Concept Of Rank Research Articles

CALCULATION OF THE RANK OF A MATRIX AND APPLICATION OF THE MAPLE COMPUTER PACKAGE

The paper is devoted to the presentation of the applied calculation methods of one of the basic concepts of higher algebra, the rank of a matrix, as well as the description of the calculation of the rank of a matrix using the MAPLE computer package. In the present paper first the concept of matrix rank is introduced and then applied methods for calculating it by applying elementary transformations to the rows of the matrix and by determining a minor of the highest order other than 0 are presented. Specific examples of calculating the rank of a matrix are considered. In addition to practical methods for calculating the rank of a matrix, also the description of the implementation of calculating the rank of a matrix using the MAPLE computer package is introduced in the paper. The calculation of all matrix ranks, considered in the paper, is also carried out in the MAPLE environment, based on detailed guidelines, as a result of which it will be possible to instantly calculate the matrix rank.

Pharmacy Compounding Regulation in the German Pharmaceutical Market. Part 2. Organisational Features (Review)

INTRODUCTION. The Russian Federation has decided to restore the system of compounding pharmacies as an element of the critical national healthcare infrastructure and pharmaceutical supply chain. To improve Russian regulatory practices, develop novel advanced approaches to pharmacy compounding and quality control, and implement these approaches, it is necessary to study relevant good compounding practices applied in healthcare systems of other countries.AIM. The study aimed to analyse the German experience in the organisation and regulation of pharmaceutical compounding to suggest recommendations for the development and implementation of Russian guidelines on good compounding and dispensing practices.DISCUSSION. This work continues a comprehensive study that delves into the current provisions of German legislation governing the system of good compounding practices. This article examines the differences between approaches to compounding by medical and pharmaceutical specialists. According to the findings, compounding by medical specialists is guided by the “free practice of medicine” principle and is subject to minimal regulatory oversight. All pharmacy organisations operate as compounding pharmacies, thereby enhancing the physical accessibility of compounded medicinal products to the population. The authors highlight the features of a process-based quality assurance system encompassing production process controls and quality control methods for compounded medicinal products. Additionally, the authors discuss the applicability of rapid test methods to compounding. In accordance with the German concept of good pharmacy practices, a compounding pharmacy may use the available validation, qualification, and verification tools in the pharmaceutical development of compounded medicinal products and may outsource its internal quality control function. Using the concept of risk ranking, compounding pharmacies may design their own sampling programmes. The article describes approaches to and requirements for organising the evaluation of compounding prescriptions. In Germany, compounding pharmacies may independently assign shelf lives to the compounded medicinal products they produce.CONCLUSIONS. Some German solutions are of considerable practical importance and are applicable to the development and implementation of Russian guidelines on good compounding and dispensing practices. In particular, pharmacy organisations may outsource the quality control of their compounded medicinal products. Additionally, pharmacies can conduct the full-scale pharmaceutical development of compounding technologies and quality control methods (including rapid test methods) using the validation, qualification, and verification tools available to drug manufacturers. Moreover, pharmacy organisations may independently assign shelf lives to the compounded medicinal products they produce. Finally, pharmacy organisations may design their individual sampling programmes.

Cross-Domain Text Mining of Pathophysiological Processes Associated with Diabetic Kidney Disease.

