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A criterion is given for the Lie algebra of infinitesimal holomorphic automorphisms of the direct product of two germs of real analytic generic CR manifolds to be equal to the direct sum of the algebras of the factors. In particular, this equality holds if the algebra of the direct product is finite-dimensional (for example, in the case of the product of holomorphically nondegenerate germs of finite Bloom–Graham type). The notion of the sum of Bloom–Graham types is introduced. It is shown that the type of a direct product is equal to the sum of the types of factors. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine the procedural relationship between the psychosocial factors of mathematics learning such as attitudes, motivation and satisfaction and academic achievement in redesigned college-level algebra course sections. Evaluation reports on the redesigned courses show that they have achieved a level of academic achievement equivalent to and / or better than traditionally taught courses, including university-level mathematics introductory courses. However, the reasons for equal or higher academic achievement are not fully documented in the literature. In this context, the academic success of the university-level algebra course designed using the Emporium model was chosen as the focus of this research study. In this manuscript, in addition to the psychosocial factors of mathematics learning, mathematics achievement in the context of university algebra was also examined. The data related to the psychosocial variables were obtained from a likert scale developed by the researcher, and academic achievement data from the final exam grades of the algebra course. Hierarchical multiple regression analysis was used to analyze the collected data. The results of the study indicaed that satisfaction from mathematics teaching was the only significant predictor of mathematics achievement in college-level algebra; learner motivation and satisfaction were determined as important predictors of attitude towards mathematics, and attitude towards mathematics played the role of mediating variable in the relationship between student satisfaction and motivation in introductory level redesigned university algebra courses. [ABSTRACT FROM AUTHOR]

In real‐world applications, large amounts of data from multiple sources come in the form of streams. This makes multi‐view feature learning cost much time when new instances rise incrementally. Dealing with these growing multi‐view data becomes a challenging problem. Some single‐view methods focus on processing the data dynamically, but they are not suitable for multi‐view data. Some online multi‐view methods are proposed to tackle it, but they ignore the influence of uncorrelated items in each view. Therefore, in this study, the authors propose a new algorithm, called Incremental Multi‐view Correlated Feature Learning (IMCFL) based on non‐negative matrix factorisation, to learn the common feature across views. By separating uncorrelated items of new instances and constructing incremental joint learning of correlated and uncorrelated features, the proposed IMCFL can eliminate the influence of uncorrelated information in the individual view and improve the effectiveness of incremental multi‐view common feature learning. Extensive experiments on real‐world datasets confirm its superiority by comparing it with other state‐of‐the‐art incremental and non‐incremental methods. [ABSTRACT FROM AUTHOR]

Let (g,[p]) be a restricted Lie algebra over an algebraically closed field k of characteristic p ≥ 3. Motivated by the behavior of geometric invariants of the so-called (g,[p])-modules of constant j-rank (j ∈ {1, . . . , p−1}), we study the projective variety E(2,g) of two-dimensional elementary abelian subalgebras. If p ≥ 5, then the topological space E(2,g/C(g)), associated to the factor algebra of g by its center C(g), is shown to be connected. We give applications concerning categories of (g,[p])-modules of constant j-rank and certain invariants, called j-degrees. [ABSTRACT FROM AUTHOR]

Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in the overhang parts of the classical radial-flux machines as well as in the main parts of the axial-flux machines. The calculation of the 3-D fields originating from these bodies is demanding. The 3-D FEA suffers from high computational burden as well as no knowledge of the field origin. Analytic techniques involve the use of elliptic integrals and complex numbers for numerical evaluation, which makes them significantly slower than the 3-D FEA. In this article, a new analytical technique is proposed to speed up the computation by a factor of 20 for the global magnetic field created by a generic magnetized body by removing complex numbers and reducing the analytic equations significantly without any loss of precision. As a result, it can compete with the conventional 3-D FEA. In addition, integral methods may contribute to the wider use of parallel processing techniques. The original expressions for the vector potential are also provided, which has its own benefits and applications. Finally, the showcased magnetized body is assessed against 3-D FEA and discussed in terms of practical applications. [ABSTRACT FROM AUTHOR]

