Matrix factorization

Recommender system recommends interesting items to users based on users' past information history. Researchers have been paying attention to improvement of algorithmic performance such as MAE and precision@K. Major techniques such as matrix factorization and learning to rank are optimized based on such evaluation metrics. However, the intrinsic Matthew Effect problem poses great threat to the fairness of the recommender system, and the unfairness problem cannot be resolved by optimization of traditional metrics. In this paper, we propose a novel algorithm that incorporates Matthew Effect reduction with the matrix factorization framework. We demonstrate that our approach can boost the fairness of the algorithm and enhances performance evaluated by traditional metrics.

An irradiation position in the 250 kW Triga reactor was characterized for instrumental neutron activation analysis of chlorine in an iron oxide matrix. Factors that affect the accuracy of the determination include variations in the reactor neutron spectrum and ...

We study the matrix factorization problem associated with an SO(2) spinning top by using the algebro-geometric approach. We derive the explicit expressions in terms of Riemann theta functions and discus some related problems including a non-compact extension and the case when the Lax matrix contains higher-order powers of the spectral parameter.

Matrix computations are both fundamental and ubiquitous in computational science and its vast application areas. Along with the development of more advanced computer systems with complex memory hierarchies, there is a continuing demand for new algorithms and library software that efficiently utilize and adapt to new architecture features. This article reviews and details some of the recent advances made by applying the paradigm of recursion to dense matrix computations on today's memory-tiered computer systems. Recursion allows for efficient utilization of a memory hierarchy and generalizes existing fixed blocking by introducing automatic variable blocking that has the potential of matching every level of a deep memory hierarchy. Novel recursive blocked algorithms offer new ways to compute factorizations such as Cholesky and QR and to solve matrix equations. In fact, the whole gamut of existing dense linear algebra factorization is beginning to be reexamined in view of the recursive paradigm. Use of recursion has led to using new hybrid data structures and optimized superscalar kernels. The results we survey include new algorithms and library software implementations for level 3 kernels, matrix factorizations, and the solution of general systems of linear equations and several common matrix equations. The software implementations we survey are robust and show impressive performance on today's high performance computing systems.

We consider the quark-antiquark Green's function in the Schwinger Model with instanton contributions taken into account. Thanks to the fact that this function may analytically be found, we draw out singular terms, which arise due to the formation of the bound state in the theorythe massive Schwinger boson. The principal term has a pole character. The residue in this pole contains contributions from various instanton sectors: 0, ±1, ±2. It is shown, that the nonzero ones change the factorizability property. The formula for the residue is compared to the Bethe-Salpeter wave function found as a field amplitude. Next, it is demonstrated, that apart from polar part, there appears in the Green's function also the weak branch point singularity of the logarithmic and dilogarithmic nature. These results are not in variance with the universally adopted S-matrix factorization.

We prove that the finitistic dimension conjecture, the Gorenstein Symmetry Conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for artin algebras which can be realized as endomorphism algebras of modules over representation-finite algebras. Note it is a question whether or not all artin algebras have such realizations. It was also shown that if every quasi-hereditary algebras has a

This paper describes a new, physically interpretable, fully automatic algorithm for removal of tissue autofluorescence (AF) from fluorescence microscopy images, by non-negative matrix factorization. Measurement of signal intensities from the concentration of certain fluorescent reporter molecules at each location within a sample of biological tissue is confounded by fluorescence produced by the tissue itself (autofluorescence). Spectral mixing models use mixing coefficients to specify how much fluorescence from each source is present and unmixing algorithms separate the two fluorescent sources. Current spectral unmixing methods for AF removal often require a priori knowledge of mixing coefficients. Those which do not, such as principal component analysis, generate negative mixing coefficients that are not physically meaningful. Non-negative matrix factorization constrains mixing coefficients to be non-negative, and has been used for spectral unmixing, but not AF removal. This paper describes a novel non-negative matrix factorization algorithm which separates fluorescent images into true signal and AF components utilizing an estimate of the dark current. We also present a test-bed, based on fluorescent beads, to compare the performance of different AF removal algorithms. Our algorithm out-performed previous state of the art on validation images.

