Showing papers on "Product (mathematics) published in 2008"

Quasilinearization and curvature of Aleksandrov spaces

Abstract: We present a new distance characterization of Aleksandrov spaces of non-positive curvature. By introducing a quasilinearization for abstract metric spaces we draw an analogy between characterization of Aleksandrov spaces and inner product spaces; the quasi-inner product is defined by means of the quadrilateral cosine—a metric substitute for the angular measure between two directions at different points. Our main result states that a geodesically connected metric space \({\left(\mathcal{M},\rho\right)}\) is an Aleksandrov \({\Re_{0}}\) domain (also known as a CAT(0) space) if and only if the quadrilateral cosine does not exceed one for every two pairs of distinct points in \({\mathcal{M}}\) . We also observe that a geodesically connected metric space \({\left(\mathcal{M},\rho\right)}\) is an \({\Re_{0}}\) domain if and only if, for every quadruple of points in \({\mathcal{M}}\) , the quadrilateral inequality (known as Euler’s inequality in \({\mathbb{R}^{2}}\)) holds. As a corollary of our main result we give necessary and sufficient conditions for a semimetric space to be an \({\Re_{0}}\) domain. Our results provide a complete solution to the Curvature Problem posed by Gromov in the context of metric spaces of non-positive curvature.

Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems

Abstract: An extended stochastic gradient algorithm is developed to estimate the parameters of Hammerstein-Wiener ARMAX models. The basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo-linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates. The obtained parameter estimates of the identification model include the product terms of the parameters of the original systems. Two methods of separating the parameter estimates of the original parameters from the product terms are discussed: the average method and the singular value decomposition method. To improve the identification accuracy, an extended stochastic gradient algorithm with a forgetting factor is presented. The simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor.

Systems and Methods for Facilitating Consumer-Dispenser Interactions

Abstract: Embodiments of the invention can include systems and methods for facilitating consumer-dispenser interactions. In one embodiment, a product dispenser is provided. The product dispenser can include a reader configured to read machine readable item. In addition, the product dispenser can include a controller in communication with the reader, and operable to execute a set of instructions to receive information from the machine readable item associated with a consumer via the reader. Moreover, the controller can be further operable to execute a set of instructions to configure at least one characteristic based at least part on the information from the machine readable item, and dispense a product.

CPM2: A core model for product data

Abstract: The initial core product model (CPM), developed at NIST for the support of in-house research projects, has been extended to create CPM2, intended to support a broad range of information relevant to product lifecycle management. CPM2 is a generic, abstract model with generic semantics. CPM2 gives equal status to three aspects of a product or artifact: its function, its form, and its behavior. Thus, CPM2 can support functional reasoning about a product in the conceptual stages of design, the recording and the modeling of its behavior in the postdesign stages as well as the "traditional" design phases. Three levels of CPM2 models, denoted as the conceptual, intermediate, and implementation models, are described. Extensions of the initial CPM are briefly presented. The facilities in CPM2 for building experimental intermediate systems are demonstrated and a short illustrative example is given. The full practical evaluation of CPM2 will require the development and use of implementation models.

Modeling and Model Checking Software Product Lines

Abstract: Software product line engineering combines the individual developments of systems to the development of a family of systems consisting of common and variable assets.In this paper we introduce the process algebra PL-CCS as a product line extension of CCS and show how to model the overall behavior of an entire family within PL-CCS. PL-CCS models incorporate behavioral variability and allow the derivation of individual systems in a systematic way due to a semantics given in terms of multi-valued modal Kripke structures. Furthermore, we introduce multi-valued modal μ-calculus as a property specification language for system families specified in PL-CCS and show how model checking techniques operate on such structures. In our setting the result of model checking is no longer a simple yesor noanswer but the set of systems of the product line that do meet the specified properties.

Golden differential geometry

Abstract: A research on the properties of the Golden structure (i.e. a polynomial structure with the structure polynomial Q ( X ) = X 2 - X - I ) is carried out in this article. The Golden proportion plays a central role in this paper. The geometry of the Golden structure on a manifold is investigated by using a corresponding almost product structure.

Higher Order Decompositions of Ordered Operator Exponentials

Abstract: We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.

Zeros of regular functions and polynomials of a quaternionic variable

Abstract: The fundamental elements of a new theory of regular functions of a quaternionic variable have been recently developed, following an idea of Cullen. In this paper we present a detailed study of the structure of the zero set of Cullen-regular functions. We prove that the zero sets of the functions under investigation consist of isolated points or isolated 2-spheres, in the 4-dimensional real space of quaternions. Moreover, the zeros of a regular function can be factored by means of a non-standard product. The Fundamental Theorem of Algebra for quaternions, and the approach here adopted lead, in particular, to a deeper insight of the geometric and algebraic properties of the zero sets of polynomials with quaternionic coefficients.

