Richards-like two species population dynamics model.

PubMed

Ribeiro, Fabiano; Cabella, Brenno Caetano Troca; Martinez, Alexandre Souto

2014-12-01

The two-species population dynamics model is the simplest paradigm of inter- and intra-species interaction. Here, we present a generalized Lotka-Volterra model with intraspecific competition, which retrieves as particular cases, some well-known models. The generalization parameter is related to the species habitat dimensionality and their interaction range. Contrary to standard models, the species coupling parameters are general, not restricted to non-negative values. Therefore, they may represent different ecological regimes, which are derived from the asymptotic solution stability analysis and are represented in a phase diagram. In this diagram, we have identified a forbidden region in the mutualism regime, and a survival/extinction transition with dependence on initial conditions for the competition regime. Also, we shed light on two types of predation and competition: weak, if there are species coexistence, or strong, if at least one species is extinguished.

Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels

NASA Astrophysics Data System (ADS)

Qian, Shouguo; Li, Gang; Shao, Fengjing; Xing, Yulong

2018-05-01

We construct and study efficient high order discontinuous Galerkin methods for the shallow water flows in open channels with irregular geometry and a non-flat bottom topography in this paper. The proposed methods are well-balanced for the still water steady state solution, and can preserve the non-negativity of wet cross section numerically. The well-balanced property is obtained via a novel source term separation and discretization. A simple positivity-preserving limiter is employed to provide efficient and robust simulations near the wetting and drying fronts. Numerical examples are performed to verify the well-balanced property, the non-negativity of the wet cross section, and good performance for both continuous and discontinuous solutions.

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

NASA Astrophysics Data System (ADS)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

On the analysis of competitive displacement in dengue disease transmission

NASA Astrophysics Data System (ADS)

Wijaya, Karunia P.; Nuraini, Nuning; Soewono, Edy; Handayani, Dewi

2014-03-01

We study a host-vector model involving the interplay of competitive displacement mechanism in a specific DENV serotype, both in human blood and mosquito blood. Using phylogenetic analysis, world virologists investigate the severe manifestations of dengue fever caused by the displacements within weakly virulent pathogens (native strains) by more virulent pathogens (invasive strains) in one serotype. We construct SIR model for human and SI model for mosquito to explore the key determinants of those displacements. Analysis of nonnegativity and boundedness of the solution as well as the basic reproduction number (R0) are taken into account for verifying the model into biological meaningfulness. To generate predictions of the outcomes of control strategies, we derive an optimal control model which involves two control apparatus: fluid infusion (for human) and fumigation (for vector). Numerical results show the dynamics of host-vector in an observation period, both under control and without control.

Global Solutions for the zero-energy Novikov–Veselov equation by inverse scattering

NASA Astrophysics Data System (ADS)

Music, Michael; Perry, Peter

2018-07-01

Using the inverse scattering method, we construct global solutions to the Novikov–Veselov equation for real-valued decaying initial data q 0 with the property that the associated Schrödinger operator is nonnegative. Such initial data are either critical (an arbitrarily small perturbation of the potential makes the operator nonpositive) or subcritical (sufficiently small perturbations of the potential preserve non-negativity of the operator). Previously, Lassas, Mueller, Siltanen and Stahel proved global existence for critical potentials, also called potentials of conductivity type. We extend their results to include the much larger class of subcritical potentials. We show that the subcritical potentials form an open set and that the critical potentials form the nowhere dense boundary of this open set. Our analysis draws on previous work of the first author and on ideas of Grinevich and Manakov.

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method.

PubMed

Wang, Qi; Wang, Huaxiang; Cui, Ziqiang; Yang, Chengyi

2012-11-01

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Usefulness of FC-TRIPLEX Chagas/Leish IgG1 as confirmatory assay for non-negative results in blood bank screening of Chagas disease.

PubMed

Campos, Fernanda Magalhães Freire; Repoles, Laura Cotta; de Araújo, Fernanda Fortes; Peruhype-Magalhães, Vanessa; Xavier, Marcelo Antônio Pascoal; Sabino, Ester Cerdeira; de Freitas Carneiro Proietti, Anna Bárbara; Andrade, Mariléia Chaves; Teixeira-Carvalho, Andréa; Martins-Filho, Olindo Assis; Gontijo, Célia Maria Ferreira

2018-04-01

A relevant issue in Chagas disease serological diagnosis regards the requirement of using several confirmatory methods to elucidate the status of non-negative results from blood bank screening. The development of a single reliable method may potentially contribute to distinguish true and false positive results. Our aim was to evaluate the performance of the multiplexed flow-cytometry anti-T. cruzi/Leishmania IgG1 serology/(FC-TRIPLEX Chagas/Leish IgG1) with three conventional confirmatory criteria (ELISA-EIA, Immunofluorescence assay-IIF and EIA/IIF consensus criterion) to define the final status of samples with actual/previous non-negative results during anti-T. cruzi ELISA-screening in blood banks. Apart from inconclusive results, the FC-TRIPLEX presented a weak agreement index with EIA, while a strong agreement was observed when either IIF or EIA/IIF consensus criteria were applied. Discriminant analysis and Spearman's correlation further corroborates the agreement scores. ROC curve analysis showed that FC-TRIPLEX performance indexes were higher when IIF and EIA/IIF consensus were used as a confirmatory criterion. Logistic regression analysis further demonstrated that the probability of FC-TRIPLEX to yield positive results was higher for inconclusive results from IIF and EIA/IIF consensus. Machine learning tools illustrated the high level of categorical agreement between FC-TRIPLEX versus IIF or EIA/IIF consensus. Together, these findings demonstrated the usefulness of FC-TRIPLEX as a tool to elucidate the status of non-negative results in blood bank screening of Chagas disease. Copyright © 2018. Published by Elsevier B.V.

KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2017-07-01

Direct definition of the Cauchy-Jost (known also as Cauchy-Baker-Akhiezer) function is given in the case of a pure solitonic solution. Properties of this function are discussed in detail using the Kadomtsev-Petviashvili II equation as an example. This enables formulation of the Darboux transformations in terms of the Cauchy-Jost function and classification of these transformations. Action of Darboux transformations on Grassmanians—i.e. on the space of soliton parameters—is derived and the relation of the Darboux transformations with the property of total nonnegativity of elements of corresponding Grassmanians is discussed. To the memory of our friend and colleague Peter P Kulish

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Coupling a Reactive Transport Code with a Global Land Surface Model for Mechanistic Biogeochemistry Representation: 1. Addressing the Challenge of Nonnegativity

DOE PAGES

Tang, Guoping; Yuan, Fengming; Bisht, Gautam; ...

2016-01-01

Reactive transport codes (e.g., PFLOTRAN) are increasingly used to improve the representation of biogeochemical processes in terrestrial ecosystem models (e.g., the Community Land Model, CLM). As CLM and PFLOTRAN use explicit and implicit time stepping, implementation of CLM biogeochemical reactions in PFLOTRAN can result in negative concentration, which is not physical and can cause numerical instability and errors. The objective of this work is to address the nonnegativity challenge to obtain accurate, efficient, and robust solutions. We illustrate the implementation of a reaction network with the CLM-CN decomposition, nitrification, denitrification, and plant nitrogen uptake reactions and test the implementation atmore » arctic, temperate, and tropical sites. We examine use of scaling back the update during each iteration (SU), log transformation (LT), and downregulating the reaction rate to account for reactant availability limitation to enforce nonnegativity. Both SU and LT guarantee nonnegativity but with implications. When a very small scaling factor occurs due to either consumption or numerical overshoot, and the iterations are deemed converged because of too small an update, SU can introduce excessive numerical error. LT involves multiplication of the Jacobian matrix by the concentration vector, which increases the condition number, decreases the time step size, and increases the computational cost. Neither SU nor SE prevents zero concentration. When the concentration is close to machine precision or 0, a small positive update stops all reactions for SU, and LT can fail due to a singular Jacobian matrix. The consumption rate has to be downregulated such that the solution to the mathematical representation is positive. A first-order rate downregulates consumption and is nonnegative, and adding a residual concentration makes it positive. For zero-order rate or when the reaction rate is not a function of a reactant, representing the availability limitation of each reactant with a Monod substrate limiting function provides a smooth transition between a zero-order rate when the reactant is abundant and first-order rate when the reactant becomes limiting. When the half saturation is small, marching through the transition may require small time step sizes to resolve the sharp change within a small range of concentration values. Our results from simple tests and CLM-PFLOTRAN simulations caution against use of SU and indicate that accurate, stable, and relatively efficient solutions can be achieved with LT and downregulation with Monod substrate limiting function and residual concentration.« less

Deep learning and non-negative matrix factorization in recognition of mammograms

NASA Astrophysics Data System (ADS)

Swiderski, Bartosz; Kurek, Jaroslaw; Osowski, Stanislaw; Kruk, Michal; Barhoumi, Walid

2017-02-01

This paper presents novel approach to the recognition of mammograms. The analyzed mammograms represent the normal and breast cancer (benign and malignant) cases. The solution applies the deep learning technique in image recognition. To obtain increased accuracy of classification the nonnegative matrix factorization and statistical self-similarity of images are applied. The images reconstructed by using these two approaches enrich the data base and thanks to this improve of quality measures of mammogram recognition (increase of accuracy, sensitivity and specificity). The results of numerical experiments performed on large DDSM data base containing more than 10000 mammograms have confirmed good accuracy of class recognition, exceeding the best results reported in the actual publications for this data base.

Entropy-Based Approach To Nonlinear Stability

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1991-01-01

NASA technical memorandum suggests schemes for numerical solution of differential equations of flow made more accurate and robust by invoking second law of thermodynamics. Proposes instead of using artificial viscosity to suppress such unphysical solutions as spurious numerical oscillations and nonlinear instabilities, one should formulate equations so that rate of production of entropy within each cell of computational grid be nonnegative, as required by second law.

Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System

NASA Astrophysics Data System (ADS)

Goluskin, David

2018-04-01

We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be proved using Lyapunov functions. Nonnegativity is enforced by requiring the polynomials to be sums of squares, a condition which is then formulated as a semidefinite program (SDP) that can be solved computationally. Although such computations are subject to numerical error, we demonstrate two ways to obtain rigorous results: using interval arithmetic to control the error of an approximate SDP solution, and finding exact analytical solutions to relatively small SDPs. Previous formulations are extended to allow for bounds depending analytically on parametric variables. These methods are illustrated using the Lorenz equations, a system with three state variables ( x, y, z) and three parameters (β ,σ ,r). Bounds are reported for infinite-time averages of all eighteen moments x^ly^mz^n up to quartic degree that are symmetric under (x,y)\\mapsto (-x,-y). These bounds apply to all solutions regardless of stability, including chaotic trajectories, periodic orbits, and equilibrium points. The analytical approach yields two novel bounds that are sharp: the mean of z^3 can be no larger than its value of (r-1)^3 at the nonzero equilibria, and the mean of xy^3 must be nonnegative. The interval arithmetic approach is applied at the standard chaotic parameters to bound eleven average moments that all appear to be maximized on the shortest periodic orbit. Our best upper bound on each such average exceeds its value on the maximizing orbit by less than 1%. Many bounds reported here are much tighter than would be possible without computer assistance.

A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials

NASA Astrophysics Data System (ADS)

Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang

2018-01-01

We consider a class of time-dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of problems covers important cases such as Fokker-Planck type equations and aggregation models, which have been studied intensively in the past decades. In this paper, we design a high order discontinuous Galerkin method for such problems. If the interaction potential is not involved, or the interaction is defined by a smooth kernel, our semi-discrete scheme admits an entropy inequality on the discrete level. Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint. Our method also applies to two dimensional problems on Cartesian meshes. Numerical examples are given to confirm the high order accuracy for smooth test cases and to demonstrate the effectiveness for preserving long time asymptotics.

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI.

PubMed

Cheng, Jian; Deriche, Rachid; Jiang, Tianzi; Shen, Dinggang; Yap, Pew-Thian

2014-11-01

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S(2). However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S(2). Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions. Copyright © 2014 Elsevier Inc. All rights reserved.

High Frequency Acoustic Propagation using Level Set Methods

DTIC Science & Technology

2007-01-01

solution of the high frequency approximation to the wave equation. Traditional solutions to the Eikonal equation in high frequency acoustics are...the Eikonal equation derived from the high frequency approximation to the wave equation, ucuH ∇±=∇ )(),( xx , with the nonnegative function c(x...For simplicity, we only consider the case ucuH ∇+=∇ )(),( xx . Two difficulties must be addressed when solving the Eikonal equation in a fixed

Circular Mixture Modeling of Color Distribution for Blind Stain Separation in Pathology Images.

PubMed

Li, Xingyu; Plataniotis, Konstantinos N

2017-01-01

In digital pathology, to address color variation and histological component colocalization in pathology images, stain decomposition is usually performed preceding spectral normalization and tissue component segmentation. This paper examines the problem of stain decomposition, which is a naturally nonnegative matrix factorization (NMF) problem in algebra, and introduces a systematical and analytical solution consisting of a circular color analysis module and an NMF-based computation module. Unlike the paradigm of existing stain decomposition algorithms where stain proportions are computed from estimated stain spectra using a matrix inverse operation directly, the introduced solution estimates stain spectra and stain depths via probabilistic reasoning individually. Since the proposed method pays extra attentions to achromatic pixels in color analysis and stain co-occurrence in pixel clustering, it achieves consistent and reliable stain decomposition with minimum decomposition residue. Particularly, aware of the periodic and angular nature of hue, we propose the use of a circular von Mises mixture model to analyze the hue distribution, and provide a complete color-based pixel soft-clustering solution to address color mixing introduced by stain overlap. This innovation combined with saturation-weighted computation makes our study effective for weak stains and broad-spectrum stains. Extensive experimentation on multiple public pathology datasets suggests that our approach outperforms state-of-the-art blind stain separation methods in terms of decomposition effectiveness.

A GRAPHICAL DIAGNOSTIC METHOD FOR ASSESSING THE ROTATION IN FACTOR ANALYTICAL MODELS OF ATMOSPHERIC POLLUTION. (R831078)

EPA Science Inventory

Factor analytic tools such as principal component analysis (PCA) and positive matrix factorization (PMF), suffer from rotational ambiguity in the results: different solutions (factors) provide equally good fits to the measured data. The PMF model imposes non-negativity of both...

On the Quasimonotonicity of a Square Linear Operator with Respect to a Nonnegative Cone

DTIC Science & Technology

1998-06-01

follows from the result from Perron (1907) and Frobenius (1912) on the theory of nonnegative matrices, which states that a nonnegative matrix has a...Dissertation 4. TITLE AND SUBTITLE ON THE QUASIMONOTONICITY OF A SQUARE LINEAR OPERATOR WITH RESPECT TO A NONNEGATIVE CONE 6. AUTHOR(S) Beaver, Philip...ABSTRACT (maximum 200 words) The question of when a square, linear operator is quasimonotone nondecreasing with respect to a nonnegative cone was posed for

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

Some Preliminary Results on an SEIARD Epidemic Model with Vaccination and Antiviral Treatment Controls and Dead-Infective Culling Action

NASA Astrophysics Data System (ADS)

De la Sen, M.; Nistal, R.; Alonso-Quesada, S.; Garrido, A. J.

2016-08-01

This paper studies the non-negativity and stability properties of the solutions of a newly proposed SEIADR model which incorporates asymptomatic and dead-infective subpopulations to those defining the standard SEIR model and, in parallel, it incorporates feedback vaccination and antiviral treatment controls.

A globally convergent Lagrange and barrier function iterative algorithm for the traveling salesman problem.

PubMed

Dang, C; Xu, L

2001-03-01

In this paper a globally convergent Lagrange and barrier function iterative algorithm is proposed for approximating a solution of the traveling salesman problem. The algorithm employs an entropy-type barrier function to deal with nonnegativity constraints and Lagrange multipliers to handle linear equality constraints, and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the algorithm searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that the nonnegativity constraints are always satisfied automatically if the step length is a number between zero and one. At each iteration the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the algorithm converges to a stationary point of the barrier problem without any condition on the objective function. Theoretical and numerical results show that the algorithm seems more effective and efficient than the softassign algorithm.

Global boundedness of solutions to a two-species chemotaxis system

NASA Astrophysics Data System (ADS)

Zhang, Qingshan; Li, Yuxiang

2015-02-01

In this paper, we consider the chemotaxis system of two species which are attracted by the same signal substance under homogeneous Neumann boundary conditions in a smooth bounded domain . We prove that if the nonnegative initial data and for some r > n, the system possesses a unique global uniformly bounded solution under some conditions on the chemotaxis sensitivity functions χ 1( w), χ 2( w) and the logistic growth coefficients μ 1, μ 2.

Analysis of a diffuse interface model of multispecies tumor growth

NASA Astrophysics Data System (ADS)

Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.

2017-04-01

We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Boundedness in a quasilinear chemotaxis-haptotaxis system with logistic source

NASA Astrophysics Data System (ADS)

Liu, Ji; Zheng, Jiashan; Wang, Yifu

2016-04-01

In this paper, we consider the quasilinear chemotaxis-haptotaxis system u_t=nabla\\cdot(D(u)nabla u)-nabla\\cdot(S_1(u)nabla v)-nabla\\cdot(S_2(u)nabla w)+uf(u,w),quad xinΩ, t > 0,v_t=Δ v-v+u,quad xinΩ, t > 0,w_t=-vw,quad xinΩ, t > 0 in a bounded smooth domain {Ωsubset R^n (n≥1)} under zero-flux boundary conditions, where the nonlinearities {D, S_1} and {S_2} are assumed to generalize the prototypes D(u)=CD(u+1)^{m-1}, S_1(u)=C_{S_1}u(u+1)^{q_1-1} quad {and} quad S_2(u)=C_{S_2}u(u+1)^{q_2-1} with {C_D,C_{S_1},C_{S_2} > 0, m,q_1,q_2in R} and {f(u,w)in C^1([0,+infty)×[0,+∞))} fulfills f(u,w)≤ r-buquad {for all} ~u≥ 0quad {and} quad w≥ 0, where {r > 0, b > 0.} Assuming nonnegative initial data {u_0(x)in W^{1,∞}(Ω),v_0(x)in W^{1,∞}(Ω)} and {w_0(x)in C^{2,α}(barΩ)} for some {αin(0,1),} we prove that (i) for {n≤2,} if q_1,q_2\\ < m+2/n-1,} then {(star)} has a unique nonnegative classical solution which is globally bounded, (ii) for {n > 2,} if {max{q_1,q_2} < m+2/n-1} and {m > 2-2/n} or {max{q_1,q_2} < m+2/n-1} and {m≤ 1,} then {(star)} has a unique nonnegative classical solution which is globally bounded.

Poster — Thur Eve — 03: Application of the non-negative matrix factorization technique to [{sup 11}C]-DTBZ dynamic PET data for the early detection of Parkinson's disease

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

Lee, Dong-Chang; Jans, Hans; McEwan, Sandy

2014-08-15

In this work, a class of non-negative matrix factorization (NMF) technique known as alternating non-negative least squares, combined with the projected gradient method, is used to analyze twenty-five [{sup 11}C]-DTBZ dynamic PET/CT brain data. For each subject, a two-factor model is assumed and two factors representing the striatum (factor 1) and the non-striatum (factor 2) tissues are extracted using the proposed NMF technique and commercially available factor analysis software “Pixies”. The extracted factor 1 and 2 curves represent the binding site of the radiotracer and describe the uptake and clearance of the radiotracer by soft tissues in the brain, respectively.more » The proposed NMF technique uses prior information about the dynamic data to obtain sample time-activity curves representing the striatum and the non-striatum tissues. These curves are then used for “warm” starting the optimization. Factor solutions from the two methods are compared graphically and quantitatively. In healthy subjects, radiotracer uptake by factors 1 and 2 are approximately 35–40% and 60–65%, respectively. The solutions are also used to develop a factor-based metric for the detection of early, untreated Parkinson's disease. The metric stratifies healthy subjects from suspected Parkinson's patients (based on the graphical method). The analysis shows that both techniques produce comparable results with similar computational time. The “semi-automatic” approach used by the NMF technique allows clinicians to manually set a starting condition for “warm” starting the optimization in order to facilitate control and efficient interaction with the data.« less

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

PubMed Central

Garić-Demirović, M.; Kulenović, M. R. S.; Nurkanović, M.

2013-01-01

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x n+1 = x n−1 2/(ax n 2 + bx n x n−1 + cx n−1 2), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x −1 and x 0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. PMID:24369451

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.

PubMed

Kim, Hyunsoo; Park, Haesun

2007-06-15

Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. The software is available as supplementary material.

Lanchester-Type Models of Warfare. Volume II

DTIC Science & Technology

1980-10-01

the so-called PERRON - FROBENIUS theorem50 for nonnegative matrices that one can guarantee that (without any further assumptions about A and B) there...always exists a vector of nonnegative values such that, for example, (7.18.6) holds. Before we state the PERRON - FROBENIUS theorem for nonnegative...a proof of this important theorem). THEOREM .5.-1.1 ( PERRON [121] and FROBENIUS [60]): Let C z 0 be an n x n matrix. Then, 1. C has a nonnegative real

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-10-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

Gradient estimates on the weighted p-Laplace heat equation

NASA Astrophysics Data System (ADS)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

Quantum Matching Theory (with new complexity-theoretic, combinatorial and topical insights on the nature of the quantum entanglement)

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

Gurvits, L.

2002-01-01

Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with non-negative entries. Based on this point of view, we introduce a definition of perfect Quantum (operator) matching. We show that the new notion inherits many 'classical' properties, but not all of them. This new notion goes somewhere beyound matroids. For separable bipartite quantum states this new notion coinsides with the full rank property of the intersection of two corresponding geometric matroids. In the classical situation, permanents are naturally associated with perfectsmore » matchings. We introduce an analog of permanents for positive operators, called Quantum Permanent and show how this generalization of the permanent is related to the Quantum Entanglement. Besides many other things, Quantum Permanents provide new rational inequalities necessary for the separability of bipartite quantum states. Using Quantum Permanents, we give deterministic poly-time algorithm to solve Hidden Matroids Intersection Problem and indicate some 'classical' complexity difficulties associated with the Quantum Entanglement. Finally, we prove that the weak membership problem for the convex set of separable bipartite density matrices is NP-HARD.« less

THz spectral data analysis and components unmixing based on non-negative matrix factorization methods

NASA Astrophysics Data System (ADS)

Ma, Yehao; Li, Xian; Huang, Pingjie; Hou, Dibo; Wang, Qiang; Zhang, Guangxin

2017-04-01

In many situations the THz spectroscopic data observed from complex samples represent the integrated result of several interrelated variables or feature components acting together. The actual information contained in the original data might be overlapping and there is a necessity to investigate various approaches for model reduction and data unmixing. The development and use of low-rank approximate nonnegative matrix factorization (NMF) and smooth constraint NMF (CNMF) algorithms for feature components extraction and identification in the fields of terahertz time domain spectroscopy (THz-TDS) data analysis are presented. The evolution and convergence properties of NMF and CNMF methods based on sparseness, independence and smoothness constraints for the resulting nonnegative matrix factors are discussed. For general NMF, its cost function is nonconvex and the result is usually susceptible to initialization and noise corruption, and may fall into local minima and lead to unstable decomposition. To reduce these drawbacks, smoothness constraint is introduced to enhance the performance of NMF. The proposed algorithms are evaluated by several THz-TDS data decomposition experiments including a binary system and a ternary system simulating some applications such as medicine tablet inspection. Results show that CNMF is more capable of finding optimal solutions and more robust for random initialization in contrast to NMF. The investigated method is promising for THz data resolution contributing to unknown mixture identification.

THz spectral data analysis and components unmixing based on non-negative matrix factorization methods.

PubMed

Ma, Yehao; Li, Xian; Huang, Pingjie; Hou, Dibo; Wang, Qiang; Zhang, Guangxin

2017-04-15

In many situations the THz spectroscopic data observed from complex samples represent the integrated result of several interrelated variables or feature components acting together. The actual information contained in the original data might be overlapping and there is a necessity to investigate various approaches for model reduction and data unmixing. The development and use of low-rank approximate nonnegative matrix factorization (NMF) and smooth constraint NMF (CNMF) algorithms for feature components extraction and identification in the fields of terahertz time domain spectroscopy (THz-TDS) data analysis are presented. The evolution and convergence properties of NMF and CNMF methods based on sparseness, independence and smoothness constraints for the resulting nonnegative matrix factors are discussed. For general NMF, its cost function is nonconvex and the result is usually susceptible to initialization and noise corruption, and may fall into local minima and lead to unstable decomposition. To reduce these drawbacks, smoothness constraint is introduced to enhance the performance of NMF. The proposed algorithms are evaluated by several THz-TDS data decomposition experiments including a binary system and a ternary system simulating some applications such as medicine tablet inspection. Results show that CNMF is more capable of finding optimal solutions and more robust for random initialization in contrast to NMF. The investigated method is promising for THz data resolution contributing to unknown mixture identification. Copyright © 2017 Elsevier B.V. All rights reserved.

Second law of thermodynamics and quantum feedback control: Maxwell's demon with weak measurements

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

Jacobs, Kurt

2009-07-15

Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. For many quantum measurements their bound was not tight. We show that a tight version of this bound follows straightforwardly from recent work on Maxwell's demon by Alicki et al. [Open Syst. Inf. Dyn. 11, 205 (2004)], for both discrete and continuous feedback control. Our analysis also shows that bare, efficient measurements always do non-negative work on a system in equilibrium, but do not add heat.

Maximum Entropy/Optimal Projection Design Synthesis for Decentralized Control of Large Space Structures

DTIC Science & Technology

1988-05-01

M 21 M2 I SI M1l[11 II1211 - - - M= II 2+111 I11-211 NONNEGATIVE CONE ORDERING Figure 25. The Matrix Majorant Is a Bound for the Hatrix Block Norm...the with respect to the cone of nonnegative -definite matrices. inequality (1.5) by the r x r nonnegative matrix equation Indeed, the majorant bound...t) eA-) e ea ’ A rT(" 3 ds, t> O , ju E [0 , 1] 0 J(G, )= tr (0,(6)R,) which is monotonically increasing in the nonnegative -definite G , cone with

Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators

NASA Astrophysics Data System (ADS)

Yu, Yue; Wu, Yong-Shi; Xie, Xincheng

2017-03-01

We study the bulk-edge correspondence in topological insulators by taking Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant in this model is Z2 invariant modulo the spectral flow of a single-parameter family of 1 + 1-dimensional Dirac operators with a global boundary condition induced by the Kramers degeneracy of the system. This spectral flow is defined as an integer which counts the difference between the number of eigenvalues of the Dirac operator family that flow from negative to non-negative and the number of eigenvalues that flow from non-negative to negative. Since the bulk states of the insulator are completely gapped and the ground state is assumed being no more degenerate except the Kramers, they do not contribute to the spectral flow and only edge states contribute to. The parity of the number of the Kramers pairs of gapless edge states is exactly the same as that of the spectral flow. This reveals the origin of the edge-bulk correspondence, i.e., why the edge states can be used to characterize the topological insulators. Furthermore, the spectral flow is related to the reduced η-invariant and thus counts both the discrete ground state degeneracy and the continuous gapless excitations, which distinguishes the topological insulator from the conventional band insulator even if the edge states open a gap due to a strong interaction between edge modes. We emphasize that these results are also valid even for a weak disordered and/or weak interacting system. The higher spectral flow to categorize the higher-dimensional topological insulators is expected.

A Novel Sky-Subtraction Method Based on Non-negative Matrix Factorisation with Sparsity for Multi-object Fibre Spectroscopy

NASA Astrophysics Data System (ADS)

Zhang, Bo; Zhang, Long; Ye, Zhongfu

2016-12-01

A novel sky-subtraction method based on non-negative matrix factorisation with sparsity is proposed in this paper. The proposed non-negative matrix factorisation with sparsity method is redesigned for sky-subtraction considering the characteristics of the skylights. It has two constraint terms, one for sparsity and the other for homogeneity. Different from the standard sky-subtraction techniques, such as the B-spline curve fitting methods and the Principal Components Analysis approaches, sky-subtraction based on non-negative matrix factorisation with sparsity method has higher accuracy and flexibility. The non-negative matrix factorisation with sparsity method has research value for the sky-subtraction on multi-object fibre spectroscopic telescope surveys. To demonstrate the effectiveness and superiority of the proposed algorithm, experiments are performed on Large Sky Area Multi-Object Fiber Spectroscopic Telescope data, as the mechanisms of the multi-object fibre spectroscopic telescopes are similar.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics

NASA Astrophysics Data System (ADS)

Wen, Zijuan; Fu, Shengmao

2009-08-01

In this paper, an n-species strongly coupled cooperating diffusive system is considered in a bounded smooth domain, subject to homogeneous Neumann boundary conditions. Employing the method of energy estimates, we obtain some conditions on the diffusion matrix and inter-specific cooperatives to ensure the global existence and uniform boundedness of a nonnegative solution. The globally asymptotical stability of the constant positive steady state is also discussed. As a consequence, all the results hold true for multi-species Lotka-Volterra type competition model and prey-predator model.

Topology of codimension-one foliations of nonnegative curvature. II

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

Bolotov, D V

We prove that a 3-connected closed manifold M of dimension n≥5 does not admit a codimension-one C{sup 2}-foliation of nonnegative curvature. In particular, this gives a complete answer to a question of Stuck on the existence of codimension-one foliations of nonnegative curvature on spheres. We also consider codimension-one C{sup 2}-foliations of nonnegative Ricci curvature on a closed manifold M with leaves having finitely generated fundamental group, and show that such a foliation is flat if and only if M is a K(π,1)-manifold. Bibliography: 13 titles.

Using Separable Nonnegative Matrix Factorization Techniques for the Analysis of Time-Resolved Raman Spectra

NASA Astrophysics Data System (ADS)

Luce, R.; Hildebrandt, P.; Kuhlmann, U.; Liesen, J.

2016-09-01

The key challenge of time-resolved Raman spectroscopy is the identification of the constituent species and the analysis of the kinetics of the underlying reaction network. In this work we present an integral approach that allows for determining both the component spectra and the rate constants simultaneously from a series of vibrational spectra. It is based on an algorithm for non-negative matrix factorization which is applied to the experimental data set following a few pre-processing steps. As a prerequisite for physically unambiguous solutions, each component spectrum must include one vibrational band that does not significantly interfere with vibrational bands of other species. The approach is applied to synthetic "experimental" spectra derived from model systems comprising a set of species with component spectra differing with respect to their degree of spectral interferences and signal-to-noise ratios. In each case, the species involved are connected via monomolecular reaction pathways. The potential and limitations of the approach for recovering the respective rate constants and component spectra are discussed.

A Study of Strong Stability of Distributed Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Cataltepe, Tayfun

1989-01-01

The strong stability of distributed systems is studied and the problem of characterizing strongly stable semigroups of operators associated with distributed systems is addressed. Main emphasis is on contractive systems. Three different approaches to characterization of strongly stable contractive semigroups are developed. The first one is an operator theoretical approach. Using the theory of dilations, it is shown that every strongly stable contractive semigroup is related to the left shift semigroup on an L(exp 2) space. Then, a decomposition for the state space which identifies strongly stable and unstable states is introduced. Based on this decomposition, conditions for a contractive semigroup to be strongly stable are obtained. Finally, extensions of Lyapunov's equation for distributed parameter systems are investigated. Sufficient conditions for weak and strong stabilities of uniformly bounded semigroups are obtained by relaxing the equivalent norm condition on the right hand side of the Lyanupov equation. These characterizations are then applied to the problem of feedback stabilization. First, it is shown via the state space decomposition that under certain conditions a contractive system (A,B) can be strongly stabilized by the feedback -B(*). Then, application of the extensions of the Lyapunov equation results in sufficient conditions for weak, strong, and exponential stabilizations of contractive systems by the feedback -B(*). Finally, it is shown that for a contractive system, the first derivative of x with respect to time = Ax + Bu (where B is any linear bounded operator), there is a related linear quadratic regulator problem and a corresponding steady state Riccati equation which always has a bounded nonnegative solution.

Greedy Algorithms for Nonnegativity-Constrained Simultaneous Sparse Recovery

PubMed Central

Kim, Daeun; Haldar, Justin P.

2016-01-01

This work proposes a family of greedy algorithms to jointly reconstruct a set of vectors that are (i) nonnegative and (ii) simultaneously sparse with a shared support set. The proposed algorithms generalize previous approaches that were designed to impose these constraints individually. Similar to previous greedy algorithms for sparse recovery, the proposed algorithms iteratively identify promising support indices. In contrast to previous approaches, the support index selection procedure has been adapted to prioritize indices that are consistent with both the nonnegativity and shared support constraints. Empirical results demonstrate for the first time that the combined use of simultaneous sparsity and nonnegativity constraints can substantially improve recovery performance relative to existing greedy algorithms that impose less signal structure. PMID:26973368

A sequential solution for anisotropic total variation image denoising with interval constraints

NASA Astrophysics Data System (ADS)

Xu, Jingyan; Noo, Frédéric

2017-09-01

We show that two problems involving the anisotropic total variation (TV) and interval constraints on the unknown variables admit, under some conditions, a simple sequential solution. Problem 1 is a constrained TV penalized image denoising problem; problem 2 is a constrained fused lasso signal approximator. The sequential solution entails finding first the solution to the unconstrained problem, and then applying a thresholding to satisfy the constraints. If the interval constraints are uniform, this sequential solution solves problem 1. If the interval constraints furthermore contain zero, the sequential solution solves problem 2. Here uniform interval constraints refer to all unknowns being constrained to the same interval. A typical example of application is image denoising in x-ray CT, where the image intensities are non-negative as they physically represent linear attenuation coefficient in the patient body. Our results are simple yet seem unknown; we establish them using the Karush-Kuhn-Tucker conditions for constrained convex optimization.

Topology of codimension-one foliations of nonnegative curvature

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

Bolotov, Dmitry V

We show that a transversely oriented C{sup 2}-foliation of codimension one with nonnegative Ricci curvature on a closed orientable manifold is a foliation with almost no holonomy. This allows us to decompose the manifold into blocks on which this foliation has a simple structure. We also show that a manifold homeomorphic to a 5-dimensional sphere does not admit a codimension-one C{sup 2}-foliation with nonnegative sectional curvature. Bibliography: 29 titles.

The Quasimonotonicity of Linear Differential Systems -The Complex Spectrum

DTIC Science & Technology

2001-09-12

proper, simplicial cone determined by the columns of B (see [10]) and that C is essentially nonnegative (see [11]). In [6], Heikkilä used Perron ...a B ≥ 0 such that Ae = B−1AB is essentially nonnegative and ir- reducible, then Perron - Frobenius theory tells us that Ae has a real eigenvalue λ1 with...systems requires that the comparison system be quasimonotone nondecreasing with respect to a cone contained in the nonnegative orthant. For linear

Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation.

PubMed

Saito, Shota; Hirata, Yoshito; Sasahara, Kazutoshi; Suzuki, Hideyuki

2015-01-01

Micro-blogging services, such as Twitter, offer opportunities to analyse user behaviour. Discovering and distinguishing behavioural patterns in micro-blogging services is valuable. However, it is difficult and challenging to distinguish users, and to track the temporal development of collective attention within distinct user groups in Twitter. In this paper, we formulate this problem as tracking matrices decomposed by Nonnegative Matrix Factorisation for time-sequential matrix data, and propose a novel extension of Nonnegative Matrix Factorisation, which we refer to as Time Evolving Nonnegative Matrix Factorisation (TENMF). In our method, we describe users and words posted in some time interval by a matrix, and use several matrices as time-sequential data. Subsequently, we apply Time Evolving Nonnegative Matrix Factorisation to these time-sequential matrices. TENMF can decompose time-sequential matrices, and can track the connection among decomposed matrices, whereas previous NMF decomposes a matrix into two lower dimension matrices arbitrarily, which might lose the time-sequential connection. Our proposed method has an adequately good performance on artificial data. Moreover, we present several results and insights from experiments using real data from Twitter.

Adaptive multi-view clustering based on nonnegative matrix factorization and pairwise co-regularization

NASA Astrophysics Data System (ADS)

Zhang, Tianzhen; Wang, Xiumei; Gao, Xinbo

2018-04-01

Nowadays, several datasets are demonstrated by multi-view, which usually include shared and complementary information. Multi-view clustering methods integrate the information of multi-view to obtain better clustering results. Nonnegative matrix factorization has become an essential and popular tool in clustering methods because of its interpretation. However, existing nonnegative matrix factorization based multi-view clustering algorithms do not consider the disagreement between views and neglects the fact that different views will have different contributions to the data distribution. In this paper, we propose a new multi-view clustering method, named adaptive multi-view clustering based on nonnegative matrix factorization and pairwise co-regularization. The proposed algorithm can obtain the parts-based representation of multi-view data by nonnegative matrix factorization. Then, pairwise co-regularization is used to measure the disagreement between views. There is only one parameter to auto learning the weight values according to the contribution of each view to data distribution. Experimental results show that the proposed algorithm outperforms several state-of-the-arts algorithms for multi-view clustering.

Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

NASA Astrophysics Data System (ADS)

Sembiring, Pasukat

2017-12-01

Processing ofdata with very large dimensions has been a hot topic in recent decades. Various techniques have been proposed in order to execute the desired information or structure. Non- Negative Matrix Factorization (NMF) based on non-negatives data has become one of the popular methods for shrinking dimensions. The main strength of this method is non-negative object, the object model by a combination of some basic non-negative parts, so as to provide a physical interpretation of the object construction. The NMF is a dimension reduction method thathasbeen used widely for numerous applications including computer vision,text mining, pattern recognitions,and bioinformatics. Mathematical formulation for NMF did not appear as a convex optimization problem and various types of algorithms have been proposed to solve the problem. The Framework of Alternative Nonnegative Least Square(ANLS) are the coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This paper proposes a new algorithm to solve NMF problem based on the framework of ANLS.This algorithm inherits the convergenceproperty of the ANLS framework to nonlinear constraints NMF formulations.

On non-negative matrix factorization algorithms for signal-dependent noise with application to electromyography data

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

Non-negative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two nonnegative matrices, W and H where V ~ WH. It has been successfully applied in the analysis and interpretation of large-scale data arising in neuroscience, computational biology and natural language processing, among other areas. A distinctive feature of NMF is its nonnegativity constraints that allow only additive linear combinations of the data, thus enabling it to learn parts that have distinct physical representations in reality. In this paper, we describe an information-theoretic approach to NMF for signal-dependent noise based on the generalized inverse Gaussian model. Specifically, we propose three novel algorithms in this setting, each based on multiplicative updates and prove monotonicity of updates using the EM algorithm. In addition, we develop algorithm-specific measures to evaluate their goodness-of-fit on data. Our methods are demonstrated using experimental data from electromyography studies as well as simulated data in the extraction of muscle synergies, and compared with existing algorithms for signal-dependent noise. PMID:24684448

Sparse nonnegative matrix factorization with ℓ0-constraints

PubMed Central

Peharz, Robert; Pernkopf, Franz

2012-01-01

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. PMID:22505792

On the asymptotic behavior of a subcritical convection-diffusion equation with nonlocal diffusion

NASA Astrophysics Data System (ADS)

Cazacu, Cristian M.; Ignat, Liviu I.; Pazoto, Ademir F.

2017-08-01

In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estimate similar to the case when the diffusion is local. First we prove that the entropy solution can be obtained by adding a small viscous term μ uxx and letting μ\\to 0 . Then, by using uniform Oleinik estimates for the viscous approximation we are able to prove the well-posedness of the entropy solutions with L 1-initial data. Using a scaling argument and hyperbolic estimates given by Oleinik’s inequality, we obtain the first term in the asymptotic behavior of the nonnegative solutions. Finally, the large time behavior of changing sign solutions is proved using the classical flux-entropy method and estimates for the nonlocal operator.

Positive solutions for nonlocal dispersal equation with spatial degeneracy

NASA Astrophysics Data System (ADS)

Sun, Jian-Wen

2018-02-01

In this paper, we consider the positive solutions of the nonlocal dispersal equation \\int \\limits _{Ω }J(x,y)[u(y)-u(x)]dy=-λ m(x)u(x)+[c(x)+ɛ ]u^p(x) \\quad { in }\\bar{Ω }, where Ω \\subset R^N is a bounded domain, λ ,ɛ and p>1 are positive constants. The dispersal kernel J and the coefficient c( x) are nonnegative, but c( x) has a degeneracy in some subdomain of Ω . In order to study the influence of heterogeneous environment on the nonlocal system, we study the sharp spatial patterns of positive solutions as ɛ → 0. We obtain that the positive solutions always have blow-up asymptotic profiles in \\bar{Ω }. Meanwhile, we find that the profiles in degeneracy domain are different from the domain without degeneracy.

Robust Controller Design: A Bounded-Input-Bounded-Output Worst-Case Approach

DTIC Science & Technology

1992-03-01

show that 2 implies 1, suppose 1 does not hold, i.e., that p(M) > 1. The Perron - Frobenius theory for nonnegative matrices states that p(M) is itself an...Pz denote the positive cones inside X, Z consisting of elements with nonnegative pointwise components. Define the operator .4 : X -* Z, decomposed...topology.) The dual cone P! again consists of the nonnegative elements in Z*. The Lagrangian can be defined as L(x,z ’) {< x,c" > + < Ax - b,z

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.

The successive projection algorithm as an initialization method for brain tumor segmentation using non-negative matrix factorization.

PubMed

Sauwen, Nicolas; Acou, Marjan; Bharath, Halandur N; Sima, Diana M; Veraart, Jelle; Maes, Frederik; Himmelreich, Uwe; Achten, Eric; Van Huffel, Sabine

2017-01-01

Non-negative matrix factorization (NMF) has become a widely used tool for additive parts-based analysis in a wide range of applications. As NMF is a non-convex problem, the quality of the solution will depend on the initialization of the factor matrices. In this study, the successive projection algorithm (SPA) is proposed as an initialization method for NMF. SPA builds on convex geometry and allocates endmembers based on successive orthogonal subspace projections of the input data. SPA is a fast and reproducible method, and it aligns well with the assumptions made in near-separable NMF analyses. SPA was applied to multi-parametric magnetic resonance imaging (MRI) datasets for brain tumor segmentation using different NMF algorithms. Comparison with common initialization methods shows that SPA achieves similar segmentation quality and it is competitive in terms of convergence rate. Whereas SPA was previously applied as a direct endmember extraction tool, we have shown improved segmentation results when using SPA as an initialization method, as it allows further enhancement of the sources during the NMF iterative procedure.