We consider three different ways of algorithmization of the Janashia-Lagvilava spectral factorization method. The first algorithm is faster than the second one, however, it is only suitable for matrices of low dimension. The second algorithm, on the other hand, can be applied to matrices of substantially larger dimension. The third algorithm is a superfast implementation of the method, but only works in the polynomial case under the additional restriction that the zeros of the determinant are not too close to the boundary. All three algorithms fully utilize the advantage of the method which carries out spectral factorization of leading principal submatrices step-by-step. The corresponding results of numerical simulations are reported in order to describe the characteristic features of each algorithm and compare them to other existing algorithms.

The usefulness of Collaborative filtering recommender system is affected by its ability to capture users' preference changes on the recommended items during recommendation process. This makes it easy for the system to satisfy users' interest over time providing good and quality recommendations. The Existing system studied fails to solicit for user inputs on the recommended items and it is also unable to incorporate users' preference changes with time which lead to poor quality recommendations. In this work, an Enhanced Movie Recommender system that recommends movies to users is presented to improve the quality of recommendations. The system solicits for users' inputs to create a user profiles. It then incorporates a set of new features (such as age and genre) to be able to predict user's preference changes with time. This enabled it to recommend movies to the users based on users new preferences. The experimental study conducted on Netflix and Movielens datasets ...

Matrix factorization methods are now widely used to recover 3D structure from 2D projections [1]. In practice, the observation matrix to be factored out has missing data, due to the limited field of view and the occlusion that occur in real video sequences. In opposition to the optimality of the SVD to factor out matrices without missing entries, the optimal solution for the missing data case is not known. In reference [2] we introduced suboptimal algorithms that proved to be more efficient than previous approaches to the factorization of matrices with missing data. In this paper we make an experimental analysis of the algorithms of [2] and demonstrate their performance in virtual reality and video compression applications. We conclude that these algorithms are: i) adequate to the amount of missing entries that may occur when processing real videos; ii) robust to the typical level of noise in practical applications; and iii) computationally as simple as the factorization of matrices without missing entries.

We present computational methods to extract and model different joints of a generic subject, in an automatic way. The input for our methods is simply a set of trajectories of 3D points, obtained from a motion capture system (MOCAP). Due to the piecewise rigidity of the skeleton, these trajectories belong to different subspaces (of the space of all possible trajectories). We use this knowledge to derive computationally simple algorithms that are able to infer joint properties from the trajectories of the 3D points. This model-free approach enables analyzing directly specific subjects, rather than requiring user-defined a priori models of the skeleton. Such data-driven models are useful in the analysis of human walk and the evaluation of joint stress for pathology detection. Also, the customized skeleton models, together with physiological muscular information, allow to accurately analyze high level performances in sports.

Let K be a field and let / 6 K[[xι,x 2 , . ,x r ]] and g 6 #[[2/1,2/2, , y s ]] be non-zero and non-invertible elements. If X (resp. Y) is a matrix factorization of / (resp. g), then we can construct the matrix factorization X §> Y of /-+• g over K [[xiyX2, -> ,x r ,yi,y2, -,ys]]i which we call the tensor product of X and y. After showing several general properties of tensor products, we will prove theorems which give bounds for the number of indecomposable components in the direct decomposition of X < §> Y.

Through this research the following research objectives should be met: * Present spectral factorization of invertible non-scalar matrices ([24] and ) in order to place the current investigation concerning factorization in a broader context. * Present a unified and coherent treatment of the factorization of singular matrices as contained in the works by Wu [29], Laffey [17] and Sourour [26]. * Investigate applications of spectral factorization to invertible matrices i.e. unipotent, positive-definite, commutator, involutory and Hermitian factorization as found in [24], [17], [18] and [26]. * Investigate the conditions under which an invertible matrix can be expressed as a product of two involutions as found in [13]. * Investigate applications of spectral factorization on singular matrices i.e. positive-semidefinite factorization as found in [26]. * The UNISA library catalogue * E-journals * MathSciNet * arXiv () * Wikipedia * JSTOR * Cambridge Journal Online * ScienceDirect

We generalize the Khovanov–Rozansky cohomology theory for n = 2 by using a homogeneous potential that depends on two parameters, to obtain the universal Khovanov-Rozansky sl(2)-link cohomology. This theory is equivalent to the universal sl(2)-link cohomology using foams, after tensoring both theories with appropriate rings.

