Nonnegative Coefficients Research Articles

Formula omitted] regularized multiplicative iterative path algorithm for non-negative generalized linear models

In regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where regression coefficients in the linear predictor are subject to non-negative constraints. Thus, non-negatively constrained regression coefficient estimation is sought by maximizing the penalized likelihood (such as the l1-norm penalty). An efficient regularization path algorithm is proposed for generalized linear models with non-negative regression coefficients. The algorithm uses multiplicative updates which are fast and simultaneous. Asymptotic results are also developed for the constrained penalized likelihood estimates. Performance of the proposed algorithm is shown in terms of computational time, accuracy of solutions and accuracy of asymptotic standard deviations.

Iterative oscillation tests for differential equations with several non-monotone arguments

Sufficient oscillation conditions involving $\limsup $ and $\liminf $ for first-order differential equations with several non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Gr\"{o}nwall inequality. Examples illustrating the significance of the results are also given.

An oscillation criterion for delay differential equations with several non-monotone arguments

The oscillatory behavior of the solutions to a differential equation with several non-monotone delay arguments and non-negative coefficients is studied. A new sufficient oscillation condition, involving lim sup, is obtained. An example illustrating the significance of the result is also given.

Simultaneous similarity classes of commuting matrices over a finite field

This paper concerns the enumeration of isomorphism classes of modules of a polynomial algebra in several variables over a finite field. This is the same as the classification of commuting tuples of matrices over a finite field up to simultaneous similarity. Let cn,k(q) denote the number of isomorphism classes of n-dimensional Fq[x1,…,xk]-modules. The generating function ∑kcn,k(q)tk is a rational function. We compute this function for n≤4. We find that its coefficients are polynomial functions in q with non-negative integer coefficients.

Cylindric partitions, characters and the Andrews–Gordon–Bressoud identities

We study the Andrews–Gordon–Bressoud (AGB) generalisations of the Rogers–Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin’s product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of algebras, the minimal model characters of algebras, and the r-string abaci generating functions, providing simple proofs for each. We then set r = 2, and use two-cylindric partitions to re-derive the AGB identities as follows. Firstly, we use Borodin’s product expression for the generating functions of the two-cylindric partitions with infinitely long parts, to obtain the product sides of the AGB identities, times a factor , which is the generating function of ordinary partitions. Next, we obtain a bijection from the two-cylindric partitions, via two-string abaci, into decorated versions of Bressoud’s restricted lattice paths. Extending Bressoud’s method of transforming between restricted paths that obey different restrictions, we obtain sum expressions with manifestly non-negative coefficients for the generating functions of the two-cylindric partitions which contains a factor . Equating the product and sum expressions of the same two-cylindric partitions, and canceling a factor of on each side, we obtain the AGB identities.

On a singular heat equation with dynamic boundary conditions

In this paper we analyze a singular heat equation of the form ϑt + �ϑ −1 = f . The singular term ϑ −1 gives rise to very fast diffusion effects. The equation is settled in a smooth bounded domain � ⊂ R 3 and complemented with a general dynamic boundary condition of the form αϑt − β� � ϑ = ∂nϑ −1 ,w here� � is the Laplace-Beltrami operator and α and β are non-negative coefficients (in particular, the homogeneous Neumann case given by α = β = 0 is included). For this problem, we first introduce a suitable weak formulation and prove a related existence result. For more regular initial data, we show that there exists at least one weak solution satisfying instantaneous regularization effects which are uniform with respect to the time variable. In this improved regularity class, uniqueness is also shown to hold.

Inequalities for Power Series with Nonnegative Coefficients via Reverses of Jensen Inequality

Abstract Some inequalities for power series with nonnegative coefficients via a reverse of Jensen inequality obtained by Dragomir and Ionescu in 1994 are given. Applications for some fundamental functions defined by power series are also provided.

DISCRETE HARDY-TYPE INEQUALITY WITH KERNEL

Necessary and sufficient conditions are given for the validity of discrete Hardy's inequality for the sum of two discrete Hardy-type operators with not necessary non-negative coefficients.

