Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum computer

Finding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future.

The effective algorithm of ensuring the integrity of the transmitted information

The problem of ensuring the integrity of the transmitted information in modern information and communication systems is considered in this paper. An optimized algorithm for detecting and correcting errors in the information transmitted over communication lines is proposed. It was developed on the basis of the results of previous studies of the error correction method based on the parity values of the coordinates of a binary matrix. An easy-to-implement, high-speed and efficient error detection algorithm is proposed which is focused on the use of small binary matrices, for example, (4 × 8) or (7 × 8) bits. In such matrices, the possible number of errors that appear in them during the transfer of information is relatively small and easily detected.

Theoretical Aspects of the Territorial Approach to Region and Supply Chain Management

The territorial approach is the basic approach to a region management. At the same time, the “territory” component is the basis of the logistics complex used in Supply Chain Management. In this regard, a need is to clarify and supplement the theory and methodology of the territorial approach to the management of both the region and the supply chains.The subject of this study is the relationship between the regional authorities and the focus enterprise of the supply chain regarding the development of the territories and resources of the region on a mutually beneficial basis.The research methods are methods of analysis and synthesis, induction and deduction, as well as classification, and the tools are binary matrices that provide for the joint use of two classification attributes of the object under study and their dichotomies.The results of this study are the management principles by the competitiveness and sustainability of the management object; classifications of approaches to the management by the region and supply chains; of territories from the point of view of the focus enterprise of the supply chain and the region; the management decisions in the interaction of regions with the links of supply chains; the sequence of the formation of supply chains and the development of territories and resources of the region on the basis of the territorial approach and the relationship between them.The obtained results allow to reduce the costs and time for the development of territories and resources of the region by reducing the lost profits of the supply chain links due to their rational placement and increasing sustainability by achieving a synergistic effect both by the region and by the supply chains.

Classification of Objects of Supply Chain Management to Ensure Their Sustainability

Classifications of objects of supply chain management create the basis for managing their sustainability. The author proposes a hierarchy of priorities regarding managed objects − systems, processes and relations, which implies creation of adequate anticrisis measures for operational management of resource flows.The objectives of the study are to clarify and supplement classifications of supply chain management objects based on their qualitative characteristics. The tasks of the study are to identify the problems of classification of objects of supply chain management, to determine the prerequisites and to determine ways to solve these problems.The methodological basis of the research is formed by the provisions of logistics as a science of resource flow management and supply chain management as a science of managing systems and processes of creating value for end users of products and/or services.Logical-structural methods and tools of binary matrices have allowed to develop classifications of flows of the first (A) and second (B) levels, creating basis for adoption of codes of those flows indicating types of systems and processes and ensuring thus their sustainability. The proposed hierarchy of prioritisation of managed objects reveals the dependences that govern the anti-crisis measures of operation management of resource flows. The research results make it possible to eliminate the contradictions between the goals of the supply chain links (suppliers) and requirement chains (consumers) and, on this basis, to organise their effective interaction.

Flows in Value Chains

Achieving the goals of enterprises and their survival in market conditions is achieved through implementation of supply chain management concepts, values, and demands focused on managing resource flows to create and deliver value to their end users.The subject of the research is relationship between consumers and suppliers as links in the supply chain that form and transform flows of values, demands, products and/or services, as well as novelty in a competitive environment.The objectives of the research are to clarify and supplement the theory and methodology of managing flows of values, demands, products and/ or services, as well as novelties while introducing and implementing management concepts for linearly ordered enterprises or chains.The tasks of the research are to clarify interrelationship of objects, management components, and types of flows; to identify the roles of the consumer and supplier as sources of flows in supply chains; to develop classification of flows considering the objects of the concepts of chain management; to create a form of a flow map regarding flows in supply chains.Research has used the methods of classification, analysis and synthesis, induction, and deduction, and the tools of binary matrices developed based on relevant qualitative characteristics of the objects under the study.The results of the research make it possible to clarify and supplement provisions regarding supply, value and demand chain management based on a systematic approach; to develop practical recommendations to reduce lost profits when managing flows in supply chains; to create prerequisites for more efficient value creation and its supply.

Implementation of the method of figurative transformations to minimizing symmetric Boolean functions

This paper reports a study that has established the possibility of improving the effectiveness of the method of figurative transformations in order to minimize symmetrical Boolean functions in the main and polynomial bases. Prospective reserves in the analytical method were identified, such as simplification of polynomial function conjuncterms using the created equivalent transformations based on the method of inserting the same conjuncterms followed by the operation of super-gluing the variables. The method of figurative transformations was extended to the process of minimizing the symmetrical Boolean functions with the help of algebra in terms of rules for simplifying the functions of the main and polynomial bases and developed equivalent transformations of conjuncterms. It was established that the simplification of symmetric Boolean functions by the method of figurative transformations is based on a flowchart with repetition, which is the actual truth table of the assigned function. This is a sufficient resource to minimize symmetrical Boolean functions that makes it possible to do without auxiliary objects, such as Karnaugh maps, cubes, etc. The perfect normal form of symmetrical functions can be represented by binary matrices that would represent the terms of symmetrical Boolean functions and the OR or XOR operation for them. The experimental study has confirmed that the method of figurative transformations that employs the 2-(n, b)-design, and 2-(n, x/b)-design combinatorial systems improves the efficiency of minimizing symmetrical Boolean functions. Compared to analogs, this makes it possible to enhance the productivity of minimizing symmetrical Boolean functions by 100‒200 %. There are grounds to assert the possibility of improving the effectiveness of minimizing symmetrical Boolean functions in the main and polynomial bases by the method of figurative transformations. This is ensured, in particular, by using the developed equivalent transformations of polynomial function conjuncterms based on the method of inserting similar conjuncterms followed by the operation of super-gluing the variables.

Identification of Somatic Mutation-Driven Immune Cells by Integrating Genomic and Transcriptome Data

Tumor somatic mutations in protein-coding regions may generate neoantigens which may trigger antitumor immune cell response. Increasing evidence supports that immune cell response may profoundly influence tumor progression. However, there are no calculated tools to systematically identify immune cells driven by specific somatic mutations. It is urgent to develop a calculated method to comprehensively detect tumor-infiltrating immune cells driven by the specific somatic mutations in cancer. We developed a novel software package (SMDIC) that enables the automated identification of somatic mutation-driven immune cell. SMDIC provides a novel pipeline to discover mutation-specific immune cells by integrating genomic and transcriptome data. The operation modes include inference of the relative abundance matrix of tumor-infiltrating immune cells, detection of differential abundance immune cells with respect to the gene mutation status, conversion of the abundance matrix of significantly dysregulated cells into two binary matrices (one for upregulated and one for downregulated cells), identification of somatic mutation-driven immune cells by comparing the gene mutation status with each immune cell in the binary matrices across all samples, and visualization of immune cell abundance of samples in different mutation status for each gene. SMDIC provides a user-friendly tool to identify somatic mutation-specific immune cell response. SMDIC may contribute to understand the mechanisms underlying anticancer immune response and find targets for cancer immunotherapy. The SMDIC was implemented as an R-based tool which was freely available from the CRAN website https://CRAN.R-project.org/package=SMDIC.