Showing papers on "Product (mathematics) published in 2018"

Digital twin – Proof of concept

Abstract: Miniaturization and price decline enable the integration of information, communication and sensor technologies into virtually any product. Products become able to sense their own state as well as the state of their environment. Paired with the ability to process and communicate this data allows for the creation of digital twins. The digital twin is a comprehensive digital representation of an individual product that will play an integral role in a fully digitalized product life cycle. To prove the digital twin concept a cyber-physical bending beam test bench was developed at DiK research lab.

Double Embeddings and CNN-based Sequence Labeling for Aspect Extraction

Abstract: One key task of fine-grained sentiment analysis of product reviews is to extract product aspects or features that users have expressed opinions on. This paper focuses on supervised aspect extraction using deep learning. Unlike other highly sophisticated supervised deep learning models, this paper proposes a novel and yet simple CNN model employing two types of pre-trained embeddings for aspect extraction: general-purpose embeddings and domain-specific embeddings. Without using any additional supervision, this model achieves surprisingly good results, outperforming state-of-the-art sophisticated existing methods. To our knowledge, this paper is the first to report such double embeddings based CNN model for aspect extraction and achieve very good results.

Outer product-based neural collaborative filtering

Abstract: In this work, we contribute a new multi-layer neural network architecture named ONCF to perform collaborative filtering. The idea is to use an outer product to explicitly model the pairwise correlations between the dimensions of the embedding space. In contrast to existing neural recommender models that combine user embedding and item embedding via a simple concatenation or element-wise product, our proposal of using outer product above the embedding layer results in a two-dimensional interaction map that is more expressive and semantically plausible. Above the interaction map obtained by outer product, we propose to employ a convolutional neural network to learn high-order correlations among embedding dimensions. Extensive experiments on two public implicit feedback data demonstrate the effectiveness of our proposed ONCF framework, in particular, the positive effect of using outer product to model the correlations between embedding dimensions in the low level of multi-layer neural recommender model.

Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm

Abstract: In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product). Induced by the t-product, we first rigorously deduce the tensor spectral norm, tensor nuclear norm, and tensor average rank, and show that the tensor nuclear norm is the convex envelope of the tensor average rank within the unit ball of the tensor spectral norm. These definitions, their relationships and properties are consistent with matrix cases. Equipped with the new tensor nuclear norm, we then solve the TRPCA problem by solving a convex program and provide the theoretical guarantee for the exact recovery. Our TRPCA model and recovery guarantee include matrix RPCA as a special case. Numerical experiments verify our results, and the applications to image recovery and background modeling problems demonstrate the effectiveness of our method.

Low-Power Approximate Multipliers Using Encoded Partial Products and Approximate Compressors

Abstract: Approximate computing has been considered to improve the accuracy-performance tradeoff in error-tolerant applications. For many of these applications, multiplication is a key arithmetic operation. Given that approximate compressors are a key element in the design of power-efficient approximate multipliers, we first propose an initial approximate 4:2 compressor that introduces a rather large error to the output. However, the number of faulty rows in the compressor’s truth table is significantly reduced by encoding its inputs using generate and propagate signals. Based on this improved compressor, two $4\times 4$ multipliers are designed with different accuracies and then are used as building blocks for scaling up to $16\,\times \,16$ and $32\times 32$ multipliers. According to the mean relative error distance (MRED), the most accurate of the proposed $16\,\times \,16$ unsigned designs has a 44% smaller power-delay product (PDP) compared to other designs with comparable accuracy. The radix-4 signed Booth multiplier constructed using the proposed compressor achieves a 52% reduction in the PDP-MRED product compared to other approximate Booth multipliers with comparable accuracy. The proposed multipliers outperform other approximate designs in image sharpening and joint photographic experts group applications by achieving higher quality outputs with lower power consumptions. For the first time, we show the applicability and practicality of approximate multipliers in multiple-input multiple-output antenna communication systems with error control coding.

Stochastic Cubic Regularization for Fast Nonconvex Optimization

Abstract: This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general smooth, nonconvex functions in only $\mathcal{\tilde{O}}(\epsilon^{-3.5})$ stochastic gradient and stochastic Hessian-vector product evaluations. The latter can be computed as efficiently as stochastic gradients. This improves upon the $\mathcal{\tilde{O}}(\epsilon^{-4})$ rate of stochastic gradient descent. Our rate matches the best-known result for finding local minima without requiring any delicate acceleration or variance-reduction techniques.