Using Separable Nonnegative Matrix Factorization Techniques for the Analysis of Time-Resolved Raman Spectra.

PubMed

Luce, Robert; Hildebrandt, Peter; Kuhlmann, Uwe; Liesen, Jörg

2016-09-01

The key challenge of time-resolved Raman spectroscopy is the identification of the constituent species and the analysis of the kinetics of the underlying reaction network. In this work we present an integral approach that allows for determining both the component spectra and the rate constants simultaneously from a series of vibrational spectra. It is based on an algorithm for nonnegative matrix factorization that is applied to the experimental data set following a few pre-processing steps. As a prerequisite for physically unambiguous solutions, each component spectrum must include one vibrational band that does not significantly interfere with the vibrational bands of other species. The approach is applied to synthetic "experimental" spectra derived from model systems comprising a set of species with component spectra differing with respect to their degree of spectral interferences and signal-to-noise ratios. In each case, the species involved are connected via monomolecular reaction pathways. The potential and limitations of the approach for recovering the respective rate constants and component spectra are discussed. © The Author(s) 2016.

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Boundedness for a 3D chemotaxis-Stokes system with porous medium diffusion and tensor-valued chemotactic sensitivity

NASA Astrophysics Data System (ADS)

Wang, Yilong; Li, Xie

2017-04-01

This paper deals with the following chemotaxis-Stokes system n_t+u\\cdot nabla n=Δ n^m-nabla \\cdot (nS(x,n,c)\\cdot nabla c), &{}quad xin Ω , t>0, c_t+u\\cdot nabla c=Δ c-nf(c),&{}quad xin Ω , t>0, u_t=Δ u+nabla P+nnabla φ ,&quad xin Ω , t>0,\\ nabla \\cdot u=0,&{}quad xin Ω , t>0. under no-flux boundary conditions in a bounded domain Ω subset R3 with smooth boundary, where m≥ 1, φ in W^{1,∞}(Ω ), f and S are given functions with values in [0, ∞) and R^{3× 3}, respectively. Here S satisfies |S(x,n,c)|7/6, which insures the global existence of bounded weak solution. Our result covers completely and improves the recent result by Wang and Cao (Discrete Contin Dyn Syst Ser B 20:3235-3254, 2015) which asserts, just in the case m=1, the global existence of solutions, but without boundedness, and that by Winkler (Calc Var Partial Differ Equ 54:3789-3828, 2015) which only involves the case of α =0 and requires the convexity of the domain.

Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis

NASA Astrophysics Data System (ADS)

Wang, Jianping; Wang, Mingxin

2018-06-01

This paper concerns the reaction-diffusion systems modeling the population dynamics of two predators and one prey with nonlinear prey-taxis. We first investigate the global existence and boundedness of the unique classical solution for the general model. Then, we study the global stabilities of nonnegative spatially homogeneous equilibria for an explicit system with type I functional responses and density-dependent death rates for the predators and logistic growth for the prey. Moreover, the convergence rates are also established.

Loss of regularity in the {K(m, n)} equations

NASA Astrophysics Data System (ADS)

Zilburg, Alon; Rosenau, Philip

2018-06-01

Using a priori estimates we prove that initially nonnegative, smooth and compactly supported solutions of the equations must lose their smoothness within a finite time. Formation of a singularity is a prerequisite for the subsequent emergence of compactons. Numerical studies are presented that demonstrate two manifestations of the emerging singularity: either propagation of the right front downstream or the formation of an oscillatory tail upstream. Formation of one type of motion does not preclude the possible formation of the other at a later time.

Non-negative Matrix Factorization for Self-calibration of Photometric Redshift Scatter in Weak-lensing Surveys

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

Zhang, Le; Yu, Yu; Zhang, Pengjie, E-mail: lezhang@sjtu.edu.cn

Photo- z error is one of the major sources of systematics degrading the accuracy of weak-lensing cosmological inferences. Zhang et al. proposed a self-calibration method combining galaxy–galaxy correlations and galaxy–shear correlations between different photo- z bins. Fisher matrix analysis shows that it can determine the rate of photo- z outliers at a level of 0.01%–1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibration process. Based on the techniques of fixed-point iteration and non-negativemore » matrix factorization, the proposed algorithm can efficiently and robustly reconstruct the scattering probabilities between the true- z and photo- z bins. The algorithm has been tested extensively by applying it to mock data from simulated stage IV weak-lensing projects. We find that the algorithm provides a successful recovery of the scatter rates at the level of 0.01%–1%, and the true mean redshifts of photo- z bins at the level of 0.001, which may satisfy the requirements in future lensing surveys.« less

Hermite Polynomials and the Inverse Problem for Collisionless Equilibria

NASA Astrophysics Data System (ADS)

Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.

2017-12-01

It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82, 905820306, 2016 2. O. Allanson, S. Troscheit & T. Neukirch: The inverse problem for collisionless plasma equilibria (invited paper for IMA Journal of Applied Mathematics, under review)

Discriminant projective non-negative matrix factorization.

PubMed

Guan, Naiyang; Zhang, Xiang; Luo, Zhigang; Tao, Dacheng; Yang, Xuejun

2013-01-01

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W(T) X as their coefficients, i.e., X≈WW(T) X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher's criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

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

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Discriminant Projective Non-Negative Matrix Factorization

PubMed Central

Guan, Naiyang; Zhang, Xiang; Luo, Zhigang; Tao, Dacheng; Yang, Xuejun

2013-01-01

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers WT X as their coefficients, i.e., X≈WWT X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher's criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms. PMID:24376680

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Asymptotics in Time, Temperature and Size for Optimization by Simulated Annealing: Theory, Practice and Applications

DTIC Science & Technology

1990-01-19

following theorem from the Perron - Frobenius theory of nonnegative matrices. Theorem 2.2 : [1] Consider an irreducible Markov chain with transition...us suppose to the contrary that both expressions are nonnegative . Then max ,01v,,= max /3,1v,,> max 3OV,,= max /3,0V max i,01v,,, -A.,. A’ ,, A.i. A...induction. For k 1, from (20) we see that (22) /3, 8 ,, _-30,A V(). Clearly, the left-hand side of (22) is nonnegative , implying that the right-hand

Non-negative matrix factorization in texture feature for classification of dementia with MRI data

NASA Astrophysics Data System (ADS)

Sarwinda, D.; Bustamam, A.; Ardaneswari, G.

2017-07-01

This paper investigates applications of non-negative matrix factorization as feature selection method to select the features from gray level co-occurrence matrix. The proposed approach is used to classify dementia using MRI data. In this study, texture analysis using gray level co-occurrence matrix is done to feature extraction. In the feature extraction process of MRI data, we found seven features from gray level co-occurrence matrix. Non-negative matrix factorization selected three features that influence of all features produced by feature extractions. A Naïve Bayes classifier is adapted to classify dementia, i.e. Alzheimer's disease, Mild Cognitive Impairment (MCI) and normal control. The experimental results show that non-negative factorization as feature selection method able to achieve an accuracy of 96.4% for classification of Alzheimer's and normal control. The proposed method also compared with other features selection methods i.e. Principal Component Analysis (PCA).

Fast alternating projection methods for constrained tomographic reconstruction

PubMed Central

Liu, Li; Han, Yongxin

2017-01-01

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification. PMID:28253298

Observer-Based Discrete-Time Nonnegative Edge Synchronization of Networked Systems.

PubMed

Su, Housheng; Wu, Han; Chen, Xia

2017-10-01

This paper studies the multi-input and multi-output discrete-time nonnegative edge synchronization of networked systems based on neighbors' output information. The communication relationship among the edges of networked systems is modeled by well-known line graph. Two observer-based edge synchronization algorithms are designed, for which some necessary and sufficient synchronization conditions are derived. Moreover, some computable sufficient synchronization conditions are obtained, in which the feedback matrix and the observer matrix are computed by solving the linear programming problems. We finally design several simulation examples to demonstrate the validity of the given nonnegative edge synchronization algorithms.

Statistical properties of color-signal spaces.

PubMed

Lenz, Reiner; Bui, Thanh Hai

2005-05-01

In applications of principal component analysis (PCA) it has often been observed that the eigenvector with the largest eigenvalue has only nonnegative entries when the vectors of the underlying stochastic process have only nonnegative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. We prove that the nonnegativity of the first eigenvector follows from the Perron-Frobenius (and Krein-Rutman theory). Experiments show also that for stochastic processes with nonnegative signals the mean vector is often very similar to the first eigenvector. This is not true in general, but we first give a heuristical explanation why we can expect such a similarity. We then derive a connection between the dominance of the first eigenvalue and the similarity between the mean and the first eigenvector and show how to check the relative size of the first eigenvalue without actually computing it. In the last part of the paper we discuss the implication of theoretical results for multispectral color processing.

Statistical properties of color-signal spaces

NASA Astrophysics Data System (ADS)

Lenz, Reiner; Hai Bui, Thanh

2005-05-01

In applications of principal component analysis (PCA) it has often been observed that the eigenvector with the largest eigenvalue has only nonnegative entries when the vectors of the underlying stochastic process have only nonnegative values. This has been used to show that the coordinate vectors in PCA are all located in a cone. We prove that the nonnegativity of the first eigenvector follows from the Perron-Frobenius (and Krein-Rutman theory). Experiments show also that for stochastic processes with nonnegative signals the mean vector is often very similar to the first eigenvector. This is not true in general, but we first give a heuristical explanation why we can expect such a similarity. We then derive a connection between the dominance of the first eigenvalue and the similarity between the mean and the first eigenvector and show how to check the relative size of the first eigenvalue without actually computing it. In the last part of the paper we discuss the implication of theoretical results for multispectral color processing.

Extraction of food consumption systems by nonnegative matrix factorization (NMF) for the assessment of food choices.

PubMed

Zetlaoui, Mélanie; Feinberg, Max; Verger, Philippe; Clémençon, Stephan

2011-12-01

In Western countries where food supply is satisfactory, consumers organize their diets around a large combination of foods. It is the purpose of this article to examine how recent nonnegative matrix factorization (NMF) techniques can be applied to food consumption data to understand these combinations. Such data are nonnegative by nature and of high dimension. The NMF model provides a representation of consumption data through latent vectors with nonnegative coefficients, that we call consumption systems (CS), in a small number. As the NMF approach may encourage sparsity of the data representation produced, the resulting CS are easily interpretable. Beyond the illustration of its properties we provide through a simple simulation result, the NMF method is applied to data issued from a French consumption survey. The numerical results thus obtained are displayed and thoroughly discussed. A clustering based on the k-means method is also achieved in the resulting latent consumption space, to recover food consumption patterns easily usable for nutritionists. © 2011, The International Biometric Society.

Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

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

Zhang, Feng-Qin, E-mail: zhafq@263.net; Liu, Rong; Chen, Yuming, E-mail: ychen@wlu.ca

In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting.

A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection

NASA Astrophysics Data System (ADS)

Korpusik, Adam

2017-02-01

We present a nonstandard finite difference scheme for a basic model of cellular immune response to viral infection. The main advantage of this approach is that it preserves the essential qualitative features of the original continuous model (non-negativity and boundedness of the solution, equilibria and their stability conditions), while being easy to implement. All of the qualitative features are preserved independently of the chosen step-size. Numerical simulations of our approach and comparison with other conventional simulation methods are presented.

Contribution of non-negative matrix factorization to the classification of remote sensing images

NASA Astrophysics Data System (ADS)

Karoui, M. S.; Deville, Y.; Hosseini, S.; Ouamri, A.; Ducrot, D.

2008-10-01

Remote sensing has become an unavoidable tool for better managing our environment, generally by realizing maps of land cover using classification techniques. The classification process requires some pre-processing, especially for data size reduction. The most usual technique is Principal Component Analysis. Another approach consists in regarding each pixel of the multispectral image as a mixture of pure elements contained in the observed area. Using Blind Source Separation (BSS) methods, one can hope to unmix each pixel and to perform the recognition of the classes constituting the observed scene. Our contribution consists in using Non-negative Matrix Factorization (NMF) combined with sparse coding as a solution to BSS, in order to generate new images (which are at least partly separated images) using HRV SPOT images from Oran area, Algeria). These images are then used as inputs of a supervised classifier integrating textural information. The results of classifications of these "separated" images show a clear improvement (correct pixel classification rate improved by more than 20%) compared to classification of initial (i.e. non separated) images. These results show the contribution of NMF as an attractive pre-processing for classification of multispectral remote sensing imagery.

Ionospheric-thermospheric UV tomography: 1. Image space reconstruction algorithms

NASA Astrophysics Data System (ADS)

Dymond, K. F.; Budzien, S. A.; Hei, M. A.

2017-03-01

We present and discuss two algorithms of the class known as Image Space Reconstruction Algorithms (ISRAs) that we are applying to the solution of large-scale ionospheric tomography problems. ISRAs have several desirable features that make them useful for ionospheric tomography. In addition to producing nonnegative solutions, ISRAs are amenable to sparse-matrix formulations and are fast, stable, and robust. We present the results of our studies of two types of ISRA: the Least Squares Positive Definite and the Richardson-Lucy algorithms. We compare their performance to the Multiplicative Algebraic Reconstruction and Conjugate Gradient Least Squares algorithms. We then discuss the use of regularization in these algorithms and present our new approach based on regularization to a partial differential equation.

A unified statistical approach to non-negative matrix factorization and probabilistic latent semantic indexing

PubMed Central

Wang, Guoli; Ebrahimi, Nader

2014-01-01

Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into the product of two nonnegative matrices, W and H, such that V ∼ W H. It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a variety of areas such as natural language processing, neuroscience, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. There has also been simultaneous development of a related statistical latent class modeling approach, namely, probabilistic latent semantic indexing (PLSI), for analyzing and interpreting co-occurrence count data arising in natural language processing. In this paper, we present a generalized statistical approach to NMF and PLSI based on Renyi's divergence between two non-negative matrices, stemming from the Poisson likelihood. Our approach unifies various competing models and provides a unique theoretical framework for these methods. We propose a unified algorithm for NMF and provide a rigorous proof of monotonicity of multiplicative updates for W and H. In addition, we generalize the relationship between NMF and PLSI within this framework. We demonstrate the applicability and utility of our approach as well as its superior performance relative to existing methods using real-life and simulated document clustering data. PMID:25821345

A unified statistical approach to non-negative matrix factorization and probabilistic latent semantic indexing.

PubMed

Devarajan, Karthik; Wang, Guoli; Ebrahimi, Nader

2015-04-01

Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into the product of two nonnegative matrices, W and H , such that V ∼ W H . It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a variety of areas such as natural language processing, neuroscience, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. There has also been simultaneous development of a related statistical latent class modeling approach, namely, probabilistic latent semantic indexing (PLSI), for analyzing and interpreting co-occurrence count data arising in natural language processing. In this paper, we present a generalized statistical approach to NMF and PLSI based on Renyi's divergence between two non-negative matrices, stemming from the Poisson likelihood. Our approach unifies various competing models and provides a unique theoretical framework for these methods. We propose a unified algorithm for NMF and provide a rigorous proof of monotonicity of multiplicative updates for W and H . In addition, we generalize the relationship between NMF and PLSI within this framework. We demonstrate the applicability and utility of our approach as well as its superior performance relative to existing methods using real-life and simulated document clustering data.

Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks

NASA Astrophysics Data System (ADS)

Shirvany, Yazdan; Hayati, Mohsen; Moradian, Rostam

2008-12-01

We present a method to solve boundary value problems using artificial neural networks (ANN). A trial solution of the differential equation is written as a feed-forward neural network containing adjustable parameters (the weights and biases). From the differential equation and its boundary conditions we prepare the energy function which is used in the back-propagation method with momentum term to update the network parameters. We improved energy function of ANN which is derived from Schrodinger equation and the boundary conditions. With this improvement of energy function we can use unsupervised training method in the ANN for solving the equation. Unsupervised training aims to minimize a non-negative energy function. We used the ANN method to solve Schrodinger equation for few quantum systems. Eigenfunctions and energy eigenvalues are calculated. Our numerical results are in agreement with their corresponding analytical solution and show the efficiency of ANN method for solving eigenvalue problems.

Applying the Zel'dovich approximation to general relativity

NASA Astrophysics Data System (ADS)

Croudace, K. M.; Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

Starting from general relativity, we give a systematic derivation of the Zel'dovich approximation describing the nonlinear evolution of collisionless dust. We begin by evolving dust along world lines, and we demonstrate that the Szekeres line element is an exact but apparently unstable solution of the evolution equations describing pancake collapse. Next, we solve the Einstein field equations by employing Hamilton-Jacobi techniques and a spatial gradient expansion. We give a prescription for evolving a primordial or 'seed' metric up to the formation of pancakes, and demonstrate its validity by rederiving the Szekeres solution approximately at third order and exactly at fifth order in spatial gradients. Finally we show that the range of validity of the expansion can be improved quite significantly if one notes that the 3-metric must have nonnegative eigenvalues. With this improvement the exact Szekeres solution is obtained after only one iteration.

Temporal model of an optically pumped co-doped solid state laser

NASA Technical Reports Server (NTRS)

Wangler, T. G.; Swetits, J. J.; Buoncristiani, A. M.

1993-01-01

Currently, research is being conducted on the optical properties of materials associated with the development of solid state lasers in the two micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are attained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.

Positivity results for indefinite sublinear elliptic problems via a continuity argument

NASA Astrophysics Data System (ADS)

Kaufmann, U.; Ramos Quoirin, H.; Umezu, K.

2017-10-01

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum principle does not apply to. Our approach is based on a continuity argument combined with variational techniques, the sub and supersolutions method and some a priori bounds. Both Dirichlet and Neumann homogeneous boundary conditions are considered. As a byproduct, we deduce some existence and uniqueness results. Finally, as an application, we derive some positivity results for indefinite concave-convex type problems.

Towards a deterministic KPZ equation with fractional diffusion: the stationary problem

NASA Astrophysics Data System (ADS)

Abdellaoui, Boumediene; Peral, Ireneo

2018-04-01

In this work, we investigate by analysis the possibility of a solution to the fractional quasilinear problem: where is a bounded regular domain ( is sufficient), , 1  <  q and f is a measurable non-negative function with suitable hypotheses. The analysis is done separately in three cases: subcritical, 1  <  q  <  2s critical, q  =  2s and supercritical, q  >  2s. The authors were partially supported by Ministerio de Economia y Competitividad under grants MTM2013-40846-P and MTM2016-80474-P (Spain).

On spectra of Lüders operations

NASA Astrophysics Data System (ADS)

Nagy, Gabriel

2008-02-01

We show that all the eigenvalues of certain generalized Lüders operations are non-negative real numbers in two cases of interest. In particular, given a commuting n-tuple A =(A1,…,An) consisting of positive operators on a Hilbert space H, satisfying ∑j =1nAj=I, we show that the spectrum of the Lüders operation: ΛA:B(H)∋X↦∑j =1nAj1/2XAj1/2∈B(H) is contained in [0,∞), so the only solution of the equation ΛA(X)=I-X is the "expected" one: X =1/2I.

Computing Nash equilibria through computational intelligence methods

NASA Astrophysics Data System (ADS)

Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N.

2005-03-01

Nash equilibrium constitutes a central solution concept in game theory. The task of detecting the Nash equilibria of a finite strategic game remains a challenging problem up-to-date. This paper investigates the effectiveness of three computational intelligence techniques, namely, covariance matrix adaptation evolution strategies, particle swarm optimization, as well as, differential evolution, to compute Nash equilibria of finite strategic games, as global minima of a real-valued, nonnegative function. An issue of particular interest is to detect more than one Nash equilibria of a game. The performance of the considered computational intelligence methods on this problem is investigated using multistart and deflection.

Effect of antibodies on pathogen dynamics with delays and two routes of infection

NASA Astrophysics Data System (ADS)

Elaiw, A. M.; Almatrafi, A. A.; Hobiny, A. D.

2018-06-01

We study the global stability of pathogen dynamics models with saturated pathogen-susceptible and infected-susceptible incidence. The models incorporate antibody immune response and three types of discrete or distributed time delays. We first show that the solutions of the model are nonnegative and ultimately bounded. We determine two threshold parameters, the basic reproduction number and antibody response activation number. We establish the existence and stability of the steady states. We study the global stability analysis of models using Lyapunov method. The numerical simulations have shown that antibodies can reduce the pathogen progression.

Estimating gene function with least squares nonnegative matrix factorization.

PubMed

Wang, Guoli; Ochs, Michael F

2007-01-01

Nonnegative matrix factorization is a machine learning algorithm that has extracted information from data in a number of fields, including imaging and spectral analysis, text mining, and microarray data analysis. One limitation with the method for linking genes through microarray data in order to estimate gene function is the high variance observed in transcription levels between different genes. Least squares nonnegative matrix factorization uses estimates of the uncertainties on the mRNA levels for each gene in each condition, to guide the algorithm to a local minimum in normalized chi2, rather than a Euclidean distance or divergence between the reconstructed data and the data itself. Herein, application of this method to microarray data is demonstrated in order to predict gene function.

Competition Between Transients in the Rate of Approach to a Fixed Point

NASA Astrophysics Data System (ADS)

Day, Judy; Rubin, Jonathan E.; Chow, Carson C.

2009-01-01

The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.

Online Solution of Two-Player Zero-Sum Games for Continuous-Time Nonlinear Systems With Completely Unknown Dynamics.

PubMed

Fu, Yue; Chai, Tianyou

2016-12-01

Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton-Jacobi-Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method.

Solution Path for Pin-SVM Classifiers With Positive and Negative $\\tau $ Values.

PubMed

Huang, Xiaolin; Shi, Lei; Suykens, Johan A K

2017-07-01

Applying the pinball loss in a support vector machine (SVM) classifier results in pin-SVM. The pinball loss is characterized by a parameter τ . Its value is related to the quantile level and different τ values are suitable for different problems. In this paper, we establish an algorithm to find the entire solution path for pin-SVM with different τ values. This algorithm is based on the fact that the optimal solution to pin-SVM is continuous and piecewise linear with respect to τ . We also show that the nonnegativity constraint on τ is not necessary, i.e., τ can be extended to negative values. First, in some applications, a negative τ leads to better accuracy. Second, τ = -1 corresponds to a simple solution that links SVM and the classical kernel rule. The solution for τ = -1 can be obtained directly and then be used as a starting point of the solution path. The proposed method efficiently traverses τ values through the solution path, and then achieves good performance by a suitable τ . In particular, τ = 0 corresponds to C-SVM, meaning that the traversal algorithm can output a result at least as good as C-SVM with respect to validation error.

A constrained robust least squares approach for contaminant release history identification

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

Nonnegative definite EAP and ODF estimation via a unified multi-shell HARDI reconstruction.

PubMed

Cheng, Jian; Jiang, Tianzi; Deriche, Rachid

2012-01-01

In High Angular Resolution Diffusion Imaging (HARDI), Orientation Distribution Function (ODF) and Ensemble Average Propagator (EAP) are two important Probability Density Functions (PDFs) which reflect the water diffusion and fiber orientations. Spherical Polar Fourier Imaging (SPFI) is a recent model-free multi-shell HARDI method which estimates both EAP and ODF from the diffusion signals with multiple b values. As physical PDFs, ODFs and EAPs are nonnegative definite respectively in their domains S2 and R3. However, existing ODF/EAP estimation methods like SPFI seldom consider this natural constraint. Although some works considered the nonnegative constraint on the given discrete samples of ODF/EAP, the estimated ODF/EAP is not guaranteed to be nonnegative definite in the whole continuous domain. The Riemannian framework for ODFs and EAPs has been proposed via the square root parameterization based on pre-estimated ODFs and EAPs by other methods like SPFI. However, there is no work on how to estimate the square root of ODF/EAP called as the wavefuntion directly from diffusion signals. In this paper, based on the Riemannian framework for ODFs/EAPs and Spherical Polar Fourier (SPF) basis representation, we propose a unified model-free multi-shell HARDI method, named as Square Root Parameterized Estimation (SRPE), to simultaneously estimate both the wavefunction of EAPs and the nonnegative definite ODFs and EAPs from diffusion signals. The experiments on synthetic data and real data showed SRPE is more robust to noise and has better EAP reconstruction than SPFI, especially for EAP profiles at large radius.

49 CFR 40.129 - What are the MRO's functions in reviewing laboratory confirmed non-negative drug test results?

Code of Federal Regulations, 2013 CFR

2013-10-01

... 49 Transportation 1 2013-10-01 2013-10-01 false What are the MRO's functions in reviewing laboratory confirmed non-negative drug test results? 40.129 Section 40.129 Transportation Office of the Secretary of Transportation PROCEDURES FOR TRANSPORTATION WORKPLACE DRUG AND ALCOHOL TESTING PROGRAMS Medical Review Officers and the Verification Proces...

Medical image classification based on multi-scale non-negative sparse coding.

PubMed

Zhang, Ruijie; Shen, Jian; Wei, Fushan; Li, Xiong; Sangaiah, Arun Kumar

2017-11-01

With the rapid development of modern medical imaging technology, medical image classification has become more and more important in medical diagnosis and clinical practice. Conventional medical image classification algorithms usually neglect the semantic gap problem between low-level features and high-level image semantic, which will largely degrade the classification performance. To solve this problem, we propose a multi-scale non-negative sparse coding based medical image classification algorithm. Firstly, Medical images are decomposed into multiple scale layers, thus diverse visual details can be extracted from different scale layers. Secondly, for each scale layer, the non-negative sparse coding model with fisher discriminative analysis is constructed to obtain the discriminative sparse representation of medical images. Then, the obtained multi-scale non-negative sparse coding features are combined to form a multi-scale feature histogram as the final representation for a medical image. Finally, SVM classifier is combined to conduct medical image classification. The experimental results demonstrate that our proposed algorithm can effectively utilize multi-scale and contextual spatial information of medical images, reduce the semantic gap in a large degree and improve medical image classification performance. Copyright © 2017 Elsevier B.V. All rights reserved.

Reconstructing metabolic flux vectors from extreme pathways: defining the alpha-spectrum.

PubMed

Wiback, Sharon J; Mahadevan, Radhakrishnan; Palsson, Bernhard Ø

2003-10-07

The move towards genome-scale analysis of cellular functions has necessitated the development of analytical (in silico) methods to understand such large and complex biochemical reaction networks. One such method is extreme pathway analysis that uses stoichiometry and thermodynamic irreversibly to define mathematically unique, systemic metabolic pathways. These extreme pathways form the edges of a high-dimensional convex cone in the flux space that contains all the attainable steady state solutions, or flux distributions, for the metabolic network. By definition, any steady state flux distribution can be described as a nonnegative linear combination of the extreme pathways. To date, much effort has been focused on calculating, defining, and understanding these extreme pathways. However, little work has been performed to determine how these extreme pathways contribute to a given steady state flux distribution. This study represents an initial effort aimed at defining how physiological steady state solutions can be reconstructed from a network's extreme pathways. In general, there is not a unique set of nonnegative weightings on the extreme pathways that produce a given steady state flux distribution but rather a range of possible values. This range can be determined using linear optimization to maximize and minimize the weightings of a particular extreme pathway in the reconstruction, resulting in what we have termed the alpha-spectrum. The alpha-spectrum defines which extreme pathways can and cannot be included in the reconstruction of a given steady state flux distribution and to what extent they individually contribute to the reconstruction. It is shown that accounting for transcriptional regulatory constraints can considerably shrink the alpha-spectrum. The alpha-spectrum is computed and interpreted for two cases; first, optimal states of a skeleton representation of core metabolism that include transcriptional regulation, and second for human red blood cell metabolism under various physiological, non-optimal conditions.

Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals

NASA Astrophysics Data System (ADS)

Wu, Guochun; Tan, Zhong

2018-06-01

In this paper, we consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in R3. When the initial data are of small energy and initial density is positive and essentially bounded, we prove the existence of a global weak solution in R3. The large-time behavior of a global weak solution is also established.

Bell-polynomial approach and Wronskian determinant solutions for three sets of differential-difference nonlinear evolution equations with symbolic computation

NASA Astrophysics Data System (ADS)

Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming

2017-10-01

Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.

Uniqueness of solutions for a mathematical model for magneto-viscoelastic flows

NASA Astrophysics Data System (ADS)

Schlömerkemper, A.; Žabenský, J.

2018-06-01

We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier–Stokes equations with evolutionary equations for the deformation gradient and for the magnetization obtained from a special case of the micromagnetic energy. It turns out that the conditions on uniqueness coincide with those for the well-known Navier–Stokes equations in bounded domains: weak solutions are unique in two spatial dimensions, and weak solutions satisfying the Prodi–Serrin conditions are unique among all weak solutions in three dimensions. That is, we obtain the so-called weak-strong uniqueness result in three spatial dimensions.

Enhancing the understanding of entropy through computation

NASA Astrophysics Data System (ADS)

Salagaram, Trisha; Chetty, Nithaya

2011-11-01

We devise an algorithm to enumerate the microstates of a system comprising N independent, distinguishable particles. The algorithm is applicable to a wide class of systems such as harmonic oscillators, free particles, spins, and other models for which there are no analytical solutions, for example, a system with single particle energy spectrum given by ɛ(p,q) = ɛ0(p2 + q4), where p and q are non-negative integers. Our algorithm enables us to determine the approach to the limit N → ∞ within the microcanonical ensemble, and makes manifest the equivalence with the canonical ensemble. Various thermodynamic quantities as a function of N can be computed using our methods.

Innovative Methods for High Resolution Imaging

DTIC Science & Technology

2012-08-02

findings, recent publication, and presentations in the areas of lenslet array imaging , wavefront encoding, and non-negative matrix factorization for...on their findings, recent publication, and presentations in the areas of lenslet array imaging , wavefront encoding, and non-negative matrix...Computational Optical Sensing and Imaging . 2007/06/18 00:00:00, . : , 2012/07/16 15:30:42 9 Kelly N. Smith, V. Paul Pauca, Arun Ross, Todd Torgersen, Michael C

Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

NASA Technical Reports Server (NTRS)

Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin

2014-01-01

This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.

Non-neural Muscle Weakness Has Limited Influence on Complexity of Motor Control during Gait

PubMed Central

Goudriaan, Marije; Shuman, Benjamin R.; Steele, Katherine M.; Van den Hauwe, Marleen; Goemans, Nathalie; Molenaers, Guy; Desloovere, Kaat

2018-01-01

Cerebral palsy (CP) and Duchenne muscular dystrophy (DMD) are neuromuscular disorders characterized by muscle weakness. Weakness in CP has neural and non-neural components, whereas in DMD, weakness can be considered as a predominantly non-neural problem. Despite the different underlying causes, weakness is a constraint for the central nervous system when controlling gait. CP demonstrates decreased complexity of motor control during gait from muscle synergy analysis, which is reflected by a higher total variance accounted for by one synergy (tVAF1). However, it remains unclear if weakness directly contributes to higher tVAF1 in CP, or whether altered tVAF1 reflects mainly neural impairments. If muscle weakness directly contributes to higher tVAF1, then tVAF1 should also be increased in DMD. To examine the etiology of increased tVAF1, muscle activity data of gluteus medius, rectus femoris, medial hamstrings, medial gastrocnemius, and tibialis anterior were measured at self-selected walking speed, and strength data from knee extensors, knee flexors, dorsiflexors and plantar flexors, were analyzed in 15 children with CP [median (IQR) age: 8.9 (2.2)], 15 boys with DMD [8.7 (3.1)], and 15 typical developing (TD) children [8.6 (2.7)]. We computed tVAF1 from 10 concatenated steps with non-negative matrix factorization, and compared tVAF1 between the three groups with a Mann-Whiney U-test. Spearman's rank correlation coefficients were used to determine if weakness in specific muscle groups contributed to altered tVAF1. No significant differences in tVAF1 were found between DMD [tVAF1: 0.60 (0.07)] and TD children [0.65 (0.07)], while tVAF1 was significantly higher in CP [(0.74 (0.09)] than in the other groups (both p < 0.005). In CP, weakness in the plantar flexors was related to higher tVAF1 (r = −0.72). In DMD, knee extensor weakness related to increased tVAF1 (r = −0.50). These results suggest that the non-neural weakness in DMD had limited influence on complexity of motor control during gait and that the higher tVAF1 in children with CP is mainly related to neural impairments caused by the brain lesion. PMID:29445330

Duality based direct resolution of unique profiles using zero concentration region information.

PubMed

Tavakkoli, Elnaz; Rajkó, Róbert; Abdollahi, Hamid

2018-07-01

Self Modeling Curve Resolution (SMCR) is a class of techniques concerned with estimating pure profiles underlying a set of measurements on chemical systems. In general, the estimated profiles are ambiguous (non-unique) except if some special conditions fulfilled. Implementing the adequate information can reduce the so-called rotational ambiguity effectively, and in the most desirable cases lead to the unique solution. Therefore, studies on circumstances resulting in unique solution are of particular importance. The conditions of unique solution can particularly be studied based on duality principle. In bilinear chemical (e.g., spectroscopic) data matrix, there is a natural duality between its row and column vector spaces using minimal constraints (non-negativity of concentrations and absorbances). In this article, the conditions of the unique solution according to duality concept and using zero concentration region information is intended to show. A simulated dataset of three components and an experimental system with synthetic mixtures containing three amino acids tyrosine, phenylalanine and tryptophan are analyzed. It is shown that in the presence of sufficient information, the reliable unique solution is obtained that is valuable in analytical qualification and for quantitative verification analysis. Copyright © 2018 Elsevier B.V. All rights reserved.

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

NASA Technical Reports Server (NTRS)

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

L(2) stability for weak solutions of the Navier-Stokes equations in R(3)

NASA Astrophysics Data System (ADS)

Secchi, P.

1985-11-01

We consider the motion of a viscous fluid filling the whole space R3, governed by the classical Navier-Stokes equations (1). Existence of global (in time) regular solutions for that system of non-linear partial differential equations is still an open problem. Up to now, the only available global existence theorem (other than for sufficiently small initial data) is that of weak (turbulent) solutions. From both the mathematical and the physical point of view, an interesting property is the stability of such weak solutions. We assume that v(t,x) is a solution, with initial datum vO(x). We suppose that the initial datum is perturbed and consider one weak solution u corresponding to the new initial velocity. Then we prove that, due to viscosity, the perturbed weak solution u approaches in a suitable norm the unperturbed one, as time goes to + infinity, without smallness assumptions on the initial perturbation.

A Comparative Study of the Application of Fluorescence Excitation-Emission Matrices Combined with Parallel Factor Analysis and Nonnegative Matrix Factorization in the Analysis of Zn Complexation by Humic Acids

PubMed Central

Boguta, Patrycja; Pieczywek, Piotr M.; Sokołowska, Zofia

2016-01-01

The main aim of this study was the application of excitation-emission fluorescence matrices (EEMs) combined with two decomposition methods: parallel factor analysis (PARAFAC) and nonnegative matrix factorization (NMF) to study the interaction mechanisms between humic acids (HAs) and Zn(II) over a wide concentration range (0–50 mg·dm−3). The influence of HA properties on Zn(II) complexation was also investigated. Stability constants, quenching degree and complexation capacity were estimated for binding sites found in raw EEM, EEM-PARAFAC and EEM-NMF data using mathematical models. A combination of EEM fluorescence analysis with one of the proposed decomposition methods enabled separation of overlapping binding sites and yielded more accurate calculations of the binding parameters. PARAFAC and NMF processing allowed finding binding sites invisible in a few raw EEM datasets as well as finding totally new maxima attributed to structures of the lowest humification. Decomposed data showed an increase in Zn complexation with an increase in humification, aromaticity and molecular weight of HAs. EEM-PARAFAC analysis also revealed that the most stable compounds were formed by structures containing the highest amounts of nitrogen. The content of oxygen-functional groups did not influence the binding parameters, mainly due to fact of higher competition of metal cation with protons. EEM spectra coupled with NMF and especially PARAFAC processing gave more adequate assessments of interactions as compared to raw EEM data and should be especially recommended for modeling of complexation processes where the fluorescence intensities (FI) changes are weak or where the processes are interfered with by the presence of other fluorophores. PMID:27782078

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

A Hybrid Algorithm for Non-negative Matrix Factorization Based on Symmetric Information Divergence

PubMed Central

Devarajan, Karthik; Ebrahimi, Nader; Soofi, Ehsan

2017-01-01

The objective of this paper is to provide a hybrid algorithm for non-negative matrix factorization based on a symmetric version of Kullback-Leibler divergence, known as intrinsic information. The convergence of the proposed algorithm is shown for several members of the exponential family such as the Gaussian, Poisson, gamma and inverse Gaussian models. The speed of this algorithm is examined and its usefulness is illustrated through some applied problems. PMID:28868206

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Structured and Collaborative Signal Models: Theory and Applications in Image, Video, and Audio Analysis

DTIC Science & Technology

2013-01-01

Received Paper 01/22/2013 12.00 E. Esser, M. Moller, S. Osher, G. Sapiro, and J . Xin. A convex modelfor non-negative matrix factorization and...Ernie Esser, Michael M¨ oller , Stanley Osher, Guillermo Sapiro, Jack Xin. A convex model for non-negative matrixfactorization and dimensionality...still have one patent pending (with Adobe): X. Bai, J . Wang, and G. Sapiro, Methods and apparatus for dynamic color modeling. Patents Awarded Awards

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

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

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE PAGES

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

2017-10-30

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Source term identification in atmospheric modelling via sparse optimization

NASA Astrophysics Data System (ADS)

Adam, Lukas; Branda, Martin; Hamburger, Thomas

2015-04-01

Inverse modelling plays an important role in identifying the amount of harmful substances released into atmosphere during major incidents such as power plant accidents or volcano eruptions. Another possible application of inverse modelling lies in the monitoring the CO2 emission limits where only observations at certain places are available and the task is to estimate the total releases at given locations. This gives rise to minimizing the discrepancy between the observations and the model predictions. There are two standard ways of solving such problems. In the first one, this discrepancy is regularized by adding additional terms. Such terms may include Tikhonov regularization, distance from a priori information or a smoothing term. The resulting, usually quadratic, problem is then solved via standard optimization solvers. The second approach assumes that the error term has a (normal) distribution and makes use of Bayesian modelling to identify the source term. Instead of following the above-mentioned approaches, we utilize techniques from the field of compressive sensing. Such techniques look for a sparsest solution (solution with the smallest number of nonzeros) of a linear system, where a maximal allowed error term may be added to this system. Even though this field is a developed one with many possible solution techniques, most of them do not consider even the simplest constraints which are naturally present in atmospheric modelling. One of such examples is the nonnegativity of release amounts. We believe that the concept of a sparse solution is natural in both problems of identification of the source location and of the time process of the source release. In the first case, it is usually assumed that there are only few release points and the task is to find them. In the second case, the time window is usually much longer than the duration of the actual release. In both cases, the optimal solution should contain a large amount of zeros, giving rise to the concept of sparsity. In the paper, we summarize several optimization techniques which are used for finding sparse solutions and propose their modifications to handle selected constraints such as nonnegativity constraints and simple linear constraints, for example the minimal or maximal amount of total release. These techniques range from successive convex approximations to solution of one nonconvex problem. On simple examples, we explain these techniques and compare them from the point of implementation simplicity, approximation capability and convergence properties. Finally, these methods will be applied on the European Tracer Experiment (ETEX) data and the results will be compared with the current state of arts techniques such as regularized least squares or Bayesian approach. The obtained results show the surprisingly good results of these techniques. This research is supported by EEA/Norwegian Financial Mechanism under project 7F14287 STRADI.

Optical implementation of systolic array processing

NASA Technical Reports Server (NTRS)

Caulfield, H. J.; Rhodes, W. T.; Foster, M. J.; Horvitz, S.

1981-01-01

Algorithms for matrix vector multiplication are implemented using acousto-optic cells for multiplication and input data transfer and using charge coupled devices detector arrays for accumulation and output of the results. No two dimensional matrix mask is required; matrix changes are implemented electronically. A system for multiplying a 50 component nonnegative real vector by a 50 by 50 nonnegative real matrix is described. Modifications for bipolar real and complex valued processing are possible, as are extensions to matrix-matrix multiplication and multiplication of a vector by multiple matrices.

Study of weak solutions for parabolic variational inequalities with nonstandard growth conditions.

PubMed

Dong, Yan

2018-01-01

In this paper, we study the degenerate parabolic variational inequality problem in a bounded domain. First, the weak solutions of the variational inequality are defined. Second, the existence and uniqueness of the solutions in the weak sense are proved by using the penalty method and the reduction method.

Natural approach to quantum dissipation

NASA Astrophysics Data System (ADS)

Taj, David; Öttinger, Hans Christian

2015-12-01

The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.

A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.

2014-01-01

Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.

Pavement crack detection combining non-negative feature with fast LoG in complex scene

NASA Astrophysics Data System (ADS)

Wang, Wanli; Zhang, Xiuhua; Hong, Hanyu

2015-12-01

Pavement crack detection is affected by much interference in the realistic situation, such as the shadow, road sign, oil stain, salt and pepper noise etc. Due to these unfavorable factors, the exist crack detection methods are difficult to distinguish the crack from background correctly. How to extract crack information effectively is the key problem to the road crack detection system. To solve this problem, a novel method for pavement crack detection based on combining non-negative feature with fast LoG is proposed. The two key novelties and benefits of this new approach are that 1) using image pixel gray value compensation to acquisit uniform image, and 2) combining non-negative feature with fast LoG to extract crack information. The image preprocessing results demonstrate that the method is indeed able to homogenize the crack image with more accurately compared to existing methods. A large number of experimental results demonstrate the proposed approach can detect the crack regions more correctly compared with traditional methods.

A novel edge-preserving nonnegative matrix factorization method for spectral unmixing

NASA Astrophysics Data System (ADS)

Bao, Wenxing; Ma, Ruishi

2015-12-01

Spectral unmixing technique is one of the key techniques to identify and classify the material in the hyperspectral image processing. A novel robust spectral unmixing method based on nonnegative matrix factorization(NMF) is presented in this paper. This paper used an edge-preserving function as hypersurface cost function to minimize the nonnegative matrix factorization. To minimize the hypersurface cost function, we constructed the updating functions for signature matrix of end-members and abundance fraction respectively. The two functions are updated alternatively. For evaluation purpose, synthetic data and real data have been used in this paper. Synthetic data is used based on end-members from USGS digital spectral library. AVIRIS Cuprite dataset have been used as real data. The spectral angle distance (SAD) and abundance angle distance(AAD) have been used in this research for assessment the performance of proposed method. The experimental results show that this method can obtain more ideal results and good accuracy for spectral unmixing than present methods.

Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels

PubMed Central

SINGER, A.; GILLESPIE, D.; NORBURY, J.; EISENBERG, R. S.

2009-01-01

Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst–Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current–voltage (I–V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I–V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages). PMID:19809600

Existence of solution for the problem with a concentrated source in a subdiffusive medium

NASA Astrophysics Data System (ADS)

Liu, H. Terence; Huang, Wei-Cheng

2018-01-01

Let 0 < α < 1, b, T be positive real numbers, Lau =ut-(Dt1-αu ) x x , where Dt1-αu denotes the Riemann-Liouville fractional derivative. This paper consider the problem Lau (x ,t )=δ (x -b )f (u (x ,t ))in (-∞ ,∞ )×(0 ,T ], subject to initial and boundaries condition u (x ,0 )=ϕ (x )in(-∞ ,∞ ),with ϕ (x )→as|x |→∞ u (x ,t )→0 for0 0, f″(u) > 0 for u > 0. By using Green's function, the problem is converted into an integral equation. It is shown that there exists tb such that for 0 ≤ t < tb, the integral equation has a unique nonnegative continuous solution u; if tb is finite, then u is unbounded in [0, tb). Then, u is proved to be the solution of the original problem.

Existence of global weak solution for a reduced gravity two and a half layer model

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

Guo, Zhenhua, E-mail: zhenhua.guo.math@gmail.com; Li, Zilai, E-mail: lizilai0917@163.com; Yao, Lei, E-mail: yaolei1056@hotmail.com

2013-12-15

We investigate the existence of global weak solution to a reduced gravity two and a half layer model in one-dimensional bounded spatial domain or periodic domain. Also, we show that any possible vacuum state has to vanish within finite time, then the weak solution becomes a unique strong one.

Mathematical analysis of the multiband BCS gap equations in superconductivity

NASA Astrophysics Data System (ADS)

Yang, Yisong

2005-01-01

In this paper, we present a mathematical analysis for the phonon-dominated multiband isotropic and anisotropic BCS gap equations at any finite temperature T. We establish the existence of a critical temperature T so that, when TT, the only nonnegative gap solution is the zero solution, representing the normal phase. Furthermore, when T=T, we prove that the only gap solution is the zero solution and that the positive gap solution depend on the temperature T

Generating subtour elimination constraints for the TSP from pure integer solutions.

PubMed

Pferschy, Ulrich; Staněk, Rostislav

2017-01-01

The traveling salesman problem ( TSP ) is one of the most prominent combinatorial optimization problems. Given a complete graph [Formula: see text] and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to optimality is a branch and cut approach . Usually the integrality constraints are relaxed first and all separation processes to identify violated inequalities are done on fractional solutions . In our approach we try to exploit the impressive performance of current ILP-solvers and work only with integer solutions without ever interfering with fractional solutions. We stick to a very simple ILP-model and relax the subtour elimination constraints only. The resulting problem is solved to integer optimality, violated constraints (which are trivial to find) are added and the process is repeated until a feasible solution is found. In order to speed up the algorithm we pursue several attempts to find as many relevant subtours as possible. These attempts are based on the clustering of vertices with additional insights gained from empirical observations and random graph theory. Computational results are performed on test instances taken from the TSPLIB95 and on random Euclidean graphs .

Structure constrained semi-nonnegative matrix factorization for EEG-based motor imagery classification.

PubMed

Lu, Na; Li, Tengfei; Pan, Jinjin; Ren, Xiaodong; Feng, Zuren; Miao, Hongyu

2015-05-01

Electroencephalogram (EEG) provides a non-invasive approach to measure the electrical activities of brain neurons and has long been employed for the development of brain-computer interface (BCI). For this purpose, various patterns/features of EEG data need to be extracted and associated with specific events like cue-paced motor imagery. However, this is a challenging task since EEG data are usually non-stationary time series with a low signal-to-noise ratio. In this study, we propose a novel method, called structure constrained semi-nonnegative matrix factorization (SCS-NMF), to extract the key patterns of EEG data in time domain by imposing the mean envelopes of event-related potentials (ERPs) as constraints on the semi-NMF procedure. The proposed method is applicable to general EEG time series, and the extracted temporal features by SCS-NMF can also be combined with other features in frequency domain to improve the performance of motor imagery classification. Real data experiments have been performed using the SCS-NMF approach for motor imagery classification, and the results clearly suggest the superiority of the proposed method. Comparison experiments have also been conducted. The compared methods include ICA, PCA, Semi-NMF, Wavelets, EMD and CSP, which further verified the effectivity of SCS-NMF. The SCS-NMF method could obtain better or competitive performance over the state of the art methods, which provides a novel solution for brain pattern analysis from the perspective of structure constraint. Copyright © 2015 Elsevier Ltd. All rights reserved.

Adaptive and neuroadaptive control for nonnegative and compartmental dynamical systems

NASA Astrophysics Data System (ADS)

Volyanskyy, Kostyantyn Y.

Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we develop a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. The proposed framework involves a novel controller architecture with additional terms in the update laws that are constructed using a moving window of the integrated system uncertainty. These terms can be used to identify the ideal system weights of the neural network as well as effectively suppress system uncertainty. Linear and nonlinear parameterizations of the system uncertainty are considered and state and output feedback neuroadaptive controllers are developed. Furthermore, we extend the developed framework to discrete-time dynamical systems. To illustrate the efficacy of the proposed approach we apply our results to an aircraft model with wing rock dynamics, a spacecraft model with unknown moment of inertia, and an unmanned combat aerial vehicle undergoing actuator failures, and compare our results with standard neuroadaptive control methods. Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A sub-class of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this dissertation, we develop direct adaptive and neuroadaptive control framework for stabilization, disturbance rejection and noise suppression for nonnegative and compartmental dynamical systems with noise and exogenous system disturbances. We then use the developed framework to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of continuing hemorrhage and hemodilution. Critical care patients, whether undergoing surgery or recovering in intensive care units, require drug administration to regulate physiological variables such as blood pressure, cardiac output, heart rate, and degree of consciousness. The rate of infusion of each administered drug is critical, requiring constant monitoring and frequent adjustments. In this dissertation, we develop a neuroadaptive output feedback control framework for nonlinear uncertain nonnegative and compartmental systems with nonnegative control inputs and noisy measurements. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space. Finally, the developed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of noisy electroencephalographic (EEG) measurements. Clinical trials demonstrate excellent regulation of unconsciousness allowing for a safe and effective administration of the anesthetic agent propofol. Furthermore, a neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. Specifically, the neuroadaptive controller guarantees that the imposed amplitude and integral input constraints are satisfied and the physical system states remain in the nonnegative orthant of the state space. The proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery in the face of infusion rate constraints and a drug dosing constraint over a specified period. In addition, the aforementioned control architecture is used to control lung volume and minute ventilation with input pressure constraints that also accounts for spontaneous breathing by the patient. Specifically, we develop a pressure- and work-limited neuroadaptive controller for mechanical ventilation based on a nonlinear multi-compartmental lung model. The control framework does not rely on any averaged data and is designed to automatically adjust the input pressure to the patient's physiological characteristics capturing lung resistance and compliance modeling uncertainty. Moreover, the controller accounts for input pressure constraints as well as work of breathing constraints. The effect of spontaneous breathing is incorporated within the lung model and the control framework. Finally, a neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.

Transactions of the Conference on Applied Mathematics and Computing (9th) Held in Minneapolis, Minnesota on 18-21 June 1991

DTIC Science & Technology

1992-03-01

the ith row of I<. The preconditioned matrix K is thus a stochastic matrix, and by the Perron - Frobenius theorem (e.g., Horn and Johnson, 1989), K...now be determined. For equations (10) and (11) to be real, the radical must be nonnegative . This condition on d defines the index zero threshold...ddhsi: sfl] [r;I,r;I] . Since h/lh is positive-definite, (3.2) shows that a , and 13, are nonnegative . This fact can be used t~ test a candidates

Algorithms for the Equilibration of Matrices and Their Application to Limited-Memory Quasi-Newton Methods

DTIC Science & Technology

2010-05-01

irreducible, by the Perron - Frobenius theorem (see, for example, Theorem 8.4.4 in [28]), the eigenvalue 1 is simple. Next, the rank-one matrix Q has the...We refer to (2.1) as the scaling equation. Although algorithms must use A, existence and unique- ness theory need consider only the nonnegative matrix...B. If p = 1 and A is nonnegative , then A = B. We reserve the term binormalization for the case p = 2. We say A is scalable if there exists x > 0

Convex Optimization Methods for Graphs and Statistical Modeling

DTIC Science & Technology

2011-06-01

of a set obtained by taking nonnegative linear combinations of elements of the set. The cone TC(x) is the set of directions to points in C from the...Proof. The tangent cone at any signed vector x? with respect to the `∞ ball is a rotation of the nonnegative orthant. Thus we only need to compute the...that ξ(B ?) 1−4ξ(B?)µ(A?) < γ in the second inequality. Sec. A.2. Proofs 167 Proof of Proposition 3.4.2 Based on the Perron - Frobenius theorem [82

Circular distributions based on nonnegative trigonometric sums.

PubMed

Fernández-Durán, J J

2004-06-01

A new family of distributions for circular random variables is proposed. It is based on nonnegative trigonometric sums and can be used to model data sets which present skewness and/or multimodality. In this family of distributions, the trigonometric moments are easily expressed in terms of the parameters of the distribution. The proposed family is applied to two data sets, one related with the directions taken by ants and the other with the directions taken by turtles, to compare their goodness of fit versus common distributions used in the literature.

On the Conservation and Convergence to Weak Solutions of Global Schemes

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Shu, Chi-Wang

2001-01-01

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff theorem concerning conservative schemes.

An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta

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

Allanson, O., E-mail: oliver.allanson@st-andrews.ac.uk; Neukirch, T., E-mail: tn3@st-andrews.ac.uk; Wilson, F., E-mail: fw237@st-andrews.ac.uk

We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution functionmore » in two of the velocity directions to a Maxwellian distribution.« less

Parabolic Systems with p, q-Growth: A Variational Approach

NASA Astrophysics Data System (ADS)

Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo

2013-10-01

We consider the evolution problem associated with a convex integrand {f : {R}^{Nn}to [0,infty)} satisfying a non-standard p, q-growth assumption. To establish the existence of solutions we introduce the concept of variational solutions. In contrast to weak solutions, that is, mappings {u\\colon Ω_T to {R}^n} which solve partial_tu-div Df(Du)=0 weakly in {Ω_T}, variational solutions exist under a much weaker assumption on the gap q - p. Here, we prove the existence of variational solutions provided the integrand f is strictly convex and 2n/n+2 < p le q < p+1. These variational solutions turn out to be unique under certain mild additional assumptions on the data. Moreover, if the gap satisfies the natural stronger assumption 2le p le q < p+ minbig \\{1,4/n big \\}, we show that variational solutions are actually weak solutions. This means that solutions u admit the necessary higher integrability of the spatial derivative Du to satisfy the parabolic system in the weak sense, that is, we prove that uin L^q_locbig(0,T; W^{1,q}_loc(Ω,{R}^N)big).

Consistent multiphase-field theory for interface driven multidomain dynamics

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.; Pusztai, Tamás; Gránásy, László

2015-11-01

We present a multiphase-field theory for describing pattern formation in multidomain and/or multicomponent systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a way of constructing the free energy surface and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism, reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations, enables the use of arbitrary pairwise equilibrium interfacial properties, penalizes multiple junctions increasingly with the number of phases, ensures non-negative entropy production and the convergence of the dynamic solutions to the equilibrium solutions, and avoids the appearance of spurious phases on binary interfaces. The approach is tested for multicomponent phase separation and grain coarsening.

A PET reconstruction formulation that enforces non-negativity in projection space for bias reduction in Y-90 imaging

NASA Astrophysics Data System (ADS)

Lim, Hongki; Dewaraja, Yuni K.; Fessler, Jeffrey A.

2018-02-01

Most existing PET image reconstruction methods impose a nonnegativity constraint in the image domain that is natural physically, but can lead to biased reconstructions. This bias is particularly problematic for Y-90 PET because of the low probability positron production and high random coincidence fraction. This paper investigates a new PET reconstruction formulation that enforces nonnegativity of the projections instead of the voxel values. This formulation allows some negative voxel values, thereby potentially reducing bias. Unlike the previously reported NEG-ML approach that modifies the Poisson log-likelihood to allow negative values, the new formulation retains the classical Poisson statistical model. To relax the non-negativity constraint embedded in the standard methods for PET reconstruction, we used an alternating direction method of multipliers (ADMM). Because choice of ADMM parameters can greatly influence convergence rate, we applied an automatic parameter selection method to improve the convergence speed. We investigated the methods using lung to liver slices of XCAT phantom. We simulated low true coincidence count-rates with high random fractions corresponding to the typical values from patient imaging in Y-90 microsphere radioembolization. We compared our new methods with standard reconstruction algorithms and NEG-ML and a regularized version thereof. Both our new method and NEG-ML allow more accurate quantification in all volumes of interest while yielding lower noise than the standard method. The performance of NEG-ML can degrade when its user-defined parameter is tuned poorly, while the proposed algorithm is robust to any count level without requiring parameter tuning.

Impact of the Choice of Normalization Method on Molecular Cancer Class Discovery Using Nonnegative Matrix Factorization.

PubMed

Yang, Haixuan; Seoighe, Cathal

2016-01-01

Nonnegative Matrix Factorization (NMF) has proved to be an effective method for unsupervised clustering analysis of gene expression data. By the nonnegativity constraint, NMF provides a decomposition of the data matrix into two matrices that have been used for clustering analysis. However, the decomposition is not unique. This allows different clustering results to be obtained, resulting in different interpretations of the decomposition. To alleviate this problem, some existing methods directly enforce uniqueness to some extent by adding regularization terms in the NMF objective function. Alternatively, various normalization methods have been applied to the factor matrices; however, the effects of the choice of normalization have not been carefully investigated. Here we investigate the performance of NMF for the task of cancer class discovery, under a wide range of normalization choices. After extensive evaluations, we observe that the maximum norm showed the best performance, although the maximum norm has not previously been used for NMF. Matlab codes are freely available from: http://maths.nuigalway.ie/~haixuanyang/pNMF/pNMF.htm.

Semi-Supervised Projective Non-Negative Matrix Factorization for Cancer Classification.

PubMed

Zhang, Xiang; Guan, Naiyang; Jia, Zhilong; Qiu, Xiaogang; Luo, Zhigang

2015-01-01

Advances in DNA microarray technologies have made gene expression profiles a significant candidate in identifying different types of cancers. Traditional learning-based cancer identification methods utilize labeled samples to train a classifier, but they are inconvenient for practical application because labels are quite expensive in the clinical cancer research community. This paper proposes a semi-supervised projective non-negative matrix factorization method (Semi-PNMF) to learn an effective classifier from both labeled and unlabeled samples, thus boosting subsequent cancer classification performance. In particular, Semi-PNMF jointly learns a non-negative subspace from concatenated labeled and unlabeled samples and indicates classes by the positions of the maximum entries of their coefficients. Because Semi-PNMF incorporates statistical information from the large volume of unlabeled samples in the learned subspace, it can learn more representative subspaces and boost classification performance. We developed a multiplicative update rule (MUR) to optimize Semi-PNMF and proved its convergence. The experimental results of cancer classification for two multiclass cancer gene expression profile datasets show that Semi-PNMF outperforms the representative methods.

Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

PubMed Central

Dordek, Yedidyah; Soudry, Daniel; Meir, Ron; Derdikman, Dori

2016-01-01

Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is −1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA. DOI: http://dx.doi.org/10.7554/eLife.10094.001 PMID:26952211

Decomposing Time Series Data by a Non-negative Matrix Factorization Algorithm with Temporally Constrained Coefficients

PubMed Central

Cheung, Vincent C. K.; Devarajan, Karthik; Severini, Giacomo; Turolla, Andrea; Bonato, Paolo

2017-01-01

The non-negative matrix factorization algorithm (NMF) decomposes a data matrix into a set of non-negative basis vectors, each scaled by a coefficient. In its original formulation, the NMF assumes the data samples and dimensions to be independently distributed, making it a less-than-ideal algorithm for the analysis of time series data with temporal correlations. Here, we seek to derive an NMF that accounts for temporal dependencies in the data by explicitly incorporating a very simple temporal constraint for the coefficients into the NMF update rules. We applied the modified algorithm to 2 multi-dimensional electromyographic data sets collected from the human upper-limb to identify muscle synergies. We found that because it reduced the number of free parameters in the model, our modified NMF made it possible to use the Akaike Information Criterion to objectively identify a model order (i.e., the number of muscle synergies composing the data) that is more functionally interpretable, and closer to the numbers previously determined using ad hoc measures. PMID:26737046

The Lp Robin problem for Laplace equations in Lipschitz and (semi-)convex domains

NASA Astrophysics Data System (ADS)

Yang, Sibei; Yang, Dachun; Yuan, Wen

2018-01-01

Let n ≥ 3 and Ω be a bounded Lipschitz domain in Rn. Assume that p ∈ (2 , ∞) and the function b ∈L∞ (∂ Ω) is non-negative, where ∂Ω denotes the boundary of Ω. Denote by ν the outward unit normal to ∂Ω. In this article, the authors give two necessary and sufficient conditions for the unique solvability of the Robin problem for the Laplace equation Δu = 0 in Ω with boundary data ∂ u / ∂ ν + bu = f ∈Lp (∂ Ω), respectively, in terms of a weak reverse Hölder inequality with exponent p or the unique solvability of the Robin problem with boundary data in some weighted L2 (∂ Ω) space. As applications, the authors obtain the unique solvability of the Robin problem for the Laplace equation in the bounded (semi-)convex domain Ω with boundary data in (weighted) Lp (∂ Ω) for any given p ∈ (1 , ∞).

Entanglement of 3000 atoms by detecting one photon

NASA Astrophysics Data System (ADS)

Vuletic, Vladan

2016-05-01

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. In particular, entangled states of many particles can be used to overcome limits on measurements performed with ensembles of independent atoms (standard quantum limit). Metrologically useful entangled states of large atomic ensembles (spin squeezed states) have been experimentally realized. These states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. We report the generation of entanglement in a large atomic ensemble via an interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, and verify an entanglement depth (the minimum number of mutually entangled atoms) that comprises 90% of the atomic ensemble containing 3100 atoms. Further technical improvement should allow the generation of more complex Schrödinger cat states, and of states the overcome the standard quantum limit.

Supplementary material for the paper Scheduling Constrained-Deadline Sporadic Parallel

DTIC Science & Technology

2014-10-18

is feasible. It can be seen in Fig. 5, that changing the domain of mbi,j,g,b from non-negative integer to non-negative real does not change the...h ′′ ∈ [0, H − 1])∧ (i ′ < i ′′ ) ∧ (h′ ≥ h′′) : xi′,j′,g′,h′ + xi′′,j′′,g′′,h′′ ≤ 1 Method 2 is like Method 1 but with the constraint above. Method...9, trp = 9,trcd = 9,twr = 10 Fig. 6: One of the systems used in our evaluation. 13

Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit

NASA Astrophysics Data System (ADS)

Constantin, Peter; Vicol, Vlad

2018-04-01

We prove that any weak space-time L^2 vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of R^2 satisfies the Euler equation if the solutions' local enstrophies are uniformly bounded. We also prove that t-a.e. weak L^2 inviscid limits of solutions of 3D Navier-Stokes equations in bounded domains are weak solutions of the Euler equation if they locally satisfy a scaling property of their second-order structure function. The conditions imposed are far away from boundaries, and wild solutions of Euler equations are not a priori excluded in the limit.

Global existence of the three-dimensional viscous quantum magnetohydrodynamic model

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

Yang, Jianwei, E-mail: yangjianwei@ncwu.edu.cn; Ju, Qiangchang, E-mail: qiangchang-ju@yahoo.com

2014-08-15

The global-in-time existence of weak solutions to the viscous quantum Magnetohydrodynamic equations in a three-dimensional torus with large data is proved. The global existence of weak solutions to the viscous quantum Magnetohydrodynamic equations is shown by using the Faedo-Galerkin method and weak compactness techniques.

Path Following in the Exact Penalty Method of Convex Programming.

PubMed

Zhou, Hua; Lange, Kenneth

2015-07-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

Path Following in the Exact Penalty Method of Convex Programming

PubMed Central

Zhou, Hua; Lange, Kenneth

2015-01-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

Partial regularity of weak solutions to a PDE system with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Xu, Xiangsheng

2018-04-01

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.

The Cucker-Smale Equation: Singular Communication Weight, Measure-Valued Solutions and Weak-Atomic Uniqueness

NASA Astrophysics Data System (ADS)

Mucha, Piotr B.; Peszek, Jan

2018-01-01

The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency, e.g. to aggregate, flock or disperse. This paper examines the kinetic Cucker-Smale equation with a singular communication weight. Given a compactly supported measure as an initial datum we construct a global in time weak measure-valued solution in the space {C_{weak}(0,∞M)}. The solution is defined as a mean-field limit of the empirical distributions of particles, the dynamics of which is governed by the Cucker-Smale particle system. The studied communication weight is {ψ(s)=|s|^{-α}} with {α \\in (0,1/2)}. This range of singularity admits the sticking of characteristics/trajectories. The second result concerns the weak-atomic uniqueness property stating that a weak solution initiated by a finite sum of atoms, i.e. Dirac deltas in the form {m_i δ_{x_i} ⊗ δ_{v_i}}, preserves its atomic structure. Hence these coincide with unique solutions to the system of ODEs associated with the Cucker-Smale particle system.

Compressed sensing with gradient total variation for low-dose CBCT reconstruction

NASA Astrophysics Data System (ADS)

Seo, Chang-Woo; Cha, Bo Kyung; Jeon, Seongchae; Huh, Young; Park, Justin C.; Lee, Byeonghun; Baek, Junghee; Kim, Eunyoung

2015-06-01

This paper describes the improvement of convergence speed with gradient total variation (GTV) in compressed sensing (CS) for low-dose cone-beam computed tomography (CBCT) reconstruction. We derive a fast algorithm for the constrained total variation (TV)-based a minimum number of noisy projections. To achieve this task we combine the GTV with a TV-norm regularization term to promote an accelerated sparsity in the X-ray attenuation characteristics of the human body. The GTV is derived from a TV and enforces more efficient computationally and faster in convergence until a desired solution is achieved. The numerical algorithm is simple and derives relatively fast convergence. We apply a gradient projection algorithm that seeks a solution iteratively in the direction of the projected gradient while enforcing a non-negatively of the found solution. In comparison with the Feldkamp, Davis, and Kress (FDK) and conventional TV algorithms, the proposed GTV algorithm showed convergence in ≤18 iterations, whereas the original TV algorithm needs at least 34 iterations in reducing 50% of the projections compared with the FDK algorithm in order to reconstruct the chest phantom images. Future investigation includes improving imaging quality, particularly regarding X-ray cone-beam scatter, and motion artifacts of CBCT reconstruction.

Subgraph augmented non-negative tensor factorization (SANTF) for modeling clinical narrative text

PubMed Central

Xin, Yu; Hochberg, Ephraim; Joshi, Rohit; Uzuner, Ozlem; Szolovits, Peter

2015-01-01

Objective Extracting medical knowledge from electronic medical records requires automated approaches to combat scalability limitations and selection biases. However, existing machine learning approaches are often regarded by clinicians as black boxes. Moreover, training data for these automated approaches at often sparsely annotated at best. The authors target unsupervised learning for modeling clinical narrative text, aiming at improving both accuracy and interpretability. Methods The authors introduce a novel framework named subgraph augmented non-negative tensor factorization (SANTF). In addition to relying on atomic features (e.g., words in clinical narrative text), SANTF automatically mines higher-order features (e.g., relations of lymphoid cells expressing antigens) from clinical narrative text by converting sentences into a graph representation and identifying important subgraphs. The authors compose a tensor using patients, higher-order features, and atomic features as its respective modes. We then apply non-negative tensor factorization to cluster patients, and simultaneously identify latent groups of higher-order features that link to patient clusters, as in clinical guidelines where a panel of immunophenotypic features and laboratory results are used to specify diagnostic criteria. Results and Conclusion SANTF demonstrated over 10% improvement in averaged F-measure on patient clustering compared to widely used non-negative matrix factorization (NMF) and k-means clustering methods. Multiple baselines were established by modeling patient data using patient-by-features matrices with different feature configurations and then performing NMF or k-means to cluster patients. Feature analysis identified latent groups of higher-order features that lead to medical insights. We also found that the latent groups of atomic features help to better correlate the latent groups of higher-order features. PMID:25862765

Experimental study on the influence of slickwater on shale permeability

NASA Astrophysics Data System (ADS)

Liu, Zhonghua; Bai, Baojun; Zhang, Zheyu; Tang, Jing; Zeng, Shunpeng; Li, Xiaogang

2018-02-01

There are two diametrically opposite views of the influence of slickwater on shale permeability among scholars at home and abroad. We used the shale outcrops rock samples from the Lower Silurian Longmaxi Formation in Sichuan Basin. The permeability of these dry samples before and after immersion in different solution systems were tested by pulse attenuation method. The experimental results show that the impregnation of different slickwater components and standard salt solution can promote the increase of the permeability of shale samples. The stress sensitivity of shale samples after liquid immersion is medium weak to weak. The sample stress sensitivity is weak after soaked by the synergist solution and Drag reducing agent solution, and the sensitivity of the sample stress is medium weak after immersed by the standard saline solution, defoamer solution and antiswelling solution; The Ki/K0 of the shale sample after liquid immersion on σi/σ0 is consistent with the exponential stress sensitive evaluation model. With the increase of soaking time, the increase of sample permeability increases first and then decreases.

The Discounted Method and Equivalence of Average Criteria for Risk-Sensitive Markov Decision Processes on Borel Spaces

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

Cavazos-Cadena, Rolando, E-mail: rcavazos@uaaan.m; Salem-Silva, Francisco, E-mail: frsalem@uv.m

2010-04-15

This note concerns discrete-time controlled Markov chains with Borel state and action spaces. Given a nonnegative cost function, the performance of a control policy is measured by the superior limit risk-sensitive average criterion associated with a constant and positive risk sensitivity coefficient. Within such a framework, the discounted approach is used (a) to establish the existence of solutions for the corresponding optimality inequality, and (b) to show that, under mild conditions on the cost function, the optimal value functions corresponding to the superior and inferior limit average criteria coincide on a certain subset of the state space. The approach ofmore » the paper relies on standard dynamic programming ideas and on a simple analytical derivation of a Tauberian relation.« less

A Perron-Frobenius theory for block matrices associated to a multiplex network

NASA Astrophysics Data System (ADS)

Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino

2015-03-01

The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.

Recovering hidden diagonal structures via non-negative matrix factorization with multiple constraints.

PubMed

Yang, Xi; Han, Guoqiang; Cai, Hongmin; Song, Yan

2017-03-31

Revealing data with intrinsically diagonal block structures is particularly useful for analyzing groups of highly correlated variables. Earlier researches based on non-negative matrix factorization (NMF) have been shown to be effective in representing such data by decomposing the observed data into two factors, where one factor is considered to be the feature and the other the expansion loading from a linear algebra perspective. If the data are sampled from multiple independent subspaces, the loading factor would possess a diagonal structure under an ideal matrix decomposition. However, the standard NMF method and its variants have not been reported to exploit this type of data via direct estimation. To address this issue, a non-negative matrix factorization with multiple constraints model is proposed in this paper. The constraints include an sparsity norm on the feature matrix and a total variational norm on each column of the loading matrix. The proposed model is shown to be capable of efficiently recovering diagonal block structures hidden in observed samples. An efficient numerical algorithm using the alternating direction method of multipliers model is proposed for optimizing the new model. Compared with several benchmark models, the proposed method performs robustly and effectively for simulated and real biological data.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

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

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation

NASA Astrophysics Data System (ADS)

Gwiazda, Piotr; Michálek, Martin; Świerczewska-Gwiazda, Agnieszka

2018-03-01

A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws; they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager's conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.

Averaging of random walks and shift-invariant measures on a Hilbert space

NASA Astrophysics Data System (ADS)

Sakbaev, V. Zh.

2017-06-01

We study random walks in a Hilbert space H and representations using them of solutions of the Cauchy problem for differential equations whose initial conditions are numerical functions on H. We construct a finitely additive analogue of the Lebesgue measure: a nonnegative finitely additive measure λ that is defined on a minimal subset ring of an infinite-dimensional Hilbert space H containing all infinite-dimensional rectangles with absolutely converging products of the side lengths and is invariant under shifts and rotations in H. We define the Hilbert space H of equivalence classes of complex-valued functions on H that are square integrable with respect to a shift-invariant measure λ. Using averaging of the shift operator in H over random vectors in H with a distribution given by a one-parameter semigroup (with respect to convolution) of Gaussian measures on H, we define a one-parameter semigroup of contracting self-adjoint transformations on H, whose generator is called the diffusion operator. We obtain a representation of solutions of the Cauchy problem for the Schrödinger equation whose Hamiltonian is the diffusion operator.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

Alternative Parameterizations for Cluster Editing

NASA Astrophysics Data System (ADS)

Komusiewicz, Christian; Uhlmann, Johannes

Given an undirected graph G and a nonnegative integer k, the NP-hard Cluster Editing problem asks whether G can be transformed into a disjoint union of cliques by applying at most k edge modifications. In the field of parameterized algorithmics, Cluster Editing has almost exclusively been studied parameterized by the solution size k. Contrastingly, in many real-world instances it can be observed that the parameter k is not really small. This observation motivates our investigation of parameterizations of Cluster Editing different from the solution size k. Our results are as follows. Cluster Editing is fixed-parameter tractable with respect to the parameter "size of a minimum cluster vertex deletion set of G", a typically much smaller parameter than k. Cluster Editing remains NP-hard on graphs with maximum degree six. A restricted but practically relevant version of Cluster Editing is fixed-parameter tractable with respect to the combined parameter "number of clusters in the target graph" and "maximum number of modified edges incident to any vertex in G". Many of our results also transfer to the NP-hard Cluster Deletion problem, where only edge deletions are allowed.

ORACLS: A system for linear-quadratic-Gaussian control law design

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Periodic, complexiton solutions and stability for a (2+1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Yin, Hui-Min; Tian, Bo; Zhao, Xin-Chao

2018-06-01

This paper presents an investigation of a (2 + 1)-dimensional variable-coefficient Gross-Pitaevskii equation in the Bose-Einstein condensation. Periodic and complexiton solutions are obtained. Solitons solutions are also gotten through the periodic solutions. Numerical solutions via the split step method are stable. Effects of the weak and strong modulation instability on the solitons are shown: the weak modulation instability permits an observable soliton, and the strong one overwhelms its development.

On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation

NASA Astrophysics Data System (ADS)

Amadori, Debora; Ha, Seung-Yeal; Park, Jinyeong

2017-01-01

The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely "the Kuramoto-Sakaguchi (KS) equation". This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results.

A quasi-likelihood approach to non-negative matrix factorization

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

A unified approach to non-negative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proven using the Expectation-Maximization algorithm. In addition, a measure to evaluate the goodness-of-fit of the resulting factorization is described. The proposed methods allow modeling of non-linear effects via appropriate link functions and are illustrated using an application in biomedical signal processing. PMID:27348511

A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

NASA Astrophysics Data System (ADS)

Bargigli, Leonardo; Viaggiu, Stefano; Lionetto, Andrea

2016-10-01

We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables {w_{ij}} describing the flow of a given commodity from agent i to agent j. This sequence can be arranged in a nonnegative matrix W which we can regard as the representation of a weighted and directed network or digraph G. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.

Continuously differentiable PIC shape functions for triangular meshes

DOE PAGES

Barnes, D. C.

2018-03-21

In this study, a new class of continuously-differentiable shape functions is developed and applied to two-dimensional electrostatic PIC simulation on an unstructured simplex (triangle) mesh. It is shown that troublesome aliasing instabilities are avoided for cold plasma simulation in which the Debye length is as small as 0.01 cell sizes. These new shape functions satisfy all requirements for PIC particle shape. They are non-negative, have compact support, and partition unity. They are given explicitly by cubic expressions in the usual triangle logical (areal) coordinates. The shape functions are not finite elements because their structure depends on the topology of themore » mesh, in particular, the number of triangles neighboring each mesh vertex. Nevertheless, they may be useful as approximations to solution of other problems in which continuity of derivatives is required or desired.« less

Airborne agent concentration analysis

DOEpatents

Gelbard, Fred

2004-02-03

A method and system for inferring airborne contaminant concentrations in rooms without contaminant sensors, based on data collected by contaminant sensors in other rooms of a building, using known airflow interconnectivity data. The method solves a least squares problem that minimizes the difference between measured and predicted contaminant sensor concentrations with respect to an unknown contaminant release time. Solutions are constrained to providing non-negative initial contaminant concentrations in all rooms. The method can be used to identify a near-optimal distribution of sensors within the building, when then number of available sensors is less than the total number of rooms. This is achieved by having a system-sensor matrix that is non-singular, and by selecting that distribution which yields the lowest condition number of all the distributions considered. The method can predict one or more contaminant initial release points from the collected data.

Continuously differentiable PIC shape functions for triangular meshes

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

Barnes, D. C.

In this study, a new class of continuously-differentiable shape functions is developed and applied to two-dimensional electrostatic PIC simulation on an unstructured simplex (triangle) mesh. It is shown that troublesome aliasing instabilities are avoided for cold plasma simulation in which the Debye length is as small as 0.01 cell sizes. These new shape functions satisfy all requirements for PIC particle shape. They are non-negative, have compact support, and partition unity. They are given explicitly by cubic expressions in the usual triangle logical (areal) coordinates. The shape functions are not finite elements because their structure depends on the topology of themore » mesh, in particular, the number of triangles neighboring each mesh vertex. Nevertheless, they may be useful as approximations to solution of other problems in which continuity of derivatives is required or desired.« less

A Reduced Basis Method with Exact-Solution Certificates for Symmetric Coercive Equations

DTIC Science & Technology

2013-11-06

the energy associated with the infinite - dimensional weak solution of parametrized symmetric coercive partial differential equations with piecewise...builds bounds with respect to the infinite - dimensional weak solution, aims to entirely remove the issue of the “truth” within the certified reduced basis...framework. We in particular introduce a reduced basis method that provides rigorous upper and lower bounds

Porous elastic system with nonlinear damping and sources terms

NASA Astrophysics Data System (ADS)

Freitas, Mirelson M.; Santos, M. L.; Langa, José A.

2018-02-01

We study the long-time behavior of porous-elastic system, focusing on the interplay between nonlinear damping and source terms. The sources may represent restoring forces, but may also be focusing thus potentially amplifying the total energy which is the primary scenario of interest. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions, and uniqueness of weak solutions. Moreover, we prove that such unique solutions depend continuously on the initial data. Under some restrictions on the parameters, we also prove that every weak solution to our system blows up in finite time, provided the initial energy is negative and the sources are more dominant than the damping in the system. Additional results are obtained via careful analysis involving the Nehari Manifold. Specifically, we prove the existence of a unique global weak solution with initial data coming from the "good" part of the potential well. For such a global solution, we prove that the total energy of the system decays exponentially or algebraically, depending on the behavior of the dissipation in the system near the origin. We also prove the existence of a global attractor.

How quantum are non-negative wavefunctions?

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

Hastings, M. B.

2016-01-15

We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a “coherent Gibbs state” form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, andmore » on the absence of a “generalized area law” [D. Aharonov et al., in Proceedings of Foundations of Computer Science (FOCS) (IEEE, 2014), p. 246; e-print arXiv.org:1410.0951] even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an “intrinsic” sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds [S. Bravyi et al., J. Math. Phys. 51, 093512 (2010)].« less

A Deep Stochastic Model for Detecting Community in Complex Networks

NASA Astrophysics Data System (ADS)

Fu, Jingcheng; Wu, Jianliang

2017-01-01

Discovering community structures is an important step to understanding the structure and dynamics of real-world networks in social science, biology and technology. In this paper, we develop a deep stochastic model based on non-negative matrix factorization to identify communities, in which there are two sets of parameters. One is the community membership matrix, of which the elements in a row correspond to the probabilities of the given node belongs to each of the given number of communities in our model, another is the community-community connection matrix, of which the element in the i-th row and j-th column represents the probability of there being an edge between a randomly chosen node from the i-th community and a randomly chosen node from the j-th community. The parameters can be evaluated by an efficient updating rule, and its convergence can be guaranteed. The community-community connection matrix in our model is more precise than the community-community connection matrix in traditional non-negative matrix factorization methods. Furthermore, the method called symmetric nonnegative matrix factorization, is a special case of our model. Finally, based on the experiments on both synthetic and real-world networks data, it can be demonstrated that our algorithm is highly effective in detecting communities.

Identifying group discriminative and age regressive sub-networks from DTI-based connectivity via a unified framework of non-negative matrix factorization and graph embedding

PubMed Central

Ghanbari, Yasser; Smith, Alex R.; Schultz, Robert T.; Verma, Ragini

2014-01-01

Diffusion tensor imaging (DTI) offers rich insights into the physical characteristics of white matter (WM) fiber tracts and their development in the brain, facilitating a network representation of brain’s traffic pathways. Such a network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these connectivity networks necessitates the development of methods that identify the connectivity building blocks or sub-network components that characterize the underlying variation in the population. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart different sources of variation in the sample, facilitating variation-specific statistical analysis. We propose a unified framework of non-negative matrix factorization and graph embedding for learning sub-network patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing variational sources in the population like age and pathology. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism that shows localized sparse sub-networks which mostly capture the changes related to pathology and developmental variations. PMID:25037933

Online Multi-Modal Robust Non-Negative Dictionary Learning for Visual Tracking

PubMed Central

Zhang, Xiang; Guan, Naiyang; Tao, Dacheng; Qiu, Xiaogang; Luo, Zhigang

2015-01-01

Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality. PMID:25961715

Online multi-modal robust non-negative dictionary learning for visual tracking.

PubMed

Zhang, Xiang; Guan, Naiyang; Tao, Dacheng; Qiu, Xiaogang; Luo, Zhigang

2015-01-01

Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality.

Robust demarcation of basal cell carcinoma by dependent component analysis-based segmentation of multi-spectral fluorescence images.

PubMed

Kopriva, Ivica; Persin, Antun; Puizina-Ivić, Neira; Mirić, Lina

2010-07-02

This study was designed to demonstrate robust performance of the novel dependent component analysis (DCA)-based approach to demarcation of the basal cell carcinoma (BCC) through unsupervised decomposition of the red-green-blue (RGB) fluorescent image of the BCC. Robustness to intensity fluctuation is due to the scale invariance property of DCA algorithms, which exploit spectral and spatial diversities between the BCC and the surrounding tissue. Used filtering-based DCA approach represents an extension of the independent component analysis (ICA) and is necessary in order to account for statistical dependence that is induced by spectral similarity between the BCC and surrounding tissue. This generates weak edges what represents a challenge for other segmentation methods as well. By comparative performance analysis with state-of-the-art image segmentation methods such as active contours (level set), K-means clustering, non-negative matrix factorization, ICA and ratio imaging we experimentally demonstrate good performance of DCA-based BCC demarcation in two demanding scenarios where intensity of the fluorescent image has been varied almost two orders of magnitude. Copyright 2010 Elsevier B.V. All rights reserved.

Concentration of perrhenate and pertechnetate solutions

DOEpatents

Knapp, F.F.; Beets, A.L.; Mirzadeh, S.; Guhlke, S.

1998-03-17

A method is described for preparing a concentrated solution of a carrier-free radioisotope which includes the steps of: (a) providing a generator column loaded with a composition containing a parent radioisotope; (b) eluting the generator column with an eluent solution which includes a salt of a weak acid to elute a target daughter radioisotope from the generator column in a first eluate; (c) eluting a cation-exchange column with the first eluate to exchange cations of the salt for hydrogen ions and to elute the target daughter radioisotope and a weak acid in a second eluate; (d) eluting an anion-exchange column with the second eluate to trap and concentrate the target daughter radioisotope and to elute the weak acid solution therefrom; and (e) eluting the concentrated target daughter radioisotope from the anion-exchange column with a saline solution. 1 fig.

Concentration of perrhenate and pertechnetate solutions

DOEpatents

Knapp, Furn F.; Beets, Arnold L.; Mirzadeh, Saed; Guhlke, Stefan

1998-01-01

A method of preparing a concentrated solution of a carrier-free radioisotope which includes the steps of: a. providing a generator column loaded with a composition containing a parent radioisotope; b. eluting the generator column with an eluent solution which includes a salt of a weak acid to elute a target daughter radioisotope from the generator column in a first eluate. c. eluting a cation-exchange column with the first eluate to exchange cations of the salt for hydrogen ions and to elute the target daughter radioisotope and a weak acid in a second eluate; d. eluting an anion-exchange column with the second eluate to trap and concentrate the target daughter radioisotope and to elute the weak acid solution therefrom; and e. eluting the concentrated target daughter radioisotope from the anion-exchange column with a saline solution.

Limited-memory fast gradient descent method for graph regularized nonnegative matrix factorization.

PubMed

Guan, Naiyang; Wei, Lei; Luo, Zhigang; Tao, Dacheng

2013-01-01

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix X[Symbol:see text]R(m x n) to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r) and H[Symbol:see text]R(r x n) (r < min {m,n}) and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.

Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects

NASA Astrophysics Data System (ADS)

Bian, Dongfen; Liu, Jitao

2017-12-01

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay rates of weak solutions and strong solution are obtained respectively.

Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations

NASA Astrophysics Data System (ADS)

Phan, Tuoc

2017-12-01

This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form ut -div [ A (x , t , u , ∇u) ] =div [ F ] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x , t)-variables, and dependent on the solution u. Global and interior weighted W 1 , p (ΩT , ω)-regularity estimates are established for weak solutions of these equations, where ω is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for ω = 1, because of the singularity of the coefficients in (x , t)-variables.

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

NASA Astrophysics Data System (ADS)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

Convection Regularization of High Wavenumbers in Turbulence ANS Shocks

DTIC Science & Technology

2011-07-31

dynamics of particles that adhere to one another upon collision and has been studied as a simple cosmological model for describing the nonlinear formation of...solution we mean a solution to the Cauchy problem in the following sense. Definition 5.1. A function u : R × [0, T ] 7→ RN is a weak solution of the...step 2 the limit function in the α → 0 limit is shown to satisfy the definition of a weak solution for the Cauchy problem. Without loss of generality

Symmetric nonnegative matrix factorization: algorithms and applications to probabilistic clustering.