Diabetic kidney disease (DKD) is the leading cause of end-stage renal disease worldwide. This study's goal was to identify the signaling drivers and pathways that modulate glomerular endothelial dysfunction in DKD via artificial intelligence-enabled literature-based discovery. Cross-domain text mining of 33+ million PubMed articles was performed with SemNet 2.0 to identify and rank multi-scalar and multi-factorial pathophysiological concepts related to DKD. A set of identified relevant genes and proteins that regulate different pathological events associated with DKD were analyzed and ranked using normalized mean HeteSim scores. High-ranking genes and proteins intersected three domains-DKD, the immune response, and glomerular endothelial cells. The top 10% of ranked concepts were mapped to the following biological functions: angiogenesis, apoptotic processes, cell adhesion, chemotaxis, growth factor signaling, vascular permeability, the nitric oxide response, oxidative stress, the cytokine response, macrophage signaling, NFκB factor activity, the TLR pathway, glucose metabolism, the inflammatory response, the ERK/MAPK signaling response, the JAK/STAT pathway, the T-cell-mediated response, the WNT/β-catenin pathway, the renin-angiotensin system, and NADPH oxidase activity. High-ranking genes and proteins were used to generate a protein-protein interaction network. The study results prioritized interactions or molecules involved in dysregulated signaling in DKD, which can be further assessed through biochemical network models or experiments.

METHOD FOR DETERMINING THE BIT GRID OVERFLOW OF A COMPUTER SYSTEM OPERATING IN THE SYSTEM OF RESIDUAL CLASSES

Context. Consideration of a set of examples of practical application of the procedure for identifying overflow of the bit grid of a computer system operating in a non-positional number system in residual classes. The object of the study is the process of processing data represented in the residual class system.
 Objective. The goal of the work is to consider and analyze examples of the bit grid overflow definition of a computer system when implementing the operation of adding two numbers in a system of residual classes based on the application of a method for determining the bit grid overflow, based on the use of the concept of number rank.
 Method. The specificity of the functioning of a computer system in a system of residual classes requires the implementation of not only modular operations, but also requires the implementation of additional, so-called non-modular operations. Non-modular operations include the operation of determining the overflow of the bit grid of a computer system in the system of residual classes. In a non-positional number system in residual classes, implementing the process of detecting overflow of the bit grid of a computer system is a difficult task to implement. The method considered in the work for determining the overflow of the bit grid is based on the use of positional features of a non-positional code of numbers in the system of residual classes, namely the true and calculated ranks of a number. The process of determining the overflow of the result of the operation of adding two numbers in the system of residual classes has been studied, since this arithmetic operation is the main, basic operation performed by a computer system.
 Results. The developed methods are justified theoretically and studied when performing arithmetic modular operations of addition, subtraction and multiplication using tabular procedures.
 Conclusions. The main advantage of the presented method is that the process of determining the overflow of the bit grid can be carried out in the dynamics of the computing process of the computer system, i.e. without stopping the solution of the problem. This circumstance makes it possible to reduce the unproductive expenditure of the computer system in the system of residual classes. In addition, this method can be used to control the operation of adding two numbers in the residual class system. This increases the reliability of obtaining the true result of the operation of adding two numbers in the system of residual classes.

Relative rank and regularization

Abstract We introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength). We also introduce the notion of relative bias. The main result of the paper is a relation between these two quantities over finite fields (as a special case, we obtain a new proof of the results in [21]). This relation allows us to get an accurate estimate for the number of points on an affine variety given by a collection of polynomials which is of high relative rank (Lemma 3.2). The key advantage of relative rank is that it allows one to perform an efficient regularization procedure which is polynomial in the initial number of polynomials (the regularization process with Schmidt rank is far worse than tower exponential). The main result allows us to replace Schmidt rank with relative rank in many key applications in combinatorics, algebraic geometry, and algebra. For example, we prove that any collection of polynomials $\mathcal P=(P_i)_{i=1}^c$ of degrees $\le d$ in a polynomial ring over an algebraically closed field of characteristic $>d$ is contained in an ideal $\mathcal I({\mathcal Q})$ , generated by a collection ${\mathcal Q}$ of polynomials of degrees $\le d$ which form a regular sequence, and ${\mathcal Q}$ is of size $\le A c^{A}$ , where $A=A(d)$ is independent of the number of variables.