We shall give some results for an integer divisible by its unitary totient. [ABSTRACT FROM AUTHOR]

Distinguishing certain and uncertain information is of crucial importance both in the scientific field in the strict sense and in the popular scientific domain. In this paper, by adopting an epistemic stance perspective on certainty and uncertainty, and a mixed procedure of analysis, which combines a bottom-up and a top-down approach, we perform a comparative study (both qualitative and quantitative) of the uncertainty linguistic markers (verbs, non-verbs, modal verbs, conditional clauses, uncertain questions, epistemic future) and their scope in three different corpora: a historical corpus of 80 biomedical articles from the British Medical Journal (BMJ) 1840–2007; a corpus of 12 biomedical articles from BMJ 2013, and a contemporary corpus of 12 scientific popular articles from Discover 2013. The variables under observation are time, structure (IMRaD vs no-IMRaD) and genre (scientific vs popular articles). We apply the Generalized Linear Models analysis in order to test whether there are statistically significant differences (1) in the amount of uncertainty among the different corpora, and (2) in the categories of uncertainty markers used by writers. The results of our analysis reveal that (1) in all corpora, the percentages of uncertainty are always much lower than that of certainty; (2) uncertainty progressively diminishes over time in biomedical articles (in conjunction with their structural changes–IMRaD–and to the increase of the BMJ Impact Factor); and (3) uncertainty is slightly higher in scientific popular articles (Discover 2013) as compared to the contemporary corpus of scientific articles (BMJ 2013). Nevertheless, in all corpora, modal verbs are the most used uncertainty markers. These results suggest that not only do scientific writers prefer to communicate their uncertainty with markers of possibility rather than those of subjectivity but also that science journalists prefer using a third-person subject followed by modal verbs rather than a first-person subject followed by mental verbs such as think or believe. [ABSTRACT FROM AUTHOR]

We present the High-Elective Resolution Modelling Emission System version 3 (HERMESv3), an open source, parallel and stand-alone multi-scale atmospheric emission modelling framework that computes gaseous and aerosol emissions for use in atmospheric chemistry models. HERMESv3 is coded in Python and consists of a global_regional module and a bottom_up module that can be either combined or executed separately. In this contribution (Part 1) we describe the global_regional module, a customizable emission processing system that calculates emissions from different sources, regions and pollutants on a user-specified global or regional grid. The user can flexibly define combinations of existing up-to-date global and regional emission inventories and apply country-specific scaling factors and masks. Each emission inventory is individually processed using user-defined vertical, temporal and speciation profiles that allow obtaining emission outputs compatible with multiple chemical mechanisms (e.g. Carbon-Bond 05). The selection and combination of emission inventories and databases is done through detailed configuration files providing the user with a widely applicable framework for designing, choosing and adjusting the emission modelling experiment without modifying the HERMESv3 source code. The generated emission fields have been successfully tested in different atmospheric chemistry models (i.e. CMAQ, WRF-Chem and NMMB-MONARCH) at multiple spatial and temporal resolutions. In a companion article (Part 2; Guevara et al., 2019) we describe the bottom_up module, which estimates emissions at the source level (e.g. road link) combining state-of-the-art bottom–up methods with local activity and emission factors. [ABSTRACT FROM AUTHOR]

Abstract Given a finite dimensional algebra over a perfect field the text introduces covering functors over the mesh category of any modulated Auslander–Reiten component of the algebra. This is applied to study the composition of irreducible morphisms between indecomposable modules in relation with the powers of the radical of the module category. [ABSTRACT FROM AUTHOR]

