Showing papers on "Product (mathematics) published in 2013"

Computer-assisted shopping and product location

Abstract: In general, techniques are described that enable crowdsourcing of product-related information. Product-related information may include availability and intra-store locations of various products at particular stores. An example system includes an interface, a memory, and one or more programmable processors configured to receive, at the interface an intra-store product location from a first client device, the intra-store product location indicating a location of a product within a store. The programmable processor(s) are further configured to store, to at least one storage device coupled to the system and in association with the product, the received intra-store product location, receive, at the interface, a request associated with the product from a second client device, and send, from the interface, the intra-store product location to the second client device in response to receiving the request associated with the product.

Analytical Approach to Parallel Repetition

Abstract: We propose an analytical framework for studying parallel repetition, a basic product operation for one-round two-player games. In this framework, we consider a relaxation of the value of a game, $\mathrm{val}_+$, and prove that for projection games, it is both multiplicative (under parallel repetition) and a good approximation for the true value. These two properties imply a parallel repetition bound as $$ \mathrm{val}(G^{\otimes k}) \approx \mathrm{val}_+(G^{\otimes k}) = \mathrm{val}_+(G)^{k} \approx \mathrm{val}(G)^{k}. $$ Using this framework, we can also give a short proof for the NP-hardness of Label-Cover$(1,\delta)$ for all $\delta>0$, starting from the basic PCP theorem. We prove the following new results: - A parallel repetition bound for projection games with small soundness. Previously, it was not known whether parallel repetition decreases the value of such games. This result implies stronger inapproximability bounds for Set-Cover and Label-Cover. - An improved bound for few parallel repetitions of projection games, showing that Raz's counterexample is tight even for a small number of repetitions. Our techniques also allow us to bound the value of the direct product of multiple games, namely, a bound on $\mathrm{val}(G_1\otimes ...\otimes G_k)$ for different projection games $G_1,...,G_k$.

Dynamic Software Product Lines

Abstract: The Software Engineering Institute (SEI) defines an SPL as a set of software-intensive systems that share a common, managed set of features satisfying the specific needs of a particular market segment or mission. A fundamental principle of SPLs is variability management, which involves separating the product line into three parts - common components, parts common to some but not all products, and individual products with their own specific requirements - and managing these throughout development. Using SPLs seeks to maximize reusable variation and eliminate wasteful generic development of components used only once. Although traditional SPL engineering recognizes that variation points are bound at different stages of development, and possibly also at runtime, it typically binds variation points before delivery of the software. In contrast, DSPL engineers typically aren't concerned with pre-runtime variation points. However, they recognize that in practice mixed approaches might be viable, where some variation points related to the environment's static properties are bound before runtime and others related to the dynamic properties are bound at runtime.

System, method and computer program product for processing image data

Abstract: A method for processing a first image having associated location data is provided. In one embodiment, the method comprises determining that a location alias exists for the location data of the first image, storing the location alias in memory in association with the first image, determining an identity of a person who appears in the first image via processing of facial data of the person from the first image, storing information of the identity of the person appearing in the first image in memory in association with the first image, outputting the first image to a display in response to a request, outputting the location alias to the display for viewing concurrently with the first image, and outputting the identity of the person who appears in the first image to the display for viewing concurrently with the first image.

Feature model extraction from large collections of informal product descriptions

Abstract: Feature Models (FMs) are used extensively in software product line engineering to help generate and validate individual product configurations and to provide support for domain analysis. As FM construction can be tedious and time-consuming, researchers have previously developed techniques for extracting FMs from sets of formally specified individual configurations, or from software requirements specifications for families of existing products. However, such artifacts are often not available. In this paper we present a novel, automated approach for constructing FMs from publicly available product descriptions found in online product repositories and marketing websites such as SoftPedia and CNET. While each individual product description provides only a partial view of features in the domain, a large set of descriptions can provide fairly comprehensive coverage. Our approach utilizes hundreds of partial product descriptions to construct an FM and is described and evaluated against antivirus product descriptions mined from SoftPedia.

