Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras

The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\mathfrak{g}$ has a quantum cluster algebra structure of skew-symmetric type. Partly motivated by a search of a ring corresponding to a quantum cluster algebra of {\em skew-symmetrizable} type, the quantum {\em virtual} Grothendieck ring, denoted by $\mathfrak{K}_q(\mathfrak{g})$, is recently introduced by Kashiwara--Oh \cite{KO23} as a subring of the quantum torus based on the $(q,t)$-Cartan matrix specialized at $q=1$. In this paper, we prove that $\mathfrak{K}_q(\mathfrak{g})$ indeed has a quantum cluster algebra structure of skew-symmetrizable type. This task essentially involves constructing distinguished bases of $\mathfrak{K}_q(\mathfrak{g})$ that will be used to make cluster variables and generalizing the quantum $T$-system associated with Kirillov--Reshetikhin modules to establish a quantum exchange relation of cluster variables. Furthermore, these distinguished bases naturally fit into the paradigm of Kazhdan--Lusztig theory and our study of these bases leads to some conjectures on quantum positivity and $q$-commutativity

One-dimensional broadband phononic crystal filter with unit cells made of two non-uniform impedance-mirrored elements

A one-dimensional finite-sized phononic crystal(PC) made of a specially-configured unit cell is proposed to realize broad bandpass, high-performance filtering. The unit cell is specially-configured with two elements having mirrored impedance distributions of each other. One element has a non-uniform impedance distribution that is so engineered as to maximize wave transmission in the pass band and to minimize transmission in the adjacent stop band while the other, exactly the mirrored distribution. The mirroring approach naturally yields the overall impedance contrast within the resulting unit cell, necessary to form stop bands in a PC of the unit cells. More importantly, the good transmission performance of the orginally-engineered element can be preserved by the approach because no additional impedance mismatch is introduced along the interface of the two impedance-mirrored elements. Extraordinary performance of the PC filter made of the proposed unit cell, such as high transmission, large bandwidth and sharp roll-off, is demonstrated by using one-dimensional longitudinal elastic wave problems. Copyright 2013 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4790638ope

Zero-frequency Bragg gap by spin-harnessed metamaterial

The Bragg gap that stops wave propagation may not be formed from zero or a very low frequency unless the periodicity of a periodic system is unrealistically large. Accordingly, the Bragg gap has been considered to be inappropriate for low frequency applications despite its broad bandwidth. Here, we report a new mechanism that allows formation of the Bragg gap starting from a nearly zero frequency. The mechanism is based on the finding that if additional spin motion is coupled with the longitudinal motion of a mass of a diatomic mechanical periodic system, the Bragg gap starting from a nearly zero frequency can be formed. The theoretical analysis shows that the effective mass and stiffness at the band gap frequencies are all positive, confirming that the formed stop band is a Bragg gap. The periodic system is realized by a spin-harnessed metamaterial which incorporates unique linkage mechanisms. The numerical and experimental validation confirmed the formation of the low-frequency Bragg gap. The zero-frequency Bragg gap is expected to open a new way to control hard-to-shield low-frequency vibration and noise

An efficient method for detection of key objects in video shots with camera motions

The most fundamental task in video processing is to partition long video sequences into a number of shots and find a key frame of each shot for indexing and browsing.keywords: Video object segmentacion, shot boundary detection, color quantization, MPEG-4/MPEG-7

Islands stretch test for measuring the interfacial fracture energy between a hard film and a soft substrate

We present a technique for measuring the interfacial fracture energy, $\Gamma_i$, between a hard thin film and a soft substrate. A periodic array of hard thin islands is fabricated on a soft substrate, which is then subjected to uniaxial tension under an optical microscope. When the applied strain reaches a critical value, delamination between the islands and the substrate starts from the edge of the islands. As the strain is increased, the interfacial cracks grow in a stable fashion. At a given applied strain, the width of the delaminated region is a unique function of the interfacial fracture energy. We have calculated the energy release rate driving the delamination as a function of delamination width, island size, island thickness, and applied strain. For a given materials system, this relationship allows determination of the interfacial fracture energy from a measurement of the delamination width. The technique is demonstrated by measuring the interfacial fracture energy of plasma-enhanced chemical vapor deposition SiNx islands on a polyimide substrate. We anticipate that this technique will find application in the flexible electronics industry where hard islands on soft substrates are a common architecture to protect active devices from fracture.Engineering and Applied Science

Application of Artificial Neural Network to Search for Gravitational-Wave Signals Associated with Short Gamma-Ray Bursts

We apply a machine learning algorithm, the artificial neural network, to the search for gravitational-wave signals associated with short gamma-ray bursts. The multi-dimensional samples consisting of data corresponding to the statistical and physical quantities from the coherent search pipeline are fed into the artificial neural network to distinguish simulated gravitational-wave signals from background noise artifacts. Our result shows that the data classification efficiency at a fixed false alarm probability is improved by the artificial neural network in comparison to the conventional detection statistic. Therefore, this algorithm increases the distance at which a gravitational-wave signal could be observed in coincidence with a gamma-ray burst. In order to demonstrate the performance, we also evaluate a few seconds of gravitational-wave data segment using the trained networks and obtain the false alarm probability. We suggest that the artificial neural network can be a complementary method to the conventional detection statistic for identifying gravitational-wave signals related to the short gamma-ray bursts.Comment: 30 pages, 10 figure