PubMed

He, Zhaoshui; Xie, Shengli; Zdunek, Rafal; Zhou, Guoxu; Cichocki, Andrzej

2011-12-01

Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.

On the regularity criterion of weak solutions for the 3D MHD equations

NASA Astrophysics Data System (ADS)

Gala, Sadek; Ragusa, Maria Alessandra

2017-12-01

The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution ( u, b) becomes regular provided that ( \

The thermal stability of the nanograin structure in a weak solute segregation system.

PubMed

Tang, Fawei; Song, Xiaoyan; Wang, Haibin; Liu, Xuemei; Nie, Zuoren

2017-02-08

A hybrid model that combines first principles calculations and thermodynamic evaluation was developed to describe the thermal stability of a nanocrystalline solid solution with weak segregation. The dependence of the solute segregation behavior on the electronic structure, solute concentration, grain size and temperature was demonstrated, using the nanocrystalline Cu-Zn system as an example. The modeling results show that the segregation energy changes with the solute concentration in a form of nonmonotonic function. The change in the total Gibbs free energy indicates that at a constant solute concentration and a given temperature, a nanocrystalline structure can remain stable when the initial grain size is controlled in a critical range. In experiments, dense nanocrystalline Cu-Zn alloy bulk was prepared, and a series of annealing experiments were performed to examine the thermal stability of the nanograins. The experimental measurements confirmed the model predictions that with a certain solute concentration, a state of steady nanograin growth can be achieved at high temperatures when the initial grain size is controlled in a critical range. The present work proposes that in weak solute segregation systems, the nanograin structure can be kept thermally stable by adjusting the solute concentration and initial grain size.

Mean Field Type Control with Congestion

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu

2016-06-15

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.

Isotropy of Angular Frequencies and Weak Chimeras with Broken Symmetry

NASA Astrophysics Data System (ADS)

Bick, Christian

2017-04-01

The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.

A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

NASA Astrophysics Data System (ADS)

Neustupa, Tomáš

2017-07-01

The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health

PubMed Central

Fogel, Paul; Gaston-Mathé, Yann; Hawkins, Douglas; Fogel, Fajwel; Luta, George; Young, S. Stanley

2016-01-01

Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA). With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability. PMID:27213413

Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health.

PubMed

Fogel, Paul; Gaston-Mathé, Yann; Hawkins, Douglas; Fogel, Fajwel; Luta, George; Young, S Stanley

2016-05-18

Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA). With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability.

Identification of regional activation by factorization of high-density surface EMG signals: A comparison of Principal Component Analysis and Non-negative Matrix factorization.

PubMed

Gallina, Alessio; Garland, S Jayne; Wakeling, James M

2018-05-22

In this study, we investigated whether principal component analysis (PCA) and non-negative matrix factorization (NMF) perform similarly for the identification of regional activation within the human vastus medialis. EMG signals from 64 locations over the VM were collected from twelve participants while performing a low-force isometric knee extension. The envelope of the EMG signal of each channel was calculated by low-pass filtering (8 Hz) the monopolar EMG signal after rectification. The data matrix was factorized using PCA and NMF, and up to 5 factors were considered for each algorithm. Association between explained variance, spatial weights and temporal scores between the two algorithms were compared using Pearson correlation. For both PCA and NMF, a single factor explained approximately 70% of the variance of the signal, while two and three factors explained just over 85% or 90%. The variance explained by PCA and NMF was highly comparable (R > 0.99). Spatial weights and temporal scores extracted with non-negative reconstruction of PCA and NMF were highly associated (all p < 0.001, mean R > 0.97). Regional VM activation can be identified using high-density surface EMG and factorization algorithms. Regional activation explains up to 30% of the variance of the signal, as identified through both PCA and NMF. Copyright © 2018 Elsevier Ltd. All rights reserved.

Non-negative infrared patch-image model: Robust target-background separation via partial sum minimization of singular values

NASA Astrophysics Data System (ADS)

Dai, Yimian; Wu, Yiquan; Song, Yu; Guo, Jun

2017-03-01

To further enhance the small targets and suppress the heavy clutters simultaneously, a robust non-negative infrared patch-image model via partial sum minimization of singular values is proposed. First, the intrinsic reason behind the undesirable performance of the state-of-the-art infrared patch-image (IPI) model when facing extremely complex backgrounds is analyzed. We point out that it lies in the mismatching of IPI model's implicit assumption of a large number of observations with the reality of deficient observations of strong edges. To fix this problem, instead of the nuclear norm, we adopt the partial sum of singular values to constrain the low-rank background patch-image, which could provide a more accurate background estimation and almost eliminate all the salient residuals in the decomposed target image. In addition, considering the fact that the infrared small target is always brighter than its adjacent background, we propose an additional non-negative constraint to the sparse target patch-image, which could not only wipe off more undesirable components ulteriorly but also accelerate the convergence rate. Finally, an algorithm based on inexact augmented Lagrange multiplier method is developed to solve the proposed model. A large number of experiments are conducted demonstrating that the proposed model has a significant improvement over the other nine competitive methods in terms of both clutter suppressing performance and convergence rate.

M-matrices with prescribed elementary divisors

NASA Astrophysics Data System (ADS)

Soto, Ricardo L.; Díaz, Roberto C.; Salas, Mario; Rojo, Oscar

2017-09-01

A real matrix A is said to be an M-matrix if it is of the form A=α I-B, where B is a nonnegative matrix with Perron eigenvalue ρ (B), and α ≥slant ρ (B) . This paper provides sufficient conditions for the existence and construction of an M-matrix A with prescribed elementary divisors, which are the characteristic polynomials of the Jordan blocks of the Jordan canonical form of A. This inverse problem on M-matrices has not been treated until now. We solve the inverse elementary divisors problem for diagonalizable M-matrices and the symmetric generalized doubly stochastic inverse M-matrix problem for lists of real numbers and for lists of complex numbers of the form Λ =\\{λ 1, a+/- bi, \\ldots, a+/- bi\\} . The constructive nature of our results allows for the computation of a solution matrix. The paper also discusses an application of M-matrices to a capacity problem in wireless communications.

Large-deviation properties of Brownian motion with dry friction.

PubMed

Chen, Yaming; Just, Wolfram

2014-10-01

We investigate piecewise-linear stochastic models with regard to the probability distribution of functionals of the stochastic processes, a question that occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase space point or in a phase space region, as well as to the motion with inertia. For a Langevin equation with discontinuous drift, we extend the so-called backward Fokker-Planck technique for non-negative support functionals to arbitrary support functionals, to derive explicit expressions for the moments of the functional. Explicit solutions for the moments and for the distribution of the so-called local time, the occupation time, and the displacement are derived for the Brownian motion with dry friction, including quantitative measures to characterize deviation from Gaussian behavior in the asymptotic long time limit.

Mathematical analysis of an age-structured population model with space-limited recruitment.

PubMed

Kamioka, Katumi

2005-11-01

In this paper, we investigate structured population model of marine invertebrate whose life stage is composed of sessile adults and pelagic larvae, such as barnacles contained in a local habitat. First we formulate the basic model as an Cauchy problem on a Banach space to discuss the existence and uniqueness of non-negative solution. Next we define the basic reproduction number R0 to formulate the invasion condition under which the larvae can successfully settle down in the completely vacant habitat. Subsequently we examine existence and stability of steady states. We show that the trivial steady state is globally asymptotically stable if R0 < or = 1, whereas it is unstable if R0 > 1. Furthermore, we show that a positive (non-trivial) steady state uniquely exists if R0 > 1 and it is locally asymptotically stable as far as absolute value of R0 - 1 is small enough.

Sparse representation-based image restoration via nonlocal supervised coding

NASA Astrophysics Data System (ADS)

Li, Ao; Chen, Deyun; Sun, Guanglu; Lin, Kezheng

2016-10-01

Sparse representation (SR) and nonlocal technique (NLT) have shown great potential in low-level image processing. However, due to the degradation of the observed image, SR and NLT may not be accurate enough to obtain a faithful restoration results when they are used independently. To improve the performance, in this paper, a nonlocal supervised coding strategy-based NLT for image restoration is proposed. The novel method has three main contributions. First, to exploit the useful nonlocal patches, a nonnegative sparse representation is introduced, whose coefficients can be utilized as the supervised weights among patches. Second, a novel objective function is proposed, which integrated the supervised weights learning and the nonlocal sparse coding to guarantee a more promising solution. Finally, to make the minimization tractable and convergence, a numerical scheme based on iterative shrinkage thresholding is developed to solve the above underdetermined inverse problem. The extensive experiments validate the effectiveness of the proposed method.

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

NASA Technical Reports Server (NTRS)

Black, Carrie; Germaschewski, Kai; Bhattacharjee, Amitava; Ng, C. S.

2013-01-01

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

NASA Astrophysics Data System (ADS)

Chiodaroli, Elisabetta; Michálek, Martin

2017-08-01

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Euler-type system and apply the methods of convex integration of De Lellis and Székelyhidi to show the existence of infinitely many global weak solutions of the studied equations for general initial data. We also introduce an appropriate notion of dissipative solutions and show the existence of suitable initial data which generate infinitely many dissipative solutions.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Skill Acquisition: Compilation of Weak-Method Problem Solutions.

ERIC Educational Resources Information Center

Anderson, John R.

According to the ACT theory of skill acquisition, cognitive skills are encoded by a set of productions, which are organized according to a hierarchical goal structure. People solve problems in new domains by applying weak problem-solving procedures to declarative knowledge they have about this domain. From these initial problem solutions,…

Attributed community mining using joint general non-negative matrix factorization with graph Laplacian

NASA Astrophysics Data System (ADS)

Chen, Zigang; Li, Lixiang; Peng, Haipeng; Liu, Yuhong; Yang, Yixian

2018-04-01

Community mining for complex social networks with link and attribute information plays an important role according to different application needs. In this paper, based on our proposed general non-negative matrix factorization (GNMF) algorithm without dimension matching constraints in our previous work, we propose the joint GNMF with graph Laplacian (LJGNMF) to implement community mining of complex social networks with link and attribute information according to different application needs. Theoretical derivation result shows that the proposed LJGNMF is fully compatible with previous methods of integrating traditional NMF and symmetric NMF. In addition, experimental results show that the proposed LJGNMF can meet the needs of different community minings by adjusting its parameters, and the effect is better than traditional NMF in the community vertices attributes entropy.

On τ-Compactness of Products of τ-Measurable Operators

NASA Astrophysics Data System (ADS)

Bikchentaev, Airat M.

2017-12-01

Let M be a von Neumann algebra of operators on a Hilbert space H, τ be a faithful normal semifinite trace on M. We obtain some new inequalities for rearrangements of τ-measurable operators products. We also establish some sufficient τ-compactness conditions for products of selfadjoint τ-measurable operators. Next we obtain a τ-compactness criterion for product of a nonnegative τ-measurable operator with an arbitrary τ-measurable operator. We construct an example that shows importance of nonnegativity for one of the factors. The similar results are obtained also for elementary operators from M. We apply our results to symmetric spaces on (M, τ ). The results are new even for the *-algebra B(H) of all linear bounded operators on H endowed with the canonical trace τ = tr.

The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle

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

Lee, Chiun-Chang, E-mail: chlee@mail.nhcue.edu.tw

2014-05-15

The present article is concerned with the charge conserving Poisson-Boltzmann (CCPB) equation in high-dimensional bounded smooth domains. The CCPB equation is a Poisson-Boltzmann type of equation with nonlocal coefficients. First, under the Robin boundary condition, we get the existence of weak solutions to this equation. The main approach is variational, based on minimization of a logarithm-type energy functional. To deal with the regularity of weak solutions, we establish a maximum modulus estimate for the standard Poisson-Boltzmann (PB) equation to show that weak solutions of the CCPB equation are essentially bounded. Then the classical solutions follow from the elliptic regularity theorem.more » Second, a maximum principle for the CCPB equation is established. In particular, we show that in the case of global electroneutrality, the solution achieves both its maximum and minimum values at the boundary. However, in the case of global non-electroneutrality, the solution may attain its maximum value at an interior point. In addition, under certain conditions on the boundary, we show that the global non-electroneutrality implies pointwise non-electroneutrality.« less

Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation

NASA Astrophysics Data System (ADS)

Chang, Xiangke; Szmigielski, Jacek

2018-02-01

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem, the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds, as well as Toda-like sorting property.

On the box-counting dimension of the potential singular set for suitable weak solutions to the 3D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Wang, Yanqing; Wu, Gang

2017-05-01

In this paper, we are concerned with the upper box-counting dimension of the set of possible singular points in the space-time of suitable weak solutions to the 3D Navier-Stokes equations. By taking full advantage of the pressure \\Pi in terms of \

Weak periodic solutions of xẍ + 1 = 0 and the Harmonic Balance Method

NASA Astrophysics Data System (ADS)

García-Saldaña, J. D.; Gasull, A.

2017-02-01

We prove that the differential equation xẍ + 1 = 0 has continuous weak periodic solutions and compute their periods. Then, we use the Harmonic Balance Method until order six to approximate these periods and to illustrate how the accuracy of the method increases with the order. Our computations rely on the Gröbner basis approach.

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth

NASA Astrophysics Data System (ADS)

Zeng, Xianzhong; Gu, Yonggeng

2018-03-01

This paper deals with a ratio-dependent predator-prey system with the crowing term and the weak growth in the prey equation. Under the condition that the coefficient λ is less than a critical value λ1D (Ω0), we obtain existence of multiple positive steady state solutions of the predator-prey system and the dynamical behaviors of its positive solutions. Our results show that the predator and the prey possess not only the common coexistence, but also the very weak coexistence which both of the predator and the prey are very low. Meantime, the persistence of the positive solutions for the corresponding parabolic type system sometime depends strictly on the ratio of its initial data. Therefore, our results may be used to explain some special phenomena which under some bad environment, the predator and the prey may still coexist.

Weakly Hydrated Surfaces and the Binding Interactions of Small Biological Solutes

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

Brady, J. W.; Tavagnacco, L.; Ehrlich, L.

2012-04-01

Extended planar hydrophobic surfaces, such as are found in the side chains of the amino acids histidine, phenylalanine, tyrosine, and tryptophan, exhibit an affinity for the weakly hydrated faces of glucopyranose. In addition, molecular species such as these, including indole, caffeine, and imidazole, exhibit a weak tendency to pair together by hydrophobic stacking in aqueous solution. These interactions can be partially understood in terms of recent models for the hydration of extended hydrophobic faces and should provide insight into the architecture of sugar-binding sites in proteins.

Weakly hydrated surfaces and the binding interactions of small biological solutes.

PubMed

Brady, John W; Tavagnacco, Letizia; Ehrlich, Laurent; Chen, Mo; Schnupf, Udo; Himmel, Michael E; Saboungi, Marie-Louise; Cesàro, Attilio

2012-04-01

Extended planar hydrophobic surfaces, such as are found in the side chains of the amino acids histidine, phenylalanine, tyrosine, and tryptophan, exhibit an affinity for the weakly hydrated faces of glucopyranose. In addition, molecular species such as these, including indole, caffeine, and imidazole, exhibit a weak tendency to pair together by hydrophobic stacking in aqueous solution. These interactions can be partially understood in terms of recent models for the hydration of extended hydrophobic faces and should provide insight into the architecture of sugar-binding sites in proteins.

Mathematical improvement of the Hopfield model for feasible solutions to the traveling salesman problem by a synapse dynamical system.

PubMed

Takahashi, Y

1998-01-01

It is well known that the Hopfield Model (HM) for neural networks to solve the Traveling Salesman Problem (TSP) suffers from three major drawbacks. (1) It can converge on nonoptimal locally minimum solutions. (2) It can converge on infeasible solutions. (3) Results are very sensitive to the careful tuning of its parameters. A number of methods have been proposed to overcome (a) well. In contrast, work on (b) and (c) has not been sufficient; techniques have not been generalized to more general optimization problems. Thus this paper mathematically resolves (b) and (c) to such an extent that the resolution can be applied to solving with some general network continuous optimization problems including the Hopfield version of the TSP. It first constructs an Extended HM (E-HM) that overcomes both (b) and (c). Fundamental techniques of the E-HM lie in the addition of a synapse dynamical system cooperated with the current HM unit dynamical system. It is this synapse dynamical system that makes the TSP constraint hold at any final states for whatever choices of the IIM parameters and an initial state. The paper then generalizes the E-HM further to a network that can solve a class of continuous optimization problems with a constraint equation where both of the objective function and the constraint function are nonnegative and continuously differentiable.

Novel third-order Lovelock wormhole solutions

NASA Astrophysics Data System (ADS)

Mehdizadeh, Mohammad Reza; Lobo, Francisco S. N.

2016-06-01

In this work, we consider wormhole geometries in third-order Lovelock gravity and investigate the possibility that these solutions satisfy the energy conditions. In this framework, by applying a specific equation of state, we obtain exact wormhole solutions, and by imposing suitable values for the parameters of the theory, we find that these geometries satisfy the weak energy condition in the vicinity of the throat, due to the presence of higher-order curvature terms. Finally, we trace out a numerical analysis, by assuming a specific redshift function, and find asymptotically flat solutions that satisfy the weak energy condition throughout the spacetime.

The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther

2018-04-01

We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

From the Highly Compressible Navier-Stokes Equations to Fast Diffusion and Porous Media Equations, Existence of Global Weak Solution for the Quasi-Solutions

NASA Astrophysics Data System (ADS)

Haspot, Boris

2016-06-01

We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.

Nonnegative matrix factorization: a blind sources separation method to extract content of fluorophores mixture media

NASA Astrophysics Data System (ADS)

Zhou, Kenneth J.; Chen, Jun

2014-03-01

The fluorophores of malignant human breast cells change their compositions that may be exposed in the fluorescence spectroscopy and blind source separation method. The content of the fluorophores mixture media such as tryptophan, collagen, elastin, NADH, and flavin were varied according to the cancer development. The native fluorescence spectra of these key fluorophores mixture media excited by the selective excitation wavelengths of 300 nm and 340 nm were analyzed using a blind source separation method: Nonnegative Matrix Factorization (NMF). The results show that the contribution from tryptophan, NADH and flavin to the fluorescence spectra of the mixture media is proportional to the content of each fluorophore. These data present a possibility that native fluorescence spectra decomposed by NMF can be used as potential native biomarkers for cancer detection evaluation of the cancer.

Nonredundant sparse feature extraction using autoencoders with receptive fields clustering.

PubMed

Ayinde, Babajide O; Zurada, Jacek M

2017-09-01

This paper proposes new techniques for data representation in the context of deep learning using agglomerative clustering. Existing autoencoder-based data representation techniques tend to produce a number of encoding and decoding receptive fields of layered autoencoders that are duplicative, thereby leading to extraction of similar features, thus resulting in filtering redundancy. We propose a way to address this problem and show that such redundancy can be eliminated. This yields smaller networks and produces unique receptive fields that extract distinct features. It is also shown that autoencoders with nonnegativity constraints on weights are capable of extracting fewer redundant features than conventional sparse autoencoders. The concept is illustrated using conventional sparse autoencoder and nonnegativity-constrained autoencoders with MNIST digits recognition, NORB normalized-uniform object data and Yale face dataset. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bird sound spectrogram decomposition through Non-Negative Matrix Factorization for the acoustic classification of bird species.

PubMed

Ludeña-Choez, Jimmy; Quispe-Soncco, Raisa; Gallardo-Antolín, Ascensión

2017-01-01

Feature extraction for Acoustic Bird Species Classification (ABSC) tasks has traditionally been based on parametric representations that were specifically developed for speech signals, such as Mel Frequency Cepstral Coefficients (MFCC). However, the discrimination capabilities of these features for ABSC could be enhanced by accounting for the vocal production mechanisms of birds, and, in particular, the spectro-temporal structure of bird sounds. In this paper, a new front-end for ABSC is proposed that incorporates this specific information through the non-negative decomposition of bird sound spectrograms. It consists of the following two different stages: short-time feature extraction and temporal feature integration. In the first stage, which aims at providing a better spectral representation of bird sounds on a frame-by-frame basis, two methods are evaluated. In the first method, cepstral-like features (NMF_CC) are extracted by using a filter bank that is automatically learned by means of the application of Non-Negative Matrix Factorization (NMF) on bird audio spectrograms. In the second method, the features are directly derived from the activation coefficients of the spectrogram decomposition as performed through NMF (H_CC). The second stage summarizes the most relevant information contained in the short-time features by computing several statistical measures over long segments. The experiments show that the use of NMF_CC and H_CC in conjunction with temporal integration significantly improves the performance of a Support Vector Machine (SVM)-based ABSC system with respect to conventional MFCC.

Identifying constituent spectra sources in multispectral images to quantify and locate cervical neoplasia

NASA Astrophysics Data System (ADS)

Baker, Kevin C.; Bambot, Shabbir

2011-02-01

Optical spectroscopy has been shown to be an effective method for detecting neoplasia. Guided Therapeutics has developed LightTouch, a non invasive device that uses a combination of reflectance and fluorescence spectroscopy for identifying early cancer of the human cervix. The combination of the multispectral information from the two spectroscopic modalities has been shown to be an effective method to screen for cervical cancer. There has however been a relative paucity of work in identifying the individual spectral components that contribute to the measured fluorescence and reflectance spectra. This work aims to identify the constituent source spectra and their concentrations. We used non-negative matrix factorization (NNMF) numerical methods to decompose the mixed multispectral data into the constituent spectra and their corresponding concentrations. NNMF is an iterative approach that factorizes the measured data into non-negative factors. The factors are chosen to minimize the root-mean-squared residual error. NNMF has shown promise for feature extraction and identification in the fields of text mining and spectral data analysis. Since both the constituent source spectra and their corresponding concentrations are assumed to be non-negative by nature NNMF is a reasonable approach to deconvolve the measured multispectral data. Supervised learning methods were then used to determine which of the constituent spectra sources best predict the amount of neoplasia. The constituent spectra sources found to best predict neoplasia were then compared with spectra of known biological chromophores.

Bird sound spectrogram decomposition through Non-Negative Matrix Factorization for the acoustic classification of bird species

PubMed Central

Quispe-Soncco, Raisa

2017-01-01

Feature extraction for Acoustic Bird Species Classification (ABSC) tasks has traditionally been based on parametric representations that were specifically developed for speech signals, such as Mel Frequency Cepstral Coefficients (MFCC). However, the discrimination capabilities of these features for ABSC could be enhanced by accounting for the vocal production mechanisms of birds, and, in particular, the spectro-temporal structure of bird sounds. In this paper, a new front-end for ABSC is proposed that incorporates this specific information through the non-negative decomposition of bird sound spectrograms. It consists of the following two different stages: short-time feature extraction and temporal feature integration. In the first stage, which aims at providing a better spectral representation of bird sounds on a frame-by-frame basis, two methods are evaluated. In the first method, cepstral-like features (NMF_CC) are extracted by using a filter bank that is automatically learned by means of the application of Non-Negative Matrix Factorization (NMF) on bird audio spectrograms. In the second method, the features are directly derived from the activation coefficients of the spectrogram decomposition as performed through NMF (H_CC). The second stage summarizes the most relevant information contained in the short-time features by computing several statistical measures over long segments. The experiments show that the use of NMF_CC and H_CC in conjunction with temporal integration significantly improves the performance of a Support Vector Machine (SVM)-based ABSC system with respect to conventional MFCC. PMID:28628630

Existence of weak solutions to degenerate p-Laplacian equations and integral formulas

NASA Astrophysics Data System (ADS)

Chua, Seng-Kee; Wheeden, Richard L.

2017-12-01

We study the problem of solving some general integral formulas and then apply the conclusions to obtain results about the existence of weak solutions of various degenerate p-Laplacian equations. We adapt Variational Calculus methods and the Mountain Pass Lemma without the Palais-Smale condition, and we use an abstract version of Lions' Concentration Compactness Principle II.

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

PubMed

Yang, Jiashi; Chen, Ziguang; Hu, Yuantai; Jiang, Shunong; Guo, Shaohua

2007-04-01

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

Quantum weak turbulence with applications to semiconductor lasers

NASA Astrophysics Data System (ADS)

Lvov, Yuri Victorovich

Based on a model Hamiltonian appropriate for the description of fermionic systems such as semiconductor lasers, we describe a natural asymptotic closure of the BBGKY hierarchy in complete analogy with that derived for classical weak turbulence. The main features of the interaction Hamiltonian are the inclusion of full Fermi statistics containing Pauli blocking and a simple, phenomenological, uniformly weak two particle interaction potential equivalent to the static screening approximation. The resulting asymytotic closure and quantum kinetic Boltzmann equation are derived in a self consistent manner without resorting to a priori statistical hypotheses or cumulant discard assumptions. We find a new class of solutions to the quantum kinetic equation which are analogous to the Kolmogorov spectra of hydrodynamics and classical weak turbulence. They involve finite fluxes of particles and energy across momentum space and are particularly relevant for describing the behavior of systems containing sources and sinks. We explore these solutions by using differential approximation to collision integral. We make a prima facie case that these finite flux solutions can be important in the context of semiconductor lasers. We show that semiconductor laser output efficiency can be improved by exciting these finite flux solutions. Numerical simulations of the semiconductor Maxwell Bloch equations support the claim.

Nonconvex Sparse Logistic Regression With Weakly Convex Regularization

NASA Astrophysics Data System (ADS)

Shen, Xinyue; Gu, Yuantao

2018-06-01

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a method based on proximal gradient descent is used to solve the general weakly convex sparse logistic regression, and its convergence behavior is studied theoretically. Then the general framework is applied to a specific weakly convex function, and a necessary and sufficient local optimality condition is provided. The solution method is instantiated in this case as an iterative firm-shrinkage algorithm, and its effectiveness is demonstrated in numerical experiments by both randomly generated and real datasets.

Nonequilibrium mechanisms of weak electrolyte electrification under the action of constant voltage

NASA Astrophysics Data System (ADS)

Stishkov, Yu. K.; Chirkov, V. A.

2016-07-01

The formation of space charge in weak electrolytes, specifically in liquid dielectrics, has been considered. An analytical solution is given to a simplified set of Nernst-Planck equations that describe the formation of nonequilibrium recombination layers in weak electrolytes. This approximate analytical solution is compared with computer simulation data for a complete set of Poisson-Nernst-Planck equations. It has been shown that the current passage in weak electrolytes can be described by a single dimensionless parameter that equals the length of a near-electrode recombination layer divided by the width of the interelectrode gap. The formation mechanism and the structure of charged nonequilibrium near-electrode layers in the nonstationary regime have been analyzed for different injection-to-conduction current ratios. It has been found that almost all charge structures encountered in weak dielectrics can be accounted for by the nonequilibrium dissociation-recombination mechanism of space charge formation.

On the Boltzmann Equation with Stochastic Kinetic Transport: Global Existence of Renormalized Martingale Solutions

NASA Astrophysics Data System (ADS)

Punshon-Smith, Samuel; Smith, Scott

2018-02-01

This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. This study includes a criterion for renormalization, the weak closedness of the solution set, and tightness of velocity averages in {{L}1}.

Investigation of pH Influence on Skin Permeation Behavior of Weak Acids Using Nonsteroidal Anti-Inflammatory Drugs.

PubMed

Chantasart, Doungdaw; Chootanasoontorn, Siriwan; Suksiriworapong, Jiraphong; Li, S Kevin

2015-10-01

As a continuing effort to understand the skin permeation behavior of weak acids and bases, the objectives of the present study were to evaluate skin permeation of nonsteroidal anti-inflammatory drugs (NSAIDs) under the influence of pH, investigate the mechanism of pH effect, and examine a previous hypothesis that the effective skin pH for drug permeation is different from donor solution pH. In vitro permeability experiments were performed in side-by-side diffusion cells with diclofenac, ibuprofen, flurbiprofen, ketoprofen, and naproxen and human skin. The donor solution pH significantly affected skin permeation of NSAIDs, whereas no effect of the receiver pH was observed. Similar to previous observations, the apparent permeability coefficient versus donor solution pH relationships deviated from the predictions (fractions of unionized NSAIDs) according to the acid/base theory. The influences of the viable epidermis barrier, polar pathway transport, ion permeation across skin, and effective skin pH were investigated. The effective pH values for skin permeation determined using the NSAIDs (weak acids) in this study were different from those obtained previously with a weak base at the same donor solution pH conditions, suggesting that the observed permeability-pH relationships could not be explained solely by possible pH differences between skin and donor solution. © 2015 Wiley Periodicals, Inc. and the American Pharmacists Association.

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

The Kardar-Parisi-Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions

NASA Astrophysics Data System (ADS)

Diehl, Joscha; Gubinelli, Massimiliano; Perkowski, Nicolas

2017-09-01

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the system are well approximated by the solution to the KPZ equation provided the microscopic interaction is weakly asymmetric. The proof is based on the martingale solutions of Gonçalves and Jara (Arch Ration Mech Anal 212(2):597-644, 2014) and the corresponding uniqueness result of Gubinelli and Perkowski (Energy solutions of KPZ are unique, 2015).

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Uniqueness Results for Weak Leray-Hopf Solutions of the Navier-Stokes System with Initial Values in Critical Spaces

NASA Astrophysics Data System (ADS)

Barker, T.

2018-03-01

The main subject of this paper concerns the establishment of certain classes of initial data, which grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. In particular, our main theorem that this holds for any solenodial initial data, with finite L_2(R^3) norm, that also belongs to certain subsets of {it{VMO}}^{-1}(R^3). As a corollary of this, we obtain the same conclusion for any solenodial u0 belonging to L2(R^3)\\cap \\dot{B}^{-1+3/p}_{p,∞}(R^3), for any 3

Corrected Implicit Monte Carlo

DOE PAGES

Cleveland, Mathew Allen; Wollaber, Allan Benton

2018-01-02

Here in this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle formore » frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.« less

Locality preserving non-negative basis learning with graph embedding.

PubMed

Ghanbari, Yasser; Herrington, John; Gur, Ruben C; Schultz, Robert T; Verma, Ragini

2013-01-01

The high dimensionality of connectivity networks necessitates the development of methods identifying the connectivity building blocks that not only characterize the patterns of brain pathology but also reveal representative population patterns. In this paper, we present a non-negative component analysis framework for learning localized and sparse sub-network patterns of connectivity matrices by decomposing them into two sets of discriminative and reconstructive bases. In order to obtain components that are designed towards extracting population differences, we exploit the geometry of the population by using a graphtheoretical scheme that imposes locality-preserving properties as well as maintaining the underlying distance between distant nodes in the original and the projected space. The effectiveness of the proposed framework is demonstrated by applying it to two clinical studies using connectivity matrices derived from DTI to study a population of subjects with ASD, as well as a developmental study of structural brain connectivity that extracts gender differences.

Characterizing muscular activities using non-negative matrix factorization from EMG channels for driver swings in golf.

PubMed

Ozaki, Yasunori; Aoki, Ryosuke; Kimura, Toshitaka; Takashima, Youichi; Yamada, Tomohiro

2016-08-01

The goal of this study is to propose a data driven approach method to characterize muscular activities of complex actions in sports such as golf from a lot of EMG channels. Two problems occur in a many channel measurement. The first problem is that it takes a lot of time to check the many channel data because of combinatorial explosion. The second problem is that it is difficult to understand muscle activities related with complex actions. To solve these problems, we propose an analysis method of multi EMG channels using Non-negative Matrix Factorization and adopt the method to driver swings in golf. We measured 26 EMG channels about 4 professional coaches of golf. The results show that the proposed method detected 9 muscle synergies and the activation of each synergy were mostly fitted by sigmoid curve (R2=0.85).

Comparative study of original recover and recover KL in separable non-negative matrix factorization for topic detection in Twitter

NASA Astrophysics Data System (ADS)

Prabandari, R. D.; Murfi, H.

2017-07-01

An increasing amount of information on social media such as Twitter requires an efficient way to find the topics so that the information can be well managed. One of an automated method for topic detection is separable non-negative matrix factorization (SNMF). SNMF assumes that each topic has at least one word that does not appear on other topics. This method uses the direct approach and gives polynomial-time complexity, while the previous methods are iterative approaches and have NP-hard complexity. There are three steps of SNMF algorithm, i.e. constructing word co-occurrences, finding anchor words, and recovering topics. In this paper, we examine two topic recover methods, namely original recover that is using algebraic manipulation and recover KL that using probability approach with Kullback-Leibler divergence. Our simulations show that recover KL provides better accuracies in term of topic recall than original recover.

Online blind source separation using incremental nonnegative matrix factorization with volume constraint.

PubMed

Zhou, Guoxu; Yang, Zuyuan; Xie, Shengli; Yang, Jun-Mei

2011-04-01

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition

NASA Astrophysics Data System (ADS)

Li, Jin; Liu, Zilong

2017-12-01

Nonnegative tensor Tucker decomposition (NTD) in a transform domain (e.g., 2D-DWT, etc) has been used in the compression of hyper-spectral images because it can remove redundancies between spectrum bands and also exploit spatial correlations of each band. However, the use of a NTD has a very high computational cost. In this paper, we propose a low complexity NTD-based compression method of hyper-spectral images. This method is based on a pair-wise multilevel grouping approach for the NTD to overcome its high computational cost. The proposed method has a low complexity under a slight decrease of the coding performance compared to conventional NTD. We experimentally confirm this method, which indicates that this method has the less processing time and keeps a better coding performance than the case that the NTD is not used. The proposed approach has a potential application in the loss compression of hyper-spectral or multi-spectral images

Corrected implicit Monte Carlo

NASA Astrophysics Data System (ADS)

Cleveland, M. A.; Wollaber, A. B.

2018-04-01

In this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle for frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. We present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.

Multiparty quantum mutual information: An alternative definition

NASA Astrophysics Data System (ADS)

Kumar, Asutosh

2017-07-01

Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two subsystems. This may, however, no longer be true for three or more party quantum systems. In this paper, we propose an alternative definition of multipartite information, taking into account the shared information between two and more parties. It is non-negative, observes monotonicity under partial trace as well as completely positive maps, and equals the multipartite information measure in literature for pure states. We then define multiparty quantum discord, and give some examples. Interestingly, we observe that quantum discord increases when a measurement is performed on a large number of subsystems. Consequently, the symmetric quantum discord, which involves a measurement on all parties, reveals the maximal quantumness. This raises a question on the interpretation of measured mutual information as a classical correlation.

Brand Suicide? Memory and Liking of Negative Brand Names

PubMed Central

Guest, Duncan; Estes, Zachary; Gibbert, Michael; Mazursky, David

2016-01-01

Negative brand names are surprisingly common in the marketplace (e.g., Poison perfume; Hell pizza, and Monster energy drink), yet their effects on consumer behavior are currently unknown. Three studies investigated the effects of negative brand name valence on brand name memory and liking of a branded product. Study 1 demonstrates that relative to non-negative brand names, negative brand names and their associated logos are better recognised. Studies 2 and 3 demonstrate that negative valence of a brand name tends to have a detrimental influence on product evaluation with evaluations worsening as negative valence increases. However, evaluation is also dependent on brand name arousal, with high arousal brand names resulting in more positive evaluations, such that moderately negative brand names are equally as attractive as some non-negative brand names. Study 3 shows evidence for affective habituation, whereby the effects of negative valence reduce with repeated exposures to some classes of negative brand name. PMID:27023872

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Brand Suicide? Memory and Liking of Negative Brand Names.

PubMed

Guest, Duncan; Estes, Zachary; Gibbert, Michael; Mazursky, David

2016-01-01

Negative brand names are surprisingly common in the marketplace (e.g., Poison perfume; Hell pizza, and Monster energy drink), yet their effects on consumer behavior are currently unknown. Three studies investigated the effects of negative brand name valence on brand name memory and liking of a branded product. Study 1 demonstrates that relative to non-negative brand names, negative brand names and their associated logos are better recognised. Studies 2 and 3 demonstrate that negative valence of a brand name tends to have a detrimental influence on product evaluation with evaluations worsening as negative valence increases. However, evaluation is also dependent on brand name arousal, with high arousal brand names resulting in more positive evaluations, such that moderately negative brand names are equally as attractive as some non-negative brand names. Study 3 shows evidence for affective habituation, whereby the effects of negative valence reduce with repeated exposures to some classes of negative brand name.

Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization

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

Chennubhotla, Chakra; Castro, Jason

2013-01-01

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain un- clear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor di- mensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner.more » We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.« less

Method for coding low entrophy data

NASA Technical Reports Server (NTRS)

Yeh, Pen-Shu (Inventor)

1995-01-01

A method of lossless data compression for efficient coding of an electronic signal of information sources of very low information rate is disclosed. In this method, S represents a non-negative source symbol set, (s(sub 0), s(sub 1), s(sub 2), ..., s(sub N-1)) of N symbols with s(sub i) = i. The difference between binary digital data is mapped into symbol set S. Consecutive symbols in symbol set S are then paired into a new symbol set Gamma which defines a non-negative symbol set containing the symbols (gamma(sub m)) obtained as the extension of the original symbol set S. These pairs are then mapped into a comma code which is defined as a coding scheme in which every codeword is terminated with the same comma pattern, such as a 1. This allows a direct coding and decoding of the n-bit positive integer digital data differences without the use of codebooks.

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

Cleveland, Mathew Allen; Wollaber, Allan Benton

Here in this work we develop a set of nonlinear correction equations to enforce a consistent time-implicit emission temperature for the original semi-implicit IMC equations. We present two possible forms of correction equations: one results in a set of non-linear, zero-dimensional, non-negative, explicit correction equations, and the other results in a non-linear, non-negative, Boltzman transport correction equation. The zero-dimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequency-dependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle formore » frequency-independent simulations, at the cost of evaluating a reduced source non-linear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequency-dependent simulations.« less

Let Your Ions Shine.

ERIC Educational Resources Information Center

Koubek, Edward

1985-01-01

Outlines a demonstration involving weak acids and bases in aqueous solutions. A standard conductivity demonstration with a solution of acetic acid yields a barely glowing light bulb; a similar result occurs with ammonia solution. However, the bulb glows brightly when the solutions are mixed. (DH)

Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow

NASA Astrophysics Data System (ADS)

Figalli, Alessio; Kang, Moon-Jin; Morales, Javier

2018-03-01

We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

PubMed

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Xu, Richard Yi Da; Luo, Xiangfeng

2018-05-01

Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

Informed Source Separation of Atmospheric and Surface Signal Contributions in Shortwave Hyperspectral Imagery using Non-negative Matrix Factorization

NASA Astrophysics Data System (ADS)

Wright, L.; Coddington, O.; Pilewskie, P.

2015-12-01

Current challenges in Earth remote sensing require improved instrument spectral resolution, spectral coverage, and radiometric accuracy. Hyperspectral instruments, deployed on both aircraft and spacecraft, are a growing class of Earth observing sensors designed to meet these challenges. They collect large amounts of spectral data, allowing thorough characterization of both atmospheric and surface properties. The higher accuracy and increased spectral and spatial resolutions of new imagers require new numerical approaches for processing imagery and separating surface and atmospheric signals. One potential approach is source separation, which allows us to determine the underlying physical causes of observed changes. Improved signal separation will allow hyperspectral instruments to better address key science questions relevant to climate change, including land-use changes, trends in clouds and atmospheric water vapor, and aerosol characteristics. In this work, we investigate a Non-negative Matrix Factorization (NMF) method for the separation of atmospheric and land surface signal sources. NMF offers marked benefits over other commonly employed techniques, including non-negativity, which avoids physically impossible results, and adaptability, which allows the method to be tailored to hyperspectral source separation. We adapt our NMF algorithm to distinguish between contributions from different physically distinct sources by introducing constraints on spectral and spatial variability and by using library spectra to inform separation. We evaluate our NMF algorithm with simulated hyperspectral images as well as hyperspectral imagery from several instruments including, the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), NASA Hyperspectral Imager for the Coastal Ocean (HICO) and National Ecological Observatory Network (NEON) Imaging Spectrometer.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Vector critical points and generalized quasi-efficient solutions in nonsmooth multi-objective programming.

PubMed

Wang, Zhen; Li, Ru; Yu, Guolin

2017-01-01

In this work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate invexities assumptions, we prove that the solutions of generalized vector variational-like inequalities in terms of the generalized Jacobian are the generalized quasi-efficient solutions of nonsmooth multi-objective programming problems. Moreover, the equivalent conditions are presented, namely, a vector critical point is a weakly quasi-efficient solution of higher order with respect to a function.

Graph Partitioning by Eigenvectors,

DTIC Science & Technology

1987-01-01

the extremal nature of eigenvalues of symmetric matrices, the interlacing theorem, monotonicity of spectral radius of nonnegative matrices, Perron ... Frobenius theory, etc. (See Varga (1962) and Lancaster and Tismenetsky (1985).) Most of the results of this paper depend on the following lemma. ABSTRACT

77 FR 2935 - Revision to Chemical Testing Regulations for Mariners and Marine Employers

Federal Register 2010, 2011, 2012, 2013, 2014

2012-01-20

... balloon shape in the ``Actions'' column. If you submit your comments by mail or hand delivery, submit them.... Medical Review Officers (MROs) Reporting Non-Negative Test Results Directly to the Coast Guard A non...

The determination of pair-distance distribution by double electron-electron resonance: regularization by the length of distance discretization with Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Dzuba, Sergei A.

2016-08-01

Pulsed double electron-electron resonance technique (DEER, or PELDOR) is applied to study conformations and aggregation of peptides, proteins, nucleic acids, and other macromolecules. For a pair of spin labels, experimental data allows for the determination of their distance distribution function, P(r). P(r) is derived as a solution of a first-kind Fredholm integral equation, which is an ill-posed problem. Here, we suggest regularization by increasing the distance discretization length to its upper limit where numerical integration still provides agreement with experiment. This upper limit is found to be well above the lower limit for which the solution instability appears because of the ill-posed nature of the problem. For solving the integral equation, Monte Carlo trials of P(r) functions are employed; this method has an obvious advantage of the fulfillment of the non-negativity constraint for P(r). The regularization by the increasing of distance discretization length for the case of overlapping broad and narrow distributions may be employed selectively, with this length being different for different distance ranges. The approach is checked for model distance distributions and for experimental data taken from literature for doubly spin-labeled DNA and peptide antibiotics.