On the background of structural changes recorded in the past ten years and the micro and macro-prudential policy mix, the Romanian banking sector has seen an improvement of the main financial and prudential indicators. At the same time, it was emphasized the linkage between the risk associated with the banking sector and the related government sector. The regulatory system in the banking field has experienced significant changes, including for the purposes of consumer protection, with a direct effect on the profitability of this sector. Commercial banks' strategies have led to changes in the balance sheet of commercial banks, as well as at the market level, by reducing their number, increasing competitiveness, reducing the vulnerability associated with the currency risk, changes in the structure of credits granted by reducing the credit intake in foreign currency in total credits, increasing the level of lending in the population sector, notably by supporting the mortgage credit, reducing external financial dependence, improvement solvency. This article aims to highlight the evolution of the profitability of the banking sector in the last decade and the main factors that have influenced the level of financial profitability. [ABSTRACT FROM AUTHOR]

Abstract Inspired by Edward Witten's questions, we compute the mutual information associated with free fermions, and we deduce many results about entropies for chiral CFT's which are embedded into free fermions, and their extensions. Such relative entropies in CFT are here computed explicitly for the first time in a mathematical rigorous way, and Our results agree with previous computations by physicists based on heuristic arguments; in addition we uncover a surprising connection with the theory of subfactors, in particular by showing that a certain duality, which is argued to be true on physical grounds, is in fact violated if the global dimension of the conformal net is greater than 1. [ABSTRACT FROM AUTHOR]

Let P : C n → C be an m -homogeneous polynomial given by P ( x ) = ∑ 1 ≤ j 1 ≤ … ≤ j m ≤ n c j 1 … j m x j 1 … x j m . Defant and Schlüters defined a non-symmetric associated m -form L P : ( C n ) m → C by L P ( x ( 1 ) , … , x ( m ) ) = ∑ 1 ≤ j 1 ≤ … ≤ j m ≤ n c j 1 … j m x j 1 ( 1 ) … x j m ( m ) . They estimated the norm of L P on ( C n , ‖ ⋅ ‖ ) m by the norm of P on ( C n , ‖ ⋅ ‖ ) times a ( c log ⁡ n ) m 2 factor for every 1-unconditional norm ‖ ⋅ ‖ on C n . A symmetrization procedure based on a card-shuffling algorithm which (together with Defant and Schlüters' argument) brings the constant term down to ( c m log ⁡ n ) m − 1 is provided. Regarding the lower bound, it is shown that the optimal constant is bigger than ( c log ⁡ n ) m / 2 when n ≫ m . Finally, the case of ℓ p -norms ‖ ⋅ ‖ p with 1 ≤ p < 2 is addressed. [ABSTRACT FROM AUTHOR]

We show that Shlyakhtenko's free Araki-Woods factors are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expectation, the normalizer remains amenable. This provides the first class of nonamenable strongly solid type III factors. [ABSTRACT FROM AUTHOR]

This paper deals with the mutual relationships between the factor group G/ζ(G) (respectively G/ζk(G)) and G′ (respectively γk+1(G) and GN). It is proved that if G/ζ(G) (respectively G/ζk(G)) has finite 0-rank, then G′ (respectively γk+1(G) and GN) also have finite 0-rank. Furthermore, bounds for the 0-ranks of G′,γk+1(G) and GN are obtained. [ABSTRACT FROM AUTHOR]

The structure of groups which have at most two isomorphism classes of central factors (B2-groups) are investigated. A complete description of B2-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble B2-groups. Also structural information about insoluble B2-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition. [ABSTRACT FROM AUTHOR]

In this article, we study a form of free transport for the interpolated free group factors, extending the work of Guionnet and Shlyakhtenko for the usual free group factors [11] . Our model for the interpolated free group factors comes from a canonical finite von Neumann algebra M ( Γ , μ ) associated to a finite, connected, weighted graph ( Γ , V , E , μ ) [12,13] . With this model, we use an operator-valued version of Voiculescu's free difference quotient introduced in [13] to state a Schwinger–Dyson equation which is valid for the generators of M ( Γ , μ ) . We construct free transport for appropriate perturbations of this equation. Also, M ( Γ , μ ) can be constructed using the machinery of Shlyakhtenko's operator-valued semicircular systems [24] . [ABSTRACT FROM AUTHOR]

