Showing papers on "Product (mathematics) published in 2014"

Model-theoretic methods in the study of elementary logic

Abstract: Publisher Summary This chapter discusses model-theoretic methods in the study of elementary logic. In order to study the structural and recursive properties of first-order theories, we introduce the notion of isomorphism of theories. Two theories are isomorphic if there is a one-to-one recursive correspondence between sentences of one theory and sentences of the other which preserves implications valid in the theories. The main result of the paper is that there exists a finitely axiomatizable theory isomorphic to a theory constructed as a product of a fixed theory and an arbitrary axiomatizable theory. The fundamental property of the theory F is that in any model, the successive rows of the array accurately reflect the operations machine M would go through if started with the tape represented by the first row of the array. However, that if the filler elements or some equivalent device had not been introduced, there would be no hope of proving that the degree of undecidability of F is at most that of T. For it could happen that even though T is decidable, the decision procedure gave for its axiom set could involve as intermediate steps the examination of proofs within, say, some system of arithmetic.

Singular values of products of random matrices and polynomial ensembles

Abstract: Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product of M complex Ginibre matrices are distributed according to a determinantal point process. We introduce the notion of a polynomial ensemble and show how their result can be interpreted as a transformation of polynomial ensembles. We also show that the squared singular values of the product of M - 1 complex Ginibre matrices with one truncated unitary matrix is a polynomial ensemble, and we derive a double integral representation for the correlation kernel associated with this ensemble. We use this to calculate the scaling limit at the hard edge, which turns out to be the same scaling limit as the one found by Kuijlaars and Zhang for the squared singular values of a product of M complex Ginibre matrices. Our final result is that these limiting kernels also appear as scaling limits for the biorthogonal ensembles of Borodin with parameter θ > 0, in case θ or 1/θ is an integer. This further supports the conjecture that these kernels have a universal character.

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.

Unbounded bivariant k-theory and correspondences in noncommutative geometry

Abstract: By adapting the algebraic notion of universal connection to the setting of unbounded KK-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of smooth algebras and a notion of differentiable C � -module. The theory of operator spaces provides the required tools. Finally, the above mentioned KK-cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples.

Hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making

Abstract: Hamacher product is a t-norm and Hamacher sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some hesitant fuzzy aggregation operators. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy multiple attribute decision making problems. Finally, a practical example for evaluating the customer satisfaction of e-commerce websites is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Comparison of exact and approximate multi-objective optimization for software product lines

Abstract: Software product lines (SPLs) allow stakeholders to manage product variants in a systematical way and derive variants by selecting features. Finding a desirable variant is often difficult, due to the huge configuration space and usually conflicting objectives (e.g., lower cost and higher performance). This scenario can be characterized as a multi-objective optimization problem applied to SPLs. We address the problem using an exact and an approximate algorithm and compare their accuracy, time consumption, scalability, parameter setting requirements on five case studies with increasing complexity. Our empirical results show that (1) it is feasible to use exact techniques for small SPL multi-objective optimization problems, and (2) approximate methods can be used for large problems but require substantial effort to find the best parameter setting for acceptable approximation which can be ameliorated with known good parameter ranges. Finally, we discuss the tradeoff between accuracy and time consumption when using exact and approximate techniques for SPL multi-objective optimization and guide stakeholders to choose one or the other in practice.

Language modeling with sum-product networks.

Abstract: Sum product networks (SPNs) are a new class of deep probabilistic models. They can contain multiple hidden layers while keeping their inference and training times tractable. An SPN consists of interleaving layers of sum nodes and product nodes. A sum node can be interpreted as a hidden variable, and a product node can be viewed as a feature capturing rich interactions among an SPN’s inputs. We show that the ability of SPN to use hidden layers to model complex dependencies among words, and its tractable inference and learning times, make it a suitable framework for a language model. Even though SPNs have been applied to a variety of vision problems [1, 2], we are the first to use it for language modeling. Our empirical comparisons with six previous language models indicate that our SPN has superior performance.

