Search results for: orthogonality

Authors: Mohammed Husein Mohammed Rashid

Abstract:

Let Τ = U |Τ| be a polar decomposition of a bounded linear operator T on a complex Hilbert space with ker U = ker |T|. T is said to be class p-w A(s,t) if (|T*|ᵗ|T|²ˢ|T*|ᵗ )ᵗᵖ/ˢ⁺ᵗ ≥|T*|²ᵗᵖ and |T|²ˢᵖ ≥ (|T|ˢ|T*|²ᵗ|T|ˢ)ˢᵖ/ˢ⁺ᵗ with 0Keywords: class p-w A (s, t), normaloid, isoloid, finite, orthogonality

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Authors: Mohsen Zahraei

Abstract:

‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

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Authors: Chang-Bin Ha, Yong-Jun Kim, Dong-Hyun Ha, Hyoung-Kyu Song

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The conventional Wi-Fi back scatter system can only process one-to-one communication between the Wi-Fi reader and the Wi-Fi tag. For improvement of throughput of the conventional system, this paper proposes the multi-to-multi communication system. In the proposed system, the interference by the multi-to-multi communication is effectively cancelled by the orthogonal multiple access based on the identification code of the tag. Although the overhead is generated by the procedure for the multi-to-multi communication, because the procedure is processed by the Wi-Fi protocol, the overhead is insignificant for the entire communication procedure. From the numerical results, it is confirmed that the proposed system has nearly proportional increased throughput in according to the number of the tag that simultaneously participates in communication.

Keywords: backscatter, multi-to-multi communication, orthogonality, Wi-Fi

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Authors: O. Poleshchuk, E. Komarov

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In this paper, semantic spaces with the properties of completeness and orthogonality (complete orthogonal semantic spaces) were chosen as models of expert evaluations. As the theoretical and practical studies have shown all the properties of complete orthogonal semantic spaces correspond to the thinking activity of experts that is why these semantic spaces were chosen for modeling. Two methods of construction such spaces were proposed. Models of comparative and fuzzy cluster analysis of expert evaluations were developed. The practical application of the developed methods has demonstrated their viability and validity.

Keywords: expert evaluation, comparative analysis, fuzzy cluster analysis, theoretical and practical studies

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Authors: Margarita Grushanina

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After several prominent central banks including European Central Bank (ECB), Federal Reserve System (Fed), Bank of Japan and Bank of England employed unconventional monetary policies in the aftermath of the financial crisis of 2008-2009 the problem of identification of the effects from such policies became of great interest. One of the main difficulties in identification of shocks from unconventional monetary policy measures in structural VAR analysis is that they often are anticipated, which leads to a non-fundamental MA representation of the VAR model. Moreover, the unconventional monetary policy actions may indirectly transmit to markets information about the future stance of the interest rate, which raises a question of the plausibility of the assumption of orthogonality between shocks from unconventional and conventional policy measures. This paper offers a method of identification that takes into account the abovementioned issues. The author uses factor-augmented VARs to increase the information set and identification through heteroskedasticity of error terms and rank restrictions on the errors’ second moments’ matrix to deal with the cross-correlation of the structural shocks.

Keywords: factor-augmented VARs, identification through heteroskedasticity, monetary policy, structural VARs

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Authors: Mohammed S. Al-Rawi, J. Bastos, J. Rodriguez

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Object detection and object recognition are essential components of every computer vision system. Despite the high computational complexity and other problems related to numerical stability and accuracy, Zernike moments of 2D images (ZMs) have shown resilience when used in object recognition and have been used in various image analysis applications. In this work, we propose a novel method for computing ZMs via Fast Fourier Transform (FFT). Notably, this is the first algorithm that can generate ZMs up to extremely high orders accurately, e.g., it can be used to generate ZMs for orders up to 1000 or even higher. Furthermore, the proposed method is also simpler and faster than the other methods due to the availability of FFT software and/or hardware. The accuracies and numerical stability of ZMs computed via FFT have been confirmed using the orthogonality property. We also introduce normalizing ZMs with Neumann factor when the image is embedded in a larger grid, and color image reconstruction based on RGB normalization of the reconstructed images. Astonishingly, higher-order image reconstruction experiments show that the proposed methods are superior, both quantitatively and subjectively, compared to the q-recursive method.

Keywords: Chebyshev polynomial, fourier transform, fast algorithms, image recognition, pseudo Zernike moments, Zernike moments

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Authors: Temidayo Otunniyi

Abstract:

This paper presents a low computational channelization algorithm for the multi-standards platform using poly phase implementation of a critically sampled hybrid Trigonometry generalized Discrete Fourier Transform, (HGDFT). An HGDFT channelization algorithm exploits the orthogonality of two trigonometry Fourier functions, together with the properties of Quadrature Mirror Filter Bank (QMFB) and Exponential Modulated filter Bank (EMFB), respectively. HGDFT shows improvement in its implementation in terms of high reconfigurability, lower filter length, parallelism, and medium computational activities. Type 1 and type 111 poly phase structures are derived for real-valued HGDFT modulation. The design specifications are decimated critically and over-sampled for both single and multi standards receiver platforms. Evaluating the performance of oversampled single standard receiver channels, the HGDFT algorithm achieved 40% complexity reduction, compared to 34% and 38% reduction in the Discrete Fourier Transform (DFT) and tree quadrature mirror filter (TQMF) algorithm. The parallel generalized discrete Fourier transform (PGDFT) and recombined generalized discrete Fourier transform (RGDFT) had 41% complexity reduction and HGDFT had a 46% reduction in oversampling multi-standards mode. While in the critically sampled multi-standard receiver channels, HGDFT had complexity reduction of 70% while both PGDFT and RGDFT had a 34% reduction.