This paper deals with the evaluation of the fractional integrals involving Saigo-Maeda operators of the product of the general class of polynomials and the H-function containing the factor xλ (xk + ck)-p in its argument. Some interesting special cases are derived. The results given by Saigo and Raina [6] and Chaurasia and Gupta [2] follow as special cases of the results proved in this paper. [ABSTRACT FROM AUTHOR]

A complex vector space V is a prehomogeneous G -module if G acts rationally on V with a Zariski-open orbit. The module is called étale if dim ⁡ V = dim ⁡ G . We study étale modules for reductive algebraic groups G with one-dimensional center. For such G , even though every étale module is a regular prehomogeneous module, its irreducible submodules have to be non-regular. For these non-regular prehomogeneous modules, we determine some strong constraints on the ranks of their simple factors. This allows us to show that there do not exist étale modules for G = GL 1 × S × ⋯ × S , with S simple. [ABSTRACT FROM AUTHOR]

In F. Azarpanah et al. (2008) [3] the authors have given some algebraic properties of the ring C ( X ) / C F ( X ) , where C F ( X ) = O β X ∖ I ( X ) . In this paper, first, we show that C ( X ) / C F ( X ) is a C -ring if and only if the set of isolated points of X is finite. Next, we generalize this work for rings C ( X ) / O A and C ( X ) / M A whenever A ⊆ β X (or just a closed one, in some cases) and then topological conditions on A for which every prime (maximal) ideal of C ( X ) / O A (resp., C ( X ) / M A ) is essential are characterized. We call a ring R an EIN -ring if for each two orthogonal ideals I , J of R which are generated by two subsets of idempotents, Ann ( I ) + Ann ( J ) = R . It is shown for a closed subset A of βX that C ( X ) / O A is an EIN -ring if and only if C ( X ) / M A is an EIN -ring if and only if A is an EF -space. Minimal ideals, socle and the intersection of all essential maximal ideals of C ( X ) / O A (resp., C ( X ) / M A ) are characterized. We prove also that dim ( C ( X ) / O A ) ≥ dim C ( X ) / M A , where dim C ( X ) / M A denotes the Goldie dimension of C ( X ) / M A , and the inequality may be strict. [ABSTRACT FROM AUTHOR]

With the rapid expansion of internet, the complex networks has become high-dimensional, sparse and redundant. Besides, the problem of link prediction in such networks has also obatined increasingly attention from different types of domains like information science, anthropology, sociology and computer sciences. It makes requirements for effective link prediction techniques to extract the most essential and relevant information for online users in internet. Therefore, this paper attempts to put forward a link prediction algorithm based on non-negative matrix factorization. In the algorithm, we reconstruct the correlation between different types of matrix through the projection of high-dimensional vector space to a low-dimensional one, and then use the similarity between the column vectors of the weight matrix as the scoring matrix. The experiment results demonstrate that the algorithm not only reduces data storage space but also effectively makes the improvements of the prediction performance during the process of sustaining a low time complexity. [ABSTRACT FROM AUTHOR]

We construct the first II 1 factors having exactly two group measure space decompositions up to unitary conjugacy. Also, for every positive integer n , we construct a II 1 factor M that has exactly n group measure space decompositions up to conjugacy by an automorphism. [ABSTRACT FROM AUTHOR]

Stretching the parameters of a Littlewood–Richardson coefficient of value 2 by a factor of n results in a coefficient of value n + 1 [12,9,19] . We give a geometric proof of a generalization for representations of quivers. [ABSTRACT FROM AUTHOR]