Exploring near-linearities in price–rate of profit trajectories and the concept of effective rank in input–output matrices

In recent years, there has been a resurgence of interest in the controversies surrounding capital theory. At the heart of these debates are the empirically observed near-linearities in the price–rate of profit and wage rate of profit curves. This article posits that these near-linearities can be attributed to the low effective rank property inherent in the economy's system matrices of input–output coefficients. This suggests that a comprehensive representation of how prices evolve in response to changes in income distribution can be achieved with only a few eigenvalues and their respective eigenvectors. Furthermore, this low-dimensional system possesses the capability to capture the majority of distinctive features that characterize the input–output structure of the economy in relation to price movements.

USER EVALUATION-DRIVEN RANKING CONCEPT

Context. The problem of personalizing search engine results, empowering users with search result management tools and developing new ranking models based on user’s subjective information needs. The object of the study was to modeling information search results in the Internet based on user ratings.
 Objective. The goal of the work is to form unique expert groups for each user, based on calculating the measure of agreement between the current user’s opinions and potential experts.
 Method. Introducing a novel method for ranking search results based on user ratings, which takes a subjective approach to the ranking process. This approach involves the formation of distinct expert groups tailored to individual users. Experts are selected based on the level of agreement between their opinions and the current user, determined by shared ratings on a specific set of web resources. User selection for the expert group is based on their weight relative to the current user, serving as a measure of agreement.
 The proposed methodology offers a fresh approach to forming unique expert groups for each user, utilizing three different strategies depending on the presence of shared ratings on a particular set of web resources between the user and potential experts.
 The developed ranking method ensures that each user receives a personalized list of web resources with a distinct order. This is accomplished by incorporating unique ratings from the expert group members associated with each user. Furthermore, each rating contributes to the ranking model of web resources with an individual weight, calculated based on an analysis of their past system activity.
 Results. The developed methods have been implemented in software and investigated for complex web data operation in real time.
 Conclusions. The conducted experiments have confirmed the effectiveness of the proposed software and recommend its practical use for solving complex web data operation in real time. Prospects for further research may include optimizing software implementations and conducting experimental investigations of the proposed methods on more complex practical tasks of various nature and dimensions

Implementasi Metode Additive Ratio Assesment (ARAS) Dalam Pemberian Promo Tiket Umroh Pada Member

PT Anugerah Quba Mandiri (AQM) Tour & Travel every year has the charm to be able to attract the attention of customers or customers on the promo route. the selection of Umrah ticket promos held by the travel party is not given to all pilgrims who register for Umrah. The promo will be given only to pilgrims who get the general qualifications set by the company. Members who have been officially registered can have the opportunity to get a promo to be given to the selected congregation, but ticket promos can only be given to one congregation, therefore it must be based on the appropriate requirements and qualifications. Members who have registered will be recorded using a computer system to record the number of members who are entitled to the ticket promo. With the large number of registered members, the company really needs a decision system that can help in making decisions on ticket promotions. A Decision Support System (SPK) that can help companies find out which members are eligible for ticket promotions using the Additive Ratio Assessment (ARAS) method. The ARAS method is a method or method of decision making that uses the concept of utility degree ranking by comparing the overall index value of each alternative to. In its implementation, the decision support system in providing promos to PT AQM tour & Travel members uses the ARAS method, obtaining effective and objective ranking results. From the results of research conducted at PT AQM Tour & Travel it can be concluded that Alternative A13 on behalf of Nurlela Br Sitepu is stated as a member who gets an Umrah ticket promo with a preference value of 0.2963.

The spectral rank of an element in a ring

The concept of the spectral rank of an element in a ring is defined, and it is shown to be a genuine generalization of the same concept first studied in the setting of a Banach algebra. Furthermore, we prove that many of the desirable properties of this rank are still valid in the more abstract setting and give several examples to support and motivate the given definition. In particular, we are able to show that a nonzero idempotent of a semiprimitive and additively torsion-free ring is minimal if and only if it has a spectral rank of one. We also discover a precise connection between the spectral rank of an element in a ring and a purely algebraic definition of rank considered only recently by N. Stopar in [Rank of elements of general rings in connection with unit-regularity, J. Pure Appl. Algebra 224 (2020) 106211]. Specifically, we are able to show that if an element [Formula: see text] has a finite algebraic rank in a semiprimitive and additively torsion-free ring, then [Formula: see text] has the exact same spectral rank. An extra condition under which the converse holds true is also provided, and connections to the socle are identified. Finally, for both of these extended notions of rank considered in the setting of a ring, we prove a generalized Frobenius Inequality.