Uniform Budgets and the Envy-Free Pricing Problem

Abstract: We consider the unit-demand min-buying pricing problem, in which we want to compute revenue maximizing prices for a set of products $\mathcal{P}$ assuming that each consumer from a set of consumer samples $\mathcal{C}$ will purchase her cheapest affordable product once prices are fixed. We focus on the special uniform-budget case, in which every consumer has only a single non-zero budget for some set of products. This constitutes a special case also of the unit-demand envy-free pricing problem. We show that, assuming specific hardness of the balanced bipartite independent set problem in constant degree graphs or hardness of refuting random 3CNF formulas, the unit-demand min-buying pricing problem with uniform budgets cannot be approximated in polynomial time within $\mathcal{O}(\log ^{\varepsilon} |\mathcal{C}|)$ for some ?> 0. This is the first result giving evidence that unit-demand envy-free pricing, as well, might be hard to approximate essentially better than within the known logarithmic ratio. We then introduce a slightly more general problem definition in which consumers are given as an explicit probability distribution and show that in this case the envy-free pricing problem can be shown to be inapproximable within $\mathcal{O}(|\mathcal{P}|^{\varepsilon})$ assuming NP $ subseteq \bigcap _{\delta >0}$ BPTIME($2^{\mathcal{O}(n^{\delta})}$). Finally, we briefly argue that all the results apply to the important setting of pricing with single-minded consumers as well.

Learning Mixtures of Product Distributions Using Correlations and Independence.

Abstract: We study the problem of learning mixtures of distributions, a natural formalization of clustering. A mixture of distributions is a collection of distributions D = {D1, . . .DT }, and mixing weights, {w1, . . . , wT } such that

Learning Mixtures of Product Distributions over Discrete Domains

Abstract: We consider the problem of learning mixtures of product distributions over discrete domains in the distribution learning framework introduced by Kearns et al [Proceedings of the $26$th Annual Symposium on Theory of Computing (STOC), Montreal, QC, 1994, ACM, New York, pp 273-282] We give a $\operatorname{poly}(n/\epsilon)$-time algorithm for learning a mixture of $k$ arbitrary product distributions over the $n$-dimensional Boolean cube $\{0,1\}^n$ to accuracy $\epsilon$, for any constant $k$ Previous polynomial-time algorithms could achieve this only for $k = 2$ product distributions; our result answers an open question stated independently in [M Cryan, Learning and Approximation Algorithms for Problems Motivated by Evolutionary Trees, PhD thesis, University of Warwick, Warwick, UK, 1999] and [Y Freund and Y Mansour, Proceedings of the $12$th Annual Conference on Computational Learning Theory, 1999, pp 183-192] We further give evidence that no polynomial-time algorithm can succeed when $k$ is superconstant, by reduction from a difficult open problem in PAC (probably approximately correct) learning Finally, we generalize our $\operatorname{poly}(n/\epsilon)$-time algorithm to learn any mixture of $k = O(1)$ product distributions over $\{0,1, \dots, b-1\}^n$, for any $b = O(1)$

Deformation-obstruction theory for complexes via Atiyah and Kodaira--Spencer classes

Abstract: We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family. We recover and generalise the obstruction class of Lowen and Lieblich, and prove that it is a product of Atiyah and Kodaira--Spencer classes. This allows us to obtain deformation-invariant virtual cycles on moduli spaces of objects of the derived category on threefolds.

Product affinity engine and method

Abstract: The present invention relates to a computerized engine and method for using the same to determine and effect product sales to customers based on customer-driven affinities relating to the products. In some embodiments, the computerized engine includes hardware and software and uses customer or transaction data or product characteristics to calculate an output relating to the affinity. In some embodiments, the computerized engine provides an output indicative of the affinity. In some embodiments, the computerized engine is coupled to a database containing the customer or transaction data or product characteristics. The system and method can also determine a reduced affinity depending on a period of time elapsed between a pair of events being related, or as a function of the age of collected affinity data.

Kinetic plasticity and the determination of product ratios for kinetic schemes leading to multiple products without rate laws — New methods based on directed graphs

Abstract: This paper presents two new and fast methods of determining product ratios for kinetic schemes leading to more than one product on which the Acree–Curtin–Hammett (ACH) principle is based. The metho...

Floer homology of cotangent bundles and the loop product

Abstract: We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas-Sullivan loop product on the singular homology of the loop space of M. We also prove related results concerning the Floer homological interpretation of the Pontrjagin product and of the Serre fibration. The techniques include a Fredholm theory for Cauchy-Riemann operators with jumping Lagrangian boundary conditions of conormal type, and a new cobordism argument replacing the standard gluing technique.

Reconciling Automation and Flexibility in Product Derivation

Abstract: Product derivation, i.e. reusing core assets to build products, did not receive sufficient attention from the product-line community, yielding a frustrating situation. On the one hand, automated product derivation approaches are inflexible; they do not allow products meeting unforeseen, customer-specific, requirements. On the other hand, approaches that consider this issue do not provide adequate methodological guidelines nor automated support. This paper proposes an integrated product derivation approach reconciling the two views to offer both flexibility and automation. First, we perform a pre-configuration of the product by selecting desired features in a generic feature model and automatically composing their related product-line core assets. Then, we adapt the pre-configured product to its customer-specific requirements via derivation primitives combined by product engineers and controlled by constraints that flexibly set product line boundaries. Our process is supported by the Kermeta meta modeling environment and illustrated through an example.