We consider the problem of classifying trades in Steiner triple systems such that each block of the trade contains one of three fixed elements. We show that the fundamental building blocks for such trades are 3 -regular graphs that are 1 -factorisable. In the process we also generate all possible 2 - and 3 -way simultaneous edge colourings of graphs with maximum degree 3 using at most 3 colours, where multiple edges but not loops are allowed. Moreover, we generate all possible Latin trades within three rows. [ABSTRACT FROM AUTHOR]

Tensor canonical polyadic decomposition (CPD), which recovers the latent factor matrices from multidimensional data, is an important tool in signal processing. In many applications, some of the factor matrices are known to have orthogonality structure, and this information can be exploited to improve the accuracy of latent factors recovery. However, existing methods for CPD with orthogonal factors all require the knowledge of tensor rank, which is difficult to acquire, and have no mechanism to handle outliers in measurements. To overcome these disadvantages, in this paper, a novel tensor CPD algorithm based on the probabilistic inference framework is devised. In particular, the problem of tensor CPD with orthogonal factors is interpreted using a probabilistic model, based on which an inference algorithm is proposed that alternatively estimates the factor matrices, recovers the tensor rank, and mitigates the outliers. Simulation results using synthetic data and real-world applications are presented to illustrate the excellent performance of the proposed algorithm in terms of accuracy and robustness. [ABSTRACT FROM AUTHOR]

We show that whenever m ≥ 1 and M 1 , … , M m are nonamenable factors in a large class of von Neumann algebras that we call C ( AO ) and which contains all free Araki–Woods factors, the tensor product factor M 1 ⊗ ‾ ⋯ ⊗ ‾ M m retains the integer m and each factor M i up to stable isomorphism, after permutation of the indices. Our approach unifies the Unique Prime Factorization (UPF) results from [33,25] and moreover provides new UPF results in the case when M 1 , … , M m are free Araki–Woods factors. In order to obtain the aforementioned UPF results, we show that Connes's bicentralizer problem has a positive solution for all type I I I 1 factors in the class C ( AO ) . [ABSTRACT FROM AUTHOR]

This article shows tight upper and lower bounds on the number of occurrences of maximal-exponent factors occurring in a word. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to classify exchange relation planar algebras with 4 dimensional 2-boxes. Besides its skein theory, we emphasize the positivity of subfactor planar algebras based on the Schur product theorem. We will discuss the lattice of projections of 2-boxes, specifically the rank of the projections. From this point, several results about biprojections are obtained. The key break of the classification is to show the existence of a biprojection. By this method, we also classify another two families of subfactor planar algebras: subfactor planar algebras generated by 2-boxes with 4 dimensional 2-boxes and at most 23 dimensional 3-boxes; subfactor planar algebras generated by 2-boxes, such that the quotient of 3-boxes by the basic construction ideal is abelian. They extend the classification of singly generated planar algebras obtained by Bisch, Jones and the author. [ABSTRACT FROM AUTHOR]

Let k be an odd natural number ≥5, and let G be a ( 6 k − 7 ) -edge-connected graph of bipartite index at least k − 1 . Then, for each mapping f : V ( G ) → N , G has a subgraph H such that each vertex v has H -degree f ( v ) modulo k . We apply this to prove that, if c : V ( G ) → Z k is a proper vertex-coloring of a graph G of chromatic number k ≥ 5 or k − 1 ≥ 6 , then each edge of G can be assigned a weight 1 or 2 such that each weighted vertex-degree of G is congruent to c modulo k . Consequently, each nonbipartite ( 6 k − 7 ) -edge-connected graph of chromatic number at most k (where k is any odd natural number ≥3) has an edge-weighting with weights 1 , 2 such that neighboring vertices have distinct weighted degrees (even after reducing these weighted degrees modulo k ). We characterize completely the bipartite graph having an edge-weighting with weights 1 , 2 such that neighboring vertices have distinct weighted degrees. In particular, that problem belongs to P while it is NP-complete for nonbipartite graphs. The characterization also implies that every 3-edge-connected bipartite graph with at least 3 vertices has such an edge-labeling, and so does every simple bipartite graph of minimum degree at least 3. [ABSTRACT FROM AUTHOR]