Faster all-pairs shortest paths via circuit complexity

Abstract: We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary edge weights. On the real RAM, where additions and comparisons of reals are unit cost (but all other operations have typical logarithmic cost), the algorithm runs in time \[\frac{n^3}{2^{\Omega(\log n)^{1/2}}}\] and is correct with high probability. On the word RAM, the algorithm runs in $n^3/2^{\Omega(\log n)^{1/2}} + n^{2+o(1)}\log M$ time for edge weights in $([0,M] \cap {\mathbb Z})\cup\{\infty\}$. Prior algorithms used either $n^3/(\log^c n)$ time for various $c \leq 2$, or $O(M^{\alpha}n^{\beta})$ time for various $\alpha > 0$ and $\beta > 2$. The new algorithm applies a tool from circuit complexity, namely the Razborov-Smolensky polynomials for approximately representing ${\sf AC}^0[p]$ circuits, to efficiently reduce a matrix product over the $(\min,+)$ algebra to a relatively small number of rectangular matrix products over ${\mathbb F}_2$, each of which are computable using a particularly efficient method due to Coppersmith. We also give a deterministic version of the algorithm running in $n^3/2^{\log^{\delta} n}$ time for some $\delta > 0$, which utilizes the Yao-Beigel-Tarui translation of ${\sf AC}^0[m]$ circuits into "nice" depth-two circuits.

An algebraic characterization of injectivity in phase retrieval

Abstract: A complex frame is a collection of vectors that span $\mathbb{C}^M$ and define measurements, called intensity measurements, on vectors in $\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely determined (up to a global phase factor) from $4M-4$ generic measurements. To prove this, we identify the set of frames defining non-injective measurements with the projection of a real variety and bound its dimension.

Scalable prediction of non-functional properties in software product lines: Footprint and memory consumption

Abstract: Context: A software product line is a family of related software products, typically created from a set of common assets Users select features to derive a product that fulfills their needs Users often expect a product to have specific non-functional properties, such as a small footprint or a bounded response time Because a product line may have an exponential number of products with respect to its features, it is usually not feasible to generate and measure non-functional properties for each possible product Objective: Our overall goal is to derive optimal products with respect to non-functional requirements by showing customers which features must be selected Method: We propose an approach to predict a product's non-functional properties based on the product's feature selection We aggregate the influence of each selected feature on a non-functional property to predict a product's properties We generate and measure a small set of products and, by comparing measurements, we approximate each feature's influence on the non-functional property in question As a research method, we conducted controlled experiments and evaluated prediction accuracy for the non-functional properties footprint and main-memory consumption But, in principle, our approach is applicable for all quantifiable non-functional properties Results: With nine software product lines, we demonstrate that our approach predicts the footprint with an average accuracy of 94%, and an accuracy of over 99% on average if feature interactions are known In a further series of experiments, we predicted main memory consumption of six customizable programs and achieved an accuracy of 89% on average Conclusion: Our experiments suggest that, with only few measurements, it is possible to accurately predict non-functional properties of products of a product line Furthermore, we show how already little domain knowledge can improve predictions and discuss trade-offs between accuracy and required number of measurements With this technique, we provide a basis for many reasoning and product-derivation approaches