Gravity current into an ambient fluid with an open surface

NASA Astrophysics Data System (ADS)

Ungarish, Marius

2017-11-01

Consider the steady-state gravity current of height h and density ρ1 that propagates into an ambient motionless fluid of height H and density ρ2 with an upper surface open to the atmosphere (open channel) at high Reynolds number. The current propagates with speed U and causes a depth decrease χ of the top surface. This is a significant extension of Benjamin's (1968) seminal solution for the fixed-top channel χ = 0 . Here the determination of χ is a part of the problem. The dimensionless parameters of the problem are a = h / H and r =ρ2 /ρ1 . We show that a control-volume analysis determines χ = χ / H and Fr = U / (g ' h)1/2 as functions of a , r , where g ' = (r-1 - 1) g is the reduced gravity. The system satisfies balance of volume and momentum (explicitly), and vorticity (implicitly). We present solutions. The predicted flows are in general dissipative, and thus physically valid only for a <=amax (r) 0.5 r where non-negative dissipation appears. The open-surface Fr (a , r) is smaller than Benjamin's Frb (a) , but the reduction is not dramatic, typically a few percent. In the Boussinesq r 1 case, χ << 1 while Fr and dissipation are close to Benjamin's values.

Sparse Representation Based Frequency Detection and Uncertainty Reduction in Blade Tip Timing Measurement for Multi-Mode Blade Vibration Monitoring

PubMed Central

Pan, Minghao; Yang, Yongmin; Guan, Fengjiao; Hu, Haifeng; Xu, Hailong

2017-01-01

The accurate monitoring of blade vibration under operating conditions is essential in turbo-machinery testing. Blade tip timing (BTT) is a promising non-contact technique for the measurement of blade vibrations. However, the BTT sampling data are inherently under-sampled and contaminated with several measurement uncertainties. How to recover frequency spectra of blade vibrations though processing these under-sampled biased signals is a bottleneck problem. A novel method of BTT signal processing for alleviating measurement uncertainties in recovery of multi-mode blade vibration frequency spectrum is proposed in this paper. The method can be divided into four phases. First, a single measurement vector model is built by exploiting that the blade vibration signals are sparse in frequency spectra. Secondly, the uniqueness of the nonnegative sparse solution is studied to achieve the vibration frequency spectrum. Thirdly, typical sources of BTT measurement uncertainties are quantitatively analyzed. Finally, an improved vibration frequency spectra recovery method is proposed to get a guaranteed level of sparse solution when measurement results are biased. Simulations and experiments are performed to prove the feasibility of the proposed method. The most outstanding advantage is that this method can prevent the recovered multi-mode vibration spectra from being affected by BTT measurement uncertainties without increasing the probe number. PMID:28758952

Distance Metric Learning via Iterated Support Vector Machines.

PubMed

Zuo, Wangmeng; Wang, Faqiang; Zhang, David; Lin, Liang; Huang, Yuchi; Meng, Deyu; Zhang, Lei

2017-07-11

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a convex or nonconvex optimization problem, while most existing methods are based on customized optimizers and become inefficient for large scale problems. In this paper, we formulate metric learning as a kernel classification problem with the positive semi-definite constraint, and solve it by iterated training of support vector machines (SVMs). The new formulation is easy to implement and efficient in training with the off-the-shelf SVM solvers. Two novel metric learning models, namely Positive-semidefinite Constrained Metric Learning (PCML) and Nonnegative-coefficient Constrained Metric Learning (NCML), are developed. Both PCML and NCML can guarantee the global optimality of their solutions. Experiments are conducted on general classification, face verification and person re-identification to evaluate our methods. Compared with the state-of-the-art approaches, our methods can achieve comparable classification accuracy and are efficient in training.

Quantifying parameter uncertainty in stochastic models using the Box Cox transformation

NASA Astrophysics Data System (ADS)

Thyer, Mark; Kuczera, George; Wang, Q. J.

2002-08-01

The Box-Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box-Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the Metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box-Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the Metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box-Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty.

Noniterative approach to the missing data problem in coherent diffraction imaging by phase retrieval.

PubMed

Nakajima, Nobuharu

2010-07-20

When a very intense beam is used for illuminating an object in coherent x-ray diffraction imaging, the intensities at the center of the diffraction pattern for the object are cut off by a beam stop that is utilized to block the intense beam. Until now, only iterative phase-retrieval methods have been applied to object reconstruction from a single diffraction pattern with a deficiency of central data due to a beam stop. As an alternative method, I present a noniterative solution in which an interpolation method based on the sampling theorem for the missing data is used for object reconstruction with our previously proposed phase-retrieval method using an aperture-array filter. Computer simulations demonstrate the reconstruction of a complex-amplitude object from a single diffraction pattern with a missing data area, which is generally difficult to treat with the iterative methods because a nonnegativity constraint cannot be used for such an object.

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

Garifullin, R. N., E-mail: rustem@matem.anrb.ru; Suleimanov, B. I., E-mail: bisul@mail.r

An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg-de Vries equation u{sub t}'+ uu{sub x}' + u{sub xxx}' = 0 and fifth-order nonautonomous ordinary differential equations. As x{sup 2} + t{sup 2} {yields}{infinity}, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r{sub i}(t, x) = tl{sub i} x/t{sup 2}.

Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.

Weak Interactions Govern the Viscosity of Concentrated Antibody Solutions: High-Throughput Analysis Using the Diffusion Interaction Parameter

PubMed Central

Connolly, Brian D.; Petry, Chris; Yadav, Sandeep; Demeule, Barthélemy; Ciaccio, Natalie; Moore, Jamie M.R.; Shire, Steven J.; Gokarn, Yatin R.

2012-01-01

Weak protein-protein interactions are thought to modulate the viscoelastic properties of concentrated antibody solutions. Predicting the viscoelastic behavior of concentrated antibodies from their dilute solution behavior is of significant interest and remains a challenge. Here, we show that the diffusion interaction parameter (kD), a component of the osmotic second virial coefficient (B2) that is amenable to high-throughput measurement in dilute solutions, correlates well with the viscosity of concentrated monoclonal antibody (mAb) solutions. We measured the kD of 29 different mAbs (IgG1 and IgG4) in four different solvent conditions (low and high ion normality) and found a linear dependence between kD and the exponential coefficient that describes the viscosity concentration profiles (|R| ≥ 0.9). Through experimentally measured effective charge measurements, under low ion normality where the electroviscous effect can dominate, we show that the mAb solution viscosity is poorly correlated with the mAb net charge (|R| ≤ 0.6). With this large data set, our results provide compelling evidence in support of weak intermolecular interactions, in contrast to the notion that the electroviscous effect is important in governing the viscoelastic behavior of concentrated mAb solutions. Our approach is particularly applicable as a screening tool for selecting mAbs with desirable viscosity properties early during lead candidate selection. PMID:22828333

Trapping proton transfer intermediates in the disordered hydrogen-bonded network of cryogenic hydrofluoric acid solutions.

PubMed

Ayotte, Patrick; Plessis, Sylvain; Marchand, Patrick

2008-08-28

A molecular-level description of the structural and dynamical aspects that are responsible for the weak acid behaviour of dilute hydrofluoric acid solutions and their unusual increased acidity at near equimolar concentrations continues to elude us. We address this problem by reporting reflection-absorption infrared spectra (RAIRS) of cryogenic HF-H(2)O binary mixtures at various compositions prepared as nanoscopic films using molecular beam techniques. Optical constants for these cryogenic solutions [n(omega) and k(omega)] are obtained by iteratively solving Fresnel equations for stratified media. Modeling of the experimental RAIRS spectra allow for a quantitative interpretation of the complex interplay between multiple reflections, optical interference and absorption effects. The evolution of the strong absorption features in the intermediate 1000-3000 cm(-1) range with increasing HF concentration reveals the presence of various ionic dissociation intermediates that are trapped in the disordered H-bonded network of cryogenic hydrofluoric acid solutions. Our findings are discussed in light of the conventional interpretation of why hydrofluoric acid is a weak acid revealing molecular-level details of the mechanism for HF ionization that may be relevant to analogous elementary processes involved in the ionization of weak acids in aqueous solutions.

Estimates of the Modeling Error of the α -Models of Turbulence in Two and Three Space Dimensions

NASA Astrophysics Data System (ADS)

Dunca, Argus A.

2017-12-01

This report investigates the convergence rate of the weak solutions w^{α } of the Leray-α , modified Leray-α , Navier-Stokes-α and the zeroth ADM turbulence models to a weak solution u of the Navier-Stokes equations. It is assumed that this weak solution u of the NSE belongs to the space L^4(0, T; H^1) . It is shown that under this regularity condition the error u-w^{α } is O(α ) in the norms L^2(0, T; H^1) and L^{∞}(0, T; L^2) , thus improving related known results. It is also shown that the averaged error \\overline{u}-\\overline{w^{α }} is higher order, O(α ^{1.5}) , in the same norms, therefore the α -regularizations considered herein approximate better filtered flow structures than the exact (unfiltered) flow velocities.

Chromatographic retention prediction and octanol-water partition coefficient determination of monobasic weak acidic compounds in ion-suppression reversed-phase liquid chromatography using acids as ion-suppressors.

PubMed

Ming, Xin; Han, Shu-ying; Qi, Zheng-chun; Sheng, Dong; Lian, Hong-zhen

2009-08-15

Although simple acids, replacing buffers, have been widely applied to suppress the ionization of weakly ionizable acidic analytes in reversed-phase liquid chromatography (RPLC), none of the previously reported works focused on the systematic studies about the retention behavior of the acidic solutes in this ion-suppression RPLC mode. The subject of this paper was therefore to investigate the retention behavior of monobasic weak acidic compounds using acetic, perchloric and phosphoric acids as the ion-suppressors. The apparent octanol-water partition coefficient (K" ow) was proposed to calibrate the octanol-water partition coefficient (K(ow)) of these weak acidic compounds, which resulted in a better linear correlation with log k(w), the logarithm of the hypothetical retention factor corresponding to neat aqueous fraction of hydroorganic mobile phase. This log K" ow-log k w linear correlation was successfully validated by the results of monocarboxylic acids and monohydrating phenols, and moreover by the results under diverse experimental conditions for the same solutes. This straightforward relationship not only can be used to effectively predict the retention values of weak acidic solutes combined with Snyder-Soczewinski equation, but also can offer a promising medium for directly measuring K(ow) data of these compounds via Collander equation. In addition, the influence of the different ion-suppressors on the retention of weak acidic compounds was also compared in this RPLC mode.

Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry

NASA Astrophysics Data System (ADS)

Zou, Z.; Scott, M. A.; Borden, M. J.; Thomas, D. C.; Dornisch, W.; Brivadis, E.

2018-05-01

In this paper we develop the isogeometric B\\'ezier dual mortar method. It is based on B\\'ezier extraction and projection and is applicable to any spline space which can be represented in B\\'ezier form (i.e., NURBS, T-splines, LR-splines, etc.). The approach weakly enforces the continuity of the solution at patch interfaces and the error can be adaptively controlled by leveraging the refineability of the underlying dual spline basis without introducing any additional degrees of freedom. We also develop weakly continuous geometry as a particular application of isogeometric B\\'ezier dual mortaring. Weakly continuous geometry is a geometry description where the weak continuity constraints are built into properly modified B\\'ezier extraction operators. As a result, multi-patch models can be processed in a solver directly without having to employ a mortaring solution strategy. We demonstrate the utility of the approach on several challenging benchmark problems. Keywords: Mortar methods, Isogeometric analysis, B\\'ezier extraction, B\\'ezier projection

Stability of cosmological detonation fronts

NASA Astrophysics Data System (ADS)

Mégevand, Ariel; Membiela, Federico Agustín

2014-05-01

The steady-state propagation of a phase-transition front is classified, according to hydrodynamics, as a deflagration or a detonation, depending on its velocity with respect to the fluid. These propagation modes are further divided into three types, namely, weak, Jouguet, and strong solutions, according to their disturbance of the fluid. However, some of these hydrodynamic modes will not be realized in a phase transition. One particular cause is the presence of instabilities. In this work we study the linear stability of weak detonations, which are generally believed to be stable. After discussing in detail the weak detonation solution, we consider small perturbations of the interface and the fluid configuration. When the balance between the driving and friction forces is taken into account, it turns out that there are actually two different kinds of weak detonations, which behave very differently as functions of the parameters. We show that the branch of stronger weak detonations are unstable, except very close to the Jouguet point, where our approach breaks down.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

49 CFR 40.129 - What are the MRO's functions in reviewing laboratory confirmed non-negative drug test results?

Code of Federal Regulations, 2010 CFR

2010-10-01

... scientist signed the form. You are not required to review any other documentation generated by the... of the CCF, containing the certifying scientist's signature. (c) With respect to verified positive...

49 CFR 40.129 - What are the MRO's functions in reviewing laboratory confirmed non-negative drug test results?

Code of Federal Regulations, 2011 CFR

2011-10-01

... scientist signed the form. You are not required to review any other documentation generated by the... of the CCF, containing the certifying scientist's signature. (c) With respect to verified positive...

Assessment and protection of esophageal mucosal integrity in patients with heartburn without esophagitis.

PubMed

Woodland, Philip; Lee, Chung; Duraisamy, Yasotha; Duraysami, Yasotha; Farré, Ricard; Dettmar, Peter; Sifrim, Daniel

2013-04-01

Intact esophageal mucosal integrity is essential to prevent symptoms during gastroesophageal reflux events. Approximately 70% of patients with heartburn have macroscopically normal esophageal mucosa. In patients with heartburn, persistent functional impairment of esophageal mucosal barrier integrity may underlie remaining symptoms. Topical protection of a functionally vulnerable mucosa may be an attractive therapeutic strategy. We aimed to evaluate esophageal mucosal functional integrity in patients with heartburn without esophagitis, and test the feasibility of an alginate-based topical mucosal protection. Three distal esophageal biopsies were obtained from 22 patients with heartburn symptoms, and 22 control subjects. In mini-Ussing chambers, the change in transepithelial electrical resistance (TER) of biopsies when exposed to neutral, weakly acidic, and acidic solutions was measured. The experiment was repeated in a further 10 patients after pretreatment of biopsies with sodium alginate, viscous control, or liquid control "protectant" solutions. Biopsy exposure to neutral solution caused no change in TER. Exposure to weakly acidic and acidic solutions caused a greater reduction in TER in patients than in controls (weakly acid -7.2% (95% confidence interval (CI) -9.9 to -4.5) vs. 3.2% (-2.2 to 8.6), P<0.05; acidic -22.8% (-31.4 to 14.1) vs. -9.4% (-17.2 to -1.6), P<0.01). Topical pretreatment with alginate but not with control solutions prevented the acid-induced decrease in TER (-1% (-5.9 to 3.9) vs. -13.5 (-24.1 to -3.0) vs. -13.2 (-21.7 to -4.8), P<0.05). Esophageal mucosa in patients with heartburn without esophagitis shows distinct vulnerability to acid and weakly acidic exposures. Experiments in vitro suggest that such vulnerable mucosa may be protected by application of an alginate-containing topical solution.

Multisystem Temperature Equilibration and the Second Law

ERIC Educational Resources Information Center

Leff, Harvey S.

1977-01-01

Shows that the entropy change during the temperature equilibration of an isolated collection of systems which may exchange heat (but not work) energy is positive when the constant-volume heat capacity of each system is a non-negative function of the temperature. (MLH)

A Feminist Critique of Solution-Focused Therapy.

ERIC Educational Resources Information Center

Dermer, Shannon B.; Hemesath, Crystal Wilhite; Russell, Candyce S.

1998-01-01

Applying the feminist critique to solution-focused therapy highlights the strengths and weaknesses of this model from a feminist perspective. Although solution-focused therapy and feminist approaches share an emphasis on competence and strengths, solution-focused theory tends to overlook gender and power differences. In general, the model falls…

Phase slips in superconducting weak links

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

Kimmel, Gregory; Glatz, Andreas; Aranson, Igor S.

2017-01-01

Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold-atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one- dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly nonlinear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires andmore » slabs. Using the numerical solution of the time-dependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.« less

Quantum weak turbulence with applications to semiconductor lasers

NASA Astrophysics Data System (ADS)

Lvov, Y. V.; Binder, R.; Newell, A. C.

1998-10-01

Based on a model Hamiltonian appropriate for the description of fermionic systems such as semiconductor lasers, we describe a natural asymptotic closure of the BBGKY hierarchy in complete analogy with that derived for classical weak turbulence. The main features of the interaction Hamiltonian are the inclusion of full Fermi statistics containing Pauli blocking and a simple, phenomenological, uniformly weak two-particle interaction potential equivalent to the static screening approximation. We find a new class of solutions to the quantum kinetic equation which are analogous to the Kolmogorov spectra of hydrodynamics and classical weak turbulence. They involve finite fluxes of particles and energy in momentum space and are particularly relevant for describing the behavior of systems containing sources and sinks. We make a prima facie case that these finite flux solutions can be important in the context of semiconductor lasers and show how they might be used to enhance laser performance.

Influence of electro-activated solutions of weak organic acid salts on microbial quality and overall appearance of blueberries during storage.

PubMed

Liato, Viacheslav; Hammami, Riadh; Aïder, Mohammed

2017-06-01

The aim of this work was to study the potential of diluted electro-activated solutions of weak organic acid salts (potassium acetate, potassium citrate and calcium lactate) to extend the shelf life of blueberries during post-harvest storage. The sanitizing capacity of these solutions was studied against pathogenic bacteria Listeria monocytogenes and E. coli O157:H7 as well as phytopathogenic fungi A. alternata, F. oxysporum and B. cinerea. The results showed that a 5-min treatment of inoculated blueberries with electro-activated solutions resulted in a 4 log CFU/g reduction in Listeria monocytogenes for all solutions. For E. coli O157:H7, the electro-activated potassium acetate and potassium citrate solutions achieved a decrease of 3.5 log CFU/g after 5 min of berry washing. The most important fungus reduction was found when blueberries were washed with an electro-activated solution of potassium acetate and a NaOCl solution. After 5 min of blueberry washing with an electro-activated potassium acetate solution, a very high reduction effect was observed for A. alternata, F. oxysporum and B. cinerea, which showed survival levels of only 2.2 ± 0.16, 0.34 ± 0.15 and 0.21 ± 0.16 log CFU/g, respectively. Regarding the effect of the washing on the organoleptic quality of blueberries, the obtained results showed no negative effect on the product color or textural profile. Finally, this work suggests that washing with electro-activated solutions of weak organic acid salts can be used to enhance the shelf-life of blueberries during post-harvest storage. Copyright © 2016 Elsevier Ltd. All rights reserved.

A graph regularized non-negative matrix factorization method for identifying microRNA-disease associations.

PubMed

Xiao, Qiu; Luo, Jiawei; Liang, Cheng; Cai, Jie; Ding, Pingjian

2017-09-01

MicroRNAs (miRNAs) play crucial roles in post-transcriptional regulations and various cellular processes. The identification of disease-related miRNAs provides great insights into the underlying pathogenesis of diseases at a system level. However, most existing computational approaches are biased towards known miRNA-disease associations, which is inappropriate for those new diseases or miRNAs without any known association information. In this study, we propose a new method with graph regularized non-negative matrix factorization in heterogeneous omics data, called GRNMF, to discover potential associations between miRNAs and diseases, especially for new diseases and miRNAs or those diseases and miRNAs with sparse known associations. First, we integrate the disease semantic information and miRNA functional information to estimate disease similarity and miRNA similarity, respectively. Considering that there is no available interaction observed for new diseases or miRNAs, a preprocessing step is developed to construct the interaction score profiles that will assist in prediction. Next, a graph regularized non-negative matrix factorization framework is utilized to simultaneously identify potential associations for all diseases. The results indicated that our proposed method can effectively prioritize disease-associated miRNAs with higher accuracy compared with other recent approaches. Moreover, case studies also demonstrated the effectiveness of GRNMF to infer unknown miRNA-disease associations for those novel diseases and miRNAs. The code of GRNMF is freely available at https://github.com/XIAO-HN/GRNMF/. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

Navigating the Functional Landscape of Transcription Factors via Non-Negative Tensor Factorization Analysis of MEDLINE Abstracts

PubMed Central

Roy, Sujoy; Yun, Daqing; Madahian, Behrouz; Berry, Michael W.; Deng, Lih-Yuan; Goldowitz, Daniel; Homayouni, Ramin

2017-01-01

In this study, we developed and evaluated a novel text-mining approach, using non-negative tensor factorization (NTF), to simultaneously extract and functionally annotate transcriptional modules consisting of sets of genes, transcription factors (TFs), and terms from MEDLINE abstracts. A sparse 3-mode term × gene × TF tensor was constructed that contained weighted frequencies of 106,895 terms in 26,781 abstracts shared among 7,695 genes and 994 TFs. The tensor was decomposed into sub-tensors using non-negative tensor factorization (NTF) across 16 different approximation ranks. Dominant entries of each of 2,861 sub-tensors were extracted to form term–gene–TF annotated transcriptional modules (ATMs). More than 94% of the ATMs were found to be enriched in at least one KEGG pathway or GO category, suggesting that the ATMs are functionally relevant. One advantage of this method is that it can discover potentially new gene–TF associations from the literature. Using a set of microarray and ChIP-Seq datasets as gold standard, we show that the precision of our method for predicting gene–TF associations is significantly higher than chance. In addition, we demonstrate that the terms in each ATM can be used to suggest new GO classifications to genes and TFs. Taken together, our results indicate that NTF is useful for simultaneous extraction and functional annotation of transcriptional regulatory networks from unstructured text, as well as for literature based discovery. A web tool called Transcriptional Regulatory Modules Extracted from Literature (TREMEL), available at http://binf1.memphis.edu/tremel, was built to enable browsing and searching of ATMs. PMID:28894735

Exploring syndrome differentiation using non-negative matrix factorization and cluster analysis in patients with atopic dermatitis.

PubMed

Yun, Younghee; Jung, Wonmo; Kim, Hyunho; Jang, Bo-Hyoung; Kim, Min-Hee; Noh, Jiseong; Ko, Seong-Gyu; Choi, Inhwa

2017-08-01

Syndrome differentiation (SD) results in a diagnostic conclusion based on a cluster of concurrent symptoms and signs, including pulse form and tongue color. In Korea, there is a strong interest in the standardization of Traditional Medicine (TM). In order to standardize TM treatment, standardization of SD should be given priority. The aim of this study was to explore the SD, or symptom clusters, of patients with atopic dermatitis (AD) using non-negative factorization methods and k-means clustering analysis. We screened 80 patients and enrolled 73 eligible patients. One TM dermatologist evaluated the symptoms/signs using an existing clinical dataset from patients with AD. This dataset was designed to collect 15 dermatologic and 18 systemic symptoms/signs associated with AD. Non-negative matrix factorization was used to decompose the original data into a matrix with three features and a weight matrix. The point of intersection of the three coordinates from each patient was placed in three-dimensional space. With five clusters, the silhouette score reached 0.484, and this was the best silhouette score obtained from two to nine clusters. Patients were clustered according to the varying severity of concurrent symptoms/signs. Through the distribution of the null hypothesis generated by 10,000 permutation tests, we found significant cluster-specific symptoms/signs from the confidence intervals in the upper and lower 2.5% of the distribution. Patients in each cluster showed differences in symptoms/signs and severity. In a clinical situation, SD and treatment are based on the practitioners' observations and clinical experience. SD, identified through informatics, can contribute to development of standardized, objective, and consistent SD for each disease. Copyright © 2017. Published by Elsevier Ltd.

Separating Atmospheric and Surface Contributions in Hyperspectral Imager for the Coastal Ocean (HICO) Scenes using Informed Non-Negative Matrix Factorization

NASA Astrophysics Data System (ADS)

Wright, L.; Coddington, O.; Pilewskie, P.

2016-12-01

Hyperspectral instruments are a growing class of Earth observing sensors designed to improve remote sensing capabilities beyond discrete multi-band sensors by providing tens to hundreds of continuous spectral channels. Improved spectral resolution, range and radiometric accuracy allow the collection of large amounts of spectral data, facilitating thorough characterization of both atmospheric and surface properties. These new instruments require novel approaches for processing imagery and separating surface and atmospheric signals. One approach is numerical source separation, which allows the determination of the underlying physical causes of observed signals. Improved source separation will enable hyperspectral imagery to better address key science questions relevant to climate change, including land-use changes, trends in clouds and atmospheric water vapor, and aerosol characteristics. We developed an Informed Non-negative Matrix Factorization (INMF) method for separating atmospheric and surface sources. INMF offers marked benefits over other commonly employed techniques including non-negativity, which avoids physically impossible results; and adaptability, which tailors the method to hyperspectral source separation. The INMF algorithm is adapted to separate contributions from physically distinct sources using constraints on spectral and spatial variability, and library spectra to improve the initial guess. We also explore methods to produce an initial guess of the spatial separation patterns. Using this INMF algorithm we decompose hyperspectral imagery from the NASA Hyperspectral Imager for the Coastal Ocean (HICO) with a focus on separating surface and atmospheric signal contributions. HICO's coastal ocean focus provides a dataset with a wide range of atmospheric conditions, including high and low aerosol optical thickness and cloud cover, with only minor contributions from the ocean surfaces in order to isolate the contributions of the multiple atmospheric sources.

Validation of Spectral Unmixing Results from Informed Non-Negative Matrix Factorization (INMF) of Hyperspectral Imagery

NASA Astrophysics Data System (ADS)

Wright, L.; Coddington, O.; Pilewskie, P.

2017-12-01

Hyperspectral instruments are a growing class of Earth observing sensors designed to improve remote sensing capabilities beyond discrete multi-band sensors by providing tens to hundreds of continuous spectral channels. Improved spectral resolution, range and radiometric accuracy allow the collection of large amounts of spectral data, facilitating thorough characterization of both atmospheric and surface properties. We describe the development of an Informed Non-Negative Matrix Factorization (INMF) spectral unmixing method to exploit this spectral information and separate atmospheric and surface signals based on their physical sources. INMF offers marked benefits over other commonly employed techniques including non-negativity, which avoids physically impossible results; and adaptability, which tailors the method to hyperspectral source separation. The INMF algorithm is adapted to separate contributions from physically distinct sources using constraints on spectral and spatial variability, and library spectra to improve the initial guess. Using this INMF algorithm we decompose hyperspectral imagery from the NASA Hyperspectral Imager for the Coastal Ocean (HICO), with a focus on separating surface and atmospheric signal contributions. HICO's coastal ocean focus provides a dataset with a wide range of atmospheric and surface conditions. These include atmospheres with varying aerosol optical thicknesses and cloud cover. HICO images also provide a range of surface conditions including deep ocean regions, with only minor contributions from the ocean surfaces; and more complex shallow coastal regions with contributions from the seafloor or suspended sediments. We provide extensive comparison of INMF decomposition results against independent measurements of physical properties. These include comparison against traditional model-based retrievals of water-leaving, aerosol, and molecular scattering radiances and other satellite products, such as aerosol optical thickness from the Moderate Resolution Imaging Spectroradiometer (MODIS).

Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

NASA Astrophysics Data System (ADS)

Kocia, Lucas; Love, Peter

2017-12-01

We show that qubit stabilizer states can be represented by non-negative quasiprobability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two—producing an exterior, or Grassmann, algebra—which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is noncontextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order ℏ0 with a finite number of terms. The T gate, which extends the Clifford gate set to one capable of universal quantum computation, requires a semiclassical expansion of the propagator to order ℏ1. We compare this approach to previous quasiprobability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasiprobability distributions from the odd d -dimensional case to d =2 qubits, which describe the noncontextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.

Rotation-induced nonlinear wavepackets in internal waves

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

Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk

2014-05-15

The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets.more » It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.« less

Entanglement with negative Wigner function of three thousand atoms heralded by one photon

NASA Astrophysics Data System (ADS)

McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan

2016-06-01

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11, 12], and very recently in large atomic ensembles [13, 14, 15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing.

Weak solutions of the three-dimensional vorticity equation with vortex singularities

NASA Technical Reports Server (NTRS)

Winckelmans, G.; Leonard, A.

1988-01-01

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Global Existence and Uniqueness of Weak and Regular Solutions of Shallow Shells with Thermal Effects

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

Menzala, G. Perla, E-mail: perla@lncc.br; Cezaro, F. Travessini De, E-mail: fabianacezaro@furg.br

2016-10-15

We study a dynamical thin shallow shell whose elastic deformations are described by a nonlinear system of Marguerre–Vlasov’s type under the presence of thermal effects. Our main result is the proof of a global existence and uniqueness of a weak solution in the case of clamped boundary conditions. Standard techniques for uniqueness do not work directly in this case. We overcame this difficulty using recent work due to Lasiecka (Appl Anal 4:1376–1422, 1998).

The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition

NASA Astrophysics Data System (ADS)

Chen, Shuhong; Tan, Zhong

2007-11-01

In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

Regular Gleason Measures and Generalized Effect Algebras

NASA Astrophysics Data System (ADS)

Dvurečenskij, Anatolij; Janda, Jiří

2015-12-01

We study measures, finitely additive measures, regular measures, and σ-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be studied in the frame of generalized effect algebras.

A note on the Drazin indices of square matrices.

PubMed

Yu, Lijun; Bu, Tianyi; Zhou, Jiang

2014-01-01

For a square matrix A, the smallest nonnegative integer k such that rank (A(k)) =rank (A(k+1)) is called the Drazin index of A. In this paper, we give some results on the Drazin indices of sum and product of square matrices.

Some identities of generalized Fibonacci sequence

NASA Astrophysics Data System (ADS)

Chong, Chin-Yoon; Cheah, C. L.; Ho, C. K.

2014-07-01

We introduced the generalized Fibonacci sequence {Un} defined by U0 = 0, U1 = 1, and Un+2 = pUn+1+qUn for all p, q∈Z+ and for all non-negative integers n. In this paper, we obtained some recursive formulas of the sequence.

This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms--theory and practice.

PubMed

Harmany, Zachary T; Marcia, Roummel F; Willett, Rebecca M

2012-03-01

Observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where the number of unknowns may potentially be larger than the number of observations and f* admits sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

shiftNMFk 1.1: Robust Nonnegative matrix factorization with kmeans clustering and signal shift, for allocation of unknown physical sources, toy version for open sourcing with publications

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

Alexandrov, Boian S.; Lliev, Filip L.; Stanev, Valentin G.

This code is a toy (short) version of CODE-2016-83. From a general perspective, the code represents an unsupervised adaptive machine learning algorithm that allows efficient and high performance de-mixing and feature extraction of a multitude of non-negative signals mixed and recorded by a network of uncorrelated sensor arrays. The code identifies the number of the mixed original signals and their locations. Further, the code also allows deciphering of signals that have been delayed in regards to the mixing process in each sensor. This code is high customizable and it can be efficiently used for a fast macro-analyses of data. Themore » code is applicable to a plethora of distinct problems: chemical decomposition, pressure transient decomposition, unknown sources/signal allocation, EM signal decomposition. An additional procedure for allocation of the unknown sources is incorporated in the code.« less

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

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

Kannan, Ramakrishnan; Sukumar, Sreenivas R.; Ballard, Grey M.

NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems formore » $$\\WW$$ and $$\\HH$$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $$\\WW$$ and $$\\HH$$ within the alternating iterations.« less

Optical biopsy using fluorescence spectroscopy for prostate cancer diagnosis

NASA Astrophysics Data System (ADS)

Wu, Binlin; Gao, Xin; Smith, Jason; Bailin, Jacob

2017-02-01

Native fluorescence spectra are acquired from fresh normal and cancerous human prostate tissues. The fluorescence data are analyzed using a multivariate analysis algorithm such as non-negative matrix factorization. The nonnegative spectral components are retrieved and attributed to the native fluorophores such as collagen, reduced nicotinamide adenine dinucleotide (NADH), and flavin adenine dinucleotide (FAD) in tissue. The retrieved weights of the components, e.g. NADH and FAD are used to estimate the relative concentrations of the native fluorophores and the redox ratio. A machine learning algorithm such as support vector machine (SVM) is used for classification to distinguish normal and cancerous tissue samples based on either the relative concentrations of NADH and FAD or the redox ratio alone. The classification performance is shown based on statistical measures such as sensitivity, specificity, and accuracy, along with the area under receiver operating characteristic (ROC) curve. A cross validation method such as leave-one-out is used to evaluate the predictive performance of the SVM classifier to avoid bias due to overfitting.

Automatic annotation of histopathological images using a latent topic model based on non-negative matrix factorization

PubMed Central

Cruz-Roa, Angel; Díaz, Gloria; Romero, Eduardo; González, Fabio A.

2011-01-01

Histopathological images are an important resource for clinical diagnosis and biomedical research. From an image understanding point of view, the automatic annotation of these images is a challenging problem. This paper presents a new method for automatic histopathological image annotation based on three complementary strategies, first, a part-based image representation, called the bag of features, which takes advantage of the natural redundancy of histopathological images for capturing the fundamental patterns of biological structures, second, a latent topic model, based on non-negative matrix factorization, which captures the high-level visual patterns hidden in the image, and, third, a probabilistic annotation model that links visual appearance of morphological and architectural features associated to 10 histopathological image annotations. The method was evaluated using 1,604 annotated images of skin tissues, which included normal and pathological architectural and morphological features, obtaining a recall of 74% and a precision of 50%, which improved a baseline annotation method based on support vector machines in a 64% and 24%, respectively. PMID:22811960

Causal Inference and Explaining Away in a Spiking Network

PubMed Central

Moreno-Bote, Rubén; Drugowitsch, Jan

2015-01-01

While the brain uses spiking neurons for communication, theoretical research on brain computations has mostly focused on non-spiking networks. The nature of spike-based algorithms that achieve complex computations, such as object probabilistic inference, is largely unknown. Here we demonstrate that a family of high-dimensional quadratic optimization problems with non-negativity constraints can be solved exactly and efficiently by a network of spiking neurons. The network naturally imposes the non-negativity of causal contributions that is fundamental to causal inference, and uses simple operations, such as linear synapses with realistic time constants, and neural spike generation and reset non-linearities. The network infers the set of most likely causes from an observation using explaining away, which is dynamically implemented by spike-based, tuned inhibition. The algorithm performs remarkably well even when the network intrinsically generates variable spike trains, the timing of spikes is scrambled by external sources of noise, or the network is mistuned. This type of network might underlie tasks such as odor identification and classification. PMID:26621426

Causal Inference and Explaining Away in a Spiking Network.

PubMed

Moreno-Bote, Rubén; Drugowitsch, Jan

2015-12-01

While the brain uses spiking neurons for communication, theoretical research on brain computations has mostly focused on non-spiking networks. The nature of spike-based algorithms that achieve complex computations, such as object probabilistic inference, is largely unknown. Here we demonstrate that a family of high-dimensional quadratic optimization problems with non-negativity constraints can be solved exactly and efficiently by a network of spiking neurons. The network naturally imposes the non-negativity of causal contributions that is fundamental to causal inference, and uses simple operations, such as linear synapses with realistic time constants, and neural spike generation and reset non-linearities. The network infers the set of most likely causes from an observation using explaining away, which is dynamically implemented by spike-based, tuned inhibition. The algorithm performs remarkably well even when the network intrinsically generates variable spike trains, the timing of spikes is scrambled by external sources of noise, or the network is mistuned. This type of network might underlie tasks such as odor identification and classification.

Blind decomposition of Herschel-HIFI spectral maps of the NGC 7023 nebula

NASA Astrophysics Data System (ADS)

Berné, O.; Joblin, C.; Deville, Y.; Pilleri, P.; Pety, J.; Teyssier, D.; Gerin, M.; Fuente, A.

2012-12-01

Large spatial-spectral surveys are more and more common in astronomy. This calls for the need of new methods to analyze such mega- to giga-pixel data-cubes. In this paper we present a method to decompose such observations into a limited and comprehensive set of components. The original data can then be interpreted in terms of linear combinations of these components. The method uses non-negative matrix factorization (NMF) to extract latent spectral end-members in the data. The number of needed end-members is estimated based on the level of noise in the data. A Monte-Carlo scheme is adopted to estimate the optimal end-members, and their standard deviations. Finally, the maps of linear coefficients are reconstructed using non-negative least squares. We apply this method to a set of hyperspectral data of the NGC 7023 nebula, obtained recently with the HIFI instrument onboard the Herschel space observatory, and provide a first interpretation of the results in terms of 3-dimensional dynamical structure of the region.

Tryptophan as key biomarker to detect gastrointestinal tract cancer using non-negative biochemical analysis of native fluorescence and Stokes Shift spectroscopy

NASA Astrophysics Data System (ADS)

Wang, Leana; Zhou, Yan; Liu, Cheng-hui; Zhou, Lixin; He, Yong; Pu, Yang; Nguyen, Thien An; Alfano, Robert R.

2015-03-01

The objective of this study was to find out the emission spectral fingerprints for discrimination of human colorectal and gastric cancer from normal tissue in vitro by applying native fluorescence. The native fluorescence (NFL) and Stokes shift spectra of seventy-two human cancerous and normal colorectal (colon, rectum) and gastric tissues were analyzed using three selected excitation wavelengths (e.g. 300 nm, 320 nm and 340 nm). Three distinct biomarkers, tryptophan, collagen and reduced nicotinamide adenine dinucleotide hydrate (NADH), were found in the samples of cancerous and normal tissues from eighteen subjects. The spectral profiles of tryptophan exhibited a sharp peak in cancerous colon tissues under a 300 nm excitation when compared with normal tissues. The changes in compositions of tryptophan, collagen, and NADH were found between colon cancer and normal tissues under an excitation of 300 nm by the non-negative basic biochemical component analysis (BBCA) model.

Community detection enhancement using non-negative matrix factorization with graph regularization

NASA Astrophysics Data System (ADS)

Liu, Xiao; Wei, Yi-Ming; Wang, Jian; Wang, Wen-Jun; He, Dong-Xiao; Song, Zhan-Jie

2016-06-01

Community detection is a meaningful task in the analysis of complex networks, which has received great concern in various domains. A plethora of exhaustive studies has made great effort and proposed many methods on community detection. Particularly, a kind of attractive one is the two-step method which first makes a preprocessing for the network and then identifies its communities. However, not all types of methods can achieve satisfactory results by using such preprocessing strategy, such as the non-negative matrix factorization (NMF) methods. In this paper, rather than using the above two-step method as most works did, we propose a graph regularized-based model to improve, specialized, the NMF-based methods for the detection of communities, namely NMFGR. In NMFGR, we introduce the similarity metric which contains both the global and local information of networks, to reflect the relationships between two nodes, so as to improve the accuracy of community detection. Experimental results on both artificial and real-world networks demonstrate the superior performance of NMFGR to some competing methods.

Estimation of quantum yields of weak fluorescence from eosin Y dimers formed in aqueous solutions.

PubMed

Enoki, Masami; Katoh, Ryuzi

2018-05-17

We studied the weak fluorescence from the dimer of eosin Y (EY) in aqueous solutions. We used a newly developed ultrathin optical cell with a thickness ranging from of the order of microns to several hundreds of microns to successfully measure the fluorescence spectra of highly concentrated aqueous solutions of EY without artifacts caused by the reabsorption of fluorescence. The spectra we obtained were similar to the fluorescence spectrum of the EY monomer; almost no fluorescence was observed from the EY dimer. By a careful comparison of the spectra of solutions at low and high concentrations of EY, we succeeded in extracting the fluorescence spectrum of the EY dimer. The fluorescence quantum yield of the EY dimer was estimated to be 0.005.

Large Deviations and Transitions Between Equilibria for Stochastic Landau-Lifshitz-Gilbert Equation

NASA Astrophysics Data System (ADS)

Brzeźniak, Zdzisław; Goldys, Ben; Jegaraj, Terence

2017-11-01

We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property. Next, we prove the large deviations principle for the small noise asymptotic of solutions using the weak convergence method. An essential ingredient of the proof is the compactness, or weak to strong continuity, of the solution map for a deterministic Landau-Lifschitz equation when considered as a transformation of external fields. We then apply this large deviations principle to show that small noise can cause magnetisation reversal. We also show the importance of the shape anisotropy parameter for reducing the disturbance of the solution caused by small noise. The problem is motivated by applications from ferromagnetic nanowires to the fabrication of magnetic memories.

Charged Vaidya solution satisfies weak energy condition

NASA Astrophysics Data System (ADS)

Chatterjee, Soumyabrata; Ganguli, Suman; Virmani, Amitabh

2016-07-01

The external matter stress-tensor supporting charged Vaidya solution appears to violate weak energy condition in certain region of the spacetime. Motivated by this, a new interpretation of charged Vaidya solution was proposed by Ori (Class Quant Grav 8:1559, 1991) in which the energy condition continues to be satisfied. In this construction, one glues an outgoing Vaidya solution to the original ingoing Vaidya solution provided the surface where the external stress-tensor vanishes is spacelike. We revisit this study and extend it to higher-dimensions, to AdS settings, and to higher-derivative f( R) theories. In asymptotically flat space context, we explore in detail the case when the mass function m( v) is proportional to the charge function q( v). When the proportionality constant ν = q(v)/m(v) lies in between zero and one, we show that the surface where the external stress-tensor vanishes is spacelike and lies in between the inner and outer apparent horizons.

On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2014-07-01

We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation.

TIME SHARING WITH AN EXPLICIT PRIORITY QUEUING DISCIPLINE.

DTIC Science & Technology

exponentially distributed service times and an ordered priority queue. Each new arrival buys a position in this queue by offering a non-negative bribe to the...parameters is investigated through numerical examples. Finally, to maximize the expected revenue per unit time accruing from bribes , an optimization

Energetics of slope flows: linear and weakly nonlinear solutions of the extended Prandtl model

NASA Astrophysics Data System (ADS)

Güttler, Ivan; Marinović, Ivana; Večenaj, Željko; Grisogono, Branko

2016-07-01

The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is proportional to the height of the low-level jet by the factor ≈4/9) do not balance and the local storage of TE attains non-zero values. In order to examine the issue of non-stationarity, the inclusion of velocity-pressure covariance in the momentum equation is suggested for future development of the extended Prandtl model.

On degenerate coupled transport processes in porous media with memory phenomena

NASA Astrophysics Data System (ADS)

Beneš, Michal; Pažanin, Igor

2018-06-01

In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant mixed Dirichlet-Neumann boundary conditions and initial conditions are considered. Existence of a global weak solution of the problem is proved by means of semidiscretization in time, proving necessary uniform estimates and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in transport coefficients are overcome by proving suitable a-priori $L^{\\infty}$-estimates based on De Giorgi and Moser iteration technique.

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

NASA Astrophysics Data System (ADS)

Chiodaroli, Elisabetta; Kreml, Ondřej

2018-04-01

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.