Collaborative filtering is a popular method for personalizing product recommendations. Maximum Margin Matrix Factorization (MMMF) has been proposed as one successful learning approach to this task and has been recently extended to structured ranking losses. In this paper we discuss a number of extensions to MMMF by introducing offset terms, item dependent regularization and a graph kernel on the recommender graph. We show equivalence between graph kernels and the recent MMMF extensions by Mnih and Salakhutdinov (Advances in Neural Information Processing Systems 20, 2008). Experimental evaluation of the introduced extensions show improved performance over the original MMMF formulation.

In this paper, we consider collaborative filtering as a ranking problem. We present a method which uses Maximum Margin Matrix Factorization and optimizes ranking instead of rating. We employ structured output prediction to optimize directly for ranking scores. Experimental results show that our method gives very good ranking scores and scales well on collaborative filtering tasks.

In this article we develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, we give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, we prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. Our approach is illustrated on the case of x, y, z /(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singularities leads to a new class of problems of linear algebra, which we call representations of decorated bunches of chains. We prove that these matrix problems have tame representation type and describe the underlying canonical forms. Contents 1. Introduction, motivation and historical remarks 2. Generalities on maximal Cohen-Macaulay modules 2.1. Maximal Cohen-Macaulay modules over surface singularities 2.2. On the category CM lf (A) 3. Main construction 4. Serre quotients and proof of Main Theorem 5. Maximal Cohen-Macaulay modules over x, y, z /(x 2 + y 3 − xyz) 6. Representations of decorated bunches of chains-I 6.1. Notation 6.2. Bimodule problems 6.3. Definition of a decorated bunch of chains 6.4. Matrix description of the category Rep(X) 6.5. Strings and Bands 7. Representations of decorated bunches of chains-II 7.1. Idea of the proof 7.2. Reduction Cases 7.3. Decorated Kronecker problem 8. Maximal Cohen-Macaulay modules over degenerate cusps-I 8.1. Maximal Cohen-Macaulay modules over x, y, z /(xyz) 8.2. Maximal Cohen-Macaulay modules over x, y, u, v /(xy, uv) 8.3. Maximal Cohen-Macaulay modules over x, y, z, u, v /(xz, xu, yu, yv, zv) 9. Singularities obtained by gluing cyclic quotient singularities 9.1. Non-isolated surface singularities obtained by gluing normal rings 9.2. Generalities about cyclic quotient singularities 9.3. Degenerate cusps and their basic properties 2. Generalities on maximal Cohen-Macaulay modules Let (A, m) be a Noetherian local ring, = A/m its residue field and d = kr. dim(A) its Krull dimension. Throughout the paper A−mod denotes the category of Noetherian (i.e. finitely generated) A-modules, whereas A−Mod stands for the category of all A-modules, Q = Q(A) is the total ring of fractions of A and P is the set of prime ideals of height 1. Definition 2.1. A Noetherian A-module M is called maximal Cohen-Macaulay if Ext i A (, M) = 0 for all 0 ≤ i < d. 2.1. Maximal Cohen-Macaulay modules over surface singularities. In this article we focus on the study of maximal Cohen-Macaulay modules over Noetherian rings of Krull dimension two, also called surface singularities. This case is actually rather special because of the following well-known lemma. Lemma 2.2. Let (A, m) be a surface singularity, N be a maximal Cohen-Macaulay Amodule and M a Noetherian A-module. Then the A-module Hom A (M, N) is maximal Cohen-Macaulay. Proof. From a free presentation A n ϕ → A m → M → 0 of M we obtain an exact sequence: 0 −→ Hom A (M, N) −→ N m ϕ * −→ N n −→ coker(ϕ *) −→ 0. Proof. From the canonical short exact sequence 0 → tor(M) → M → M/ tor(M) → 0 we get the isomorphism M/ tor(M) ∨ → M ∨. Since M/ tor(M) is a maximal Cohen-Macaulay A-module and ∨ is a dualizing functor, we get two natural isomorphisms M/ tor(M)

