A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

Why your customers’ social identities matter

The article looks at the role of consumers' social identities in their purchasing decisions, and hence in the creation of effective marketing strategies. It says that people generally belong to multiple social groups, any one of which may have the most salience for them in a given situation. It reports on social psychology research on how a person's connection with a particular social identity can be triggered and discusses the idea in the context of marketing products including the Toyota Prius hybrid-electric automobile, Nescafé instant coffee, and the Jeep all-terrain vehicle. INSET: Lessons of the Stanford Prison Experiment.

Projecting social and discursive identities through code-switching on facebook: the case of Greek Cypriots

Two varieties of Greek are spoken on the island of Cyprus: the local dialect, namely the Greek-Cypriot Dialect (GCD), and Standard Modern Greek (SMG). English is also influential, as Cyprus was an English colony until 1960. The dialect is rarely employed for everyday written purposes; however, it is now evident in computer-mediated communication (CMC). As a contribution to the field of code-switching in writing, this study examines how Greek-Cypriot internet users employ GCD, SMG, and English in their Facebook interactions. In particular, we investigate how identities (discursive and social) are performed and indexed through the linguistic choices of Greek-Cypriot internet users. The findings indicate that switches to GCD add a humorous tone and express solidarity and informality. SMG is mostly used for ‘official’ statements, and it is preferred by mature internet users, while English is used with expressions of affect and evaluative comments.

I owe you: age-related similarities and differences in associative memory for gains and losses

Older adults often experience associative memory impairments but can sometimes remember important information. The current experiments investigate potential age-related similarities and differences associate memory for gains and losses. Younger and older participants were presented with faces and associated dollar amounts, which indicated how much money the person “owed” the participant, and were later given a cued recall test for the dollar amount. Experiment 1 examined face-dollar amount pairs while Experiment 2 included negative dollar amounts to examine both gains and losses. While younger adults recalled more information relative to older adults, both groups were more accurate in recalling the correct value associated with high value faces compared to lower value faces and remembered gist-information about the values. However, negative values (losses) did not have a strong impact on recall among older adults versus younger adults, illustrating important associative memory differences between younger and older adults.

Marketing the Damaged Self: The Construction of Identity in Advertisements Directed Towards People with HIV/AIDS

This paper explores the identities projected in advertisements directed towards HIV positive individuals and people with AIDS. Fifty such advertisements were collected from three popular American magazines for gay men over a period of seven months. Analysis of the ads reveals a paradoxical presentation of people with HIV/AIDS, which offers simultaneous conflicting images of hope and fear, power and weakness, innocence and guilt. An interactive sociolinguistic model through which this contradictory discourse might be understood is presented, drawing on Goffman’s insights on stigma management and the presentation of the self in social interaction. Advertisements directed towards people with HIV/AIDS, it is suggested, present a contradictory discourse in which the advertisers are positioned as ‘the wise’, offering to mediate the conflicting identities of the stigmatized. The identity values enacted in this contradictory discourse are further measured against American conceptions of communication and the self as observed by Carbaugh and others. The possible consequences of these positionings on the roles made available to people with HIV/AIDS in the wider social context are discussed.

Foliations and polynomial diffeomorphisms of R(3)

Let Y = (f, g, h): R(3) -> R(3) be a C(2) map and let Spec(Y) denote the set of eigenvalues of the derivative DY(p), when p varies in R(3). We begin proving that if, for some epsilon > 0, Spec(Y) boolean AND (-epsilon, epsilon) = empty set, then the foliation F(k), with k is an element of {f, g, h}, made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek`s Jacobian Conjecture for polynomial maps of R(n).

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

Involutions of RA Loops

Let L be an RA loop, that is, a loop whose loop ring over any coefficient ring R is an alternative, but not associative, ring. Let l bar right arrow l(theta) denote an involution on L and extend it linearly to the loop ring RL. An element alpha is an element of RL is symmetric if alpha(theta) = alpha and skew-symmetric if alpha(theta) = -alpha. In this paper, we show that there exists an involution making the symmetric elements of RL commute if and only if the characteristic of R is 2 or theta is the canonical involution on L, and an involution making the skew-symmetric elements of RL commute if and only if the characteristic of R is 2 or 4.

Skew-symmetric identities of octonions

Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skew-symmetric identities and central polynomials of octonions are classified. (C) 2008 Elsevier B.V. All rights reserved.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

HYPERBOLICITY OF SEMIGROUP ALGEBRAS II

In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Z-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant`s Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras. (C) 2009 Elsevier Inc. All rights reserved.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.