Supporting the Fight against Corruption in Nigeria through the Whistle Blower Policy: Challenges and Prospects

This paper examined the impact of the whistle blower policy since its inception in Nigeria. It analysed the concept of corruption and corruption perception index ranking of Nigeria by Transparency International. The paper identified the challenges of whistle blower policy in Nigeria to include the negative effect of the policy on the whistle blower, such as; victimization, witch hunting, retaliation, denial of related benefits, recrimination, suspension from work, outright dismissal from service by the employer and lack of sufficient laws to protect the whistle blower .The paper looked at the whistle blower policy as a step in the right direction towards fighting corruption in Nigeria. To this end, the paper recommended, among others, that the whistle blower protection bill should be signed into law and be adequately enforced, while other enabling laws aimed at fighting corruption should be strengthened. This will make the cost of corruption greater than the benefit as culprits would be made to face the wrath of the law no matter who is involved.

The Conceptual Independence of Health Status, Respiratory Symptoms and Dyspnea in Chronic Obstructive Pulmonary Disease in Real Clinical Practice.

The hypothesis that health status is the highest ranking concept, followed by respiratory symptoms and dyspnea as the lowest ranking concepts in subjects with chronic obstructive pulmonary disease (COPD) was tested in a real clinical setting with 157 subjects with stable COPD. Spearman's rank correlation coefficients for scores of health status using the COPD Assessment Test (CAT), respiratory symptoms using the COPD Evaluating Respiratory Symptoms (E-RS) and dyspnea using Dyspnea-12 (D-12) between any two were 0.6 to 0.7. Upon categorizing the patients as "abnormal" or "normal" according to the threshold, it was found that 30 patients (19.1%) had dyspnea, respiratory symptoms and impaired health status. Dyspnea was considered an important part of respiratory symptoms, though seven patients had dyspnea but no respiratory symptoms. There were 10 patients who had respiratory symptoms without dyspnea but without health status problems. Furthermore, there were six patients who had both dyspnea and respiratory symptoms but whose health status was classified as fine. Thus, the hypothesis was correct in approximately 85% of cases.

GAAMmf: genetic algorithm with aggressive mutation and decreasing feature set for feature selection

This paper introduces a modified version of a genetic algorithm with aggressive mutation (GAAM), one of the genetic algorithms (GAs) used for feature selection. The modification proposed in this study expands the original GAAM’s capabilities by allowing not only feature selection but also feature reduction. To obtain this effect, we applied the concept of ranks used in the non-dominated sorting genetic algorithm (NSGA) and the concept of penalty term used in the Holland genetic algorithm. With those two concepts, we managed to balance the importance of two competing criteria in the GAAM fitness function: classification accuracy and the feature subset’s size. To assess the algorithm’s effectiveness, we evaluated it on eleven datasets with different characteristics and compared the results with eight reference methods: GAAM, Melting GAAM, Holland GA with a penalty term, NSGA-II, Correlation-based Feature Selection, Lasso, Sequential Forward Selection, and IniPG (an algorithm for particle swarm optimisation). The main conclusion drawn from this study is that the genetic algorithm with aggressive mutation and decreasing feature set (GAAMmf) introduced in this paper returned feature sets with a significantly smaller number of features than almost all reference methods. Furthermore, GAAMmf outperformed most of the methods in terms of classification accuracy (except the original GAAM). In contrast to Holland GA and NSGA-II, GAAMmf was able to perform the feature reduction task for all datasets, regardless of the initial number of features.