This is a survey article about properties of Cohen-Macaulay modules over surface singularities. We discuss properties of the Macaulayfication functor, reflexive modules over simple, quotient and minimally elliptic singularities, geometric and algebraic McKay Correspondence. Finally, we describe matrix factorizations corresponding to indecomposable Cohen-Macaulay modules over the non-isolated singularities A∞ and D∞.

This is a survey article about properties of Cohen-Macaulay modules over surface singularities. We discuss properties of the Macaulayfication functor, reflexive modules over simple, quotient and minimally elliptic singularities, geometric and algebraic McKay Correspondence. Finally, we describe matrix factorizations corresponding to indecomposable Cohen-Macaulay modules over the non-isolated singularities A∞ and D∞. 2. Generalities about Cohen-Macaulay modules Let (A, m) be a Noetherian local ring, k = A/m its residue field and d = kr. dim(A) its Krull dimension. Throughout the paper A − mod denotes the category of Noetherian (i.e. finitely generated) A-modules, whereas A − Mod stands for the category of all A-modules. In this section we collect some basic facts about Cohen-Macaulay modules. Definition 2.1. For a Noetherian A-module M its depth is defined as depth A (M) = inf i≥0 i Ext i A (k, M) = 0. Lemma 2.2. Let M be a Noetherian A-module. Then we have: depth A (M) ≤ dim(M) := kr. dim A/ ann(M) , in particular, the depth of a Noetherian module is always finite. Moreover, if I = ann A (M) then depth A (M) = depth A/I (M). Hence, in what follows, we shall write depth(M) for the depth of M , omitting the subscript.

The Barzilai-Borwein method offers efficient step sizes for large-scale unconstrained optimization problems. However, it may not guarantee global convergence for nonquadratic objective functions. Simulated annealingbased on Barzilai-Borwein (SABB) method addresses this issue by incorporating a simulated annealing rule. This work proposes a novel step-size strategy for the SABB method, referred to as the SABBm method. Furthermore, we introduce two stabilized variants: SABBstab and SABBmstab. SABBstab combines a simulated annealing rule with a stabilization step to ensure convergence. SABBmstab builds upon SABBstab,

In this paper the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the decomposition of the main hypothesis into two sub-hypotheses, the likelihood ratio test statistic is easily obtained as well as its exact moments. Its exact distribution is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes. A real data example is studied and a simulation is also conducted.

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning 1 regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parameter when data arrives sequentially and the underlying distribution is non-stationary (implying the choice of optimal regularization parameter is itself time-varying). We propose a framework through which to infer an adaptive regularization parameter. Our approach employs an 1 penalty constraint where the corresponding sparsity parameter is iteratively updated via stochastic gradient descent. This serves to reformulate the choice of regularization parameter in a principled framework for online learning. The proposed method is derived for linear regression and subsequently extended to generalized linear models. We validate our approach using simulated and real datasets and present an application to a neuroimaging dataset.

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning $\ell_1$ regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parameter when data arrives sequentially and the underlying distribution is non-stationary (implying the choice of optimal regularization parameter is itself time-varying). We propose a novel framework through which to infer an adaptive regularization parameter. Our approach employs an $\ell_1$ penalty constraint where the corresponding sparsity parameter is iteratively updated via stochastic gradient descent. This serves to reformulate the choice of regularization parameter in a principled framework for online learning and allows for the derivation of convergence guarantees in a non-stochasti...