A survey on applications of semi-tensor product method in engineering

Abstract: Semi-tensor product (STP) of matrices has attracted more and more attention from both control theory and engineering in the last two decades. This paper presents a comprehensive survey on the applications of STP method in engineering. Firstly, some preliminary results on STP method are recalled. Secondly, some applications of STP method in engineering, including gene regulation, power system, wireless communication, smart grid, information security, combustion engine and vehicle control, are reviewed. Finally, some potential applications of STP method are predicted.

Function-Hiding Inner Product Encryption Is Practical

Abstract: In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages. Given a secret key for a function f, and a ciphertext for a message x, a decryptor learns f(x) and nothing else about x. Inner product encryption is a special case of functional encryption where both secret keys and ciphertext are associated with vectors. The combination of a secret key for a vector \({\mathbf {x}}\) and a ciphertext for a vector \(\mathbf {y}\) reveal \(\langle {\mathbf {x}}, \mathbf {y}\rangle \) and nothing more about \(\mathbf {y}\). An inner product encryption scheme is function-hiding if the keys and ciphertexts reveal no additional information about both \({\mathbf {x}}\) and \(\mathbf {y}\) beyond their inner product.

Nonsingularity of Grain-like cascade FSRs via semi-tensor product

Abstract: In this paper, Grain-like cascade feedback shift registers (FSRs) are regarded as two Boolean networks (BNs), and the semi-tensor product (STP) of the matrices is used to convert the Grain-like cascade FSRs into an equivalent linear equation. Based on the STP, a novel method is proposed herein to investigate the nonsingularity of Grain-like cascade FSRs. First, we investigate the property of the state transition matrix of Grain-like cascade FSRs. We then propose their sufficient and necessary nonsingularity condition. Next, we regard the Grain-like cascade FSRs as Boolean control networks (BCNs) and further provide a sufficient condition of their nonsingularity. Finally, two examples are provided to illustrate the results obtained in this paper.

F-theory and AdS3/CFT2 (2,0)

Abstract: We continue to develop the program initiated in [1] of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d $$ \mathcal{N}=\left(0,2\right) $$ supersymmetry,wederivethegeneralconditionsonthegeometryforTypeIIB AdS3 solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold $$ {\mathcal{Y}}_8^{\tau } $$ , which is elliptically fibered over a base $$ {\tilde{\mathrm{\mathcal{M}}}}_6 $$ . We construct two classes of solutions given in terms of a product ansatz $$ \tilde{{\mathrm{\mathcal{M}}}_6}=\varSigma \times {\mathrm{M}}_4 $$ , where Σ is a complex curve and $$ {\tilde{\mathrm{\mathcal{M}}}}_4 $$ is locally a Kahler surface. In the first class $$ {\tilde{\mathrm{\mathcal{M}}}}_4 $$ is globally a Kahler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS3 × K3 × ℳ 5 , dual to 2d (0, 2) SCFTs, and AdS3 × S3/Γ × CY3, dual to 2d (0, 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d $$ \mathcal{N}=\left(2,2\right) $$ supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d $$ \mathcal{N}=1 $$ SCFTs.

Several nonlocal sets of multipartite pure orthogonal product states

Abstract: It is known that there exist sets of pure orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are nonlocal sets which exhibit nonlocality without entanglement. These nonlocal sets can be completable or uncompletable. In this work both completable and uncompletable small nonlocal sets of multipartite orthogonal product states are constructed. Apart from nonlocality, these sets have other interesting properties. In particular, the completable sets lead to the construction of a class of complete orthogonal product bases with the property that if such a basis is given then no state can be eliminated from that basis by performing orthogonality-preserving measurements. On the other hand, an uncompletable set of the present kind contains several Shifts unextendible product bases (UPBs) that belong to qubit subspaces. Identifying these subspace UPBs, it is possible to obtain a class of high-dimensional multipartite bound entangled states. Finally, it is shown that a two-qubit maximally entangled Bell state shared between any two parties is sufficient as a resource to distinguish the states of any completable set (of the above kind) perfectly by LOCC. This constitutes an example where the amount of entanglement, sufficient to accomplish the aforesaid task, depends neither on the dimension of the individual subsystems nor on the number of parties.

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 pr...

PointCNN: Convolution On $\mathcal{X}$-Transformed Points

Abstract: We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point clouds are irregular and unordered, thus directly convolving kernels against features associated with the points, will result in desertion of shape information and variance to point ordering. To address these problems, we propose to learn an $\mathcal{X}$-transformation from the input points, to simultaneously promote two causes. The first is the weighting of the input features associated with the points, and the second is the permutation of the points into a latent and potentially canonical order. Element-wise product and sum operations of the typical convolution operator are subsequently applied on the $\mathcal{X}$-transformed features. The proposed method is a generalization of typical CNNs to feature learning from point clouds, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks.

