

Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intrasubspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that l 1 -, l 2 -, l ∞ -, and nuclear-norm-based linear projection spaces share the property of intrasubspace projection dominance, i.e., the coefficients over intrasubspace data points are larger than those over intersubspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-graph. The subspace clustering and subspace learning algorithms are developed upon L2-graph. We conduct comprehensive experiment on subspace learning, image clustering, and motion segmentation and consider several quantitative benchmarks classification/clustering accuracy, normalized mutual information, and running time. Results show that L2-graph outperforms many state-of-the-art methods in our experiments, including L1-graph, low rank representation (LRR), and latent LRR, least square regression, sparse subspace clustering, and locally linear representation.

Superresolution Modeling of Calcium Release in the Heart

PubMed Central

Walker, Mark A.; Williams, George S.B.; Kohl, Tobias; Lehnart, Stephan E.; Jafri, M. Saleet; Greenstein, Joseph L.; Lederer, W.J.; Winslow, Raimond L.

2014-01-01

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cellular contraction during cardiac excitation-contraction coupling. The fundamental element of CICR in the heart is the calcium (Ca2+) spark, which arises from a cluster of ryanodine receptors (RyR). Opening of these RyR clusters is triggered to produce a local, regenerative release of Ca2+ from the sarcoplasmic reticulum (SR). The Ca2+ leak out of the SR is an important process for cellular Ca2+ management, and it is critically influenced by spark fidelity, i.e., the probability that a spontaneous RyR opening triggers a Ca2+ spark. Here, we present a detailed, three-dimensional model of a cardiac Ca2+ release unit that incorporates diffusion, intracellular buffering systems, and stochastically gated ion channels. The model exhibits realistic Ca2+ sparks and robust Ca2+ spark termination across a wide range of geometries and conditions. Furthermore, the model captures the details of Ca2+ spark and nonspark-based SR Ca2+ leak, and it produces normal excitation-contraction coupling gain. We show that SR luminal Ca2+-dependent regulation of the RyR is not critical for spark termination, but it can explain the exponential rise in the SR Ca2+ leak-load relationship demonstrated in previous experimental work. Perturbations to subspace dimensions, which have been observed in experimental models of disease, strongly alter Ca2+ spark dynamics. In addition, we find that the structure of RyR clusters also influences Ca2+ release properties due to variations in inter-RyR coupling via local subspace Ca2+ concentration ([Ca2+]ss). These results are illustrated for RyR clusters based on super-resolution stimulated emission depletion microscopy. Finally, we present a believed-novel approach by which the spark fidelity of a RyR cluster can be predicted from structural information of the cluster using the maximum eigenvalue of its adjacency matrix. These results provide critical insights into CICR dynamics in heart, under normal and pathological conditions. PMID:25517166

Robust uncertainty evaluation for system identification on distributed wireless platforms

NASA Astrophysics Data System (ADS)

Crinière, Antoine; Döhler, Michael; Le Cam, Vincent; Mevel, Laurent

2016-04-01

Health monitoring of civil structures by system identification procedures from automatic control is now accepted as a valid approach. These methods provide frequencies and modeshapes from the structure over time. For a continuous monitoring the excitation of a structure is usually ambient, thus unknown and assumed to be noise. Hence, all estimates from the vibration measurements are realizations of random variables with inherent uncertainty due to (unknown) process and measurement noise and finite data length. The underlying algorithms are usually running under Matlab under the assumption of large memory pool and considerable computational power. Even under these premises, computational and memory usage are heavy and not realistic for being embedded in on-site sensor platforms such as the PEGASE platform. Moreover, the current push for distributed wireless systems calls for algorithmic adaptation for lowering data exchanges and maximizing local processing. Finally, the recent breakthrough in system identification allows us to process both frequency information and its related uncertainty together from one and only one data sequence, at the expense of computational and memory explosion that require even more careful attention than before. The current approach will focus on presenting a system identification procedure called multi-setup subspace identification that allows to process both frequencies and their related variances from a set of interconnected wireless systems with all computation running locally within the limited memory pool of each system before being merged on a host supervisor. Careful attention will be given to data exchanges and I/O satisfying OGC standards, as well as minimizing memory footprints and maximizing computational efficiency. Those systems are built in a way of autonomous operations on field and could be later included in a wide distributed architecture such as the Cloud2SM project. The usefulness of these strategies is illustrated on data from a progressive damage action on a prestressed concrete bridge. References [1] E. Carden and P. Fanning. Vibration based condition monitoring: a review. Structural Health Monitoring, 3(4):355-377, 2004. [2] M. Döhler and L. Mevel. Efficient multi-order uncertainty computation for stochastic subspace identification. Mechanical Systems and Signal Processing, 38(2):346-366, 2013. [3] M.Döhler, L. Mevel. Modular subspace-based system identification from multi-setup measurements. IEEE Transactions on Automatic Control, 57(11):2951-2956, 2012. [4] M. Döhler, X.-B. Lam, and L. Mevel. Uncertainty quantification for modal parameters from stochastic subspace identification on multi-setup measurements. MechanicalSystems and Signal Processing, 36(2):562-581, 2013. [5] A Crinière, J Dumoulin, L Mevel, G Andrade-Barosso, M Simonin. The Cloud2SM Project.European Geosciences Union General Assembly (EGU2015), Apr 2015, Vienne, Austria. 2015.

Factor analysis of auto-associative neural networks with application in speaker verification.

PubMed

Garimella, Sri; Hermansky, Hynek

2013-04-01

Auto-associative neural network (AANN) is a fully connected feed-forward neural network, trained to reconstruct its input at its output through a hidden compression layer, which has fewer numbers of nodes than the dimensionality of input. AANNs are used to model speakers in speaker verification, where a speaker-specific AANN model is obtained by adapting (or retraining) the universal background model (UBM) AANN, an AANN trained on multiple held out speakers, using corresponding speaker data. When the amount of speaker data is limited, this adaptation procedure may lead to overfitting as all the parameters of UBM-AANN are adapted. In this paper, we introduce and develop the factor analysis theory of AANNs to alleviate this problem. We hypothesize that only the weight matrix connecting the last nonlinear hidden layer and the output layer is speaker-specific, and further restrict it to a common low-dimensional subspace during adaptation. The subspace is learned using large amounts of development data, and is held fixed during adaptation. Thus, only the coordinates in a subspace, also known as i-vector, need to be estimated using speaker-specific data. The update equations are derived for learning both the common low-dimensional subspace and the i-vectors corresponding to speakers in the subspace. The resultant i-vector representation is used as a feature for the probabilistic linear discriminant analysis model. The proposed system shows promising results on the NIST-08 speaker recognition evaluation (SRE), and yields a 23% relative improvement in equal error rate over the previously proposed weighted least squares-based subspace AANNs system. The experiments on NIST-10 SRE confirm that these improvements are consistent and generalize across datasets.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

NASA Astrophysics Data System (ADS)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases.

Beating the curse of dimension with accurate statistics for the Fokker-Planck equation in complex turbulent systems.

PubMed

Chen, Nan; Majda, Andrew J

2017-12-05

Solving the Fokker-Planck equation for high-dimensional complex dynamical systems is an important issue. Recently, the authors developed efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures, which contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy with a small number of samples [Formula: see text], where a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious Gaussian kernel density estimation in the remaining low-dimensional subspace. In this article, two effective strategies are developed and incorporated into these algorithms. The first strategy involves a judicious block decomposition of the conditional covariance matrix such that the evolutions of different blocks have no interactions, which allows an extremely efficient parallel computation due to the small size of each individual block. The second strategy exploits statistical symmetry for a further reduction of [Formula: see text] The resulting algorithms can efficiently solve the Fokker-Planck equation with strongly non-Gaussian PDFs in much higher dimensions even with orders in the millions and thus beat the curse of dimension. The algorithms are applied to a [Formula: see text]-dimensional stochastic coupled FitzHugh-Nagumo model for excitable media. An accurate recovery of both the transient and equilibrium non-Gaussian PDFs requires only [Formula: see text] samples! In addition, the block decomposition facilitates the algorithms to efficiently capture the distinct non-Gaussian features at different locations in a [Formula: see text]-dimensional two-layer inhomogeneous Lorenz 96 model, using only [Formula: see text] samples. Copyright © 2017 the Author(s). Published by PNAS.

A new method to real-normalize measured complex modes

NASA Technical Reports Server (NTRS)

Wei, Max L.; Allemang, Randall J.; Zhang, Qiang; Brown, David L.

1987-01-01

A time domain subspace iteration technique is presented to compute a set of normal modes from the measured complex modes. By using the proposed method, a large number of physical coordinates are reduced to a smaller number of model or principal coordinates. Subspace free decay time responses are computed using properly scaled complex modal vectors. Companion matrix for the general case of nonproportional damping is then derived in the selected vector subspace. Subspace normal modes are obtained through eigenvalue solution of the (M sub N) sup -1 (K sub N) matrix and transformed back to the physical coordinates to get a set of normal modes. A numerical example is presented to demonstrate the outlined theory.

Signatures of large-scale and local climates on the demography of white-tailed ptarmigan in Rocky Mountain National Park, Colorado, USA.

PubMed

Wang, Guiming; Hobbs, N Thompson; Galbraith, Hector; Giesen, Kenneth M

2002-09-01

Global climate change may impact wildlife populations by affecting local weather patterns, which, in turn, can impact a variety of ecological processes. However, it is not clear that local variations in ecological processes can be explained by large-scale patterns of climate. The North Atlantic oscillation (NAO) is a large-scale climate phenomenon that has been shown to influence the population dynamics of some animals. Although effects of the NAO on vertebrate population dynamics have been studied, it remains uncertain whether it broadly predicts the impact of weather on species. We examined the ability of local weather data and the NAO to explain the annual variation in population dynamics of white-tailed ptarmigan ( Lagopus leucurus) in Rocky Mountain National Park, USA. We performed canonical correlation analysis on the demographic subspace of ptarmigan and local-climate subspace defined by the empirical orthogonal function (EOF) using data from 1975 to 1999. We found that two subspaces were significantly correlated on the first canonical variable. The Pearson correlation coefficient of the first EOF values of the demographic and local-climate subspaces was significant. The population density and the first EOF of local-climate subspace influenced the ptarmigan population with 1-year lags in the Gompertz model. However, the NAO index was neither related to the first two EOF of local-climate subspace nor to the first EOF of the demographic subspace of ptarmigan. Moreover, the NAO index was not a significant term in the Gompertz model for the ptarmigan population. Therefore, local climate had stronger signature on the demography of ptarmigan than did a large-scale index, i.e., the NAO index. We conclude that local responses of wildlife populations to changing climate may not be adequately explained by models that project large-scale climatic patterns.

Adaptive low-rank subspace learning with online optimization for robust visual tracking.

PubMed

Liu, Risheng; Wang, Di; Han, Yuzhuo; Fan, Xin; Luo, Zhongxuan

2017-04-01

In recent years, sparse and low-rank models have been widely used to formulate appearance subspace for visual tracking. However, most existing methods only consider the sparsity or low-rankness of the coefficients, which is not sufficient enough for appearance subspace learning on complex video sequences. Moreover, as both the low-rank and the column sparse measures are tightly related to all the samples in the sequences, it is challenging to incrementally solve optimization problems with both nuclear norm and column sparse norm on sequentially obtained video data. To address above limitations, this paper develops a novel low-rank subspace learning with adaptive penalization (LSAP) framework for subspace based robust visual tracking. Different from previous work, which often simply decomposes observations as low-rank features and sparse errors, LSAP simultaneously learns the subspace basis, low-rank coefficients and column sparse errors to formulate appearance subspace. Within LSAP framework, we introduce a Hadamard production based regularization to incorporate rich generative/discriminative structure constraints to adaptively penalize the coefficients for subspace learning. It is shown that such adaptive penalization can significantly improve the robustness of LSAP on severely corrupted dataset. To utilize LSAP for online visual tracking, we also develop an efficient incremental optimization scheme for nuclear norm and column sparse norm minimizations. Experiments on 50 challenging video sequences demonstrate that our tracker outperforms other state-of-the-art methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Polarimetric subspace target detector for SAR data based on the Huynen dihedral model

NASA Astrophysics Data System (ADS)

Larson, Victor J.; Novak, Leslie M.

1995-06-01

Two new polarimetric subspace target detectors are developed based on a dihedral signal model for bright peaks within a spatially extended target signature. The first is a coherent dihedral target detector based on the exact Huynen model for a dihedral. The second is a noncoherent dihedral target detector based on the Huynen model with an extra unknown phase term. Expressions for these polarimetric subspace target detectors are developed for both additive Gaussian clutter and more general additive spherically invariant random vector clutter including the K-distribution. For the case of Gaussian clutter with unknown clutter parameters, constant false alarm rate implementations of these polarimetric subspace target detectors are developed. The performance of these dihedral detectors is demonstrated with real millimeter-wave fully polarimetric SAR data. The coherent dihedral detector which is developed with a more accurate description of a dihedral offers no performance advantage over the noncoherent dihedral detector which is computationally more attractive. The dihedral detectors do a better job of separating a set of tactical military targets from natural clutter compared to a detector that assumes no knowledge about the polarimetric structure of the target signal.

BI-sparsity pursuit for robust subspace recovery

DOE PAGES

Bian, Xiao; Krim, Hamid

2015-09-01

Here, the success of sparse models in computer vision and machine learning in many real-world applications, may be attributed in large part, to the fact that many high dimensional data are distributed in a union of low dimensional subspaces. The underlying structure may, however, be adversely affected by sparse errors, thus inducing additional complexity in recovering it. In this paper, we propose a bi-sparse model as a framework to investigate and analyze this problem, and provide as a result , a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We additionally demonstrate the effectiveness ofmore » our method by experiments on real-world vision data.« less

Cyclo-stationary linear parameter time-varying subspace realization method applied for identification of horizontal-axis wind turbines

NASA Astrophysics Data System (ADS)

Velazquez, Antonio; Swartz, R. Andrew

2013-04-01

Wind energy is becoming increasingly important worldwide as an alternative renewable energy source. Economical, maintenance and operation are critical issues for large slender dynamic structures, especially for remote offshore wind farms. Health monitoring systems are very promising instruments to assure reliability and good performance of the structure. These sensing and control technologies are typically informed by models based on mechanics or data-driven identification techniques in the time and/or frequency domain. Frequency response functions are popular but are difficult to realize autonomously for structures of higher order and having overlapping frequency content. Instead, time-domain techniques have shown powerful advantages from a practical point of view (e.g. embedded algorithms in wireless-sensor networks), being more suitable to differentiate closely-related modes. Customarily, time-varying effects are often neglected or dismissed to simplify the analysis, but such is not the case for wind loaded structures with spinning multibodies. A more complex scenario is constituted when dealing with both periodic mechanisms responsible for the vibration shaft of the rotor-blade system, and the wind tower substructure interaction. Transformations of the cyclic effects on the vibration data can be applied to isolate inertia quantities different from rotating-generated forces that are typically non-stationary in nature. After applying these transformations, structural identification can be carried out by stationary techniques via data-correlated Eigensystem realizations. In this paper an exploration of a periodic stationary or cyclo-stationary subspace identification technique is presented here by means of a modified Eigensystem Realization Algorithm (ERA) via Stochastic Subspace Identification (SSI) and Linear Parameter Time-Varying (LPTV) techniques. Structural response is assumed under stationary ambient excitation produced by a Gaussian (white) noise assembled in the operative range bandwidth of horizontal-axis wind turbines. ERA-OKID analysis is driven by correlation-function matrices from the stationary ambient response aiming to reduce noise effects. Singular value decomposition (SVD) and eigenvalue analysis are computed in a last stage to get frequencies and mode shapes. Proposed assumptions are carefully weighted to account for the uncertainty of the environment the wind turbines are subjected to. A numerical example is presented based on data acquisition carried out in a BWC XL.1 low power wind turbine device installed in University of California at Davis. Finally, comments and observations are provided on how this subspace realization technique can be extended for modal-parameter identification using exclusively ambient vibration data.

Synthetic Modeling of Autonomous Learning with a Chaotic Neural Network

NASA Astrophysics Data System (ADS)

Funabashi, Masatoshi

We investigate the possible role of intermittent chaotic dynamics called chaotic itinerancy, in interaction with nonsupervised learnings that reinforce and weaken the neural connection depending on the dynamics itself. We first performed hierarchical stability analysis of the Chaotic Neural Network model (CNN) according to the structure of invariant subspaces. Irregular transition between two attractor ruins with positive maximum Lyapunov exponent was triggered by the blowout bifurcation of the attractor spaces, and was associated with riddled basins structure. We secondly modeled two autonomous learnings, Hebbian learning and spike-timing-dependent plasticity (STDP) rule, and simulated the effect on the chaotic itinerancy state of CNN. Hebbian learning increased the residence time on attractor ruins, and produced novel attractors in the minimum higher-dimensional subspace. It also augmented the neuronal synchrony and established the uniform modularity in chaotic itinerancy. STDP rule reduced the residence time on attractor ruins, and brought a wide range of periodicity in emerged attractors, possibly including strange attractors. Both learning rules selectively destroyed and preserved the specific invariant subspaces, depending on the neuron synchrony of the subspace where the orbits are situated. Computational rationale of the autonomous learning is discussed in connectionist perspective.

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

High-Dimensional Bayesian Geostatistics

PubMed Central

Banerjee, Sudipto

2017-01-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as “priors” for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings. PMID:29391920

High-Dimensional Bayesian Geostatistics.

PubMed

Banerjee, Sudipto

2017-06-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as "priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings.

Exact solution of mean-field plus an extended T = 1 nuclear pairing Hamiltonian in the seniority-zero symmetric subspace

NASA Astrophysics Data System (ADS)

Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Dai, Lianrong; Draayer, Jerry P.

2018-05-01

An extended pairing Hamiltonian that describes multi-pair interactions among isospin T = 1 and angular momentum J = 0 neutron-neutron, proton-proton, and neutron-proton pairs in a spherical mean field, such as the spherical shell model, is proposed based on the standard T = 1 pairing formalism. The advantage of the model lies in the fact that numerical solutions within the seniority-zero symmetric subspace can be obtained more easily and with less computational time than those calculated from the mean-field plus standard T = 1 pairing model. Thus, large-scale calculations within the seniority-zero symmetric subspace of the model is feasible. As an example of the application, the average neutron-proton interaction in even-even N ∼ Z nuclei that can be suitably described in the f5 pg9 shell is estimated in the present model, with a focus on the role of np-pairing correlations.

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

PubMed Central

Ando, Tadashi; Chow, Edmond; Saad, Yousef; Skolnick, Jeffrey

2012-01-01

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N2) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the “block” version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions. PMID:22897254

Active Subspace Methods for Data-Intensive Inverse Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qiqi

2017-04-27

The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.

A description of the location and structure of the essential spectrum of a model operator in a subspace of a Fock space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yodgorov, G R; Ismail, F; Muminov, Z I

2014-12-31

We consider a certain model operator acting in a subspace of a fermionic Fock space. We obtain an analogue of Faddeev's equation. We describe the location of the essential spectrum of the operator under consideration and show that the essential spectrum consists of the union of at most four segments. Bibliography: 19 titles.

Exploring the Tomlin-Varadarajan quantum constraints in U (1 )3 loop quantum gravity: Solutions and the Minkowski theorem

NASA Astrophysics Data System (ADS)

Lewandowski, Jerzy; Lin, Chun-Yen

2017-03-01

We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space, which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that involves the condition known from the Minkowski theorem on polyhedra, and the second class satisfying a weaker form of the spatial diffeomorphism invariance.

Projection methods for the numerical solution of Markov chain models

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

A hybrid approach to generating search subspaces in dynamically constrained 4-dimensional data assimilation

NASA Astrophysics Data System (ADS)

Yaremchuk, Max; Martin, Paul; Beattie, Christopher

2017-09-01

Development and maintenance of the linearized and adjoint code for advanced circulation models is a challenging issue, requiring a significant proportion of total effort in operational data assimilation (DA). The ensemble-based DA techniques provide a derivative-free alternative, which appears to be competitive with variational methods in many practical applications. This article proposes a hybrid scheme for generating the search subspaces in the adjoint-free 4-dimensional DA method (a4dVar) that does not use a predefined ensemble. The method resembles 4dVar in that the optimal solution is strongly constrained by model dynamics and search directions are supplied iteratively using information from the current and previous model trajectories generated in the process of optimization. In contrast to 4dVar, which produces a single search direction from exact gradient information, a4dVar employs an ensemble of directions to form a subspace in order to proceed. In the earlier versions of a4dVar, search subspaces were built using the leading EOFs of either the model trajectory or the projections of the model-data misfits onto the range of the background error covariance (BEC) matrix at the current iteration. In the present study, we blend both approaches and explore a hybrid scheme of ensemble generation in order to improve the performance and flexibility of the algorithm. In addition, we introduce balance constraints into the BEC structure and periodically augment the search ensemble with BEC eigenvectors to avoid repeating minimization over already explored subspaces. Performance of the proposed hybrid a4dVar (ha4dVar) method is compared with that of standard 4dVar in a realistic regional configuration assimilating real data into the Navy Coastal Ocean Model (NCOM). It is shown that the ha4dVar converges faster than a4dVar and can be potentially competitive with 4dvar both in terms of the required computational time and the forecast skill.

Molecular activity prediction by means of supervised subspace projection based ensembles of classifiers.

PubMed

Cerruela García, G; García-Pedrajas, N; Luque Ruiz, I; Gómez-Nieto, M Á

2018-03-01

This paper proposes a method for molecular activity prediction in QSAR studies using ensembles of classifiers constructed by means of two supervised subspace projection methods, namely nonparametric discriminant analysis (NDA) and hybrid discriminant analysis (HDA). We studied the performance of the proposed ensembles compared to classical ensemble methods using four molecular datasets and eight different models for the representation of the molecular structure. Using several measures and statistical tests for classifier comparison, we observe that our proposal improves the classification results with respect to classical ensemble methods. Therefore, we show that ensembles constructed using supervised subspace projections offer an effective way of creating classifiers in cheminformatics.

Greedy subspace clustering.

DOT National Transportation Integrated Search

2016-09-01

We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets ...

Quantum stopping times stochastic integral in the interacting Fock space

NASA Astrophysics Data System (ADS)

Kang, Yuanbao

2015-08-01

Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L2(ℝ+), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L2(ℝ+) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γτ] ⊗ Γ[τ, where Γτ] and Γ[τ stand for the part "before τ" and the part "after τ," respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.

SIMULTANEOUS MULTISLICE MAGNETIC RESONANCE FINGERPRINTING WITH LOW-RANK AND SUBSPACE MODELING

PubMed Central

Zhao, Bo; Bilgic, Berkin; Adalsteinsson, Elfar; Griswold, Mark A.; Wald, Lawrence L.; Setsompop, Kawin

2018-01-01

Magnetic resonance fingerprinting (MRF) is a new quantitative imaging paradigm that enables simultaneous acquisition of multiple magnetic resonance tissue parameters (e.g., T1, T2, and spin density). Recently, MRF has been integrated with simultaneous multislice (SMS) acquisitions to enable volumetric imaging with faster scan time. In this paper, we present a new image reconstruction method based on low-rank and subspace modeling for improved SMS-MRF. Here the low-rank model exploits strong spatiotemporal correlation among contrast-weighted images, while the subspace model captures the temporal evolution of magnetization dynamics. With the proposed model, the image reconstruction problem is formulated as a convex optimization problem, for which we develop an algorithm based on variable splitting and the alternating direction method of multipliers. The performance of the proposed method has been evaluated by numerical experiments, and the results demonstrate that the proposed method leads to improved accuracy over the conventional approach. Practically, the proposed method has a potential to allow for a 3x speedup with minimal reconstruction error, resulting in less than 5 sec imaging time per slice. PMID:29060594

Single and multiple object tracking using log-euclidean Riemannian subspace and block-division appearance model.

PubMed

Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei

2012-12-01

Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.

Simultaneous multislice magnetic resonance fingerprinting with low-rank and subspace modeling.

PubMed

Bo Zhao; Bilgic, Berkin; Adalsteinsson, Elfar; Griswold, Mark A; Wald, Lawrence L; Setsompop, Kawin

2017-07-01

Magnetic resonance fingerprinting (MRF) is a new quantitative imaging paradigm that enables simultaneous acquisition of multiple magnetic resonance tissue parameters (e.g., T 1 , T 2 , and spin density). Recently, MRF has been integrated with simultaneous multislice (SMS) acquisitions to enable volumetric imaging with faster scan time. In this paper, we present a new image reconstruction method based on low-rank and subspace modeling for improved SMS-MRF. Here the low-rank model exploits strong spatiotemporal correlation among contrast-weighted images, while the subspace model captures the temporal evolution of magnetization dynamics. With the proposed model, the image reconstruction problem is formulated as a convex optimization problem, for which we develop an algorithm based on variable splitting and the alternating direction method of multipliers. The performance of the proposed method has been evaluated by numerical experiments, and the results demonstrate that the proposed method leads to improved accuracy over the conventional approach. Practically, the proposed method has a potential to allow for a 3× speedup with minimal reconstruction error, resulting in less than 5 sec imaging time per slice.

Hyperspectral material identification on radiance data using single-atmosphere or multiple-atmosphere modeling

NASA Astrophysics Data System (ADS)

Mariano, Adrian V.; Grossmann, John M.

2010-11-01

Reflectance-domain methods convert hyperspectral data from radiance to reflectance using an atmospheric compensation model. Material detection and identification are performed by comparing the compensated data to target reflectance spectra. We introduce two radiance-domain approaches, Single atmosphere Adaptive Cosine Estimator (SACE) and Multiple atmosphere ACE (MACE) in which the target reflectance spectra are instead converted into sensor-reaching radiance using physics-based models. For SACE, known illumination and atmospheric conditions are incorporated in a single atmospheric model. For MACE the conditions are unknown so the algorithm uses many atmospheric models to cover the range of environmental variability, and it approximates the result using a subspace model. This approach is sometimes called the invariant method, and requires the choice of a subspace dimension for the model. We compare these two radiance-domain approaches to a Reflectance-domain ACE (RACE) approach on a HYDICE image featuring concealed materials. All three algorithms use the ACE detector, and all three techniques are able to detect most of the hidden materials in the imagery. For MACE we observe a strong dependence on the choice of the material subspace dimension. Increasing this value can lead to a decline in performance.

Inverse gravity modeling for depth varying density structures through genetic algorithm, triangulated facet representation, and switching routines

NASA Astrophysics Data System (ADS)

King, Thomas Steven

A hybrid gravity modeling method is developed to investigate the structure of sedimentary mass bodies. The method incorporates as constraints surficial basement/sediment contacts and topography of a mass target with a quadratically varying density distribution. The inverse modeling utilizes a genetic algorithm (GA) to scan a wide range of the solution space to determine initial models and the Marquardt-Levenberg (ML) nonlinear inversion to determine final models that meet pre-assigned misfit criteria, thus providing an estimate of model variability and uncertainty. The surface modeling technique modifies Delaunay triangulation by allowing individual facets to be manually constructed and non-convex boundaries to be incorporated into the triangulation scheme. The sedimentary body is represented by a set of uneven prisms and edge elements, comprised of tetrahedrons, capped by polyhedrons. Each underlying prism and edge element's top surface is located by determining its point of tangency with the overlying terrain. The remaining overlying mass is gravitationally evaluated and subtracted from the observation points. Inversion then proceeds in the usual sense, but on an irregular tiered surface with each element's density defined relative to their top surface. Efficiency is particularly important due to the large number of facets evaluated for surface representations and the many repeated element evaluations of the stochastic GA. The gravitation of prisms, triangular faceted polygons, and tetrahedrons can be formulated in different ways, either mathematically or by physical approximations, each having distinct characteristics, such as evaluation time, accuracy over various spatial ranges, and computational singularities. A decision tree or switching routine is constructed for each element by combining these characteristics into a single cohesive package that optimizes the computation for accuracy and speed while avoiding singularities. The GA incorporates a subspace technique and parameter dependency to maintain model smoothness during development, thus minimizing creating nonphysical models. The stochastic GA explores the solution space, producing a broad range of unbiased initial models, while the ML inversion is deterministic and thus quickly converges to the final model. The combination allows many solution models to be determined from the same observed data.

The New Quantum Logic

NASA Astrophysics Data System (ADS)

Griffiths, Robert B.

2014-06-01

It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or decoherent histories interpretation of quantum mechanics by using a modified form of quantum logic to discuss quantum properties (subspaces of the quantum Hilbert space), and treating quantum time development as a stochastic process. The histories approach in turn gives rise to some conceptual difficulties, in particular the correct choice of a framework (probabilistic sample space) or family of histories, and these are discussed. The central issue is that the principle of unicity, the idea that there is a unique single true description of the world, is incompatible with our current understanding of quantum mechanics.

Subspace-based interference removal methods for a multichannel biomagnetic sensor array.

PubMed

Sekihara, Kensuke; Nagarajan, Srikantan S

2017-10-01

In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain. It defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.

Subspace-based interference removal methods for a multichannel biomagnetic sensor array

NASA Astrophysics Data System (ADS)

Sekihara, Kensuke; Nagarajan, Srikantan S.

2017-10-01

Objective. In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain. Approach. It defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.

Indoor Subspacing to Implement Indoorgml for Indoor Navigation

NASA Astrophysics Data System (ADS)

Jung, H.; Lee, J.

2015-10-01

According to an increasing demand for indoor navigation, there are great attempts to develop applicable indoor network. Representation for a room as a node is not sufficient to apply complex and large buildings. As OGC established IndoorGML, subspacing to partition the space for constructing logical network is introduced. Concerning subspacing for indoor network, transition space like halls or corridors also have to be considered. This study presents the subspacing process for creating an indoor network in shopping mall. Furthermore, categorization of transition space is performed and subspacing of this space is considered. Hall and squares in mall is especially defined for subspacing. Finally, implementation of subspacing process for indoor network is presented.

Stochastic wave-function simulation of irreversible emission processes for open quantum systems in a non-Markovian environment

NASA Astrophysics Data System (ADS)

Polyakov, Evgeny A.; Rubtsov, Alexey N.

2018-02-01

When conducting the numerical simulation of quantum transport, the main obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The Quantum Monte Carlo simulation techniques, while being capable of treating the problems of high dimension, are hindered by the so-called "sign problem". In the quantum transport, we have fundamental asymmetry between the processes of emission and absorption of environment excitations: the emitted excitations are rapidly and irreversibly scattered away. Whereas only a small part of these excitations is absorbed back by the open subsystem, thus exercising the non-Markovian self-action of the subsystem onto itself. We were able to devise a method for the exact simulation of the dominant quantum emission processes, while taking into account the small backaction effects in an approximate self-consistent way. Such an approach allows us to efficiently conduct simulations of real-time dynamics of small quantum subsystems immersed in non-Markovian bath for large times, reaching the quasistationary regime. As an example we calculate the spatial quench dynamics of Kondo cloud for a bozonized Kodno impurity model.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body bases.

PubMed

Reboredo, Fernando A; Kim, Jeongnim

2014-02-21

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

NASA Astrophysics Data System (ADS)

Reboredo, Fernando A.; Kim, Jeongnim

2014-02-01

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.

Switching LPV Control for High Performance Tactical Aircraft

NASA Technical Reports Server (NTRS)

Lu, Bei; Wu, Fen; Kim, SungWan

2004-01-01

This paper examines a switching Linear Parameter-Varying (LPV) control approach to determine if it is practical to use for flight control designs within a wide angle of attack region. The approach is based on multiple parameter-dependent Lyapunov functions. The full parameter space is partitioned into overlapping subspaces and a family of LPV controllers are designed, each suitable for a specific parameter subspace. The hysteresis switching logic is used to accomplish the transition among different parameter subspaces. The proposed switching LPV control scheme is applied to an F-16 aircraft model with different actuator dynamics in low and high angle of attack regions. The nonlinear simulation results show that the aircraft performs well when switching among different angle of attack regions.

Sliding Window Generalized Kernel Affine Projection Algorithm Using Projection Mappings

NASA Astrophysics Data System (ADS)

Slavakis, Konstantinos; Theodoridis, Sergios

2008-12-01

Very recently, a solution to the kernel-based online classification problem has been given by the adaptive projected subgradient method (APSM). The developed algorithm can be considered as a generalization of a kernel affine projection algorithm (APA) and the kernel normalized least mean squares (NLMS). Furthermore, sparsification of the resulting kernel series expansion was achieved by imposing a closed ball (convex set) constraint on the norm of the classifiers. This paper presents another sparsification method for the APSM approach to the online classification task by generating a sequence of linear subspaces in a reproducing kernel Hilbert space (RKHS). To cope with the inherent memory limitations of online systems and to embed tracking capabilities to the design, an upper bound on the dimension of the linear subspaces is imposed. The underlying principle of the design is the notion of projection mappings. Classification is performed by metric projection mappings, sparsification is achieved by orthogonal projections, while the online system's memory requirements and tracking are attained by oblique projections. The resulting sparsification scheme shows strong similarities with the classical sliding window adaptive schemes. The proposed design is validated by the adaptive equalization problem of a nonlinear communication channel, and is compared with classical and recent stochastic gradient descent techniques, as well as with the APSM's solution where sparsification is performed by a closed ball constraint on the norm of the classifiers.

Inverse regression-based uncertainty quantification algorithms for high-dimensional models: Theory and practice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Weixuan; Lin, Guang; Li, Bing

2016-09-01

A well-known challenge in uncertainty quantification (UQ) is the "curse of dimensionality". However, many high-dimensional UQ problems are essentially low-dimensional, because the randomness of the quantity of interest (QoI) is caused only by uncertain parameters varying within a low-dimensional subspace, known as the sufficient dimension reduction (SDR) subspace. Motivated by this observation, we propose and demonstrate in this paper an inverse regression-based UQ approach (IRUQ) for high-dimensional problems. Specifically, we use an inverse regression procedure to estimate the SDR subspace and then convert the original problem to a low-dimensional one, which can be efficiently solved by building a response surface model such as a polynomial chaos expansion. The novelty and advantages of the proposed approach is seen in its computational efficiency and practicality. Comparing with Monte Carlo, the traditionally preferred approach for high-dimensional UQ, IRUQ with a comparable cost generally gives much more accurate solutions even for high-dimensional problems, and even when the dimension reduction is not exactly sufficient. Theoretically, IRUQ is proved to converge twice as fast as the approach it uses seeking the SDR subspace. For example, while a sliced inverse regression method converges to the SDR subspace at the rate ofmore » $$O(n^{-1/2})$$, the corresponding IRUQ converges at $$O(n^{-1})$$. IRUQ also provides several desired conveniences in practice. It is non-intrusive, requiring only a simulator to generate realizations of the QoI, and there is no need to compute the high-dimensional gradient of the QoI. Finally, error bars can be derived for the estimation results reported by IRUQ.« less

Stochastic density functional theory at finite temperatures

NASA Astrophysics Data System (ADS)

Cytter, Yael; Rabani, Eran; Neuhauser, Daniel; Baer, Roi

2018-03-01

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O Quantum stopping times stochastic integral in the interacting Fock space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Yuanbao, E-mail: kangyuanb@163.com

Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L{sup 2}(ℝ{sup +}), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over amore » subspace of L{sup 2}(ℝ{sup +}) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ{sub τ]} ⊗ Γ{sub [τ}, where Γ{sub τ]} and Γ{sub [τ} stand for the part “before τ” and the part “after τ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.« less

Subspace-Aware Index Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kailkhura, Bhavya; Theagarajan, Lakshmi Narasimhan; Varshney, Pramod K.

In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications (e.g., multimedia), the data to be transmitted may lie (or can be well approximated) in a low-dimensional subspace. We exploit this low-dimensional structure of the data using an algebraic framework to solve the index coding problem (referred to as subspace-aware index coding) as opposed to the traditional index coding problem which is subspace-unaware. Also, we propose an efficient algorithm based on the alternating minimization approach to obtain near optimal index codes for both subspace-aware and -unawaremore » cases. In conclusion, our simulations indicate that under certain conditions, a significant throughput gain (about 90%) can be achieved by subspace-aware index codes over conventional subspace-unaware index codes.« less

Subspace-Aware Index Codes

DOE PAGES

Kailkhura, Bhavya; Theagarajan, Lakshmi Narasimhan; Varshney, Pramod K.

2017-04-12

In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications (e.g., multimedia), the data to be transmitted may lie (or can be well approximated) in a low-dimensional subspace. We exploit this low-dimensional structure of the data using an algebraic framework to solve the index coding problem (referred to as subspace-aware index coding) as opposed to the traditional index coding problem which is subspace-unaware. Also, we propose an efficient algorithm based on the alternating minimization approach to obtain near optimal index codes for both subspace-aware and -unawaremore » cases. In conclusion, our simulations indicate that under certain conditions, a significant throughput gain (about 90%) can be achieved by subspace-aware index codes over conventional subspace-unaware index codes.« less

A comparative study on book shelf structure based on different domain modal analysis

NASA Astrophysics Data System (ADS)

Sabamehr, Ardalan; Roy, Timir Baran; Bagchi, Ashutosh

2017-04-01

Structural Health Monitoring (SHM) based on the vibration of structures has been very attractive topic for researchers in different fields such as: civil, aeronautical and mechanical engineering. The aim of this paper is to compare three most common modal identification techniques such as Frequency Domain Decomposition (FDD), Stochastic Subspace Identification (SSI) and Continuous Wavelet Transform (CWT) to find modal properties (such as natural frequency, mode shape and damping ratio) of three story book shelf steel structure which was built in Concordia University Lab. The modified Complex Morlet wavelet have been selected for wavelet in order to use asymptotic signal rather than real one with variable bandwidth and wavelet central frequency. So, CWT is able to detect instantaneous modulus and phase by use of local maxima ridge detection.

