Showing papers on "Product (mathematics) published in 2012"

Evaluation of Brand Extensions: The Role of Product Feature Similarity and Brand Concept

Abstract: This article examines two factors that differentiate between successful and unsuccessful brand extensions: product feature similarity and brand concept consistency. The results reveal that, in identifying brand extensions, consumers take into account not only information about the product-level feature similarity between the new product and the products already associated with the brand, but also the concept consistency between the brand concept and the extension. For both function-oriented and prestige-oriented brand names, the most favorable reactions occur when brand extensions are made with high brand concept consistency and high product feature similarity. In addition, the relative impact of these two factors differs to some extent, depending on the nature of the brand-name concept. When a brand's concept is consistent with those of its extension products, the prestige brand seems to have greater extendibility to products with low feature similarity than the functional brand does. Copyright 1991 by the University of Chicago.

System, method, and computer program product for improving memory systems

Abstract: A system, method, and computer program product are provided for a memory system. The system includes a first semiconductor platform including at least one first circuit, and at least one additional semiconductor platform stacked with the first semiconductor platform and including at least one additional circuit.

Type checking annotation-based product lines

Abstract: Software product line engineering is an efficient means of generating a family of program variants for a domain from a single code base. However, because of the potentially high number of possible program variants, it is difficult to test them all and ensure properties like type safety for the entire product line. We present a product-line-aware type system that can type check an entire software product line without generating each variant in isolation. Specifically, we extend the Featherweight Java calculus with feature annotations for product-line development and prove formally that all program variants generated from a well typed product line are well typed. Furthermore, we present a solution to the problem of typing mutually exclusive features. We discuss how results from our formalization helped implement our own product-line tool CIDE for full Java and report of our experience with detecting type errors in four existing software product line implementations.

On extracting feature models from product descriptions

Abstract: In product line engineering, domain analysis is the process of analyzing related products to identify their common and variable features. This process is generally carried out by experts on the basis of existing product descriptions, which are expressed in a more or less structured way. Modeling and reasoning about product descriptions are error-prone and time consuming tasks. Feature models (FMs) constitute popular means to specify product commonalities and variabilities in a compact way, and to provide automated support to the domain analysis process. This paper aims at easing the transition from product descriptions expressed in a tabular format to FMs accurately representing them. This process is parameterized through a dedicated language and high-level directives (e.g., products/features scoping). We guarantee that the resulting FM represents the set of legal feature combinations supported by the considered products and has a readable tree hierarchy together with variability information. We report on our experiments based on public data and characterize the properties of the derived FMs.

A note on polytopes for scattering amplitudes

Abstract: In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the essential ideas with the elementary geometry of polygons in $ \mathbb{C}{\mathbb{P}^{{2}}} $ , we interpret the 1-loop MHV integrand as the volume of a polytope in $ \mathbb{C}{\mathbb{P}^{{3}}} $ × $ \mathbb{C}{\mathbb{P}^{{3}}} $ , which can be thought of as the space obtained by taking the geometric dual of the Wilson loop in each $ \mathbb{C}{\mathbb{P}^{{3}}} $ of the product. We then review the polytope picture for the NMHV tree amplitude and give it a more direct and intrinsic definition as the geometric dual of a canonical “square” of the Wilson-Loop polygon, living in a certain extension of momentum-twistor space into $ \mathbb{C}{\mathbb{P}^{{4}}} $ . In both cases, one natural class of triangulations of the polytope produces the BCFW/CSW representations of the amplitudes; another class of triangulations leads to a striking new form, which is both remarkably simple as well as manifestly cyclic and local.

On the classification of warped product Einstein metrics

Abstract: The question of when an Einstein metric can be written as a warped product is posed in the text Einstein metrics by Besse. Recently, there have been some interesting results about these spaces found by Kim–Kim, Case–Shu–Wei, and Case. They take the perspective of studying these metrics by studying the equation on the base of the warped product. The resulting equation is similar to the Ricci soliton equation and is a natural equation from the work of Bakry– Emery and their collaborators on curvature dimension inequalities. We will also take this perspective and prove two new results: one is an extension of the work of Kim and Kim and Case-Shu-Wei to manifolds with boundary; the other is a classi…cation result of warped products Einstein metrics over locally conformally ‡at base space.

System and method for generating an alternative product recommendation

Abstract: A method and system for automatically generating a self-updating naturally-reading narrative product summary including assertions about a selected product. In one embodiment, the system and method includes evaluating an existing narrative product summary, comparing an existing attribute name, attribute value, attribute unit, and assertion model, respectively, to a current attribute name, attribute value, attribute unit, and assertion model to determine if one of the comparisons shows a change. The system and method further determines a new attribute associated with the selected product, selects an alternative product, retrieves a new assertion model with assertions that describe the selected product and identify an alternative product in a natural manner. The system and method then generates a naturally-reading narrative product summary by combining the new attribute with the new retrieved assertion model, and by combining the selected alternative product with another retrieved assertion model to recommend the selected alternative product in the narrative.