From symplectic measurements to the Mahler conjecture

Abstract: In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains and Mahler’s conjecture on the volume product of centrally symmetric convex bodies. More precisely, we show that if for convex bodies of fixed volume in the classical phase space the Hofer–Zehnder capacity is maximized by the Euclidean ball, then a hypercube is a minimizer for the volume product among centrally symmetric convex bodies.

Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks

Abstract: This paper investigates the output controllability problem of temporal Boolean networks with inputs (control nodes) and outputs (controlled nodes). A temporal Boolean network is a logical dynamic system describing cellular networks with time delays. Using semi-tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems. Some necessary and sufficient conditions on the output controllability via two kinds of inputs are obtained by providing corresponding reachable sets. Two examples are given to illustrate the obtained results.

Higgs branch localization of $\mathcal{N}=1$ theories on $S^3 \times S^1$

Abstract: We apply the method of Higgs branch localization to the $\mathcal{N}=1$ supersymmetric partition function on $S^3\times S^1.$ As a result, we show that it can be written as the product of an elliptic vortex and anti-vortex partition function summed over a finite number of Higgs vacua.

Lifting model transformations to product lines

Abstract: Software product lines and model transformations are two techniques used in industry for managing the development of highly complex software. Product line approaches simplify the handling of software variants while model transformations automate software manipulations such as refactoring, optimization, code generation, etc. While these techniques are well understood independently, combining them to get the benefit of both poses a challenge because most model transformations apply to individual models while model-level product lines represent sets of models. In this paper, we address this challenge by providing an approach for automatically ``lifting'' model transformations so that they can be applied to product lines. We illustrate our approach using a case study and evaluate it through a set of experiments.

The balanced tensor product of module categories

Abstract: The balanced tensor product M (x)_A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N. The balanced tensor product M [x]_C N of two module categories over a monoidal linear category C is the linear category corepresenting C-balanced right-exact bilinear functors out of the product category M x N. We show that the balanced tensor product can be realized as a category of bimodule objects in C, provided the monoidal linear category is finite and rigid.

Nearly Overconvergent Modular Forms

Abstract: We introduce and study finite slope nearly overconvergent (elliptic) modular forms We give an application of this notion to the construction of the Rankin-Selberg p-adic L-function on the product of two eigencurves

Emotional design method of product presented in multi-dimensional variables based on Kansei Engineering

Abstract: In the fiercely competitive product market, product designs have already moved from the product-oriented approach to a marketing-oriented approach, and gradually to a customer-oriented approach Therefore, it is of high necessity to study users’ emotional needs aroused by the product's multi-dimensional design variables This paper contributes a systematically emotional design method of products’ hard interface based on Kansei Engineering (KE), which can be used to design a product that echoes users’ emotions Based on the representative pairwise Kansei image words and multi-dimensional key design variables obtained by the consumer-oriented techniques, the KE models are established Finally, the integration of KE models and Genetic Algorithm is employed to search for a near-optimal design scheme This proposed method is effectively demonstrated in terms of the mini digital camera It can be used in various design cases to optimise the product emotional design

Nonlocality of orthogonal product basis quantum states

Abstract: In this paper, we mainly study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum systems. In the Hilbert space of $3\ensuremath{\bigotimes}3$, Walgate and Hardy [Phys. Rev. Lett. 89, 147901 (2002)] presented a very simple proof for nonlocality of nine orthogonal product basis quantum states which are given by Bennett et al. [Phys. Rev. A 59, 1070 (1999)]. In the quantum system of $d\ensuremath{\bigotimes}d$, where $d$ is odd, we construct ${d}^{2}$ orthogonal product basis quantum states and prove these states are locally indistinguishable. Then we are able to construct some locally indistinguishable product basis quantum states in the multipartite systems. All these results reveal the phenomenon of ``nonlocality without entanglement.''

Store shelf imaging system

Abstract: A store profile generation system includes a mobile base and an image capture assembly mounted on the base. The assembly includes at least one image capture device for acquiring images of product display units in a product facility, product labels being associated with the product display units which include product-related data. A control unit acquires the images captured by the at least one image capture device at a sequence of locations of the mobile base in the product facility. The control unit extracts the product-related data from the acquired images and constructs a store profile indicating locations of the product labels throughout the product facility, based on the extracted product-related data. The store profile can be used for generating new product labels for a sale in an appropriate order for a person to match to the appropriate locations in a single pass through the store.

Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem

Abstract: We will prove a decomposition for Wasserstein geodesics in the following sense: let (X, d, m) be a non-branching metric measure space verifying \({\mathsf{CD}_{loc}(K,N)}\) or equivalently \({\mathsf{CD}^{*}(K,N)}\). We prove that every geodesic \({\mu_{t}}\) in the L2-Wasserstein space, with \({\mu_{t} \ll m}\), is decomposable as the product of two densities, one corresponding to a geodesic with support of codimension one verifying \({\mathsf{CD}^{*}(K,N-1)}\), and the other associated with a precise one dimensional measure, provided the length map enjoys local Lipschitz regularity. The motivation for our decomposition is in the use of the component evolving like \({\mathsf{CD}^{*}}\) in the globalization problem. For a particular class of optimal transportation we prove the linearity in time of the other component, obtaining therefore the global \({\mathsf{CD}(K,N)}\) for \({\mu_{t}}\). The result can be therefore interpret as a globalization theorem for \({\mathsf{CD}(K,N)}\) for this class of optimal transportation, or as a “self-improving property” for \({\mathsf{CD}^{*}(K,N)}\). Assuming more regularity, namely in the setting of infinitesimally strictly convex metric measure space, the one dimensional density is the product of two differentials giving more insight on the density decomposition.

DeltaJ 1.5: delta-oriented programming for Java 1.5

Abstract: Delta-oriented programming (DOP) is a modular, yet flexible approach to implement software product lines. In DOP, a product line is implemented by a set of deltas, which are containers of modifications to a program. A delta-oriented product line is specified by its code base, i.e., the set of delta modules, and a product line declaration specifying the set of possible product variants. In this paper, we present DOP for Java 1.5 extending previous proof-of-concept realizations of DOP for simple core Java-like languages. The novel prototypical implementation DeltaJ 1.5 provides full integrated access to the object-oriented features of Java. The extensions include delta operations to fully integrate the Java package system, to declare and modify interfaces, to explicitly change the inheritance hierarchy, to access nested types and enum types, to alter field declarations, and to unambiguously remove overloaded methods. Furthermore, we improve the specification of the product line declaration by providing a separate language. We have evaluated DeltaJ 1.5 using a case study.

IHS R&D Belarus: Cross-domain extraction of product features using CRF

Abstract: This paper describes the aspect extraction system submitted by IHS R&D Belarus team at the SemEval-2014 shared task related to Aspect-Based Sentiment Analysis. Our system is based on IHS Goldfire linguistic processor and uses a rich set of lexical, syntactic and statistical features in CRF model. We participated in two domain-specific tasks – restaurants and laptops – with the same system trained on a mixed corpus of reviews. Among submissions of constrained systems from 28 teams, our submission was ranked first in laptop domain and fourth in restaurant domain for the subtask A devoted to aspect extraction.

Polymerizable composition for optical material and optical material

Abstract: Disclosed is a polymerizable composition for an optical material containing polyisocyanate (a) which is obtained from a plant-derived raw material and includes a modified product of aliphatic polyisocyanate, alicyclic polyisocyanate (b), and polyol (c) which has a hydroxyl value of 300 mgKOH/g to 650 mgKOH/g and the average number of functional groups of 2 or more and less than 7, and which is obtained from a plant-derived raw material.

Matrix product codes over finite commutative Frobenius rings

Abstract: Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product codes are also explicitly described in terms of matrix product codes.

Extended k - Q product formulas for capacitive- and inductive-coupling wireless power transfer schemes

Abstract: This paper presents versatile formulas that characterize wireless power transfer schemes in arbitrary coupling topologies. Maximum available coupling efficiency is formulated in two-port immittance matrix domain invariant to source and load conditions. Key performance index k-Q product is extended to general cases even where resonance or filtering model is inapplicable. Typical capacitiveand inductive-coupling schemes are shown with their k-Q product instances.