Extraction of Endmembers From Hyperspectral Images Using A Weighted Fuzzy Purified-Means Clustering Model

Hyperspectral endmembers are the spectra of pure materials that are responsible for generating the mixed pixels in hyperspectral images (HSIs). Hyperspectral endmember extraction (HEE) is essentially an inverse problem, where the unknown endmembers are inferred from the spectral measurements. Efficient extraction of endmembers in HSI relies on a well-defined generative model that captures key factors in HSI generation process, such as the clustering effect in the spatial domain and the noise heterogeneity effect in the spectral domain. This paper presents a weighted fuzzy purified-means (WFP-means) clustering model for HEE, where the endmembers are modeled as mean vectors of individual classes, and the fractional contributions of individual endmembers, called abundances, are treated as soft class membership. Accordingly, an endmember is estimated as the weighted mean of purified pixels in HSI, while the abundances are estimated as the nonnegative regression coefficients. In contrast to a mixed pixel that consists of multiple endmembers, a “purified pixel” is due to a single endmember. The introduction of the concept of “purified pixels” into the fuzzy clustering model leads to an elegant optimization scheme. Moreover, the proposed model accounts for the noise variance heterogeneity issue, which is essential for achieving unbiased abundance estimation. The proposed method is tested on both simulated and real HSI, in comparison with several other HEE methods. The results demonstrate that the proposed method compares favorably with respect to the referenced methods in terms of both endmember and abundance estimation.

Approximate solution to integral equation with logarithmic kernel of special form

Based on the quadrature formula with non-negative coefficients for integral with a special logarithmic kernel, we construct and substantiate a computational pattern for solving integral equation derived from the boundary-value problem for a function, which is harmonic in the unit disk under the boundary condition of the third kind. We obtain uniform estimates of deviations of the quadrature formula and the approximate solution to integral equation.

On the extreme points of moments sets

Necessary and sufficient conditions for a measure to be an extreme point of the set of measures on a given measurable space with prescribed generalized moments are given, as well as an application to extremal problems over such moment sets; these conditions are expressed in terms of atomic partitions of the measurable space. It is also shown that every such extreme measure can be adequately represented by a linear combination of k Dirac probability measures with nonnegative coefficients, where k is the number of restrictions on moments; moreover, when the measurable space has appropriate topological properties, the phrase “can be adequately represented by” here can be replaced simply by “is”. Applications to specific extremal problems are also given, including an exact lower bound on the exponential moments of truncated random variables, exact lower bounds on generalized moments of the interarrival distribution in queuing systems, and probability measures on product spaces with prescribed generalized marginal moments.

Further irreducibility criteria for polynomials with non-negative coefficients

Further irreducibility criteria for polynomials with non-negative coefficients

Void Fraction Based Two Phase Flow Model of Supersaturated Moist Air

The article deals with the developed of the model of supersaturated moist air flow with condensation. The proposed model is suitable especially for the cases where the rate of change of state variables in the flow field is slow like the flow in natural draft wet-cooling towers and in general the low Mach number flow. Void fraction of gas phase is included in governing equations. Homogeneous equilibrium model, where the two phases are well mixed and have the same velocity, is used. The results of the numerical solutions of the convergent nozzle are presented. The numerical fluxes are based on AUSM + -up scheme and temporal discretization is based on four stage order three explicit strong stability preserving Runge-Kutta method with non-negative coefficients.

Modular properties of characters of the W3 algebra

In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of $W_0^n$ for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single $W_0$ inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.

A Probabilistic Approach to Generalized Zeckendorf Decompositions

Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence. The expansions are finite sequences of nonnegative integer coefficients (satisfying certain technical conditions to guarantee uniqueness of the decomposition) and which can be viewed as analogues of sequences of variable-length words made from some fixed alphabet. In this paper we present a new approach and construction for uniform measures on expansions, identifying them as the distribution of a Markov chain conditioned not to hit a set. This gives a unified approach that allows us to easily recover results on the expansions from analogous results for Markov chains, and in this paper we focus on laws of large numbers, central limit theorems for sums of digits, and statements on gaps (zeros) in expansions. We expect the approach to prove useful in other similar contexts.

Price of Stability in Polynomial Congestion Games

The price of anarchy (PoA) in congestion games has attracted a lot of research over the past decade. This has resulted in a thorough understanding of this concept. In contrast, the price of stability (PoS), which is an equally interesting concept, is much less understood. In this article, we consider congestion games with polynomial cost functions with nonnegative coefficients and maximum degree d . We give matching bounds for the PoS in such games—that is, our technique provides the exact value for any degree d . For linear congestion games, tight bounds were previously known. Those bounds hold even for the more restricted case of dominant equilibria, which may not exist. We give a separation result showing that this is not possible for congestion games with quadratic cost functions—in other words, the PoA for the subclass of games that admit a dominant strategy equilibrium is strictly smaller than the PoS for the general class.