Improving Semantic Information Retrieval Using Multinomial Naive Bayes Classifier and Bayesian Networks

This research proposes a new approach to improve information retrieval systems based on a multinomial naive Bayes classifier (MNBC), Bayesian networks (BNs), and a multi-terminology which includes MeSH thesaurus (Medical Subject Headings) and SNOMED CT (Systematized Nomenclature of Medicine of Clinical Terms). Our approach, which is entitled improving semantic information retrieval (IMSIR), extracts and disambiguates concepts and retrieves documents. Relevant concepts of ambiguous terms were selected using probability measures and biomedical terminologies. Concepts are also extracted using an MNBC. The UMLS (Unified Medical Language System) thesaurus was then used to filter and rank concepts. Finally, we exploited a Bayesian network to match documents and queries using a conceptual representation. Our main contribution in this paper is to combine a supervised method (MNBC) and an unsupervised method (BN) to extract concepts from documents and queries. We also propose filtering the extracted concepts in order to keep relevant ones. Experiments of IMSIR using the two corpora, the OHSUMED corpus and the Clinical Trial (CT) corpus, were interesting because their results outperformed those of the baseline: the P@50 improvement rate was +36.5% over the baseline when the CT corpus was used.

Darwin’s dark matter: utter extinction

ABSTRACT Species that died without leaving descendants Darwin called ‘utterly extinct’. They far outnumber the ancestors of all living things, so they resemble the dark matter of modern cosmology, which far outweighs visible matter. He realized in 1837 that their absence is what creates the groups in a natural classification. In his Notebook B he combined the idea that species multiply with the idea that ancestors' relatives must mostly be extinct. The fossil Megatherium was utterly extinct. The iconic branching ‘I think’ diagram shows extinction causing the origin of genera by eliminating intermediate species. Darwin’s concept of taxonomic ranks, starting with the genus, was informed by his interaction with taxonomists. Based on his familiarity with demography, Darwin reasoned that the survival of transitional forms was unlikely, which helped him decide to focus at the species level. When drafting his theory in the 1840s, he left out these speculative ideas, but they emerged again in the 1850s when he realized his theory needed a cause for branches to diverge. His ecological answer worked at the species level, but his Principle of Divergence was unconvincing at higher taxonomic levels. In the Origin, Darwin repeatedly insisted on the importance of utter extinction.

On Ranks of Matrices over Noncommutative Domains

We consider matrices with entries in some domain, i.e., in a ring, not necessarily commutative, not containing non-trivial zero divisors. The concepts of the row rank and the column rank are discussed. (Coefficients of linear dependencies belong to the domain ; left coefficients are used for rows, right coefficients for columns.) Assuming that the domain satisfies the Ore conditions, i.e., the existence of non-zero left and right common multiples for arbitrary non-zero elements, it is proven that these row and column ranks are equal, which allows us to speak about the rank of a matrix without specifying which rank (row or column) is meant. In fact, the existence of non-zero left and right common multiples for arbitrary non-zero elements of is a necessary and sufficient condition for the equality of the row and column ranks of an arbitrary matrix over. An algorithm for calculating the rank of a given matrix is proposed. Our Maple implementation of this algorithm covers the domains of differential and (-)difference operators, both ordinary and with partial derivatives and differences.

Attributes Reduction on SE-ISI Concept Lattice for an Incomplete Context Using Object Ranking

The formal concept of lattice plays a vital role in knowledge discovery. Reduction of the attribute has many applications in machine learning technology and data mining fields. In this paper, we introduce an object ranking concept to define a consistency set and the reduction of the attributes by structural features. An incomplete information system works on the three-way concepts using the SE-ISI Context. The granular was emphasized with join (meet) irreducible sets using the object ranking concepts. A dual operator is defined based on the object ranking concepts and its properties and conditions are verified. Hence, this elaborates on the four kinds of reduction of the attributes. The ordered pairs give the knowledge of the attributes that deal with the interval set of both the approximation of rough set theory concerning the objects. Therefore, the relationship between four kinds of reduction of the attribute was appropriate to access the consistency set using the object ranking concepts by some of the theorems and examples.