The Polyanalytic Ginibre Ensembles

Abstract: For integers n,q=1,2,3,… , let Pol n,q denote the ${\mathbb{C}}$ -linear space of polynomials in z and $\bar{z}$ , of degree ≤n−1 in z and of degree ≤q−1 in $\bar{z}$ . We supply Pol n,q with the inner product structure of $$\begin{aligned} L^2 \bigl({\mathbb{C}},\mathrm{e}^{-m|z|^2} {\mathrm{d}}A \bigr),\quad \mbox {where } {\mathrm{d}}A(z)=\pi^{-1}{\mathrm{d}}x {\mathrm{d}}y,\ z= x+ {\mathrm{i}}y; \end{aligned}$$ the resulting Hilbert space is denoted by Pol m,n,q . Here, it is assumed that m is a positive real. We let K m,n,q denote the reproducing kernel of Pol m,n,q , and study the associated determinantal process, in the limit as m,n→+∞ while n=m+O(1); the number q, the degree of polyanalyticity, is kept fixed. We call these processes polyanalytic Ginibre ensembles, because they generalize the Ginibre ensemble—the eigenvalue process of random (normal) matrices with Gaussian weight. There is a physical interpretation in terms of a system of free fermions in a uniform magnetic field so that a fixed number of the first Landau levels have been filled. We consider local blow-ups of the polyanalytic Ginibre ensembles around points in the spectral droplet, which is here the closed unit disk $\bar{\mathbb{D}}:=\{z\in{\mathbb{C}}:|z|\le1\}$ . We obtain asymptotics for the blow-up process, using a blow-up to characteristic distance m −1/2; the typical distance is the same both for interior and for boundary points of $\bar{\mathbb{D}}$ . This amounts to obtaining the asymptotical behavior of the generating kernel K m,n,q . Following (Ameur et al. in Commun. Pure Appl. Math. 63(12):1533–1584, 2010), the asymptotics of the K m,n,q are rather conveniently expressed in terms of the Berezin measure (and density) For interior points |z|<1, we obtain that ${\mathrm{d}}B^{\langle z\rangle}_{m,n,q}(w)\to{\mathrm{d}}\delta_{z} $ in the weak-star sense, where δ z denotes the unit point mass at z. Moreover, if we blow up to the scale of m −1/2 around z, we get convergence to a measure which is Gaussian for q=1, but exhibits more complicated Fresnel zone behavior for q>1. In contrast, for exterior points |z|>1, we have instead that ${\mathrm{d}}B^{\langle z\rangle}_{m,n,q}(w) \to{\mathrm{d}}\omega(w,z, {\mathbb{D}}^{e}) $ , where ${\mathrm{d}}\omega(w,z,{\mathbb{D}}^{e})$ is the harmonic measure at z with respect to the exterior disk ${\mathbb{D}}^{e}:= \{w\in{\mathbb{C}}:\, |w|>1\}$ . For boundary points, |z|=1, the Berezin measure ${\mathrm{d}}B^{\langle z\rangle}_{m,n,q}$ converges to the unit point mass at z, as with interior points, but the blow-up to the scale m −1/2 exhibits quite different behavior at boundary points compared with interior points. We also obtain the asymptotic boundary behavior of the 1-point function at the coarser local scale q 1/2 m −1/2.

Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization

Abstract: We give a test that can distinguish efficiently between product states of n quantum systems and states that are far from product. If applied to a state |ψ〉 whose maximum overlap with a product state is 1 − e, the test passes with probability 1 − Θ(e), regardless of n or the local dimensions of the individual systems. The test uses two copies of |ψ〉. We prove correctness of this test as a special case of a more general result regarding stability of maximum output purity of the depolarizing channel.A key application of the test is to quantum Merlin-Arthur games with multiple Merlins, where we obtain several structural results that had been previously conjectured, including the fact that efficient soundness amplification is possible and that two Merlins can simulate many Merlins: QMA(k) = QMA(2) for k ≥ 2. Building on a previous result of Aaronson et al., this implies that there is an efficient quantum algorithm to verify 3-SAT with constant soundness, given two unentangled proofs of O(√n) qubits. We also show how QMA(2) with log-sized proofs is equivalent to a large number of problems, some related to quantum information (such as testing separability of mixed states) as well as problems without any apparent connection to quantum mechanics (such as computing injective tensor norms of 3-index tensors). As a consequence, we obtain many hardness-of-approximation results, as well as potential algorithmic applications of methods for approximating QMA(2) acceptance probabilities.Finally, our test can also be used to construct an efficient test for determining whether a unitary operator is a tensor product, which is a generalization of classical linearity testing.

A Tropical Intersection Product in Matroidal Fans

Abstract: We construct an intersection product on tropical cycles contained in the Bergman fan of a matroid. To do this we first establish a connection between the operations of deletion and restriction in matroid theory and tropical modifications as defined by Mikhalkin in [Proceedings of the International Congress of Mathematicians, Vol. II, European Mathematical Society, Zurich, 2006, pp. 827--852]. This product generalizes the product of Allermann and Rau [Math. Z., 264 (2010), pp. 633--670] and Allermann [Tropical intersection products on smooth varieties, J. Eur. Math. Soc. (JEMS), 14 (2012), pp. 107--126] and also provides an alternative procedure for intersecting cycles which is not based on intersecting with Cartier divisors. Also, we simplify the definition in the case of one-dimensional fan cycles in two-dimensional matroidal fans and give an application of the intersection product to realiability questions in tropical geometry.