A High-Performance Gate Engineered InGaN Dopingless Tunnel FET

Abstract: A gate engineered InGaN dopingless tunnel FET (DL-TFET) using the charge plasma concept is proposed and investigated by silvaco Atlas simulation. In0.75Ga0.25N is a direct gap semiconductor, and the effective tunneling mass of electron and hole is smaller than that of silicon, which induces that the drain current and average subthreshold swing (SSavg) of InGaN DL-TFET improve $\text {1.3}\times \text {10}^{\text {2}}$ times and 51.1% than that of Si DL-TFET at the overdrive voltage of 0.5 V, respectively. What is more, better device performances are achieved by gate engineering with appropriate “In” fraction, proper space between the gate and source ( ${L}_{\text {gs}}$ ), and appropriate tunneling gate work function ( $\Phi _{\text {TG}}$ ). The direct-current, RF, and energy-efficient performance studies show that SSavg of 7.9 mV/dec, an on-state current ( ${I}_{ \mathrm{\scriptscriptstyle ON}}$ ) of $\text {8.02} \times \text {10}^{-\text {5}}$ A/ $\mu \text{m}$ , a cutoff frequency ( ${f}_{T}$ ) of 119 GHz, and an energy delay product of 0.64 fJ-ps/ $\mu \text{m}$ can be obtained in the proposed TFET. This paper indicates that the gate engineered InGaN DL-TFET is a promising TFET for low-power RF and digital logic applications.

Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

Abstract: We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling ${f}^{2}(\ensuremath{\phi}){F}_{\ensuremath{\mu}\ensuremath{ u}}{F}^{\ensuremath{\mu}\ensuremath{ u}}$ of the electromagnetic field to the inflaton field $\ensuremath{\phi}$. We consider the case where the coupling function $f(\ensuremath{\phi})$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter $\ensuremath{\epsilon}$ and inflaton energy density, ${\ensuremath{\rho}}_{E}\ensuremath{\sim}\ensuremath{\epsilon}{\ensuremath{\rho}}_{\mathrm{inf}}$. It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index ${n}_{B}=2$ for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below ${10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{G}$. It is worth emphasizing that since the effective electric charge of particles ${e}_{\mathrm{eff}}=e/f$ is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike $f\ensuremath{\propto}{a}^{\ensuremath{\alpha}}$ and Ratra-type $f=\mathrm{exp}(\ensuremath{\beta}\ensuremath{\phi}/{M}_{p})$ coupling functions.

Search for beautiful tetraquarks in the $\Upsilon(1S)\mu\mu$ invariant-mass spectrum

Abstract: The $\Upsilon(1S)\mu^+\mu^-$ invariant-mass distribution is investigated for a possible exotic meson state composed of two $b$ quarks and two $\overline{b}$ quarks, $X_{b\overline{b}b\overline{b}}$. The analysis is based on a data sample of $pp$ collisions recorded with the LHCb detector at centre-of-mass energies $\sqrt{s} =$ 7, 8 and 13 TeV, corresponding to an integrated luminosity of 6.3 fb$^{-1}$. No significant excess is found, and upper limits are set on the product of the production cross-section and the branching fraction as functions of the mass of the $X_{b\overline{b}b\overline{b}}$ state. The limits are set in the fiducial volume where all muons have pseudorapidity in the range $[2.0,5.0]$, and the $X_{b\overline{b}b\overline{b}}$ state has rapidity in the range $[2.0,4.5]$ and transverse momentum less than 15 GeV/$c$.

A classification of product sampling for software product lines

Abstract: The analysis of software product lines is challenging due to the potentially large number of products, which grow exponentially in terms of the number of features. Product sampling is a technique used to avoid exhaustive testing, which is often infeasible. In this paper, we propose a classification for product sampling techniques and classify the existing literature accordingly. We distinguish the important characteristics of such approaches based on the information used for sampling, the kind of algorithm, and the achieved coverage criteria. Furthermore, we give an overview on existing tools and evaluations of product sampling techniques. We share our insights on the state-of-the-art of product sampling and discuss potential future work.

Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases

Abstract: In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable C∗-algebra by a twisted ${\mathbb {R}}^{d}$ -action. The spectral triple allows us to employ the non-unital local index formula to obtain the higher Chern numbers in the continuous setting with complex observable algebra. In the case of the crossed product of a compact disorder space, the pairing can be extended to a larger algebra closely related to dynamical localisation, as in the tight-binding approximation. The Kasparov module allows us to exploit the Wiener–Hopf extension and the Kasparov product to obtain a bulk-boundary correspondence for continuous models of disordered topological phases.