Verification Techniques for Parameter Selection and Bayesian Model Calibration Presented for an HIV Model

NASA Astrophysics Data System (ADS)

Wentworth, Mami Tonoe

Uncertainty quantification plays an important role when making predictive estimates of model responses. In this context, uncertainty quantification is defined as quantifying and reducing uncertainties, and the objective is to quantify uncertainties in parameter, model and measurements, and propagate the uncertainties through the model, so that one can make a predictive estimate with quantified uncertainties. Two of the aspects of uncertainty quantification that must be performed prior to propagating uncertainties are model calibration and parameter selection. There are several efficient techniques for these processes; however, the accuracy of these methods are often not verified. This is the motivation for our work, and in this dissertation, we present and illustrate verification frameworks for model calibration and parameter selection in the context of biological and physical models. First, HIV models, developed and improved by [2, 3, 8], describe the viral infection dynamics of an HIV disease. These are also used to make predictive estimates of viral loads and T-cell counts and to construct an optimal control for drug therapy. Estimating input parameters is an essential step prior to uncertainty quantification. However, not all the parameters are identifiable, implying that they cannot be uniquely determined by the observations. These unidentifiable parameters can be partially removed by performing parameter selection, a process in which parameters that have minimal impacts on the model response are determined. We provide verification techniques for Bayesian model calibration and parameter selection for an HIV model. As an example of a physical model, we employ a heat model with experimental measurements presented in [10]. A steady-state heat model represents a prototypical behavior for heat conduction and diffusion process involved in a thermal-hydraulic model, which is a part of nuclear reactor models. We employ this simple heat model to illustrate verification techniques for model calibration. For Bayesian model calibration, we employ adaptive Metropolis algorithms to construct densities for input parameters in the heat model and the HIV model. To quantify the uncertainty in the parameters, we employ two MCMC algorithms: Delayed Rejection Adaptive Metropolis (DRAM) [33] and Differential Evolution Adaptive Metropolis (DREAM) [66, 68]. The densities obtained using these methods are compared to those obtained through the direct numerical evaluation of the Bayes' formula. We also combine uncertainties in input parameters and measurement errors to construct predictive estimates for a model response. A significant emphasis is on the development and illustration of techniques to verify the accuracy of sampling-based Metropolis algorithms. We verify the accuracy of DRAM and DREAM by comparing chains, densities and correlations obtained using DRAM, DREAM and the direct evaluation of Bayes formula. We also perform similar analysis for credible and prediction intervals for responses. Once the parameters are estimated, we employ energy statistics test [63, 64] to compare the densities obtained by different methods for the HIV model. The energy statistics are used to test the equality of distributions. We also consider parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs. We illustrate these techniques for a dynamic HIV model but note that the parameter selection and verification framework is applicable to a wide range of biological and physical models. To accommodate the nonlinear input to output relations, which are typical for such models, we focus on global sensitivity analysis techniques, including those based on partial correlations, Sobol indices based on second-order model representations, and Morris indices, as well as a parameter selection technique based on standard errors. A significant objective is to provide verification strategies to assess the accuracy of those techniques, which we illustrate in the context of the HIV model. Finally, we examine active subspace methods as an alternative to parameter subset selection techniques. The objective of active subspace methods is to determine the subspace of inputs that most strongly affect the model response, and to reduce the dimension of the input space. The major difference between active subspace methods and parameter selection techniques is that parameter selection identifies influential parameters whereas subspace selection identifies a linear combination of parameters that impacts the model responses significantly. We employ active subspace methods discussed in [22] for the HIV model and present a verification that the active subspace successfully reduces the input dimensions.

Overview of Krylov subspace methods with applications to control problems

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.

Noise-robust unsupervised spike sorting based on discriminative subspace learning with outlier handling.

PubMed

Keshtkaran, Mohammad Reza; Yang, Zhi

2017-06-01

Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. Most of the feature extraction and dimensionality reduction techniques that have been used for spike sorting give a projection subspace which is not necessarily the most discriminative one. Therefore, the clusters which appear inherently separable in some discriminative subspace may overlap if projected using conventional feature extraction approaches leading to a poor sorting accuracy especially when the noise level is high. In this paper, we propose a noise-robust and unsupervised spike sorting algorithm based on learning discriminative spike features for clustering. The proposed algorithm uses discriminative subspace learning to extract low dimensional and most discriminative features from the spike waveforms and perform clustering with automatic detection of the number of the clusters. The core part of the algorithm involves iterative subspace selection using linear discriminant analysis and clustering using Gaussian mixture model with outlier detection. A statistical test in the discriminative subspace is proposed to automatically detect the number of the clusters. Comparative results on publicly available simulated and real in vivo datasets demonstrate that our algorithm achieves substantially improved cluster distinction leading to higher sorting accuracy and more reliable detection of clusters which are highly overlapping and not detectable using conventional feature extraction techniques such as principal component analysis or wavelets. By providing more accurate information about the activity of more number of individual neurons with high robustness to neural noise and outliers, the proposed unsupervised spike sorting algorithm facilitates more detailed and accurate analysis of single- and multi-unit activities in neuroscience and brain machine interface studies.

Noise-robust unsupervised spike sorting based on discriminative subspace learning with outlier handling

NASA Astrophysics Data System (ADS)

Keshtkaran, Mohammad Reza; Yang, Zhi

2017-06-01

Objective. Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. Most of the feature extraction and dimensionality reduction techniques that have been used for spike sorting give a projection subspace which is not necessarily the most discriminative one. Therefore, the clusters which appear inherently separable in some discriminative subspace may overlap if projected using conventional feature extraction approaches leading to a poor sorting accuracy especially when the noise level is high. In this paper, we propose a noise-robust and unsupervised spike sorting algorithm based on learning discriminative spike features for clustering. Approach. The proposed algorithm uses discriminative subspace learning to extract low dimensional and most discriminative features from the spike waveforms and perform clustering with automatic detection of the number of the clusters. The core part of the algorithm involves iterative subspace selection using linear discriminant analysis and clustering using Gaussian mixture model with outlier detection. A statistical test in the discriminative subspace is proposed to automatically detect the number of the clusters. Main results. Comparative results on publicly available simulated and real in vivo datasets demonstrate that our algorithm achieves substantially improved cluster distinction leading to higher sorting accuracy and more reliable detection of clusters which are highly overlapping and not detectable using conventional feature extraction techniques such as principal component analysis or wavelets. Significance. By providing more accurate information about the activity of more number of individual neurons with high robustness to neural noise and outliers, the proposed unsupervised spike sorting algorithm facilitates more detailed and accurate analysis of single- and multi-unit activities in neuroscience and brain machine interface studies.

A Bayesian approach to model structural error and input variability in groundwater modeling

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Lin, Y. F. F.; Liang, F.

2015-12-01

Effective water resource management typically relies on numerical models to analyze groundwater flow and solute transport processes. Model structural error (due to simplification and/or misrepresentation of the "true" environmental system) and input forcing variability (which commonly arises since some inputs are uncontrolled or estimated with high uncertainty) are ubiquitous in groundwater models. Calibration that overlooks errors in model structure and input data can lead to biased parameter estimates and compromised predictions. We present a fully Bayesian approach for a complete assessment of uncertainty for spatially distributed groundwater models. The approach explicitly recognizes stochastic input and uses data-driven error models based on nonparametric kernel methods to account for model structural error. We employ exploratory data analysis to assist in specifying informative prior for error models to improve identifiability. The inference is facilitated by an efficient sampling algorithm based on DREAM-ZS and a parameter subspace multiple-try strategy to reduce the required number of forward simulations of the groundwater model. We demonstrate the Bayesian approach through a synthetic case study of surface-ground water interaction under changing pumping conditions. It is found that explicit treatment of errors in model structure and input data (groundwater pumping rate) has substantial impact on the posterior distribution of groundwater model parameters. Using error models reduces predictive bias caused by parameter compensation. In addition, input variability increases parametric and predictive uncertainty. The Bayesian approach allows for a comparison among the contributions from various error sources, which could inform future model improvement and data collection efforts on how to best direct resources towards reducing predictive uncertainty.

Advanced Stochastic Collocation Methods for Polynomial Chaos in RAVEN

NASA Astrophysics Data System (ADS)

Talbot, Paul W.

As experiment complexity in fields such as nuclear engineering continually increases, so does the demand for robust computational methods to simulate them. In many simulations, input design parameters and intrinsic experiment properties are sources of uncertainty. Often small perturbations in uncertain parameters have significant impact on the experiment outcome. For instance, in nuclear fuel performance, small changes in fuel thermal conductivity can greatly affect maximum stress on the surrounding cladding. The difficulty quantifying input uncertainty impact in such systems has grown with the complexity of numerical models. Traditionally, uncertainty quantification has been approached using random sampling methods like Monte Carlo. For some models, the input parametric space and corresponding response output space is sufficiently explored with few low-cost calculations. For other models, it is computationally costly to obtain good understanding of the output space. To combat the expense of random sampling, this research explores the possibilities of using advanced methods in Stochastic Collocation for generalized Polynomial Chaos (SCgPC) as an alternative to traditional uncertainty quantification techniques such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) methods for applications in nuclear engineering. We consider traditional SCgPC construction strategies as well as truncated polynomial spaces using Total Degree and Hyperbolic Cross constructions. We also consider applying anisotropy (unequal treatment of different dimensions) to the polynomial space, and offer methods whereby optimal levels of anisotropy can be approximated. We contribute development to existing adaptive polynomial construction strategies. Finally, we consider High-Dimensional Model Reduction (HDMR) expansions, using SCgPC representations for the subspace terms, and contribute new adaptive methods to construct them. We apply these methods on a series of models of increasing complexity. We use analytic models of various levels of complexity, then demonstrate performance on two engineering-scale problems: a single-physics nuclear reactor neutronics problem, and a multiphysics fuel cell problem coupling fuels performance and neutronics. Lastly, we demonstrate sensitivity analysis for a time-dependent fuels performance problem. We demonstrate the application of all the algorithms in RAVEN, a production-level uncertainty quantification framework.

Sub-grid scale models for discontinuous Galerkin methods based on the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric; Duraisamy, Karthk

2017-11-01

The optimal prediction framework of Chorin et al., which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived closure models. The M-Z formalism provides a methodology to reformulate a high-dimensional Markovian dynamical system as a lower-dimensional, non-Markovian (non-local) system. In this lower-dimensional system, the effects of the unresolved scales on the resolved scales are non-local and appear as a convolution integral. The non-Markovian system is an exact statement of the original dynamics and is used as a starting point for model development. In this work, we investigate the development of M-Z-based closures model within the context of the Variational Multiscale Method (VMS). The method relies on a decomposition of the solution space into two orthogonal subspaces. The impact of the unresolved subspace on the resolved subspace is shown to be non-local in time and is modeled through the M-Z-formalism. The models are applied to hierarchical discontinuous Galerkin discretizations. Commonalities between the M-Z closures and conventional flux schemes are explored. This work was supported in part by AFOSR under the project ''LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

Indoor Modelling from Slam-Based Laser Scanner: Door Detection to Envelope Reconstruction

NASA Astrophysics Data System (ADS)

Díaz-Vilariño, L.; Verbree, E.; Zlatanova, S.; Diakité, A.

2017-09-01

Updated and detailed indoor models are being increasingly demanded for various applications such as emergency management or navigational assistance. The consolidation of new portable and mobile acquisition systems has led to a higher availability of 3D point cloud data from indoors. In this work, we explore the combined use of point clouds and trajectories from SLAM-based laser scanner to automate the reconstruction of building indoors. The methodology starts by door detection, since doors represent transitions from one indoor space to other, which constitutes an initial approach about the global configuration of the point cloud into building rooms. For this purpose, the trajectory is used to create a vertical point cloud profile in which doors are detected as local minimum of vertical distances. As point cloud and trajectory are related by time stamp, this feature is used to subdivide the point cloud into subspaces according to the location of the doors. The correspondence between subspaces and building rooms is not unambiguous. One subspace always corresponds to one room, but one room is not necessarily depicted by just one subspace, for example, in case of a room containing several doors and in which the acquisition is performed in a discontinue way. The labelling problem is formulated as combinatorial approach solved as a minimum energy optimization. Once the point cloud is subdivided into building rooms, envelop (conformed by walls, ceilings and floors) is reconstructed for each space. The connectivity between spaces is included by adding the previously detected doors to the reconstructed model. The methodology is tested in a real case study.

Tachyon condensation due to domain-wall annihilation in Bose-Einstein condensates.

PubMed

Takeuchi, Hiromitsu; Kasamatsu, Kenichi; Tsubota, Makoto; Nitta, Muneto

2012-12-14

We show theoretically that a domain-wall annihilation in two-component Bose-Einstein condensates causes tachyon condensation accompanied by spontaneous symmetry breaking in a two-dimensional subspace. Three-dimensional vortex formation from domain-wall annihilations is considered a kink formation in subspace. Numerical experiments reveal that the subspatial dynamics obey the dynamic scaling law of phase-ordering kinetics. This model is experimentally feasible and provides insights into how the extra dimensions influence subspatial phase transition in higher-dimensional space.

An adaptive optimal control for smart structures based on the subspace tracking identification technique

NASA Astrophysics Data System (ADS)

Ripamonti, Francesco; Resta, Ferruccio; Borroni, Massimo; Cazzulani, Gabriele

2014-04-01

A new method for the real-time identification of mechanical system modal parameters is used in order to design different adaptive control logics aiming to reduce the vibrations in a carbon fiber plate smart structure. It is instrumented with three piezoelectric actuators, three accelerometers and three strain gauges. The real-time identification is based on a recursive subspace tracking algorithm whose outputs are elaborated by an ARMA model. A statistical approach is finally applied to choose the modal parameter correct values. These are given in input to model-based control logics such as a gain scheduling and an adaptive LQR control.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE PAGES

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

2016-05-25

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Unsupervised spike sorting based on discriminative subspace learning.

PubMed

Keshtkaran, Mohammad Reza; Yang, Zhi

2014-01-01

Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. In this paper, we present two unsupervised spike sorting algorithms based on discriminative subspace learning. The first algorithm simultaneously learns the discriminative feature subspace and performs clustering. It uses histogram of features in the most discriminative projection to detect the number of neurons. The second algorithm performs hierarchical divisive clustering that learns a discriminative 1-dimensional subspace for clustering in each level of the hierarchy until achieving almost unimodal distribution in the subspace. The algorithms are tested on synthetic and in-vivo data, and are compared against two widely used spike sorting methods. The comparative results demonstrate that our spike sorting methods can achieve substantially higher accuracy in lower dimensional feature space, and they are highly robust to noise. Moreover, they provide significantly better cluster separability in the learned subspace than in the subspace obtained by principal component analysis or wavelet transform.

Variational second order density matrix study of F3-: importance of subspace constraints for size-consistency.

PubMed

van Aggelen, Helen; Verstichel, Brecht; Bultinck, Patrick; Van Neck, Dimitri; Ayers, Paul W; Cooper, David L

2011-02-07

Variational second order density matrix theory under "two-positivity" constraints tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F(3)(-) by applying subspace energy constraints on mono- and diatomic subspaces of the molecular basis space. Monoatomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting second order density matrix method does not exactly correspond to a system of noninteracting units.

Sparse PCA with Oracle Property.

PubMed

Gu, Quanquan; Wang, Zhaoran; Liu, Han

In this paper, we study the estimation of the k -dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank- k , and attains a [Formula: see text] statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

Sparse PCA with Oracle Property

PubMed Central

Gu, Quanquan; Wang, Zhaoran; Liu, Han

2014-01-01

In this paper, we study the estimation of the k-dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-k, and attains a s/n statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets. PMID:25684971

Slope angle estimation method based on sparse subspace clustering for probe safe landing

NASA Astrophysics Data System (ADS)

Li, Haibo; Cao, Yunfeng; Ding, Meng; Zhuang, Likui

2018-06-01

To avoid planetary probes landing on steep slopes where they may slip or tip over, a new method of slope angle estimation based on sparse subspace clustering is proposed to improve accuracy. First, a coordinate system is defined and established to describe the measured data of light detection and ranging (LIDAR). Second, this data is processed and expressed with a sparse representation. Third, on this basis, the data is made to cluster to determine which subspace it belongs to. Fourth, eliminating outliers in subspace, the correct data points are used for the fitting planes. Finally, the vectors normal to the planes are obtained using the plane model, and the angle between the normal vectors is obtained through calculation. Based on the geometric relationship, this angle is equal in value to the slope angle. The proposed method was tested in a series of experiments. The experimental results show that this method can effectively estimate the slope angle, can overcome the influence of noise and obtain an exact slope angle. Compared with other methods, this method can minimize the measuring errors and further improve the estimation accuracy of the slope angle.

Non-Cooperative Target Recognition by Means of Singular Value Decomposition Applied to Radar High Resolution Range Profiles †

PubMed Central

López-Rodríguez, Patricia; Escot-Bocanegra, David; Fernández-Recio, Raúl; Bravo, Ignacio

2015-01-01

Radar high resolution range profiles are widely used among the target recognition community for the detection and identification of flying targets. In this paper, singular value decomposition is applied to extract the relevant information and to model each aircraft as a subspace. The identification algorithm is based on angle between subspaces and takes place in a transformed domain. In order to have a wide database of radar signatures and evaluate the performance, simulated range profiles are used as the recognition database while the test samples comprise data of actual range profiles collected in a measurement campaign. Thanks to the modeling of aircraft as subspaces only the valuable information of each target is used in the recognition process. Thus, one of the main advantages of using singular value decomposition, is that it helps to overcome the notable dissimilarities found in the shape and signal-to-noise ratio between actual and simulated profiles due to their difference in nature. Despite these differences, the recognition rates obtained with the algorithm are quite promising. PMID:25551484

CLAss-Specific Subspace Kernel Representations and Adaptive Margin Slack Minimization for Large Scale Classification.

PubMed

Yu, Yinan; Diamantaras, Konstantinos I; McKelvey, Tomas; Kung, Sun-Yuan

2018-02-01

In kernel-based classification models, given limited computational power and storage capacity, operations over the full kernel matrix becomes prohibitive. In this paper, we propose a new supervised learning framework using kernel models for sequential data processing. The framework is based on two components that both aim at enhancing the classification capability with a subset selection scheme. The first part is a subspace projection technique in the reproducing kernel Hilbert space using a CLAss-specific Subspace Kernel representation for kernel approximation. In the second part, we propose a novel structural risk minimization algorithm called the adaptive margin slack minimization to iteratively improve the classification accuracy by an adaptive data selection. We motivate each part separately, and then integrate them into learning frameworks for large scale data. We propose two such frameworks: the memory efficient sequential processing for sequential data processing and the parallelized sequential processing for distributed computing with sequential data acquisition. We test our methods on several benchmark data sets and compared with the state-of-the-art techniques to verify the validity of the proposed techniques.

Development of Subspace-based Hybrid Monte Carlo-Deterministric Algorithms for Reactor Physics Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdel-Khalik, Hany S.; Zhang, Qiong

2014-05-20

The development of hybrid Monte-Carlo-Deterministic (MC-DT) approaches, taking place over the past few decades, have primarily focused on shielding and detection applications where the analysis requires a small number of responses, i.e. at the detector locations(s). This work further develops a recently introduced global variance reduction approach, denoted by the SUBSPACE approach is designed to allow the use of MC simulation, currently limited to benchmarking calculations, for routine engineering calculations. By way of demonstration, the SUBSPACE approach is applied to assembly level calculations used to generate the few-group homogenized cross-sections. These models are typically expensive and need to be executedmore » in the order of 10 3 - 10 5 times to properly characterize the few-group cross-sections for downstream core-wide calculations. Applicability to k-eigenvalue core-wide models is also demonstrated in this work. Given the favorable results obtained in this work, we believe the applicability of the MC method for reactor analysis calculations could be realized in the near future.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

Conformational states and folding pathways of peptides revealed by principal-independent component analyses.

PubMed

Nguyen, Phuong H

2007-05-15

Principal component analysis is a powerful method for projecting multidimensional conformational space of peptides or proteins onto lower dimensional subspaces in which the main conformations are present, making it easier to reveal the structures of molecules from e.g. molecular dynamics simulation trajectories. However, the identification of all conformational states is still difficult if the subspaces consist of more than two dimensions. This is mainly due to the fact that the principal components are not independent with each other, and states in the subspaces cannot be visualized. In this work, we propose a simple and fast scheme that allows one to obtain all conformational states in the subspaces. The basic idea is that instead of directly identifying the states in the subspace spanned by principal components, we first transform this subspace into another subspace formed by components that are independent of one other. These independent components are obtained from the principal components by employing the independent component analysis method. Because of independence between components, all states in this new subspace are defined as all possible combinations of the states obtained from each single independent component. This makes the conformational analysis much simpler. We test the performance of the method by analyzing the conformations of the glycine tripeptide and the alanine hexapeptide. The analyses show that our method is simple and quickly reveal all conformational states in the subspaces. The folding pathways between the identified states of the alanine hexapeptide are analyzed and discussed in some detail. 2007 Wiley-Liss, Inc.

A hyperspectral imagery anomaly detection algorithm based on local three-dimensional orthogonal subspace projection

NASA Astrophysics Data System (ADS)

Zhang, Xing; Wen, Gongjian

2015-10-01

Anomaly detection (AD) becomes increasingly important in hyperspectral imagery analysis with many practical applications. Local orthogonal subspace projection (LOSP) detector is a popular anomaly detector which exploits local endmembers/eigenvectors around the pixel under test (PUT) to construct background subspace. However, this subspace only takes advantage of the spectral information, but the spatial correlat ion of the background clutter is neglected, which leads to the anomaly detection result sensitive to the accuracy of the estimated subspace. In this paper, a local three dimensional orthogonal subspace projection (3D-LOSP) algorithm is proposed. Firstly, under the jointly use of both spectral and spatial information, three directional background subspaces are created along the image height direction, the image width direction and the spectral direction, respectively. Then, the three corresponding orthogonal subspaces are calculated. After that, each vector along three direction of the local cube is projected onto the corresponding orthogonal subspace. Finally, a composite score is given through the three direction operators. In 3D-LOSP, the anomalies are redefined as the target not only spectrally different to the background, but also spatially distinct. Thanks to the addition of the spatial information, the robustness of the anomaly detection result has been improved greatly by the proposed 3D-LOSP algorithm. It is noteworthy that the proposed algorithm is an expansion of LOSP and this ideology can inspire many other spectral-based anomaly detection methods. Experiments with real hyperspectral images have proved the stability of the detection result.

Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model.

PubMed

Smirnova, Alexandra; deCamp, Linda; Chowell, Gerardo

2017-05-02

Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous studies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polynomials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov's) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabilizing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014-2015 Ebola epidemic in West Africa.

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

USGS Publications Warehouse

Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.

2011-01-01

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.

Visual tracking based on the sparse representation of the PCA subspace

NASA Astrophysics Data System (ADS)

Chen, Dian-bing; Zhu, Ming; Wang, Hui-li

2017-09-01

We construct a collaborative model of the sparse representation and the subspace representation. First, we represent the tracking target in the principle component analysis (PCA) subspace, and then we employ an L 1 regularization to restrict the sparsity of the residual term, an L 2 regularization term to restrict the sparsity of the representation coefficients, and an L 2 norm to restrict the distance between the reconstruction and the target. Then we implement the algorithm in the particle filter framework. Furthermore, an iterative method is presented to get the global minimum of the residual and the coefficients. Finally, an alternative template update scheme is adopted to avoid the tracking drift which is caused by the inaccurate update. In the experiment, we test the algorithm on 9 sequences, and compare the results with 5 state-of-art methods. According to the results, we can conclude that our algorithm is more robust than the other methods.

Glove-based approach to online signature verification.

PubMed

Kamel, Nidal S; Sayeed, Shohel; Ellis, Grant A

2008-06-01

Utilizing the multiple degrees of freedom offered by the data glove for each finger and the hand, a novel on-line signature verification system using the Singular Value Decomposition (SVD) numerical tool for signature classification and verification is presented. The proposed technique is based on the Singular Value Decomposition in finding r singular vectors sensing the maximal energy of glove data matrix A, called principal subspace, so the effective dimensionality of A can be reduced. Having modeled the data glove signature through its r-principal subspace, signature authentication is performed by finding the angles between the different subspaces. A demonstration of the data glove is presented as an effective high-bandwidth data entry device for signature verification. This SVD-based signature verification technique is tested and its performance is shown to be able to recognize forgery signatures with a false acceptance rate of less than 1.2%.

Fast dimension reduction and integrative clustering of multi-omics data using low-rank approximation: application to cancer molecular classification.

PubMed

Wu, Dingming; Wang, Dongfang; Zhang, Michael Q; Gu, Jin

2015-12-01

One major goal of large-scale cancer omics study is to identify molecular subtypes for more accurate cancer diagnoses and treatments. To deal with high-dimensional cancer multi-omics data, a promising strategy is to find an effective low-dimensional subspace of the original data and then cluster cancer samples in the reduced subspace. However, due to data-type diversity and big data volume, few methods can integrative and efficiently find the principal low-dimensional manifold of the high-dimensional cancer multi-omics data. In this study, we proposed a novel low-rank approximation based integrative probabilistic model to fast find the shared principal subspace across multiple data types: the convexity of the low-rank regularized likelihood function of the probabilistic model ensures efficient and stable model fitting. Candidate molecular subtypes can be identified by unsupervised clustering hundreds of cancer samples in the reduced low-dimensional subspace. On testing datasets, our method LRAcluster (low-rank approximation based multi-omics data clustering) runs much faster with better clustering performances than the existing method. Then, we applied LRAcluster on large-scale cancer multi-omics data from TCGA. The pan-cancer analysis results show that the cancers of different tissue origins are generally grouped as independent clusters, except squamous-like carcinomas. While the single cancer type analysis suggests that the omics data have different subtyping abilities for different cancer types. LRAcluster is a very useful method for fast dimension reduction and unsupervised clustering of large-scale multi-omics data. LRAcluster is implemented in R and freely available via http://bioinfo.au.tsinghua.edu.cn/software/lracluster/ .

Macromolecule mapping of the brain using ultrashort-TE acquisition and reference-based metabolite removal.

PubMed

Lam, Fan; Li, Yudu; Clifford, Bryan; Liang, Zhi-Pei

2018-05-01

To develop a practical method for mapping macromolecule distribution in the brain using ultrashort-TE MRSI data. An FID-based chemical shift imaging acquisition without metabolite-nulling pulses was used to acquire ultrashort-TE MRSI data that capture the macromolecule signals with high signal-to-noise-ratio (SNR) efficiency. To remove the metabolite signals from the ultrashort-TE data, single voxel spectroscopy data were obtained to determine a set of high-quality metabolite reference spectra. These spectra were then incorporated into a generalized series (GS) model to represent general metabolite spatiospectral distributions. A time-segmented algorithm was developed to back-extrapolate the GS model-based metabolite distribution from truncated FIDs and remove it from the MRSI data. Numerical simulations and in vivo experiments have been performed to evaluate the proposed method. Simulation results demonstrate accurate metabolite signal extrapolation by the proposed method given a high-quality reference. For in vivo experiments, the proposed method is able to produce spatiospectral distributions of macromolecules in the brain with high SNR from data acquired in about 10 minutes. We further demonstrate that the high-dimensional macromolecule spatiospectral distribution resides in a low-dimensional subspace. This finding provides a new opportunity to use subspace models for quantification and accelerated macromolecule mapping. Robustness of the proposed method is also demonstrated using multiple data sets from the same and different subjects. The proposed method is able to obtain macromolecule distributions in the brain from ultrashort-TE acquisitions. It can also be used for acquiring training data to determine a low-dimensional subspace to represent the macromolecule signals for subspace-based MRSI. Magn Reson Med 79:2460-2469, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

An alternative subspace approach to EEG dipole source localization

NASA Astrophysics Data System (ADS)

Xu, Xiao-Liang; Xu, Bobby; He, Bin

2004-01-01

In the present study, we investigate a new approach to electroencephalography (EEG) three-dimensional (3D) dipole source localization by using a non-recursive subspace algorithm called FINES. In estimating source dipole locations, the present approach employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of the entire estimated noise-only subspace in the case of classic MUSIC. The subspace spanned by this vector set is, in the sense of principal angle, closest to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanced accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors. The present computer simulations show, in EEG 3D dipole source localization, that compared to classic MUSIC, FINES has (1) better resolvability of two closely spaced dipolar sources and (2) better estimation accuracy of source locations. In comparison with RAP-MUSIC, FINES' performance is also better for the cases studied when the noise level is high and/or correlations among dipole sources exist.

Nonadiabatic holonomic quantum computation in decoherence-free subspaces.

PubMed

Xu, G F; Zhang, J; Tong, D M; Sjöqvist, Erik; Kwek, L C

2012-10-26

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Seismic noise attenuation using an online subspace tracking algorithm

NASA Astrophysics Data System (ADS)

Zhou, Yatong; Li, Shuhua; Zhang, Dong; Chen, Yangkang

2018-02-01

We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-the-art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVD-based singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.

Investigating phonon-mediated interactions with polar molecules

NASA Astrophysics Data System (ADS)

Sous, John; Madison, Kirk; Berciu, Mona; Krems, Roman

2017-04-01

We show that an ensemble of polar molecules in an optical lattice realizes the Peierls polaron model for hard-core particles/ pseudospins. We analyze the quasiparticle spectrum in the one-particle subspace, the two-particle subspace and at finite concentrations. We derive an effective model that describes the low-energy behavior of the system. We show that the Hamiltonian includes phonon-mediated repulsions and phonon-mediated ``pair-hopping'' terms which move the particle pair as a whole. We show that microwave excitations of the system exhibit signatures of these interactions. These results pave the way for the experimental observation of phonon-mediated repulsion. This work was supported by NSERC of Canada and the Stewart Blusson Quantum Matter Institute.

Hypercyclic subspaces for Frechet space operators

NASA Astrophysics Data System (ADS)

Petersson, Henrik

2006-07-01

A continuous linear operator is hypercyclic if there is an such that the orbit {Tnx} is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that it is possible to characterize Banach space operators that have a hypercyclic subspace, i.e., an infinite dimensional closed subspace of, except for zero, hypercyclic vectors. The following is known to hold: A Banach space operator T has a hypercyclic subspace if there is a sequence (ni) and an infinite dimensional closed subspace such that T is hereditarily hypercyclic for (ni) and Tni->0 pointwise on E. In this note we extend this result to the setting of Frechet spaces that admit a continuous norm, and study some applications for important function spaces. As an application we also prove that any infinite dimensional separable Frechet space with a continuous norm admits an operator with a hypercyclic subspace.

On iterative processes in the Krylov-Sonneveld subspaces

NASA Astrophysics Data System (ADS)

Ilin, Valery P.

2016-10-01

The iterative Induced Dimension Reduction (IDR) methods are considered for solving large systems of linear algebraic equations (SLAEs) with nonsingular nonsymmetric matrices. These approaches are investigated by many authors and are charachterized sometimes as the alternative to the classical processes of Krylov type. The key moments of the IDR algorithms consist in the construction of the embedded Sonneveld subspaces, which have the decreasing dimensions and use the orthogonalization to some fixed subspace. Other independent approaches for research and optimization of the iterations are based on the augmented and modified Krylov subspaces by using the aggregation and deflation procedures with present various low rank approximations of the original matrices. The goal of this paper is to show, that IDR method in Sonneveld subspaces present an original interpretation of the modified algorithms in the Krylov subspaces. In particular, such description is given for the multi-preconditioned semi-conjugate direction methods which are actual for the parallel algebraic domain decomposition approaches.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

A novel manifold-manifold distance index applied to looseness state assessment of viscoelastic sandwich structures

NASA Astrophysics Data System (ADS)

Sun, Chuang; Zhang, Zhousuo; Guo, Ting; Luo, Xue; Qu, Jinxiu; Zhang, Chenxuan; Cheng, Wei; Li, Bing

2014-06-01

Viscoelastic sandwich structures (VSS) are widely used in mechanical equipment; their state assessment is necessary to detect structural states and to keep equipment running with high reliability. This paper proposes a novel manifold-manifold distance-based assessment (M2DBA) method for assessing the looseness state in VSSs. In the M2DBA method, a manifold-manifold distance is viewed as a health index. To design the index, response signals from the structure are firstly acquired by condition monitoring technology and a Hankel matrix is constructed by using the response signals to describe state patterns of the VSS. Thereafter, a subspace analysis method, that is, principal component analysis (PCA), is performed to extract the condition subspace hidden in the Hankel matrix. From the subspace, pattern changes in dynamic structural properties are characterized. Further, a Grassmann manifold (GM) is formed by organizing a set of subspaces. The manifold is mapped to a reproducing kernel Hilbert space (RKHS), where support vector data description (SVDD) is used to model the manifold as a hypersphere. Finally, a health index is defined as the cosine of the angle between the hypersphere centers corresponding to the structural baseline state and the looseness state. The defined health index contains similarity information existing in the two structural states, so structural looseness states can be effectively identified. Moreover, the health index is derived by analysis of the global properties of subspace sets, which is different from traditional subspace analysis methods. The effectiveness of the health index for state assessment is validated by test data collected from a VSS subjected to different degrees of looseness. The results show that the health index is a very effective metric for detecting the occurrence and extension of structural looseness. Comparison results indicate that the defined index outperforms some existing state-of-the-art ones.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body basis expansions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Jeongnim; Reboredo, Fernando A.

The self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem. Phys. {\\bf 136}, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. {\\bf 89}, 6316 (1988)] are blended to obtain a method for the calculation of thermodynamic properties of many-body systems at low temperatures. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric trial wave functions. A statistical method is derived for the calculation of finite temperature properties of many-body systemsmore » near the ground state. In the process we also obtain a parallel algorithm that optimizes the many-body basis of a small subspace of the many-body Hilbert space. This small subspace is optimized to have maximum overlap with the one expanded by the lower energy eigenstates of a many-body Hamiltonian. We show in a model system that the Helmholtz free energy is minimized within this subspace as the iteration number increases. We show that the subspace expanded by the small basis systematically converges towards the subspace expanded by the lowest energy eigenstates. Possible applications of this method to calculate the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.« less

Principal component and clustering analysis on molecular dynamics data of the ribosomal L11·23S subdomain.

PubMed

Wolf, Antje; Kirschner, Karl N

2013-02-01

With improvements in computer speed and algorithm efficiency, MD simulations are sampling larger amounts of molecular and biomolecular conformations. Being able to qualitatively and quantitatively sift these conformations into meaningful groups is a difficult and important task, especially when considering the structure-activity paradigm. Here we present a study that combines two popular techniques, principal component (PC) analysis and clustering, for revealing major conformational changes that occur in molecular dynamics (MD) simulations. Specifically, we explored how clustering different PC subspaces effects the resulting clusters versus clustering the complete trajectory data. As a case example, we used the trajectory data from an explicitly solvated simulation of a bacteria's L11·23S ribosomal subdomain, which is a target of thiopeptide antibiotics. Clustering was performed, using K-means and average-linkage algorithms, on data involving the first two to the first five PC subspace dimensions. For the average-linkage algorithm we found that data-point membership, cluster shape, and cluster size depended on the selected PC subspace data. In contrast, K-means provided very consistent results regardless of the selected subspace. Since we present results on a single model system, generalization concerning the clustering of different PC subspaces of other molecular systems is currently premature. However, our hope is that this study illustrates a) the complexities in selecting the appropriate clustering algorithm, b) the complexities in interpreting and validating their results, and c) by combining PC analysis with subsequent clustering valuable dynamic and conformational information can be obtained.

Characterizing L1-norm best-fit subspaces

NASA Astrophysics Data System (ADS)

Brooks, J. Paul; Dulá, José H.

2017-05-01

Fitting affine objects to data is the basis of many tools and methodologies in statistics, machine learning, and signal processing. The L1 norm is often employed to produce subspaces exhibiting a robustness to outliers and faulty observations. The L1-norm best-fit subspace problem is directly formulated as a nonlinear, nonconvex, and nondifferentiable optimization problem. The case when the subspace is a hyperplane can be solved to global optimality efficiently by solving a series of linear programs. The problem of finding the best-fit line has recently been shown to be NP-hard. We present necessary conditions for optimality for the best-fit subspace problem, and use them to characterize properties of optimal solutions.

Quantum error suppression with commuting Hamiltonians: two local is too local.

PubMed

Marvian, Iman; Lidar, Daniel A

2014-12-31

We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

Mode Shape Estimation Algorithms Under Ambient Conditions: A Comparative Review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dosiek, Luke; Zhou, Ning; Pierre, John W.