Optimised ensemble learning-based IoT-enabled heart disease monitoring system: an optimal fuzzy ranking concept

ABSTRACT Generally, patients with heart diseases enquire for medical services while sick. They will not experience sickness often until they reach the last stage of heart disease, and so the damages are not reversible. Thus, the solution for reducing the death rate of heart disease healthcare is becoming the passive medical care type. Physicians usually monitor the physical status of patients, which helps in deciding when to provide medical services by considering the real-time analysis of patients. Moreover, a significant division of pervasive clinical care is taken as the development of practical monitoring systems. An IoT approaches are overwhelming the progression in addressing the issue of heart disease patient care since they can modify the service mode in a pervasive way. A remote monitoring model is more significant for realising pervasive healthcare services. Here, an ‘optimised ensemble learning’-based IoT-enabled heart disease monitoring system through an optimised ensemble fuzzy ranking (OEFR) strategy, deep feature extraction and heuristic improvement. Moreover, the hyperparameter of each classifier is optimised through a new improved dingo optimiser (I-DOX) algorithm. Throughout the result analysis, the accuracy of the designed I-DOX-based OEFR model is attained 96.72%. Thus, the analysis exhibits an overall performance analysis in terms of high performance.

Rank partition functions and truncated theta identities

In 1944, Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank satisfying the properties hypothesized for it by Dyson was discovered in 1988 by G. E. Andrews and F. G. Garvan. In this paper, we introduce truncated forms for two theta identities involving the generating functions for partitions with non-negative rank and non-negative crank. As corollaries we derive new infinite families of linear inequalities for the partition function p(n). The number of Garden of Eden partitions are also considered in this context in order to provide other infinite families of linear inequalities for p(n).

From regression rank scores to robust inference for censored quantile regression

AbstractQuantile regression for right‐ or left‐censored outcomes has attracted attention due to its ability to accommodate heterogeneity in regression analysis of survival times. Rank‐based inferential methods have desirable properties for quantile regression analysis, but censored data poses challenges to the general concept of ranking. In this article, we propose a notion of censored quantile regression rank scores, which enables us to construct rank‐based tests for quantile regression coefficients at a single quantile or over a quantile region. A model‐based bootstrap algorithm is proposed to implement the tests. We also illustrate the advantage of focusing on a quantile region instead of a single quantile level when testing the effect of certain covariates in a quantile regression framework.

Application of MCDM and Taguchi super ranking concept for materials selection problem

Material selection is a topic of pivotal importance in the optimal design and development of industrial products. Increasing demand for high-performance materials with desirable and tailor-made properties is expected to drive the future market. This paper examines the application of multicriteria decision-making techniques like AHP, TOPSIS, EDAS, VIKOR, and Taguchi-based super ranking concepts for the selection of optimal aluminum alloy material for the sheet metal forming process. The criteria used to evaluate the optimal material selection were identified as yield strength, tensile strength, thermal conductivity, impact, density, specific heat, coefficient of thermal expansion, and % elongation. The most ranked aluminum material frequency is selected for sheet metal forming simulation using DEFORM, a process simulation FEM-based tool. An integrated Taguchi DOE and process simulation were carried out for the best-ranked AA2024 aluminum material. The results showed that the MCDM and Taguchi-based super ranking concept provides an intelligent and methodical assessment for solving material selection from a finite set of alternatives for the sheet metal forming process. The group decision behavior, agility, and flexibility in including multiple decision-making criteria for overall comparative analysis of materials, and manufacturing processes with uncertainty make MCDM methods a definitive tool for materials and manufacturing process selection.