The analysis of any Hessenberg matrix as a product of a companion matrix and a triangular matrix is presented in this paper. The factors are explicitly given on terms of the entries of the Hessenberg matrix and, further, various factorizations are undertaken. Applications to comrade and confederate matrices, as well as for the corresponding block cases, are included. [ABSTRACT FROM AUTHOR]

It is conjectured that for every pair ( ℓ , m ) of odd integers greater than 2 with m ≡ 1 ( mod ℓ ) , there exists a cyclic two-factorization of K ℓ m having exactly ( m − 1 ) / 2 factors of type ℓ m and all the others of type m ℓ . The authors prove the conjecture in the affirmative when ℓ ≡ 1 ( mod 4 ) and m ≥ ℓ 2 − ℓ + 1 . [ABSTRACT FROM AUTHOR]

The extraction of the B → K ⁎ transition form factors from lattice data is studied, applying non-relativistic effective field theory in a finite volume. The possible mixing of πK and ηK states is taken into account. The two-channel analogue of the Lellouch–Lüscher formula is reproduced. Due to the resonance nature of the K ⁎ , an equation is derived, which allows to determine the form factors at the pole position in a process-independent manner. The infinitely-narrow width approximation of the results is discussed. [ABSTRACT FROM AUTHOR]

A new strategy for updating preconditioners by polynomial interpolation of factors of approximate inverse factorizations is proposed here. The computational cost per iteration is linear in the number of degree of freedom, the same order of most of the strategies for updating an incomplete factorization proposed in the last decade. The effectiveness of the technique is confirmed by some experiments. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation and a degree bound d and computes the irreducible factors of degree at most d of f in time polynomial in the lacunary size of f and in d . Our algorithm, which is valid for any field of zero characteristic, is based on a new gap theorem that enables reducing the problem to several instances of (a) the univariate case and (b) low-degree multivariate factorization. The reduction algorithms we propose are elementary in that they only manipulate the exponent vectors of the input polynomial. The proof of correctness and the complexity bounds rely on the Newton polytope of the polynomial, where the underlying valued field consists of Puiseux series in a single variable. [ABSTRACT FROM AUTHOR]

We give a general description of the discrete decompositions of type III factors arising as central summands of free product von Neumann algebras based on our previous works. This enables us to give several precise structural results on type III free product factors. [ABSTRACT FROM AUTHOR]

We study boundary singular points of suitable weak solutions to the three dimensional incompressible magnetohydrodynamic equations. By using the generalised Hausdorff measure we estimate the size of boundary singular points and present the improved range of powers of logarithmic factors. [ABSTRACT FROM AUTHOR]

If D = ( V, A) is a digraph, its competition graph ( with loops) CGl( D) has the vertex set V and { u, v} ⊆ V is an edge of CGl( D) if and only if there is a vertex w ∈ V such that ( u, w), ( v, w) ∈ A. In CGl( D), loops { v} are allowed only if v is the only predecessor of a certain vertex w ∈ V. For several products D1 ⚬ D2 of digraphs D1 and D2, we investigate the relations between the competition graphs of the factors D1, D2 and the competition graph of their product D1 ⚬ D2. [ABSTRACT FROM AUTHOR]

This paper is a continued investigation of the structure of Lie algebras in relation to their chief factors, using concepts that are analogous to corresponding ones in group theory. The first section investigates the structure of Lie algebras with a core-free maximal subalgebra. The results obtained are then used in section two to consider the relationship of two chief factors of L being L -connected, a weaker equivalence relation on the set of chief factors than that of being isomorphic as L -modules. A strengthened form of the Jordan–Hölder Theorem in which Frattini chief factors correspond is also established for every Lie algebra. The final section introduces the concept of a crown, a notion introduced in group theory by Gaschütz, and shows that it gives much information about the chief factors. [ABSTRACT FROM AUTHOR]