Abstract—This paper provides a comparative review of five existing ambient electromechanical mode shape estimation algorithms, i.e., the Transfer Function (TF), Spectral, Frequency Domain Decomposition (FDD), Channel Matching, and Subspace Methods. It is also shown that the TF Method is a general approach to estimating mode shape and that the Spectral, FDD, and Channel Matching Methods are actually special cases of it. Additionally, some of the variations of the Subspace Method are reviewed and the Numerical algorithm for Subspace State Space System IDentification (N4SID) is implemented. The five algorithms are then compared using data simulated from a 17-machine model of themore » Western Electricity Coordinating Council (WECC) under ambient conditions with both low and high damping, as well as during the case where ambient data is disrupted by an oscillatory ringdown. The performance of the algorithms is compared using the statistics from Monte Carlo Simulations and results from measured WECC data, and a discussion of the practical issues surrounding their implementation, including cases where power system probing is an option, is provided. The paper concludes with some recommendations as to the appropriate use of the various techniques. Index Terms—Electromechanical mode shape, small-signal stability, phasor measurement units (PMU), system identification, N4SID, subspace.« less

Dual signal subspace projection (DSSP): a novel algorithm for removing large interference in biomagnetic measurements

NASA Astrophysics Data System (ADS)

Sekihara, Kensuke; Kawabata, Yuya; Ushio, Shuta; Sumiya, Satoshi; Kawabata, Shigenori; Adachi, Yoshiaki; Nagarajan, Srikantan S.

2016-06-01

Objective. In functional electrophysiological imaging, signals are often contaminated by interference that can be of considerable magnitude compared to the signals of interest. This paper proposes a novel algorithm for removing such interferences that does not require separate noise measurements. Approach. The algorithm is based on a dual definition of the signal subspace in the spatial- and time-domains. Since the algorithm makes use of this duality, it is named the dual signal subspace projection (DSSP). The DSSP algorithm first projects the columns of the measured data matrix onto the inside and outside of the spatial-domain signal subspace, creating a set of two preprocessed data matrices. The intersection of the row spans of these two matrices is estimated as the time-domain interference subspace. The original data matrix is projected onto the subspace that is orthogonal to this interference subspace. Main results. The DSSP algorithm is validated by using the computer simulation, and using two sets of real biomagnetic data: spinal cord evoked field data measured from a healthy volunteer and magnetoencephalography data from a patient with a vagus nerve stimulator. Significance. The proposed DSSP algorithm is effective for removing overlapped interference in a wide variety of biomagnetic measurements.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

View subspaces for indexing and retrieval of 3D models

NASA Astrophysics Data System (ADS)

Dutagaci, Helin; Godil, Afzal; Sankur, Bülent; Yemez, Yücel

2010-02-01

View-based indexing schemes for 3D object retrieval are gaining popularity since they provide good retrieval results. These schemes are coherent with the theory that humans recognize objects based on their 2D appearances. The viewbased techniques also allow users to search with various queries such as binary images, range images and even 2D sketches. The previous view-based techniques use classical 2D shape descriptors such as Fourier invariants, Zernike moments, Scale Invariant Feature Transform-based local features and 2D Digital Fourier Transform coefficients. These methods describe each object independent of others. In this work, we explore data driven subspace models, such as Principal Component Analysis, Independent Component Analysis and Nonnegative Matrix Factorization to describe the shape information of the views. We treat the depth images obtained from various points of the view sphere as 2D intensity images and train a subspace to extract the inherent structure of the views within a database. We also show the benefit of categorizing shapes according to their eigenvalue spread. Both the shape categorization and data-driven feature set conjectures are tested on the PSB database and compared with the competitor view-based 3D shape retrieval algorithms.

Optimal mode transformations for linear-optical cluster-state generation

DOE PAGES

Uskov, Dmitry B.; Lougovski, Pavel; Alsing, Paul M.; ...

2015-06-15

In this paper, we analyze the generation of linear-optical cluster states (LOCSs) via sequential addition of one and two qubits. Existing approaches employ the stochastic linear-optical two-qubit controlled-Z (CZ) gate with success rate of 1/9 per operation. The question of optimality of the CZ gate with respect to LOCS generation has remained open. We report that there are alternative schemes to the CZ gate that are exponentially more efficient and show that sequential LOCS growth is indeed globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. Finally,more » we show that the maximal success rate of postselected entangling n photonic qubits or m Bell pairs into a cluster is (1/2) n-1 and (1/4) m-1, respectively, with no ancilla photons, and we give an explicit optical description of the optimal mode transformations.« less

An accelerated subspace iteration for eigenvector derivatives

NASA Technical Reports Server (NTRS)

Ting, Tienko

1991-01-01

An accelerated subspace iteration method for calculating eigenvector derivatives has been developed. Factors affecting the effectiveness and the reliability of the subspace iteration are identified, and effective strategies concerning these factors are presented. The method has been implemented, and the results of a demonstration problem are presented.

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

NASA Astrophysics Data System (ADS)

Szalai, Robert; Ehrhardt, David; Haller, George

2017-06-01

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. This model identification utilizes Taken's delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding. The SSMs are then constructed for the sampling map using the parametrization method for invariant manifolds, which assumes that the manifold is an embedding of, rather than a graph over, a spectral subspace. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

Improving deep convolutional neural networks with mixed maxout units.

PubMed

Zhao, Hui-Zhen; Liu, Fu-Xian; Li, Long-Yue

2017-01-01

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that "non-maximal features are unable to deliver" and "feature mapping subspace pooling is insufficient," we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying different convolutional transformations over the same input and then calculating the expected values according to their exponential probabilities. Moreover, we introduce the Bernoulli distribution to balance the maximum values with the expected values of the feature mappings subspace. Finally, we design a simple model to verify the pooling ability of mixout units and a Mixout-units-based Network-in-Network (NiN) model to analyze the feature learning ability of the mixout models. We argue that our proposed units improve the pooling ability and that mixout models can achieve better feature learning and classification performance.

Modulated Hebb-Oja learning rule--a method for principal subspace analysis.

PubMed

Jankovic, Marko V; Ogawa, Hidemitsu

2006-03-01

This paper presents analysis of the recently proposed modulated Hebb-Oja (MHO) method that performs linear mapping to a lower-dimensional subspace. Principal component subspace is the method that will be analyzed. Comparing to some other well-known methods for yielding principal component subspace (e.g., Oja's Subspace Learning Algorithm), the proposed method has one feature that could be seen as desirable from the biological point of view--synaptic efficacy learning rule does not need the explicit information about the value of the other efficacies to make individual efficacy modification. Also, the simplicity of the "neural circuits" that perform global computations and a fact that their number does not depend on the number of input and output neurons, could be seen as good features of the proposed method.

Current harmonics elimination control method for six-phase PM synchronous motor drives.

PubMed

Yuan, Lei; Chen, Ming-liang; Shen, Jian-qing; Xiao, Fei

2015-11-01

To reduce the undesired 5th and 7th stator harmonic current in the six-phase permanent magnet synchronous motor (PMSM), an improved vector control algorithm was proposed based on vector space decomposition (VSD) transformation method, which can control the fundamental and harmonic subspace separately. To improve the traditional VSD technology, a novel synchronous rotating coordinate transformation matrix was presented in this paper, and only using the traditional PI controller in d-q subspace can meet the non-static difference adjustment, the controller parameter design method is given by employing internal model principle. Moreover, the current PI controller parallel with resonant controller is employed in x-y subspace to realize the specific 5th and 7th harmonic component compensation. In addition, a new six-phase SVPWM algorithm based on VSD transformation theory is also proposed. Simulation and experimental results verify the effectiveness of current decoupling vector controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Finite element model updating of a prestressed concrete box girder bridge using subproblem approximation

NASA Astrophysics Data System (ADS)

Chen, G. W.; Omenzetter, P.

2016-04-01

This paper presents the implementation of an updating procedure for the finite element model (FEM) of a prestressed concrete continuous box-girder highway off-ramp bridge. Ambient vibration testing was conducted to excite the bridge, assisted by linear chirp sweepings induced by two small electrodynamic shakes deployed to enhance the excitation levels, since the bridge was closed to traffic. The data-driven stochastic subspace identification method was executed to recover the modal properties from measurement data. An initial FEM was developed and correlation between the experimental modal results and their analytical counterparts was studied. Modelling of the pier and abutment bearings was carefully adjusted to reflect the real operational conditions of the bridge. The subproblem approximation method was subsequently utilized to automatically update the FEM. For this purpose, the influences of bearing stiffness, and mass density and Young's modulus of materials were examined as uncertain parameters using sensitivity analysis. The updating objective function was defined based on a summation of squared values of relative errors of natural frequencies between the FEM and experimentation. All the identified modes were used as the target responses with the purpose of putting more constrains for the optimization process and decreasing the number of potentially feasible combinations for parameter changes. The updated FEM of the bridge was able to produce sufficient improvements in natural frequencies in most modes of interest, and can serve for a more precise dynamic response prediction or future investigation of the bridge health.

Conjunctive patches subspace learning with side information for collaborative image retrieval.

PubMed

Zhang, Lining; Wang, Lipo; Lin, Weisi

2012-08-01

Content-Based Image Retrieval (CBIR) has attracted substantial attention during the past few years for its potential practical applications to image management. A variety of Relevance Feedback (RF) schemes have been designed to bridge the semantic gap between the low-level visual features and the high-level semantic concepts for an image retrieval task. Various Collaborative Image Retrieval (CIR) schemes aim to utilize the user historical feedback log data with similar and dissimilar pairwise constraints to improve the performance of a CBIR system. However, existing subspace learning approaches with explicit label information cannot be applied for a CIR task, although the subspace learning techniques play a key role in various computer vision tasks, e.g., face recognition and image classification. In this paper, we propose a novel subspace learning framework, i.e., Conjunctive Patches Subspace Learning (CPSL) with side information, for learning an effective semantic subspace by exploiting the user historical feedback log data for a CIR task. The CPSL can effectively integrate the discriminative information of labeled log images, the geometrical information of labeled log images and the weakly similar information of unlabeled images together to learn a reliable subspace. We formally formulate this problem into a constrained optimization problem and then present a new subspace learning technique to exploit the user historical feedback log data. Extensive experiments on both synthetic data sets and a real-world image database demonstrate the effectiveness of the proposed scheme in improving the performance of a CBIR system by exploiting the user historical feedback log data.

Reverse time migration by Krylov subspace reduced order modeling

NASA Astrophysics Data System (ADS)

Basir, Hadi Mahdavi; Javaherian, Abdolrahim; Shomali, Zaher Hossein; Firouz-Abadi, Roohollah Dehghani; Gholamy, Shaban Ali

2018-04-01

Imaging is a key step in seismic data processing. To date, a myriad of advanced pre-stack depth migration approaches have been developed; however, reverse time migration (RTM) is still considered as the high-end imaging algorithm. The main limitations associated with the performance cost of reverse time migration are the intensive computation of the forward and backward simulations, time consumption, and memory allocation related to imaging condition. Based on the reduced order modeling, we proposed an algorithm, which can be adapted to all the aforementioned factors. Our proposed method benefit from Krylov subspaces method to compute certain mode shapes of the velocity model computed by as an orthogonal base of reduced order modeling. Reverse time migration by reduced order modeling is helpful concerning the highly parallel computation and strongly reduces the memory requirement of reverse time migration. The synthetic model results showed that suggested method can decrease the computational costs of reverse time migration by several orders of magnitudes, compared with reverse time migration by finite element method.

Subspace in Linear Algebra: Investigating Students' Concept Images and Interactions with the Formal Definition

ERIC Educational Resources Information Center

Wawro, Megan; Sweeney, George F.; Rabin, Jeffrey M.

2011-01-01

This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling.

PubMed

Zhao, Bo; Setsompop, Kawin; Adalsteinsson, Elfar; Gagoski, Borjan; Ye, Huihui; Ma, Dan; Jiang, Yun; Ellen Grant, P; Griswold, Mark A; Wald, Lawrence L

2018-02-01

This article introduces a constrained imaging method based on low-rank and subspace modeling to improve the accuracy and speed of MR fingerprinting (MRF). A new model-based imaging method is developed for MRF to reconstruct high-quality time-series images and accurate tissue parameter maps (e.g., T 1 , T 2 , and spin density maps). Specifically, the proposed method exploits low-rank approximations of MRF time-series images, and further enforces temporal subspace constraints to capture magnetization dynamics. This allows the time-series image reconstruction problem to be formulated as a simple linear least-squares problem, which enables efficient computation. After image reconstruction, tissue parameter maps are estimated via dictionary-based pattern matching, as in the conventional approach. The effectiveness of the proposed method was evaluated with in vivo experiments. Compared with the conventional MRF reconstruction, the proposed method reconstructs time-series images with significantly reduced aliasing artifacts and noise contamination. Although the conventional approach exhibits some robustness to these corruptions, the improved time-series image reconstruction in turn provides more accurate tissue parameter maps. The improvement is pronounced especially when the acquisition time becomes short. The proposed method significantly improves the accuracy of MRF, and also reduces data acquisition time. Magn Reson Med 79:933-942, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Normal and abnormal tissue identification system and method for medical images such as digital mammograms

NASA Technical Reports Server (NTRS)

Heine, John J. (Inventor); Clarke, Laurence P. (Inventor); Deans, Stanley R. (Inventor); Stauduhar, Richard Paul (Inventor); Cullers, David Kent (Inventor)

2001-01-01

A system and method for analyzing a medical image to determine whether an abnormality is present, for example, in digital mammograms, includes the application of a wavelet expansion to a raw image to obtain subspace images of varying resolution. At least one subspace image is selected that has a resolution commensurate with a desired predetermined detection resolution range. A functional form of a probability distribution function is determined for each selected subspace image, and an optimal statistical normal image region test is determined for each selected subspace image. A threshold level for the probability distribution function is established from the optimal statistical normal image region test for each selected subspace image. A region size comprising at least one sector is defined, and an output image is created that includes a combination of all regions for each selected subspace image. Each region has a first value when the region intensity level is above the threshold and a second value when the region intensity level is below the threshold. This permits the localization of a potential abnormality within the image.

Formulating face verification with semidefinite programming.

PubMed

Yan, Shuicheng; Liu, Jianzhuang; Tang, Xiaoou; Huang, Thomas S

2007-11-01

This paper presents a unified solution to three unsolved problems existing in face verification with subspace learning techniques: selection of verification threshold, automatic determination of subspace dimension, and deducing feature fusing weights. In contrast to previous algorithms which search for the projection matrix directly, our new algorithm investigates a similarity metric matrix (SMM). With a certain verification threshold, this matrix is learned by a semidefinite programming approach, along with the constraints of the kindred pairs with similarity larger than the threshold, and inhomogeneous pairs with similarity smaller than the threshold. Then, the subspace dimension and the feature fusing weights are simultaneously inferred from the singular value decomposition of the derived SMM. In addition, the weighted and tensor extensions are proposed to further improve the algorithmic effectiveness and efficiency, respectively. Essentially, the verification is conducted within an affine subspace in this new algorithm and is, hence, called the affine subspace for verification (ASV). Extensive experiments show that the ASV can achieve encouraging face verification accuracy in comparison to other subspace algorithms, even without the need to explore any parameters.

Sparsity-aware tight frame learning with adaptive subspace recognition for multiple fault diagnosis

NASA Astrophysics Data System (ADS)

Zhang, Han; Chen, Xuefeng; Du, Zhaohui; Yang, Boyuan

2017-09-01

It is a challenging problem to design excellent dictionaries to sparsely represent diverse fault information and simultaneously discriminate different fault sources. Therefore, this paper describes and analyzes a novel multiple feature recognition framework which incorporates the tight frame learning technique with an adaptive subspace recognition strategy. The proposed framework consists of four stages. Firstly, by introducing the tight frame constraint into the popular dictionary learning model, the proposed tight frame learning model could be formulated as a nonconvex optimization problem which can be solved by alternatively implementing hard thresholding operation and singular value decomposition. Secondly, the noises are effectively eliminated through transform sparse coding techniques. Thirdly, the denoised signal is decoupled into discriminative feature subspaces by each tight frame filter. Finally, in guidance of elaborately designed fault related sensitive indexes, latent fault feature subspaces can be adaptively recognized and multiple faults are diagnosed simultaneously. Extensive numerical experiments are sequently implemented to investigate the sparsifying capability of the learned tight frame as well as its comprehensive denoising performance. Most importantly, the feasibility and superiority of the proposed framework is verified through performing multiple fault diagnosis of motor bearings. Compared with the state-of-the-art fault detection techniques, some important advantages have been observed: firstly, the proposed framework incorporates the physical prior with the data-driven strategy and naturally multiple fault feature with similar oscillation morphology can be adaptively decoupled. Secondly, the tight frame dictionary directly learned from the noisy observation can significantly promote the sparsity of fault features compared to analytical tight frames. Thirdly, a satisfactory complete signal space description property is guaranteed and thus weak feature leakage problem is avoided compared to typical learning methods.

A Subspace Approach to the Structural Decomposition and Identification of Ankle Joint Dynamic Stiffness.

PubMed

Jalaleddini, Kian; Tehrani, Ehsan Sobhani; Kearney, Robert E

2017-06-01

The purpose of this paper is to present a structural decomposition subspace (SDSS) method for decomposition of the joint torque to intrinsic, reflexive, and voluntary torques and identification of joint dynamic stiffness. First, it formulates a novel state-space representation for the joint dynamic stiffness modeled by a parallel-cascade structure with a concise parameter set that provides a direct link between the state-space representation matrices and the parallel-cascade parameters. Second, it presents a subspace method for the identification of the new state-space model that involves two steps: 1) the decomposition of the intrinsic and reflex pathways and 2) the identification of an impulse response model of the intrinsic pathway and a Hammerstein model of the reflex pathway. Extensive simulation studies demonstrate that SDSS has significant performance advantages over some other methods. Thus, SDSS was more robust under high noise conditions, converging where others failed; it was more accurate, giving estimates with lower bias and random errors. The method also worked well in practice and yielded high-quality estimates of intrinsic and reflex stiffnesses when applied to experimental data at three muscle activation levels. The simulation and experimental results demonstrate that SDSS accurately decomposes the intrinsic and reflex torques and provides accurate estimates of physiologically meaningful parameters. SDSS will be a valuable tool for studying joint stiffness under functionally important conditions. It has important clinical implications for the diagnosis, assessment, objective quantification, and monitoring of neuromuscular diseases that change the muscle tone.

Removal of nuisance signals from limited and sparse 1H MRSI data using a union-of-subspaces model.

PubMed

Ma, Chao; Lam, Fan; Johnson, Curtis L; Liang, Zhi-Pei

2016-02-01

To remove nuisance signals (e.g., water and lipid signals) for (1) H MRSI data collected from the brain with limited and/or sparse (k, t)-space coverage. A union-of-subspace model is proposed for removing nuisance signals. The model exploits the partial separability of both the nuisance signals and the metabolite signal, and decomposes an MRSI dataset into several sets of generalized voxels that share the same spectral distributions. This model enables the estimation of the nuisance signals from an MRSI dataset that has limited and/or sparse (k, t)-space coverage. The proposed method has been evaluated using in vivo MRSI data. For conventional chemical shift imaging data with limited k-space coverage, the proposed method produced "lipid-free" spectra without lipid suppression during data acquisition at 130 ms echo time. For sparse (k, t)-space data acquired with conventional pulses for water and lipid suppression, the proposed method was also able to remove the remaining water and lipid signals with negligible residuals. Nuisance signals in (1) H MRSI data reside in low-dimensional subspaces. This property can be utilized for estimation and removal of nuisance signals from (1) H MRSI data even when they have limited and/or sparse coverage of (k, t)-space. The proposed method should prove useful especially for accelerated high-resolution (1) H MRSI of the brain. © 2015 Wiley Periodicals, Inc.

Local Subspace Classifier with Transform-Invariance for Image Classification

NASA Astrophysics Data System (ADS)

Hotta, Seiji

A family of linear subspace classifiers called local subspace classifier (LSC) outperforms the k-nearest neighbor rule (kNN) and conventional subspace classifiers in handwritten digit classification. However, LSC suffers very high sensitivity to image transformations because it uses projection and the Euclidean distances for classification. In this paper, I present a combination of a local subspace classifier (LSC) and a tangent distance (TD) for improving accuracy of handwritten digit recognition. In this classification rule, we can deal with transform-invariance easily because we are able to use tangent vectors for approximation of transformations. However, we cannot use tangent vectors in other type of images such as color images. Hence, kernel LSC (KLSC) is proposed for incorporating transform-invariance into LSC via kernel mapping. The performance of the proposed methods is verified with the experiments on handwritten digit and color image classification.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reboredo, Fernando A.; Kim, Jeongnim

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspacemore » of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.« less

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

Geometric mean for subspace selection.

PubMed

Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

2009-02-01

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 Elsevier Ireland Ltd. All rights reserved.

A variable structure approach to robust control of VTOL aircraft

NASA Technical Reports Server (NTRS)

Calise, A. J.; Kramer, F.

1982-01-01

This paper examines the application of variable structure control theory to the design of a flight control system for the AV-8A Harrier in a hover mode. The objective in variable structure design is to confine the motion to a subspace of the total state space. The motion in this subspace is insensitive to system parameter variations and external disturbances that lie in the range space of the control. A switching type of control law results from the design procedure. The control system was designed to track a vector velocity command defined in the body frame. For comparison purposes, a proportional controller was designed using optimal linear regulator theory. Both control designs were first evaluated for transient response performance using a linearized model, then a nonlinear simulation study of a hovering approach to landing was conducted. Wind turbulence was modeled using a 1052 destroyer class air wake model.

Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Yang, Gang; Li, Jialin; Zhang, Dianfa

2018-01-01

A randomized subspace-based robust principal component analysis (RSRPCA) method for anomaly detection in hyperspectral imagery (HSI) is proposed. The RSRPCA combines advantages of randomized column subspace and robust principal component analysis (RPCA). It assumes that the background has low-rank properties, and the anomalies are sparse and do not lie in the column subspace of the background. First, RSRPCA implements random sampling to sketch the original HSI dataset from columns and to construct a randomized column subspace of the background. Structured random projections are also adopted to sketch the HSI dataset from rows. Sketching from columns and rows could greatly reduce the computational requirements of RSRPCA. Second, the RSRPCA adopts the columnwise RPCA (CWRPCA) to eliminate negative effects of sampled anomaly pixels and that purifies the previous randomized column subspace by removing sampled anomaly columns. The CWRPCA decomposes the submatrix of the HSI data into a low-rank matrix (i.e., background component), a noisy matrix (i.e., noise component), and a sparse anomaly matrix (i.e., anomaly component) with only a small proportion of nonzero columns. The algorithm of inexact augmented Lagrange multiplier is utilized to optimize the CWRPCA problem and estimate the sparse matrix. Nonzero columns of the sparse anomaly matrix point to sampled anomaly columns in the submatrix. Third, all the pixels are projected onto the complemental subspace of the purified randomized column subspace of the background and the anomaly pixels in the original HSI data are finally exactly located. Several experiments on three real hyperspectral images are carefully designed to investigate the detection performance of RSRPCA, and the results are compared with four state-of-the-art methods. Experimental results show that the proposed RSRPCA outperforms four comparison methods both in detection performance and in computational time.

Zeno subspace in quantum-walk dynamics

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.

2010-11-01

We investigate discrete-time quantum-walk evolution under the influence of periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace P(0,t) is compared with the survival probability after frequent (n) measurements at interval τ=t/n, P(0,τ)n. We show that P(0,τ)n>P(0,t) leads to the quantum Zeno effect in position subspace when a parameter θ in the quantum coin operations and frequency of measurements is greater than the critical value, θ>θc and n>nc. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the potential to play a significant role in quantum tasks such as preserving the quantum state of the particle at any particular position, and to understand the Zeno dynamics in a multidimensional system that is highly transient in nature.

Individualized statistical learning from medical image databases: application to identification of brain lesions.

PubMed

Erus, Guray; Zacharaki, Evangelia I; Davatzikos, Christos

2014-04-01

This paper presents a method for capturing statistical variation of normal imaging phenotypes, with emphasis on brain structure. The method aims to estimate the statistical variation of a normative set of images from healthy individuals, and identify abnormalities as deviations from normality. A direct estimation of the statistical variation of the entire volumetric image is challenged by the high-dimensionality of images relative to smaller sample sizes. To overcome this limitation, we iteratively sample a large number of lower dimensional subspaces that capture image characteristics ranging from fine and localized to coarser and more global. Within each subspace, a "target-specific" feature selection strategy is applied to further reduce the dimensionality, by considering only imaging characteristics present in a test subject's images. Marginal probability density functions of selected features are estimated through PCA models, in conjunction with an "estimability" criterion that limits the dimensionality of estimated probability densities according to available sample size and underlying anatomy variation. A test sample is iteratively projected to the subspaces of these marginals as determined by PCA models, and its trajectory delineates potential abnormalities. The method is applied to segmentation of various brain lesion types, and to simulated data on which superiority of the iterative method over straight PCA is demonstrated. Copyright © 2014 Elsevier B.V. All rights reserved.

Skin subspace color modeling for daytime and nighttime group activity recognition in confined operational spaces

NASA Astrophysics Data System (ADS)

Shirkhodaie, Amir; Poshtyar, Azin; Chan, Alex; Hu, Shuowen

2016-05-01

In many military and homeland security persistent surveillance applications, accurate detection of different skin colors in varying observability and illumination conditions is a valuable capability for video analytics. One of those applications is In-Vehicle Group Activity (IVGA) recognition, in which significant changes in observability and illumination may occur during the course of a specific human group activity of interest. Most of the existing skin color detection algorithms, however, are unable to perform satisfactorily in confined operational spaces with partial observability and occultation, as well as under diverse and changing levels of illumination intensity, reflection, and diffraction. In this paper, we investigate the salient features of ten popular color spaces for skin subspace color modeling. More specifically, we examine the advantages and disadvantages of each of these color spaces, as well as the stability and suitability of their features in differentiating skin colors under various illumination conditions. The salient features of different color subspaces are methodically discussed and graphically presented. Furthermore, we present robust and adaptive algorithms for skin color detection based on this analysis. Through examples, we demonstrate the efficiency and effectiveness of these new color skin detection algorithms and discuss their applicability for skin detection in IVGA recognition applications.

Spatially Correlated Sparse MIMO Channel Path Delay Estimation in Scattering Environments Based on Signal Subspace Tracking

PubMed Central

Chargé, Pascal; Bazzi, Oussama; Ding, Yuehua

2018-01-01

A parametric scheme for spatially correlated sparse multiple-input multiple-output (MIMO) channel path delay estimation in scattering environments is presented in this paper. In MIMO outdoor communication scenarios, channel impulse responses (CIRs) of different transmit–receive antenna pairs are often supposed to be sparse due to a few significant scatterers, and share a common sparse pattern, such that path delays are assumed to be equal for every transmit–receive antenna pair. In some existing works, an exact common support condition is exploited, where the path delays are considered equal for every transmit–receive antenna pair, meanwhile ignoring the influence of scattering. A more realistic channel model is proposed in this paper, where due to scatterers in the environment, the received signals are modeled as clusters of multi-rays around a nominal or mean time delay at different antenna elements, resulting in a non-strictly exact common support phenomenon. A method for estimating the channel mean path delays is then derived based on the subspace approach, and the tracking of the effective dimension of the signal subspace that changes due to the wireless environment. The proposed method shows an improved channel mean path delays estimation performance in comparison with the conventional estimation methods. PMID:29734797

Spatially Correlated Sparse MIMO Channel Path Delay Estimation in Scattering Environments Based on Signal Subspace Tracking.

PubMed

Mohydeen, Ali; Chargé, Pascal; Wang, Yide; Bazzi, Oussama; Ding, Yuehua

2018-05-06

A parametric scheme for spatially correlated sparse multiple-input multiple-output (MIMO) channel path delay estimation in scattering environments is presented in this paper. In MIMO outdoor communication scenarios, channel impulse responses (CIRs) of different transmit⁻receive antenna pairs are often supposed to be sparse due to a few significant scatterers, and share a common sparse pattern, such that path delays are assumed to be equal for every transmit⁻receive antenna pair. In some existing works, an exact common support condition is exploited, where the path delays are considered equal for every transmit⁻receive antenna pair, meanwhile ignoring the influence of scattering. A more realistic channel model is proposed in this paper, where due to scatterers in the environment, the received signals are modeled as clusters of multi-rays around a nominal or mean time delay at different antenna elements, resulting in a non-strictly exact common support phenomenon. A method for estimating the channel mean path delays is then derived based on the subspace approach, and the tracking of the effective dimension of the signal subspace that changes due to the wireless environment. The proposed method shows an improved channel mean path delays estimation performance in comparison with the conventional estimation methods.

Structured Kernel Subspace Learning for Autonomous Robot Navigation.

PubMed

Kim, Eunwoo; Choi, Sungjoon; Oh, Songhwai

2018-02-14

This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for predicting the motion of a pedestrian and controlling a robot to avoid incoming pedestrians, it is still difficult to safely navigate in a dynamic environment due to challenges, such as the varying quality and complexity of training data with unwanted noises. This paper addresses these challenges simultaneously by proposing a robust kernel subspace learning algorithm based on the recent advances in nuclear-norm and l 1 -norm minimization. We model the motion of a pedestrian and the robot controller using Gaussian processes. The proposed method efficiently approximates a kernel matrix used in Gaussian process regression by learning low-rank structured matrix (with symmetric positive semi-definiteness) to find an orthogonal basis, which eliminates the effects of erroneous and inconsistent data. Based on structured kernel subspace learning, we propose a robust motion model and motion controller for safe navigation in dynamic environments. We evaluate the proposed robust kernel learning in various tasks, including regression, motion prediction, and motion control problems, and demonstrate that the proposed learning-based systems are robust against outliers and outperform existing regression and navigation methods.

Individualized Statistical Learning from Medical Image Databases: Application to Identification of Brain Lesions

PubMed Central

Erus, Guray; Zacharaki, Evangelia I.; Davatzikos, Christos

2014-01-01

This paper presents a method for capturing statistical variation of normal imaging phenotypes, with emphasis on brain structure. The method aims to estimate the statistical variation of a normative set of images from healthy individuals, and identify abnormalities as deviations from normality. A direct estimation of the statistical variation of the entire volumetric image is challenged by the high-dimensionality of images relative to smaller sample sizes. To overcome this limitation, we iteratively sample a large number of lower dimensional subspaces that capture image characteristics ranging from fine and localized to coarser and more global. Within each subspace, a “target-specific” feature selection strategy is applied to further reduce the dimensionality, by considering only imaging characteristics present in a test subject’s images. Marginal probability density functions of selected features are estimated through PCA models, in conjunction with an “estimability” criterion that limits the dimensionality of estimated probability densities according to available sample size and underlying anatomy variation. A test sample is iteratively projected to the subspaces of these marginals as determined by PCA models, and its trajectory delineates potential abnormalities. The method is applied to segmentation of various brain lesion types, and to simulated data on which superiority of the iterative method over straight PCA is demonstrated. PMID:24607564

Mining subspace clusters from DNA microarray data using large itemset techniques.

PubMed

Chang, Ye-In; Chen, Jiun-Rung; Tsai, Yueh-Chi

2009-05-01

Mining subspace clusters from the DNA microarrays could help researchers identify those genes which commonly contribute to a disease, where a subspace cluster indicates a subset of genes whose expression levels are similar under a subset of conditions. Since in a DNA microarray, the number of genes is far larger than the number of conditions, those previous proposed algorithms which compute the maximum dimension sets (MDSs) for any two genes will take a long time to mine subspace clusters. In this article, we propose the Large Itemset-Based Clustering (LISC) algorithm for mining subspace clusters. Instead of constructing MDSs for any two genes, we construct only MDSs for any two conditions. Then, we transform the task of finding the maximal possible gene sets into the problem of mining large itemsets from the condition-pair MDSs. Since we are only interested in those subspace clusters with gene sets as large as possible, it is desirable to pay attention to those gene sets which have reasonable large support values in the condition-pair MDSs. From our simulation results, we show that the proposed algorithm needs shorter processing time than those previous proposed algorithms which need to construct gene-pair MDSs.

Active Subspaces of Airfoil Shape Parameterizations

NASA Astrophysics Data System (ADS)

Grey, Zachary J.; Constantine, Paul G.

2018-05-01

Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flow field with a parameterized geometry is a popular test problem for design methodologies. We examine two particular airfoil shape parameterizations, PARSEC and CST, and study the active subspaces present in two common design quantities of interest, transonic lift and drag coefficients, under each shape parameterization. We mathematically relate the two parameterizations with a common polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical airfoil properties. In particular, we obtain and interpret a two-dimensional approximation of both transonic lift and drag, and we show how these approximation inform a multi-objective design problem.

Adiabatic evolution of decoherence-free subspaces and its shortcuts

NASA Astrophysics Data System (ADS)

Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.

2017-10-01

The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.

Separation of the atmospheric variability into non-Gaussian multidimensional sources by projection pursuit techniques

NASA Astrophysics Data System (ADS)

Pires, Carlos A. L.; Ribeiro, Andreia F. S.

2017-02-01

We develop an expansion of space-distributed time series into statistically independent uncorrelated subspaces (statistical sources) of low-dimension and exhibiting enhanced non-Gaussian probability distributions with geometrically simple chosen shapes (projection pursuit rationale). The method relies upon a generalization of the principal component analysis that is optimal for Gaussian mixed signals and of the independent component analysis (ICA), optimized to split non-Gaussian scalar sources. The proposed method, supported by information theory concepts and methods, is the independent subspace analysis (ISA) that looks for multi-dimensional, intrinsically synergetic subspaces such as dyads (2D) and triads (3D), not separable by ICA. Basically, we optimize rotated variables maximizing certain nonlinear correlations (contrast functions) coming from the non-Gaussianity of the joint distribution. As a by-product, it provides nonlinear variable changes `unfolding' the subspaces into nearly Gaussian scalars of easier post-processing. Moreover, the new variables still work as nonlinear data exploratory indices of the non-Gaussian variability of the analysed climatic and geophysical fields. The method (ISA, followed by nonlinear unfolding) is tested into three datasets. The first one comes from the Lorenz'63 three-dimensional chaotic model, showing a clear separation into a non-Gaussian dyad plus an independent scalar. The second one is a mixture of propagating waves of random correlated phases in which the emergence of triadic wave resonances imprints a statistical signature in terms of a non-Gaussian non-separable triad. Finally the method is applied to the monthly variability of a high-dimensional quasi-geostrophic (QG) atmospheric model, applied to the Northern Hemispheric winter. We find that quite enhanced non-Gaussian dyads of parabolic shape, perform much better than the unrotated variables in which concerns the separation of the four model's centroid regimes (positive and negative phases of the Arctic Oscillation and of the North Atlantic Oscillation). Triads are also likely in the QG model but of weaker expression than dyads due to the imposed shape and dimension. The study emphasizes the existence of nonlinear dyadic and triadic nonlinear teleconnections.

Automated modal parameter estimation using correlation analysis and bootstrap sampling

NASA Astrophysics Data System (ADS)

Yaghoubi, Vahid; Vakilzadeh, Majid K.; Abrahamsson, Thomas J. S.

2018-02-01

The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods have been developed to automate this procedure. The common approach is to identify models with different orders and cluster similar modes together. However, most proposed methods based on this approach suffer from high-dimensional optimization problems in either the estimation or clustering step. To overcome this problem, this study presents an algorithm for autonomous modal parameter estimation in which the only required optimization is performed in a three-dimensional space. To this end, a subspace-based identification method is employed for the estimation and a non-iterative correlation-based method is used for the clustering. This clustering is at the heart of the paper. The keys to success are correlation metrics that are able to treat the problems of spatial eigenvector aliasing and nonunique eigenvectors of coalescent modes simultaneously. The algorithm commences by the identification of an excessively high-order model from frequency response function test data. The high number of modes of this model provides bases for two subspaces: one for likely physical modes of the tested system and one for its complement dubbed the subspace of noise modes. By employing the bootstrap resampling technique, several subsets are generated from the same basic dataset and for each of them a model is identified to form a set of models. Then, by correlation analysis with the two aforementioned subspaces, highly correlated modes of these models which appear repeatedly are clustered together and the noise modes are collected in a so-called Trashbox cluster. Stray noise modes attracted to the mode clusters are trimmed away in a second step by correlation analysis. The final step of the algorithm is a fuzzy c-means clustering procedure applied to a three-dimensional feature space to assign a degree of physicalness to each cluster. The proposed algorithm is applied to two case studies: one with synthetic data and one with real test data obtained from a hammer impact test. The results indicate that the algorithm successfully clusters similar modes and gives a reasonable quantification of the extent to which each cluster is physical.

Improving deep convolutional neural networks with mixed maxout units

PubMed Central

Liu, Fu-xian; Li, Long-yue

2017-01-01

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that “non-maximal features are unable to deliver” and “feature mapping subspace pooling is insufficient,” we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying different convolutional transformations over the same input and then calculating the expected values according to their exponential probabilities. Moreover, we introduce the Bernoulli distribution to balance the maximum values with the expected values of the feature mappings subspace. Finally, we design a simple model to verify the pooling ability of mixout units and a Mixout-units-based Network-in-Network (NiN) model to analyze the feature learning ability of the mixout models. We argue that our proposed units improve the pooling ability and that mixout models can achieve better feature learning and classification performance. PMID:28727737

Fast and robust reconstruction for fluorescence molecular tomography via a sparsity adaptive subspace pursuit method.