Spectral Approximation on the Unit Ball

Abstract: Spectral approximation by polynomials on the unit ball is studied in the frame of the Sobolev spaces $W^{s}_p(\mathbb{B}^d)$, $1

System, Method, And Apparatus For Purchasing, Dispensing, Or Sampling Of Products

Abstract: A product dispenser is configured to dispense products subject to a warning and products not subject to a warning, the product dispenser further configured to transmit a product warning notice only in response to a request to dispense a product subject to the warning. In another embodiment, a product dispenser is configured to dispense a food or beverage product and provide information indicative of an attribute of the food or beverage product, such as nutrition facts, as it is being dispensed. In another embodiment, a product dispenser is configured to enable a user to request a customized product from the product dispenser, to determine a first profile for the customized product blend, compare the first profile to a second profile, and reformulate the customized product blend to a dispensed product blend comprising a third profile approximating the second idealized profile.

Extending structures for Lie algebras

Abstract: Let \(\mathfrak{g }\) be a Lie algebra, \(E\) a vector space containing \(\mathfrak{g }\) as a subspace. The paper is devoted to the extending structures problem which asks for the classification of all Lie algebra structures on \(E\) such that \(\mathfrak{g }\) is a Lie subalgebra of \(E\). A general product, called the unified product, is introduced as a tool for our approach. Let \(V\) be a complement of \(\mathfrak{g }\) in \(E\): the unified product \(\mathfrak{g } \, atural \, V\) is associated to a system \((\triangleleft , \, \triangleright , \, f, \{-, \, -\})\) consisting of two actions \(\triangleleft \) and \(\triangleright \), a generalized cocycle \(f\) and a twisted Jacobi bracket \(\{-, \, -\}\) on \(V\). There exists a Lie algebra structure \([-,-]\) on \(E\) containing \(\mathfrak{g }\) as a Lie subalgebra if and only if there exists an isomorphism of Lie algebras \((E, [-,-]) \cong \mathfrak{g } \, atural \, V\). All such Lie algebra structures on \(E\) are classified by two cohomological type objects which are explicitly constructed. The first one \(\mathcal{H }^{2}_{\mathfrak{g }} (V, \mathfrak{g })\) will classify all Lie algebra structures on \(E\) up to an isomorphism that stabilizes \(\mathfrak{g }\) while the second object \(\mathcal{H }^{2} (V, \mathfrak{g })\) provides the classification from the view point of the extension problem. Several examples that compute both classifying objects \(\mathcal{H }^{2}_{\mathfrak{g }} (V, \mathfrak{g })\) and \(\mathcal{H }^{2} (V, \mathfrak{g })\) are worked out in detail in the case of flag extending structures.

Observability conditions of Boolean control networks

Abstract: SUMMARY Observability is a basic, yet challenging, issue when studying Boolean control networks (BCNs). Recently, a criterion for observability of controllable BCNs was proposed by using the algebraic representation of logical dynamics based on the technique of the semi-tensor product of matrices. In this paper, we present new necessary and sufficient conditions guaranteeing observability of a BCN without preassuming its controllability. The conditions are hence more general. Some examples are worked out to illustrate the obtained results. Copyright © 2013 John Wiley & Sons, Ltd.

System and method for presenting true product dimensions within an augmented real-world setting

Abstract: Methods, systems, computer-readable media, and apparatuses for presenting a representation of an augmented real-world setting are presented. In some embodiments, a method includes presenting a representation of an augmented real-world setting. The method includes capturing a plurality of images of a real-world setting. The method also includes analyzing one or more real-world objects within the plurality of images of the real-world setting. The method further includes receiving information pertaining to a real-world product, wherein the information is indicative of first physical dimensions of the real-world product during a first mode of operation and second physical dimensions of the real-world product during a second mode of operation and overlaying an augmented reality object depicting the real-world product during the first mode of operation, and having the first physical dimensions, within at least one of the plurality of images of the real-world setting, based at least in part on the analyzing step.