For given m × n matrices G and F over an arbitrary field F , necessary and sufficient conditions (in terms of rank, amongst others) are presented for F to divide G with a square-zero quotient. These results are then used to extend the results of Novak [3] on square-zero factorization to matrices over an arbitrary field. The ranks that the square-zero factors can have are also investigated. Formulae are also presented by which these quotients can be constructed when this type of division is possible. [ABSTRACT FROM AUTHOR]

Target representation is a necessary component for a robust tracker. However, during tracking, many complicated factors may make the accumulated errors in the representation significantly large, leading to tracking drift. This paper aims to improve the robustness of target representation to avoid the influence of the accumulated errors, such that the tracker only acquires the information that facilitates tracking and ignores the distractions. We observe that the locally mutual relations between the feature observations of temporally obtained targets are beneficial to the subspace representation in visual tracking. Thus, we propose a novel subspace learning algorithm for visual tracking, which imposes joint row-wise sparsity structure on the target subspace to adaptively exclude distractive information. The sparsity is induced by exploiting the locally mutual relations between the feature observations during learning. To this end, we formulate tracking as a subspace sparsity inducing problem. A large number of experiments on various challenging video sequences demonstrate that our tracker outperforms many other state-of-the-art trackers. [ABSTRACT FROM AUTHOR]

Let G be the general linear group of degree n over an algebraically closed field K of characteristic p > 0 . We study the m -fold tensor product S ¯ ( E ) ⊗ m of the truncated symmetric algebra S ¯ ( E ) of the symmetric algebra S ( E ) of the natural module E for G . We are particularly interested in the set of partitions λ occurring as the highest weight of a composition factor of S ¯ ( E ) ⊗ m . We explain how the determination of these composition factors is related to the determination of the set of composition factors of the m -fold tensor product S ( E ) ⊗ m of the symmetric algebra. We give a complete description of the composition factors of S ¯ ( E ) ⊗ m in terms of “distinguished” partitions. Our main interest is in the classical case, but since the quantised version is essentially no more difficult we express our results in the general context throughout. [ABSTRACT FROM AUTHOR]

We first point out that the product of a subparacompact D C -like space and a subparacompact D -space is a D -space. As a main result, we use elementary submodels to prove that any countable product of subparacompact D C -like spaces is a D -space. More generally, we prove that any uncountable product of subparacompact D C -like spaces is a D -space if and only if all but countably many of the factors are compact. [ABSTRACT FROM AUTHOR]

Motivation: Within any given tissue, gene expression levels can vary extensively among individuals. Such heterogeneity can be caused by genetic and epigenetic variability and may contribute to disease. The abundance of experimental data now enables the identification of features of gene expression profiles that are shared across tissues and those that are tissue-specific. While most current research is concerned with characterizing differential expression by comparing mean expression profiles across tissues, it is believed that a significant difference in a gene expression's variance across tissues may also be associated with molecular mechanisms that are important for tissue development and function. Results: We propose a sparse multi-view matrix factorization (sMVMF) algorithm to jointly analyse gene expression measurements in multiple tissues, where each tissue provides a different 'view' of the underlying organism. The proposed methodology can be interpreted as an extension of principal component analysis in that it provides the means to decompose the total sample variance in each tissue into the sum of two components: one capturing the variance that is shared across tissues and one isolating the tissue-specific variances. sMVMF has been used to jointly model mRNA expression profiles in three tissues obtained from a large and well-phenotyped twins cohort, TwinsUK. Using sMVMF, we are able to prioritize genes based on whether their variation patterns are specific to each tissue. Furthermore, using DNA methylation profiles available, we provide supporting evidence that adipose-specific gene expression patterns may be driven by epigenetic effects. Availability and implementation: Python code is available at http://wwwf.imperial.ac.uk/~gmontana/. [ABSTRACT FROM AUTHOR]