In the context of adopting the competency-based approach (CBA) as a new teaching methodology in sub-Saharan countries, and particularly in Côte d'Ivoire, the development of learning content that is aligned with the economic, socio-cultural, and scientific needs of society is of paramount importance. Educational experts have therefore proposed competencies and associated tasks for educational programs. However, these learning contents often face issues of task redundancy. The present paper aims to address this problem by proposing a hybrid approach to educational item clustering, combining weighted multi-relational matrix factorization (WMRMF) and Cohen's Kappa (Sk) techniques (Sk-WMRMF). This approach takes into account not only student performance and achievements but also a novel reflexive relationship, "tasks-require-tasks". To evaluate the Sk-WMRMF approach, we conducted a survey among students in general secondary schools in Côte d'Ivoire. With an accepted task redundancy threshold of 0.185, an RMSE score of 0.198, and an improvement rate of 90.47% in the "tasks-skills" mapping, the results demonstrate that Sk-WMRMF enhances the elaboration of "task-skill" mappings. This not only improves learning content but also facilitates the updating of curricula in accordance with the CBA approach.

The recommendation system plays an essential role in the modern era and used by many prestigious applications. The recommendation system has made the collection of apps, creating a global village, and growth for abundant information. This paper represents the overview of Approaches and techniques generated in the Collaborative Filtering based recommendation system [1]. The recommendation system derived into Collaborative Filtering, Content-based, and hybrid-based approaches. This paper classifies collaborative filtering using various approaches like matrix factorization, user-based recommendation, item-based recommendation. This survey also tells the road map for research in this area.

It is well-known that the Tucker decomposition of a multi-dimensional tensor is not unique, because its factors are subject to rotation ambiguities similar to matrix factorization models. Inspired by the recent success in the identifiability of nonnegative matrix factorization, the goal of this work is to achieve similar results for nonnegative Tucker decomposition (NTD). We propose to add a matrix volume regularization as the identifiability criterion, and show that NTD is indeed identifiable if all of the Tucker factors satisfy the sufficiently scattered condition. We then derive an algorithm to solve the modified formulation of NTD that minimizes the generalized Kullback-Leibler divergence of the approximation plus the proposed matrix volume regularization. Numerical experiments show the effectiveness of the proposed method.

Most efficient algorithms for rotating 2D images are based on the succession of three translations, following the lines, then the columns and the lines of the image again (LCL). These translations result from the decomposition of the rotation matrix into a product of an upper triangular matrix, a lower triangular matrix and an upper triangular matrix (ULU). We have shown in this paper that the decomposition of the rotation matrix is not unique and have separated it into a product of a lower triangular matrix, an upper triangular matrix and a lower triangular matrix (LUL). This new decomposition led to a new algorithm based on a succession of three translations following the columns, then the lines and the columns of the images again (CLC). Statistical analysis of experimental results showed that the computational complexity of images rotation does not depend significantly (p>0.05) on the factorization ULU or LUL, whereas the precision depends on it significantly (p<0.05). Each of the two algorithms of rotation is more precise for certain images and for certain angles. The method can be generalized in a case of 3D image rotation using the Euler angles.

One of the methods to obtain Frobenius manifold structures is via DGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra construction. An important problem is how to identify Frobenius manifold structures constructed from two different DGBV algebras. For DGBV algebras with suitable conditions, we show the functorial property of a construction of deformations of the multiplicative structures of their cohomology. In particular, we show that quasi-isomorphic DGBV algebras yield identifiable Frobenius manifold structures.

Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. One of the main issues of knowledge discovery is knowledge reduction. The objective of this paper is to investigate the knowledge reduction in FCA and propose a method based on Non-Negative Matrix Factorization (NMF) for addressing the issue. Experiments on real world and benchmark datasets offer the evidence for the performance of the proposed method. c

We study the moduli and determine a homotopy type of the space of all generalized Morse functions on d-manifolds for given d. This moduli space is closely connected to the moduli space of all Morse functions studied in the paper math.AT/0212321, and the classifying space of the corresponding cobordism category.