PubMed

Ye, Jinzuo; Chi, Chongwei; Xue, Zhenwen; Wu, Ping; An, Yu; Xu, Han; Zhang, Shuang; Tian, Jie

2014-02-01

Fluorescence molecular tomography (FMT), as a promising imaging modality, can three-dimensionally locate the specific tumor position in small animals. However, it remains challenging for effective and robust reconstruction of fluorescent probe distribution in animals. In this paper, we present a novel method based on sparsity adaptive subspace pursuit (SASP) for FMT reconstruction. Some innovative strategies including subspace projection, the bottom-up sparsity adaptive approach, and backtracking technique are associated with the SASP method, which guarantees the accuracy, efficiency, and robustness for FMT reconstruction. Three numerical experiments based on a mouse-mimicking heterogeneous phantom have been performed to validate the feasibility of the SASP method. The results show that the proposed SASP method can achieve satisfactory source localization with a bias less than 1mm; the efficiency of the method is much faster than mainstream reconstruction methods; and this approach is robust even under quite ill-posed condition. Furthermore, we have applied this method to an in vivo mouse model, and the results demonstrate the feasibility of the practical FMT application with the SASP method.

Multi-subject subspace alignment for non-stationary EEG-based emotion recognition.

PubMed

Chai, Xin; Wang, Qisong; Zhao, Yongping; Liu, Xin; Liu, Dan; Bai, Ou

2018-01-01

Emotion recognition based on EEG signals is a critical component in Human-Machine collaborative environments and psychiatric health diagnoses. However, EEG patterns have been found to vary across subjects due to user fatigue, different electrode placements, and varying impedances, etc. This problem renders the performance of EEG-based emotion recognition highly specific to subjects, requiring time-consuming individual calibration sessions to adapt an emotion recognition system to new subjects. Recently, domain adaptation (DA) strategies have achieved a great deal success in dealing with inter-subject adaptation. However, most of them can only adapt one subject to another subject, which limits their applicability in real-world scenarios. To alleviate this issue, a novel unsupervised DA strategy called Multi-Subject Subspace Alignment (MSSA) is proposed in this paper, which takes advantage of subspace alignment solution and multi-subject information in a unified framework to build personalized models without user-specific labeled data. Experiments on a public EEG dataset known as SEED verify the effectiveness and superiority of MSSA over other state of the art methods for dealing with multi-subject scenarios.

Manifold learning-based subspace distance for machinery damage assessment

NASA Astrophysics Data System (ADS)

Sun, Chuang; Zhang, Zhousuo; He, Zhengjia; Shen, Zhongjie; Chen, Binqiang

2016-03-01

Damage assessment is very meaningful to keep safety and reliability of machinery components, and vibration analysis is an effective way to carry out the damage assessment. In this paper, a damage index is designed by performing manifold distance analysis on vibration signal. To calculate the index, vibration signal is collected firstly, and feature extraction is carried out to obtain statistical features that can capture signal characteristics comprehensively. Then, manifold learning algorithm is utilized to decompose feature matrix to be a subspace, that is, manifold subspace. The manifold learning algorithm seeks to keep local relationship of the feature matrix, which is more meaningful for damage assessment. Finally, Grassmann distance between manifold subspaces is defined as a damage index. The Grassmann distance reflecting manifold structure is a suitable metric to measure distance between subspaces in the manifold. The defined damage index is applied to damage assessment of a rotor and the bearing, and the result validates its effectiveness for damage assessment of machinery component.

Visual exploration of high-dimensional data through subspace analysis and dynamic projections

DOE PAGES

Liu, S.; Wang, B.; Thiagarajan, J. J.; ...

2015-06-01

Here, we introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that createmore » smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Visual Exploration of High-Dimensional Data through Subspace Analysis and Dynamic Projections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, S.; Wang, B.; Thiagarajan, Jayaraman J.

2015-06-01

We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smoothmore » animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Inverse regression-based uncertainty quantification algorithms for high-dimensional models: Theory and practice

NASA Astrophysics Data System (ADS)

Li, Weixuan; Lin, Guang; Li, Bing

2016-09-01

Many uncertainty quantification (UQ) approaches suffer from the curse of dimensionality, that is, their computational costs become intractable for problems involving a large number of uncertainty parameters. In these situations, the classic Monte Carlo often remains the preferred method of choice because its convergence rate O (n - 1 / 2), where n is the required number of model simulations, does not depend on the dimension of the problem. However, many high-dimensional UQ problems are intrinsically low-dimensional, because the variation of the quantity of interest (QoI) is often caused by only a few latent parameters varying within a low-dimensional subspace, known as the sufficient dimension reduction (SDR) subspace in the statistics literature. Motivated by this observation, we propose two inverse regression-based UQ algorithms (IRUQ) for high-dimensional problems. Both algorithms use inverse regression to convert the original high-dimensional problem to a low-dimensional one, which is then efficiently solved by building a response surface for the reduced model, for example via the polynomial chaos expansion. The first algorithm, which is for the situations where an exact SDR subspace exists, is proved to converge at rate O (n-1), hence much faster than MC. The second algorithm, which doesn't require an exact SDR, employs the reduced model as a control variate to reduce the error of the MC estimate. The accuracy gain could still be significant, depending on how well the reduced model approximates the original high-dimensional one. IRUQ also provides several additional practical advantages: it is non-intrusive; it does not require computing the high-dimensional gradient of the QoI; and it reports an error bar so the user knows how reliable the result is.

Subarray Processing for Projection-based RFI Mitigation in Radio Astronomical Interferometers

NASA Astrophysics Data System (ADS)

Burnett, Mitchell C.; Jeffs, Brian D.; Black, Richard A.; Warnick, Karl F.

2018-04-01

Radio Frequency Interference (RFI) is a major problem for observations in Radio Astronomy (RA). Adaptive spatial filtering techniques such as subspace projection are promising candidates for RFI mitigation; however, for radio interferometric imaging arrays, these have primarily been used in engineering demonstration experiments rather than mainstream scientific observations. This paper considers one reason that adoption of such algorithms is limited: RFI decorrelates across the interferometric array because of long baseline lengths. This occurs when the relative RFI time delay along a baseline is large compared to the frequency channel inverse bandwidth used in the processing chain. Maximum achievable excision of the RFI is limited by covariance matrix estimation error when identifying interference subspace parameters, and decorrelation of the RFI introduces errors that corrupt the subspace estimate, rendering subspace projection ineffective over the entire array. In this work, we present an algorithm that overcomes this challenge of decorrelation by applying subspace projection via subarray processing (SP-SAP). Each subarray is designed to have a set of elements with high mutual correlation in the interferer for better estimation of subspace parameters. In an RFI simulation scenario for the proposed ngVLA interferometric imaging array with 15 kHz channel bandwidth for correlator processing, we show that compared to the former approach of applying subspace projection on the full array, SP-SAP improves mitigation of the RFI on the order of 9 dB. An example of improved image synthesis and reduced RFI artifacts for a simulated image “phantom” using the SP-SAP algorithm is presented.

Evolution of resistance to anti-cancer therapy during general dosing schedules

PubMed Central

Foo, Jasmine; Michor, Franziska

2009-01-01

Anti-cancer drugs targeted to specific oncogenic pathways have shown promising therapeutic results in the past few years; however, drug resistance remains an important obstacle for these therapies. Resistance to these drugs can emerge due to a variety of reasons including genetic or epigenetic changes which alter the binding site of the drug target, cellular metabolism or export mechanisms. Obtaining a better understanding of the evolution of resistant populations during therapy may enable the design of more effective therapeutic regimens which prevent or delay progression of disease due to resistance. In this paper, we use stochastic mathematical models to study the evolutionary dynamics of resistance under time-varying dosing schedules and pharmacokinetic effects. The populations of sensitive and resistant cells are modeled as multi-type non-homogeneous birth-death processes in which the drug concentration affects the birth and death rates of both the sensitive and resistant cell populations in continuous time. This flexible model allows us to consider the effects of generalized treatment strategies as well as detailed pharmacokinetic phenomena such as drug elimination and accumulation over multiple doses. We develop estimates for the probability of developing resistance and moments of the size of the resistant cell population. With these estimates, we optimize treatment schedules over a subspace of tolerated schedules to minimize the risk of disease progression due to resistance as well as locate ideal schedules for controlling the population size of resistant clones in situations where resistance is inevitable. Our methodology can be used to describe dynamics of resistance arising due to a single (epi)genetic alteration in any tumor type. PMID:20004211

Subspace methods for identification of human ankle joint stiffness.

PubMed

Zhao, Y; Westwick, D T; Kearney, R E

2011-11-01

Joint stiffness, the dynamic relationship between the angular position of a joint and the torque acting about it, describes the dynamic, mechanical behavior of a joint during posture and movement. Joint stiffness arises from both intrinsic and reflex mechanisms, but the torques due to these mechanisms cannot be measured separately experimentally, since they appear and change together. Therefore, the direct estimation of the intrinsic and reflex stiffnesses is difficult. In this paper, we present a new, two-step procedure to estimate the intrinsic and reflex components of ankle stiffness. In the first step, a discrete-time, subspace-based method is used to estimate a state-space model for overall stiffness from the measured overall torque and then predict the intrinsic and reflex torques. In the second step, continuous-time models for the intrinsic and reflex stiffnesses are estimated from the predicted intrinsic and reflex torques. Simulations and experimental results demonstrate that the algorithm estimates the intrinsic and reflex stiffnesses accurately. The new subspace-based algorithm has three advantages over previous algorithms: 1) It does not require iteration, and therefore, will always converge to an optimal solution; 2) it provides better estimates for data with high noise or short sample lengths; and 3) it provides much more accurate results for data acquired under the closed-loop conditions, that prevail when subjects interact with compliant loads.

Identifying Optimal Measurement Subspace for the Ensemble Kalman Filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ning; Huang, Zhenyu; Welch, Greg

2012-05-24

To reduce the computational load of the ensemble Kalman filter while maintaining its efficacy, an optimization algorithm based on the generalized eigenvalue decomposition method is proposed for identifying the most informative measurement subspace. When the number of measurements is large, the proposed algorithm can be used to make an effective tradeoff between computational complexity and estimation accuracy. This algorithm also can be extended to other Kalman filters for measurement subspace selection.

Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value Decomposition (SVD)

DTIC Science & Technology

2017-09-27

ARL-TR-8161•SEP 2017 US Army Research Laboratory Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value...originator. ARL-TR-8161•SEP 2017 US Army Research Laboratory Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value...unlimited. October 2015–January 2016 US Army Research Laboratory ATTN: RDRL-CIH-C Aberdeen Proving Ground, MD 21005-5066 primary author’s email

Position, Location, Place and Area: AN Indoor Perspective

NASA Astrophysics Data System (ADS)

Sithole, George; Zlatanova, Sisi

2016-06-01

Over the last decade, harnessing the commercial potential of smart mobile devices in indoor environments has spurred interest in indoor mapping and navigation. Users experience indoor environments differently. For this reason navigational models have to be designed to adapt to a user's personality, and to reflect as many cognitive maps as possible. This paper presents an extension of a previously proposed framework. In this extension the notion of placement is accounted for, thereby enabling one aspect of the `personalised indoor experience'. In the paper, firstly referential expressions are used as a tool to discuss the different ways of thinking of placement within indoor spaces. Next, placement is expressed in terms of the concept of Position, Location, Place and Area. Finally, the previously proposed framework is extended to include these concepts of placement. An example is provided of the use of the extended framework. Notable characteristics of the framework are: (1) Sub-spaces, resources and agents can simultaneously possess different types of placement, e.g., a person in a room can have an xyz position and a location defined by the room number. While these entities can simultaneously have different forms of placement, only one is dominant. (2) Sub-spaces, resources and agents are capable of possessing modifiers that alter their access and usage. (3) Sub-spaces inherit the modifiers of the resources or agents contained in them. (4) Unlike conventional navigational models which treat resources and obstacles as different types of entities, in the proposed framework there are only resources and whether a resource is an obstacle is determined by a modifier that determines whether a user can access the resource. The power of the framework is that it blends the geometry and topology of space, the influence of human activity within sub-spaces together with the different notions of placement in a way that is simple and yet very flexible.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining.

PubMed

Cheng, Wenlong; Zhao, Mingbo; Xiong, Naixue; Chui, Kwok Tai

2017-07-15

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l ₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating l p -norm and Schatten p -norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions

USGS Publications Warehouse

Friedly, John C.; Rubin, Jacob

1992-01-01

A new approach is applied to the problem of modeling solute transport accompanied by many chemical reactions. The approach, based on concepts of the concentration space and its stoichiometric subspaces, uses elements of the subspaces as primary dependent variables. It is shown that the resulting model equations are compact in form, isolate the chemical reaction expressions from flow expressions, and can be used for either equilibrium or kinetically controlled reactions. The implications of the results on numerical algorithms for solving the equations are discussed. The application of the theory is illustrated throughout with examples involving a simple but broadly representative set of reactions previously considered in the literature. Numerical results are presented for four interconnected reactions: a homogeneous complexation reaction, two sorption reactions, and a dissolution/precipitation reaction. Three cases are considered: (1) four kinetically controlled reactions, (2) four equilibrium-controlled reactions, and (3) a system with two kinetically controlled reactions and two equilibrium-controlled reactions.

Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.

PubMed

Sun, Yanfeng; Gao, Junbin; Hong, Xia; Mishra, Bamdev; Yin, Baocai

2016-03-01

Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.

An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems

NASA Astrophysics Data System (ADS)

Nigro, P. S. B.; Anndif, M.; Teixeira, Y.; Pimenta, P. M.; Wriggers, P.

2016-04-01

Model Order Reduction (MOR) methods are employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).

Subspace Methods for Massive and Messy Data

DTIC Science & Technology

2017-07-12

Subspace Methods for Massive and Messy Data The views, opinions and/or findings contained in this report are those of the author(s) and should not...AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 REPORT DOCUMENTATION PAGE 11. SPONSOR...Number: W911NF-14-1-0634 Organization: University of Michigan - Ann Arbor Title: Subspace Methods for Massive and Messy Data Report Term: 0-Other

Geometry aware Stationary Subspace Analysis

DTIC Science & Technology

2016-11-22

approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain computer interface ( BCI ...context of brain computer interface ( BCI ) data analysis, two such note-worthy methods are stationary subspace analysis (SSA) (von Bünau et al., 2009a... BCI systems, is sCSP. Its goal is to project the data onto a subspace in which the various data classes are more separable. The sCSP method directs

Locally indistinguishable subspaces spanned by three-qubit unextendible product bases

NASA Astrophysics Data System (ADS)

Duan, Runyao; Xin, Yu; Ying, Mingsheng

2010-03-01

We study the local distinguishability of general multiqubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that the local distinguishability of multiqubit states can be decided efficiently. Another useful consequence is that a set of orthogonal n-qubit states is locally distinguishable only if the summation of their orthogonal Schmidt numbers is less than the total dimension 2n. Employing these results, we show that any orthonormal basis of a subspace spanned by arbitrary three-qubit orthogonal unextendible product bases (UPB) cannot be exactly distinguishable by local operations and classical communication. This not only reveals another intrinsic property of three-qubit orthogonal UPB but also provides a class of locally indistinguishable subspaces with dimension 4. We also explicitly construct locally indistinguishable subspaces with dimensions 3 and 5, respectively. Similar to the bipartite case, these results on multipartite locally indistinguishable subspaces can be used to estimate the one-shot environment-assisted classical capacity of a class of quantum broadcast channels.

Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods

NASA Technical Reports Server (NTRS)

Sidi, Avram

1992-01-01

Let F(z) be a vectored-valued function F: C approaches C sup N, which is analytic at z=0 and meromorphic in a neighborhood of z=0, and let its Maclaurin series be given. We use vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series in conjunction with power iterations to develop bona fide generalizations of the power method for an arbitrary N X N matrix that may be diagonalizable or not. These generalizations can be used to obtain simultaneously several of the largest distinct eigenvalues and the corresponding invariant subspaces, and present a detailed convergence theory for them. In addition, it is shown that the generalized power methods of this work are equivalent to some Krylov subspace methods, among them the methods of Arnoldi and Lanczos. Thus, the theory provides a set of completely new results and constructions for these Krylov subspace methods. This theory suggests at the same time a new mode of usage for these Krylov subspace methods that were observed to possess computational advantages over their common mode of usage.

Sparse subspace clustering for data with missing entries and high-rank matrix completion.

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Systematic Constraint Selection Strategy for Rate-Controlled Constrained-Equilibrium Modeling of Complex Nonequilibrium Chemical Kinetics

NASA Astrophysics Data System (ADS)

Beretta, Gian Paolo; Rivadossi, Luca; Janbozorgi, Mohammad

2018-04-01

Rate-Controlled Constrained-Equilibrium (RCCE) modeling of complex chemical kinetics provides acceptable accuracies with much fewer differential equations than for the fully Detailed Kinetic Model (DKM). Since its introduction by James C. Keck, a drawback of the RCCE scheme has been the absence of an automatable, systematic procedure to identify the constraints that most effectively warrant a desired level of approximation for a given range of initial, boundary, and thermodynamic conditions. An optimal constraint identification has been recently proposed. Given a DKM with S species, E elements, and R reactions, the procedure starts by running a probe DKM simulation to compute an S-vector that we call overall degree of disequilibrium (ODoD) because its scalar product with the S-vector formed by the stoichiometric coefficients of any reaction yields its degree of disequilibrium (DoD). The ODoD vector evolves in the same (S-E)-dimensional stoichiometric subspace spanned by the R stoichiometric S-vectors. Next we construct the rank-(S-E) matrix of ODoD traces obtained from the probe DKM numerical simulation and compute its singular value decomposition (SVD). By retaining only the first C largest singular values of the SVD and setting to zero all the others we obtain the best rank-C approximation of the matrix of ODoD traces whereby its columns span a C-dimensional subspace of the stoichiometric subspace. This in turn yields the best approximation of the evolution of the ODoD vector in terms of only C parameters that we call the constraint potentials. The resulting order-C RCCE approximate model reduces the number of independent differential equations related to species, mass, and energy balances from S+2 to C+E+2, with substantial computational savings when C ≪ S-E.

Dissatisfaction of Compact Picard Condition (CPC) with GRACE satellite data and its treatment by Generalized Tikhonov in Sobolev subspace

NASA Astrophysics Data System (ADS)

AllahTavakoli, Y.; Bagheri, H.; Safari, A.; Sharifi, M.

2012-04-01

This paper is mainly aiming to prove that the stripy noises in the map of earth's surface mass-density changes derived from GRACE Satellites gravimetry, is due to a dissatisfaction of Compact Picard Condition (CPC) with the GRACE data in the inversion of the Newton Integral Equation over the thin layer of earth; and hence the paper proposes the regularization strategies as efficient tools to treat the Ill-posedness and consequently to de-strip the data. First of all, we preferred to slightly modify the mathematical model of earth's surface mass-density changes developed creatively first by J. Wahr and et.al (1998), according to the all their previous assumptions plus taking into consideration the effect of the earth topography. By the modification we expect that some uncertainties in the prior model have been reduced to some extent. Then we analyzed the CPC on the model and we demonstrated how to perform Generalized Tikhonov regularization in Sobolev subspace for overcoming the instability of the problem. Then we applied the strategy in some simulations and case studies to validate our ideas. The simulations confirm that the stripy noises in the GRACE-derived map of the mass-density changes are due to the CPC dissatisfaction and furthermore the case studies show that Generalized Tikhonov regularization in Sobolev subspace is an influential filtering tool to de-strip the noisy data. Also, the case studies interestingly show that the effect of the topography is comparable to the effect of the load Love numbers on the Wahr's model; hence it may be taken into consideration when the load Love numbers have been taken into account.

Observation of entanglement witnesses for orbital angular momentum states

NASA Astrophysics Data System (ADS)

Agnew, M.; Leach, J.; Boyd, R. W.

2012-06-01

Entanglement witnesses provide an efficient means of determining the level of entanglement of a system using the minimum number of measurements. Here we demonstrate the observation of two-dimensional entanglement witnesses in the high-dimensional basis of orbital angular momentum (OAM). In this case, the number of potentially entangled subspaces scales as d(d - 1)/2, where d is the dimension of the space. The choice of OAM as a basis is relevant as each subspace is not necessarily maximally entangled, thus providing the necessary state for certain tests of nonlocality. The expectation value of the witness gives an estimate of the state of each two-dimensional subspace belonging to the d-dimensional Hilbert space. These measurements demonstrate the degree of entanglement and therefore the suitability of the resulting subspaces for quantum information applications.

Recovering task fMRI signals from highly under-sampled data with low-rank and temporal subspace constraints.

PubMed

Chiew, Mark; Graedel, Nadine N; Miller, Karla L

2018-07-01

Recent developments in highly accelerated fMRI data acquisition have employed low-rank and/or sparsity constraints for image reconstruction, as an alternative to conventional, time-independent parallel imaging. When under-sampling factors are high or the signals of interest are low-variance, however, functional data recovery can be poor or incomplete. We introduce a method for improving reconstruction fidelity using external constraints, like an experimental design matrix, to partially orient the estimated fMRI temporal subspace. Combining these external constraints with low-rank constraints introduces a new image reconstruction model that is analogous to using a mixture of subspace-decomposition (PCA/ICA) and regression (GLM) models in fMRI analysis. We show that this approach improves fMRI reconstruction quality in simulations and experimental data, focusing on the model problem of detecting subtle 1-s latency shifts between brain regions in a block-design task-fMRI experiment. Successful latency discrimination is shown at acceleration factors up to R = 16 in a radial-Cartesian acquisition. We show that this approach works with approximate, or not perfectly informative constraints, where the derived benefit is commensurate with the information content contained in the constraints. The proposed method extends low-rank approximation methods for under-sampled fMRI data acquisition by leveraging knowledge of expected task-based variance in the data, enabling improvements in the speed and efficiency of fMRI data acquisition without the loss of subtle features. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

A Robust Sound Source Localization Approach for Microphone Array with Model Errors

NASA Astrophysics Data System (ADS)

Xiao, Hua; Shao, Huai-Zong; Peng, Qi-Cong

In this paper, a robust sound source localization approach is proposed. The approach retains good performance even when model errors exist. Compared with previous work in this field, the contributions of this paper are as follows. First, an improved broad-band and near-field array model is proposed. It takes array gain, phase perturbations into account and is based on the actual positions of the elements. It can be used in arbitrary planar geometry arrays. Second, a subspace model errors estimation algorithm and a Weighted 2-Dimension Multiple Signal Classification (W2D-MUSIC) algorithm are proposed. The subspace model errors estimation algorithm estimates unknown parameters of the array model, i. e., gain, phase perturbations, and positions of the elements, with high accuracy. The performance of this algorithm is improved with the increasing of SNR or number of snapshots. The W2D-MUSIC algorithm based on the improved array model is implemented to locate sound sources. These two algorithms compose the robust sound source approach. The more accurate steering vectors can be provided for further processing such as adaptive beamforming algorithm. Numerical examples confirm effectiveness of this proposed approach.

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

PubMed

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

NASA Technical Reports Server (NTRS)

Gupta, V. K.; Zillmer, S. D.; Allison, R. E.

1986-01-01

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

Integrating motion, illumination, and structure in video sequences with applications in illumination-invariant tracking.

PubMed

Xu, Yilei; Roy-Chowdhury, Amit K

2007-05-01

In this paper, we present a theory for combining the effects of motion, illumination, 3D structure, albedo, and camera parameters in a sequence of images obtained by a perspective camera. We show that the set of all Lambertian reflectance functions of a moving object, at any position, illuminated by arbitrarily distant light sources, lies "close" to a bilinear subspace consisting of nine illumination variables and six motion variables. This result implies that, given an arbitrary video sequence, it is possible to recover the 3D structure, motion, and illumination conditions simultaneously using the bilinear subspace formulation. The derivation builds upon existing work on linear subspace representations of reflectance by generalizing it to moving objects. Lighting can change slowly or suddenly, locally or globally, and can originate from a combination of point and extended sources. We experimentally compare the results of our theory with ground truth data and also provide results on real data by using video sequences of a 3D face and the entire human body with various combinations of motion and illumination directions. We also show results of our theory in estimating 3D motion and illumination model parameters from a video sequence.

Reweighted mass center based object-oriented sparse subspace clustering for hyperspectral images

NASA Astrophysics Data System (ADS)

Zhai, Han; Zhang, Hongyan; Zhang, Liangpei; Li, Pingxiang

2016-10-01

Considering the inevitable obstacles faced by the pixel-based clustering methods, such as salt-and-pepper noise, high computational complexity, and the lack of spatial information, a reweighted mass center based object-oriented sparse subspace clustering (RMC-OOSSC) algorithm for hyperspectral images (HSIs) is proposed. First, the mean-shift segmentation method is utilized to oversegment the HSI to obtain meaningful objects. Second, a distance reweighted mass center learning model is presented to extract the representative and discriminative features for each object. Third, assuming that all the objects are sampled from a union of subspaces, it is natural to apply the SSC algorithm to the HSI. Faced with the high correlation among the hyperspectral objects, a weighting scheme is adopted to ensure that the highly correlated objects are preferred in the procedure of sparse representation, to reduce the representation errors. Two widely used hyperspectral datasets were utilized to test the performance of the proposed RMC-OOSSC algorithm, obtaining high clustering accuracies (overall accuracy) of 71.98% and 89.57%, respectively. The experimental results show that the proposed method clearly improves the clustering performance with respect to the other state-of-the-art clustering methods, and it significantly reduces the computational time.

Entanglement dynamics of coupled qubits and a semi-decoherence free subspace

NASA Astrophysics Data System (ADS)

Campagnano, Gabriele; Hamma, Alioscia; Weiss, Ulrich

2010-01-01

We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the cases of (I) two independent bosonic baths and (II) one common bath. We find that in the case (II) the existence of a decoherence-free subspace (DFS) makes entanglement dynamics very rich. We show that when the system is initially in a state with a component in the DFS the relaxation time is surprisingly long, showing the existence of semi-decoherence free subspaces.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

NASA Astrophysics Data System (ADS)

Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

2014-09-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

Optimal design of focused experiments and surveys

NASA Astrophysics Data System (ADS)

Curtis, Andrew

1999-10-01

Experiments and surveys are often performed to obtain data that constrain some previously underconstrained model. Often, constraints are most desired in a particular subspace of model space. Experiment design optimization requires that the quality of any particular design can be both quantified and then maximized. This study shows how the quality can be defined such that it depends on the amount of information that is focused in the particular subspace of interest. In addition, algorithms are presented which allow one particular focused quality measure (from the class of focused measures) to be evaluated efficiently. A subclass of focused quality measures is also related to the standard variance and resolution measures from linearized inverse theory. The theory presented here requires that the relationship between model parameters and data can be linearized around a reference model without significant loss of information. Physical and financial constraints define the space of possible experiment designs. Cross-well tomographic examples are presented, plus a strategy for survey design to maximize information about linear combinations of parameters such as bulk modulus, κ =λ+ 2μ/3.

Unification theory of optimal life histories and linear demographic models in internal stochasticity.

PubMed

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.

Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

PubMed Central

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258

Stochastic Lanchester Air-to-Air Campaign Model: Model Description and Users Guides

DTIC Science & Technology

2009-01-01

STOCHASTIC LANCHESTER AIR-TO-AIR CAMPAIGN MODEL MODEL DESCRIPTION AND USERS GUIDES—2009 REPORT PA702T1 Rober t V. Hemm Jr. Dav id A . Lee...LMI © 2009. ALL RIGHTS RESERVED. Stochastic Lanchester Air-to-Air Campaign Model: Model Description and Users Guides—2009 PA702T1/JANUARY...2009 Executive Summary This report documents the latest version of the Stochastic Lanchester Air-to-Air Campaign Model (SLAACM), developed by LMI for

Stochastic Multi-Timescale Power System Operations With Variable Wind Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Hongyu; Krad, Ibrahim; Florita, Anthony

This paper describes a novel set of stochastic unit commitment and economic dispatch models that consider stochastic loads and variable generation at multiple operational timescales. The stochastic model includes four distinct stages: stochastic day-ahead security-constrained unit commitment (SCUC), stochastic real-time SCUC, stochastic real-time security-constrained economic dispatch (SCED), and deterministic automatic generation control (AGC). These sub-models are integrated together such that they are continually updated with decisions passed from one to another. The progressive hedging algorithm (PHA) is applied to solve the stochastic models to maintain the computational tractability of the proposed models. Comparative case studies with deterministic approaches are conductedmore » in low wind and high wind penetration scenarios to highlight the advantages of the proposed methodology, one with perfect forecasts and the other with current state-of-the-art but imperfect deterministic forecasts. The effectiveness of the proposed method is evaluated with sensitivity tests using both economic and reliability metrics to provide a broader view of its impact.« less

Multiclassifier information fusion methods for microarray pattern recognition

NASA Astrophysics Data System (ADS)

Braun, Jerome J.; Glina, Yan; Judson, Nicholas; Herzig-Marx, Rachel

2004-04-01

This paper addresses automatic recognition of microarray patterns, a capability that could have a major significance for medical diagnostics, enabling development of diagnostic tools for automatic discrimination of specific diseases. The paper presents multiclassifier information fusion methods for microarray pattern recognition. The input space partitioning approach based on fitness measures that constitute an a-priori gauging of classification efficacy for each subspace is investigated. Methods for generation of fitness measures, generation of input subspaces and their use in the multiclassifier fusion architecture are presented. In particular, two-level quantification of fitness that accounts for the quality of each subspace as well as the quality of individual neighborhoods within the subspace is described. Individual-subspace classifiers are Support Vector Machine based. The decision fusion stage fuses the information from mulitple SVMs along with the multi-level fitness information. Final decision fusion stage techniques, including weighted fusion as well as Dempster-Shafer theory based fusion are investigated. It should be noted that while the above methods are discussed in the context of microarray pattern recognition, they are applicable to a broader range of discrimination problems, in particular to problems involving a large number of information sources irreducible to a low-dimensional feature space.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors.

PubMed

El-Diasty, Mohammed; Pagiatakis, Spiros

2009-01-01

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

Stochastic effects in a seasonally forced epidemic model

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.

2010-10-01

The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Extended Krylov subspaces approximations of matrix functions. Application to computational electromagnetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Druskin, V.; Lee, Ping; Knizhnerman, L.

There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

NASA Astrophysics Data System (ADS)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.

Agent based reasoning for the non-linear stochastic models of long-range memory

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Gontis, V.

2012-02-01

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

The Role of High-Dimensional Diffusive Search, Stabilization, and Frustration in Protein Folding

PubMed Central

Rimratchada, Supreecha; McLeish, Tom C.B.; Radford, Sheena E.; Paci, Emanuele

2014-01-01

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold. PMID:24739172

Margin-Wide Earthquake Subspace Scanning Along the Cascadia Subduction Zone Using the Cascadia Initiative Amphibious Dataset

NASA Astrophysics Data System (ADS)

Morton, E.; Bilek, S. L.; Rowe, C. A.

2017-12-01

Understanding the spatial extent and behavior of the interplate contact in the Cascadia Subduction Zone (CSZ) may prove pivotal to preparation for future great earthquakes, such as the M9 event of 1700. Current and historic seismic catalogs are limited in their integrity by their short duration, given the recurrence rate of great earthquakes, and by their rather high magnitude of completeness for the interplate seismic zone, due to its offshore distance from these land-based networks. This issue is addressed via the 2011-2015 Cascadia Initiative (CI) amphibious seismic array deployment, which combined coastal land seismometers with more than 60 ocean-bottom seismometers (OBS) situated directly above the presumed plate interface. We search the CI dataset for small, previously undetected interplate earthquakes to identify seismic patches on the megathrust. Using the automated subspace detection method, we search for previously undetected events. Our subspace comprises eigenvectors derived from CI OBS and on-land waveforms extracted for existing catalog events that appear to have occurred on the plate interface. Previous work focused on analysis of two repeating event clusters off the coast of Oregon spanning all 4 years of deployment. Here we expand earlier results to include detection and location analysis to the entire CSZ margin during the first year of CI deployment, with more than 200 new events detected for the central portion of the margin. Template events used for subspace scanning primarily occurred beneath the land surface along the coast, at the downdip edge of modeled high slip patches for the 1700 event, with most concentrated at the northwestern edge of the Olympic Peninsula.

Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment II.

PubMed

Liu, Meng; Wang, Ke

2010-12-07

This is a continuation of our paper [Liu, M., Wang, K., 2010. Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment, J. Theor. Biol. 264, 934-944]. Taking both white noise and colored noise into account, a stochastic single-species model under regime switching in a polluted environment is studied. Sufficient conditions for extinction, stochastic nonpersistence in the mean, stochastic weak persistence and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is obtained. The results show that a different type of noise has a different effect on the survival results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spill, Fabian, E-mail: fspill@bu.edu; Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139; Guerrero, Pilar

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and smallmore » in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.« less

Diagnostic tools for mixing models of stream water chemistry

USGS Publications Warehouse

Hooper, Richard P.

2003-01-01

Mixing models provide a useful null hypothesis against which to evaluate processes controlling stream water chemical data. Because conservative mixing of end‐members with constant concentration is a linear process, a number of simple mathematical and multivariate statistical methods can be applied to this problem. Although mixing models have been most typically used in the context of mixing soil and groundwater end‐members, an extension of the mathematics of mixing models is presented that assesses the “fit” of a multivariate data set to a lower dimensional mixing subspace without the need for explicitly identified end‐members. Diagnostic tools are developed to determine the approximate rank of the data set and to assess lack of fit of the data. This permits identification of processes that violate the assumptions of the mixing model and can suggest the dominant processes controlling stream water chemical variation. These same diagnostic tools can be used to assess the fit of the chemistry of one site into the mixing subspace of a different site, thereby permitting an assessment of the consistency of controlling end‐members across sites. This technique is applied to a number of sites at the Panola Mountain Research Watershed located near Atlanta, Georgia.

Scalable Methods for Uncertainty Quantification, Data Assimilation and Target Accuracy Assessment for Multi-Physics Advanced Simulation of Light Water Reactors

NASA Astrophysics Data System (ADS)

Khuwaileh, Bassam

High fidelity simulation of nuclear reactors entails large scale applications characterized with high dimensionality and tremendous complexity where various physics models are integrated in the form of coupled models (e.g. neutronic with thermal-hydraulic feedback). Each of the coupled modules represents a high fidelity formulation of the first principles governing the physics of interest. Therefore, new developments in high fidelity multi-physics simulation and the corresponding sensitivity/uncertainty quantification analysis are paramount to the development and competitiveness of reactors achieved through enhanced understanding of the design and safety margins. Accordingly, this dissertation introduces efficient and scalable algorithms for performing efficient Uncertainty Quantification (UQ), Data Assimilation (DA) and Target Accuracy Assessment (TAA) for large scale, multi-physics reactor design and safety problems. This dissertation builds upon previous efforts for adaptive core simulation and reduced order modeling algorithms and extends these efforts towards coupled multi-physics models with feedback. The core idea is to recast the reactor physics analysis in terms of reduced order models. This can be achieved via identifying the important/influential degrees of freedom (DoF) via the subspace analysis, such that the required analysis can be recast by considering the important DoF only. In this dissertation, efficient algorithms for lower dimensional subspace construction have been developed for single physics and multi-physics applications with feedback. Then the reduced subspace is used to solve realistic, large scale forward (UQ) and inverse problems (DA and TAA). Once the elite set of DoF is determined, the uncertainty/sensitivity/target accuracy assessment and data assimilation analysis can be performed accurately and efficiently for large scale, high dimensional multi-physics nuclear engineering applications. Hence, in this work a Karhunen-Loeve (KL) based algorithm previously developed to quantify the uncertainty for single physics models is extended for large scale multi-physics coupled problems with feedback effect. Moreover, a non-linear surrogate based UQ approach is developed, used and compared to performance of the KL approach and brute force Monte Carlo (MC) approach. On the other hand, an efficient Data Assimilation (DA) algorithm is developed to assess information about model's parameters: nuclear data cross-sections and thermal-hydraulics parameters. Two improvements are introduced in order to perform DA on the high dimensional problems. First, a goal-oriented surrogate model can be used to replace the original models in the depletion sequence (MPACT -- COBRA-TF - ORIGEN). Second, approximating the complex and high dimensional solution space with a lower dimensional subspace makes the sampling process necessary for DA possible for high dimensional problems. Moreover, safety analysis and design optimization depend on the accurate prediction of various reactor attributes. Predictions can be enhanced by reducing the uncertainty associated with the attributes of interest. Accordingly, an inverse problem can be defined and solved to assess the contributions from sources of uncertainty; and experimental effort can be subsequently directed to further improve the uncertainty associated with these sources. In this dissertation a subspace-based gradient-free and nonlinear algorithm for inverse uncertainty quantification namely the Target Accuracy Assessment (TAA) has been developed and tested. The ideas proposed in this dissertation were first validated using lattice physics applications simulated using SCALE6.1 package (Pressurized Water Reactor (PWR) and Boiling Water Reactor (BWR) lattice models). Ultimately, the algorithms proposed her were applied to perform UQ and DA for assembly level (CASL progression problem number 6) and core wide problems representing Watts Bar Nuclear 1 (WBN1) for cycle 1 of depletion (CASL Progression Problem Number 9) modeled via simulated using VERA-CS which consists of several multi-physics coupled models. The analysis and algorithms developed in this dissertation were encoded and implemented in a newly developed tool kit algorithms for Reduced Order Modeling based Uncertainty/Sensitivity Estimator (ROMUSE).