Keywords: software defined radio, channelization, critical sample rate, over-sample rate

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Authors: Mohd Harun, Cini Varghese, Eldho Varghese, Seema Jaggi

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Hybridization crosses find a vital role in breeding experiments to evaluate the combining abilities of individual parental lines or crosses for creation of lines with desirable qualities. There are various ways of obtaining progenies and further studying the combining ability effects of the lines taken in a breeding programme. Some of the most common methods are diallel or two-way cross, triallel or three-way cross, tetra-allele or four-way cross. These techniques help the breeders to improve the quantitative traits which are of economical as well as nutritional importance in crops and animals. Amongst these methods, tetra-allele cross provides extra information in terms of the higher specific combining ability (sca) effects and the hybrids thus produced exhibit individual as well as population buffering mechanism because of the broad genetic base. Most of the common commercial hybrids in corn are either three-way or four-way cross hybrids. Tetra-allele cross came out as the most practical and acceptable scheme for the production of slaughter pigs having fast growth rate, good feed efficiency, and carcass quality. Tetra-allele crosses are mostly used for exploitation of heterosis in case of commercial silkworm production. Experimental designs involving tetra-allele crosses have been studied extensively in literature. Optimality of designs has also been considered as a researchable issue. In practical situations, it is advisable to include sca effects in the model as this information is needed by the breeder to improve economically and nutritionally important quantitative traits. Thus, a model that provides information regarding the specific traits by utilizing sca effects along with general combining ability (gca) effects may help the breeders to deal with the problem of various stresses. In this paper, a model for experimental designs involving tetra-allele crosses that incorporates both gca and sca has been defined. Optimality aspects of such designs have been discussed incorporating sca effects in the model. Orthogonality conditions have been derived for block designs ensuring estimation of contrasts among the gca effects, after eliminating the nuisance factors, independently from sca effects. User friendly SAS macro and web solution (webPTC) have been developed for the generation and analysis of such designs.

Keywords: general combining ability, optimality, specific combining ability, tetra-allele cross, webPTC

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Authors: Leila Safazadeh, Brad Berron

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Self-assembled monolayers have tremendous impact in interfacial science, due to the unique opportunity they offer to tailor surface properties. Low-density self-assembled monolayers are an emerging class of monolayers where the environment-interfacing portion of the adsorbate has a greater level of conformational freedom when compared to traditional monolayer chemistries. This greater range of motion and increased spacing between surface-bound molecules offers new opportunities in tailoring adsorption phenomena in sensing systems. In particular, we expect low-density surfaces to offer a unique opportunity to intercalate surface bound ligands into the secondary structure of protiens and other macromolecules. Additionally, as many conventional sensing surfaces are built upon gold surfaces (SPR or QCM), these surfaces must be compatible with gold substrates. Here, we present the first stable method of generating low-density self assembled monolayer surfaces on gold for the analysis of their interactions with protein targets. Our approach is based on the 2:1 addition of thiol-yne chemistry to develop new classes of y-shaped adsorbates on gold, where the environment-interfacing group is spaced laterally from neighboring chemical groups. This technique involves an initial deposition of a crystalline monolayer of 1,10 decanedithiol on the gold substrate, followed by grafting of a low-packed monolayer on through a photoinitiated thiol-yne reaction in presence of light. Orthogonality of the thiol-yne chemistry (commonly referred to as a click chemistry) allows for preparation of low-density monolayers with variety of functional groups. To date, carboxyl, amine, alcohol, and alkyl terminated monolayers have been prepared using this core technology. Results from surface characterization techniques such as FTIR, contact angle goniometry and electrochemical impedance spectroscopy confirm the proposed low chain-chain interactions of the environment interfacing groups. Reductive desorption measurements suggest a higher stability for the click-LDMs compared to traditional SAMs, along with the equivalent packing density at the substrate interface, which confirms the proposed stability of the monolayer-gold interface. In addition, contact angle measurements change in the presence of an applied potential, supporting our description of a surface structure which allows the alkyl chains to freely orient themselves in response to different environments. We are studying the differences in protein adsorption phenomena between well packed and our loosely packed surfaces, and we expect this data will be ready to present at the GRC meeting. This work aims to contribute biotechnology science in the following manner: Molecularly imprinted polymers are a promising recognition mode with several advantages over natural antibodies in the recognition of small molecules. However, because of their bulk polymer structure, they are poorly suited for the rapid diffusion desired for recognition of proteins and other macromolecules. Molecularly imprinted monolayers are an emerging class of materials where the surface is imprinted, and there is not a bulk material to impede mass transfer. Further, the short distance between the binding site and the signal transduction material improves many modes of detection. My dissertation project is to develop a new chemistry for protein-imprinted self-assembled monolayers on gold, for incorporation into SPR sensors. Our unique contribution is the spatial imprinting of not only physical cues (seen in current imprinted monolayer techniques), but to also incorporate complementary chemical cues. This is accomplished through a photo-click grafting of preassembled ligands around a protein template. This conference is important for my development as a graduate student to broaden my appreciation of the sensor development beyond surface chemistry.

Keywords: low-density self-assembled monolayers, thiol-yne click reaction, molecular imprinting

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