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Agricultural burning has been subject to intense debate in Eastern Washington. Rural communities are concerned about health impacts related to smoke exposure from field burning. However, the short-duration excursions of smoke often do not violate air quality standards at locations where air quality monitors are situated. The purpose of this study was to characterize the air quality in Pullman, WA during the fall 2002 prescribed field burning season, as part of a larger study conducted to examine community exposure to agricultural burning smoke and the related short-term health effects. Data collected included continuous PM 2.5, PM 10 , CO 2 , nitrogen oxides, and 12-h integrated PM 2.5 , OC, EC, and levoglucosan (a biomass burning marker). Four episodes were defined when three consecutive 30-min PM 2.5 averages exceeded 40 mg m À3 . Two source-receptor models; the chemical mass balance model (CMB) and positive matrix factorization (PMF) were used to estimate smoke intrusion from regional agricultural burning. During this study, the average PM 2.5 , OC, and EC were similar during the daytime and nighttime, while LG was twice as high during the night. The CMB results showed major contributions of PM 2.5 from soil (38%), vegetative burning (35%), and sulfate aerosol (20%), and much less from vehicles (2%) and cooking (1%). The 3-source profiles generated by PMF were consistent with those selected for CMB modeling. The PM 2.5 estimates from these two models were highly correlated for individual sources. The LG, NO x , CO 2 , OC, and apportioned PM 2.5 from vegetative burning and soil were higher during the episodes than during non-episode days, while EC and PM 2.5 from secondary sulfate, vehicles, and cooking sources were similar throughout the study. We characterized the episodes of agricultural field burning with elevated LG, OC, and biomass burning contribution to PM 2.5 .

During must fermentation by Saccharomyces cerevisiae strains thousands of volatile aroma compounds are formed. The objective of the present work was to adapt computational approaches to analyze pheno-metabolomic diversity of a S. cerevisiae strain collection with different origins. Phenotypic and genetic characterization together with individual must fermentations were performed, and metabolites relevant to aromatic profiles were determined. Experimental results were projected onto a common coordinates system, revealing 17 statistical-relevant multi-dimensional modules, combining sets of mostcorrelated features of noteworthy biological importance. The present method allowed, as a breakthrough, to combine genetic, phenotypic and metabolomic data, which has not been possible so far due to difficulties in comparing different types of data. Therefore, the proposed computational approach revealed as successful to shed light into the holistic characterization of S. cerevisiae pheno-metabolome in must fermentative conditions. This will allow the identification of combined relevant features with application in selection of good winemaking strains.

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial role in enabling and improving data science computations with many new developments being fueled by the availability of data and computing resources.

Let C be a smooth projective curve of genus g ≥ 2 and let N be the moduli space of stable rank 2 vector bundles on C of odd degree. We construct a semi-orthogonal decomposition of the bounded derived category of N conjectured by Narasimhan. It has two blocks for each i-th symmetric power of C for i = 0, .., g − 2 and one block for the (g − 1)-st symmetric power. We conjecture that the subcategory generated by our blocks has a trivial semiorthogonal complement, proving the full Narasimhan conjecture. Our proof is based on an analysis of wall-crossing between moduli spaces of stable pairs, combining classical vector bundles techniques with the method of windows.

The notion of Ann-categories is a categorification of the ring structure. Regular Ann-categories were classified by Shukla algebraic cohomology. In this article, we state and prove the precise theorem on classification for the general case due to Mac Lane cohomology for rings. And an application for classification problem of ring extensions is also introduced.

Particulate matter less than 2.5 microns in diameter (PM 2.5) has been linked with a wide range of adverse health effects. Determination of the sources of PM 2.5 most responsible for these health effects could lead to improved understanding of the mechanisms of such effects and more targeted regulation. This has provided the impetus for the Denver Aerosol Sources and Health (DASH) study, a multi-year source apportionment and health effects study relying on detailed inorganic and organic PM 2.5 speciation measurements. In this study, PM 2.5 source apportionment is performed by coupling positive matrix factorization (PMF) with daily speciated PM 2.5 measurements including inorganic ions, elemental carbon (EC) and organic carbon (OC), and organic molecular markers. A qualitative comparison is made between two models, PMF2 and ME2, commonly used for solving the PMF problem. Many previous studies have incorporated chemical mass balance (CMB) for organic molecular marker source apportionment on limited data sets, but the DASH data set is large enough to use multivariate factor analysis techniques such as PMF.