Detecting coupled collective motions in protein by independent subspace analysis

NASA Astrophysics Data System (ADS)

Sakuraba, Shun; Joti, Yasumasa; Kitao, Akio

2010-11-01

Protein dynamics evolves in a high-dimensional space, comprising aharmonic, strongly correlated motional modes. Such correlation often plays an important role in analyzing protein function. In order to identify significantly correlated collective motions, here we employ independent subspace analysis based on the subspace joint approximate diagonalization of eigenmatrices algorithm for the analysis of molecular dynamics (MD) simulation trajectories. From the 100 ns MD simulation of T4 lysozyme, we extract several independent subspaces in each of which collective modes are significantly correlated, and identify the other modes as independent. This method successfully detects the modes along which long-tailed non-Gaussian probability distributions are obtained. Based on the time cross-correlation analysis, we identified a series of events among domain motions and more localized motions in the protein, indicating the connection between the functionally relevant phenomena which have been independently revealed by experiments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mosher, J.C.; Leahy, R.M.

A new method for source localization is described that is based on a modification of the well known multiple signal classification (MUSIC) algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace, but errors in the estimate can make location of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix, and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection is then performed in this reduced subspace. Using the metric of principal angles,more » the authors describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation, the authors demonstrate the improved Monte Carlo performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods, S and IES-MUSIC.« less

Independence and totalness of subspaces in phase space methods

NASA Astrophysics Data System (ADS)

Vourdas, A.

2018-04-01

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

Modelling the cancer growth process by Stochastic Differential Equations with the effect of Chondroitin Sulfate (CS) as anticancer therapeutics

NASA Astrophysics Data System (ADS)

Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina

2017-09-01

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

Spatial prediction of landslides using a hybrid machine learning approach based on Random Subspace and Classification and Regression Trees

NASA Astrophysics Data System (ADS)

Pham, Binh Thai; Prakash, Indra; Tien Bui, Dieu

2018-02-01

A hybrid machine learning approach of Random Subspace (RSS) and Classification And Regression Trees (CART) is proposed to develop a model named RSSCART for spatial prediction of landslides. This model is a combination of the RSS method which is known as an efficient ensemble technique and the CART which is a state of the art classifier. The Luc Yen district of Yen Bai province, a prominent landslide prone area of Viet Nam, was selected for the model development. Performance of the RSSCART model was evaluated through the Receiver Operating Characteristic (ROC) curve, statistical analysis methods, and the Chi Square test. Results were compared with other benchmark landslide models namely Support Vector Machines (SVM), single CART, Naïve Bayes Trees (NBT), and Logistic Regression (LR). In the development of model, ten important landslide affecting factors related with geomorphology, geology and geo-environment were considered namely slope angles, elevation, slope aspect, curvature, lithology, distance to faults, distance to rivers, distance to roads, and rainfall. Performance of the RSSCART model (AUC = 0.841) is the best compared with other popular landslide models namely SVM (0.835), single CART (0.822), NBT (0.821), and LR (0.723). These results indicate that performance of the RSSCART is a promising method for spatial landslide prediction.

Forward and backward uncertainty propagation: an oxidation ditch modelling example.

PubMed

Abusam, A; Keesman, K J; van Straten, G

2003-01-01

In the field of water technology, forward uncertainty propagation is frequently used, whereas backward uncertainty propagation is rarely used. In forward uncertainty analysis, one moves from a given (or assumed) parameter subspace towards the corresponding distribution of the output or objective function. However, in the backward uncertainty propagation, one moves in the reverse direction, from the distribution function towards the parameter subspace. Backward uncertainty propagation, which is a generalisation of parameter estimation error analysis, gives information essential for designing experimental or monitoring programmes, and for tighter bounding of parameter uncertainty intervals. The procedure of carrying out backward uncertainty propagation is illustrated in this technical note by working example for an oxidation ditch wastewater treatment plant. Results obtained have demonstrated that essential information can be achieved by carrying out backward uncertainty propagation analysis.

Time series analysis of collective motions in proteins

NASA Astrophysics Data System (ADS)

Alakent, Burak; Doruker, Pemra; ćamurdan, Mehmet C.

2004-01-01

The dynamics of α-amylase inhibitor tendamistat around its native state is investigated using time series analysis of the principal components of the Cα atomic displacements obtained from molecular dynamics trajectories. Collective motion along a principal component is modeled as a homogeneous nonstationary process, which is the result of the damped oscillations in local minima superimposed on a random walk. The motion in local minima is described by a stationary autoregressive moving average model, consisting of the frequency, damping factor, moving average parameters and random shock terms. Frequencies for the first 50 principal components are found to be in the 3-25 cm-1 range, which are well correlated with the principal component indices and also with atomistic normal mode analysis results. Damping factors, though their correlation is less pronounced, decrease as principal component indices increase, indicating that low frequency motions are less affected by friction. The existence of a positive moving average parameter indicates that the stochastic force term is likely to disturb the mode in opposite directions for two successive sampling times, showing the modes tendency to stay close to minimum. All these four parameters affect the mean square fluctuations of a principal mode within a single minimum. The inter-minima transitions are described by a random walk model, which is driven by a random shock term considerably smaller than that for the intra-minimum motion. The principal modes are classified into three subspaces based on their dynamics: essential, semiconstrained, and constrained, at least in partial consistency with previous studies. The Gaussian-type distributions of the intermediate modes, called "semiconstrained" modes, are explained by asserting that this random walk behavior is not completely free but between energy barriers.

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.

LRSSLMDA: Laplacian Regularized Sparse Subspace Learning for MiRNA-Disease Association prediction

PubMed Central

Huang, Li

2017-01-01

Predicting novel microRNA (miRNA)-disease associations is clinically significant due to miRNAs’ potential roles of diagnostic biomarkers and therapeutic targets for various human diseases. Previous studies have demonstrated the viability of utilizing different types of biological data to computationally infer new disease-related miRNAs. Yet researchers face the challenge of how to effectively integrate diverse datasets and make reliable predictions. In this study, we presented a computational model named Laplacian Regularized Sparse Subspace Learning for MiRNA-Disease Association prediction (LRSSLMDA), which projected miRNAs/diseases’ statistical feature profile and graph theoretical feature profile to a common subspace. It used Laplacian regularization to preserve the local structures of the training data and a L1-norm constraint to select important miRNA/disease features for prediction. The strength of dimensionality reduction enabled the model to be easily extended to much higher dimensional datasets than those exploited in this study. Experimental results showed that LRSSLMDA outperformed ten previous models: the AUC of 0.9178 in global leave-one-out cross validation (LOOCV) and the AUC of 0.8418 in local LOOCV indicated the model’s superior prediction accuracy; and the average AUC of 0.9181+/-0.0004 in 5-fold cross validation justified its accuracy and stability. In addition, three types of case studies further demonstrated its predictive power. Potential miRNAs related to Colon Neoplasms, Lymphoma, Kidney Neoplasms, Esophageal Neoplasms and Breast Neoplasms were predicted by LRSSLMDA. Respectively, 98%, 88%, 96%, 98% and 98% out of the top 50 predictions were validated by experimental evidences. Therefore, we conclude that LRSSLMDA would be a valuable computational tool for miRNA-disease association prediction. PMID:29253885

Ca2+-induced delayed afterdepolarizations are triggered by dyadic subspace Ca2+ affirming that increasing SERCA reduces aftercontractions

PubMed Central

Noble, Penelope J.; Noble, Denis

2011-01-01

Ca2+-induced delayed afterdepolarizations (DADs) are depolarizations that occur after full repolarization. They have been observed across multiple species and cell types. Experimental results have indicated that the main cause of DADs is Ca2+ overload. The main hypothesis as to their initiation has been Ca2+ overflow from the overloaded sarcoplasmic reticulum (SR). Our results using 37 previously published mathematical models provide evidence that Ca2+-induced DADs are initiated by the same mechanism as Ca2+-induced Ca2+ release, i.e., the modulation of the opening of ryanodine receptors (RyR) by Ca2+ in the dyadic subspace; an SR overflow mechanism was not necessary for the induction of DADs in any of the models. The SR Ca2+ level is better viewed as a modulator of the appearance of DADs and the magnitude of Ca2+ release. The threshold for the total Ca2+ level within the cell (not only the SR) at which Ca2+ oscillations arise in the models is close to their baseline level (∼1- to 3-fold). It is most sensitive to changes in the maximum sarco(endo)plasmic reticulum Ca2+-ATPase (SERCA) pump rate (directly proportional), the opening probability of RyRs, and the Ca2+ diffusion rate from the dyadic subspace into the cytosol (both indirectly proportional), indicating that the appearance of DADs is multifactorial. This shift in emphasis away from SR overload as the trigger for DADs toward a multifactorial analysis could explain why SERCA overexpression has been shown to suppress DADs (while increasing contractility) and why DADs appear during heart failure (at low SR Ca2+ levels). PMID:21666112

Formulation d'un modele mathematique par des techniques d'estimation de parametres a partir de donnees de vol pour l'helicoptere Bell 427 et l'avion F/A-18 servant a la recherches en aeroservoelasticite

NASA Astrophysics Data System (ADS)

Nadeau-Beaulieu, Michel

In this thesis, three mathematical models are built from flight test data for different aircraft design applications: a ground dynamics model for the Bell 427 helicopter, a prediction model for the rotor and engine parameters for the same helicopter type and a simulation model for the aeroelastic deflections of the F/A-18. In the ground dynamics application, the model structure is derived from physics where the normal force between the helicopter and the ground is modelled as a vertical spring and the frictional force is modelled with static and dynamic friction coefficients. The ground dynamics model coefficients are optimized to ensure that the model matches the landing data within the FAA (Federal Aviation Administration) tolerance bands for a level D flight simulator. In the rotor and engine application, rotors torques (main and tail), the engine torque and main rotor speed are estimated using a state-space model. The model inputs are nonlinear terms derived from the pilot control inputs and the helicopter states. The model parameters are identified using the subspace method and are further optimised with the Levenberg-Marquardt minimisation algorithm. The model built with the subspace method provides an excellent estimate of the outputs within the FAA tolerance bands. The F/A-18 aeroelastic state-space model is built from flight test. The research concerning this model is divided in two parts. Firstly, the deflection of a given structural surface on the aircraft following a differential ailerons control input is represented by a Multiple Inputs Single Outputs linear model whose inputs are the ailerons positions and the structural surfaces deflections. Secondly, a single state-space model is used to represent the deflection of the aircraft wings and trailing edge flaps following any control input. In this case the model is made non-linear by multiplying model inputs into higher order terms and using these terms as the inputs of the state-space equations. In both cases, the identification method is the subspace method. Most fit coefficients between the estimated and the measured signals are above 73% and most correlation coefficient are higher than 90%.

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

PubMed

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

Gompertzian stochastic model with delay effect to cervical cancer growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model

NASA Astrophysics Data System (ADS)

Zheng, Fei; Zhu, Jiang

2017-04-01

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño-Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.

Pipeline Processing with an Iterative, Context-based Detection Model

DTIC Science & Technology

2014-04-19

stripping the incoming data stream of repeating and irrelevant signals prior to running primary detectors , adaptive beamforming and matched field processing...framework, pattern detectors , correlation detectors , subspace detectors , matched field detectors , nuclear explosion monitoring 16. SECURITY CLASSIFICATION...10 5. Teleseismic paths from earthquakes in

A Gaussian-based rank approximation for subspace clustering

NASA Astrophysics Data System (ADS)

Xu, Fei; Peng, Chong; Hu, Yunhong; He, Guoping

2018-04-01

Low-rank representation (LRR) has been shown successful in seeking low-rank structures of data relationships in a union of subspaces. Generally, LRR and LRR-based variants need to solve the nuclear norm-based minimization problems. Beyond the success of such methods, it has been widely noted that the nuclear norm may not be a good rank approximation because it simply adds all singular values of a matrix together and thus large singular values may dominant the weight. This results in far from satisfactory rank approximation and may degrade the performance of lowrank models based on the nuclear norm. In this paper, we propose a novel nonconvex rank approximation based on the Gaussian distribution function, which has demanding properties to be a better rank approximation than the nuclear norm. Then a low-rank model is proposed based on the new rank approximation with application to motion segmentation. Experimental results have shown significant improvements and verified the effectiveness of our method.

Effects of stochastic sodium channels on extracellular excitation of myelinated nerve fibers.

PubMed

Mino, Hiroyuki; Grill, Warren M

2002-06-01

The effects of the stochastic gating properties of sodium channels on the extracellular excitation properties of mammalian nerve fibers was determined by computer simulation. To reduce computation time, a hybrid multicompartment cable model including five central nodes of Ranvier containing stochastic sodium channels and 16 flanking nodes containing detenninistic membrane dynamics was developed. The excitation properties of the hybrid cable model were comparable with those of a full stochastic cable model including 21 nodes of Ranvier containing stochastic sodium channels, indicating the validity of the hybrid cable model. The hybrid cable model was used to investigate whether or not the excitation properties of extracellularly activated fibers were influenced by the stochastic gating of sodium channels, including spike latencies, strength-duration (SD), current-distance (IX), and recruitment properties. The stochastic properties of the sodium channels in the hybrid cable model had the greatest impact when considering the temporal dynamics of nerve fibers, i.e., a large variability in latencies, while they did not influence the SD, IX, or recruitment properties as compared with those of the conventional deterministic cable model. These findings suggest that inclusion of stochastic nodes is not important for model-based design of stimulus waveforms for activation of motor nerve fibers. However, in cases where temporal fine structure is important, for example in sensory neural prostheses in the auditory and visual systems, the stochastic properties of the sodium channels may play a key role in the design of stimulus waveforms.

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Scalable Robust Principal Component Analysis Using Grassmann Averages.

PubMed

Hauberg, Sren; Feragen, Aasa; Enficiaud, Raffi; Black, Michael J

2016-11-01

In large datasets, manual data verification is impossible, and we must expect the number of outliers to increase with data size. While principal component analysis (PCA) can reduce data size, and scalable solutions exist, it is well-known that outliers can arbitrarily corrupt the results. Unfortunately, state-of-the-art approaches for robust PCA are not scalable. We note that in a zero-mean dataset, each observation spans a one-dimensional subspace, giving a point on the Grassmann manifold. We show that the average subspace corresponds to the leading principal component for Gaussian data. We provide a simple algorithm for computing this Grassmann Average ( GA), and show that the subspace estimate is less sensitive to outliers than PCA for general distributions. Because averages can be efficiently computed, we immediately gain scalability. We exploit robust averaging to formulate the Robust Grassmann Average (RGA) as a form of robust PCA. The resulting Trimmed Grassmann Average ( TGA) is appropriate for computer vision because it is robust to pixel outliers. The algorithm has linear computational complexity and minimal memory requirements. We demonstrate TGA for background modeling, video restoration, and shadow removal. We show scalability by performing robust PCA on the entire Star Wars IV movie; a task beyond any current method. Source code is available online.

Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates

NASA Astrophysics Data System (ADS)

Chang, Zhengbo; Meng, Xinzhu; Lu, Xiao

2017-04-01

This paper presents a stochastic SIRS epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis, and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model. We firstly investigate the boundness and extinction of the stochastic system. Furthermore, we use Ito's formula, the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases. The results indicate that stochastic fluctuations can suppress the disease outbreak. Finally, numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results.

New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1998-01-01

Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.

Gravitational instantons, self-duality, and geometric flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bourliot, F.; Estes, J.; Petropoulos, P. M.

2010-05-15

We discuss four-dimensional 'spatially homogeneous' gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein equations. They are endowed with a product structure RxM{sub 3} leading to a foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of homogeneous subspaces, the dynamics coincides with a geometric flow on the three-dimensional slice, driven by the Ricci tensor plus an so(3) gauge connection. The flowing metric is related to the vielbein of the subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi-Civita connection.

On the Convergence of an Implicitly Restarted Arnoldi Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lehoucq, Richard B.

We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM computes a nested sequence of approximations for the partial Schur decomposition associated with the dominant invariant subspace of a matrix.

Portfolios and the market geometry

NASA Astrophysics Data System (ADS)

Eleutério, Samuel; Araújo, Tanya; Vilela Mendes, R.

2014-09-01

A geometric analysis of return time series, performed in the past, implied that most of the systematic information in the market is contained in a space of small dimension. Here we have explored subspaces of this space to find out the relative performance of portfolios formed from companies that have the largest projections in each one of the subspaces. As expected, it was found that the best performance portfolios are associated with some of the small eigenvalue subspaces and not to the dominant dimensions. This is found to occur in a systematic fashion over an extended period (1990-2008).

Adaptive bearing estimation and tracking of multiple targets in a realistic passive sonar scenario

NASA Astrophysics Data System (ADS)

Rajagopal, R.; Challa, Subhash; Faruqi, Farhan A.; Rao, P. R.

1997-06-01

In a realistic passive sonar environment, the received signal consists of multipath arrivals from closely separated moving targets. The signals are contaminated by spatially correlated noise. The differential MUSIC has been proposed to estimate the DOAs in such a scenario. This method estimates the 'noise subspace' in order to estimate the DOAs. However, the 'noise subspace' estimate has to be updated as and when new data become available. In order to save the computational costs, a new adaptive noise subspace estimation algorithm is proposed in this paper. The salient features of the proposed algorithm are: (1) Noise subspace estimation is done by QR decomposition of the difference matrix which is formed from the data covariance matrix. Thus, as compared to standard eigen-decomposition based methods which require O(N3) computations, the proposed method requires only O(N2) computations. (2) Noise subspace is updated by updating the QR decomposition. (3) The proposed algorithm works in a realistic sonar environment. In the second part of the paper, the estimated bearing values are used to track multiple targets. In order to achieve this, the nonlinear system/linear measurement extended Kalman filtering proposed is applied. Computer simulation results are also presented to support the theory.

Integrated head package cable carrier for a nuclear power plant

DOEpatents

Meuschke, Robert E.; Trombola, Daniel M.

1995-01-01

A cabling arrangement is provided for a nuclear reactor located within a containment. Structure inside the containment is characterized by a wall having a near side surrounding the reactor vessel defining a cavity, an operating deck outside the cavity, a sub-space below the deck and on a far side of the wall spaced from the near side, and an operating area above the deck. The arrangement includes a movable frame supporting a plurality of cables extending through the frame, each connectable at a first end to a head package on the reactor vessel and each having a second end located in the sub-space. The frame is movable, with the cables, between a first position during normal operation of the reactor when the cables are connected to the head package, located outside the sub-space proximate the head package, and a second position during refueling when the cables are disconnected from the head package, located in the sub-space. In a preferred embodiment, the frame straddles the top of the wall in a substantially horizontal orientation in the first position, pivots about an end distal from the head package to a substantially vertically oriented intermediate position, and is guided, while remaining about vertically oriented, along a track in the sub-space to the second position.

Low-Rank Tensor Subspace Learning for RGB-D Action Recognition.

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

Since RGB-D action data inherently equip with extra depth information compared with RGB data, recently many works employ RGB-D data in a third-order tensor representation containing spatio-temporal structure to find a subspace for action recognition. However, there are two main challenges of these methods. First, the dimension of subspace is usually fixed manually. Second, preserving local information by finding intraclass and inter-class neighbors from a manifold is highly timeconsuming. In this paper, we learn a tensor subspace, whose dimension is learned automatically by low-rank learning, for RGB-D action recognition. Particularly, the tensor samples are factorized to obtain three Projection Matrices (PMs) by Tucker Decomposition, where all the PMs are performed by nuclear norm in a close-form to obtain the tensor ranks which are used as tensor subspace dimension. Additionally, we extract the discriminant and local information from a manifold using a graph constraint. This graph preserves the local knowledge inherently, which is faster than the previous way by calculating both the intra-class and inter-class neighbors of each sample. We evaluate the proposed method on four widely used RGB-D action datasets including MSRDailyActivity3D, MSRActionPairs, MSRActionPairs skeleton and UTKinect-Action3D datasets, and the experimental results show higher accuracy and efficiency of the proposed method.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

NASA Astrophysics Data System (ADS)

Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial

2016-09-01

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tripathy, Rohit, E-mail: rtripath@purdue.edu; Bilionis, Ilias, E-mail: ibilion@purdue.edu; Gonzalez, Marcial, E-mail: marcial-gonzalez@purdue.edu

2016-09-15

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range ofmore » physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.« less

Stochastic Human Exposure and Dose Simulation Model for Pesticides

EPA Science Inventory

SHEDS-Pesticides (Stochastic Human Exposure and Dose Simulation Model for Pesticides) is a physically-based stochastic model developed to quantify exposure and dose of humans to multimedia, multipathway pollutants. Probabilistic inputs are combined in physical/mechanistic algorit...

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction

DTIC Science & Technology

2016-02-25

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction We have completed a short program of theoretical research...on dimensional reduction and approximation of models based on quantum stochastic differential equations. Our primary results lie in the area of...2211 quantum probability, quantum stochastic differential equations REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR

Feedforward Inhibition and Synaptic Scaling – Two Sides of the Same Coin?

PubMed Central

Lücke, Jörg

2012-01-01

Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing. PMID:22457610

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

Feedforward inhibition and synaptic scaling--two sides of the same coin?

PubMed

Keck, Christian; Savin, Cristina; Lücke, Jörg

2012-01-01

Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing.

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

NASA Astrophysics Data System (ADS)

Chen, Can; Kang, Yanmei

2017-01-01

A stochastic multi-strain SIS epidemic model is formulated by introducing Lévy noise into the disease transmission rate of each strain. First, we prove that the stochastic model admits a unique global positive solution, and, by the comparison theorem, we show that the solution remains within a positively invariant set almost surely. Next we investigate stochastic stability of the disease-free equilibrium, including stability in probability and pth moment asymptotic stability. Then sufficient conditions for persistence in the mean of the disease are established. Finally, based on an Euler scheme for Lévy-driven stochastic differential equations, numerical simulations for a stochastic two-strain model are carried out to verify the theoretical results. Moreover, numerical comparison results of the stochastic two-strain model and the deterministic version are also given. Lévy noise can cause the two strains to become extinct almost surely, even though there is a dominant strain that persists in the deterministic model. It can be concluded that the introduction of Lévy noise reduces the disease extinction threshold, which indicates that Lévy noise may suppress the disease outbreak.

Multiple Source DF (Direction Finding) Signal Processing: An Experimental System,

DTIC Science & Technology

The MUltiple SIgnal Characterization ( MUSIC ) algorithm is an implementation of the Signal Subspace Approach to provide parameter estimates of...the signal subspace (obtained from the received data) and the array manifold (obtained via array calibration). The MUSIC algorithm has been

Stochastic dynamics of melt ponds and sea ice-albedo climate feedback

NASA Astrophysics Data System (ADS)

Sudakov, Ivan

Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.

Effects of Stochastic Traffic Flow Model on Expected System Performance

DTIC Science & Technology

2012-12-01

NSWC-PCD has made considerable improvements to their pedestrian flow modeling . In addition to the linear paths, the 2011 version now includes...using stochastic paths. 2.2 Linear Paths vs. Stochastic Paths 2.2.1 Linear Paths and Direct Maximum Pd Calculation Modeling pedestrian traffic flow...as a stochastic process begins with the linear path model . Let the detec- tion area be R x C voxels. This creates C 2 total linear paths, path(Cs

Human Guidance Behavior Decomposition and Modeling

NASA Astrophysics Data System (ADS)

Feit, Andrew James

Trained humans are capable of high performance, adaptable, and robust first-person dynamic motion guidance behavior. This behavior is exhibited in a wide variety of activities such as driving, piloting aircraft, skiing, biking, and many others. Human performance in such activities far exceeds the current capability of autonomous systems in terms of adaptability to new tasks, real-time motion planning, robustness, and trading safety for performance. The present work investigates the structure of human dynamic motion guidance that enables these performance qualities. This work uses a first-person experimental framework that presents a driving task to the subject, measuring control inputs, vehicle motion, and operator visual gaze movement. The resulting data is decomposed into subspace segment clusters that form primitive elements of action-perception interactive behavior. Subspace clusters are defined by both agent-environment system dynamic constraints and operator control strategies. A key contribution of this work is to define transitions between subspace cluster segments, or subgoals, as points where the set of active constraints, either system or operator defined, changes. This definition provides necessary conditions to determine transition points for a given task-environment scenario that allow a solution trajectory to be planned from known behavior elements. In addition, human gaze behavior during this task contains predictive behavior elements, indicating that the identified control modes are internally modeled. Based on these ideas, a generative, autonomous guidance framework is introduced that efficiently generates optimal dynamic motion behavior in new tasks. The new subgoal planning algorithm is shown to generate solutions to certain tasks more quickly than existing approaches currently used in robotics.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

PubMed

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

SNP selection and classification of genome-wide SNP data using stratified sampling random forests.

PubMed

Wu, Qingyao; Ye, Yunming; Liu, Yang; Ng, Michael K

2012-09-01

For high dimensional genome-wide association (GWA) case-control data of complex disease, there are usually a large portion of single-nucleotide polymorphisms (SNPs) that are irrelevant with the disease. A simple random sampling method in random forest using default mtry parameter to choose feature subspace, will select too many subspaces without informative SNPs. Exhaustive searching an optimal mtry is often required in order to include useful and relevant SNPs and get rid of vast of non-informative SNPs. However, it is too time-consuming and not favorable in GWA for high-dimensional data. The main aim of this paper is to propose a stratified sampling method for feature subspace selection to generate decision trees in a random forest for GWA high-dimensional data. Our idea is to design an equal-width discretization scheme for informativeness to divide SNPs into multiple groups. In feature subspace selection, we randomly select the same number of SNPs from each group and combine them to form a subspace to generate a decision tree. The advantage of this stratified sampling procedure can make sure each subspace contains enough useful SNPs, but can avoid a very high computational cost of exhaustive search of an optimal mtry, and maintain the randomness of a random forest. We employ two genome-wide SNP data sets (Parkinson case-control data comprised of 408 803 SNPs and Alzheimer case-control data comprised of 380 157 SNPs) to demonstrate that the proposed stratified sampling method is effective, and it can generate better random forest with higher accuracy and lower error bound than those by Breiman's random forest generation method. For Parkinson data, we also show some interesting genes identified by the method, which may be associated with neurological disorders for further biological investigations.

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Stochastic Petri Net extension of a yeast cell cycle model.

PubMed

Mura, Ivan; Csikász-Nagy, Attila

2008-10-21

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.

Stochasticity and determinism in models of hematopoiesis.

PubMed

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Hybrid ODE/SSA methods and the cell cycle model

NASA Astrophysics Data System (ADS)

Wang, S.; Chen, M.; Cao, Y.

2017-07-01

Stochastic effect in cellular systems has been an important topic in systems biology. Stochastic modeling and simulation methods are important tools to study stochastic effect. Given the low efficiency of stochastic simulation algorithms, the hybrid method, which combines an ordinary differential equation (ODE) system with a stochastic chemically reacting system, shows its unique advantages in the modeling and simulation of biochemical systems. The efficiency of hybrid method is usually limited by reactions in the stochastic subsystem, which are modeled and simulated using Gillespie's framework and frequently interrupt the integration of the ODE subsystem. In this paper we develop an efficient implementation approach for the hybrid method coupled with traditional ODE solvers. We also compare the efficiency of hybrid methods with three widely used ODE solvers RADAU5, DASSL, and DLSODAR. Numerical experiments with three biochemical models are presented. A detailed discussion is presented for the performances of three ODE solvers.

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A',B,B', are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell's inequality is violated.

Study on individual stochastic model of GNSS observations for precise kinematic applications

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik; Szpunar, Ryszard

2015-04-01

The proper definition of mathematical positioning model, which is defined by functional and stochastic models, is a prerequisite to obtain the optimal estimation of unknown parameters. Especially important in this definition is realistic modelling of stochastic properties of observations, which are more receiver-dependent and time-varying than deterministic relationships. This is particularly true with respect to precise kinematic applications which are characterized by weakening model strength. In this case, incorrect or simplified definition of stochastic model causes that the performance of ambiguity resolution and accuracy of position estimation can be limited. In this study we investigate the methods of describing the measurement noise of GNSS observations and its impact to derive precise kinematic positioning model. In particular stochastic modelling of individual components of the variance-covariance matrix of observation noise performed using observations from a very short baseline and laboratory GNSS signal generator, is analyzed. Experimental test results indicate that the utilizing the individual stochastic model of observations including elevation dependency and cross-correlation instead of assumption that raw measurements are independent with the same variance improves the performance of ambiguity resolution as well as rover positioning accuracy. This shows that the proposed stochastic assessment method could be a important part in complex calibration procedure of GNSS equipment.

Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

PubMed

Zhang, Cheng; Lai, Chun-Liang; Pettitt, B Montgomery

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

ERIC Educational Resources Information Center

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit

NASA Astrophysics Data System (ADS)

Danilin, S.; Vepsäläinen, A.; Paraoanu, G. S.

2018-05-01

Quantum state manipulation with gates based on geometric phases acquired during cyclic operations promises inherent fault-tolerance and resilience to local fluctuations in the control parameters. Here we create a general non-Abelian and non-adiabatic holonomic gate acting in the (∣0〉, ∣2〉) subspace of a three-level (qutrit) transmon device fabricated in a fully coplanar design. Experimentally, this is realized by simultaneously coupling the first two transitions by microwave pulses with amplitudes and phases defined such that the condition of parallel transport is fulfilled. We demonstrate the creation of arbitrary superpositions in this subspace by changing the amplitudes of the pulses and the relative phase between them. We use two-photon pulses acting in the holonomic subspace to reveal the coherence of the state created by the geometric gate pulses and to prepare different superposition states. We also test the action of holonomic NOT and Hadamard gates on superpositions in the (| 0> ,| 2> ) subspace.

New subspace methods for ATR

NASA Astrophysics Data System (ADS)

Zhang, Peng; Peng, Jing; Sims, S. Richard F.

2005-05-01

In ATR applications, each feature is a convolution of an image with a filter. It is important to use most discriminant features to produce compact representations. We propose two novel subspace methods for dimension reduction to address limitations associated with Fukunaga-Koontz Transform (FKT). The first method, Scatter-FKT, assumes that target is more homogeneous, while clutter can be anything other than target and anywhere. Thus, instead of estimating a clutter covariance matrix, Scatter-FKT computes a clutter scatter matrix that measures the spread of clutter from the target mean. We choose dimensions along which the difference in variation between target and clutter is most pronounced. When the target follows a Gaussian distribution, Scatter-FKT can be viewed as a generalization of FKT. The second method, Optimal Bayesian Subspace, is derived from the optimal Bayesian classifier. It selects dimensions such that the minimum Bayes error rate can be achieved. When both target and clutter follow Gaussian distributions, OBS computes optimal subspace representations. We compare our methods against FKT using character image as well as IR data.

Improvement in the Accuracy of Matching by Different Feature Subspaces in Traffic Sign Recognition

NASA Astrophysics Data System (ADS)

Ihara, Arihito; Fujiyoshi, Hironobu; Takaki, Masanari; Kumon, Hiroaki; Tamatsu, Yukimasa

A technique for recognizing traffic signs from an image taken with an in-vehicle camera has already been proposed as driver's drive assist. SIFT feature is used for traffic sign recognition, because it is robust to changes in scaling and rotating of the traffic sign. However, it is difficult to process in real-time because the computation cost of the SIFT feature extraction and matching is expensive. This paper presents a method of traffic sign recognition based on keypoint classifier by AdaBoost using PCA-SIFT features in different feature subspaces. Each subspace is constructed from gradients of traffic sign images and general images respectively. A detected keypoint is projected to both subspaces, and then the AdaBoost employs to classy into whether the keypoint is on the traffic sign or not. Experimental results show that the computation cost for keypoint matching can be reduced to about 1/2 compared with the conventional method.

Metastable decoherence-free subspaces and electromagnetically induced transparency in interacting many-body systems

NASA Astrophysics Data System (ADS)

Macieszczak, Katarzyna; Zhou, YanLi; Hofferberth, Sebastian; Garrahan, Juan P.; Li, Weibin; Lesanovsky, Igor

2017-10-01

We investigate the dynamics of a generic interacting many-body system under conditions of electromagnetically induced transparency (EIT). This problem is of current relevance due to its connection to nonlinear optical media realized by Rydberg atoms. In an interacting system the structure of the dynamics and the approach to the stationary state becomes far more complex than in the case of conventional EIT. In particular, we discuss the emergence of a metastable decoherence-free subspace, whose dimension for a single Rydberg excitation grows linearly in the number of atoms. On approach to stationarity this leads to a slow dynamics, which renders the typical assumption of fast relaxation invalid. We derive analytically the effective nonequilibrium dynamics in the decoherence-free subspace, which features coherent and dissipative two-body interactions. We discuss the use of this scenario for the preparation of collective entangled dark states and the realization of general unitary dynamics within the spin-wave subspace.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

NASA Astrophysics Data System (ADS)

Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.

2018-06-01

The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.

Some Stochastic-Duel Models of Combat.

DTIC Science & Technology

1983-03-01

AD-R127 879 SOME STOCHASTIC- DUEL MODELS OF CONBAT(U) NAVAL - / POSTGRADUATE SCHOOL MONTEREY CA J S CHOE MAR 83 UNCLASSiIED FC1/Ehhh1; F/ 12/ ,iE...SCHOOL Monterey, California DTIC ELECTE :MAY 10 1983 "T !H ES IS SOME STOCHASTIC- DUEL MODELS OF COMBAT by Jum Soo Choe March 1983 Thesis Advisor: J. G...TYPE OF RETORT a PERIOD COVIOCe Master’s Thesis Some Stochastic- Duel Models of Combat March 1983 S. PERFORINGi *no. 44POOi umet 7. AUTHORW.) a

Network embedding-based representation learning for single cell RNA-seq data.

PubMed

Li, Xiangyu; Chen, Weizheng; Chen, Yang; Zhang, Xuegong; Gu, Jin; Zhang, Michael Q

2017-11-02

Single cell RNA-seq (scRNA-seq) techniques can reveal valuable insights of cell-to-cell heterogeneities. Projection of high-dimensional data into a low-dimensional subspace is a powerful strategy in general for mining such big data. However, scRNA-seq suffers from higher noise and lower coverage than traditional bulk RNA-seq, hence bringing in new computational difficulties. One major challenge is how to deal with the frequent drop-out events. The events, usually caused by the stochastic burst effect in gene transcription and the technical failure of RNA transcript capture, often render traditional dimension reduction methods work inefficiently. To overcome this problem, we have developed a novel Single Cell Representation Learning (SCRL) method based on network embedding. This method can efficiently implement data-driven non-linear projection and incorporate prior biological knowledge (such as pathway information) to learn more meaningful low-dimensional representations for both cells and genes. Benchmark results show that SCRL outperforms other dimensional reduction methods on several recent scRNA-seq datasets. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems

NASA Astrophysics Data System (ADS)

Park, Won-Kwang

2015-02-01

Multi-frequency subspace migration imaging techniques are usually adopted for the non-iterative imaging of unknown electromagnetic targets, such as cracks in concrete walls or bridges and anti-personnel mines in the ground, in the inverse scattering problems. It is confirmed that this technique is very fast, effective, robust, and can not only be applied to full- but also to limited-view inverse problems if a suitable number of incidents and corresponding scattered fields are applied and collected. However, in many works, the application of such techniques is heuristic. With the motivation of such heuristic application, this study analyzes the structure of the imaging functional employed in the subspace migration imaging technique in two-dimensional full- and limited-view inverse scattering problems when the unknown targets are arbitrary-shaped, arc-like perfectly conducting cracks located in the two-dimensional homogeneous space. In contrast to the statistical approach based on statistical hypothesis testing, our approach is based on the fact that the subspace migration imaging functional can be expressed by a linear combination of the Bessel functions of integer order of the first kind. This is based on the structure of the Multi-Static Response (MSR) matrix collected in the far-field at nonzero frequency in either Transverse Magnetic (TM) mode (Dirichlet boundary condition) or Transverse Electric (TE) mode (Neumann boundary condition). The investigation of the expression of imaging functionals gives us certain properties of subspace migration and explains why multi-frequency enhances imaging resolution. In particular, we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident fields are applied. Consequently, we introduce a weighted multi-frequency imaging functional and confirm that it is an improved version of subspace migration in TM mode. Various results of numerical simulations performed on the far-field data affected by large amounts of random noise are similar to the analytical results derived in this study, and they provide a direction for future studies.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-01-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-06-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

A spatial stochastic programming model for timber and core area management under risk of stand-replacing fire

Treesearch

Dung Tuan Nguyen

2012-01-01

Forest harvest scheduling has been modeled using deterministic and stochastic programming models. Past models seldom address explicit spatial forest management concerns under the influence of natural disturbances. In this research study, we employ multistage full recourse stochastic programming models to explore the challenges and advantages of building spatial...