On steady motion of viscoelastic fluid of Oldroyd type

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

Baranovskii, E. S., E-mail: esbaranovskii@gmail.com

2014-06-01

We consider a mathematical model describing the steady motion of a viscoelastic medium of Oldroyd type under the Navier slip condition at the boundary. In the rheological relation, we use the objective regularized Jaumann derivative. We prove the solubility of the corresponding boundary-value problem in the weak setting. We obtain an estimate for the norm of a solution in terms of the data of the problem. We show that the solution set is sequentially weakly closed. Furthermore, we give an analytic solution of the boundary-value problem describing the flow of a viscoelastic fluid in a flat channel under a slipmore » condition at the walls. Bibliography: 13 titles. (paper)« less

Anxiety sensitivity among Cambodian refugees with panic disorder: A factor analytic investigation.

PubMed

Hinton, Devon E; Pich, Vuth; Safren, Steven A; Pollack, Mark H; McNally, Richard J

2006-01-01

Among Cambodian refugees with panic disorder (N = 208), we performed two factor analyses, one with the ASI, another with an Augmented ASI (consisting of the 16-item ASI supplemented with a 9-item addendum that assesses additional Cambodian concerns about anxiety-related sensations). The principal component analysis of the ASI yielded a 3-factor solution (I, "Weak Heart Concerns"; II, "Social Concerns"; III, "Control Concerns"); the Augmented ASI, a 4-factor solution: I, "Wind Attack Concerns"; II, "Weak Heart Concerns"; III, "Social Concerns"; and IV, "Control Concerns." The item clustering within the factor solution of both the ASI and Augmented ASI illustrates the role of cultural syndromes in generating fear of mental and bodily events.

Assessment of chemical exchange in tryptophan-albumin solution through (19)F multicomponent transverse relaxation dispersion analysis.

PubMed

Lin, Ping-Chang

2015-06-01

A number of NMR methods possess the capability of probing chemical exchange dynamics in solution. However, certain drawbacks limit the applications of these NMR approaches, particularly, to a complex system. Here, we propose a procedure that integrates the regularized nonnegative least squares (NNLS) analysis of multiexponential T2 relaxation into Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments to probe chemical exchange in a multicompartmental system. The proposed procedure was validated through analysis of (19)F T2 relaxation data of 6-fluoro-DL-tryptophan in a two-compartment solution with and without bovine serum albumin. Given the regularized NNLS analysis of a T2 relaxation curve acquired, for example, at the CPMG frequency υ CPMG  = 125, the nature of two distinct peaks in the associated T2 distribution spectrum indicated 6-fluoro-DL-tryptophan either retaining the free state, with geometric mean */multiplicative standard deviation (MSD) = 1851.2 ms */1.51, or undergoing free/albumin-bound interconversion, with geometric mean */MSD = 236.8 ms */1.54, in the two-compartment system. Quantities of the individual tryptophan species were accurately reflected by the associated T2 peak areas, with an interconversion state-to-free state ratio of 0.45 ± 0.11. Furthermore, the CPMG relaxation dispersion analysis estimated the exchange rate between the free and albumin-bound states in this fluorinated tryptophan analog and the corresponding dissociation constant of the fluorinated tryptophan-albumin complex in the chemical-exchanging, two-compartment system.

Changes in the electric dipole vector of human serum albumin due to complexing with fatty acids.

PubMed Central

Scheider, W; Dintzis, H M; Oncley, J L

1976-01-01

The magnitude of the electric dipole vector of human serum albumin, as measured by the dielectric increment of the isoionic solution, is found to be a sensitive, monotonic indicator of the number of moles (up to at least 5) of long chain fatty acid complexed. The sensitivity is about three times as great as it is in bovine albumin. New methods of analysis of the frequency dispersion of the dielectric constant were developed to ascertain if molecular shape changes also accompany the complexing with fatty acid. Direct two-component rotary diffusion constant analysis is found to be too strongly affected by cross modulation between small systematic errors and physically significant data components to be a reliable measure of structural modification. Multicomponent relaxation profiles are more useful as recognition patterns for structural comparisons, but the equations involved are ill-conditioned and solutions based on standard least-squares regression contain mathematical artifacts which mask the physically significant spectrum. By constraining the solution to non-negative coefficients, the magnitude of the artifacts is reduced to well below the magnitudes of the spectral components. Profiles calculated in this way show no evidence of significant dipole direction or molecular shape change as the albumin is complexed with 1 mol of fatty acid. In these experiments albumin was defatted by incubation with adipose tissue at physiological pH, which avoids passing the protein through the pH of the N-F transition usually required in defatting. Addition of fatty acid from soluion in small amounts of ethanol appears to form a complex indistinguishable from the "native" complex. PMID:6087

Ionospheric-thermospheric UV tomography: 3. A multisensor technique for creating full-orbit reconstructions of atmospheric UV emission

NASA Astrophysics Data System (ADS)

Hei, Matthew A.; Budzien, Scott A.; Dymond, Kenneth F.; Nicholas, Andrew C.; Paxton, Larry J.; Schaefer, Robert K.; Groves, Keith M.

2017-07-01

We present the Volume Emission Rate Tomography (VERT) technique for inverting satellite-based, multisensor limb and nadir measurements of atmospheric ultraviolet emission to create whole-orbit reconstructions of atmospheric volume emission rate. The VERT approach is more general than previous ionospheric tomography methods because it can reconstruct the volume emission rate field irrespective of the particular excitation mechanisms (e.g., radiative recombination, photoelectron impact excitation, and energetic particle precipitation in auroras); physical models are then applied to interpret the airglow. The technique was developed and tested using data from the Special Sensor Ultraviolet Limb Imager and Special Sensor Ultraviolet Spectrographic Imager instruments aboard the Defense Meteorological Satellite Program F-18 spacecraft and planned for use with upcoming remote sensing missions. The technique incorporates several features to optimize the tomographic solutions, such as the use of a nonnegative algorithm (Richardson-Lucy, RL) that explicitly accounts for the Poisson statistics inherent in optical measurements, capability to include extinction effects due to resonant scattering and absorption of the photons from the lines of sight, a pseudodiffusion-based regularization scheme implemented between iterations of the RL code to produce smoother solutions, and the capability to estimate error bars on the solutions. Tests using simulated atmospheric emissions verify that the technique performs well in a variety of situations, including daytime, nighttime, and even in the challenging terminator regions. Lastly, we consider ionospheric nightglow and validate reconstructions of the nighttime electron density against Advanced Research Project Agency (ARPA) Long-range Tracking and Identification Radar (ALTAIR) incoherent scatter radar data.

The Full Kostant-Toda Hierarchy on the Positive Flag Variety

NASA Astrophysics Data System (ADS)

Kodama, Yuji; Williams, Lauren

2015-04-01

We study some geometric and combinatorial aspects of the solution to the full Kostant-Toda (f-KT) hierarchy, when the initial data is given by an arbitrary point on the totally non-negative (tnn) flag variety of . The f-KT flows on the tnn flag variety are complete, and we show that their asymptotics are completely determined by the cell decomposition of the tnn flag variety given by Rietsch (Total positivity and real flag varieties. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, 1998). Our results represent the first results on the asymptotics of the f-KT hierarchy (and even the f-KT lattice); moreover, our results are not confined to the generic flow, but cover non-generic flows as well. We define the f-KT flow on the weight space via the moment map, and show that the closure of each f-KT flow forms an interesting convex polytope which we call a Bruhat interval polytope. In particular, the Bruhat interval polytope for the generic flow is the permutohedron of the symmetric group . We also prove analogous results for the full symmetric Toda hierarchy, by mapping our f-KT solutions to those of the full symmetric Toda hierarchy. In the appendix we show that Bruhat interval polytopes are generalized permutohedra, in the sense of Postnikov (Int. Math. Res. Not. IMRN (6):1026-1106, 2009).

Identifying all moiety conservation laws in genome-scale metabolic networks.

PubMed

De Martino, Andrea; De Martino, Daniele; Mulet, Roberto; Pagnani, Andrea

2014-01-01

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

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

Tang, J. Y.; Riley, W. J.

We present a generic flux limiter to account for mass limitations from an arbitrary number of substrates in a biogeochemical reaction network. The flux limiter is based on the observation that substrate (e.g., nitrogen, phosphorus) limitation in biogeochemical models can be represented as to ensure mass conservative and non-negative numerical solutions to the governing ordinary differential equations. Application of the flux limiter includes two steps: (1) formulation of the biogeochemical processes with a matrix of stoichiometric coefficients and (2) application of Liebig's law of the minimum using the dynamic stoichiometric relationship of the reactants. This approach contrasts with the ad hoc down-regulationmore » approaches that are implemented in many existing models (such as CLM4.5 and the ACME (Accelerated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced modelers. Through an example implementation with a CENTURY-like decomposition model that includes carbon, nitrogen, and phosphorus, we show that our approach (1) produced almost identical results to that from the ad hoc down-regulation approaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited conditions where the simple clipping approach failed, (3) successfully avoided the potential conceptual ambiguities that are implied by those ad hoc down-regulation approaches. We expect our approach will make future biogeochemical models easier to improve and more robust.« less

Navier-Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

NASA Astrophysics Data System (ADS)

Hishida, Toshiaki; Maremonti, Paolo

2017-11-01

Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity - h(t)u_∞ with constant vector u_∞ \\in R^3{\\setminus }{0}. Finn raised the question whether his steady solutions are attainable as limits for t→ ∞ of unsteady solutions starting from motionless state when h(t)=1 after some finite time and h(0)=0 (starting problem). This was affirmatively solved by Galdi et al. (Arch Ration Mech Anal 138:307-318, 1997) for small u_∞. We study some generalized situation in which unsteady solutions start from large motions being in L^3 . We then conclude that the steady solutions for small u_∞ are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which h(t)=0 after some finite time and h(0)=1 (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large u_∞ is.

Navier-Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

NASA Astrophysics Data System (ADS)

Hishida, Toshiaki; Maremonti, Paolo

2018-06-01

Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity - h(t)u_∞ with constant vector u_∞ \\in R^3{\\setminus }{0}. Finn raised the question whether his steady solutions are attainable as limits for t→ ∞ of unsteady solutions starting from motionless state when h(t)=1 after some finite time and h(0)=0 (starting problem). This was affirmatively solved by Galdi et al. (Arch Ration Mech Anal 138:307-318, 1997) for small u_∞. We study some generalized situation in which unsteady solutions start from large motions being in L^3. We then conclude that the steady solutions for small u_∞ are still attainable as limits of evolution of those fluid motions which are found as a sort of weak solutions. The opposite situation, in which h(t)=0 after some finite time and h(0)=1 (landing problem), is also discussed. In this latter case, the rest state is attainable no matter how large u_∞ is.

Comment on ``The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs'' [J. Math. Phys. 52, 063512 (2011)

NASA Astrophysics Data System (ADS)

Golénia, Sylvain; Schumacher, Christoph

2013-06-01

In this comment we answer negatively to our conjecture concerning the deficiency indices. More precisely, given any non-negative integer n, there is locally finite graph on which the adjacency matrix has deficiency indices (n, n).

Geometric quadratic stochastic operator on countable infinite set

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

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-02-03

In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

Uncovering Mental Representations with Markov Chain Monte Carlo

ERIC Educational Resources Information Center

Sanborn, Adam N.; Griffiths, Thomas L.; Shiffrin, Richard M.

2010-01-01

A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these…

On Nth roots of positive operators

NASA Technical Reports Server (NTRS)

Brown, D. R.; Omalley, M. J.

1978-01-01

A bounded operator A on a Hilbert space H was positive. These operators were symmetric, and as such constitute a natural generalization of nonnegative real diagonal matrices. The following result is thus both well known and not surprising: A positive operator has a unique positive square root (under operator composition).

Preservation of physical properties with Ensemble-type Kalman Filter Algorithms

NASA Astrophysics Data System (ADS)

Janjic, T.

2017-12-01

We show the behavior of the localized Ensemble Kalman filter (EnKF) with respect to preservation of positivity, conservation of mass, energy and enstrophy in toy models that conserve these properties. In order to preserve physical properties in the analysis as well as to deal with the non-Gaussianity in an EnKF framework, Janjic et al. 2014 proposed the use of physically based constraints in the analysis step to constrain the solution. In particular, constraints were used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In the study, mass and positivity were both preserved by formulating the filter update as a set of quadratic programming problems that incorporate nonnegativity constraints. Simple numerical experiments indicated that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that were more physically plausible both for individual ensemble members and for the ensemble mean. Moreover, in experiments designed to mimic the most important characteristics of convective motion, it is shown that the mass conservation- and positivity-constrained rain significantly suppresses noise seen in localized EnKF results. This is highly desirable in order to avoid spurious storms from appearing in the forecast starting from this initial condition (Lange and Craig 2014). In addition, the root mean square error is reduced for all fields and total mass of the rain is correctly simulated. Similarly, the enstrophy, divergence, as well as energy spectra can as well be strongly affected by localization radius, thinning interval, and inflation and depend on the variable that is observed (Zeng and Janjic, 2016). We constructed the ensemble data assimilation algorithm that conserves mass, total energy and enstrophy (Zeng et al., 2017). With 2D shallow water model experiments, it is found that the conservation of enstrophy within the data assimilation effectively avoids the spurious energy cascade of rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The 14-day deterministic and ensemble free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction.

Representation of Muscle Synergies in the Primate Brain.

PubMed

Overduin, Simon A; d'Avella, Andrea; Roh, Jinsook; Carmena, Jose M; Bizzi, Emilio

2015-09-16

Evidence suggests that the CNS uses motor primitives to simplify movement control, but whether it actually stores primitives instead of computing solutions on the fly to satisfy task demands is a controversial and still-unanswered possibility. Also in contention is whether these primitives take the form of time-invariant muscle coactivations ("spatial" synergies) or time-varying muscle commands ("spatiotemporal" synergies). Here, we examined forelimb muscle patterns and motor cortical spiking data in rhesus macaques (Macaca mulatta) handling objects of variable shape and size. From these data, we extracted both spatiotemporal and spatial synergies using non-negative decomposition. Each spatiotemporal synergy represents a sequence of muscular or neural activations that appeared to recur frequently during the animals' behavior. Key features of the spatiotemporal synergies (including their dimensionality, timing, and amplitude modulation) were independently observed in the muscular and neural data. In addition, both at the muscular and neural levels, these spatiotemporal synergies could be readily reconstructed as sequential activations of spatial synergies (a subset of those extracted independently from the task data), suggestive of a hierarchical relationship between the two levels of synergies. The possibility that motor cortex may execute even complex skill using spatiotemporal synergies has novel implications for the design of neuroprosthetic devices, which could gain computational efficiency by adopting the discrete and low-dimensional control that these primitives imply. We studied the motor cortical and forearm muscular activity of rhesus macaques (Macaca mulatta) as they reached, grasped, and carried objects of varied shape and size. We applied non-negative matrix factorization separately to the cortical and muscular data to reduce their dimensionality to a smaller set of time-varying "spatiotemporal" synergies. Each synergy represents a sequence of cortical or muscular activity that recurred frequently during the animals' behavior. Salient features of the synergies (including their dimensionality, timing, and amplitude modulation) were observed at both the cortical and muscular levels. The possibility that the brain may execute even complex behaviors using spatiotemporal synergies has implications for neuroprosthetic algorithm design, which could become more computationally efficient by adopting the discrete and low-dimensional control that they afford. Copyright © 2015 the authors 0270-6474/15/3512615-10$15.00/0.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space

NASA Astrophysics Data System (ADS)

Crisford, Toby; Santos, Jorge E.

2017-05-01

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space.

PubMed

Crisford, Toby; Santos, Jorge E

2017-05-05

We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

pH-Dependent Liquid-Liquid Phase Separation of Highly Supersaturated Solutions of Weakly Basic Drugs.

PubMed

Indulkar, Anura S; Box, Karl J; Taylor, Robert; Ruiz, Rebeca; Taylor, Lynne S

2015-07-06

Supersaturated solutions of poorly aqueous soluble drugs can be formed both in vivo and in vitro. For example, increases in pH during gastrointestinal transit can decrease the aqueous solubility of weakly basic drugs resulting in supersaturation, in particular when exiting the acidic stomach environment. Recently, it has been observed that highly supersaturated solutions of drugs with low aqueous solubility can undergo liquid-liquid phase separation (LLPS) prior to crystallization, forming a turbid solution such that the concentration of the drug in the continuous solution phase corresponds to the amorphous solubility while the colloidal phase is composed of a disordered drug-rich phase. Although it is well established that the equilibrium solubility of crystalline weakly basic drugs follows the Henderson-Hasselbalch relationship, the impact of pH on the LLPS phenomenon or the amorphous solubility has not been explored. In this work, the LLPS concentration of three weakly basic compounds-clotrimazole, nicardipine, and atazanavir-was determined as a function of pH using three different methods and was compared to the predicted amorphous solubility, which was calculated from the pH-dependent crystalline solubility and by estimating the free energy difference between the amorphous and crystalline forms. It was observed that, similar to crystalline solubility, the experimental amorphous solubility at any pH follows the Henderson-Hasselbalch relation and can be predicted if the amorphous solubility of the free base is known. Excellent agreement between the LLPS concentration and the predicted amorphous solubility was observed. Dissolution studies of amorphous drugs showed that the solution concentration can reach the corresponding LLPS concentration at that pH. Solid-state analysis of the precipitated material confirmed the amorphous nature. This work provides insight into the pH-dependent precipitation behavior of poorly water-soluble compounds and provides a fundamental basis with which to understand the performance of supersaturating dosage forms.

Triple loop heat exchanger for an absorption refrigeration system

DOEpatents

Reimann, Robert C.

1984-01-01

A triple loop heat exchanger for an absorption refrigeration system is disclosed. The triple loop heat exchanger comprises portions of a strong solution line for conducting relatively hot, strong solution from a generator to a solution heat exchanger of the absorption refrigeration system, conduit means for conducting relatively cool, weak solution from the solution heat exchanger to the generator, and a bypass system for conducting strong solution from the generator around the strong solution line and around the solution heat exchanger to an absorber of the refrigeration system when strong solution builds up in the generator to an undesirable level. The strong solution line and the conduit means are in heat exchange relationship with each other in the triple loop heat exchanger so that, during normal operation of the refrigeration system, heat is exchanged between the relatively hot, strong solution flowing through the strong solution line and the relatively cool, weak solution flowing through the conduit means. Also, the strong solution line and the bypass system are in heat exchange relationship in the triple loop heat exchanger so that if the normal flow path of relatively hot, strong solution flowing from the generator to an absorber is blocked, then this relatively, hot strong solution which will then be flowing through the bypass system in the triple loop heat exchanger, is brought into heat exchange relationship with any strong solution which may have solidified in the strong solution line in the triple loop heat exchanger to thereby aid in desolidifying any such solidified strong solution.

Global existence of weak solutions to dissipative transport equations with nonlocal velocity

NASA Astrophysics Data System (ADS)

Bae, Hantaek; Granero-Belinchón, Rafael; Lazar, Omar

2018-04-01

We consider 1D dissipative transport equations with nonlocal velocity field: where is a nonlocal operator given by a Fourier multiplier. We especially consider two types of nonlocal operators: (1) , the Hilbert transform, (2) . In this paper, we show several global existence of weak solutions depending on the range of γ, δ and α. When , we take initial data having finite energy, while we take initial data in weighted function spaces (in the real variables or in the Fourier variables), which have infinite energy, when .

Transfer of energy in Camassa-Holm and related models by use of nonunique characteristics

NASA Astrophysics Data System (ADS)

Jamróz, Grzegorz

2017-02-01

We study the propagation of energy density in finite-energy weak solutions of the Camassa-Holm and related equations. Developing the methods based on generalized nonunique characteristics, we show that the parts of energy related to positive and negative slopes are one-sided weakly continuous and of bounded variation, which allows us to define certain measures of dissipation of both parts of energy. The result is a step towards the open problem of uniqueness of dissipative solutions of the Camassa-Holm equation.

Homoclinic snaking in the discrete Swift-Hohenberg equation

NASA Astrophysics Data System (ADS)

Kusdiantara, R.; Susanto, H.

2017-12-01

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization effect on the bifurcation behavior, where we identify three regions of the coupling parameter, i.e., strong, weak, and intermediate coupling. Within the regions, the discrete Swift-Hohenberg equation behaves either similarly or differently from the continuum limit. In the intermediate coupling region, multiple Maxwell points can occur for the periodic solutions and may cause irregular snaking and isolas. Numerical continuation is used to obtain and analyze localized and periodic solutions for each case. Theoretical analysis for the snaking and stability of the corresponding solutions is provided in the weak coupling region.

An interior-point method for total variation regularized positron emission tomography image reconstruction

NASA Astrophysics Data System (ADS)

Bai, Bing

2012-03-01

There has been a lot of work on total variation (TV) regularized tomographic image reconstruction recently. Many of them use gradient-based optimization algorithms with a differentiable approximation of the TV functional. In this paper we apply TV regularization in Positron Emission Tomography (PET) image reconstruction. We reconstruct the PET image in a Bayesian framework, using Poisson noise model and TV prior functional. The original optimization problem is transformed to an equivalent problem with inequality constraints by adding auxiliary variables. Then we use an interior point method with logarithmic barrier functions to solve the constrained optimization problem. In this method, a series of points approaching the solution from inside the feasible region are found by solving a sequence of subproblems characterized by an increasing positive parameter. We use preconditioned conjugate gradient (PCG) algorithm to solve the subproblems directly. The nonnegativity constraint is enforced by bend line search. The exact expression of the TV functional is used in our calculations. Simulation results show that the algorithm converges fast and the convergence is insensitive to the values of the regularization and reconstruction parameters.

Solution to a gene divergence problem under arbitrary stable nucleotide transition probabilities

NASA Technical Reports Server (NTRS)

Holmquist, R.

1976-01-01

A nucleic acid chain, L nucleotides in length, with the specific base sequence B(1)B(2) ... B(L) is defined by the L-dimensional vector B = (B(1), B(2), ..., B(L)). For twelve given constant non-negative transition probabilities that, in a specified position, the base B is replaced by the base B' in a single step, an exact analytical expression is derived for the probability that the position goes from base B to B' in X steps. Assuming that each base mutates independently of the others, an exact expression is derived for the probability that the initial gene sequence B goes to a sequence B' = (B'(1), B'(2), ..., B'(L)) after X = (X(1), X(2), ..., X(L)) base replacements. The resulting equations allow a more precise accounting for the effects of Darwinian natural selection in molecular evolution than does the idealized (biologically less accurate) assumption that each of the four nucleotides is equally likely to mutate to and be fixed as one of the other three. Illustrative applications of the theory to some problems of biological evolution are given.

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable. [noting unstable convolution subsystem forward control and time varying nonlinear feedback

NASA Technical Reports Server (NTRS)

Callier, F. M.; Desoer, C. A.

1973-01-01

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Hydrogen Bond Lifetimes and Energetics for Solute-Solvent Complexes Studied with 2D-IR Vibrational Echo Spectroscopy

PubMed Central

Zheng, Junrong; Fayer, Michael D.

2008-01-01

Weak π hydrogen bonded solute-solvent complexes are studied with ultrafast two dimensional infrared (2D-IR) vibrational echo chemical exchange spectroscopy, temperature dependent IR absorption spectroscopy, and density functional theory calculations. Eight solute-solvent complexes composed of a number of phenol derivatives and various benzene derivatives are investigated. The complexes are formed between the phenol derivative (solute) in a mixed solvent of the benzene derivative and CCl4. The time dependence of the 2D-IR vibrational echo spectra of the phenol hydroxyl stretch is used to directly determine the dissociation and formation rates of the hydrogen bonded complexes. The dissociation rates of the weak hydrogen bonds are found to be strongly correlated with their formation enthalpies. The correlation can be described with an equation similar to the Arrhenius equation. The results are discussed in terms of transition state theory. PMID:17373792

On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

We study some non-parabolic diffusion problems in one space dimension, where the diffusion flux exhibits forward and backward nature of the Perona–Malik, Höllig or non-Fourier type. Classical weak solutions to such problems are constructed in a way to capture some expected and unexpected properties, including anomalous asymptotic behaviors and energy dissipation or allocation. Specific properties of solutions will depend on the type of the diffusion flux, but the primary method of our study relies on reformulating diffusion equations involved as an inhomogeneous partial differential inclusion and on constructing solutions from the differential inclusion by a combination of the convex integration and Baire’s category methods. In doing so, we introduce the appropriate notion of subsolutions of the partial differential inclusion and their transition gauge, which plays a pivotal role in dealing with some specific features of the constructed weak solutions.

Detection of aniline oligomers on polyaniline-gold interface using resonance Raman scattering.

PubMed

Trchová, Miroslava; Morávková, Zuzana; Dybal, Jiří; Stejskal, Jaroslav

2014-01-22

In situ deposited conducting polyaniline films prepared by the oxidation of aniline with ammonium peroxydisulfate in aqueous media of various acidities on gold and silicon supports were characterized by Raman spectroscopy. Enhanced Raman bands were found in the spectra of polyaniline films produced in the solutions of weak acids or in water on gold surface. These bands were weak for the films prepared in solutions of a strong acid on a gold support. The same bands are present in the Raman spectra of the reaction intermediates deposited during aniline oxidation in water or aqueous solutions of weak or strong acids on silicon removed from the reaction mixture at the beginning of the reaction. Such films are formed by aniline oligomers adsorbed on the surface. They were detected on the polyaniline-gold interface using resonance Raman scattering on the final films deposited on gold. The surface resonance Raman spectroscopy of the monolayer of oligomers found in the bulk polyaniline film makes this method advantageous in surface science, with many applications in electrochemistry, catalysis, and biophysical, polymer, or analytical chemistry.

Analysis of the autonomous problem about coupled active non-Newtonian multi-seepage in sparse medium

NASA Astrophysics Data System (ADS)

Deng, Shuxian; Li, Hongen

2017-10-01

The flow field of non-Newtonian fluid in sparse medium was analyzed by computational fluid dynamics (CFD) method. The results show that the axial velocity and radial velocity of the non-Newtonian fluid are larger than those of the Newtonian fluid due to the coupling of the viscosity of the non-Newtonian fluid and the shear rate, and the tangential velocity is less than that of the Newtonian fluid. These differences lead to the difference in the sparse medium Non-Newtonian fluids are of a special nature. The influence of the weight function on the global existence and blasting of the problem is discussed by analyzing the non-Newtonian percolation equation with nonlocal and weighted non-local Dirichlet boundary conditions. According to the non-Newtonian percolation equation, we define the weak solution of the problem and expound the local existence of the weak solution. Then we construct the test function and prove the weak comparison principle by using the Grown well inequality. The overall existence and blasting are analyzed by constructing the upper and lower solutions.

Cosmic Reionization On Computers: Numerical and Physical Convergence

DOE PAGES

Gnedin, Nickolay Y.

2016-04-01

In this paper I show that simulations of reionization performed under the Cosmic Reionization On Computers (CROC) project do converge in space and mass, albeit rather slowly. A fully converged solution (for a given star formation and feedback model) can be determined at a level of precision of about 20%, but such a solution is useless in practice, since achieving it in production-grade simulations would require a large set of runs at various mass and spatial resolutions, and computational resources for such an undertaking are not yet readily available. In order to make progress in the interim, I introduce amore » weak convergence correction factor in the star formation recipe, which allows one to approximate the fully converged solution with finite resolution simulations. The accuracy of weakly converged simulations approaches a comparable, ~20% level of precision for star formation histories of individual galactic halos and other galactic properties that are directly related to star formation rates, like stellar masses and metallicities. Yet other properties of model galaxies, for example, their HI masses, are recovered in the weakly converged runs only within a factor of two.« less

Cosmic Reionization On Computers: Numerical and Physical Convergence

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

Gnedin, Nickolay Y.

In this paper I show that simulations of reionization performed under the Cosmic Reionization On Computers (CROC) project do converge in space and mass, albeit rather slowly. A fully converged solution (for a given star formation and feedback model) can be determined at a level of precision of about 20%, but such a solution is useless in practice, since achieving it in production-grade simulations would require a large set of runs at various mass and spatial resolutions, and computational resources for such an undertaking are not yet readily available. In order to make progress in the interim, I introduce amore » weak convergence correction factor in the star formation recipe, which allows one to approximate the fully converged solution with finite resolution simulations. The accuracy of weakly converged simulations approaches a comparable, ~20% level of precision for star formation histories of individual galactic halos and other galactic properties that are directly related to star formation rates, like stellar masses and metallicities. Yet other properties of model galaxies, for example, their HI masses, are recovered in the weakly converged runs only within a factor of two.« less

Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields

NASA Astrophysics Data System (ADS)

Frants, E. A.; Ganchenko, G. S.; Shelistov, V. S.; Amiroudine, S.; Demekhin, E. A.

2018-02-01

Electrokinetics and the movement of charge-selective micro-granules in an electrolyte solution under the influence of an external electric field are investigated theoretically. Straightforward perturbation analysis is applied to a thin electric double layer and a weak external field, while a numerical solution is used for moderate electric fields. The asymptotic solution enables the determination of the salt concentration, electric charge distribution, and electro-osmotic velocity fields. It may also be used to obtain a simple analytical formula for the electrophoretic velocity in the case of quasi-equilibrium electrophoresis (electrophoresis of the first kind). This formula differs from the famous Helmholtz-Smoluchowski relation, which applies to dielectric microparticles, but not to ion-selective granules. Numerical calculations are used to validate the derived formula for weak external electric fields, but for moderate fields, nonlinear effects lead to a significant increase in electrophoretic mobility and to a transition from quasi-equilibrium electrophoresis of the first kind to nonequilibrium electrophoresis of the second kind. Theoretical results are successfully compared with experimental data.

Cysteine as a green corrosion inhibitor for Cu37Zn brass in neutral and weakly alkaline sulphate solutions.

PubMed

Radovanović, Milan B; Petrović, Marija B; Simonović, Ana T; Milić, Snežana M; Antonijević, Milan M

2013-07-01

The aim of this study was to investigate electrochemical properties of brass in neutral and weakly alkaline solutions in the presence of cysteine as a nontoxic and ecological corrosion inhibitor. Potentiodynamic measurements, open circuit potential measurements, as well as chronoamperometric measurements were the methods used during investigation of the inhibitory effect of cysteine on the corrosion behaviour of brass. Potentiodynamic measurements showed that cysteine behaves as a mixed-type inhibitor in the investigated media. Based on polarization curves for brass in a weakly alkaline solution of sodium sulphate at varying cysteine concentrations, an interaction occurs between Cu(+) ions and the inhibitor, resulting in the formation of a protective complex on the electrode surface. The results of chronoamperometric measurements confirm the results obtained by potentiodynamic measurements. Optical microphotography of the brass surface also confirms the formation of a protective film in the presence of a 1 × 10(-4) mol/dm(3) cysteine. Adsorption of cysteine on the brass surface proceeds according to the Langmuir adsorption isotherm.

Essentially nonoscillatory postprocessing filtering methods

NASA Technical Reports Server (NTRS)

Lafon, F.; Osher, S.

1992-01-01

High order accurate centered flux approximations used in the computation of numerical solutions to nonlinear partial differential equations produce large oscillations in regions of sharp transitions. Here, we present a new class of filtering methods denoted by Essentially Nonoscillatory Least Squares (ENOLS), which constructs an upgraded filtered solution that is close to the physically correct weak solution of the original evolution equation. Our method relies on the evaluation of a least squares polynomial approximation to oscillatory data using a set of points which is determined via the ENO network. Numerical results are given in one and two space dimensions for both scalar and systems of hyperbolic conservation laws. Computational running time, efficiency, and robustness of method are illustrated in various examples such as Riemann initial data for both Burgers' and Euler's equations of gas dynamics. In all standard cases, the filtered solution appears to converge numerically to the correct solution of the original problem. Some interesting results based on nonstandard central difference schemes, which exactly preserve entropy, and have been recently shown generally not to be weakly convergent to a solution of the conservation law, are also obtained using our filters.

Role of Self-Association and Supersaturation in Oral Absorption of a Poorly Soluble Weakly Basic Drug.

PubMed

Narang, Ajit S; Badawy, Sherif; Ye, Qingmei; Patel, Dhaval; Vincent, Maria; Raghavan, Krishnaswamy; Huang, Yande; Yamniuk, Aaron; Vig, Balvinder; Crison, John; Derbin, George; Xu, Yan; Ramirez, Antonio; Galella, Michael; Rinaldi, Frank A

2015-08-01

Precipitation of weakly basic drugs in intestinal fluids can affect oral drug absorption. In this study, the implications of self-association of brivanib alaninate in acidic aqueous solution, leading to supersaturation at basic pH condition, on its solubility and oral absorption were investigated. Self-association of brivanib alaninate was investigated by proton NMR spectroscopy, surface tension measurement, dynamic light scattering, isothermal titration calorimetry, and molecular modeling. Drug solubility was determined in various pH media, and its tendency to supersaturate upon pH shift was investigated in buffered and biorelevant aqueous solutions. Pharmacokinetic modeling of human oral drug absorption was utilized for parameter sensitivity analyses of input variables. Brivanib alaninate exhibited continuous, and pH- and concentration-dependent self-association. This phenomenon resulted in positive deviation of drug solubility at acidic pH and the formation of a stable supersaturated drug solution in pH-shift assays. Consistent with the supersaturation phenomenon observed in vitro, oral absorption simulations necessitated invoking long precipitation time in the intestine to successfully predict in vivo data. Self-association of a weakly basic drug in acidic aqueous solution can increase its oral absorption by supersaturation and precipitation resistance at the intestinal pH. This consideration is important to the selection of parameters for oral absorption simulation.

A Zero Property for Integrals

ERIC Educational Resources Information Center

Abu-Saris, Raghib M.

2009-01-01

In this note, we show that if the integral of a continuous function, h, vanishes over an interval [a, b], then so does the integral of w(x)h(x) over [a, c] for some c in (a, b), where w is a monotonic increasing (decreasing) function on [a, b] with w(a) is non-negative (non-positive).

A triangular property of the associated Legendre functions

NASA Technical Reports Server (NTRS)

Fineschi, S.; Landi Degl'innocenti, E.

1990-01-01

A mathematical formula is introduced and proved which relates the associated Legendre functions with given nonnegative integral indices. The application of this formula in simplifying the calculation of collisional electron-atom cross sections higher than the dipole is mentioned. A proof of the stated identity using the Gegenbauer polynomials and their generating function is given.

Statistical Methodology for the Analysis of Repeated Duration Data in Behavioral Studies

ERIC Educational Resources Information Center

Letué, Frédérique; Martinez, Marie-José; Samson, Adeline; Vilain, Anne; Vilain, Coriandre

2018-01-01

Purpose: Repeated duration data are frequently used in behavioral studies. Classical linear or log-linear mixed models are often inadequate to analyze such data, because they usually consist of nonnegative and skew-distributed variables. Therefore, we recommend use of a statistical methodology specific to duration data. Method: We propose a…

Dissipative Work in Thermodynamics

ERIC Educational Resources Information Center

Anacleto, Joaquim; Pereira, Mario G.; Ferreira, J. M.

2011-01-01

This work explores the concept of dissipative work and shows that such a kind of work is an invariant non-negative quantity. This feature is then used to get a new insight into adiabatic irreversible processes; for instance, why the final temperature in any adiabatic irreversible process is always higher than that attained in a reversible process…

The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Harada, Kyouji; Morimoto, Munenori; Sakakihara, Michio

2004-03-01

Several preconditioned iterative methods reported in the literature have been used for improving the convergence rate of the Gauss-Seidel method. In this article, on the basis of nonnegative matrix, comparisons between some splittings for such preconditioned matrices are derived. Simple numerical examples are also given.

Efficient and Accurate Computation of Non-Negative Anisotropic Group Scattering Cross Sections for Discrete Ordinates and Monte Carlo Radiation Transport

DTIC Science & Technology

2002-07-01

Date Kirk A. Mathews (Advisor) James T. Moore (Dean’s Representative) Charles J. Bridgman (Member...Adler-Adler, and Kalbach -Mann representations of the scatter cross sections that are used for some isotopes in ENDF/B-VI are not included. They are not

Action Recognition Using Nonnegative Action Component Representation and Sparse Basis Selection.

PubMed

Wang, Haoran; Yuan, Chunfeng; Hu, Weiming; Ling, Haibin; Yang, Wankou; Sun, Changyin

2014-02-01

In this paper, we propose using high-level action units to represent human actions in videos and, based on such units, a novel sparse model is developed for human action recognition. There are three interconnected components in our approach. First, we propose a new context-aware spatial-temporal descriptor, named locally weighted word context, to improve the discriminability of the traditionally used local spatial-temporal descriptors. Second, from the statistics of the context-aware descriptors, we learn action units using the graph regularized nonnegative matrix factorization, which leads to a part-based representation and encodes the geometrical information. These units effectively bridge the semantic gap in action recognition. Third, we propose a sparse model based on a joint l2,1-norm to preserve the representative items and suppress noise in the action units. Intuitively, when learning the dictionary for action representation, the sparse model captures the fact that actions from the same class share similar units. The proposed approach is evaluated on several publicly available data sets. The experimental results and analysis clearly demonstrate the effectiveness of the proposed approach.

A time series model: First-order integer-valued autoregressive (INAR(1))

NASA Astrophysics Data System (ADS)

Simarmata, D. M.; Novkaniza, F.; Widyaningsih, Y.

2017-07-01

Nonnegative integer-valued time series arises in many applications. A time series model: first-order Integer-valued AutoRegressive (INAR(1)) is constructed by binomial thinning operator to model nonnegative integer-valued time series. INAR (1) depends on one period from the process before. The parameter of the model can be estimated by Conditional Least Squares (CLS). Specification of INAR(1) is following the specification of (AR(1)). Forecasting in INAR(1) uses median or Bayesian forecasting methodology. Median forecasting methodology obtains integer s, which is cumulative density function (CDF) until s, is more than or equal to 0.5. Bayesian forecasting methodology forecasts h-step-ahead of generating the parameter of the model and parameter of innovation term using Adaptive Rejection Metropolis Sampling within Gibbs sampling (ARMS), then finding the least integer s, where CDF until s is more than or equal to u . u is a value taken from the Uniform(0,1) distribution. INAR(1) is applied on pneumonia case in Penjaringan, Jakarta Utara, January 2008 until April 2016 monthly.

Using Dynamic Multi-Task Non-Negative Matrix Factorization to Detect the Evolution of User Preferences in Collaborative Filtering

PubMed Central

Ju, Bin; Qian, Yuntao; Ye, Minchao; Ni, Rong; Zhu, Chenxi

2015-01-01

Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time. PMID:26270539

Using Dynamic Multi-Task Non-Negative Matrix Factorization to Detect the Evolution of User Preferences in Collaborative Filtering.

PubMed

Ju, Bin; Qian, Yuntao; Ye, Minchao; Ni, Rong; Zhu, Chenxi

2015-01-01

Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time.

UTOPIAN: user-driven topic modeling based on interactive nonnegative matrix factorization.

PubMed

Choo, Jaegul; Lee, Changhyun; Reddy, Chandan K; Park, Haesun

2013-12-01

Topic modeling has been widely used for analyzing text document collections. Recently, there have been significant advancements in various topic modeling techniques, particularly in the form of probabilistic graphical modeling. State-of-the-art techniques such as Latent Dirichlet Allocation (LDA) have been successfully applied in visual text analytics. However, most of the widely-used methods based on probabilistic modeling have drawbacks in terms of consistency from multiple runs and empirical convergence. Furthermore, due to the complicatedness in the formulation and the algorithm, LDA cannot easily incorporate various types of user feedback. To tackle this problem, we propose a reliable and flexible visual analytics system for topic modeling called UTOPIAN (User-driven Topic modeling based on Interactive Nonnegative Matrix Factorization). Centered around its semi-supervised formulation, UTOPIAN enables users to interact with the topic modeling method and steer the result in a user-driven manner. We demonstrate the capability of UTOPIAN via several usage scenarios with real-world document corpuses such as InfoVis/VAST paper data set and product review data sets.

Peak picking NMR spectral data using non-negative matrix factorization.

PubMed

Tikole, Suhas; Jaravine, Victor; Rogov, Vladimir; Dötsch, Volker; Güntert, Peter

2014-02-11

Simple peak-picking algorithms, such as those based on lineshape fitting, perform well when peaks are completely resolved in multidimensional NMR spectra, but often produce wrong intensities and frequencies for overlapping peak clusters. For example, NOESY-type spectra have considerable overlaps leading to significant peak-picking intensity errors, which can result in erroneous structural restraints. Precise frequencies are critical for unambiguous resonance assignments. To alleviate this problem, a more sophisticated peaks decomposition algorithm, based on non-negative matrix factorization (NMF), was developed. We produce peak shapes from Fourier-transformed NMR spectra. Apart from its main goal of deriving components from spectra and producing peak lists automatically, the NMF approach can also be applied if the positions of some peaks are known a priori, e.g. from consistently referenced spectral dimensions of other experiments. Application of the NMF algorithm to a three-dimensional peak list of the 23 kDa bi-domain section of the RcsD protein (RcsD-ABL-HPt, residues 688-890) as well as to synthetic HSQC data shows that peaks can be picked accurately also in spectral regions with strong overlap.

Fitting a circular distribution based on nonnegative trigonometric sums for wind direction in Malaysia

NASA Astrophysics Data System (ADS)

Masseran, Nurulkamal; Razali, Ahmad Mahir; Ibrahim, Kamarulzaman; Zaharim, Azami; Sopian, Kamaruzzaman

2015-02-01

Wind direction has a substantial effect on the environment and human lives. As examples, the wind direction influences the dispersion of particulate matter in the air and affects the construction of engineering structures, such as towers, bridges, and tall buildings. Therefore, a statistical analysis of the wind direction provides important information about the wind regime at a particular location. In addition, knowledge of the wind direction and wind speed can be used to derive information about the energy potential. This study investigated the characteristics of the wind regime of Mersing, Malaysia. A circular distribution based on Nonnegative Trigonometric Sums (NNTS) was fitted to a histogram of the average hourly wind direction data. The Newton-like manifold algorithm was used to estimate the parameter of each component of the NNTS model. Next, the suitability of each NNTS model was judged based on a graphical representation and Akaike's Information Criteria. The study found that the NNTS model with six or more components was able to fit the wind directional data for the Mersing station.