Infrastructure vs. Mobile Sensing-The Evolving Landscape There has been a surge of enthusiasm around the paradigm of participatory urban sensing, which views a citizen-centric distributed and mobile sensing substrate as one of the most promising ways to gather various types of urban information, such as environmental parameters & pollution levels, traffic congestion, popularity of events at various public spaces, etc. In parallel, there have also been significant recent deployments, perhaps less heralded, of infrastructure or ambient sensors, especially in public spaces, such as malls, airports and stadiums. The panel seeks to understand the limits of each of these individual sensing paradigms observed in practice, due to challenges such as resource limitations, privacy, user interfaces and data quality. It will also discuss how the combined capabilities of participatory and infrastructure sensing can be effectively harnessed, for novel urban computing applications.

A description of Cohen-Macaulay modules over cusp surface singularities and over unimodule hypersurface singularities of type T is given. It is proved that among minimally elliptic singularities and their quotients only simple elliptic and cusps are tame, all others are wild (with respect to the classification of Cohen-Macaulay modules).

We have initiated a structural genomics project based on selected protein families, with the representatives for structural studies obtained from the genome of E. coli. A total of 160 genes have been cloned to date, with 126 successfully overexpressing soluble protein with at least one fusion system. We are currently applying robotics methods allowing cloning in an automated manner. Target genes have been cloned as N-terminal fusions with GST, (His)6, or (His)8 affinity tags. Over 60 proteins have so far been purified to homogeneity. Purified proteins are further characterized for homogeneity and suitable solution properties using a combination of dynamic light scattering and electrophoretic methods. Purified protein samples are screened for initial crystallization conditions in 96-well format using a sparse-matrix approach. A specialized database has been developed to follow the progress of various proteins and to store all relevant experimental data (http://sgen.bri.nrc.ca/bsgi). Web-based software for displaying and searching the information from this local database and for tracking deposited structures in the PDB as well as the progress of other structural genomics projects has been developed. To date, crystals have been obtained for 37 of the purified proteins. of these, diffraction quality crystals were obtained for 16 proteins. Using SeMet-substituted proteins we have determined the structures of 13 of these proteins by MAD phasing. Structures determined include 2amino-3-ketobutyrate CoA ligase, part of the threonine salvage pathway, MoeA protein, involved in molydopterin biosynthesis, histidinol phosphate aminotransferase and L-histidinol dehydrogenase, two enzymes associated with histidine biosynthesis, and RsuA, a 16S rRNA psuedouridine synthase.

Optimization algorithms typically require the solution of many systems of linear equations Bkyk b,. When large numbers of variables or constraints are present, these linear systems could account for much of the total computation time. Both direct and iterative equation solvers are needed in practice. Unfortunately, most of the off-the-shelf solvers are designed for single systems, whereas optimization problems give rise to hundreds or thousands of systems. To avoid refactorization, or to speed the convergence of an iterative method, it is essential to note that B is related to Bk_ 1. We review various sparse matrices that arise in optimization, and discuss compromises that are currently being made in dealing with them. Since significant advances continue to be made with single-system solvers, we give special attention to methods that allow such solvers to be used repeatedly on a sequence of modified systems (e.g., the product-form update; use of the Schur complement). The speed of factorizing a matrix then becomes relatively less important than the efficiency of subsequent solves with very many right-hand sides. At the same time, we hope that future improvements to linear-equation software will be oriented more specifically to the case of related matrices B k.

When describing active-set methods for linearly constrained optimization, it is often convenient to treat all constraints in a uniform manner. However, in many problems the linear constraints include simple bounds on the variables as well as general constraints. Special treatment of bound constraints in the implementation of a null-space active-set method yields significant advantages in computational effort and storage requirements. In this paper, we describe a particular implementation of the constraint-related steps of a null-space active-set method when the constraint matrix is dense and bounds are treated separately. These steps involve updates to the TQ factorization of the working set of constraints and the Cholesky factorization of the projected Hessian (or Hessian approximation).