A spatial stochastic programming model for timber and core area management under risk of fires

Treesearch

Yu Wei; Michael Bevers; Dung Nguyen; Erin Belval

2014-01-01

Previous stochastic models in harvest scheduling seldom address explicit spatial management concerns under the influence of natural disturbances. We employ multistage stochastic programming models to explore the challenges and advantages of building spatial optimization models that account for the influences of random stand-replacing fires. Our exploratory test models...

On spectral synthesis on zero-dimensional Abelian groups

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2013-09-01

Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is said to be an invariant subspace if it is invariant with respect to the translations \\tau_y\\colon f(x)\\mapsto f(x+y), y\\in G. In the paper, it is proved that any invariant subspace \\mathscr H admits spectral synthesis, that is, \\mathscr H coincides with the closed linear span of the characters of G belonging to \\mathscr H. Bibliography: 25 titles.

Conditioned invariant subspaces, disturbance decoupling and solutions of rational matrix equations

NASA Technical Reports Server (NTRS)

Li, Z.; Sastry, S. S.

1986-01-01

Conditioned invariant subspaces are introduced both in terms of output injection and in terms of state estimation. Various properties of these subspaces are explored and the problem of disturbance decoupling by output injection (OIP) is defined. It is then shown that OIP is equivalent to the problem of disturbance decoupled estimation as introduced in Willems (1982) and Willems and Commault (1980). Both solvability conditions and a description of solutions for a class of rational matrix equations of the form X(s)M(s) = Q(s) on several ways are given in state-space form. Finally, the problem of output stabilization with respect to a disturbance is briefly addressed.

Essential uncontrollability of discrete linear, time-invariant, dynamical systems

NASA Technical Reports Server (NTRS)

Cliff, E. M.

1975-01-01

The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

PubMed Central

Gao, Fei; Li, Ye; Novak, Igor L.; Slepchenko, Boris M.

2016-01-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell. PMID:27959915

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Use of paired simple and complex models to reduce predictive bias and quantify uncertainty

NASA Astrophysics Data System (ADS)

Doherty, John; Christensen, Steen

2011-12-01

Modern environmental management and decision-making is based on the use of increasingly complex numerical models. Such models have the advantage of allowing representation of complex processes and heterogeneous system property distributions inasmuch as these are understood at any particular study site. The latter are often represented stochastically, this reflecting knowledge of the character of system heterogeneity at the same time as it reflects a lack of knowledge of its spatial details. Unfortunately, however, complex models are often difficult to calibrate because of their long run times and sometimes questionable numerical stability. Analysis of predictive uncertainty is also a difficult undertaking when using models such as these. Such analysis must reflect a lack of knowledge of spatial hydraulic property details. At the same time, it must be subject to constraints on the spatial variability of these details born of the necessity for model outputs to replicate observations of historical system behavior. In contrast, the rapid run times and general numerical reliability of simple models often promulgates good calibration and ready implementation of sophisticated methods of calibration-constrained uncertainty analysis. Unfortunately, however, many system and process details on which uncertainty may depend are, by design, omitted from simple models. This can lead to underestimation of the uncertainty associated with many predictions of management interest. The present paper proposes a methodology that attempts to overcome the problems associated with complex models on the one hand and simple models on the other hand, while allowing access to the benefits each of them offers. It provides a theoretical analysis of the simplification process from a subspace point of view, this yielding insights into the costs of model simplification, and into how some of these costs may be reduced. It then describes a methodology for paired model usage through which predictive bias of a simplified model can be detected and corrected, and postcalibration predictive uncertainty can be quantified. The methodology is demonstrated using a synthetic example based on groundwater modeling environments commonly encountered in northern Europe and North America.

Subspace Signal Processing in Structured Noise

DTIC Science & Technology

1990-12-01

1.7 Motivation for the Model ....... ........................... 8 1.8 E x am p les...S). We do not require that H be orthogonal to S. * 1.7 Motivation for the Model The linear model is quite versatile in terms of the types of signals...cross terms zero, we choose . = (SHs)- mS~u’ (3.69) This implies that = Ps4 , (3.70) and S t s (3.71) : = Ps . RPs -. The last step is to maximize

Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment.

PubMed

Liu, Meng; Wang, Ke

2010-06-07

A new single-species model disturbed by both white noise and colored noise in a polluted environment is developed and analyzed. Sufficient criteria for extinction, stochastic nonpersistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the species are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. The results show that both white and colored environmental noises have sufficient effect to the survival results. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

A Problem-Centered Approach to Canonical Matrix Forms

ERIC Educational Resources Information Center

Sylvestre, Jeremy

2014-01-01

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

Multi-Level Reduced Order Modeling Equipped with Probabilistic Error Bounds

NASA Astrophysics Data System (ADS)

Abdo, Mohammad Gamal Mohammad Mostafa

This thesis develops robust reduced order modeling (ROM) techniques to achieve the needed efficiency to render feasible the use of high fidelity tools for routine engineering analyses. Markedly different from the state-of-the-art ROM techniques, our work focuses only on techniques which can quantify the credibility of the reduction which can be measured with the reduction errors upper-bounded for the envisaged range of ROM model application. Our objective is two-fold. First, further developments of ROM techniques are proposed when conventional ROM techniques are too taxing to be computationally practical. This is achieved via a multi-level ROM methodology designed to take advantage of the multi-scale modeling strategy typically employed for computationally taxing models such as those associated with the modeling of nuclear reactor behavior. Second, the discrepancies between the original model and ROM model predictions over the full range of model application conditions are upper-bounded in a probabilistic sense with high probability. ROM techniques may be classified into two broad categories: surrogate construction techniques and dimensionality reduction techniques, with the latter being the primary focus of this work. We focus on dimensionality reduction, because it offers a rigorous approach by which reduction errors can be quantified via upper-bounds that are met in a probabilistic sense. Surrogate techniques typically rely on fitting a parametric model form to the original model at a number of training points, with the residual of the fit taken as a measure of the prediction accuracy of the surrogate. This approach, however, does not generally guarantee that the surrogate model predictions at points not included in the training process will be bound by the error estimated from the fitting residual. Dimensionality reduction techniques however employ a different philosophy to render the reduction, wherein randomized snapshots of the model variables, such as the model parameters, responses, or state variables, are projected onto lower dimensional subspaces, referred to as the "active subspaces", which are selected to capture a user-defined portion of the snapshots variations. Once determined, the ROM model application involves constraining the variables to the active subspaces. In doing so, the contribution from the variables discarded components can be estimated using a fundamental theorem from random matrix theory which has its roots in Dixon's theory, developed in 1983. This theory was initially presented for linear matrix operators. The thesis extends this theorem's results to allow reduction of general smooth nonlinear operators. The result is an approach by which the adequacy of a given active subspace determined using a given set of snapshots, generated either using the full high fidelity model, or other models with lower fidelity, can be assessed, which provides insight to the analyst on the type of snapshots required to reach a reduction that can satisfy user-defined preset tolerance limits on the reduction errors. Reactor physics calculations are employed as a test bed for the proposed developments. The focus will be on reducing the effective dimensionality of the various data streams such as the cross-section data and the neutron flux. The developed methods will be applied to representative assembly level calculations, where the size of the cross-section and flux spaces are typically large, as required by downstream core calculations, in order to capture the broad range of conditions expected during reactor operation. (Abstract shortened by ProQuest.).

Model selection for integrated pest management with stochasticity.

PubMed

Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel

2018-04-07

In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.

Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control

NASA Astrophysics Data System (ADS)

Gao, Shujing; Zhong, Deming; Zhang, Yan

2018-04-01

In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.

Stochastic and deterministic models for agricultural production networks.

PubMed

Bai, P; Banks, H T; Dediu, S; Govan, A Y; Last, M; Lloyd, A L; Nguyen, H K; Olufsen, M S; Rempala, G; Slenning, B D

2007-07-01

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.

From Complex to Simple: Interdisciplinary Stochastic Models

ERIC Educational Resources Information Center

Mazilu, D. A.; Zamora, G.; Mazilu, I.

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

One-Week Module on Stochastic Groundwater Modeling

ERIC Educational Resources Information Center

Mays, David C.

2010-01-01

This article describes a one-week introduction to stochastic groundwater modeling, intended for the end of a first course on groundwater hydrology, or the beginning of a second course on stochastic hydrogeology or groundwater modeling. The motivation for this work is to strengthen groundwater education, which has been identified among the factors…

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

PubMed

Maliyoni, Milliward; Chirove, Faraimunashe; Gaff, Holly D; Govinder, Keshlan S

2017-09-01

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Stochastic Watershed Models for Risk Based Decision Making

NASA Astrophysics Data System (ADS)

Vogel, R. M.

2017-12-01

Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Stochastic growth logistic model with aftereffect for batch fermentation process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grosso, Marcos; Kalstein, Adrian; Parisi, Gustavo

The native state of a protein consists of an equilibrium of conformational states on an energy landscape rather than existing as a single static state. The co-existence of conformers with different ligand-affinities in a dynamical equilibrium is the basis for the conformational selection model for ligand binding. In this context, the development of theoretical methods that allow us to analyze not only the structural changes but also changes in the fluctuation patterns between conformers will contribute to elucidate the differential properties acquired upon ligand binding. Molecular dynamics simulations can provide the required information to explore these features. Its use inmore » combination with subsequent essential dynamics analysis allows separating large concerted conformational rearrangements from irrelevant fluctuations. We present a novel procedure to define the size and composition of essential dynamics subspaces associated with ligand-bound and ligand-free conformations. These definitions allow us to compare essential dynamics subspaces between different conformers. Our procedure attempts to emphasize the main similarities and differences between the different essential dynamics in an unbiased way. Essential dynamics subspaces associated to conformational transitions can also be analyzed. As a test case, we study the glutaminase interacting protein (GIP), composed of a single PDZ domain. Both GIP ligand-free state and glutaminase L peptide-bound states are analyzed. Our findings concerning the relative changes in the flexibility pattern upon binding are in good agreement with experimental Nuclear Magnetic Resonance data.« less

Deterministic and stochastic CTMC models from Zika disease transmission

NASA Astrophysics Data System (ADS)

Zevika, Mona; Soewono, Edy

2018-03-01

Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.

Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device

NASA Astrophysics Data System (ADS)

La Cour, Brian R.; Ostrove, Corey I.

2017-01-01

This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition to the usual unitary gate operations. Although bandwidth requirements will limit the scale of problems that can be solved by this method, it can nevertheless provide a significant computational advantage for problems of limited size. In particular, we find that, for the same number of noisy oracle calls, the proposed subspace projection method provides a higher probability of success for finding a solution than does an single application of Grover's algorithm on the same device.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

NASA Astrophysics Data System (ADS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

PubMed

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-10-15

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

PubMed Central

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-01-01

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. PMID:26478601

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

Cell survival fraction estimation based on the probability densities of domain and cell nucleus specific energies using improved microdosimetric kinetic models.

PubMed

Sato, Tatsuhiko; Furusawa, Yoshiya

2012-10-01

Estimation of the survival fractions of cells irradiated with various particles over a wide linear energy transfer (LET) range is of great importance in the treatment planning of charged-particle therapy. Two computational models were developed for estimating survival fractions based on the concept of the microdosimetric kinetic model. They were designated as the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models. The former model takes into account the stochastic natures of both domain and cell nucleus specific energies, whereas the latter model represents the stochastic nature of domain specific energy by its approximated mean value and variance to reduce the computational time. The probability densities of the domain and cell nucleus specific energies are the fundamental quantities for expressing survival fractions in these models. These densities are calculated using the microdosimetric and LET-estimator functions implemented in the Particle and Heavy Ion Transport code System (PHITS) in combination with the convolution or database method. Both the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models can reproduce the measured survival fractions for high-LET and high-dose irradiations, whereas a previously proposed microdosimetric kinetic model predicts lower values for these fractions, mainly due to intrinsic ignorance of the stochastic nature of cell nucleus specific energies in the calculation. The models we developed should contribute to a better understanding of the mechanism of cell inactivation, as well as improve the accuracy of treatment planning of charged-particle therapy.

Krylov subspace methods on supercomputers

NASA Technical Reports Server (NTRS)

Saad, Youcef

1988-01-01

A short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers is presented. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance. A conservative approach to derive effective iterative techniques for supercomputers has been to find efficient parallel/vector implementations of the standard algorithms. The main source of difficulty in the incomplete factorization preconditionings is in the solution of the triangular systems at each step. A few approaches consisting of implementing efficient forward and backward triangular solutions are described in detail. Polynomial preconditioning as an alternative to standard incomplete factorization techniques is also discussed. Another efficient approach is to reorder the equations so as to improve the structure of the matrix to achieve better parallelism or vectorization. An overview of these and other ideas and their effectiveness or potential for different types of architectures is given.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Optimal sensor placement for spatial lattice structure based on genetic algorithms

NASA Astrophysics Data System (ADS)

Liu, Wei; Gao, Wei-cheng; Sun, Yi; Xu, Min-jian

2008-10-01

Optimal sensor placement technique plays a key role in structural health monitoring of spatial lattice structures. This paper considers the problem of locating sensors on a spatial lattice structure with the aim of maximizing the data information so that structural dynamic behavior can be fully characterized. Based on the criterion of optimal sensor placement for modal test, an improved genetic algorithm is introduced to find the optimal placement of sensors. The modal strain energy (MSE) and the modal assurance criterion (MAC) have been taken as the fitness function, respectively, so that three placement designs were produced. The decimal two-dimension array coding method instead of binary coding method is proposed to code the solution. Forced mutation operator is introduced when the identical genes appear via the crossover procedure. A computational simulation of a 12-bay plain truss model has been implemented to demonstrate the feasibility of the three optimal algorithms above. The obtained optimal sensor placements using the improved genetic algorithm are compared with those gained by exiting genetic algorithm using the binary coding method. Further the comparison criterion based on the mean square error between the finite element method (FEM) mode shapes and the Guyan expansion mode shapes identified by data-driven stochastic subspace identification (SSI-DATA) method are employed to demonstrate the advantage of the different fitness function. The results showed that some innovations in genetic algorithm proposed in this paper can enlarge the genes storage and improve the convergence of the algorithm. More importantly, the three optimal sensor placement methods can all provide the reliable results and identify the vibration characteristics of the 12-bay plain truss model accurately.

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

DTIC Science & Technology

2012-03-22

with performance profiles, Math. Program., 91 (2002), pp. 201–213. [6] P. DRINEAS, R. KANNAN, AND M. W. MAHONEY , Fast Monte Carlo algorithms for matrices...computing invariant subspaces of non-Hermitian matri- ces, Numer. Math., 25 ( 1975 /76), pp. 123–136. [25] , Matrix algorithms Vol. II: Eigensystems

Basis adaptation in homogeneous chaos spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tipireddy, Ramakrishna; Ghanem, Roger

2014-02-01

We present a new meth for the characterization of subspaces associated with low-dimensional quantities of interet (QoI). The probability density function of these QoI is found to be concentrated around one-dimensional subspaces for which we develop projection operators. Our approach builds on the properties of Gaussian Hilbert spaces and associated tensor product spaces.

The minimal SUSY B - L model: from the unification scale to the LHC

DOE PAGES

Ovrut, Burt A.; Purves, Austin; Spinner, Sogee

2015-06-26

Here, this paper introduces a random statistical scan over the high-energy initial parameter space of the minimal SUSY B - L model — denoted as the B - L MSSM. Each initial set of points is renormalization group evolved to the electroweak scale — being subjected, sequentially, to the requirement of radiative B - L and electroweak symmetry breaking, the present experimental lower bounds on the B - L vector boson and sparticle masses, as well as the lightest neutral Higgs mass of ~125 GeV. The subspace of initial parameters that satisfies all such constraints is presented, shown to bemore » robust and to contain a wide range of different configurations of soft supersymmetry breaking masses. The low-energy predictions of each such “valid” point — such as the sparticle mass spectrum and, in particular, the LSP — are computed and then statistically analyzed over the full subspace of valid points. Finally, the amount of fine-tuning required is quantified and compared to the MSSM computed using an identical random scan. The B - L MSSM is shown to generically require less fine-tuninng.« less

Fast image interpolation via random forests.

PubMed

Huang, Jun-Jie; Siu, Wan-Chi; Liu, Tian-Rui

2015-10-01

This paper proposes a two-stage framework for fast image interpolation via random forests (FIRF). The proposed FIRF method gives high accuracy, as well as requires low computation. The underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low-resolution image patch to high-resolution image patch. The FIRF framework consists of two stages. Stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image, while Stage 2 further refines the Stage 1 interpolated image. By varying the number of decision trees in the random forests and the number of stages applied, the proposed FIRF method can realize computationally scalable image interpolation. Extensive experimental results show that the proposed FIRF(3, 2) method achieves more than 0.3 dB improvement in peak signal-to-noise ratio over the state-of-the-art nonlocal autoregressive modeling (NARM) method. Moreover, the proposed FIRF(1, 1) obtains similar or better results as NARM while only takes its 0.3% computational time.

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

Tests of oceanic stochastic parameterisation in a seasonal forecast system.

NASA Astrophysics Data System (ADS)

Cooper, Fenwick; Andrejczuk, Miroslaw; Juricke, Stephan; Zanna, Laure; Palmer, Tim

2015-04-01

Over seasonal time scales, our aim is to compare the relative impact of ocean initial condition and model uncertainty, upon the ocean forecast skill and reliability. Over seasonal timescales we compare four oceanic stochastic parameterisation schemes applied in a 1x1 degree ocean model (NEMO) with a fully coupled T159 atmosphere (ECMWF IFS). The relative impacts upon the ocean of the resulting eddy induced activity, wind forcing and typical initial condition perturbations are quantified. Following the historical success of stochastic parameterisation in the atmosphere, two of the parameterisations tested were multiplicitave in nature: A stochastic variation of the Gent-McWilliams scheme and a stochastic diffusion scheme. We also consider a surface flux parameterisation (similar to that introduced by Williams, 2012), and stochastic perturbation of the equation of state (similar to that introduced by Brankart, 2013). The amplitude of the stochastic term in the Williams (2012) scheme was set to the physically reasonable amplitude considered in that paper. The amplitude of the stochastic term in each of the other schemes was increased to the limits of model stability. As expected, variability was increased. Up to 1 month after initialisation, ensemble spread induced by stochastic parameterisation is greater than that induced by the atmosphere, whilst being smaller than the initial condition perturbations currently used at ECMWF. After 1 month, the wind forcing becomes the dominant source of model ocean variability, even at depth.

Validation of the Poisson Stochastic Radiative Transfer Model

NASA Technical Reports Server (NTRS)

Zhuravleva, Tatiana; Marshak, Alexander

2004-01-01

A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough

PubMed Central

Black, Andrew J.; McKane, Alan J.

2010-01-01

Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle. PMID:20164086

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org. PMID:26063822

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

Visual characterization and diversity quantification of chemical libraries: 2. Analysis and selection of size-independent, subspace-specific diversity indices.

PubMed

Colliandre, Lionel; Le Guilloux, Vincent; Bourg, Stephane; Morin-Allory, Luc

2012-02-27

High Throughput Screening (HTS) is a standard technique widely used to find hit compounds in drug discovery projects. The high costs associated with such experiments have highlighted the need to carefully design screening libraries in order to avoid wasting resources. Molecular diversity is an established concept that has been used to this end for many years. In this article, a new approach to quantify the molecular diversity of screening libraries is presented. The approach is based on the Delimited Reference Chemical Subspace (DRCS) methodology, a new method that can be used to delimit the densest subspace spanned by a reference library in a reduced 2D continuous space. A total of 22 diversity indices were implemented or adapted to this methodology, which is used here to remove outliers and obtain a relevant cell-based partition of the subspace. The behavior of these indices was assessed and compared in various extreme situations and with respect to a set of theoretical rules that a diversity function should satisfy when libraries of different sizes have to be compared. Some gold standard indices are found inappropriate in such a context, while none of the tested indices behave perfectly in all cases. Five DRCS-based indices accounting for different aspects of diversity were finally selected, and a simple framework is proposed to use them effectively. Various libraries have been profiled with respect to more specific subspaces, which further illustrate the interest of the method.

Time-oriented hierarchical method for computation of principal components using subspace learning algorithm.

PubMed

Jankovic, Marko; Ogawa, Hidemitsu

2004-10-01

Principal Component Analysis (PCA) and Principal Subspace Analysis (PSA) are classic techniques in statistical data analysis, feature extraction and data compression. Given a set of multivariate measurements, PCA and PSA provide a smaller set of "basis vectors" with less redundancy, and a subspace spanned by them, respectively. Artificial neurons and neural networks have been shown to perform PSA and PCA when gradient ascent (descent) learning rules are used, which is related to the constrained maximization (minimization) of statistical objective functions. Due to their low complexity, such algorithms and their implementation in neural networks are potentially useful in cases of tracking slow changes of correlations in the input data or in updating eigenvectors with new samples. In this paper we propose PCA learning algorithm that is fully homogeneous with respect to neurons. The algorithm is obtained by modification of one of the most famous PSA learning algorithms--Subspace Learning Algorithm (SLA). Modification of the algorithm is based on Time-Oriented Hierarchical Method (TOHM). The method uses two distinct time scales. On a faster time scale PSA algorithm is responsible for the "behavior" of all output neurons. On a slower scale, output neurons will compete for fulfillment of their "own interests". On this scale, basis vectors in the principal subspace are rotated toward the principal eigenvectors. At the end of the paper it will be briefly analyzed how (or why) time-oriented hierarchical method can be used for transformation of any of the existing neural network PSA method, into PCA method.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Fei; Huang, Yongxi

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

DOE PAGES

Xie, Fei; Huang, Yongxi

2018-02-04

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

Improved Detection of Local Earthquakes in the Vienna Basin (Austria), using Subspace Detectors

NASA Astrophysics Data System (ADS)

Apoloner, Maria-Theresia; Caffagni, Enrico; Bokelmann, Götz

2016-04-01

The Vienna Basin in Eastern Austria is densely populated and highly-developed; it is also a region of low to moderate seismicity, yet the seismological network coverage is relatively sparse. This demands improving our capability of earthquake detection by testing new methods, enlarging the existing local earthquake catalogue. This contributes to imaging tectonic fault zones for better understanding seismic hazard, also through improved earthquake statistics (b-value, magnitude of completeness). Detection of low-magnitude earthquakes or events for which the highest amplitudes slightly exceed the signal-to-noise-ratio (SNR), may be possible by using standard methods like the short-term over long-term average (STA/LTA). However, due to sparse network coverage and high background noise, such a technique may not detect all potentially recoverable events. Yet, earthquakes originating from the same source region and relatively close to each other, should be characterized by similarity in seismic waveforms, at a given station. Therefore, waveform similarity can be exploited by using specific techniques such as correlation-template based (also known as matched filtering) or subspace detection methods (based on the subspace theory). Matching techniques basically require a reference or template event, usually characterized by high waveform coherence in the array receivers, and high SNR, which is cross-correlated with the continuous data. Instead, subspace detection methods overcome in principle the necessity of defining template events as single events, but use a subspace extracted from multiple events. This approach theoretically should be more robust in detecting signals that exhibit a strong variability (e.g. because of source or magnitude). In this study we scan the continuous data recorded in the Vienna Basin with a subspace detector to identify additional events. This will allow us to estimate the increase of the seismicity rate in the local earthquake catalogue, therefore providing an evaluation of network performance and efficiency of the method.

Information theoretic partitioning and confidence based weight assignment for multi-classifier decision level fusion in hyperspectral target recognition applications

NASA Astrophysics Data System (ADS)

Prasad, S.; Bruce, L. M.

2007-04-01

There is a growing interest in using multiple sources for automatic target recognition (ATR) applications. One approach is to take multiple, independent observations of a phenomenon and perform a feature level or a decision level fusion for ATR. This paper proposes a method to utilize these types of multi-source fusion techniques to exploit hyperspectral data when only a small number of training pixels are available. Conventional hyperspectral image based ATR techniques project the high dimensional reflectance signature onto a lower dimensional subspace using techniques such as Principal Components Analysis (PCA), Fisher's linear discriminant analysis (LDA), subspace LDA and stepwise LDA. While some of these techniques attempt to solve the curse of dimensionality, or small sample size problem, these are not necessarily optimal projections. In this paper, we present a divide and conquer approach to address the small sample size problem. The hyperspectral space is partitioned into contiguous subspaces such that the discriminative information within each subspace is maximized, and the statistical dependence between subspaces is minimized. We then treat each subspace as a separate source in a multi-source multi-classifier setup and test various decision fusion schemes to determine their efficacy. Unlike previous approaches which use correlation between variables for band grouping, we study the efficacy of higher order statistical information (using average mutual information) for a bottom up band grouping. We also propose a confidence measure based decision fusion technique, where the weights associated with various classifiers are based on their confidence in recognizing the training data. To this end, training accuracies of all classifiers are used for weight assignment in the fusion process of test pixels. The proposed methods are tested using hyperspectral data with known ground truth, such that the efficacy can be quantitatively measured in terms of target recognition accuracies.

Machine learning from computer simulations with applications in rail vehicle dynamics

NASA Astrophysics Data System (ADS)

Taheri, Mehdi; Ahmadian, Mehdi

2016-05-01

The application of stochastic modelling for learning the behaviour of a multibody dynamics (MBD) models is investigated. Post-processing data from a simulation run are used to train the stochastic model that estimates the relationship between model inputs (suspension relative displacement and velocity) and the output (sum of suspension forces). The stochastic model can be used to reduce the computational burden of the MBD model by replacing a computationally expensive subsystem in the model (suspension subsystem). With minor changes, the stochastic modelling technique is able to learn the behaviour of a physical system and integrate its behaviour within MBD models. The technique is highly advantageous for MBD models where real-time simulations are necessary, or with models that have a large number of repeated substructures, e.g. modelling a train with a large number of railcars. The fact that the training data are acquired prior to the development of the stochastic model discards the conventional sampling plan strategies like Latin Hypercube sampling plans where simulations are performed using the inputs dictated by the sampling plan. Since the sampling plan greatly influences the overall accuracy and efficiency of the stochastic predictions, a sampling plan suitable for the process is developed where the most space-filling subset of the acquired data with ? number of sample points that best describes the dynamic behaviour of the system under study is selected as the training data.

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

A chance-constrained stochastic approach to intermodal container routing problems.

PubMed

Zhao, Yi; Liu, Ronghui; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost.

A chance-constrained stochastic approach to intermodal container routing problems

PubMed Central

Zhao, Yi; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost. PMID:29438389

A stochastic SIS epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming

2017-11-01

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s < 1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

Stochastic volatility of the futures prices of emission allowances: A Bayesian approach

NASA Astrophysics Data System (ADS)

Kim, Jungmu; Park, Yuen Jung; Ryu, Doojin

2017-01-01

Understanding the stochastic nature of the spot volatility of emission allowances is crucial for risk management in emissions markets. In this study, by adopting a stochastic volatility model with or without jumps to represent the dynamics of European Union Allowances (EUA) futures prices, we estimate the daily volatilities and model parameters by using the Markov Chain Monte Carlo method for stochastic volatility (SV), stochastic volatility with return jumps (SVJ) and stochastic volatility with correlated jumps (SVCJ) models. Our empirical results reveal three important features of emissions markets. First, the data presented herein suggest that EUA futures prices exhibit significant stochastic volatility. Second, the leverage effect is noticeable regardless of whether or not jumps are included. Third, the inclusion of jumps has a significant impact on the estimation of the volatility dynamics. Finally, the market becomes very volatile and large jumps occur at the beginning of a new phase. These findings are important for policy makers and regulators.

Optimal Control Inventory Stochastic With Production Deteriorating

NASA Astrophysics Data System (ADS)

Affandi, Pardi

2018-01-01

In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.

Stochastic Game Analysis and Latency Awareness for Self-Adaptation

DTIC Science & Technology

2014-01-01

this paper, we introduce a formal analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to quantify the...Additional Key Words and Phrases: Proactive adaptation, Stochastic multiplayer games , Latency 1. INTRODUCTION When planning how to adapt, self-adaptive...contribution of this paper is twofold: (1) A novel analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to

Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances

NASA Astrophysics Data System (ADS)

Zhang, Weiwei; Meng, Xinzhu

2018-02-01

In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal diffusion appears much slower than the particle velocity of each molecule. The concept of stochastic triggering originates in the Brownian walk model [Ide, 2008], and the present study introduces the stochastic dynamics into dynamic simulations. The stochastic dynamic model has the potential to explain both regular and slow earthquakes more realistically.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Re-Sonification of Objects, Events, and Environments

NASA Astrophysics Data System (ADS)

Fink, Alex M.

Digital sound synthesis allows the creation of a great variety of sounds. Focusing on interesting or ecologically valid sounds for music, simulation, aesthetics, or other purposes limits the otherwise vast digital audio palette. Tools for creating such sounds vary from arbitrary methods of altering recordings to precise simulations of vibrating objects. In this work, methods of sound synthesis by re-sonification are considered. Re-sonification, herein, refers to the general process of analyzing, possibly transforming, and resynthesizing or reusing recorded sounds in meaningful ways, to convey information. Applied to soundscapes, re-sonification is presented as a means of conveying activity within an environment. Applied to the sounds of objects, this work examines modeling the perception of objects as well as their physical properties and the ability to simulate interactive events with such objects. To create soundscapes to re-sonify geographic environments, a method of automated soundscape design is presented. Using recorded sounds that are classified based on acoustic, social, semantic, and geographic information, this method produces stochastically generated soundscapes to re-sonify selected geographic areas. Drawing on prior knowledge, local sounds and those deemed similar comprise a locale's soundscape. In the context of re-sonifying events, this work examines processes for modeling and estimating the excitations of sounding objects. These include plucking, striking, rubbing, and any interaction that imparts energy into a system, affecting the resultant sound. A method of estimating a linear system's input, constrained to a signal-subspace, is presented and applied toward improving the estimation of percussive excitations for re-sonification. To work toward robust recording-based modeling and re-sonification of objects, new implementations of banded waveguide (BWG) models are proposed for object modeling and sound synthesis. Previous implementations of BWGs use arbitrary model parameters and may produce a range of simulations that do not match digital waveguide or modal models of the same design. Subject to linear excitations, some models proposed here behave identically to other equivalently designed physical models. Under nonlinear interactions, such as bowing, many of the proposed implementations exhibit improvements in the attack characteristics of synthesized sounds.

Density scaling for multiplets

NASA Astrophysics Data System (ADS)

Nagy, Á.

2011-02-01

Generalized Kohn-Sham equations are presented for lowest-lying multiplets. The way of treating non-integer particle numbers is coupled with an earlier method of the author. The fundamental quantity of the theory is the subspace density. The Kohn-Sham equations are similar to the conventional Kohn-Sham equations. The difference is that the subspace density is used instead of the density and the Kohn-Sham potential is different for different subspaces. The exchange-correlation functional is studied using density scaling. It is shown that there exists a value of the scaling factor ζ for which the correlation energy disappears. Generalized OPM and Krieger-Li-Iafrate (KLI) methods incorporating correlation are presented. The ζKLI method, being as simple as the original KLI method, is proposed for multiplets.

Primary decomposition of zero-dimensional ideals over finite fields

NASA Astrophysics Data System (ADS)

Gao, Shuhong; Wan, Daqing; Wang, Mingsheng

2009-03-01

A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp's algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a complete decomposition. Unlike previous approaches for decomposing multivariate polynomial systems, the new method does not need primality testing nor any generic projection, instead it reduces the general decomposition problem directly to root finding of univariate polynomials over the ground field. Also, it is shown how Groebner basis structure can be used to get partial primary decomposition without any root finding.

Modeling the lake eutrophication stochastic ecosystem and the research of its stability.

PubMed

Wang, Bo; Qi, Qianqian

2018-06-01

In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e., nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0,  0.388644) and (0.66003825,  1.0), there only exists a stable equilibrium state and the additive noise intensity could not change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be capable of effectively explaining the regime shift theory and agreed with the realistic analyze. These conclusions also confirms the two paths for the system to move from one stable state to another proposed by Beisner et al. [3], which may help understand the occurrence mechanism related to the lake eutrophication from the view point of the stochastic model and mathematical analysis. Copyright © 2018 Elsevier Inc. All rights reserved.

Importance of vesicle release stochasticity in neuro-spike communication.

PubMed

Ramezani, Hamideh; Akan, Ozgur B

2017-07-01

Aim of this paper is proposing a stochastic model for vesicle release process, a part of neuro-spike communication. Hence, we study biological events occurring in this process and use microphysiological simulations to observe functionality of these events. Since the most important source of variability in vesicle release probability is opening of voltage dependent calcium channels (VDCCs) followed by influx of calcium ions through these channels, we propose a stochastic model for this event, while using a deterministic model for other variability sources. To capture the stochasticity of calcium influx to pre-synaptic neuron in our model, we study its statistics and find that it can be modeled by a distribution defined based on Normal and Logistic distributions.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Stochastic Modeling of Laminar-Turbulent Transition

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Choudhari, Meelan

2002-01-01

Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

Stochastic modeling of consumer preferences for health care institutions.

PubMed

Malhotra, N K

1983-01-01

This paper proposes a stochastic procedure for modeling consumer preferences via LOGIT analysis. First, a simple, non-technical exposition of the use of a stochastic approach in health care marketing is presented. Second, a study illustrating the application of the LOGIT model in assessing consumer preferences for hospitals is given. The paper concludes with several implications of the proposed approach.

Fusion of Hard and Soft Information in Nonparametric Density Estimation

DTIC Science & Technology

2015-06-10

and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum...particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output...an essential step in simulation analysis and stochastic optimization is the generation of probability densities for input random variables; see for

The threshold of a stochastic avian-human influenza epidemic model with psychological effect

NASA Astrophysics Data System (ADS)

Zhang, Fengrong; Zhang, Xinhong

2018-02-01

In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.

Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model

NASA Astrophysics Data System (ADS)

Xue, Chi; Goldenfeld, Nigel

2017-12-01

The "kill the winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the kill the winner paradigm and show that the stable coexistence state of the deterministic kill the winner model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promotes the high diversity of the ecosystem by generating a persistent population flux of species.

Stochastic mixed-mode oscillations in a three-species predator-prey model

NASA Astrophysics Data System (ADS)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

Tsunamis: stochastic models of occurrence and generation mechanisms

USGS Publications Warehouse

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

Conditional Subspace Clustering of Skill Mastery: Identifying Skills that Separate Students

ERIC Educational Resources Information Center

Nugent, Rebecca; Ayers, Elizabeth; Dean, Nema

2009-01-01

In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. We adopt a faster, simpler approach:…

Addressing model uncertainty through stochastic parameter perturbations within the High Resolution Rapid Refresh (HRRR) ensemble

NASA Astrophysics Data System (ADS)

Wolff, J.; Jankov, I.; Beck, J.; Carson, L.; Frimel, J.; Harrold, M.; Jiang, H.

2016-12-01

It is well known that global and regional numerical weather prediction ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system for addressing the deficiencies in ensemble modeling is the use of stochastic physics to represent model-related uncertainty. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), Stochastic Perturbation of Physics Tendencies (SPPT), or some combination of all three. The focus of this study is to assess the model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) when using stochastic approaches. For this purpose, the test utilized a single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model, with ensemble members produced by employing stochastic methods. Parameter perturbations were employed in the Rapid Update Cycle (RUC) land surface model and Mellor-Yamada-Nakanishi-Niino (MYNN) planetary boundary layer scheme. Results will be presented in terms of bias, error, spread, skill, accuracy, reliability, and sharpness using the Model Evaluation Tools (MET) verification package. Due to the high level of complexity of running a frequently updating (hourly), high spatial resolution (3 km), large domain (CONUS) ensemble system, extensive high performance computing (HPC) resources were needed to meet this objective. Supercomputing resources were provided through the National Center for Atmospheric Research (NCAR) Strategic Capability (NSC) project support, allowing for a more extensive set of tests over multiple seasons, consequently leading to more robust results. Through the use of these stochastic innovations and powerful supercomputing at NCAR, further insights and advancements in ensemble forecasting at convection-permitting scales will be possible.

Detecting and characterizing coal mine related seismicity in the Western U.S. using subspace methods

NASA Astrophysics Data System (ADS)

Chambers, Derrick J. A.; Koper, Keith D.; Pankow, Kristine L.; McCarter, Michael K.

2015-11-01

We present an approach for subspace detection of small seismic events that includes methods for estimating magnitudes and associating detections from multiple stations into unique events. The process is used to identify mining related seismicity from a surface coal mine and an underground coal mining district, both located in the Western U.S. Using a blasting log and a locally derived seismic catalogue as ground truth, we assess detector performance in terms of verified detections, false positives and failed detections. We are able to correctly identify over 95 per cent of the surface coal mine blasts and about 33 per cent of the events from the underground mining district, while keeping the number of potential false positives relatively low by requiring all detections to occur on two stations. We find that most of the potential false detections for the underground coal district are genuine events missed by the local seismic network, demonstrating the usefulness of regional subspace detectors in augmenting local catalogues. We note a trade-off in detection performance between stations at smaller source-receiver distances, which have increased signal-to-noise ratio, and stations at larger distances, which have greater waveform similarity. We also explore the increased detection capabilities of a single higher dimension subspace detector, compared to multiple lower dimension detectors, in identifying events that can be described as linear combinations of training events. We find, in our data set, that such an advantage can be significant, justifying the use of a subspace detection scheme over conventional correlation methods.