Gauge Theories on ALE Space and Super Liouville Correlation Functions

Abstract: We present a relation between $${\mathcal{N}=2}$$ quiver gauge theories on the ALE space $${\mathcal{O}_{\mathbb{P}^1}(-2)}$$ and correlators of $${\mathcal{N}=1}$$ super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the $${\mathcal{N}=2^*}$$ instanton partition function is given by the product of the character of $${\widehat{SU}(2)_2}$$ times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.

Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates

Abstract: An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold α > 0 such that \({|\Delta(E)| \gtrsim q}\) whenever \({|E| \gtrsim q^{\alpha}}\), where \({E \subset {\mathbb {F}}_q^d}\), the d-dimensional vector space over a finite field with q elements (not necessarily prime). Here \({\Delta(E)=\{{(x_1-y_1)}^2+\dots+{(x_d-y_d)}^2: x,y \in E\}}\). Iosevich and Rudnev (Trans Am Math Soc 359(12):6127–6142, 2007) established the threshold \({\frac{d+1}{2}}\), and in Hart et al. (Trans Am Math Soc 363:3255–3275, 2011) proved that this exponent is sharp in odd dimensions. In two dimensions we improve the exponent to \({\tfrac{4}{3}}\), consistent with the corresponding exponent in Euclidean space obtained by Wolff (Int Math Res Not 10:547–567, 1999). The pinned distance set \({\Delta_y(E)=\{{(x_1-y_1)}^2+\dots+{(x_d-y_d)}^2: x\in E\}}\) for a pin \({y\in E}\) has been studied in the Euclidean setting. Peres and Schlag (Duke Math J 102:193–251, 2000) showed that if the Hausdorff dimension of a set E is greater than \({\tfrac{d+1}{2}}\), then the Lebesgue measure of Δy(E) is positive for almost every pin y. In this paper, we obtain the analogous result in the finite field setting. In addition, the same result is shown to be true for the pinned dot product set \({\Pi_y(E)=\{x\cdot y: x\in E\}}\). Under the additional assumption that the set E has Cartesian product structure we improve the pinned threshold for both distances and dot products to \({\frac{d^2}{2d-1}}\). The pinned dot product result for Cartesian products implies the following sum-product result. Let \({A\subset \mathbb F_q}\) and \({z\in \mathbb F^*_q}\). If \({|A|\geq q^{\frac{d}{2d-1}}}\) then there exists a subset \({E'\subset A\times \dots \times A=A^{d-1}}\) with \({|E'|\gtrsim |A|^{d-1}}\) such that for any \({(a_1,\dots, a_{d-1}) \in E'}\), $$ |a_1A+a_2A+\dots +a_{d-1}A+zA| > \frac{q}{2}$$ where \({a_j A=\{a_ja:a \in A\},j=1,\dots,d-1}\). A generalization of the Falconer distance problem is to determine the minimal α > 0 such that E contains a congruent copy of a positive proportion of k-simplices whenever \({|E| \gtrsim q^{\alpha}}\). Here the authors improve on known results (for k > 3) using Fourier analytic methods, showing that α may be taken to be \({\frac{d+k}{2}}\).

Size consistency error in the antisymmetric geminal power wave function can be completely removed.

Abstract: The accurate but expensive product of geminals ansatz may be approximated by a geminal power, but this approach sacrifices size consistency. Here, we show both analytically and numerically that a size consistent form very similar to the product of geminals can be recovered using a network of location-specific Jastrow factors. Upon variational energy minimization, the network creates particle number projections that remove the charge fluctuations responsible for size inconsistency. This polynomial cost approach captures strong many-electron correlations, giving a maximum error of just $1.8\text{ }\text{ }\mathrm{kcal}/\mathrm{mol}$ during the double-bond dissociation of ${\mathrm{H}}_{2}\mathrm{O}$ in an STO-3G atomic orbital basis.

On product graphs

Abstract: In this paper we study product graphs and obtain some results. Wealso indicate the scope of its applications in a variety of fields.

Model checking software product lines with SNIP

Abstract: We present SNIP, an efficient model checker for software product lines (SPLs). Variability in software product lines is generally expressed in terms of features, and the number of potential products is exponential in the number of features. Whereas classical model checkers are only capable of checking properties against each individual product in the product line, SNIP exploits specifically designed algorithms to check all products in a single step. This is done by using a concise mathematical structure for product line behaviour, that exploits similarities and represents the behaviour of all products in a compact manner. Specification of an SPL in SNIP relies on the combination of two specification languages: TVL to describe the variability in the product line, and fPromela to describe the behaviour of the individual products. SNIP is thus one of the first tools equipped with specification languages to formally express both the variability and the behaviours of the products of the product line. The paper assesses SNIP and suggests that this is the first model checker for SPLs that can be used outside the academic arena.