Dynamics of a Nonlocal Dispersal Model with a Nonlocal Reaction Term

NASA Astrophysics Data System (ADS)

Ma, Li; Guo, Shangjiang; Chen, Ting

In this paper, we study a class of nonlocal dispersal problem with a nonlocal term arising in population dynamics: ut = 𝒟u + u λ ‑ f(u) ‑∫ΩK(x,y)g(u(y))dy,in Ω × (0, +∞), u(x, 0) = u0(x) ≥ 0, in Ω,u = 0, in ℝN\\Ω × (0, +∞), where Ω ⊂ ℝN (N ≥ 1) is a bounded domain, λ ∈ ℝ, 𝒟u(x,t) =∫ΩJ(x ‑ y)[u(y,t) ‑ u(x,t)]dy represents the nonlocal dispersal operator with continuous and non-negative dispersal kernel. The kernel K ∈ C(Ω¯ ×Ω¯) is assumed to be non-negative and is allowed to have a degeneracy in a smooth subdomain Ω0 of Ω. When K is either positive or vanishes in a subdomain, we respectively investigate the existence, multiplicity and asymptotical stability of positive steady states under the local/global variation of parameter by means of sub-supersolution method, Lyapunov-Schmidt reduction, and bifurcation theory.

Physician performance assessment using a composite quality index.

PubMed

Liu, Kaibo; Jain, Shabnam; Shi, Jianjun

2013-07-10

Assessing physician performance is important for the purposes of measuring and improving quality of service and reducing healthcare delivery costs. In recent years, physician performance scorecards have been used to provide feedback on individual measures; however, one key challenge is how to develop a composite quality index that combines multiple measures for overall physician performance evaluation. A controversy arises over establishing appropriate weights to combine indicators in multiple dimensions, and cannot be easily resolved. In this study, we proposed a generic unsupervised learning approach to develop a single composite index for physician performance assessment by using non-negative principal component analysis. We developed a new algorithm named iterative quadratic programming to solve the numerical issue in the non-negative principal component analysis approach. We conducted real case studies to demonstrate the performance of the proposed method. We provided interpretations from both statistical and clinical perspectives to evaluate the developed composite ranking score in practice. In addition, we implemented the root cause assessment techniques to explain physician performance for improvement purposes. Copyright © 2012 John Wiley & Sons, Ltd.

ShiftNMFk 1.2

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

Alexandrov, Boian S.; Vesselinov, Velimir V.; Stanev, Valentin

The ShiftNMFk1.2 code, or as we call it, GreenNMFk, represents a hybrid algorithm combining unsupervised adaptive machine learning and Green's function inverse method. GreenNMFk allows an efficient and high performance de-mixing and feature extraction of a multitude of nonnegative signals that change their shape propagating through the medium. The signals are mixed and recorded by a network of uncorrelated sensors. The code couples Non-negative Matrix Factorization (NMF) and inverse-analysis Green's functions method. GreenNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green's function of the governing partial differential equation to identifymore » the unknown sources and their charecteristics. GreenNMF can be applied directly to any problem controlled by a known partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations. Full GreenNMFk method is a subject LANL U.S. Patent application S133364.000 August, 2017. The ShiftNMFk 1.2 version here is a toy version of this method that can work with a limited number of unknown sources (4 or less).« less

The Comparison Between Nmf and Ica in Pigment Mixture Identification of Ancient Chinese Paintings

NASA Astrophysics Data System (ADS)

Liu, Y.; Lyu, S.; Hou, M.; Yin, Q.

2018-04-01

Since the colour in painting cultural relics observed by our naked eyes or hyperspectral cameras is usually a mixture of several kinds of pigments, the mixed pigments analysis will be an important subject in the field of ancient painting conservation and restoration. This paper aims to find a more effective method to confirm the types of every pure pigment from mixture on the surface of paintings. Firstly, we adopted two kinds of blind source separation algorithms, which are independent component analysis and non-negative matrix factorization, to extract the pure pigment component from mixed spectrum respectively. Moreover, we matched the separated pure spectrum with the pigments spectra library built by our team to determine the pigment type. Furthermore, three kinds of data including simulation data, mixed pigments spectral data measured in laboratory, and the spectral data of an ancient painting were chosen to evaluate the performance of the different algorithms. And the accuracy was compared between the two algorithms. Finally, the experimental results show that non-negative matrix factorization method is more suitable for endmember extraction in the field of ancient painting conservation and restoration.

Nonnegative constraint analysis of key fluorophores within human breast cancer using native fluorescence spectroscopy excited by selective wavelength of 300 nm

NASA Astrophysics Data System (ADS)

Pu, Yang; Sordillo, Laura A.; Alfano, Robert R.

2015-03-01

Native fluorescence spectroscopy offers an important role in cancer discrimination. It is widely acknowledged that the emission spectrum of tissue is a superposition of spectra of various salient fluorophores. In this study, the native fluorescence spectra of human cancerous and normal breast tissues excited by selected wavelength of 300 nm are used to investigate the key building block fluorophores: tryptophan and reduced nicotinamide adenine dinucleotide (NADH). The basis spectra of these key fluorophores' contribution to the tissue emission spectra are obtained by nonnegative constraint analysis. The emission spectra of human cancerous and normal tissue samples are projected onto the fluorophore spectral subspace. Since previous studies indicate that tryptophan and NADH are key fluorophores related with tumor evolution, it is essential to obtain their information from tissue fluorescence but discard the redundancy. To evaluate the efficacy of for cancer detection, linear discriminant analysis (LDA) classifier is used to evaluate the sensitivity, and specificity. This research demonstrates that the native fluorescence spectroscopy measurements are effective to detect changes of fluorophores' compositions in tissues due to the development of cancer.

An automatic search of Alzheimer patterns using a nonnegative matrix factorization

NASA Astrophysics Data System (ADS)

Giraldo, Diana L.; García-Arteaga, Juan D.; Romero, Eduardo

2013-11-01

This paper presents a fully automatic method that condenses relevant morphometric information from a database of magnetic resonance images (MR) labeled as either normal (NC) or Alzheimer's disease (AD). The proposed method generates class templates using Nonnegative Matrix Factorization (NMF) which will be used to develop an NC/AD classi cator. It then nds regions of interest (ROI) with discerning inter-class properties. by inspecting the di erence volume of the two class templates. From these templates local probability distribution functions associated to low level features such as intensities, orientation and edges within the found ROI are calculated. A sample brain volume can then be characterized by a similarity measure in the ROI to both the normal and the pathological templates. These characteristics feed a simple binary SVM classi er which, when tested with an experimental group extracted from a public brain MR dataset (OASIS), reveals an equal error rate measure which is better than the state-of-the-art tested on the same dataset (0:9 in the former and 0:8 in the latter).

Discriminative non-negative matrix factorization (DNMF) and its application to the fault diagnosis of diesel engine

NASA Astrophysics Data System (ADS)

Yang, Yong-sheng; Ming, An-bo; Zhang, You-yun; Zhu, Yong-sheng

2017-10-01

Diesel engines, widely used in engineering, are very important for the running of equipments and their fault diagnosis have attracted much attention. In the past several decades, the image based fault diagnosis methods have provided efficient ways for the diesel engine fault diagnosis. By introducing the class information into the traditional non-negative matrix factorization (NMF), an improved NMF algorithm named as discriminative NMF (DNMF) was developed and a novel imaged based fault diagnosis method was proposed by the combination of the DNMF and the KNN classifier. Experiments performed on the fault diagnosis of diesel engine were used to validate the efficacy of the proposed method. It is shown that the fault conditions of diesel engine can be efficiently classified by the proposed method using the coefficient matrix obtained by DNMF. Compared with the original NMF (ONMF) and principle component analysis (PCA), the DNMF can represent the class information more efficiently because the class characters of basis matrices obtained by the DNMF are more visible than those in the basis matrices obtained by the ONMF and PCA.

Nonlinear hyperspectral unmixing based on sparse non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Li, Jing; Li, Xiaorun; Zhao, Liaoying

2016-01-01

Hyperspectral unmixing aims at extracting pure material spectra, accompanied by their corresponding proportions, from a mixed pixel. Owing to modeling more accurate distribution of real material, nonlinear mixing models (non-LMM) are usually considered to hold better performance than LMMs in complicated scenarios. In the past years, numerous nonlinear models have been successfully applied to hyperspectral unmixing. However, most non-LMMs only think of sum-to-one constraint or positivity constraint while the widespread sparsity among real materials mixing is the very factor that cannot be ignored. That is, for non-LMMs, a pixel is usually composed of a few spectral signatures of different materials from all the pure pixel set. Thus, in this paper, a smooth sparsity constraint is incorporated into the state-of-the-art Fan nonlinear model to exploit the sparsity feature in nonlinear model and use it to enhance the unmixing performance. This sparsity-constrained Fan model is solved with the non-negative matrix factorization. The algorithm was implemented on synthetic and real hyperspectral data and presented its advantage over those competing algorithms in the experiments.

Lubricant Foaming and Aeration Study. Part 1

DTIC Science & Technology

1983-11-23

referred the stability of foam lamellae to its influence. This property is the two-dimensional analog of ordinary viscosity and its coefficient is...dimensions •- MT-. Weakly foaming solutions have little surface viscosity , soap solutions a moderate amount, and some solutions of proteins , saponin, etc...changes might occur in the surface properties . All surface viscosities previously reported had been measured while the solutions had been exposed for

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

A musculoskeletal model of human locomotion driven by a low dimensional set of impulsive excitation primitives

PubMed Central

Sartori, Massimo; Gizzi, Leonardo; Lloyd, David G.; Farina, Dario

2013-01-01

Human locomotion has been described as being generated by an impulsive (burst-like) excitation of groups of musculotendon units, with timing dependent on the biomechanical goal of the task. Despite this view being supported by many experimental observations on specific locomotion tasks, it is still unknown if the same impulsive controller (i.e., a low-dimensional set of time-delayed excitastion primitives) can be used as input drive for large musculoskeletal models across different human locomotion tasks. For this purpose, we extracted, with non-negative matrix factorization, five non-negative factors from a large sample of muscle electromyograms in two healthy subjects during four motor tasks. These included walking, running, sidestepping, and crossover cutting maneuvers. The extracted non-negative factors were then averaged and parameterized to obtain task-generic Gaussian-shaped impulsive excitation curves or primitives. These were used to drive a subject-specific musculoskeletal model of the human lower extremity. Results showed that the same set of five impulsive excitation primitives could be used to predict the dynamics of 34 musculotendon units and the resulting hip, knee and ankle joint moments (i.e., NRMSE = 0.18 ± 0.08, and R2 = 0.73 ± 0.22 across all tasks and subjects) without substantial loss of accuracy with respect to using experimental electromyograms (i.e., NRMSE = 0.16 ± 0.07, and R2 = 0.78 ± 0.18 across all tasks and subjects). Results support the hypothesis that biomechanically different motor tasks might share similar neuromuscular control strategies. This might have implications in neurorehabilitation technologies such as human-machine interfaces for the torque-driven, proportional control of powered prostheses and orthoses. In this, device control commands (i.e., predicted joint torque) could be derived without direct experimental data but relying on simple parameterized Gaussian-shaped curves, thus decreasing the input drive complexity and the number of needed sensors. PMID:23805099

A musculoskeletal model of human locomotion driven by a low dimensional set of impulsive excitation primitives.

PubMed

Sartori, Massimo; Gizzi, Leonardo; Lloyd, David G; Farina, Dario

2013-01-01

Human locomotion has been described as being generated by an impulsive (burst-like) excitation of groups of musculotendon units, with timing dependent on the biomechanical goal of the task. Despite this view being supported by many experimental observations on specific locomotion tasks, it is still unknown if the same impulsive controller (i.e., a low-dimensional set of time-delayed excitastion primitives) can be used as input drive for large musculoskeletal models across different human locomotion tasks. For this purpose, we extracted, with non-negative matrix factorization, five non-negative factors from a large sample of muscle electromyograms in two healthy subjects during four motor tasks. These included walking, running, sidestepping, and crossover cutting maneuvers. The extracted non-negative factors were then averaged and parameterized to obtain task-generic Gaussian-shaped impulsive excitation curves or primitives. These were used to drive a subject-specific musculoskeletal model of the human lower extremity. Results showed that the same set of five impulsive excitation primitives could be used to predict the dynamics of 34 musculotendon units and the resulting hip, knee and ankle joint moments (i.e., NRMSE = 0.18 ± 0.08, and R (2) = 0.73 ± 0.22 across all tasks and subjects) without substantial loss of accuracy with respect to using experimental electromyograms (i.e., NRMSE = 0.16 ± 0.07, and R (2) = 0.78 ± 0.18 across all tasks and subjects). Results support the hypothesis that biomechanically different motor tasks might share similar neuromuscular control strategies. This might have implications in neurorehabilitation technologies such as human-machine interfaces for the torque-driven, proportional control of powered prostheses and orthoses. In this, device control commands (i.e., predicted joint torque) could be derived without direct experimental data but relying on simple parameterized Gaussian-shaped curves, thus decreasing the input drive complexity and the number of needed sensors.

Asymmetric diffraction by atomic gratings with optical PT symmetry in the Raman-Nath regime

NASA Astrophysics Data System (ADS)

Shui, Tao; Yang, Wen-Xing; Liu, Shaopeng; Li, Ling; Zhu, Zhonghu

2018-03-01

We propose and analyze an efficient scheme for the lopsided Raman-Nath diffraction of one-dimensional (1 D ) and two-dimensional (2 D ) atomic gratings with periodic parity-time (PT )-symmetric refractive index. The atomic grating is constructed by the cold-atomic vapor with two isotopes of rubidium, which is driven by weak probe field and space-dependent control field. Using experimentally achievable parameters, we identify the conditions under which PT -symmetric refractive index allows us to observe the lopsided Raman-Nath diffraction phenomenon and improve the diffraction efficiencies beyond what is achievable in a conventional atomic grating. The nontrivial atomic grating is a superposition of an amplitude grating and a phase grating. It is found that the lopsided Raman-Nath diffraction at the exceptional point (EP) of PT -symmetric grating originates from constructive and destructive interferences between the amplitude and phase gratings. Furthermore, we show that the PT -phase transition from unbroken to broken PT -symmetric regimes can modify the asymmetric distribution of the diffraction spectrum and that the diffraction efficiencies in the non-negative diffraction orders can be significantly enhanced when the atomic grating is pushed into a broken PT -symmetric phase. In addition, we also analyze the influence of the grating thickness on the diffraction spectrum. Our scheme may provide the possibility to design a gain-beam splitter with tunable splitting ratio and other optical components in integrated optics.

The transformation of weak saturated soils using piles-drains for improving its mechanical properties

NASA Astrophysics Data System (ADS)

Ter-Martirosyan, Z. G.; Ter-Martirosyan, A. Z.; Sidorov, V. V.

2018-04-01

In practice of increased responsibility structures design there are often weak saturated clayey soils with low characteristics of deformability and strength take place on the construction site. In these cases, foundations using piles-drains of sandy or coarse material are recommended by norms, which is able to bear the load and to accelerate the consolidation process. The presented solutions include an analytical solution of the interaction problem between piles and slab raft foundation with the surrounding soil of the base with the possibility of extension of pile shaft. The closed-form solutions to determine the stresses in pile shaft and in the soil under the foundation slab are obtained. The article presents the results of large scale tests in the pilot area construction of major energy facilities in Russia.

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Determining modes for the 3D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Cheskidov, Alexey; Dai, Mimi; Kavlie, Landon

2018-07-01

We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blows up, its time average is uniformly bounded for all solutions on the weak global attractor. The bound is compared to Kolmogorov's dissipation wavenumber and the Grashof constant.

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

Liu, L; Han, Y; Jin, M

Purpose: To develop an iterative reconstruction method for X-ray CT, in which the reconstruction can quickly converge to the desired solution with much reduced projection views. Methods: The reconstruction is formulated as a convex feasibility problem, i.e. the solution is an intersection of three convex sets: 1) data fidelity (DF) set – the L2 norm of the difference of observed projections and those from the reconstructed image is no greater than an error bound; 2) non-negativity of image voxels (NN) set; and 3) piecewise constant (PC) set - the total variation (TV) of the reconstructed image is no greater thanmore » an upper bound. The solution can be found by applying projection onto convex sets (POCS) sequentially for these three convex sets. Specifically, the algebraic reconstruction technique and setting negative voxels as zero are used for projection onto the DF and NN sets, respectively, while the projection onto the PC set is achieved by solving a standard Rudin, Osher, and Fatemi (ROF) model. The proposed method is named as full sequential POCS (FS-POCS), which is tested using the Shepp-Logan phantom and the Catphan600 phantom and compared with two similar algorithms, TV-POCS and CP-TV. Results: Using the Shepp-Logan phantom, the root mean square error (RMSE) of reconstructed images changing along with the number of iterations is used as the convergence measurement. In general, FS- POCS converges faster than TV-POCS and CP-TV, especially with fewer projection views. FS-POCS can also achieve accurate reconstruction of cone-beam CT of the Catphan600 phantom using only 54 views, comparable to that of FDK using 364 views. Conclusion: We developed an efficient iterative reconstruction for sparse-view CT using full sequential POCS. The simulation and physical phantom data demonstrated the computational efficiency and effectiveness of FS-POCS.« less

Entire-Dataset Analysis of NMR Fast-Exchange Titration Spectra: A Mg2+ Titration Analysis for HIV-1 Ribonuclease H Domain.

PubMed

Karki, Ichhuk; Christen, Martin T; Spiriti, Justin; Slack, Ryan L; Oda, Masayuki; Kanaori, Kenji; Zuckerman, Daniel M; Ishima, Rieko

2016-12-15

This article communicates our study to elucidate the molecular determinants of weak Mg 2+ interaction with the ribonuclease H (RNH) domain of HIV-1 reverse transcriptase in solution. As the interaction is weak (a ligand-dissociation constant >1 mM), nonspecific Mg 2+ interaction with the protein or interaction of the protein with other solutes that are present in the buffer solution can confound the observed Mg 2+ -titration data. To investigate these indirect effects, we monitored changes in the chemical shifts of backbone amides of RNH by recording NMR 1 H- 15 N heteronuclear single-quantum coherence spectra upon titration of Mg 2+ into an RNH solution. We performed the titration under three different conditions: (1) in the absence of NaCl, (2) in the presence of 50 mM NaCl, and (3) at a constant 160 mM Cl - concentration. Careful analysis of these three sets of titration data, along with molecular dynamics simulation data of RNH with Na + and Cl - ions, demonstrates two characteristic phenomena distinct from the specific Mg 2+ interaction with the active site: (1) weak interaction of Mg 2+ , as a salt, with the substrate-handle region of the protein and (2) overall apparent lower Mg 2+ affinity in the absence of NaCl compared to that in the presence of 50 mM NaCl. A possible explanation may be that the titrated MgCl 2 is consumed as a salt and interacts with RNH in the absence of NaCl. In addition, our data suggest that Na + increases the kinetic rate of the specific Mg 2+ interaction at the active site of RNH. Taken together, our study provides biophysical insight into the mechanism of weak metal interaction on a protein.

Hydration and ion pair formation in aqueous Y(3+)-salt solutions.

PubMed

Rudolph, Wolfram W; Irmer, Gert

2015-11-14

Raman spectra of aqueous yttrium perchlorate, triflate (trifluoromethanesulfonate), chloride and nitrate solutions were measured over a broad concentration range (0.198-3.252 mol L(-1)). The spectra range from low wavenumbers to 4200 cm(-1). A very weak mode at 384 cm(-1) with a full width at half height at 50 cm(-1) in the isotropic spectrum suggests that the Y(3+)- octa-aqua ion is thermodynamically stable in dilute perchlorate solutions (∼0.5 mol L(-1)) while in concentrated perchlorate solutions outer-sphere ion pairs and contact ion pairs are formed. The octa-hydrate, [Y(OH2)8](3+) was also detected in a 1.10 mol L(-1) aqueous Y(CF3SO3)3 solution. Furthermore, very weak and broad depolarized modes could be detected which are assigned to [Y(OH2)8](3+)(aq) at 100, 166, 234 and 320 cm(-1) confirming that a hexa-hydrate is not compatible with the hydrated species in solution. In yttrium chloride solutions contact ion pair formation was detected over the measured concentration range from 0.479-3.212 mol L(-1). The contact ion pairs in YCl3(aq) are fairly weak and disappear with dilution. At a concentration <0.2 mol L(-1) almost all complexes have disappeared. In YCl3 solutions, with additional HCl, chloro-complexes of the type [Y(OH2)8-nCln](+3-n) (n = 1,2) are formed. The Y(NO3)3(aq) spectra were compared with a spectrum of a dilute NaNO3 solution and it was concluded that in Y(NO3)3(aq) over the concentration range from 2.035-0.198 mol L(-1) nitrato-complexes [Y(OH2)8-n(NO3)ln](+3-n) (n = 1,2) are formed. The nitrato-complexes are weak and disappear with dilution <0.1 mol L(-1). DFT geometry optimizations and frequency calculations are reported for both the yttrium-water cluster in the gas phase and the cluster within a polarizable continuum model in order to implicitly describe the presence of the bulk solvent. The bond distance and angle for the square antiprismatic cluster geometry of [Y(OH2)8](3+) with the polarizable dielectric continuum is in good agreement with data from recent structural experimental measurements. The DFT frequency of the Y-O stretching mode of the [Y(OH2)8](3+) cluster, in a polarizable continuum, is at 372 cm(-1) in satisfactory agreement with the experimental value.

Methods for Scaling to Doubly Stochastic Form,

DTIC Science & Technology

1981-06-26

Frobenius -Konig Theorem (MARCUS and MINC [1964],p 97) A nonnegative n xn matrix without support contains an s x t zero subma- trix where: s +t =n + -3...that YA(k) has row sums 1. Then normalize the columns by a diagonal similarity transform defined as follows: Let x = (zx , • z,,) be a left Perron vector

Anticipatory and consummatory components of the experience of pleasure in schizophrenia: cross-cultural validation and extension.

PubMed

Chan, Raymond C K; Wang, Ya; Huang, Jia; Shi, Yanfang; Wang, Yuna; Hong, Xiaohong; Ma, Zheng; Li, Zhanjian; Lai, M K; Kring, Ann M

2010-01-30

This study examined anticipatory and consummatory pleasure in schizophrenia patients with and without negative symptoms. Negative symptom patients experienced less anticipatory pleasure than non-negative symptom patients; only one facet of consummatory pleasure was unaffected in negative schizophrenia. Greater pleasure deficits were correlated with more severe positive and negative symptoms.

ON THE STRONG EXTREMUM PRINCIPLE FOR A \\mathrm{D}-(\\Pi, \\Omega)-ELLIPTICALLY CONNECTED OPERATOR OF SECOND ORDER

NASA Astrophysics Data System (ADS)

Kamynin, L. I.; Himčenko, B. N.

1981-02-01

In this paper the strong extremum principle is proved for a certain new class of second order operators with nonnegative characteristic form, without requiring the smoothness of their coefficients, which is essential in the converse of Raševskiĭ's theorem on completely nonholonomic systems. Bibliography: 19 titles.

Electrolyte diodes with weak acids and bases. I. Theory and an approximate analytical solution.

PubMed

Iván, Kristóf; Simon, Péter L; Wittmann, Mária; Noszticzius, Zoltán

2005-10-22

Until now acid-base diodes and transistors applied strong mineral acids and bases exclusively. In this work properties of electrolyte diodes with weak electrolytes are studied and compared with those of diodes with strong ones to show the advantages of weak acids and bases in these applications. The theoretical model is a one dimensional piece of gel containing fixed ionizable groups and connecting reservoirs of an acid and a base. The electric current flowing through the gel is measured as a function of the applied voltage. The steady-state current-voltage characteristic (CVC) of such a gel looks like that of a diode under these conditions. Results of our theoretical, numerical, and experimental investigations are reported in two parts. In this first, theoretical part governing equations necessary to calculate the steady-state CVC of a reverse-biased electrolyte diode are presented together with an approximate analytical solution of this reaction-diffusion-ionic migration problem. The applied approximations are quasielectroneutrality and quasiequilibrium. It is shown that the gel can be divided into an alkaline and an acidic zone separated by a middle weakly acidic region. As a further approximation it is assumed that the ionization of the fixed acidic groups is complete in the alkaline zone and that it is completely suppressed in the acidic one. The general solution given here describes the CVC and the potential and ionic concentration profiles of diodes applying either strong or weak electrolytes. It is proven that previous formulas valid for a strong acid-strong base diode can be regarded as a special case of the more general formulas presented here.

A review on symmetries for certain Aedes aegypti models

NASA Astrophysics Data System (ADS)

Freire, Igor Leite; Torrisi, Mariano

2015-04-01

We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

Replace-approximation method for ambiguous solutions in factor analysis of ultrasonic hepatic perfusion

NASA Astrophysics Data System (ADS)

Zhang, Ji; Ding, Mingyue; Yuchi, Ming; Hou, Wenguang; Ye, Huashan; Qiu, Wu

2010-03-01

Factor analysis is an efficient technique to the analysis of dynamic structures in medical image sequences and recently has been used in contrast-enhanced ultrasound (CEUS) of hepatic perfusion. Time-intensity curves (TICs) extracted by factor analysis can provide much more diagnostic information for radiologists and improve the diagnostic rate of focal liver lesions (FLLs). However, one of the major drawbacks of factor analysis of dynamic structures (FADS) is nonuniqueness of the result when only the non-negativity criterion is used. In this paper, we propose a new method of replace-approximation based on apex-seeking for ambiguous FADS solutions. Due to a partial overlap of different structures, factor curves are assumed to be approximately replaced by the curves existing in medical image sequences. Therefore, how to find optimal curves is the key point of the technique. No matter how many structures are assumed, our method always starts to seek apexes from one-dimensional space where the original high-dimensional data is mapped. By finding two stable apexes from one dimensional space, the method can ascertain the third one. The process can be continued until all structures are found. This technique were tested on two phantoms of blood perfusion and compared to the two variants of apex-seeking method. The results showed that the technique outperformed two variants in comparison of region of interest measurements from phantom data. It can be applied to the estimation of TICs derived from CEUS images and separation of different physiological regions in hepatic perfusion.

Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models

DOE PAGES

Tang, J. Y.; Riley, W. J.

2016-02-05

We present a generic flux limiter to account for mass limitations from an arbitrary number of substrates in a biogeochemical reaction network. The flux limiter is based on the observation that substrate (e.g., nitrogen, phosphorus) limitation in biogeochemical models can be represented as to ensure mass conservative and non-negative numerical solutions to the governing ordinary differential equations. Application of the flux limiter includes two steps: (1) formulation of the biogeochemical processes with a matrix of stoichiometric coefficients and (2) application of Liebig's law of the minimum using the dynamic stoichiometric relationship of the reactants. This approach contrasts with the ad hoc down-regulationmore » approaches that are implemented in many existing models (such as CLM4.5 and the ACME (Accelerated Climate Modeling for Energy) Land Model (ALM)) of carbon and nutrient interactions, which are error prone when adding new processes, even for experienced modelers. Through an example implementation with a CENTURY-like decomposition model that includes carbon, nitrogen, and phosphorus, we show that our approach (1) produced almost identical results to that from the ad hoc down-regulation approaches under non-limiting nutrient conditions, (2) properly resolved the negative solutions under substrate-limited conditions where the simple clipping approach failed, (3) successfully avoided the potential conceptual ambiguities that are implied by those ad hoc down-regulation approaches. We expect our approach will make future biogeochemical models easier to improve and more robust.« less

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

NASA Astrophysics Data System (ADS)

Mingione, Giuseppe

We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type If the vector fields a and b are Hölder continuous with respect to the variable x with exponent α, then the Hausdorff dimension of the singular set of any weak solution is at most n-2α.

Global and Local Existence for the Dissipative Critical SQG Equation with Small Oscillations

NASA Astrophysics Data System (ADS)

Lazar, Omar

2015-09-01

This article is devoted to the study of the critical dissipative surface quasi-geostrophic ( SQG) equation in . For any initial data belonging to the space , we show that the critical (SQG) equation has at least one global weak solution in time for all 1/4 ≤ s ≤ 1/2 and at least one local weak solution in time for all 0 < s < 1/4. The proof for the global existence is based on a new energy inequality which improves the one obtain in Lazar (Commun Math Phys 322:73-93, 2013) whereas the local existence uses more refined energy estimates based on Besov space techniques.

Influence of Weak Base Addition to Hole-Collecting Buffer Layers in Polymer:Fullerene Solar Cells.

PubMed

Seo, Jooyeok; Park, Soohyeong; Song, Myeonghun; Jeong, Jaehoon; Lee, Chulyeon; Kim, Hwajeong; Kim, Youngkyoo

2017-02-09

We report the effect of weak base addition to acidic polymer hole-collecting layers in normal-type polymer:fullerene solar cells. Varying amounts of the weak base aniline (AN) were added to solutions of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS). The acidity of the aniline-added PEDOT:PSS solutions gradually decreased from pH = 1.74 (AN = 0 mol% ) to pH = 4.24 (AN = 1.8 mol %). The electrical conductivity of the PEDOT:PSS-AN films did not change much with the pH value, while the ratio of conductivity between out-of-plane and in-plane directions was dependent on the pH of solutions. The highest power conversion efficiency (PCE) was obtained at pH = 2.52, even though all devices with the PEDOT:PSS-AN layers exhibited better PCE than those with the pristine PEDOT:PSS layers. Atomic force microscopy investigation revealed that the size of PEDOT:PSS domains became smaller as the pH increased. The stability test for 100 h illumination under one sun condition disclosed that the PCE decay was relatively slower for the devices with the PEDOT:PSS-AN layers than for those with pristine PEDOT:PSS layers.

Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Huang, Xiangdi

2017-02-01

One of the most influential fundamental tools in harmonic analysis is the Riesz transforms. It maps Lp functions to Lp functions for any p ∈ (1 , ∞) which plays an important role in singular operators. As an application in fluid dynamics, the norm equivalence between ‖∇u‖Lp and ‖ div u ‖ Lp +‖ curl u ‖ Lp is well established for p ∈ (1 , ∞). However, since Riesz operators sent bounded functions only to BMO functions, there is no hope to bound ‖∇u‖L∞ in terms of ‖ div u ‖ L∞ +‖ curl u ‖ L∞. As pointed out by Hoff (2006) [11], this is the main obstacle to obtain uniqueness of weak solutions for isentropic compressible flows. Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞ ≤ (2 + 1 / N)‖ div u ‖ L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.

Chain Conformation and Dynamics in Spin-Assisted Weak Polyelectrolyte Multilayers

DOE PAGES

Zhuk, Aliaksandr; Selin, Victor; Zhuk, Iryna; ...

2015-03-13

In this paper, we report on the effect of the deposition technique on film layering, stability, and chain mobility in weak polyelectrolyte layer-by-layer (LbL) films. Ellipsometry and neutron reflectometry (NR) showed that shear forces arising during spin-assisted assembly lead to smaller amounts of adsorbed polyelectrolytes within LbL films, result in a higher degree of internal film order, and dramatically improve stability of assemblies in salt solutions as compared to dip-assisted LbL assemblies. The underlying flattening of polyelectrolyte chains in spin-assisted LbL films was also revealed as an increase in ionization degree of the assembled weak polyelectrolytes. As demonstrated by fluorescencemore » recovery after photobleaching (FRAP), strong binding between spin-deposited polyelectrolytes results in a significant slowdown of chain diffusion in salt solutions as compared to dip-deposited films. Moreover, salt-induced chain intermixing in the direction perpendicular to the substrate is largely inhibited in spin-deposited films, resulting in only subdiffusional (<2 Å) chain displacements even after 200 h exposure to 1 M NaCl solutions. Finally, this persistence of polyelectrolyte layering has important ramifications for multistage drug delivery and optical applications of LbL assemblies.« less

Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters

NASA Astrophysics Data System (ADS)

Safari, Mohammad S.; Vorontsova, Maria A.; Poling-Skutvik, Ryan; Vekilov, Peter G.; Conrad, Jacinta C.

2015-10-01

Nanoparticle dynamics impact a wide range of biological transport processes and applications in nanomedicine and natural resource engineering. Differential dynamic microscopy (DDM) was recently developed to quantify the dynamics of submicron particles in solutions from fluctuations of intensity in optical micrographs. Differential dynamic microscopy is well established for monodisperse particle populations, but has not been applied to solutions containing weakly scattering polydisperse biological nanoparticles. Here we use bright-field DDM (BDDM) to measure the dynamics of protein-rich liquid clusters, whose size ranges from tens to hundreds of nanometers and whose total volume fraction is less than 10-5. With solutions of two proteins, hemoglobin A and lysozyme, we evaluate the cluster diffusion coefficients from the dependence of the diffusive relaxation time on the scattering wave vector. We establish that for weakly scattering populations, an optimal thickness of the sample chamber exists at which the BDDM signal is maximized at the smallest sample volume. The average cluster diffusion coefficient measured using BDDM is consistently lower than that obtained from dynamic light scattering at a scattering angle of 90∘. This apparent discrepancy is due to Mie scattering from the polydisperse cluster population, in which larger clusters preferentially scatter more light in the forward direction.

Shale Failure Mechanics and Intervention Measures in Underground Coal Mines: Results From 50 Years of Ground Control Safety Research

PubMed Central

2015-01-01

Ground control research in underground coal mines has been ongoing for over 50 years. One of the most problematic issues in underground coal mines is roof failures associated with weak shale. This paper will present a historical narrative on the research the National Institute for Occupational Safety and Health has conducted in relation to rock mechanics and shale. This paper begins by first discussing how shale is classified in relation to coal mining. Characterizing and planning for weak roof sequences is an important step in developing an engineering solution to prevent roof failures. Next, the failure mechanics associated with the weak characteristics of shale will be discussed. Understanding these failure mechanics also aids in applying the correct engineering solutions. The various solutions that have been implemented in the underground coal mining industry to control the different modes of failure will be summarized. Finally, a discussion on current and future research relating to rock mechanics and shale is presented. The overall goal of the paper is to share the collective ground control experience of controlling roof structures dominated by shale rock in underground coal mining. PMID:26549926

Shale Failure Mechanics and Intervention Measures in Underground Coal Mines: Results From 50 Years of Ground Control Safety Research.

PubMed

Murphy, M M

2016-02-01

Ground control research in underground coal mines has been ongoing for over 50 years. One of the most problematic issues in underground coal mines is roof failures associated with weak shale. This paper will present a historical narrative on the research the National Institute for Occupational Safety and Health has conducted in relation to rock mechanics and shale. This paper begins by first discussing how shale is classified in relation to coal mining. Characterizing and planning for weak roof sequences is an important step in developing an engineering solution to prevent roof failures. Next, the failure mechanics associated with the weak characteristics of shale will be discussed. Understanding these failure mechanics also aids in applying the correct engineering solutions. The various solutions that have been implemented in the underground coal mining industry to control the different modes of failure will be summarized. Finally, a discussion on current and future research relating to rock mechanics and shale is presented. The overall goal of the paper is to share the collective ground control experience of controlling roof structures dominated by shale rock in underground coal mining.

Shale Failure Mechanics and Intervention Measures in Underground Coal Mines: Results From 50 Years of Ground Control Safety Research

NASA Astrophysics Data System (ADS)

Murphy, M. M.

2016-02-01

Ground control research in underground coal mines has been ongoing for over 50 years. One of the most problematic issues in underground coal mines is roof failures associated with weak shale. This paper will present a historical narrative on the research the National Institute for Occupational Safety and Health has conducted in relation to rock mechanics and shale. This paper begins by first discussing how shale is classified in relation to coal mining. Characterizing and planning for weak roof sequences is an important step in developing an engineering solution to prevent roof failures. Next, the failure mechanics associated with the weak characteristics of shale will be discussed. Understanding these failure mechanics also aids in applying the correct engineering solutions. The various solutions that have been implemented in the underground coal mining industry to control the different modes of failure will be summarized. Finally, a discussion on current and future research relating to rock mechanics and shale is presented. The overall goal of the paper is to share the collective ground control experience of controlling roof structures dominated by shale rock in underground coal mining.

Global well-posedness and asymptotic behavior of solutions for the three-dimensional MHD equations with Hall and ion-slip effects

NASA Astrophysics Data System (ADS)

Zhao, Xiaopeng; Zhu, Mingxuan

2018-04-01

In this paper, we consider the small initial data global well-posedness of solutions for the magnetohydrodynamics with Hall and ion-slip effects in R^3. In addition, we also establish the temporal decay estimates for the weak solutions. With these estimates in hand, we study the algebraic time decay for higher-order Sobolev norms of small initial data solutions.

How cocrystals of weakly basic drugs and acidic coformers might modulate solubility and stability.

PubMed

Kuminek, G; Rodríguez-Hornedo, N; Siedler, S; Rocha, H V A; Cuffini, S L; Cardoso, S G

2016-04-30

Cocrystals of a weakly basic drug (nevirapine) with acidic coformers are shown to alter the solubility dependence on pH, and to exhibit a pHmax above which a less soluble cocrystal becomes more soluble than the drug. The cocrystal solubility advantage can be dialed up or down by solution pH.

Weakly anomalous diffusion with non-Gaussian propagators

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.

2012-08-01

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.

Propagation Characteristics Of Weakly Guiding Optical Fibers

NASA Technical Reports Server (NTRS)

Manshadi, Farzin

1992-01-01

Report discusses electromagnetic propagation characteristics of weakly guiding optical-fiber structures having complicated shapes with cross-sectional dimensions of order of wavelength. Coupling, power-dividing, and transition dielectric-waveguide structures analyzed. Basic data computed by scalar-wave, fast-Fourier-transform (SW-FFT) technique, based on numerical solution of scalar version of wave equation by forward-marching fast-Fourier-transform method.

On flows of viscoelastic fluids under threshold-slip boundary conditions

NASA Astrophysics Data System (ADS)

Baranovskii, E. S.

2018-03-01

We investigate a boundary-value problem for the steady isothermal flow of an incompressible viscoelastic fluid of Oldroyd type in a 3D bounded domain with impermeable walls. We use the Fujita threshold-slip boundary condition. This condition states that the fluid can slip along a solid surface when the shear stresses reach a certain critical value; otherwise the slipping velocity is zero. Assuming that the flow domain is not rotationally symmetric, we prove an existence theorem for the corresponding slip problem in the framework of weak solutions. The proof uses methods for solving variational inequalities with pseudo-monotone operators and convex functionals, the method of introduction of auxiliary viscosity, as well as a passage-to-limit procedure based on energy estimates of approximate solutions, Korn’s inequality, and compactness arguments. Also, some properties and estimates of weak solutions are established.

Fabrication and processing of high-strength densely packed carbon nanotube yarns without solution processes.

PubMed

Liu, Kai; Zhu, Feng; Liu, Liang; Sun, Yinghui; Fan, Shoushan; Jiang, Kaili

2012-06-07

Defects of carbon nanotubes, weak tube-tube interactions, and weak carbon nanotube joints are bottlenecks for obtaining high-strength carbon nanotube yarns. Some solution processes are usually required to overcome these drawbacks. Here we fabricate ultra-long and densely packed pure carbon nanotube yarns by a two-rotator twisting setup with the aid of some tensioning rods. The densely packed structure enhances the tube-tube interactions, thus making high tensile strengths of carbon nanotube yarns up to 1.6 GPa. We further use a sweeping laser to thermally treat as-produced yarns for recovering defects of carbon nanotubes and possibly welding carbon nanotube joints, which improves their Young's modulus by up to ∼70%. The spinning and laser sweeping processes are solution-free and capable of being assembled together to produce high-strength yarns continuously as desired.

Titration of Monoprotic Acids with Sodium Hydroxide Contaminated by Sodium Carbonate.

ERIC Educational Resources Information Center

Michalowski, Tadeusz

1988-01-01

Discusses the effects of using carbon dioxide contaminated sodium hydroxide solution as a titrant for a solution of a weak monoprotic acid and the resulting distortion of the titration curve in comparison to one obtained when an uncontaminated titrant is used. (CW)

Conformal bootstrap at large charge

NASA Astrophysics Data System (ADS)

Jafferis, Daniel; Mukhametzhanov, Baur; Zhiboedov, Alexander

2018-05-01

We consider unitary CFTs with continuous global symmetries in d > 2. We consider a state created by the lightest operator of large charge Q ≫ 1 and analyze the correlator of two light charged operators in this state. We assume that the correlator admits a well-defined large Q expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists. We find that the crossing equations admit a consistent truncation, where only a finite number N of Regge trajectories contribute to the correlator at leading nontrivial order. We classify all such truncated solutions to the crossing. For one Regge trajectory N = 1, the solution is unique and given by the effective field theory of a Goldstone mode. For two or more Regge trajectories N ≥ 2, the solutions are encoded in roots of a certain degree N polynomial. Some of the solutions admit a simple weakly coupled EFT description, whereas others do not. In the weakly coupled case, each Regge trajectory corresponds to a field in the effective Lagrangian.

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Li, Fucai

2018-03-01

In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

Center of Excellence in Theoretical Geoplasma Research

DTIC Science & Technology

1989-11-10

iii) First results of closed-form solutions of the3 Balescu -Lenard-Poisson equations for collisional plasmas were reported I REPORT November 10, 1989...Basu, "Solutions of the Linearized Balescu -Lenard-Poisson Equations for a Weakly-Collisional Plasma: Some New Results". [511 American Geophysical Union

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

Iterative Methods for Elliptic Problems and the Discovery of ’q’.

DTIC Science & Technology

1984-07-01

K = M’IlN LN 12 is a nonnegative irreducible matrix. Hence the Perron - Frobenius theory [19] tells us that there is exactly one eigenvalue A with W = p...earlier, the Perron - Frobenius theory implies that p is itself an eigenvalue. However, as we have said, in this instance the eigenvalue problem (l.12a

Positivity of Curvature-Squared Corrections in Gravity

NASA Astrophysics Data System (ADS)

Cheung, Clifford; Remmen, Grant N.

2017-02-01

We study the Gauss-Bonnet (GB) term as the leading higher-curvature correction to pure Einstein gravity. Assuming a tree-level ultraviolet completion free of ghosts or tachyons, we prove that the GB term has a nonnegative coefficient in dimensions greater than 4. Our result follows from unitarity of the spectral representation for a general ultraviolet completion of the GB term.

A Complete Description of Cones and Polytopes Including Hypervolumes of All Facets of a Polytope

ERIC Educational Resources Information Center

Jubete, F.; Castillo, E.