On Reverse Hypercontractivity

Abstract: We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new comparison lemma for Dirichlet forms and an extension of the Stroock–Varopoulos inequality. A consequence of our analysis is that all simple operators \({L = Id - \mathbb{E}}\) as well as their tensors satisfy uniform reverse hypercontractive inequalities. That is, for all q < p < 1 and every positive valued function f for \({t \geq \log \frac{1-q}{1-p}}\) we have \({\| e^{-tL}f\|_{q} \geq \| f\|_{p}}\). This should be contrasted with the case of hypercontractive inequalities for simple operators where t is known to depend not only on p and q but also on the underlying space. The new reverse hypercontractive inequalities established here imply new mixing and isoperimetric results for short random walks in product spaces, for certain card-shufflings, for Glauber dynamics in high-temperatures spin systems as well as for queueing processes. The inequalities further imply a quantitative Arrow impossibility theorem for general product distributions and inverse polynomial bounds in the number of players for the non-interactive correlation distillation problem with m-sided dice.

Classical dynamics of chemical reactions in a quantum spirit

Abstract: Molecular beam experiments provide fascinating data on how atoms move in the course of chemical reactions. In order to theoretically reproduce these data at relatively low computational cost and to interpret them, nuclei are often treated as classical particles, even though we have known for about a century that, in the range of energies usually available to chemical systems, their motion is best described by the laws of quantum mechanics. Nevertheless, over the last decade this approximation has been shown to work unexpectedly well, provided that a few constraints are introduced into the calculations in order to take into account the quantisation of product internal motions. Why this is so and the nature of the previous constraints are the central issues of this review article.

On Uncertainty Principle for Quaternionic Linear Canonical Transform

Abstract: We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a 2D Gaussian signal minimizes the uncertainty.

The Cost of Continuity: Performance of Iterative Solvers on Isogeometric Finite Elements

Abstract: In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using $C^0$ B-splines, which span traditional finite element spaces, and $C^{p-1}$ B-splines, which represent maximum continuity. We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size $h$ and polynomial order of approximation $p$ in addition to the aforementioned continuity of the basis. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most $\left.{33p^2}\middle/{8}\right.$ times more expensive for the more cont...

Optimum granularity level of modular product design architecture

Abstract: In modular architectures, Design Structure Matrix (DSM) is used to cluster product components into modules with minimum interfaces externally and maximum internal integration between components. However, DSM is a flat connectivity map that does not capture the layered nature of the product structure. Hierarchical clustering (cladistics) is proposed to automatically build product hierarchical architecture from DSM. The resulting clustering tree represents product architecture while its depth represents its granularity. The optimum granularity level and number of modules are determined, indicating the potential product and process platforms. A case study of automobile body-in-white of 38 components is used to demonstrate the capabilities and superior results quality of the presented technique.

Determining an Unbounded Potential from Cauchy Data in Admissible Geometries

Abstract: In [4] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Eucli...

ProVeLines: a product line of verifiers for software product lines

Abstract: Software Product Lines (SPLs) are families of similar software products built from a common set of features. As the number of products of an SPL is potentially exponential in the number of its features, the model checking problem is harder than for single software. A practical way to face this exponential blow-up is to reuse common behaviour between products. We previously introduced Featured Transition Systems (FTS), a mathematical model that serves as a basis for efficient SPL model checking techniques. In this paper, we present ProVeLines, a product line of verifiers for SPLs that incorporates the results of over three years of research on formal verification of SPLs. Being itself a product line, our tool is flexible and extensible, and offers a wide range of solutions for SPL modelling and verification.