On the structure of gradient Yamabe solitons

Abstract: We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.

Guts of Surfaces and the Colored Jones Polynomial

Abstract: 1 Introduction.- 2 Decomposition into 3-balls.- 3 Ideal Polyhedra.- 4 I-bundles and essential product disks.- 5 Guts and fibers.- 6 Recognizing essential product disks.- 7 Diagrams without non-prime arcs.- 8 Montesinos links.- 9 Applications.- 10 Discussion and questions.

Product registration and tracking system

Abstract: A server for registration of products may include a processor and computer storage. The processor may be configured to receive, via a network, a communication from a product application executed on a computing device, the communication including a product identification (ID) associated with a product and an indication of registration of the product by a user of the product application. The processor may further be configured to register the product at least by storing, in the computer storage, the product ID and a relationship between the product and an identification of the user of the product application. The processor may further be configured to send a subsequent communication to the product application on the computing device based on the registration of the product.

The refined BPS index from stable pair invariants

Abstract: A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi-Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with respect to a C* action on the stable pair moduli space, or alternatively the equivariant index of Nekrasov and Okounkov. This effectively calculates the refined index for M-theory reduced on these Calabi-Yau geometries. Based on physical expectations we propose a product formula for the refined invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local P^1. We explicitly compute refined invariants in low degree for local P^2 and local P^1 x P^1 and check that they agree with the predictions of the direct integration of the generalized holomorphic anomaly and with the product formula. The modularity of the expressions obtained in the direct integration approach allows us to relate the generating function of refined PT invariants on appropriate geometries to Nekrasov's partition function and a refinement of Chern-Simons theory on a lens space. We also relate our product formula to wallcrossing.

$${\mathbb{G}_a^ M}$$ degeneration of flag varieties

Abstract: Let \({\mathcal{F}_\lambda}\) be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module Vλ. We define a flat degeneration \({\mathcal{F}_\lambda^a}\) , which is a \({\mathbb{G}^M_a}\) variety. Moreover, there exists a larger group Ga acting on \({\mathcal{F}_\lambda^a}\) , which is a degeneration of the group G. The group Ga contains \({\mathbb{G}^M_a}\) as a normal subgroup. If G is of type A, then the degenerate flag varieties can be embedde‘d into the product of Grassmannians and thus to the product of projective spaces. The defining ideal of \({\mathcal{F}_\lambda}\) is generated by the set of degenerate Plucker relations. We prove that the coordinate ring of \({\mathcal{F}_\lambda^a}\) is isomorphic to a direct sum of dual PBW-graded \({\mathfrak{g}}\) -modules. We also prove that there exists bases in multi-homogeneous components of the coordinate rings, parametrized by the semistandard PBW-tableux, which are analogs of semistandard tableaux.

Family-based deductive verification of software product lines

Abstract: A software product line is a set of similar software products that share a common code base. While software product lines can be implemented efficiently using feature-oriented programming, verifying each product individually does not scale, especially if human effort is required (e.g., as in interactive theorem proving). We present a family-based approach of deductive verification to prove the correctness of a software product line efficiently. We illustrate and evaluate our approach for software product lines written in a feature-oriented dialect of Java and specified using the Java Modeling Language. We show that the theorem prover KeY can be used off-the-shelf for this task, without any modifications. Compared to the individual verification of each product, our approach reduces the verification time needed for our case study by more than 85%.

Method and Apparatus for Managing Product Placement on Store Shelf

Abstract: A method and apparatus for attending to a supply of product at a position on a store shelf involves receiving an electronic image of the position on a store shelf and comparing the electronic image to a previous electronic image of the position on the store shelf. Depending of the difference, if any, between the two images, generating an indication to attend to the supply of product at the position on the store shelf.

Solving Fuzzy Relational Equations Via Semitensor Product

Abstract: The problem of solving max-min fuzzy relational equations is investigated. First, we show that if there is a solution, then there is a corresponding solution within the set of parameters [briefly, the parameter set solution (PSS)]. Then, the semitensor product of matrices is used to convert the logical equations into algebraic equations via the vector expression of logical variables. Under this form, every PSS can be obtained. It is proved that all the solutions can be revealed from their corresponding PSS. Some examples are presented to demonstrate the algorithm to solve fuzzy relational equations.