2007-01-01

In this paper methods and algorithms for identifying the main elements (edges and facets of any dimension) of a cone and a polytope, and calculating the corresponding hypervolumes are presented. The cones and polytopes are supposed to be given as the non-negative linear combination and the convex hull generated by a, not necessarily minimal, set…

Lobb's Generalization of Catalan's Parenthesization Problem

ERIC Educational Resources Information Center

Koshy, Thomas

2009-01-01

A. Lobb discovered an interesting generalization of Catalan's parenthesization problem, namely: Find the number L(n, m) of arrangements of n + m positive ones and n - m negative ones such that every partial sum is nonnegative, where 0 = m = n. This article uses Lobb's formula, L(n, m) = (2m + 1)/(n + m + 1) C(2n, n + m), where C is the usual…

A Mixed-Effects Heterogeneous Negative Binomial Model for Postfire Conifer Regeneration in Northeastern California, USA

Treesearch

Justin S. Crotteau; Martin W. Ritchie; J. Morgan Varner

2014-01-01

Many western USA fire regimes are typified by mixed-severity fire, which compounds the variability inherent to natural regeneration densities in associated forests. Tree regeneration data are often discrete and nonnegative; accordingly, we fit a series of Poisson and negative binomial variation models to conifer seedling counts across four distinct burn severities and...

Spline smoothing of histograms by linear programming

NASA Technical Reports Server (NTRS)

Bennett, J. O.

1972-01-01

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

Teaching Tip: When a Matrix and Its Inverse Are Stochastic

ERIC Educational Resources Information Center

Ding, J.; Rhee, N. H.

2013-01-01

A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

Robust extraction of basis functions for simultaneous and proportional myoelectric control via sparse non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Lin, Chuang; Wang, Binghui; Jiang, Ning; Farina, Dario

2018-04-01

Objective. This paper proposes a novel simultaneous and proportional multiple degree of freedom (DOF) myoelectric control method for active prostheses. Approach. The approach is based on non-negative matrix factorization (NMF) of surface EMG signals with the inclusion of sparseness constraints. By applying a sparseness constraint to the control signal matrix, it is possible to extract the basis information from arbitrary movements (quasi-unsupervised approach) for multiple DOFs concurrently. Main Results. In online testing based on target hitting, able-bodied subjects reached a greater throughput (TP) when using sparse NMF (SNMF) than with classic NMF or with linear regression (LR). Accordingly, the completion time (CT) was shorter for SNMF than NMF or LR. The same observations were made in two patients with unilateral limb deficiencies. Significance. The addition of sparseness constraints to NMF allows for a quasi-unsupervised approach to myoelectric control with superior results with respect to previous methods for the simultaneous and proportional control of multi-DOF. The proposed factorization algorithm allows robust simultaneous and proportional control, is superior to previous supervised algorithms, and, because of minimal supervision, paves the way to online adaptation in myoelectric control.

Blind beam-hardening correction from Poisson measurements

NASA Astrophysics Data System (ADS)

Gu, Renliang; Dogandžić, Aleksandar

2016-02-01

We develop a sparse image reconstruction method for Poisson-distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements and express the mass- attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate-descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov's proximal-gradient (NPG) step for estimating the density map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) step for estimating the incident-spectrum parameters. To accelerate convergence of the density- map NPG steps, we apply function restart and a step-size selection scheme that accounts for varying local Lipschitz constants of the Poisson NLL. Real X-ray CT reconstruction examples demonstrate the performance of the proposed scheme.

Graph regularized nonnegative matrix factorization for temporal link prediction in dynamic networks

NASA Astrophysics Data System (ADS)

Ma, Xiaoke; Sun, Penggang; Wang, Yu

2018-04-01

Many networks derived from society and nature are temporal and incomplete. The temporal link prediction problem in networks is to predict links at time T + 1 based on a given temporal network from time 1 to T, which is essential to important applications. The current algorithms either predict the temporal links by collapsing the dynamic networks or collapsing features derived from each network, which are criticized for ignoring the connection among slices. to overcome the issue, we propose a novel graph regularized nonnegative matrix factorization algorithm (GrNMF) for the temporal link prediction problem without collapsing the dynamic networks. To obtain the feature for each network from 1 to t, GrNMF factorizes the matrix associated with networks by setting the rest networks as regularization, which provides a better way to characterize the topological information of temporal links. Then, the GrNMF algorithm collapses the feature matrices to predict temporal links. Compared with state-of-the-art methods, the proposed algorithm exhibits significantly improved accuracy by avoiding the collapse of temporal networks. Experimental results of a number of artificial and real temporal networks illustrate that the proposed method is not only more accurate but also more robust than state-of-the-art approaches.

Non-negative Matrix Factorization and Co-clustering: A Promising Tool for Multi-tasks Bearing Fault Diagnosis

NASA Astrophysics Data System (ADS)

Shen, Fei; Chen, Chao; Yan, Ruqiang

2017-05-01

Classical bearing fault diagnosis methods, being designed according to one specific task, always pay attention to the effectiveness of extracted features and the final diagnostic performance. However, most of these approaches suffer from inefficiency when multiple tasks exist, especially in a real-time diagnostic scenario. A fault diagnosis method based on Non-negative Matrix Factorization (NMF) and Co-clustering strategy is proposed to overcome this limitation. Firstly, some high-dimensional matrixes are constructed using the Short-Time Fourier Transform (STFT) features, where the dimension of each matrix equals to the number of target tasks. Then, the NMF algorithm is carried out to obtain different components in each dimension direction through optimized matching, such as Euclidean distance and divergence distance. Finally, a Co-clustering technique based on information entropy is utilized to realize classification of each component. To verity the effectiveness of the proposed approach, a series of bearing data sets were analysed in this research. The tests indicated that although the diagnostic performance of single task is comparable to traditional clustering methods such as K-mean algorithm and Guassian Mixture Model, the accuracy and computational efficiency in multi-tasks fault diagnosis are improved.

Nonnegative Tensor Factorization Approach Applied to Fission Chamber’s Output Signals Blind Source Separation

NASA Astrophysics Data System (ADS)

Laassiri, M.; Hamzaoui, E.-M.; Cherkaoui El Moursli, R.

2018-02-01

Inside nuclear reactors, gamma-rays emitted from nuclei together with the neutrons introduce unwanted backgrounds in neutron spectra. For this reason, powerful extraction methods are needed to extract useful neutron signal from recorded mixture and thus to obtain clearer neutron flux spectrum. Actually, several techniques have been developed to discriminate between neutrons and gamma-rays in a mixed radiation field. Most of these techniques, tackle using analogue discrimination methods. Others propose to use some organic scintillators to achieve the discrimination task. Recently, systems based on digital signal processors are commercially available to replace the analog systems. As alternative to these systems, we aim in this work to verify the feasibility of using a Nonnegative Tensor Factorization (NTF) to blind extract neutron component from mixture signals recorded at the output of fission chamber (WL-7657). This last have been simulated through the Geant4 linked to Garfield++ using a 252Cf neutron source. To achieve our objective of obtaining the best possible neutron-gamma discrimination, we have applied the two different NTF algorithms, which have been found to be the best methods that allow us to analyse this kind of nuclear data.

Peak picking NMR spectral data using non-negative matrix factorization

PubMed Central

2014-01-01

Background Simple peak-picking algorithms, such as those based on lineshape fitting, perform well when peaks are completely resolved in multidimensional NMR spectra, but often produce wrong intensities and frequencies for overlapping peak clusters. For example, NOESY-type spectra have considerable overlaps leading to significant peak-picking intensity errors, which can result in erroneous structural restraints. Precise frequencies are critical for unambiguous resonance assignments. Results To alleviate this problem, a more sophisticated peaks decomposition algorithm, based on non-negative matrix factorization (NMF), was developed. We produce peak shapes from Fourier-transformed NMR spectra. Apart from its main goal of deriving components from spectra and producing peak lists automatically, the NMF approach can also be applied if the positions of some peaks are known a priori, e.g. from consistently referenced spectral dimensions of other experiments. Conclusions Application of the NMF algorithm to a three-dimensional peak list of the 23 kDa bi-domain section of the RcsD protein (RcsD-ABL-HPt, residues 688-890) as well as to synthetic HSQC data shows that peaks can be picked accurately also in spectral regions with strong overlap. PMID:24511909

Tuning of Muscle Synergies During Walking Along Rectilinear and Curvilinear Trajectories in Humans.

PubMed

Chia Bejarano, Noelia; Pedrocchi, Alessandra; Nardone, Antonio; Schieppati, Marco; Baccinelli, Walter; Monticone, Marco; Ferrigno, Giancarlo; Ferrante, Simona

2017-05-01

The aim of this study was to develop a methodology based on muscle synergies to investigate whether rectilinear and curvilinear walking shared the same neuro-motor organization, and how this organization was fine-tuned by the walking condition. Thirteen healthy subjects walked on rectilinear and curvilinear paths. Electromyographic data from thirteen back and lower-limb muscles were acquired, together with kinematic data using inertial sensors. Four macroscopically invariant muscle synergies, extracted through non-negative matrix factorization, proved a shared modular organization across conditions. The fine-tuning of muscle synergies was studied through non-negative matrix reconstruction, applied by fixing muscle weights or activation profiles to those of the rectilinear condition. The activation profiles tended to be recruited for a longer period and with a larger amplitude during curvilinear walking. The muscles of the posterior side of the lower limb were those mainly influenced by the fine-tuning, with the muscles inside the rotation path being more active than the outer muscles. This study shows that rectilinear and curvilinear walking share a unique motor command. However, a fine-tuning in muscle synergies is introduced during curvilinear conditions, adapting the kinematic strategy to the new biomechanical needs.

Supervised non-negative tensor factorization for automatic hyperspectral feature extraction and target discrimination

NASA Astrophysics Data System (ADS)

Anderson, Dylan; Bapst, Aleksander; Coon, Joshua; Pung, Aaron; Kudenov, Michael

2017-05-01

Hyperspectral imaging provides a highly discriminative and powerful signature for target detection and discrimination. Recent literature has shown that considering additional target characteristics, such as spatial or temporal profiles, simultaneously with spectral content can greatly increase classifier performance. Considering these additional characteristics in a traditional discriminative algorithm requires a feature extraction step be performed first. An example of such a pipeline is computing a filter bank response to extract spatial features followed by a support vector machine (SVM) to discriminate between targets. This decoupling between feature extraction and target discrimination yields features that are suboptimal for discrimination, reducing performance. This performance reduction is especially pronounced when the number of features or available data is limited. In this paper, we propose the use of Supervised Nonnegative Tensor Factorization (SNTF) to jointly perform feature extraction and target discrimination over hyperspectral data products. SNTF learns a tensor factorization and a classification boundary from labeled training data simultaneously. This ensures that the features learned via tensor factorization are optimal for both summarizing the input data and separating the targets of interest. Practical considerations for applying SNTF to hyperspectral data are presented, and results from this framework are compared to decoupled feature extraction/target discrimination pipelines.

Modeling Polio Data Using the First Order Non-Negative Integer-Valued Autoregressive, INAR(1), Model

NASA Astrophysics Data System (ADS)

Vazifedan, Turaj; Shitan, Mahendran

Time series data may consists of counts, such as the number of road accidents, the number of patients in a certain hospital, the number of customers waiting for service at a certain time and etc. When the value of the observations are large it is usual to use Gaussian Autoregressive Moving Average (ARMA) process to model the time series. However if the observed counts are small, it is not appropriate to use ARMA process to model the observed phenomenon. In such cases we need to model the time series data by using Non-Negative Integer valued Autoregressive (INAR) process. The modeling of counts data is based on the binomial thinning operator. In this paper we illustrate the modeling of counts data using the monthly number of Poliomyelitis data in United States between January 1970 until December 1983. We applied the AR(1), Poisson regression model and INAR(1) model and the suitability of these models were assessed by using the Index of Agreement(I.A.). We found that INAR(1) model is more appropriate in the sense it had a better I.A. and it is natural since the data are counts.

Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods

NASA Astrophysics Data System (ADS)

Ma, Xiaoke; Wang, Bingbo; Yu, Liang

2018-01-01

Community detection is fundamental for revealing the structure-functionality relationship in complex networks, which involves two issues-the quantitative function for community as well as algorithms to discover communities. Despite significant research on either of them, few attempt has been made to establish the connection between the two issues. To attack this problem, a generalized quantification function is proposed for community in weighted networks, which provides a framework that unifies several well-known measures. Then, we prove that the trace optimization of the proposed measure is equivalent with the objective functions of algorithms such as nonnegative matrix factorization, kernel K-means as well as spectral clustering. It serves as the theoretical foundation for designing algorithms for community detection. On the second issue, a semi-supervised spectral clustering algorithm is developed by exploring the equivalence relation via combining the nonnegative matrix factorization and spectral clustering. Different from the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the spectral algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method improves the accuracy of the traditional spectral algorithms in community detection.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

NASA Astrophysics Data System (ADS)

Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Flocking particles in a non-Newtonian shear thickening fluid

NASA Astrophysics Data System (ADS)

Mucha, Piotr B.; Peszek, Jan; Pokorný, Milan

2018-06-01

We prove the existence of strong solutions to the Cucker–Smale flocking model coupled with an incompressible viscous non-Newtonian fluid with the stress tensor of a power–law structure for . The fluid part of the system admits strong solutions while the solutions to the CS part are weak. The coupling is performed through a drag force on a periodic spatial domain . Additionally, we construct a Lyapunov functional determining the large time behavior of solutions to the system.

"Permanence" - An Adaptationist Solution to Fermi's Paradox?

NASA Astrophysics Data System (ADS)

Cirkovic, Milan M.

A new solution of Fermi's paradox sketched by SF writer Karl Schroeder in his 2002. novel Permanence is investigated. It is argued that this solution is tightly connected with adaptationism - a widely discussed working hypothesis in evolutionary biology. Schroeder's hypothesis has important ramifications for astrobiology, SETI projects, and future studies. Its weaknesses should be explored without succumbing to the emotional reactions often accompanying adaptationist explanations.

Multi-Periodic Waves in Shallow Water

DTIC Science & Technology

1992-09-01

models-the Kadomtsev - Petviashvili (KP) equation . The KP equation describes the evolu- tion of weakly nonlinear, weakly two-dimensional waves on water of...experimentally. The analytical model is a family of periodic solutions of the Kadomtsev -Petviashuili equation . The experiments demonstrate the accuracy... Petviashvili Equation (with Norman Schef- fner & Harvey Segur). Proceedings, Nonlinear Water Waves Workshop, University of Bristol. England, 1991. Resonant

How cocrystals of weakly basic drugs and acidic coformers might modulate solubility and stability

PubMed Central

Kuminek, G.; Rodríguez-Hornedo, N.; Siedler, S.; Rocha, H. V. A.; Cuffini, S. L.; Cardoso, S. G.

2016-01-01

Cocrystals of a weakly basic drug (nevirapine) with acidic coformers are shown to alter the solubility dependence on pH, and to exhibit a pHmax above which a less soluble cocrystal becomes more soluble than the drug. The cocrystal solubility advantage can be dialed up or down by solution pH. PMID:27042997

[The effect of pemolin on the mitotic activity of Vicia faba L (author's transl)].

PubMed

Brabec, F; Röper, W

1976-02-01

The effect of diverse concentrations of 5-phenyl-2-imino-4-oxazolidone (PIO, pemolin, Tradon) on the mitotic activity in lateral roots of Vicia faba L. was studied by aerated and non-aerated hydrocultivation with and without mineral nutrition, respectively. With optimal conditions (aerated nutrient solution) weak PIO-concentrations, most significantly 10(-6) g/ml, effected a marked increase of the mitotic index. Contrarily, strong PIO-concentrations (10(-4) and 3 X 10(-4) g/ml = saturated solution) significantly decreased the mitotic index though simultaneously preserving the mitotic activity in long-term experiments, when on account of nutrient deficiency it had already collapsed in weak PIO-concentrations and the controls. The activating effect of weak PIO-concentrations compared with the controls is more significant in stress situations (nutrient deficiency, O2-deficiency) than under optimal conditions. Furthermore a slight acceleration of mid-mitotic phases (metaphase--anaphase) recognized by a marked decrease in percentage of these phases, can be stated with weak PIO-concentrations, again particularly so with 10(-6) g/ml. In total, dependent on concentration, pemolin presumably may either activate or suppress cell metabolism and particularly the mitotic cycle. The exact site of action of the substance is still unknown.

Structure, optical and phonon properties of bulk and nanocrystalline Al2-xScx(WO4)3 solid solutions doped with Cr3+

NASA Astrophysics Data System (ADS)

Mączka, M.; Hermanowicz, K.; Pietraszko, A.; Yordanova, A.; Koseva, I.

2014-01-01

Pure and Cr3+ doped nanosized Al2-xScx(WO4)3 solid solutions were prepared by co-precipitation method as well as Al2-xScx(WO4)3 single crystals were grown by high-temperature flux method. The obtained samples were characterized by X-ray, Raman, IR, absorption and luminescence methods. Single crystal X-ray diffraction showed that AlSc(WO4)3 is orthorhombic at room temperature with space group Pnca and trivalent cations are statistically distributed. Raman and IR studies showed that Al2-xScx(WO4)3 solid solutions show "two mode" behavior. They also showed that vibrational properties of nanosized samples have been weakly modified in comparison with the bulk materials. The luminescence and absorption spectra revealed that chromium ions occupy two sites of weak and strong crystal field strength.

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods

PubMed Central

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-01-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Alternating least squares with penalty functions.

PubMed

Gemperline, Paul J; Cash, Eric

2003-08-15

A new algorithm for self-modeling curve resolution (SMCR) that yields improved results by incorporating soft constraints is described. The method uses least squares penalty functions to implement constraints in an alternating least squares algorithm, including nonnegativity, unimodality, equality, and closure constraints. By using least squares penalty functions, soft constraints are formulated rather than hard constraints. Significant benefits are (obtained using soft constraints, especially in the form of fewer distortions due to noise in resolved profiles. Soft equality constraints can also be used to introduce incomplete or partial reference information into SMCR solutions. Four different examples demonstrating application of the new method are presented, including resolution of overlapped HPLC-DAD peaks, flow injection analysis data, and batch reaction data measured by UV/visible and near-infrared spectroscopy (NIR). Each example was selected to show one aspect of the significant advantages of soft constraints over traditionally used hard constraints. Incomplete or partial reference information into self-modeling curve resolution models is described. The method offers a substantial improvement in the ability to resolve time-dependent concentration profiles from mixture spectra recorded as a function of time.

Spectral Unmixing Analysis of Time Series Landsat 8 Images

NASA Astrophysics Data System (ADS)

Zhuo, R.; Xu, L.; Peng, J.; Chen, Y.

2018-05-01

Temporal analysis of Landsat 8 images opens up new opportunities in the unmixing procedure. Although spectral analysis of time series Landsat imagery has its own advantage, it has rarely been studied. Nevertheless, using the temporal information can provide improved unmixing performance when compared to independent image analyses. Moreover, different land cover types may demonstrate different temporal patterns, which can aid the discrimination of different natures. Therefore, this letter presents time series K-P-Means, a new solution to the problem of unmixing time series Landsat imagery. The proposed approach is to obtain the "purified" pixels in order to achieve optimal unmixing performance. The vertex component analysis (VCA) is used to extract endmembers for endmember initialization. First, nonnegative least square (NNLS) is used to estimate abundance maps by using the endmember. Then, the estimated endmember is the mean value of "purified" pixels, which is the residual of the mixed pixel after excluding the contribution of all nondominant endmembers. Assembling two main steps (abundance estimation and endmember update) into the iterative optimization framework generates the complete algorithm. Experiments using both simulated and real Landsat 8 images show that the proposed "joint unmixing" approach provides more accurate endmember and abundance estimation results compared with "separate unmixing" approach.

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.

PubMed

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-05-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L 2 -norm regularization. However, sparse representation methods via L 1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L 1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.

Fault detection, isolation, and diagnosis of self-validating multifunctional sensors.

PubMed

Yang, Jing-Li; Chen, Yin-Sheng; Zhang, Li-Li; Sun, Zhen

2016-06-01

A novel fault detection, isolation, and diagnosis (FDID) strategy for self-validating multifunctional sensors is presented in this paper. The sparse non-negative matrix factorization-based method can effectively detect faults by using the squared prediction error (SPE) statistic, and the variables contribution plots based on SPE statistic can help to locate and isolate the faulty sensitive units. The complete ensemble empirical mode decomposition is employed to decompose the fault signals to a series of intrinsic mode functions (IMFs) and a residual. The sample entropy (SampEn)-weighted energy values of each IMFs and the residual are estimated to represent the characteristics of the fault signals. Multi-class support vector machine is introduced to identify the fault mode with the purpose of diagnosing status of the faulty sensitive units. The performance of the proposed strategy is compared with other fault detection strategies such as principal component analysis, independent component analysis, and fault diagnosis strategies such as empirical mode decomposition coupled with support vector machine. The proposed strategy is fully evaluated in a real self-validating multifunctional sensors experimental system, and the experimental results demonstrate that the proposed strategy provides an excellent solution to the FDID research topic of self-validating multifunctional sensors.

Equilibrium problems for Raney densities

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng; Zinn-Justin, Paul

2015-07-01

The Raney numbers are a class of combinatorial numbers generalising the Fuss-Catalan numbers. They are indexed by a pair of positive real numbers (p, r) with p > 1 and 0 < r ⩽ p, and form the moments of a probability density function. For certain (p, r) the latter has the interpretation as the density of squared singular values for certain random matrix ensembles, and in this context equilibrium problems characterising the Raney densities for (p, r) = (θ + 1, 1) and (θ/2 + 1, 1/2) have recently been proposed. Using two different techniques—one based on the Wiener-Hopf method for the solution of integral equations and the other on an analysis of the algebraic equation satisfied by the Green's function—we establish the validity of the equilibrium problems for general θ > 0 and similarly use both methods to identify the equilibrium problem for (p, r) = (θ/q + 1, 1/q), θ > 0 and q \\in Z+ . The Wiener-Hopf method is used to extend the latter to parameters (p, r) = (θ/q + 1, m + 1/q) for m a non-negative integer, and also to identify the equilibrium problem for a family of densities with moments given by certain binomial coefficients.

Collective phase description of oscillatory convection

NASA Astrophysics Data System (ADS)

Kawamura, Yoji; Nakao, Hiroya

2013-12-01

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shaw cells exhibiting oscillatory convection on the basis of the derived phase equations.

Taste does not determine daily intake of dilute sugar solutions in mice

PubMed Central

Beltran, F.; Benton, L.; Cheng, S.; Gieseke, J.; Gillman, J.; Spain, H. N.

2010-01-01

When a rodent licks a sweet-tasting solution, taste circuits in the central nervous system that facilitate stimulus identification, motivate intake, and prepare the body for digestion are activated. Here, we asked whether taste also determines daily intake of sugar solutions in C57BL/6 mice. We tested several dilute concentrations of glucose (167, 250, and 333 mM) and fructose (167, 250, and 333 mM). In addition, we tested saccharin (38 mM), alone and in binary mixture with each of the sugar concentrations, to manipulate sweet taste intensity while holding caloric value constant. In experiment 1, we measured taste responsiveness to the sweetener solutions in two ways: chorda tympani nerve responses and short-term lick tests. For both measures, the mice exhibited the following relative magnitude of responsiveness: binary mixtures > saccharin > individual sugars. In experiment 2, we asked whether the taste measures reliably predicted daily intake of the sweetener solutions. No such relationship was observed. The glucose solutions elicited weak taste responses but high daily intakes, whereas the fructose solutions elicited weak taste responses and low daily intakes. On the other hand, the saccharin + glucose solutions elicited strong taste responses and high daily intakes, while the saccharin + fructose solutions elicited strong taste responses but low daily intakes. Overall, we found that 1) daily intake of the sweetener solutions varied independently of the magnitude of the taste responses and 2) the solutions containing glucose stimulated substantially higher daily intakes than did the solutions containing isomolar concentrations of fructose. Given prior work demonstrating greater postoral stimulation of feeding by glucose than fructose, we propose that the magnitude of postoral nutritive stimulation plays a more important role than does taste in determining daily intake of dilute sugar solutions. PMID:20702804

Finite element solution of optimal control problems with state-control inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1992-01-01

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

Phase structure of NJL model with weak renormalization group

NASA Astrophysics Data System (ADS)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation.

PubMed

Wen, Xiao-Yong; Yan, Zhenya

2015-12-01

We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.

How do bubbles grow in a weakly supersaturated solution?

NASA Astrophysics Data System (ADS)

Enriquez, Oscar; Sun, Chao; Lohse, Detlef; Prosperetti, Andrea; van der Meer, Devaraj

2013-11-01

Beer, champagne and soft-drinks are water-based solutions which owe their ``bubbliness'' to a moderate degree of carbon dioxide supersaturation. Bubbles grow sequentially from nucleation sites due to solute concentration gradients and detach due to buoyancy. The leading mass transfer mechanism is diffusion, but the advection caused by the moving surface also plays an important role. Now, what happens at the limit of very weak supersaturation? We take an experimental look at CO2 bubbles growing in water under such a condition. Nucleation sites are provided by hydrophobic micro-cavities on a silicon chip, therefore controlling the number and position of bubbles. Although advection is negligible, measured growth rates for an isolated bubble differ noticeably from a purely diffusive theoretical solution. We can explain the differences as effects of the concentration boundary layer around the bubble. Initially, its interaction with the surface on which the bubble grows slows the process down. Later on, the growth rate is enhanced by buoyancy effects caused by the depletion of the solute in the surroundings of the bubble. When neighboring bubbles are brought into play they interact through their boundary layers, further slowing down their growth rates.

Effect of correlations on the polarizability of the one component plasma

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

Carini, P.R.

Correlational effects on the dynamical polarizability ..cap alpha..(k,..omega..) of the one component plasma (OCP) are investigated in both the weak (..gamma.. < 1) and strong (..gamma.. < 1) coupling regions (..gamma.. is the plasma parameter, ..gamma.. = k/sup 3//4..pi..n where k/sup -1/ is the Debye length and n is the number density. In the weak coupling region a numerical solution is presented over a wide range of frequencies of the complete first order (in ..gamma..) correction to the dynamical polarizability which fully accounts for dynamical screening effects and is exact in the long wavelength and weak coupling limits (k ..-->..more » 0, ..gamma.. ..-->.. 0). This complete result is compared with a similar numerical solution for the dynamical polarizability obtained from the Golden-Kalman (GK) dynamical theory for strongly coupled plasmas. Contrary to previous results reported in the literature it was found that both theories predict the change in the dispersion of the long wavelength plasmons due to finite ..gamma.. effects to be that the slope of the plasmon dispersion curve decreases from its Bohm-Gross value as the plasma parameter increases from 0. In the strong coupling region two hydrodynamical model solutions of the GK dynamical theory for the polarizability are presented.« less

One-Dimensional Quantum Walks with One Defect

NASA Astrophysics Data System (ADS)

Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the nonnegative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities to the origin.

Enforced Sparse Non-Negative Matrix Factorization

DTIC Science & Technology

2016-01-23

documents to find interesting pieces of information. With limited resources, analysts often employ automated text - mining tools that highlight common...represented as an undirected bipartite graph. It has become a common method for generating topic models of text data because it is known to produce good results...model and the convergence rate of the underlying algorithm. I. Introduction A common analyst challenge is searching through large quantities of text

Inequalities and Monotonicity of the Ratio of the Geometric Means of a Positive Arithmetic Sequence with Unit Difference

ERIC Educational Resources Information Center

Qi, Feng

2003-01-01

For any nonnegative integer "k" and natural numbers "n" and "m," the equations presented in this paper demonstrate the inequalities obtained on the ratio for the geometric means of a positive arithmetic sequence with unit difference, where alpha epsilon [vertical bar]0,1[vertical bar] is a constant. Using the ideas and methods of Chen (2002),…

A Network Thermodynamic Framework for the Analysis and Control Design of Large-Scale Dynamical Systems

DTIC Science & Technology

2006-03-31

Nonnegative Dynamical Sys- tems................................................. 18 2.10. Adaptive Control for General Anesthesia and Intensive Care...Unit Sedation 20 2.11. Neural Network Adaptive Control for Intensive Care Unit Sedation and In- traoperative Anesthesia ...control for operating room hypnosis and intefisive care unit sedation. 1.3. Goals of this Report The main goal of this report is to summarize the

Continuous Control Artificial Potential Function Methods and Optimal Control

DTIC Science & Technology

2014-03-27

21 CW Clohessy - Wiltshire . . . . . . . . . . . . . . . . . . . . . . 26 CV Chase Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 26 TV Target... Clohessy - Wiltshire equa- tions2) until the time rate of change of potential became nonnegative. At that time, a thrust impulse was applied to make the...3.2. 2The Clohessy - Wiltshire equations are introduced in Section 3.5. 7 to eliminate oscillation around the goal point [8, 9]. Such a method is

A Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

DTIC Science & Technology

2012-08-01

model appears in cosmic microwave background analysis [10] which solves min A,Y λ 2 trace ( (ABY − X)>C−1(ABY − X) ) + r(Y), subject to A ∈ D (1.5...and “×n” represent outer product and tensor-matrix multiplication, respectively. (The necessary background of tensor is reviewed in Sec. 3) Most

Higher order derivatives of R-Jacobi polynomials

NASA Astrophysics Data System (ADS)

Das, Sourav; Swaminathan, A.

2016-06-01

In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon.

PubMed

McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan

2015-03-26

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized, but these states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. Non-Gaussian entangled states have been produced in small ensembles of ions, and very recently in large atomic ensembles. Here we generate entanglement in a large atomic ensemble via an interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function--an important hallmark of non-classicality--and verify an entanglement depth (the minimum number of mutually entangled atoms) of 2,910 ± 190 out of 3,100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. Although the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.

Aqueous Ammonia or Ammonium Hydroxide? Identifying a Base as Strong or Weak

ERIC Educational Resources Information Center

Sanger, Michael J.; Danner, Matthew

2010-01-01

When grocery stores sell solutions of ammonia, they are labeled "ammonia"; however, when the same solution is purchased from chemical supply stores, they are labeled "ammonium hydroxide". The goal of this experiment is for students to determine which name is more appropriate. In this experiment, students use several different experimental methods…

Science Notes: Dilution of a Weak Acid

ERIC Educational Resources Information Center

Talbot, Christopher; Wai, Chooi Khee

2014-01-01

This "Science note" arose out of practical work involving the dilution of ethanoic acid, the measurement of the pH of the diluted solutions and calculation of the acid dissociation constant, K[subscript a], for each diluted solution. The students expected the calculated values of K[subscript a] to be constant but they found that the…

HydroCrowd: a citizen science snapshot to assess the spatial control of nitrogen solutes in surface waters

PubMed Central

Breuer, Lutz; Hiery, Noreen; Kraft, Philipp; Bach, Martin; Aubert, Alice H.; Frede, Hans-Georg

2015-01-01

We organized a crowdsourcing experiment in the form of a snapshot sampling campaign to assess the spatial distribution of nitrogen solutes, namely, nitrate, ammonium and dissolved organic nitrogen (DON), in German surface waters. In particular, we investigated (i) whether crowdsourcing is a reasonable sampling method in hydrology and (ii) what the effects of population density, soil humus content and arable land were on actual nitrogen solute concentrations and surface water quality. The statistical analyses revealed a significant correlation between nitrate and arable land (0.46), as well as soil humus content (0.37) but a weak correlation with population density (0.12). DON correlations were weak but significant with humus content (0.14) and arable land (0.13). The mean contribution of DON to total dissolved nitrogen was 22%. Samples were classified as water quality class II or above, following the European Water Framework Directive for nitrate and ammonium (53% and 82%, respectively). Crowdsourcing turned out to be a useful method to assess the spatial distribution of stream solutes, as considerable amounts of samples were collected with comparatively little effort. PMID:26561200

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Phospholipid bilayer affinities and solvation characteristics by electrokinetic chromatography with a nanodisc pseudostationary phase.

PubMed

Penny, William M; Steele, Harmen B; Ross, J B Alexander; Palmer, Christopher P

2017-03-01

Phospholipid bilayer nanodiscs composed of 1,2-dimyristoyl-sn-glycero-3-phosphocholine and synthetic maleic acid-styrene copolymer belts have been introduced as a pseudostationary phase (PSP) in electrokinetic chromatography and demonstrated good performance. The nanodiscs provide a suitable migration range and high theoretical plate counts. Using this nanodisc pseudostationary phase, the affinity of the bilayer structure for probe solutes was determined and characterized. Good correlation is observed between retention factors and octanol water partition coefficients for particular categories of solutes, but the general correlation is weak primarily because the nanodiscs show stronger affinity than octanol for hydrogen bond donors. This suggests that a more appropriate application of this technology is to measure and characterize interactions between solutes and lipid bilayers directly. Linear solvation energy relationship analysis of the nanodisc-solute interactions in this study demonstrates that the nanodiscs provide a solvation environment with low cohesivity and weak hydrogen bond donating ability, and provide relatively strong hydrogen bond acceptor strength. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Asymptotically suboptimal control of weakly interconnected dynamical systems

NASA Astrophysics Data System (ADS)

Dmitruk, N. M.; Kalinin, A. I.

2016-10-01

Optimal control problems for a group of systems with weak dynamical interconnections between its constituent subsystems are considered. A method for decentralized control is proposed which distributes the control actions between several controllers calculating in real time control inputs only for theirs subsystems based on the solution of the local optimal control problem. The local problem is solved by asymptotic methods that employ the representation of the weak interconnection by a small parameter. Combination of decentralized control and asymptotic methods allows to significantly reduce the dimension of the problems that have to be solved in the course of the control process.

New Turaev braided group categories and weak (co)quasi-Turaev group coalgebras

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

Zhang, Xiaohui, E-mail: zxhhhhh@gmail.com; Wang, Shuanhong, E-mail: shuanhwang2002@yahoo.com

In order to construct a class of new braided crossed G-categories with nontrivial associativity and unit constraints, we study the G-graded monoidal category over a family of algebras (H{sub α}){sub α∈G} and introduce the notion of a weak (co)quasi-Turaev G-(co)algebra. Then we prove that the category of (co)representations of (co)quasitriangular weak (co)quasi-Turaev π-(co)algebras is exactly a braided crossed G-category. In fact, this (co)quasitriangular structure provides a solution to a generalized quantum Yang-Baxter type equation.

Solute boundary layer on a rotating crystal

NASA Astrophysics Data System (ADS)

Povinelli, Michelle L.; Korpela, Seppo A.; Chait, Arnon

1994-11-01

A perturbation analysis has been carried out for the solutal boundary layer next to a rotating crystal. Our aim is to extend the classical results of Burton, Prim and Slicher [1] in order to obtain higher order terms in asymptotic expansions for the concentration field and boundary-layer thickness. Expressions for the effective segregation coefficient are directly obtained from the concentration solution in the two limits that correspond to weak and strong rotation.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Variation and decomposition of the partial molar volume of small gas molecules in different organic solvents derived from molecular dynamics simulations.

PubMed

Klähn, Marco; Martin, Alistair; Cheong, Daniel W; Garland, Marc V

2013-12-28

The partial molar volumes, V(i), of the gas solutes H2, CO, and CO2, solvated in acetone, methanol, heptane, and diethylether are determined computationally in the limit of infinite dilution and standard conditions. Solutions are described with molecular dynamics simulations in combination with the OPLS-aa force field for solvents and customized force field for solutes. V(i) is determined with the direct method, while the composition of V(i) is studied with Kirkwood-Buff integrals (KBIs). Subsequently, the amount of unoccupied space and size of pre-formed cavities in pure solvents is determined. Additionally, the shape of individual solvent cages is analyzed. Calculated V(i) deviate only 3.4 cm(3) mol(-1) (7.1%) from experimental literature values. Experimental V(i) variations across solutions are reproduced qualitatively and also quantitatively in most cases. The KBI analysis identifies differences in solute induced solvent reorganization in the immediate vicinity of H2 (<0.7 nm) and solvent reorganization up to the third solvation shell of CO and CO2 (<1.6 nm) as the origin of V(i) variations. In all solutions, larger V(i) are found in solvents that exhibit weak internal interactions, low cohesive energy density and large compressibility. Weak internal interactions facilitate solvent displacement by thermal solute movement, which enhances the size of solvent cages and thus V(i). Additionally, attractive electrostatic interactions of CO2 and the solvents, which do not depend on internal solvent interactions only, partially reversed the V(i) trends observed in H2 and CO solutions where electrostatic interactions with the solvents are absent. More empty space and larger pre-formed cavities are found in solvents with weak internal interactions, however, no evidence is found that solutes in any considered solvent are accommodated in pre-formed cavities. Individual solvent cages are found to be elongated in the negative direction of solute movement. This wake behind the moving solute is more pronounced in case of mobile H2 and in solvents with weaker internal interactions. However, deviations from a spherical solvent cage shape do not influence solute-solvent radial distribution functions after averaging over all solvent cage orientations and hence do not change V(i). Overall, the applied methodology reproduces V(i) and its variations reliably and the used V(i) decompositions identify the underlying reasons behind observed V(i) variations.

Variation and decomposition of the partial molar volume of small gas molecules in different organic solvents derived from molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Klähn, Marco; Martin, Alistair; Cheong, Daniel W.; Garland, Marc V.

2013-12-01

The partial molar volumes, bar V_i, of the gas solutes H2, CO, and CO2, solvated in acetone, methanol, heptane, and diethylether are determined computationally in the limit of infinite dilution and standard conditions. Solutions are described with molecular dynamics simulations in combination with the OPLS-aa force field for solvents and customized force field for solutes. bar V_i is determined with the direct method, while the composition of bar V_i is studied with Kirkwood-Buff integrals (KBIs). Subsequently, the amount of unoccupied space and size of pre-formed cavities in pure solvents is determined. Additionally, the shape of individual solvent cages is analyzed. Calculated bar V_i deviate only 3.4 cm3 mol-1 (7.1%) from experimental literature values. Experimental bar V_i variations across solutions are reproduced qualitatively and also quantitatively in most cases. The KBI analysis identifies differences in solute induced solvent reorganization in the immediate vicinity of H2 (<0.7 nm) and solvent reorganization up to the third solvation shell of CO and CO2 (<1.6 nm) as the origin of bar V_i variations. In all solutions, larger bar V_i are found in solvents that exhibit weak internal interactions, low cohesive energy density and large compressibility. Weak internal interactions facilitate solvent displacement by thermal solute movement, which enhances the size of solvent cages and thus bar V_i. Additionally, attractive electrostatic interactions of CO2 and the solvents, which do not depend on internal solvent interactions only, partially reversed the bar V_i trends observed in H2 and CO solutions where electrostatic interactions with the solvents are absent. More empty space and larger pre-formed cavities are found in solvents with weak internal interactions, however, no evidence is found that solutes in any considered solvent are accommodated in pre-formed cavities. Individual solvent cages are found to be elongated in the negative direction of solute movement. This wake behind the moving solute is more pronounced in case of mobile H2 and in solvents with weaker internal interactions. However, deviations from a spherical solvent cage shape do not influence solute-solvent radial distribution functions after averaging over all solvent cage orientations and hence do not change bar V_i. Overall, the applied methodology reproduces bar V_i and its variations reliably and the used bar V_i decompositions identify the underlying reasons behind observed bar V_i variations.

Collective phase description of oscillatory convection

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

Kawamura, Yoji, E-mail: ykawamura@jamstec.go.jp; Nakao, Hiroya

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shawmore » cells exhibiting oscillatory convection on the basis of the derived phase equations.« less

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

NASA Astrophysics Data System (ADS)

Barré, J.; Bernardin, C.; Chetrite, R.

2018-02-01

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31-45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.

Shock-jump conditions in a general medium: weak-solution approach

NASA Astrophysics Data System (ADS)

Forbes, L. K.; Krzysik, O. A.

2017-05-01

General conservation laws are considered, and the concept of a weak solution is extended to the case of an equation involving three space variables and time. Four-dimensional vector calculus is used to develop general jump conditions at a shock wave in the material. To illustrate the use of this result, jump conditions at a shock in unsteady three-dimensional compressible gas flow are presented. It is then proved rigorously that these reduce to the commonly assumed conditions in coordinates normal and tangential to the shock face. A similar calculation is also outlined for an unsteady three-dimensional shock in magnetohydrodynamics, and in a chemically reactive fluid. The technique is available for determining shock-jump conditions in quite general continuous media.

A/GATECH DOSP Fabrication

DTIC Science & Technology

1993-11-01

developer and then bleached with a rehalogenating bleach and finally re-developed with a weak citric acid developer. The final result of this processing...refraction forming a phase hologram. The plate is then immersed in a weak solution of citric acid , and illuminated with a bright light. The citric acid ...also results in NP complexity due to the combinational^ explosive number of permutations of splits that must be examined. By limiting the degree to

Periodic Solution and Stationary Distribution of Stochastic Predator-Prey Models with Higher-Order Perturbation

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2018-04-01

In this paper, two stochastic predator-prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii's theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.

Automatic photometric titrations of calcium and magnesium in carbonate rocks

USGS Publications Warehouse

Shapiro, L.; Brannock, W.W.

1955-01-01

Rapid nonsubjective methods have been developed for the determination of calcium and magnesium in carbonate rocks. From a single solution of the sample, calcium is titrated directly, and magnesium is titrated after a rapid removal of R2O3 and precipitation of calcium as the tungstate. A concentrated and a dilute solution of disodium ethylenediamine tetraacetate are used as titrants. The concentrated solution is added almost to the end point, then the weak solution is added in an automatic titrator to determine the end point precisely.

Noncommutative wormhole solutions in F(T, T𝒢) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

2017-04-01

This paper is devoted to the study of static spherically symmetric wormhole solutions along with noncommutative geometry in the background of F(T, T𝒢) gravity. We assume a nonzero redshift function as well as two well-known models of this gravity and discuss the behavior of null/weak energy conditions graphically. We conclude that there does not exist any physically acceptable wormhole solution for the first model, but there is a chance to develop physically acceptable wormhole solution in a particular region for the second model.

Statistical classification techniques for engineering and climatic data samples

NASA Technical Reports Server (NTRS)

Temple, E. C.; Shipman, J. R.

1981-01-01

Fisher's sample linear discriminant function is modified through an appropriate alteration of the common sample variance-covariance matrix. The alteration consists of adding nonnegative values to the eigenvalues of the sample variance covariance matrix. The desired results of this modification is to increase the number of correct classifications by the new linear discriminant function over Fisher's function. This study is limited to the two-group discriminant problem.

Supersymmetric extensions of K field theories

NASA Astrophysics Data System (ADS)

Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.

2012-02-01

We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.