Contractivity-preserving explicit multistep Hermite–Obrechkoff series differential equation solvers

New optimal, contractivity-preserving (CP), explicit, d-derivative, k-step Hermite–Obrechkoff series methods of order p up to $$p=20$$ , denoted by CP HO(d, k, p), with nonnegative coefficients are constructed. These methods are used to solve nonstiff first-order initial value problems $$y'=f(t,y)$$ , $$y(t_0)=y_0$$ . The upper bound $$p_u$$ of order p of HO(d, k, p) can reach, approximately, as high as 2.4 times the number of derivatives d. The stability regions of HO(d, k, p) have generally a good shape and grow with decreasing $$p-d$$ . We, first, note that three selected CP HO methods: 4-derivative 7-step HO of order 13, denoted by HO(4, 7, 13), 5-derivative 6-step HO of order 13, denoted by HO(5, 6, 13), and 9-derivative 2-step HO of order 13, denoted by CMDAHO(13) compare favorably with Adams–Cowell of order 13, denoted by AC(13), in solving standard N-body problems over an interval of 1000 periods on the basis of the relative error of energy as a function of the CPU time. Next, the three HO methods compare positively with AC(13) in solving standard N-body problems on the basis of the growth of relative positional error and relative energy error over 10, 000 periods of integration. Finally, these three methods compare also well with P-stable methods of Cash and Franco et al. on some quasi periodic, second-order linear and nonlinear problems. The coefficients of selected HO methods are listed in the appendix.

Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data.

Modeling the covariance matrix of multivariate longitudinal data is more challenging as compared to its univariate counterpart due to the presence of correlations among multiple responses. The modified Cholesky block decomposition reduces the task of covariance modeling into parsimonious modeling of its two matrix factors: the regression coefficient matrices and the innovation covariance matrices. These parameters are statistically interpretable, however ensuring positive-definiteness of several (innovation) covariance matrices presents itself as a new challenge. We address this problem using a subclass of Anderson's (1973) linear covariance models and model several covariance matrices using linear combinations of known positive-definite basis matrices with unknown non-negative scalar coefficients. A novelty of this approach is that positive-definiteness is guaranteed by construction; it removes a drawback of Anderson's model and hence makes linear covariance models more realistic and viable in practice. Maximum likelihood estimates are computed using a simple iterative majorization-minimization algorithm. The estimators are shown to be asymptotically normal and consistent. Simulation and a data example illustrate the applicability of the proposed method in providing good models for the covariance structure of a multivariate longitudinal data.

Optimized projections for nonnegative linear reconstruction classification

Nonnegative linear reconstruction measure can produce the sparse nonnegative representation coefficients which are concentrated on the similar training samples. The samples with the same class-label are generally more similar than those with different class-labels. Based on this, we develop a nonnegative linear reconstruction based classifiers (NLRC). To enhance the classification performance, we design a feature extractor based on the same decisional rule of NLRC, such that the extracted features are most suitable to NLRC. The proposed feature extractor, nonnegative linear reconstruction projection (NLRP), and NLRC share a common decisional rule, and thus the features extracted by NLRP fit NLRC well in theory. The feasibility and effectiveness of the proposed recognition system are verified on the Yale face database, the AR face database the PolyU finger knuckle print database, and the palmprint database with promising results.

Learning to Detect Anomalies in Surveillance Video

Detecting anomalies in surveillance videos, that is, finding events or objects with low probability of occurrence, is a practical and challenging research topic in computer vision community. In this paper, we put forward a novel unsupervised learning framework for anomaly detection. At feature level, we propose a Sparse Semi-nonnegative Matrix Factorization (SSMF) to learn local patterns at each pixel, and a Histogram of Nonnegative Coefficients (HNC) can be constructed as local feature which is more expressive than previously used features like Histogram of Oriented Gradients (HOG). At model level, we learn a probability model which takes the spatial and temporal contextual information into consideration. Our framework is totally unsupervised requiring no human-labeled training data. With more expressive features and more complicated model, our framework can accurately detect and localize anomalies in surveillance video. We carried out extensive experiments on several benchmark video datasets for anomaly detection, and the results demonstrate the superiority of our framework to state-of-the-art approaches, validating the effectiveness of our framework.