System and method for identifying retail products and determining retail product arrangements

Abstract: Systems and methods for determining product arrangement are provided. The method includes: receiving one or more images, the one or more images reflecting a retail arrangement of at least one product, processing, with a processor executing code, the one or more images to: (a) identify the at least one product, and (b) determine the retail arrangement of the at least one product, computing, based on (a) an identification of the at least one product and (b) a determination of a retail arrangement of the at least one product, one or more performance indicators, the one or more performance indicators reflecting compliance with one or more retail arrangement guidelines established with respect to the at least one product, and providing feedback based on the one or more performance indicators. Other embodiments of the various aspects include corresponding systems, apparatus, and computer program products.

A Note on Contiguity and Hellinger Distance

Abstract: For n = 1, 2, … let (X n1, A n1), …, (X nn , A nn ) be arbitrary measurable spaces. Let P ni and Q ni be probability measures defined on (X ni , A ni ), i = 1, …, n; n = 1, 2, …, and let \(P_n^{\left( n \right)} = \prod\limits_{i = 1}^n {{P_{ni}}}\) and \(Q_n^{\left( n \right)} = \prod\limits_{i = 1}^n {{Q_{ni}}}\) denote the product probability measures. For each i and n let X ni be the identity map from X ni onto X ni . Then P ni and Q ni represent the two possible distributions of the random element X ni as well as the probability measures of the underlying probability space. Obviously X n1, …, X nn are independent under both \(P_n^{\left( n \right)}\) and \(Q_n^{\left( n \right)}\) (n = 1, 2, …).

Evolutionary search-based test generation for software product line feature models

Abstract: Product line-based software engineering is a paradigm that models the commonalities and variabilities of different applications of a given domain of interest within a unique framework and enhances rapid and low cost development of new applications based on reuse engineering principles. Despite the numerous advantages of software product lines, it is quite challenging to comprehensively test them. This is due to the fact that a product line can potentially represent many different applications; therefore, testing a single product line requires the test of its various applications. Theoretically, a product line with n software features can be a source for the development of 2n application. This requires the test of 2n applications if a brute-force comprehensive testing strategy is adopted. In this paper, we propose an evolutionary testing approach based on Genetic Algorithms to explore the configuration space of a software product line feature model in order to automatically generate test suites. We will show through the use of several publicly-available product line feature models that the proposed approach is able to generate test suites of O(n) size complexity as opposed to O(2n) while at the same time form a suitable tradeoff balance between error coverage and feature coverage in its generated test suites.

New proofs of Plünnecke-type estimates for product sets in groups

Abstract: We present a new method to bound the cardinality of product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset inequalities for commutative groups. A new proof of a theorem of Tao on triple products, which generalises these inequalities when no assumption on commutativity is made. A further generalisation of the Plunnecke-Ruzsa inequalities in general groups.

On-shelf tracking system

Abstract: A system to be installed on a merchandising unit having one or more inventory zones, one or more units of product, one or more product sensors, a mounting structure, and an electromagnetic signal processor. The one or more inventory zones can present the one or more units of product in several different arrangements. The one or more product sensors, each at least associated operatively with one of the one or more inventory zones, converts a sensed quantity of the one or more units of product into a respective analog electromagnetic signal. The mounting structure secures the one or more product sensors to the merchandising unit relative to the one or more units of product so that the one or more product sensors sense a quantity of the one or more units of product. The electromagnetic signal processor in communication with the one or more product sensors can sample output from the one or more product sensors periodically and converts the analog signal into a digital signal.

Tropical intersection theory from toric varieties

Abstract: We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on compact toric varieties. These objects fit into the framework of tropical intersection theory developed by Allermann and Rau. Standard facts about intersection theory on toric varieties are applied to show that the definitions of tropical intersection product on tropical cycles in $${\mathbb{R}^n}$$ given by Allermann–Rau and Mikhalkin are equivalent. We introduce an induced tropical intersection theory on subvarieties on a toric variety. This gives a conceptual proof that the intersection of tropical ψ-classes on $${\overline{\mathcal{M}}_{0,n}}$$ used by Kerber and Markwig computes classical intersection numbers.

The Regularized Siegel-Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula

Abstract: In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis.

Generating better partial covering arrays by modeling weights on sub-product lines

Abstract: Combinatorial interaction testing is an approach for testing product lines. A set of products to test can be set up from the covering array generated from a feature model. The products occurring in a partial covering array, however, may not focus on the important feature interactions nor resemble any actual product in the market. Knowledge about which interactions are prevalent in the market can be modeled by assigning weights to sub-product lines. Such models enable a covering array generator to select important interactions to cover first for a partial covering array, enable it to construct products resembling those in the market and enable it to suggest simple changes to an existing set of products to test for incremental adaption to market changes. We report experiences from the application of weighted combinatorial interaction testing for test product selection on an industrial product line, TOMRA's Reverse Vending Machines.