Modeling and building software product lines with pure:variants

Abstract: The demonstration shows how flexible product line (PL) architectures can be built by using the modeling capabilities provided by pure::variants [2], a commercial tool for SPLD.

Seminormal forms and Gram determinants for cellular algebras

Abstract: This paper develops an abstract framework for constructing ``seminormal forms'' for cellular algebras. That is, given a cellular R-algebra A which is equipped with a family of JM-elements we give a general technique for constructing orthogonal bases for A, and for all of its irreducible representations, when the JM-elements separate A. The seminormal forms for A are defined over the field of fractions of R. Significantly, we show that the Gram determinant of each irreducible A-module is equal to a product of certain structure constants coming from the seminormal basis of A. In the non-separated case we use our seminormal forms to give an explicit basis for a block decomposition of A. The appendix, by Marcos Soriano, gives a general construction of a complete set of orthogonal idempotents for an algera starting from a set of elements which act on the algebra in an upper triangular fashion. The appendix shows that constructions with "Jucys-Murphy elements"depend, ultimately, on the Cayley-Hamilton theorem.

Improving maximum margin matrix factorization

Abstract: 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 ...

The Classification of Surfaces with pg = q = 0 Isogenous to a Product of Curves

Abstract: We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \\PP^1 x \\PP^1 we find 17 families which we explicitly describe. We reduce the problem to a combinatorial description of certain generating systems for finite groups which we solve using also MAGMA's library of groups of small order.

Power Domination in Product Graphs

Abstract: The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number $\gamma_P(G)$ of $G$ is the minimum cardinality of a power dominating set. Dorfling and Henning [Discrete Appl. Math., 154 (2006), pp. 1023-1027] determined the power domination number of the Cartesian product of paths. In this paper the power domination number is determined for all direct products of paths except for the odd component of the direct product of two odd paths. For instance, if $n$ is even and $C$ a connected component of $P_m\times P_n$, where $m$ is odd or $m\geq n$, then $\gamma_P(C)=\left\lceil n/4 \right\rceil$. For the strong product we prove that $\gamma_P(P_n \boxtimes P_m) = \max\{\lceil n/3\rceil, \lceil (n+m-2)/4\rceil\}$, unless $3m-n-6 \equiv 4\pmod 8$. The power domination number is also determined for an arbitrary lexicographic product.

A fuzzy CBR technique for generating product ideas

Abstract: This paper presents a fuzzy CBR (case-based reasoning) technique for generating new product ideas from a product database for enhancing the functions of a given product (called the baseline product). In the database, a product is modeled by a 100-attribute vector, 87 of which are used to model the use-scenario and 13 are used to describe the manufacturing/recycling features. Based on the use-scenario attributes and their relative weights - determined by a fuzzy AHP technique, a fuzzy CBR retrieving mechanism is developed to retrieve product-ideas that tend to enhance the functions of the baseline product. Based on the manufacturing/recycling features, a fuzzy CBR mechanism is developed to screen the retrieved product ideas in order to obtain a higher ratio of valuable product ideas. Experiments indicate that the retrieving-and-filtering mechanism outperforms the prior retrieving-only mechanism in terms of generating a higher ratio of valuable product ideas.

On iterated twisted tensor products of algebras

Abstract: We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors and give some examples of algebras that can be described within our theory. We prove a certain result (called "invariance under twisting") for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrel...

System and method for providing contemporaneous product information with animated virtual representations

Abstract: A system and method for providing contemporaneous product information with animated virtual representations includes identifying a product by detecting a marker with a user device. Based upon the product, an animated virtual representation is generated in a display of the user device. Information about the product is conveyed to the user by virtual interaction with the animated virtual representation.

Electronic device and method of controlling mode thereof and mobile communication terminal

Abstract: A mobile communication terminal, an electronic device, a computer program product, and a method of controlling including receiving a control signal for controlling a predetermined area; and controlling a size and an operating mode of a screen by the control signal. Therefore, various operation modes can be easily selected, and a plurality of touch signals can be recognized and processed.

Similarity matching of products based on multiple classification schemes

Abstract: In embodiments of the present invention improved capabilities are described for identifying a first classification scheme associated with product attributes of a first grouping of products, identifying a second classification scheme associated with product attributes of a second grouping of products, and receiving a record of data relating to an item, the classification of which is uncertain. It may also involve receiving a dictionary of attributes associated with products and assigning the item to at least one of the classification schemes based on probabilistic matching among the attributes in the classification schemes, the attributes in the dictionary of attributes and the known attributes of the item.

System and method for rating plural products

Abstract: A system and method for rating of each of plural products comprising identifying plurality of attributes associated with a category of product, applying a scalar structure for each attribute to provide scalar value of each attribute for each of the plural products, determining an incremental competitive index for each attribute of each product based on the scalar value of each attribute and a number of products having the scalar value, and rating each product based on the determined competitive index.