Digital super-resolution refers to computational techniques that exploit the generalized sampling theorem to extend image resolution beyond the pixel spacing of the detector, but not beyond the optical limit (Nyquist spatial frequency) of the lens. The approach to digital super-resolution taken by the PERIODIC multi-lenslet camera project is to solve a forward model which describes the effects of sub-pixel shifts, optical blur, and detector sampling as a product of matrix factors. The associated system matrix is often ill-conditioned, and convergence of iterative methods to solve for the high-resolution image may be slow. We investigate the use of pupil phase encoding in a multi-lenslet camera system as a means to physically precondition and regularize the computational super-resolution problem. This is an integrated optical-digital approach that has been previously demonstrated with cubic type and pseudo-random phase elements. Traditional multi-frame phase diversity for imaging through atmospheric turbulence uses a known smooth phase perturbation to help recover a time series of point spread functions corresponding to random phase errors. In the context of a multi-lenslet camera system, a known pseudo-random or cubic phase error may be used to help recover an array of unknown point spread functions corresponding to manufacturing and focus variations among the lenslets. * We suspect this to be a result of using CGLS with a constant, instead of optimal, number of iterations.

In today's world, people are flooded with a lot of information, and no. of choices are overwhelming. For example, in any online shopping platform such as Amazon, if we search for a particular product, thousands of results appear and it becomes very difficult to select an item from vast pool of options. The growth of digital information and the number of users over the Internet has created a potential problem of information overload. The recommendation system solves this problem by searching through a large volume of data and providing personalized content to the user. This paper describes the introduction to the recommendation system, its three main types-content-based filtering, collaborative filtering, and hybrid filtering, and addresses the data sparsity problem. This paper proposed a collaborative filtering approach using matrix factorization to mitigate the sparsity problem and improve the quality of the recommendation.

For finite Lie algebras, it is shown that characters can be defined first for Weyl orbits and then for irreducible representations. For $A_N$ Lie algebras, weight multiplicities can then be calculated by only stating that characters are equivalent to Schur functions. This also means that to calculate characters there is no need to sum over Weyl groups. The compatibility with

Constructions are given of Noetherian maximal orders that are finitely presented algebras over a field K, defined by monomial relations. In order to do this, it is shown that the underlying homogeneous information determines the algebraic structure of the algebra. So, it is natural to consider such algebras as semigroup algebras K[S] and to investigate the structure of the monoid S. The relationship between the prime ideals of the algebra and those of the monoid S is one of the main tools. Results analogous to fundamental facts known for the prime spectrum of algebras graded by a finite group are obtained. This is then applied to characterize a large class of prime Noetherian maximal orders that satisfy a polynomial identity, based on a special class of submonoids of polycyclic-by-finite groups. The main results are illustrated with new constructions of concrete classes of finitely presented algebras of this type.

Linked Open Data cloud is being conceived and published to improve the usability and performance of various applications including Recommender System. While most of the existing works incorporate semantic web information into recommendation system by exploiting content based method, we introduced a collaborative filtering based semantic dual probabilistic matrix factorization approach. We have used semantic item features, generated in an unsupervised manner and incorporated them into user-item preference matrix for recommendation by co-factoring two matrices. To mitigate the difficulty of high dimensionality, sparsity and possible noise in the semantic item-property matrix, Singular Value Decomposition was used as an unsupervised preprocessing step. To evaluate our new approach, RMSE are compared with 10 state-of-art algorithms especially Probabilistic Matrix Factorization which our method is based on, Precision is also compared between our method and PMF. Although similar dual matrix factorization approaches exist but most of them deal with very small item property matrix with abundant entries while our approach introduced a high dimensional and sparse item property matrix through an unsupervised automatic way which also alleviate the efforts to create those item property matrices.