Measuring the similarity of charts in graphical statistics

Figures used in statistics and other sciences play a vital role in understanding and analyzing the problems under study. Due to the complexity and diversity of these problems, figures such as cartograms, choropleth maps, or radar charts take various geometric forms. Their visual evaluation from the view of geometric similarity is essential but insufficient. This paper proposes and theoretically justifies new metrics based on graph theory. They make it possible to quickly determine the degree of similarity of the statistical figures used in the research procedure. The new metrics were used to 1. Determine the similarity of the domestic route networks of major U.S. airlines, 2. Determine the similarity of the distribution of votes cast in U.S. presidential election in each state in 2016 and 2020, 3. Compare radar charts of some countries, constructed based on the Global Competitiveness Index, 4. Analyze the similarity of neutrosophic double line graphs representing sets of approximate (neutrosophic) numbers. This improves analytical capabilities concerning various processes mapped with well-known types of statistical charts, such as choropleth maps, radar charts, etc.

Fractal dimension complexity of gravitation fractals in central place theory

Settlement centers of various types, including cities, produce basins of attraction whose shape can be regular or complexly irregular (from the point of view of geometry). This complexity depends in part on properties of the space surrounding a settlement. This paper demonstrates that by introducing a dynamic approach to space and by including an equation of motion and space resistance, a dramatic change in the stylized static CPT (Central Place Theory) image occurs. As a result of the interplay of gravitational forces, basins of attraction arise around cities, whose boundaries appear to be fractals. This study provides a wealth of spatial fractal complex images which may change the traditional understanding of CPT.

Sustainable Development of Polish Macroregions-Study by Means of the Kernel Discriminant Coordinates Method

The aim of this study was to investigate if the macroregions of Poland are homogeneous in terms of the observed spatio-temporal data characterizing their sustainable development. So far, works related to the sustainable development of selected territorial units have been based on data relating to a specific year rather than many years. The solution to the problem of macroregion homogeneity goes through two stages. In step one, the original spatio-temporal data space (matrix space) was transformed into a kernel discriminant coordinates space. The obtained kernel discriminant coordinates function as synthetic measures of the level of sustainable development of Polish macroregions. These measures contain complete information on the values of 27 diagnostic features examined over 15 years. In the second step, cluster analysis was used in order to identify groups of homogeneous macroregions in the space of kernel discriminant coordinates. The agglomeration method and the Ward method were chosen as commonly used methods. By means of both methods, three super macroregions composed of homogeneous macroregions were identified. Within the kernel discriminant coordinates, the differentiating power of a selected set of 27 features characterizing the sustainable development of macroregions was also assessed. To this end, five different and most commonly used methods of discriminant analysis were used to test the correctness of the classification. Depending on the method, the classification errors amounted to zero or were close to zero, which proves a well-chosen set of diagnostic features. Although the data relate only to a specific country (Poland), the presented statistical methodology is universal and can be applied to any territorial unit and spatial-temporal dynamic data.

Reactive oxygen and nitrogen species in the course of B-CLL

PURPOSE

The study objective was to investigate the production of NO, cGMP and superoxide anion radical by neutrophils, and to examine alterations in serum or plasma total nitric oxide, MDA and cGMP levels in B-CLL patients.

MATERIAL AND METHODS

PMNs were isolated from 20 patients with B-CLL. Total nitrite was measured in cell supernatants and serum by Griess method. The generation of superoxide anion radical by cells was estimated using cytochrom-c reduction test. The cGMP level in cell supernatants and plasma was assessed by ELISA kit whereas serum MDA level using a spectrophotometric assay by Guege and Aus.

RESULTS

The PMNs in B-CLL patients were characterised by impaired NO generation and enhanced cGMP production. Contrary to the control group, no significant effect was found of rhlL-15 and rhIL-18 on the release of these mediators by PMNs. Superoxide anion radical release by PMNs was decrease. Serum MDA and plasma cGMP levels were elevated in B-CLL patients as compared to the controls.

CONCLUSIONS

The reduced production of nitric oxide and superoxide anion radicals by PMNs in B-CLL may impair the cytotoxic effect of neutrophils on leukaemic B cells. Low secretion of nitric oxide by PMNs and high levels of cGMP in PMN supernatants suggest that activation of guanyl cyclase (sGC) in these patients may occur in the presence of agents other than nitric oxide. Moreover, the findings indicate the enhancement of lipid peroxidation with the progression of the neoplastic process in B-CLL patients.

Transverse ligament of the knee in human embryos aged 7 and 8 weeks

The aim of the study was to trace the transverse ligament of the knee in staged human embryos. Investigations were carried out on 42 embryos of developmental stages 18-23 (44-56 postovulatory days) from the collection of the Department of Anatomy in Poznań. It was found that in embryos at stage 19 peripheral condensation of the mesenchymal interzone of knee joint, located anteriorly to the primordia of the cruciate ligaments, was recognizable. Clearly visible cellular primordium of the transverse ligament, connected with the medial and lateral menisci, was observed in stage 22. The primordium consisted of oval cells, arranged into densely packed parallel strands. The cells were greater than those forming the menisci. In embryos at stage 23 all intraarticular elements (articular surfaces, menisci and their ligaments, cruciate ligaments and transverse ligament) of the knee joint were clearly evident.

Early development of the cruciate ligaments in staged human embryos

Investigations were carried out on 43 serially sectioned human embryos of developmental stages 18 to 23. The homogeneous interzone of the future knee joint is observed in embryos at stage 18. During stage 19 this interzone is differentiated into dense, intensively stained, peripheral parts, which are the primordia of menisci and the medial portion, in which the cruciate ligaments are formed. All structures of the interior of the knee joint are more clearly delineated during stage 20, and they are well developed during the last embryonic week (stages 21-23).

Variation in morphology of the biceps brachii and coracobrachialis muscles associated with abnormal course of blood vessels and nerves

On the right upper limb, during laboratory dissection the low division of the common trunk of the musculocutaneous nerve and the lateral root of the median nerve, low fusion of two roots of the median nerve as well as accessory heads of the coracobrachialis and biceps brachii muscles were found. The axillary and brachial arteries showed abnormal course.