We study continuous wavelet transforms associated to matrix dilation groups giving rise to an irreducible square-integrable quasi-regular representation on L²(Rd). It turns out that these representations are integrable as well, with respect to a wide variety of weights, thus allowing to consistently quantify wavelet coefficient decay via coorbit space norms. We then show that these spaces always admit an atomic decomposition in terms of bandlimited Schwartz wavelets. We exhibit spaces of Schwartz functions contained in all coorbit spaces, and dense in most of them. We also present an example showing that for a consistent definition of coorbit spaces, the irreducibility requirement cannot be easily dispensed with. We then address the question of how to predict wavelet coefficient decay from vanishing moment assumptions. To this end, we introduce a new condition on the open dual orbit associated to a dilation group: If the orbit is temperately embedded, it is possible to derive rather general weighted mixed Lp-estimates for the wavelet coefficients from vanishing moment conditions on the wavelet and the analyzed function. These estimates have various applications: They provide very explicit admissibility conditions for wavelets and integrable vectors, as well as sufficient criteria for membership in coorbit spaces. As a further consequence, one obtains a transparent way of identifying elements of coorbit spaces with certain (cosets of) tempered distributions. We then show that, for every dilation group in dimension two, the associated dual orbit is temperately embedded. In particular, the general results derived in this paper apply to the shearlet group and its associated family of coorbit spaces, where they complement and generalize the known results. [ABSTRACT FROM AUTHOR]

A new method for the analysis of a multivariate dataset depending on several factors is proposed. It is called AoV-PLS (Analysis of Variance-PLS). It is based on the decomposition of the dataset into the main effects, the interactions effects and possibly the residual matrix using a model akin to analysis of variance (ANOVA). Each effect is considered in turn and assessed through the use of a Partial Least Square regression (PLS-regression). The connection of AoV-PLS to competing methods such as ANOVA-PCA and ANOVA-Simultaneous Component Analysis (ASCA) is emphasized and these methods are compared on the basis of a dataset pertaining to metabolomics field. [ABSTRACT FROM AUTHOR]

Due to the improvement of living standards, higher level of ergonomic performance is required for the products. As a result, the ergonomic evaluation has become one of the key points in the decisions making of modern products, especially the complex products. Aiming at improving the situation that the methods for ergonomic evaluation and decision making are one-sided and discrete, this paper proposed several methods for measuring multiply factors and data format of products and built a comprehensive evaluation and decision making system. In this system, the data supplied by soft hardware and specialists were calculated separately to gain the preliminary scores, and the preliminary scores were processed to get the final results for the decision making using the AHP-GRA analytic hierarchy process-gray relational analysis method proposed in this paper. [ABSTRACT FROM AUTHOR]

We show that the continuous core of any type III free product factor has no Cartan subalgebra. This is a complement to previous works due to Houdayer–Ricard and Boutonnet–Houdayer–Raum. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present a straightforward proof of the well-known fact that a positive semi-definite polynomial matrix can be written as the product of a polynomial matrix and its associated (Hermitian) transposed. For polynomial matrices with complex coefficients both factors also have complex coefficients and can be taken of the same size as the original matrix. For polynomial matrices with real coefficients both factors may have real coefficients, but then the left factor may need twice as many columns as the original matrix, and analogously for the right factor. [Copyright &y& Elsevier]

Abstract: We prove that the stable rank of any pullback (fibre product) does not exceed the stable ranks of factors. We obtain also another result bounding the stable rank of a ring by the stable ranks of its factor rings. [Copyright &y& Elsevier]

Let G be a graph and ƒ : V (G) → {2, 3, ...}. A spanning subgraph F is called strong ƒ-star of G if each component of F is a star whose center x satisfies degF (x) ≤ f(x) and F is an induced subgraph of G. In this paper, we prove that G has a strong f-star factor if and only if oddca(G - S) ≤ Px2S f(x) for all S ⊂ V (G), where oddca(G) denotes the number of odd complete-cacti of G. [ABSTRACT FROM AUTHOR]