Supporting keyword search in product database: a probabilistic approach

Abstract: The ability to let users search for products conveniently in product database is critical to the success of e-commerce. Although structured query languages (e.g. SQL) can be used to effectively access the product database, it is very difficult for end users to learn and use. In this paper, we study how to optimize search over structured product entities (represented by specifications) with keyword queries such as "cheap gaming laptop". One major difficulty in this problem is the vocabulary gap between the specifications of products in the database and the keywords people use in search queries. To solve the problem, we propose a novel probabilistic entity retrieval model based on query generation, where the entities would be ranked for a given keyword query based on the likelihood that a user who likes an entity would pose the query. Different ways to estimate the model parameters would lead to different variants of ranking functions. We start with simple estimates based on the specifications of entities, and then leverage user reviews and product search logs to improve the estimation. Multiple estimation algorithms are developed based on Maximum Likelihood and Maximum a Posteriori estimators. We evaluate the proposed product entity retrieval models on two newly created product search test collections. The results show that the proposed model significantly outperforms the existing retrieval models, benefiting from the modeling of attribute-level relevance. Despite the focus on product retrieval, the proposed modeling method is general and opens up many new opportunities in analyzing structured entity data with unstructured text data. We show the proposed probabilistic model can be easily adapted for many interesting applications including facet generation and review annotation.

Warped product pointwise semi-slant submanifolds of Kähler manifolds

Abstract: It is known that there exist no warped product semi-slant submanifolds in Kaehler manifolds \\cite{Sahin}. Recently, Chen and Garay studied pointwise-slant submanifolds of almost Hermitian manifolds in \\cite{CG} and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant submanifolds of Kaehler manifolds and then we show that there exists non-trivial warped product pointwise semi-slant submanifolds of Kaehler manifold by giving an example, contrary to the semi-slant case. We present a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such warped product submanifolds in Kaehler manifolds. The equality case is also considered.

Active Knowledge for the Situation-driven Control of Product Definition

Abstract: The current product model consists of features and unstructured contextual connections in order to relate features. The feature modifies the previous state of the product model producing contextual connections with previously defined features. Active knowledge is applied for the adaptive modification of product model features in the case of a changed situation or event. Starting from this state-of-the-art, the authors of this paper introduced a new method to achieve higher-level and more advanced active feature driven product model definition. As part of the related research program, new situation driven model definition processes and model entities are explained in this paper. Higher-level knowledge representation in the product model is motivated by a recent trend in industrial product modeling systems towards more advanced and efficient situation-based self- adaptive model generation. The proposed model represents one of the possible future ways of product model development for product lifecycle management (PLM) systems on the global or product level of decisions. Its implementation will be new application-oriented model entity generation and representation utilizing existing modeling resources in industrial PLM systems by use of application programming interfaces (API).

Recovering traceability between features and code in product variants

Abstract: Many companies offer a palette of similar software products though they do not necessarily have a Software Product Line (SPL). Rather, they start building and selling individual products which they then adapt, customize and extend for different customers. As the number of product variants increases, these companies then face the severe problem of having to maintain them all. Software Product Lines can be helpful here - not so much as a platform for creating new products but as a means of maintaining the existing ones with their shared features. Here, an important first step is to determine where features are implemented in the source code and in what product variants. To this end, this paper presents a novel technique for deriving the traceability between features and code in product variants by matching code overlaps and feature overlaps. This is a difficult problem because a feature's implementation not only covers its basic functionality (which does not change across product variants) but may include code that deals with feature interaction issues and thus changes depending on the combination of features present in a product variant. We empirically evaluated the approach on three non-trivial case studies of different sizes and domains and found that our approach correctly identifies feature to code traces except for code that traces to multiple disjunctive features, a rare case involving less than 1% of the code.

Performance regression manager for large scale systems

Abstract: System and computer program product to perform an operation comprising generating, based on a first output generated by a first execution instance of a command, a first output file specifying a value of at least one performance metric, wherein the first output file is formatted according to a predefined format, comparing the value of the at least one performance metric in the first output file to a value of the performance metric in a second output file, the second output file having been generated based on a second output generated by a second execution instance of the command, and outputting for display an indication a result of the comparison of the value of the at least one performance metric of the first output file to the value of the at least one performance metric of the second output file.

Discrete shape modeling for skin model representation

Abstract: Nowadays, the management of product geometrical variations during the whole product development process is an important issue for companies’ competitiveness. During the design phase, geometric func...