Hyperspectral Super-Resolution of Locally Low Rank Images From Complementary Multisource Data.

PubMed

Veganzones, Miguel A; Simoes, Miguel; Licciardi, Giorgio; Yokoya, Naoto; Bioucas-Dias, Jose M; Chanussot, Jocelyn

2016-01-01

Remote sensing hyperspectral images (HSIs) are quite often low rank, in the sense that the data belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial resolution multispectral images in order to obtain super-resolution HSI. Most approaches adopt an unmixing or a matrix factorization perspective. The derived methods have led to state-of-the-art results when the spectral information lies in a low-dimensional subspace/manifold. However, if the subspace/manifold dimensionality spanned by the complete data set is large, i.e., larger than the number of multispectral bands, the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill-posed. In this paper, we propose a local approach to cope with this difficulty. Fundamentally, we exploit the fact that real world HSIs are locally low rank, that is, pixels acquired from a given spatial neighborhood span a very low-dimensional subspace/manifold, i.e., lower or equal than the number of multispectral bands. Thus, we propose to partition the image into patches and solve the data fusion problem independently for each patch. This way, in each patch the subspace/manifold dimensionality is low enough, such that the problem is not ill-posed anymore. We propose two alternative approaches to define the hyperspectral super-resolution through local dictionary learning using endmember induction algorithms. We also explore two alternatives to define the local regions, using sliding windows and binary partition trees. The effectiveness of the proposed approaches is illustrated with synthetic and semi real data.

Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein-Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Pavluchenko, Sergey A.; Toporensky, Alexey

2018-05-01

In this paper we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies—spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part of the paper we consider the cosmological evolution of spaces that are the product of two isotropic and spatially curved subspaces. It is demonstrated that the dynamics in D=2 (the number of extra dimensions) and D ≥ 3 is different. It was already known that for the Λ -term case there is a regime with "stabilization" of extra dimensions, where the expansion rate of the three-dimensional subspace as well as the scale factor (the "size") associated with extra dimensions reaches a constant value. This regime is achieved if the curvature of the extra dimensions is negative. We demonstrate that it takes place only if the number of extra dimensions is D ≥ 3. In the second part of the paper we study the influence of the initial anisotropy. Our study reveals that the transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with three expanding and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. However, the details of the dynamics in D=2 and D ≥ 3 are different. Combining the two described effects allows us to construct a scenario in D ≥ 3, where isotropization of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

The ISI distribution of the stochastic Hodgkin-Huxley neuron.

PubMed

Rowat, Peter F; Greenwood, Priscilla E

2014-01-01

The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.

A stochastic visco-hyperelastic model of human placenta tissue for finite element crash simulations.

PubMed

Hu, Jingwen; Klinich, Kathleen D; Miller, Carl S; Rupp, Jonathan D; Nazmi, Giseli; Pearlman, Mark D; Schneider, Lawrence W

2011-03-01

Placental abruption is the most common cause of fetal deaths in motor-vehicle crashes, but studies on the mechanical properties of human placenta are rare. This study presents a new method of developing a stochastic visco-hyperelastic material model of human placenta tissue using a combination of uniaxial tensile testing, specimen-specific finite element (FE) modeling, and stochastic optimization techniques. In our previous study, uniaxial tensile tests of 21 placenta specimens have been performed using a strain rate of 12/s. In this study, additional uniaxial tensile tests were performed using strain rates of 1/s and 0.1/s on 25 placenta specimens. Response corridors for the three loading rates were developed based on the normalized data achieved by test reconstructions of each specimen using specimen-specific FE models. Material parameters of a visco-hyperelastic model and their associated standard deviations were tuned to match both the means and standard deviations of all three response corridors using a stochastic optimization method. The results show a very good agreement between the tested and simulated response corridors, indicating that stochastic analysis can improve estimation of variability in material model parameters. The proposed method can be applied to develop stochastic material models of other biological soft tissues.

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

PubMed

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Active shape models unleashed

NASA Astrophysics Data System (ADS)

Kirschner, Matthias; Wesarg, Stefan

2011-03-01

Active Shape Models (ASMs) are a popular family of segmentation algorithms which combine local appearance models for boundary detection with a statistical shape model (SSM). They are especially popular in medical imaging due to their ability for fast and accurate segmentation of anatomical structures even in large and noisy 3D images. A well-known limitation of ASMs is that the shape constraints are over-restrictive, because the segmentations are bounded by the Principal Component Analysis (PCA) subspace learned from the training data. To overcome this limitation, we propose a new energy minimization approach which combines an external image energy with an internal shape model energy. Our shape energy uses the Distance From Feature Space (DFFS) concept to allow deviations from the PCA subspace in a theoretically sound and computationally fast way. In contrast to previous approaches, our model does not rely on post-processing with constrained free-form deformation or additional complex local energy models. In addition to the energy minimization approach, we propose a new method for liver detection, a new method for initializing an SSM and an improved k-Nearest Neighbour (kNN)-classifier for boundary detection. Our ASM is evaluated with leave-one-out tests on a data set with 34 tomographic CT scans of the liver and is compared to an ASM with standard shape constraints. The quantitative results of our experiments show that we achieve higher segmentation accuracy with our energy minimization approach than with standard shape constraints.nym

Blind Source Separation for Unimodal and Multimodal Brain Networks: A Unifying Framework for Subspace Modeling

PubMed Central

Silva, Rogers F.; Plis, Sergey M.; Sui, Jing; Pattichis, Marios S.; Adalı, Tülay; Calhoun, Vince D.

2016-01-01

In the past decade, numerous advances in the study of the human brain were fostered by successful applications of blind source separation (BSS) methods to a wide range of imaging modalities. The main focus has been on extracting “networks” represented as the underlying latent sources. While the broad success in learning latent representations from multiple datasets has promoted the wide presence of BSS in modern neuroscience, it also introduced a wide variety of objective functions, underlying graphical structures, and parameter constraints for each method. Such diversity, combined with a host of datatype-specific know-how, can cause a sense of disorder and confusion, hampering a practitioner’s judgment and impeding further development. We organize the diverse landscape of BSS models by exposing its key features and combining them to establish a novel unifying view of the area. In the process, we unveil important connections among models according to their properties and subspace structures. Consequently, a high-level descriptive structure is exposed, ultimately helping practitioners select the right model for their applications. Equipped with that knowledge, we review the current state of BSS applications to neuroimaging. The gained insight into model connections elicits a broader sense of generalization, highlighting several directions for model development. In light of that, we discuss emerging multi-dataset multidimensional (MDM) models and summarize their benefits for the study of the healthy brain and disease-related changes. PMID:28461840

On spectral synthesis on element-wise compact Abelian groups

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2015-08-01

Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.

N-Screen Aware Multicriteria Hybrid Recommender System Using Weight Based Subspace Clustering

PubMed Central

Ullah, Farman; Lee, Sungchang

2014-01-01

This paper presents a recommender system for N-screen services in which users have multiple devices with different capabilities. In N-screen services, a user can use various devices in different locations and time and can change a device while the service is running. N-screen aware recommendation seeks to improve the user experience with recommended content by considering the user N-screen device attributes such as screen resolution, media codec, remaining battery time, and access network and the user temporal usage pattern information that are not considered in existing recommender systems. For N-screen aware recommendation support, this work introduces a user device profile collaboration agent, manager, and N-screen control server to acquire and manage the user N-screen devices profile. Furthermore, a multicriteria hybrid framework is suggested that incorporates the N-screen devices information with user preferences and demographics. In addition, we propose an individual feature and subspace weight based clustering (IFSWC) to assign different weights to each subspace and each feature within a subspace in the hybrid framework. The proposed system improves the accuracy, precision, scalability, sparsity, and cold start issues. The simulation results demonstrate the effectiveness and prove the aforementioned statements. PMID:25152921

Wavelet Analyses of F/A-18 Aeroelastic and Aeroservoelastic Flight Test Data

NASA Technical Reports Server (NTRS)

Brenner, Martin J.

1997-01-01

Time-frequency signal representations combined with subspace identification methods were used to analyze aeroelastic flight data from the F/A-18 Systems Research Aircraft (SRA) and aeroservoelastic data from the F/A-18 High Alpha Research Vehicle (HARV). The F/A-18 SRA data were produced from a wingtip excitation system that generated linear frequency chirps and logarithmic sweeps. HARV data were acquired from digital Schroeder-phased and sinc pulse excitation signals to actuator commands. Nondilated continuous Morlet wavelets implemented as a filter bank were chosen for the time-frequency analysis to eliminate phase distortion as it occurs with sliding window discrete Fourier transform techniques. Wavelet coefficients were filtered to reduce effects of noise and nonlinear distortions identically in all inputs and outputs. Cleaned reconstructed time domain signals were used to compute improved transfer functions. Time and frequency domain subspace identification methods were applied to enhanced reconstructed time domain data and improved transfer functions, respectively. Time domain subspace performed poorly, even with the enhanced data, compared with frequency domain techniques. A frequency domain subspace method is shown to produce better results with the data processed using the Morlet time-frequency technique.

Anomaly Detection in Moving-Camera Video Sequences Using Principal Subspace Analysis

DOE PAGES

Thomaz, Lucas A.; Jardim, Eric; da Silva, Allan F.; ...

2017-10-16

This study presents a family of algorithms based on sparse decompositions that detect anomalies in video sequences obtained from slow moving cameras. These algorithms start by computing the union of subspaces that best represents all the frames from a reference (anomaly free) video as a low-rank projection plus a sparse residue. Then, they perform a low-rank representation of a target (possibly anomalous) video by taking advantage of both the union of subspaces and the sparse residue computed from the reference video. Such algorithms provide good detection results while at the same time obviating the need for previous video synchronization. However,more » this is obtained at the cost of a large computational complexity, which hinders their applicability. Another contribution of this paper approaches this problem by using intrinsic properties of the obtained data representation in order to restrict the search space to the most relevant subspaces, providing computational complexity gains of up to two orders of magnitude. The developed algorithms are shown to cope well with videos acquired in challenging scenarios, as verified by the analysis of 59 videos from the VDAO database that comprises videos with abandoned objects in a cluttered industrial scenario.« less

Anomaly Detection in Moving-Camera Video Sequences Using Principal Subspace Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomaz, Lucas A.; Jardim, Eric; da Silva, Allan F.

This study presents a family of algorithms based on sparse decompositions that detect anomalies in video sequences obtained from slow moving cameras. These algorithms start by computing the union of subspaces that best represents all the frames from a reference (anomaly free) video as a low-rank projection plus a sparse residue. Then, they perform a low-rank representation of a target (possibly anomalous) video by taking advantage of both the union of subspaces and the sparse residue computed from the reference video. Such algorithms provide good detection results while at the same time obviating the need for previous video synchronization. However,more » this is obtained at the cost of a large computational complexity, which hinders their applicability. Another contribution of this paper approaches this problem by using intrinsic properties of the obtained data representation in order to restrict the search space to the most relevant subspaces, providing computational complexity gains of up to two orders of magnitude. The developed algorithms are shown to cope well with videos acquired in challenging scenarios, as verified by the analysis of 59 videos from the VDAO database that comprises videos with abandoned objects in a cluttered industrial scenario.« less

Constrained Low-Rank Learning Using Least Squares-Based Regularization.

PubMed

Li, Ping; Yu, Jun; Wang, Meng; Zhang, Luming; Cai, Deng; Li, Xuelong

2017-12-01

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. Moreover, the low-dimensional representation of original data can be paired with some informative structure by imposing an appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a novel constrained LRR method. The objective function is formulated as a constrained nuclear norm minimization problem, which can be solved by the inexact augmented Lagrange multiplier algorithm. Extensive experiments on image classification, human pose estimation, and robust face recovery have confirmed the superiority of our method.

Biomedical image classification based on a cascade of an SVM with a reject option and subspace analysis.

PubMed

Lin, Dongyun; Sun, Lei; Toh, Kar-Ann; Zhang, Jing Bo; Lin, Zhiping

2018-05-01

Automated biomedical image classification could confront the challenges of high level noise, image blur, illumination variation and complicated geometric correspondence among various categorical biomedical patterns in practice. To handle these challenges, we propose a cascade method consisting of two stages for biomedical image classification. At stage 1, we propose a confidence score based classification rule with a reject option for a preliminary decision using the support vector machine (SVM). The testing images going through stage 1 are separated into two groups based on their confidence scores. Those testing images with sufficiently high confidence scores are classified at stage 1 while the others with low confidence scores are rejected and fed to stage 2. At stage 2, the rejected images from stage 1 are first processed by a subspace analysis technique called eigenfeature regularization and extraction (ERE), and then classified by another SVM trained in the transformed subspace learned by ERE. At both stages, images are represented based on two types of local features, i.e., SIFT and SURF, respectively. They are encoded using various bag-of-words (BoW) models to handle biomedical patterns with and without geometric correspondence, respectively. Extensive experiments are implemented to evaluate the proposed method on three benchmark real-world biomedical image datasets. The proposed method significantly outperforms several competing state-of-the-art methods in terms of classification accuracy. Copyright © 2018 Elsevier Ltd. All rights reserved.

On the analysis and comparison of conformer-specific essential dynamics upon ligand binding to a protein.

PubMed

Grosso, Marcos; Kalstein, Adrian; Parisi, Gustavo; Roitberg, Adrian E; Fernandez-Alberti, Sebastian

2015-06-28

The native state of a protein consists of an equilibrium of conformational states on an energy landscape rather than existing as a single static state. The co-existence of conformers with different ligand-affinities in a dynamical equilibrium is the basis for the conformational selection model for ligand binding. In this context, the development of theoretical methods that allow us to analyze not only the structural changes but also changes in the fluctuation patterns between conformers will contribute to elucidate the differential properties acquired upon ligand binding. Molecular dynamics simulations can provide the required information to explore these features. Its use in combination with subsequent essential dynamics analysis allows separating large concerted conformational rearrangements from irrelevant fluctuations. We present a novel procedure to define the size and composition of essential dynamics subspaces associated with ligand-bound and ligand-free conformations. These definitions allow us to compare essential dynamics subspaces between different conformers. Our procedure attempts to emphasize the main similarities and differences between the different essential dynamics in an unbiased way. Essential dynamics subspaces associated to conformational transitions can also be analyzed. As a test case, we study the glutaminase interacting protein (GIP), composed of a single PDZ domain. Both GIP ligand-free state and glutaminase L peptide-bound states are analyzed. Our findings concerning the relative changes in the flexibility pattern upon binding are in good agreement with experimental Nuclear Magnetic Resonance data.

On the analysis and comparison of conformer-specific essential dynamics upon ligand binding to a protein

NASA Astrophysics Data System (ADS)

Grosso, Marcos; Kalstein, Adrian; Parisi, Gustavo; Roitberg, Adrian E.; Fernandez-Alberti, Sebastian

2015-06-01

The native state of a protein consists of an equilibrium of conformational states on an energy landscape rather than existing as a single static state. The co-existence of conformers with different ligand-affinities in a dynamical equilibrium is the basis for the conformational selection model for ligand binding. In this context, the development of theoretical methods that allow us to analyze not only the structural changes but also changes in the fluctuation patterns between conformers will contribute to elucidate the differential properties acquired upon ligand binding. Molecular dynamics simulations can provide the required information to explore these features. Its use in combination with subsequent essential dynamics analysis allows separating large concerted conformational rearrangements from irrelevant fluctuations. We present a novel procedure to define the size and composition of essential dynamics subspaces associated with ligand-bound and ligand-free conformations. These definitions allow us to compare essential dynamics subspaces between different conformers. Our procedure attempts to emphasize the main similarities and differences between the different essential dynamics in an unbiased way. Essential dynamics subspaces associated to conformational transitions can also be analyzed. As a test case, we study the glutaminase interacting protein (GIP), composed of a single PDZ domain. Both GIP ligand-free state and glutaminase L peptide-bound states are analyzed. Our findings concerning the relative changes in the flexibility pattern upon binding are in good agreement with experimental Nuclear Magnetic Resonance data.

Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ceccato, Alessandro; Frezzato, Diego, E-mail: diego.frezzato@unipd.it; Nicolini, Paolo

In this work, we deal with general reactive systems involving N species and M elementary reactions under applicability of the mass-action law. Starting from the dynamic variables introduced in two previous works [P. Nicolini and D. Frezzato, J. Chem. Phys. 138(23), 234101 (2013); 138(23), 234102 (2013)], we turn to a new representation in which the system state is specified in a (N × M){sup 2}-dimensional space by a point whose coordinates have physical dimension of inverse-of-time. By adopting hyper-spherical coordinates (a set of dimensionless “angular” variables and a single “radial” one with physical dimension of inverse-of-time) and by examining themore » properties of their evolution law both formally and numerically on model kinetic schemes, we show that the system evolves towards the equilibrium as being attracted by a sequence of fixed subspaces (one at a time) each associated with a compact domain of the concentration space. Thus, we point out that also for general non-linear kinetics there exist fixed “objects” on the global scale, although they are conceived in such an abstract and extended space. Moreover, we propose a link between the persistence of the belonging of a trajectory to such subspaces and the closeness to the slow manifold which would be perceived by looking at the bundling of the trajectories in the concentration space.« less

Acceleration of GPU-based Krylov solvers via data transfer reduction

DOE PAGES

Anzt, Hartwig; Tomov, Stanimire; Luszczek, Piotr; ...

2015-04-08

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to reduce certain data communications, and hence fail to leverage the full potential of the accelerator. In this study, we target the acceleration of Krylov subspace iterative methods for graphicsmore » processing units, and in particular the Biconjugate Gradient Stabilized solver that significant improvement can be achieved by reformulating the method to reduce data-communications through application-specific kernels instead of using the generic BLAS kernels, e.g. as provided by NVIDIA’s cuBLAS library, and by designing a graphics processing unit specific sparse matrix-vector product kernel that is able to more efficiently use the graphics processing unit’s computing power. Furthermore, we derive a model estimating the performance improvement, and use experimental data to validate the expected runtime savings. Finally, considering that the derived implementation achieves significantly higher performance, we assert that similar optimizations addressing algorithm structure, as well as sparse matrix-vector, are crucial for the subsequent development of high-performance graphics processing units accelerated Krylov subspace iterative methods.« less

Dynamics of a stochastic HIV-1 infection model with logistic growth

NASA Astrophysics Data System (ADS)

Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan

2017-03-01

This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.

Stochastic Radiative Transfer Model for Contaminated Rough Surfaces: A Framework for Detection System Design

DTIC Science & Technology

2013-11-01

STOCHASTIC RADIATIVE TRANSFER MODEL FOR CONTAMINATED ROUGH SURFACES: A...of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid ...COVERED (From - To) Jan 2013 - Sep 2013 4. TITLE AND SUBTITLE Stochastic Radiative Transfer Model for Contaminated Rough Surfaces: A Framework for

Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

PubMed

Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong

2014-12-01

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

Evaluation of Stochastic Rainfall Models in Capturing Climate Variability for Future Drought and Flood Risk Assessment

NASA Astrophysics Data System (ADS)

Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Kiem, A.; Nadeeka, P. M.

2016-12-01

One of the key objectives of stochastic rainfall modelling is to capture the full variability of climate system for future drought and flood risk assessment. However, it is not clear how well these models can capture the future climate variability when they are calibrated to Global/Regional Climate Model data (GCM/RCM) as these datasets are usually available for very short future period/s (e.g. 20 years). This study has assessed the ability of two stochastic daily rainfall models to capture climate variability by calibrating them to a dynamically downscaled RCM dataset in an east Australian catchment for 1990-2010, 2020-2040, and 2060-2080 epochs. The two stochastic models are: (1) a hierarchical Markov Chain (MC) model, which we developed in a previous study and (2) a semi-parametric MC model developed by Mehrotra and Sharma (2007). Our hierarchical model uses stochastic parameters of MC and Gamma distribution, while the semi-parametric model uses a modified MC process with memory of past periods and kernel density estimation. This study has generated multiple realizations of rainfall series by using parameters of each model calibrated to the RCM dataset for each epoch. The generated rainfall series are used to generate synthetic streamflow by using a SimHyd hydrology model. Assessing the synthetic rainfall and streamflow series, this study has found that both stochastic models can incorporate a range of variability in rainfall as well as streamflow generation for both current and future periods. However, the hierarchical model tends to overestimate the multiyear variability of wet spell lengths (therefore, is less likely to simulate long periods of drought and flood), while the semi-parametric model tends to overestimate the mean annual rainfall depths and streamflow volumes (hence, simulated droughts are likely to be less severe). Sensitivity of these limitations of both stochastic models in terms of future drought and flood risk assessment will be discussed.

Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

NASA Astrophysics Data System (ADS)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using all three stochastic approaches to address model uncertainty. Results from the stochastic perturbation testing were compared to a baseline multi-physics control ensemble. For probabilistic forecast performance the Model Evaluation Tools (MET) verification package was used.

Partial ASL extensions for stochastic programming.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

Expedited Holonomic Quantum Computation via Net Zero-Energy-Cost Control in Decoherence-Free Subspace.

PubMed

Pyshkin, P V; Luo, Da-Wei; Jing, Jun; You, J Q; Wu, Lian-Ao

2016-11-25

Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. This control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an expedited holonomic quantum computation protocol.

Expedited Holonomic Quantum Computation via Net Zero-Energy-Cost Control in Decoherence-Free Subspace

PubMed Central

Pyshkin, P. V.; Luo, Da-Wei; Jing, Jun; You, J. Q.; Wu, Lian-Ao

2016-01-01

Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. This control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an expedited holonomic quantum computation protocol. PMID:27886234

A sub-space greedy search method for efficient Bayesian Network inference.

PubMed

Zhang, Qing; Cao, Yong; Li, Yong; Zhu, Yanming; Sun, Samuel S M; Guo, Dianjing

2011-09-01

Bayesian network (BN) has been successfully used to infer the regulatory relationships of genes from microarray dataset. However, one major limitation of BN approach is the computational cost because the calculation time grows more than exponentially with the dimension of the dataset. In this paper, we propose a sub-space greedy search method for efficient Bayesian Network inference. Particularly, this method limits the greedy search space by only selecting gene pairs with higher partial correlation coefficients. Using both synthetic and real data, we demonstrate that the proposed method achieved comparable results with standard greedy search method yet saved ∼50% of the computational time. We believe that sub-space search method can be widely used for efficient BN inference in systems biology. Copyright © 2011 Elsevier Ltd. All rights reserved.

Geometrical eigen-subspace framework based molecular conformation representation for efficient structure recognition and comparison

NASA Astrophysics Data System (ADS)

Li, Xiao-Tian; Yang, Xiao-Bao; Zhao, Yu-Jun

2017-04-01

We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace projection function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.

Experimental creation of quantum Zeno subspaces by repeated multi-spin projections in diamond

NASA Astrophysics Data System (ADS)

Kalb, N.; Cramer, J.; Twitchen, D. J.; Markham, M.; Hanson, R.; Taminiau, T. H.

2016-10-01

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

PubMed

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

NASA Astrophysics Data System (ADS)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Information-theoretic model selection for optimal prediction of stochastic dynamical systems from data

NASA Astrophysics Data System (ADS)

Darmon, David

2018-03-01

In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error

NASA Astrophysics Data System (ADS)

El-Diasty, M.; El-Rabbany, A.; Pagiatakis, S.

2007-11-01

We examine the effect of varying the temperature points on MEMS inertial sensors' noise models using Allan variance and least-squares spectral analysis (LSSA). Allan variance is a method of representing root-mean-square random drift error as a function of averaging times. LSSA is an alternative to the classical Fourier methods and has been applied successfully by a number of researchers in the study of the noise characteristics of experimental series. Static data sets are collected at different temperature points using two MEMS-based IMUs, namely MotionPakII and Crossbow AHRS300CC. The performance of the two MEMS inertial sensors is predicted from the Allan variance estimation results at different temperature points and the LSSA is used to study the noise characteristics and define the sensors' stochastic model parameters. It is shown that the stochastic characteristics of MEMS-based inertial sensors can be identified using Allan variance estimation and LSSA and the sensors' stochastic model parameters are temperature dependent. Also, the Kaiser window FIR low-pass filter is used to investigate the effect of de-noising stage on the stochastic model. It is shown that the stochastic model is also dependent on the chosen cut-off frequency.

Attenuation Factors for B(E2) in the Microscopic Description of Multiphonon States ---A Simple Model Analysis---

NASA Astrophysics Data System (ADS)

Matsuyanagi, K.

1982-05-01

With an exactly solvable O(4) model of Piepenbring, Silvestre-Brac and Szymanski, we demonstrate that the attenuation factor for the B(E2) values, derived by the lowest-order approximation of the multiphonon method, takes excellent care of the kinematical anharmonicity effects, if multiphonon states are defined in the intrinsic subspace orthogonal to the pairing rotation. It is also shown that the other attenuation effect characterizing the interacting boson model is not a dominant effect in the model analysed here.

A developmental basis for stochasticity in floral organ numbers

PubMed Central

Kitazawa, Miho S.; Fujimoto, Koichi

2014-01-01

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. PMID:25404932

A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

PubMed Central

2006-01-01

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

Studying Resist Stochastics with the Multivariate Poisson Propagation Model

DOE PAGES

Naulleau, Patrick; Anderson, Christopher; Chao, Weilun; ...

2014-01-01

Progress in the ultimate performance of extreme ultraviolet resist has arguably decelerated in recent years suggesting an approach to stochastic limits both in photon counts and material parameters. Here we report on the performance of a variety of leading extreme ultraviolet resist both with and without chemical amplification. The measured performance is compared to stochastic modeling results using the Multivariate Poisson Propagation Model. The results show that the best materials are indeed nearing modeled performance limits.

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Stochastic Ocean Eddy Perturbations in a Coupled General Circulation Model.

NASA Astrophysics Data System (ADS)

Howe, N.; Williams, P. D.; Gregory, J. M.; Smith, R. S.

2014-12-01

High-resolution ocean models, which are eddy permitting and resolving, require large computing resources to produce centuries worth of data. Also, some previous studies have suggested that increasing resolution does not necessarily solve the problem of unresolved scales, because it simply introduces a new set of unresolved scales. Applying stochastic parameterisations to ocean models is one solution that is expected to improve the representation of small-scale (eddy) effects without increasing run-time. Stochastic parameterisation has been shown to have an impact in atmosphere-only models and idealised ocean models, but has not previously been studied in ocean general circulation models. Here we apply simple stochastic perturbations to the ocean temperature and salinity tendencies in the low-resolution coupled climate model, FAMOUS. The stochastic perturbations are implemented according to T(t) = T(t-1) + (ΔT(t) + ξ(t)), where T is temperature or salinity, ΔT is the corresponding deterministic increment in one time step, and ξ(t) is Gaussian noise. We use high-resolution HiGEM data coarse-grained to the FAMOUS grid to provide information about the magnitude and spatio-temporal correlation structure of the noise to be added to the lower resolution model. Here we present results of adding white and red noise, showing the impacts of an additive stochastic perturbation on mean climate state and variability in an AOGCM.

Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread

NASA Astrophysics Data System (ADS)

Billings, Lora; Bollt, Erik M.; Schwartz, Ira B.

2002-06-01

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

Explicit treatment for Dirichlet, Neumann and Cauchy boundary conditions in POD-based reduction of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2018-05-01

In recent years, proper orthogonal decomposition (POD) has become a popular model reduction method in the field of groundwater modeling. It is used to mitigate the problem of long run times that are often associated with physically-based modeling of natural systems, especially for parameter estimation and uncertainty analysis. POD-based techniques reproduce groundwater head fields sufficiently accurate for a variety of applications. However, no study has investigated how POD techniques affect the accuracy of different boundary conditions found in groundwater models. We show that the current treatment of boundary conditions in POD causes inaccuracies for these boundaries in the reduced models. We provide an improved method that splits the POD projection space into a subspace orthogonal to the boundary conditions and a separate subspace that enforces the boundary conditions. To test the method for Dirichlet, Neumann and Cauchy boundary conditions, four simple transient 1D-groundwater models, as well as a more complex 3D model, are set up and reduced both by standard POD and POD with the new extension. We show that, in contrast to standard POD, the new method satisfies both Dirichlet and Neumann boundary conditions. It can also be applied to Cauchy boundaries, where the flux error of standard POD is reduced by its head-independent contribution. The extension essentially shifts the focus of the projection towards the boundary conditions. Therefore, we see a slight trade-off between errors at model boundaries and overall accuracy of the reduced model. The proposed POD extension is recommended where exact treatment of boundary conditions is required.

Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Hong; Aziz, H M Abdul; Young, Stan

Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections.more » In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.« less

Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies

NASA Astrophysics Data System (ADS)

Williams, Paul; Howe, Nicola; Gregory, Jonathan; Smith, Robin; Joshi, Manoj

2016-04-01

In climate simulations, the impacts of the sub-grid scales on the resolved scales are conventionally represented using deterministic closure schemes, which assume that the impacts are uniquely determined by the resolved scales. Stochastic parameterization relaxes this assumption, by sampling the sub-grid variability in a computationally inexpensive manner. This presentation shows that the simulated climatological state of the ocean is improved in many respects by implementing a simple stochastic parameterization of ocean eddies into a coupled atmosphere-ocean general circulation model. Simulations from a high-resolution, eddy-permitting ocean model are used to calculate the eddy statistics needed to inject realistic stochastic noise into a low-resolution, non-eddy-permitting version of the same model. A suite of four stochastic experiments is then run to test the sensitivity of the simulated climate to the noise definition, by varying the noise amplitude and decorrelation time within reasonable limits. The addition of zero-mean noise to the ocean temperature tendency is found to have a non-zero effect on the mean climate. Specifically, in terms of the ocean temperature and salinity fields both at the surface and at depth, the noise reduces many of the biases in the low-resolution model and causes it to more closely resemble the high-resolution model. The variability of the strength of the global ocean thermohaline circulation is also improved. It is concluded that stochastic ocean perturbations can yield reductions in climate model error that are comparable to those obtained by refining the resolution, but without the increased computational cost. Therefore, stochastic parameterizations of ocean eddies have the potential to significantly improve climate simulations. Reference PD Williams, NJ Howe, JM Gregory, RS Smith, and MM Joshi (2016) Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies. Journal of Climate, under revision.

Disentangling Mechanisms That Mediate the Balance Between Stochastic and Deterministic Processes in Microbial Succession

DOE PAGES

Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan D.; ...

2015-03-17

Despite growing recognition that deterministic and stochastic factors simultaneously influence bacterial communities, little is known about mechanisms shifting their relative importance. To better understand underlying mechanisms, we developed a conceptual model linking ecosystem development during primary succession to shifts in the stochastic/deterministic balance. To evaluate the conceptual model we coupled spatiotemporal data on soil bacterial communities with environmental conditions spanning 105 years of salt marsh development. At the local scale there was a progression from stochasticity to determinism due to Na accumulation with increasing ecosystem age, supporting a main element of the conceptual model. At the regional-scale, soil organic mattermore » (SOM) governed the relative influence of stochasticity and the type of deterministic ecological selection, suggesting scale-dependency in how deterministic ecological selection is imposed. Analysis of a new ecological simulation model supported these conceptual inferences. Looking forward, we propose an extended conceptual model that integrates primary and secondary succession in microbial systems.« less

Stochastic-field cavitation model

NASA Astrophysics Data System (ADS)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

A cavitation model based on Eulerian stochastic fields

NASA Astrophysics Data System (ADS)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Stochastic-field cavitation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.

2013-07-15

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less

Modeling of stochastic motion of bacteria propelled spherical microbeads

NASA Astrophysics Data System (ADS)

Arabagi, Veaceslav; Behkam, Bahareh; Cheung, Eugene; Sitti, Metin

2011-06-01

This work proposes a stochastic dynamic model of bacteria propelled spherical microbeads as potential swimming microrobotic bodies. Small numbers of S. marcescens bacteria are attached with their bodies to surfaces of spherical microbeads. Average-behavior stochastic models that are normally adopted when studying such biological systems are generally not effective for cases in which a small number of agents are interacting in a complex manner, hence a stochastic model is proposed to simulate the behavior of 8-41 bacteria assembled on a curved surface. Flexibility of the flagellar hook is studied via comparing simulated and experimental results for scenarios of increasing bead size and the number of attached bacteria on a bead. Although requiring more experimental data to yield an exact, certain flagellar hook stiffness value, the examined results favor a stiffer flagella. The stochastic model is intended to be used as a design and simulation tool for future potential targeted drug delivery and disease diagnosis applications of bacteria propelled microrobots.

Model reduction and frequency residuals for a robust estimation of nonlinearities in subspace identification

NASA Astrophysics Data System (ADS)

De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.

2017-09-01

The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.

Ground motion simulation for the 23 August 2011, Mineral, Virginia earthquake using physics-based and stochastic broadband methods

USGS Publications Warehouse

Sun, Xiaodan; Hartzell, Stephen; Rezaeian, Sanaz

2015-01-01

Three broadband simulation methods are used to generate synthetic ground motions for the 2011 Mineral, Virginia, earthquake and compare with observed motions. The methods include a physics‐based model by Hartzell et al. (1999, 2005), a stochastic source‐based model by Boore (2009), and a stochastic site‐based model by Rezaeian and Der Kiureghian (2010, 2012). The ground‐motion dataset consists of 40 stations within 600 km of the epicenter. Several metrics are used to validate the simulations: (1) overall bias of response spectra and Fourier spectra (from 0.1 to 10 Hz); (2) spatial distribution of residuals for GMRotI50 peak ground acceleration (PGA), peak ground velocity, and pseudospectral acceleration (PSA) at various periods; (3) comparison with ground‐motion prediction equations (GMPEs) for the eastern United States. Our results show that (1) the physics‐based model provides satisfactory overall bias from 0.1 to 10 Hz and produces more realistic synthetic waveforms; (2) the stochastic site‐based model also yields more realistic synthetic waveforms and performs superiorly for frequencies greater than about 1 Hz; (3) the stochastic source‐based model has larger bias at lower frequencies (<0.5  Hz) and cannot reproduce the varying frequency content in the time domain. The spatial distribution of GMRotI50 residuals shows that there is no obvious pattern with distance in the simulation bias, but there is some azimuthal variability. The comparison between synthetics and GMPEs shows similar fall‐off with distance for all three models, comparable PGA and PSA amplitudes for the physics‐based and stochastic site‐based models, and systematic lower amplitudes for the stochastic source‐based model at lower frequencies (<0.5  Hz).

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

PubMed

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

DOE PAGES

Moon, Jae; Manuel, Lance; Churchfield, Matthew; ...

2017-12-28

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field,more » including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study's overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.« less

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moon, Jae; Manuel, Lance; Churchfield, Matthew

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field,more » including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study's overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.« less

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

NASA Astrophysics Data System (ADS)

Spettl, A.; Wimmer, R.; Werz, T.; Heinze, M.; Odenbach, S.; Krill, C. E., III; Schmidt, V.

2015-09-01

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al-Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

Inflow forecasting model construction with stochastic time series for coordinated dam operation

NASA Astrophysics Data System (ADS)

Kim, T.; Jung, Y.; Kim, H.; Heo, J. H.

2014-12-01

Dam inflow forecasting is one of the most important tasks in dam operation for an effective water resources management and control. In general, dam inflow forecasting with stochastic time series model is possible to apply when the data is stationary because most of stochastic process based on stationarity. However, recent hydrological data cannot be satisfied the stationarity anymore because of climate change. Therefore a stochastic time series model, which can consider seasonality and trend in the data series, named SARIMAX(Seasonal Autoregressive Integrated Average with eXternal variable) model were constructed in this study. This SARIMAX model could increase the performance of stochastic time series model by considering the nonstationarity components and external variable such as precipitation. For application, the models were constructed for four coordinated dams on Han river in South Korea with monthly time series data. As a result, the models of each dam have similar performance and it would be possible to use the model for coordinated dam operation.Acknowledgement This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-NH-12-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

Influence of stochastic sea ice parametrization on climate and the role of atmosphere–sea ice–ocean interaction

PubMed Central

Juricke, Stephan; Jung, Thomas

2014-01-01

The influence of a stochastic sea ice strength parametrization on the mean climate is investigated in a coupled atmosphere–sea ice–ocean model. The results are compared with an uncoupled simulation with a prescribed atmosphere. It is found that the stochastic sea ice parametrization causes an effective weakening of the sea ice. In the uncoupled model this leads to an Arctic sea ice volume increase of about 10–20% after an accumulation period of approximately 20–30 years. In the coupled model, no such increase is found. Rather, the stochastic perturbations lead to a spatial redistribution of the Arctic sea ice thickness field. A mechanism involving a slightly negative atmospheric feedback is proposed that can explain the different responses in the coupled and uncoupled system. Changes in integrated Antarctic sea ice quantities caused by the stochastic parametrization are generally small, as memory is lost during the melting season because of an almost complete loss of sea ice. However, stochastic sea ice perturbations affect regional sea ice characteristics in the Southern Hemisphere, both in the uncoupled and coupled model. Remote impacts of the stochastic sea ice parametrization on the mean climate of non-polar regions were found to be small. PMID:24842027

Quantum Foundations of Quantum Information

NASA Astrophysics Data System (ADS)

Griffiths, Robert

2009-03-01

The main foundational issue for quantum information is: What is quantum information about? What does it refer to? Classical information typically refers to physical properties, and since classical is a subset of quantum information (assuming the world is quantum mechanical), quantum information should--and, it will be argued, does--refer to quantum physical properties represented by projectors on appropriate subspaces of a quantum Hilbert space. All sorts of microscopic and macroscopic properties, not just measurement outcomes, can be represented in this way, and are thus a proper subject of quantum information. The Stern-Gerlach experiment illustrates this. When properties are compatible, which is to say their projectors commute, Shannon's classical information theory based on statistical correlations extends without difficulty or change to the quantum case. When projectors do not commute, giving rise to characteristic quantum effects, a foundation for the subject can still be constructed by replacing the ``measurement and wave-function collapse'' found in textbooks--an efficient calculational tool, but one giving rise to numerous conceptual difficulties--with a fully consistent and paradox free stochastic formulation of standard quantum mechanics. This formulation is particularly helpful in that it contains no nonlocal superluminal influences; the reason the latter carry no information is that they do not exist.

