matrix construction
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Author(s):  
S. T. Dougherty ◽  
Adrian Korban ◽  
Serap Şahinkaya ◽  
Deniz Ustun

AbstractIn this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring $$M_k(R)$$ M k ( R ) and the ring R,  where R is the commutative Frobenius ring. We show that codes over the ring $$M_k(R)$$ M k ( R ) are one sided ideals in the group matrix ring $$M_k(R)G$$ M k ( R ) G and the corresponding codes over the ring R are $$G^k$$ G k -codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes.


Author(s):  
Tianyue Jiang ◽  
Chendan Liu ◽  
Xiao Xu ◽  
Bingfang He ◽  
Ran Mo

Exploiting enzyme-catalyzed reactions to manipulate molecular assembly has been considered as an attractive bottom-up nanofabrication approach to developing a variety of nano-, micro-, and macroscale structures. Upon enzymatic catalysis, peptides and their derivatives transform to assemblable building blocks that form ordered architecture by non-covalent interactions. The peptide assemblies with unique characteristics have great potential for applications in bionanotechnology and biomedicine. In this mini review, we describe typical mechanisms of the protease-instructed peptide assembly via bond-cleaving or bond-forming reactions, and outline biomedical applications of the peptide assemblies, such as drug depot, sustained release, controlled release, gelation-regulated cytotoxicity, and matrix construction.


2021 ◽  
Vol 284 ◽  
pp. 07005
Author(s):  
Oleg Meleshko ◽  
Nataliia Prokopenko ◽  
Olena Gudz

The article is devoted to determining the features of the shadow economy's impact on financial security. For this purpose the following are carried out: generalization of calculation indicators in the shadow economy; influence assessment level of the shadow economy on the volume of gross domestic product (further-GDP); based matrix paired correlation coefficients integral indicator of financial security and factors of shadow economy by various methods; conducted surveillance on the dynamics of the integral index of financial security and the level of the shadow economy, calculated using monetary means and integral measure of financial security of cash in UAH and the dollar; investigated the interconnection statistical indicators and indicators of financial security dynamics of cash in the economy; evaluated the safety performance of non-banking financial market and the volume of cash in dollar terms in dynamics; Then a matrix construction paired correlation coefficients tax rate component of financial security and the coefficients of the shadow economy, estimated by different methodological approaches; monitored security tax rate and share of loss-making enterprises and statistical significance is estimated regression equation pair of security and tax number of unprofitable enterprises.


2020 ◽  
pp. 17-26
Author(s):  
Vera Serkova ◽  

The article analyzes the matrix as a special form of understanding and describing the phenomena of a foreign culture. The principles of the formation of ideas about the "cultural disadvantage" of Russians are analyzed. Over time, the "Western" discourse about Russia becomes more sophisticated and harsher; it can take the form of economic sanctions, political pressure, recommendations, and clothe itself in the form of "soft" and "hard" power. But its structure remains unchanged, which allows us to see the matrix basis of this kind of representations. The matrix construction is used as a set of initial assessments in the attitude of "cultural disadvantage". To analyze the matrix construction as an organization of ideas about a different culture, the authors of the 19th century Germaine de Stael and Astolphe de Custine are involved, who, to varying degrees, expressed their ideas about the "cultural disadvantage" of Russians. In modern discourse, this practice has found expression in the Eurocentric theoretical constructions of S. Huntington and L. Harrison. The contradiction between the Eurocentric thesis about the uniqueness of Western culture and tactical, pragmatic, applied programs of reforming and reformatting non-European cultures according to the European model is shown. The article analyzes the main points of criticism of Eurocentrism by E. Said in his concept of "orientalism". The concept of the "east", in a broad sense, is formed in the European tradition not as an alternative to the West, but as its invention, its quasi-object. "East" is a special tactic of opposing the "center" and the periphery, of historical progress beyond historical immobility. The East does not correlate with the usual scale of periodization of European culture. It always remains backward by definition, due to the absence of Western stages of development (the Enlightenment, as an option – the Renaissance, modernity, imperialism and similar historical periods).


Author(s):  
Juanjuan Luo ◽  
Huadong Ma ◽  
Dongqing Zhou

Abstract Similarity matrix has a significant effect on the performance of the spectral clustering, and how to determine the neighborhood in the similarity matrix effectively is one of its main difficulties. In this paper, a “divide and conquer” strategy is proposed to model the similarity matrix construction task by adopting Multiobjective evolutionary algorithm (MOEA). The whole procedure is divided into two phases, phase I aims to determine the nonzero entries of the similarity matrix, and Phase II aims to determine the value of the nonzero entries of the similarity matrix. In phase I, the main contribution is that we model the task as a biobjective dynamic optimization problem, which optimizes the diversity and the similarity at the same time. It makes each individual determine one nonzero entry for each sample, and the encoding length decreases to O(N) in contrast with the non-ensemble multiobjective spectral clustering. In addition, a specific initialization operator and diversity preservation strategy are proposed during this phase. In phase II, three ensemble strategies are designed to determine the value of the nonzero value of the similarity matrix. Furthermore, this Pareto ensemble framework is extended to semi-supervised clustering by transforming the semi-supervised information to constraints. In contrast with the previous multiobjective evolutionary-based spectral clustering algorithms, the proposed Pareto ensemble-based framework makes a balance between time cost and the clustering accuracy, which is demonstrated in the experiments section.


2020 ◽  
Vol 1 (10) ◽  
pp. 213-230
Author(s):  
Yu. P. Borisov

The complex processes involved in the generation of the image of the hero by the narrator and the perception of this image by the epic audience are studied. A comprehensive analysis of epic formulas with a matrix construction is carried out in order to identify their reference models. The novelty of the work lies in the fact that for the first time the problems of human speech-thinking activity on the basis of the epic formulas of the Yakut olonkho are considered. As a result of the research, the author comes to the conclusion that when revealing the image of the hero, the narrator uses the parallels as a referent: property of the material / property of the image. It is noted that, in turn, the recipients decipher these constructions thanks to the background knowledge about the referent, in particular, about the property of the described material, which is mentally brought under the image of a hero. According to the author, the very structure of the organization of matrix structures does not allow the olonkhosut to completely replace the components that form the referent. Moreover, it is stated that the structure of the analyzed constructions ignores even gender differences in describing the image of heroic women. It is pointed out that the described processes, when the narrator recites certain analyzed epic formulas, occur in a very short time.


Optik ◽  
2020 ◽  
Vol 220 ◽  
pp. 164783
Author(s):  
Qi Qin ◽  
Yan Liu ◽  
Zhongwei Tan ◽  
Muguang Wang ◽  
Fengping Yan

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