The Drazin inverse of an even-order tensor and its application to singular tensor equations

Abstract: The notion of the Moore–Penrose inverses of matrices was recently extended from matrix space to even-order tensor space with Einstein product in the literature. In this paper, we further study the properties of even-order tensors with Einstein product. We define the index and characterize the invertibility of an even-order square tensor. We also extend the notion of the Drazin inverse of a square matrix to an even-order square tensor. An expression for the Drazin inverse through the core-nilpotent decomposition for a tensor of even-order is obtained. As an application, the Drazin inverse solution of the singular linear tensor equation A ∗ X = B will also be included.

Overlaps with arbitrary two-site states in the XXZ spin chain

Abstract: We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the Quench Action and Quantum Transfer Matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states the formula is found to be correct even in chains with odd length, where existing methods can not be applied. It is also pointed out, that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no $\mathcal{O}(1)$ piece in the Quench Action.

Outer Product-based Neural Collaborative Filtering

Abstract: In this work, we contribute a new multi-layer neural network architecture named ONCF to perform collaborative filtering. The idea is to use an outer product to explicitly model the pairwise correlations between the dimensions of the embedding space. In contrast to existing neural recommender models that combine user embedding and item embedding via a simple concatenation or element-wise product, our proposal of using outer product above the embedding layer results in a two-dimensional interaction map that is more expressive and semantically plausible. Above the interaction map obtained by outer product, we propose to employ a convolutional neural network to learn high-order correlations among embedding dimensions. Extensive experiments on two public implicit feedback data demonstrate the effectiveness of our proposed ONCF framework, in particular, the positive effect of using outer product to model the correlations between embedding dimensions in the low level of multi-layer neural recommender model. The experiment codes are available at: this https URL

Direct observation of forward-scattering oscillations in the H+HD→H2+D reaction.

Abstract: Accurate measurements of product state-resolved angular distributions are central to fundamental studies of chemical reaction dynamics. Yet, fine quantum-mechanical structures in product angular distributions of a reactive scattering process, such as the fast oscillations in the forward-scattering direction, have never been observed experimentally and the nature of these oscillations has not been fully explored. Here we report the crossed-molecular-beam experimental observation of these fast forward-scattering oscillations in the product angular distribution of the benchmark chemical reaction, H + HD → H2 + D. Clear oscillatory structures are observed for the H2(v' = 0, j' = 1, 3) product states at a collision energy of 1.35 eV, in excellent agreement with the quantum-mechanical dynamics calculations. Our analysis reveals that the oscillatory forward-scattering components are mainly contributed by the total angular momentum J around 28. The partial waves and impact parameters responsible for the forward scatterings are also determined from these observed oscillations, providing crucial dynamics information on the transient reaction process.

Non-Hermitian random matrices with a variance profile (I): deterministic equivalents and limiting ESDs

Abstract: For each $n$, let $A_n=(\sigma _{ij})$ be an $n\times n$ deterministic matrix and let $X_n=(X_{ij})$ be an $n\times n$ random matrix with i.i.d. centered entries of unit variance. We study the asymptotic behavior of the empirical spectral distribution $\mu _n^Y$ of the rescaled entry-wise product \[ Y_n = \left (\frac 1{\sqrt{n} } \sigma _{ij}X_{ij}\right ). \] For our main result we provide a deterministic sequence of probability measures $\mu _n$, each described by a family of Master Equations, such that the difference $\mu ^Y_n - \mu _n$ converges weakly in probability to the zero measure. A key feature of our results is to allow some of the entries $\sigma _{ij}$ to vanish, provided that the standard deviation profiles $A_n$ satisfy a certain quantitative irreducibility property. An important step is to obtain quantitative bounds on the solutions to an associate system of Schwinger–Dyson equations, which we accomplish in the general sparse setting using a novel graphical bootstrap argument.

Allocating products on shelves under merchandising rules: Multi-level product families with display directions

Abstract: Retailers’ individual products are categorized as part of product families. Merchandising rules specify how the products should be arranged on the shelves using product families, creating more structured displays capable of increasing the viewers’ attention. This paper presents a novel mixed integer programming formulation for the Shelf Space Allocation Problem considering two innovative features emerging from merchandising rules: hierarchical product families and display directions. The formulation uses single commodity flow constraints to model product sequencing and explores the product families’ hierarchy to reduce the combinatorial nature of the problem. Based on the formulation, a mathematical programming-based heuristic was also developed that uses product families to decompose the problem into a sequence of sub-problems. To improve performance, its original design was adapted following two directions: recovery from infeasible solutions and reduction of solution times. A new set of real case benchmark instances is also provided, which was used to assess the formulation and the matheuristic. This approach will allow retailers to efficiently create planograms capable of following merchandising rules and optimizing shelf space revenue.