A Simple and Accurate Model to Predict Responses to Multi-electrode Stimulation in the Retina

PubMed Central

Maturana, Matias I.; Apollo, Nicholas V.; Hadjinicolaou, Alex E.; Garrett, David J.; Cloherty, Shaun L.; Kameneva, Tatiana; Grayden, David B.; Ibbotson, Michael R.; Meffin, Hamish

2016-01-01

Implantable electrode arrays are widely used in therapeutic stimulation of the nervous system (e.g. cochlear, retinal, and cortical implants). Currently, most neural prostheses use serial stimulation (i.e. one electrode at a time) despite this severely limiting the repertoire of stimuli that can be applied. Methods to reliably predict the outcome of multi-electrode stimulation have not been available. Here, we demonstrate that a linear-nonlinear model accurately predicts neural responses to arbitrary patterns of stimulation using in vitro recordings from single retinal ganglion cells (RGCs) stimulated with a subretinal multi-electrode array. In the model, the stimulus is projected onto a low-dimensional subspace and then undergoes a nonlinear transformation to produce an estimate of spiking probability. The low-dimensional subspace is estimated using principal components analysis, which gives the neuron’s electrical receptive field (ERF), i.e. the electrodes to which the neuron is most sensitive. Our model suggests that stimulation proportional to the ERF yields a higher efficacy given a fixed amount of power when compared to equal amplitude stimulation on up to three electrodes. We find that the model captures the responses of all the cells recorded in the study, suggesting that it will generalize to most cell types in the retina. The model is computationally efficient to evaluate and, therefore, appropriate for future real-time applications including stimulation strategies that make use of recorded neural activity to improve the stimulation strategy. PMID:27035143

Constraint-Free Theories of Gravitation

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.; Robinson, R. Steve; Wahlquist, Hugo D.

1998-01-01

Lovelock actions (more precisely, extended Gauss-Bonnet forms) when varied as Cartan forms on subspaces of higher dimensional flat Riemannian manifolds, generate well set, causal exterior differential systems. In particular, the Einstein- Hilbert action 4-form, varied on a 4 dimensional subspace of E(sub 10) yields a well set generalized theory of gravity having no constraints. Rcci-flat solutions are selected by initial conditions on a bounding 3-space.

Application of Subspace Detection to the 6 November 2011 M5.6 Prague, Oklahoma Aftershock Sequence

NASA Astrophysics Data System (ADS)

McMahon, N. D.; Benz, H.; Johnson, C. E.; Aster, R. C.; McNamara, D. E.

2015-12-01

Subspace detection is a powerful tool for the identification of small seismic events. Subspace detectors improve upon single-event matched filtering techniques by using multiple orthogonal waveform templates whose linear combinations characterize a range of observed signals from previously identified earthquakes. Subspace detectors running on multiple stations can significantly increasing the number of locatable events, lowering the catalog's magnitude of completeness and thus providing extraordinary detail on the kinematics of the aftershock process. The 6 November 2011 M5.6 earthquake near Prague, Oklahoma is the largest earthquake instrumentally recorded in Oklahoma history and the largest earthquake resultant from deep wastewater injection. A M4.8 foreshock on 5 November 2011 and the M5.6 mainshock triggered tens of thousands of detectable aftershocks along a 20 km splay of the Wilzetta Fault Zone known as the Meeker-Prague fault. In response to this unprecedented earthquake, 21 temporary seismic stations were deployed surrounding the seismic activity. We utilized a catalog of 767 previously located aftershocks to construct subspace detectors for the 21 temporary and 10 closest permanent seismic stations. Subspace detection identified more than 500,000 new arrival-time observations, which associated into more than 20,000 locatable earthquakes. The associated earthquakes were relocated using the Bayesloc multiple-event locator, resulting in ~7,000 earthquakes with hypocentral uncertainties of less than 500 m. The relocated seismicity provides unique insight into the spatio-temporal evolution of the aftershock sequence along the Wilzetta Fault Zone and its associated structures. We find that the crystalline basement and overlying sedimentary Arbuckle formation accommodate the majority of aftershocks. While we observe aftershocks along the entire 20 km length of the Meeker-Prague fault, the vast majority of earthquakes were confined to a 9 km wide by 9 km deep surface striking N54°E and dipping 83° to the northwest near the junction of the splay with the main Wilzetta fault structure. Relocated seismicity shows off-fault stress-related interaction to distances of 10 km or more from the mainshock, including clustered seismicity to the northwest and southeast of the mainshock.

Two-polariton bound states in the Jaynes-Cummings-Hubbard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Max T. C.; Law, C. K.

2011-05-15

We examine the eigenstates of the one-dimensional Jaynes-Cummings-Hubbard model in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunneling rate between cavities exceeds a critical value. We determine the critical value as a function of the quasimomentum quantum number, and indicate that the bound states carry a strong correlation in which the two polaritons appear to be spatially confined together.

Superspace models for S-3

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.

2003-11-01

The simplest supersymmetric extension of the group SO(4) is discussed. The superalgebra is realized in a superspace whose Bosonic subspace is the surface of a sphere S-3 embedded in four-dimensional Euclidean space. By using Fermionic coordinates in this superspace, which are chiral symplectic Majorana spinors, it proves possible to devise superfield models involving a complex scalar, a pair of chiral symplectic Majorana spinors, and a complex auxiliary scalar. Kinetic terms involve operators that are isometry generators on S-3.

Chemical event chain model of coupled genetic oscillators.

PubMed

Jörg, David J; Morelli, Luis G; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Chemical event chain model of coupled genetic oscillators

NASA Astrophysics Data System (ADS)

Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Stochastic modelling of intermittency.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2010-01-13

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series. This journal is © 2010 The Royal Society

Low Frequency Predictive Skill Despite Structural Instability and Model Error

DTIC Science & Technology

2014-09-30

Majda, based on earlier theoretical work. 1. Dynamic Stochastic Superresolution of sparseley observed turbulent systems M. Branicki (Post doc...of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by...resolving subgridscale turbulence through Dynamic Stochastic Superresolution utilizing aliased grids is a potential breakthrough for practical online

Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2016-11-01

In this paper, we consider a stochastic non-autonomous SISV epidemic model. For the non-autonomous periodic system, firstly, we get the threshold of the system which determines whether the epidemic occurs or not. Then in the case of persistence, we show that there exists at least one nontrivial positive periodic solution of the stochastic system.

Predicting the Stochastic Properties of the Shallow Subsurface for Improved Geophysical Modeling

NASA Astrophysics Data System (ADS)

Stroujkova, A.; Vynne, J.; Bonner, J.; Lewkowicz, J.

2005-12-01

Strong ground motion data from numerous explosive field experiments and from moderate to large earthquakes show significant variations in amplitude and waveform shape with respect to both azimuth and range. Attempts to model these variations using deterministic models have often been unsuccessful. It has been hypothesized that a stochastic description of the geological medium is a more realistic approach. To estimate the stochastic properties of the shallow subsurface, we use Measurement While Drilling (MWD) data, which are routinely collected by mines in order to facilitate design of blast patterns. The parameters, such as rotation speed of the drill, torque, and penetration rate, are used to compute the rock's Specific Energy (SE), which is then related to a blastability index. We use values of SE measured at two different mines and calibrated to laboratory measurements of rock properties to determine correlation lengths of the subsurface rocks in 2D, needed to obtain 2D and 3D stochastic models. The stochastic models are then combined with the deterministic models and used to compute synthetic seismic waveforms.

Appropriate Domain Size for Groundwater Flow Modeling with a Discrete Fracture Network Model.

PubMed

Ji, Sung-Hoon; Koh, Yong-Kwon

2017-01-01

When a discrete fracture network (DFN) is constructed from statistical conceptualization, uncertainty in simulating the hydraulic characteristics of a fracture network can arise due to the domain size. In this study, the appropriate domain size, where less significant uncertainty in the stochastic DFN model is expected, was suggested for the Korea Atomic Energy Research Institute Underground Research Tunnel (KURT) site. The stochastic DFN model for the site was established, and the appropriate domain size was determined with the density of the percolating cluster and the percolation probability using the stochastically generated DFNs for various domain sizes. The applicability of the appropriate domain size to our study site was evaluated by comparing the statistical properties of stochastically generated fractures of varying domain sizes and estimating the uncertainty in the equivalent permeability of the generated DFNs. Our results show that the uncertainty of the stochastic DFN model is acceptable when the modeling domain is larger than the determined appropriate domain size, and the appropriate domain size concept is applicable to our study site. © 2016, National Ground Water Association.

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

NASA Astrophysics Data System (ADS)

Pham, Minh Tu; Vernieuwe, Hilde; De Baets, Bernard; Verhoest, Niko E. C.

2018-02-01

A hydrological impact analysis concerns the study of the consequences of certain scenarios on one or more variables or fluxes in the hydrological cycle. In such an exercise, discharge is often considered, as floods originating from extremely high discharges often cause damage. Investigating the impact of extreme discharges generally requires long time series of precipitation and evapotranspiration to be used to force a rainfall-runoff model. However, such kinds of data may not be available and one should resort to stochastically generated time series, even though the impact of using such data on the overall discharge, and especially on the extreme discharge events, is not well studied. In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Notwithstanding this finding, it can be concluded that using a coupled stochastic rainfall-evapotranspiration model has great potential for hydrological impact analysis.

Stochastic simulations on a model of circadian rhythm generation.

PubMed

Miura, Shigehiro; Shimokawa, Tetsuya; Nomura, Taishin

2008-01-01

Biological phenomena are often modeled by differential equations, where states of a model system are described by continuous real values. When we consider concentrations of molecules as dynamical variables for a set of biochemical reactions, we implicitly assume that numbers of the molecules are large enough so that their changes can be regarded as continuous and they are described deterministically. However, for a system with small numbers of molecules, changes in their numbers are apparently discrete and molecular noises become significant. In such cases, models with deterministic differential equations may be inappropriate, and the reactions must be described by stochastic equations. In this study, we focus a clock gene expression for a circadian rhythm generation, which is known as a system involving small numbers of molecules. Thus it is appropriate for the system to be modeled by stochastic equations and analyzed by methodologies of stochastic simulations. The interlocked feedback model proposed by Ueda et al. as a set of deterministic ordinary differential equations provides a basis of our analyses. We apply two stochastic simulation methods, namely Gillespie's direct method and the stochastic differential equation method also by Gillespie, to the interlocked feedback model. To this end, we first reformulated the original differential equations back to elementary chemical reactions. With those reactions, we simulate and analyze the dynamics of the model using two methods in order to compare them with the dynamics obtained from the original deterministic model and to characterize dynamics how they depend on the simulation methodologies.

Pipeline Processing With an Iterative, Context-Based Detection Model

DTIC Science & Technology

2015-04-19

pattern detectors , correlation detectors , subspace detectors , matched field detectors , nuclear explosion monitoring 16. SECURITY CLASSIFICATION OF: 17...38 13. 3 days of SPAO-BHZ data which is dominated by signals from nearby icequakes. .... 39 14. (Top) 94 detections produced by detector ...92532 and (bottom) 148 detections from detector 92541 produced during the first run of the framework. .................................. 40 15. The 49

The trust-region self-consistent field method in Kohn-Sham density-functional theory.

PubMed

Thøgersen, Lea; Olsen, Jeppe; Köhn, Andreas; Jørgensen, Poul; Sałek, Paweł; Helgaker, Trygve

2005-08-15

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

About the Subdivision of Indoor Spaces in Indoorgml

NASA Astrophysics Data System (ADS)

Diakité, A. A.; Zlatanova, S.; Li, K.-J.

2017-10-01

Boosted by the dynamic urbanization of cities, indoor environments are getting more and more complex in order to be able to host people properly. While most of our time is spent inside buildings, the need of GIS tools to assist our daily activities that can become tedious, such as indoor navigation or facility management, became more and more urgent. In that perspective, the IndoorGML standard is aiming to address the gaps left by other standards regarding the spatial modelling for indoor navigation. It includes several concepts such as the organization of the spaces into cells along with their network representation and the possibility to represent multiple connected layers. However, being at its first stage, several concepts of the standard could be improved. One of these is the cell subspacing that is not enough discussed in the current version of the standard. In this paper, we explore all the aspects involved in the subdivision process, from the identification of the navigable and non-navigable space cells to the generation of a navigation graph. We propose several criteria on which the indoor sub-spacing can rely to be automatically performed and and illustrate them on a 3D indoor model.

Subspace Compressive GLRT Detector for MIMO Radar in the Presence of Clutter.

PubMed

Bolisetti, Siva Karteek; Patwary, Mohammad; Ahmed, Khawza; Soliman, Abdel-Hamid; Abdel-Maguid, Mohamed

2015-01-01

The problem of optimising the target detection performance of MIMO radar in the presence of clutter is considered. The increased false alarm rate which is a consequence of the presence of clutter returns is known to seriously degrade the target detection performance of the radar target detector, especially under low SNR conditions. In this paper, a mathematical model is proposed to optimise the target detection performance of a MIMO radar detector in the presence of clutter. The number of samples that are required to be processed by a radar target detector regulates the amount of processing burden while achieving a given detection reliability. While Subspace Compressive GLRT (SSC-GLRT) detector is known to give optimised radar target detection performance with reduced computational complexity, it however suffers a significant deterioration in target detection performance in the presence of clutter. In this paper we provide evidence that the proposed mathematical model for SSC-GLRT detector outperforms the existing detectors in the presence of clutter. The performance analysis of the existing detectors and the proposed SSC-GLRT detector for MIMO radar in the presence of clutter are provided in this paper.

Deterministic and stochastic models for middle east respiratory syndrome (MERS)

NASA Astrophysics Data System (ADS)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

PubMed

Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

2018-06-12

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

Multiple fault separation and detection by joint subspace learning for the health assessment of wind turbine gearboxes

NASA Astrophysics Data System (ADS)

Du, Zhaohui; Chen, Xuefeng; Zhang, Han; Zi, Yanyang; Yan, Ruqiang

2017-09-01

The gearbox of a wind turbine (WT) has dominant failure rates and highest downtime loss among all WT subsystems. Thus, gearbox health assessment for maintenance cost reduction is of paramount importance. The concurrence of multiple faults in gearbox components is a common phenomenon due to fault induction mechanism. This problem should be considered before planning to replace the components of the WT gearbox. Therefore, the key fault patterns should be reliably identified from noisy observation data for the development of an effective maintenance strategy. However, most of the existing studies focusing on multiple fault diagnosis always suffer from inappropriate division of fault information in order to satisfy various rigorous decomposition principles or statistical assumptions, such as the smooth envelope principle of ensemble empirical mode decomposition and the mutual independence assumption of independent component analysis. Thus, this paper presents a joint subspace learning-based multiple fault detection (JSL-MFD) technique to construct different subspaces adaptively for different fault patterns. Its main advantage is its capability to learn multiple fault subspaces directly from the observation signal itself. It can also sparsely concentrate the feature information into a few dominant subspace coefficients. Furthermore, it can eliminate noise by simply performing coefficient shrinkage operations. Consequently, multiple fault patterns are reliably identified by utilizing the maximum fault information criterion. The superiority of JSL-MFD in multiple fault separation and detection is comprehensively investigated and verified by the analysis of a data set of a 750 kW WT gearbox. Results show that JSL-MFD is superior to a state-of-the-art technique in detecting hidden fault patterns and enhancing detection accuracy.

Evolutionary-inspired probabilistic search for enhancing sampling of local minima in the protein energy surface

PubMed Central

2012-01-01

Background Despite computational challenges, elucidating conformations that a protein system assumes under physiologic conditions for the purpose of biological activity is a central problem in computational structural biology. While these conformations are associated with low energies in the energy surface that underlies the protein conformational space, few existing conformational search algorithms focus on explicitly sampling low-energy local minima in the protein energy surface. Methods This work proposes a novel probabilistic search framework, PLOW, that explicitly samples low-energy local minima in the protein energy surface. The framework combines algorithmic ingredients from evolutionary computation and computational structural biology to effectively explore the subspace of local minima. A greedy local search maps a conformation sampled in conformational space to a nearby local minimum. A perturbation move jumps out of a local minimum to obtain a new starting conformation for the greedy local search. The process repeats in an iterative fashion, resulting in a trajectory-based exploration of the subspace of local minima. Results and conclusions The analysis of PLOW's performance shows that, by navigating only the subspace of local minima, PLOW is able to sample conformations near a protein's native structure, either more effectively or as well as state-of-the-art methods that focus on reproducing the native structure for a protein system. Analysis of the actual subspace of local minima shows that PLOW samples this subspace more effectively that a naive sampling approach. Additional theoretical analysis reveals that the perturbation function employed by PLOW is key to its ability to sample a diverse set of low-energy conformations. This analysis also suggests directions for further research and novel applications for the proposed framework. PMID:22759582

Application of Earthquake Subspace Detectors at Kilauea and Mauna Loa Volcanoes, Hawai`i

NASA Astrophysics Data System (ADS)

Okubo, P.; Benz, H.; Yeck, W.

2016-12-01

Recent studies have demonstrated the capabilities of earthquake subspace detectors for detailed cataloging and tracking of seismicity in a number of regions and settings. We are exploring the application of subspace detectors at the United States Geological Survey's Hawaiian Volcano Observatory (HVO) to analyze seismicity at Kilauea and Mauna Loa volcanoes. Elevated levels of microseismicity and occasional swarms of earthquakes associated with active volcanism here present cataloging challenges due the sheer numbers of earthquakes and an intrinsically low signal-to-noise environment featuring oceanic microseism and volcanic tremor in the ambient seismic background. With high-quality continuous recording of seismic data at HVO, we apply subspace detectors (Harris and Dodge, 2011, Bull. Seismol. Soc. Am., doi: 10.1785/0120100103) during intervals of noteworthy seismicity. Waveform templates are drawn from Magnitude 2 and larger earthquakes within clusters of earthquakes cataloged in the HVO seismic database. At Kilauea, we focus on seismic swarms in the summit caldera region where, despite continuing eruptions from vents in the summit region and in the east rift zone, geodetic measurements reflect a relatively inflated volcanic state. We also focus on seismicity beneath and adjacent to Mauna Loa's summit caldera that appears to be associated with geodetic expressions of gradual volcanic inflation, and where precursory seismicity clustered prior to both Mauna Loa's most recent eruptions in 1975 and 1984. We recover several times more earthquakes with the subspace detectors - down to roughly 2 magnitude units below the templates, based on relative amplitudes - compared to the numbers of cataloged earthquakes. The increased numbers of detected earthquakes in these clusters, and the ability to associate and locate them, allow us to infer details of the spatial and temporal distributions and possible variations in stresses within these key regions of the volcanoes.

Direct lifts of coupled cell networks

NASA Astrophysics Data System (ADS)

Dias, A. P. S.; Moreira, C. S.

2018-04-01

In networks of dynamical systems, there are spaces defined in terms of equalities of cell coordinates which are flow-invariant under any dynamical system that has a form consistent with the given underlying network structure—the network synchrony subspaces. Given a network and one of its synchrony subspaces, any system with a form consistent with the network, restricted to the synchrony subspace, defines a new system which is consistent with a smaller network, called the quotient network of the original network by the synchrony subspace. Moreover, any system associated with the quotient can be interpreted as the restriction to the synchrony subspace of a system associated with the original network. We call the larger network a lift of the smaller network, and a lift can be interpreted as a result of the cellular splitting of the smaller network. In this paper, we address the question of the uniqueness in this lifting process in terms of the networks’ topologies. A lift G of a given network Q is said to be direct when there are no intermediate lifts of Q between them. We provide necessary and sufficient conditions for a lift of a general network to be direct. Our results characterize direct lifts using the subnetworks of all splitting cells of Q and of all split cells of G. We show that G is a direct lift of Q if and only if either the split subnetwork is a direct lift or consists of two copies of the splitting subnetwork. These results are then applied to the class of regular uniform networks and to the special classes of ring networks and acyclic networks. We also illustrate that one of the applications of our results is to the lifting bifurcation problem.

Stochastic modeling of experimental chaotic time series.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2007-01-26

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

Using independent component analysis for electrical impedance tomography

NASA Astrophysics Data System (ADS)

Yan, Peimin; Mo, Yulong

2004-05-01

Independent component analysis (ICA) is a way to resolve signals into independent components based on the statistical characteristics of the signals. It is a method for factoring probability densities of measured signals into a set of densities that are as statistically independent as possible under the assumptions of a linear model. Electrical impedance tomography (EIT) is used to detect variations of the electric conductivity of the human body. Because there are variations of the conductivity distributions inside the body, EIT presents multi-channel data. In order to get all information contained in different location of tissue it is necessary to image the individual conductivity distribution. In this paper we consider to apply ICA to EIT on the signal subspace (individual conductivity distribution). Using ICA the signal subspace will then be decomposed into statistically independent components. The individual conductivity distribution can be reconstructed by the sensitivity theorem in this paper. Compute simulations show that the full information contained in the multi-conductivity distribution will be obtained by this method.

Robust subspace clustering via joint weighted Schatten-p norm and Lq norm minimization

NASA Astrophysics Data System (ADS)

Zhang, Tao; Tang, Zhenmin; Liu, Qing

2017-05-01

Low-rank representation (LRR) has been successfully applied to subspace clustering. However, the nuclear norm in the standard LRR is not optimal for approximating the rank function in many real-world applications. Meanwhile, the L21 norm in LRR also fails to characterize various noises properly. To address the above issues, we propose an improved LRR method, which achieves low rank property via the new formulation with weighted Schatten-p norm and Lq norm (WSPQ). Specifically, the nuclear norm is generalized to be the Schatten-p norm and different weights are assigned to the singular values, and thus it can approximate the rank function more accurately. In addition, Lq norm is further incorporated into WSPQ to model different noises and improve the robustness. An efficient algorithm based on the inexact augmented Lagrange multiplier method is designed for the formulated problem. Extensive experiments on face clustering and motion segmentation clearly demonstrate the superiority of the proposed WSPQ over several state-of-the-art methods.

Structured sparse linear graph embedding.

PubMed

Wang, Haixian

2012-03-01

Subspace learning is a core issue in pattern recognition and machine learning. Linear graph embedding (LGE) is a general framework for subspace learning. In this paper, we propose a structured sparse extension to LGE (SSLGE) by introducing a structured sparsity-inducing norm into LGE. Specifically, SSLGE casts the projection bases learning into a regression-type optimization problem, and then the structured sparsity regularization is applied to the regression coefficients. The regularization selects a subset of features and meanwhile encodes high-order information reflecting a priori structure information of the data. The SSLGE technique provides a unified framework for discovering structured sparse subspace. Computationally, by using a variational equality and the Procrustes transformation, SSLGE is efficiently solved with closed-form updates. Experimental results on face image show the effectiveness of the proposed method. Copyright © 2011 Elsevier Ltd. All rights reserved.

Data-Driven Modeling of Complex Systems by means of a Dynamical ANN

NASA Astrophysics Data System (ADS)

Seleznev, A.; Mukhin, D.; Gavrilov, A.; Loskutov, E.; Feigin, A.

2017-12-01

The data-driven methods for modeling and prognosis of complex dynamical systems become more and more popular in various fields due to growth of high-resolution data. We distinguish the two basic steps in such an approach: (i) determining the phase subspace of the system, or embedding, from available time series and (ii) constructing an evolution operator acting in this reduced subspace. In this work we suggest a novel approach combining these two steps by means of construction of an artificial neural network (ANN) with special topology. The proposed ANN-based model, on the one hand, projects the data onto a low-dimensional manifold, and, on the other hand, models a dynamical system on this manifold. Actually, this is a recurrent multilayer ANN which has internal dynamics and capable of generating time series. Very important point of the proposed methodology is the optimization of the model allowing us to avoid overfitting: we use Bayesian criterion to optimize the ANN structure and estimate both the degree of evolution operator nonlinearity and the complexity of nonlinear manifold which the data are projected on. The proposed modeling technique will be applied to the analysis of high-dimensional dynamical systems: Lorenz'96 model of atmospheric turbulence, producing high-dimensional space-time chaos, and quasi-geostrophic three-layer model of the Earth's atmosphere with the natural orography, describing the dynamics of synoptical vortexes as well as mesoscale blocking systems. The possibility of application of the proposed methodology to analyze real measured data is also discussed. The study was supported by the Russian Science Foundation (grant #16-12-10198).

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Stochastic receding horizon control: application to an octopedal robot

NASA Astrophysics Data System (ADS)

Shah, Shridhar K.; Tanner, Herbert G.

2013-06-01

Miniature autonomous systems are being developed under ARL's Micro Autonomous Systems and Technology (MAST). These systems can only be fitted with a small-size processor, and their motion behavior is inherently uncertain due to manufacturing and platform-ground interactions. One way to capture this uncertainty is through a stochastic model. This paper deals with stochastic motion control design and implementation for MAST- specific eight-legged miniature crawling robots, which have been kinematically modeled as systems exhibiting the behavior of a Dubin's car with stochastic noise. The control design takes the form of stochastic receding horizon control, and is implemented on a Gumstix Overo Fire COM with 720 MHz processor and 512 MB RAM, weighing 5.5 g. The experimental results show the effectiveness of this control law for miniature autonomous systems perturbed by stochastic noise.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology

NASA Astrophysics Data System (ADS)

Fridström, R.; Chapman, B. E.; Almagri, A. F.; Frassinetti, L.; Brunsell, P. R.; Nishizawa, T.; Sarff, J. S.

2018-06-01

In a magnetically confined plasma with a stochastic magnetic field, the dependence of the perpendicular viscosity on the magnetic fluctuation amplitude is measured for the first time. With a controlled, ˜ tenfold variation in the fluctuation amplitude, the viscosity increases ˜100 -fold, exhibiting the same fluctuation-amplitude-squared dependence as the predicted rate of stochastic field line diffusion. The absolute value of the viscosity is well predicted by a model based on momentum transport in a stochastic field, the first in-depth test of this model.

Simulating biological processes: stochastic physics from whole cells to colonies.

PubMed

Earnest, Tyler M; Cole, John A; Luthey-Schulten, Zaida

2018-05-01

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a 'minimal cell'. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Simulating biological processes: stochastic physics from whole cells to colonies

NASA Astrophysics Data System (ADS)

Earnest, Tyler M.; Cole, John A.; Luthey-Schulten, Zaida

2018-05-01

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a ‘minimal cell’. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Model-assisted probability of detection of flaws in aluminum blocks using polynomial chaos expansions

NASA Astrophysics Data System (ADS)

Du, Xiaosong; Leifsson, Leifur; Grandin, Robert; Meeker, William; Roberts, Ronald; Song, Jiming

2018-04-01

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination with model-assisted POD (MAPOD) methods. With the development of advanced physics-based methods, such as ultrasonic NDT testing, the empirical information, needed for POD methods, can be reduced. However, performing accurate numerical simulations can be prohibitively time-consuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through the physics-based simulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using non-intrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary least-squares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw in an aluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation model for this case, which is the UTSim2 model.

Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate.

PubMed

Christen, Alejandra; Maulén-Yañez, M Angélica; González-Olivares, Eduardo; Curé, Michel

2018-03-01

In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker-Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.

Minimal Krylov Subspaces for Dimension Reduction

DTIC Science & Technology

2013-01-01

these applications realized a maximal compute time improvement with minimal Krylov subspaces. More recently, Halko et . al . [36] have investigated... Halko et . al . proposed a variety of them in [36], but we focus on the “direct eigenvalue approximation for Hermitian matri- ces with random...result due to Halko et . al . Theorem 5 ( Halko , Martinsson and Tropp [36]). Let A ∈ Rn×m be the input matrix with partitioned singular value

On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators

NASA Technical Reports Server (NTRS)

Bykhovskiy, E. B.; Smirnov, N. V.

1983-01-01

The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.

Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups

NASA Astrophysics Data System (ADS)

Brannan, Michael; Collins, Benoît

2018-03-01

In this paper we describe a class of highly entangled subspaces of a tensor product of finite-dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of d-positive maps on matrix algebras is also presented.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation.

PubMed

Zimmer, Christoph

2016-01-01

Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.

A Channelization-Based DOA Estimation Method for Wideband Signals

PubMed Central

Guo, Rui; Zhang, Yue; Lin, Qianqiang; Chen, Zengping

2016-01-01

In this paper, we propose a novel direction of arrival (DOA) estimation method for wideband signals with sensor arrays. The proposed method splits the wideband array output into multiple frequency sub-channels and estimates the signal parameters using a digital channelization receiver. Based on the output sub-channels, a channelization-based incoherent signal subspace method (Channelization-ISM) and a channelization-based test of orthogonality of projected subspaces method (Channelization-TOPS) are proposed. Channelization-ISM applies narrowband signal subspace methods on each sub-channel independently. Then the arithmetic mean or geometric mean of the estimated DOAs from each sub-channel gives the final result. Channelization-TOPS measures the orthogonality between the signal and the noise subspaces of the output sub-channels to estimate DOAs. The proposed channelization-based method isolates signals in different bandwidths reasonably and improves the output SNR. It outperforms the conventional ISM and TOPS methods on estimation accuracy and dynamic range, especially in real environments. Besides, the parallel processing architecture makes it easy to implement on hardware. A wideband digital array radar (DAR) using direct wideband radio frequency (RF) digitization is presented. Experiments carried out in a microwave anechoic chamber with the wideband DAR are presented to demonstrate the performance. The results verify the effectiveness of the proposed method. PMID:27384566

Integrated feature extraction and selection for neuroimage classification

NASA Astrophysics Data System (ADS)

Fan, Yong; Shen, Dinggang

2009-02-01

Feature extraction and selection are of great importance in neuroimage classification for identifying informative features and reducing feature dimensionality, which are generally implemented as two separate steps. This paper presents an integrated feature extraction and selection algorithm with two iterative steps: constrained subspace learning based feature extraction and support vector machine (SVM) based feature selection. The subspace learning based feature extraction focuses on the brain regions with higher possibility of being affected by the disease under study, while the possibility of brain regions being affected by disease is estimated by the SVM based feature selection, in conjunction with SVM classification. This algorithm can not only take into account the inter-correlation among different brain regions, but also overcome the limitation of traditional subspace learning based feature extraction methods. To achieve robust performance and optimal selection of parameters involved in feature extraction, selection, and classification, a bootstrapping strategy is used to generate multiple versions of training and testing sets for parameter optimization, according to the classification performance measured by the area under the ROC (receiver operating characteristic) curve. The integrated feature extraction and selection method is applied to a structural MR image based Alzheimer's disease (AD) study with 98 non-demented and 100 demented subjects. Cross-validation results indicate that the proposed algorithm can improve performance of the traditional subspace learning based classification.

Similarity preserving low-rank representation for enhanced data representation and effective subspace learning.

PubMed

Zhang, Zhao; Yan, Shuicheng; Zhao, Mingbo

2014-05-01

Latent Low-Rank Representation (LatLRR) delivers robust and promising results for subspace recovery and feature extraction through mining the so-called hidden effects, but the locality of both similar principal and salient features cannot be preserved in the optimizations. To solve this issue for achieving enhanced performance, a boosted version of LatLRR, referred to as Regularized Low-Rank Representation (rLRR), is proposed through explicitly including an appropriate Laplacian regularization that can maximally preserve the similarity among local features. Resembling LatLRR, rLRR decomposes given data matrix from two directions by seeking a pair of low-rank matrices. But the similarities of principal and salient features can be effectively preserved by rLRR. As a result, the correlated features are well grouped and the robustness of representations is also enhanced. Based on the outputted bi-directional low-rank codes by rLRR, an unsupervised subspace learning framework termed Low-rank Similarity Preserving Projections (LSPP) is also derived for feature learning. The supervised extension of LSPP is also discussed for discriminant subspace learning. The validity of rLRR is examined by robust representation and decomposition of real images. Results demonstrated the superiority of our rLRR and LSPP in comparison to other related state-of-the-art algorithms. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochastic Parameterization: Toward a New View of Weather and Climate Models

DOE PAGES

Berner, Judith; Achatz, Ulrich; Batté, Lauriane; ...

2017-03-31

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans,more » land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined« less

Stochastic Parameterization: Toward a New View of Weather and Climate Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berner, Judith; Achatz, Ulrich; Batté, Lauriane

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans,more » land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined« less

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Stochastic simulation of human pulmonary blood flow and transit time frequency distribution based on anatomic and elasticity data.

PubMed

Huang, Wei; Shi, Jun; Yen, R T

2012-12-01

The objective of our study was to develop a computing program for computing the transit time frequency distributions of red blood cell in human pulmonary circulation, based on our anatomic and elasticity data of blood vessels in human lung. A stochastic simulation model was introduced to simulate blood flow in human pulmonary circulation. In the stochastic simulation model, the connectivity data of pulmonary blood vessels in human lung was converted into a probability matrix. Based on this model, the transit time of red blood cell in human pulmonary circulation and the output blood pressure were studied. Additionally, the stochastic simulation model can be used to predict the changes of blood flow in human pulmonary circulation with the advantage of the lower computing cost and the higher flexibility. In conclusion, a stochastic simulation approach was introduced to simulate the blood flow in the hierarchical structure of a pulmonary circulation system, and to calculate the transit time distributions and the blood pressure outputs.

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Moroz, I.; Palmer, T.

2015-12-01

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic ensemble forecasts, and a number of different techniques have been proposed for this purpose. Stochastic convection parameterization schemes use random numbers to represent the difference between a deterministic parameterization scheme and the true atmosphere, accounting for the unresolved sub grid-scale variability associated with convective clouds. An alternative approach varies the values of poorly constrained physical parameters in the model to represent the uncertainty in these parameters. This study presents new perturbed parameter schemes for use in the European Centre for Medium Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parametrisation scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are changed between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, Stochastically Perturbed Parametrisation Tendencies (SPPT), and to a model which does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parametrisation in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skilful representations of model uncertainty due to convection parametrisation. Reference: H. M. Christensen, I. M. Moroz, and T. N. Palmer, 2015: Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization. J. Atmos. Sci., 72, 2525-2544.

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Ping; Song, Heda; Wang, Hong

Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improvemore » modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.« less

LLNL Location and Detection Research

DOE Office of Scientific and Technical Information (OSTI.GOV)

Myers, S C; Harris, D B; Anderson, M L

2003-07-16

We present two LLNL research projects in the topical areas of location and detection. The first project assesses epicenter accuracy using a multiple-event location algorithm, and the second project employs waveform subspace Correlation to detect and identify events at Fennoscandian mines. Accurately located seismic events are the bases of location calibration. A well-characterized set of calibration events enables new Earth model development, empirical calibration, and validation of models. In a recent study, Bondar et al. (2003) develop network coverage criteria for assessing the accuracy of event locations that are determined using single-event, linearized inversion methods. These criteria are conservative andmore » are meant for application to large bulletins where emphasis is on catalog completeness and any given event location may be improved through detailed analysis or application of advanced algorithms. Relative event location techniques are touted as advancements that may improve absolute location accuracy by (1) ensuring an internally consistent dataset, (2) constraining a subset of events to known locations, and (3) taking advantage of station and event correlation structure. Here we present the preliminary phase of this work in which we use Nevada Test Site (NTS) nuclear explosions, with known locations, to test the effect of travel-time model accuracy on relative location accuracy. Like previous studies, we find that the reference velocity-model and relative-location accuracy are highly correlated. We also find that metrics based on travel-time residual of relocated events are not a reliable for assessing either velocity-model or relative-location accuracy. In the topical area of detection, we develop specialized correlation (subspace) detectors for the principal mines surrounding the ARCES station located in the European Arctic. Our objective is to provide efficient screens for explosions occurring in the mines of the Kola Peninsula (Kovdor, Zapolyarny, Olenogorsk, Khibiny) and the major iron mines of northern Sweden (Malmberget, Kiruna). In excess of 90% of the events detected by the ARCES station are mining explosions, and a significant fraction are from these northern mining groups. The primary challenge in developing waveform correlation detectors is the degree of variation in the source time histories of the shots, which can result in poor correlation among events even in close proximity. Our approach to solving this problem is to use lagged subspace correlation detectors, which offer some prospect of compensating for variation and uncertainty in source time functions.« less

Stochastic models of the Social Security trust funds.

PubMed

Burdick, Clark; Manchester, Joyce

Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.