Asymmetric circular graph with Hosoya index and negative continued fractions

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

How Marketing Instruments Affect Consumer Behavior in Times of Economic Turbulence

This article analyzes the behavioural changes in groups of consumers and households on the market with individual commodities, based on the classification of individual reasonable consumption. Consumers expressed the degree of influence in their decision-making on satisfying their needs through selected key marketing factors such as price, brand, quality, habits and experience, advertising, recommendation from friends and relatives, packaging, discounts, new items, and so on. The analysis sought to determine whether the changes in the economic situation in the Czech Republic have an impact on the degree of marketing instrument influence on consumer behavior and decision-making. To express the degree of influence 10 point opinion scale is used. Thanks to the investigation taking place in 2007 with 609 respondents and in 2013 with 516 respondents, it was possible, it was possible to deal with the search for evidence of differences in the importance of individual factors using the Wilcoxon test. In 2013, attention was also paid to the degree of influence of some marketing tools such as price, quality and discount events on consumer behavior and decision-making in selected groups of households created by different income levels and different level of education achieved by the head of the household. The influence is expressed by radial graphs.

Eye tracking for visualization evaluation: Reading values on linear versus radial graphs

An eye tracking methodology can help uncover subtle cognitive processing stages that are otherwise difficult to observe in visualization evaluation studies. Pros and cons of eye tracking methods are discussed here, including common analysis metrics. One example metric is the initial time at which all elements of a visualization that are required to complete a task have been viewed. An illustrative eye tracking study was conducted to compare how radial and linear graphs support value lookup tasks for both one and two data-dimensions. Linear and radial versions of bar, line, area, and scatter graphs were presented to 32 participants, who each completed a counterbalanced series of tasks. Tasks were completed more quickly on linear graphs than on those with a radial layout. Scanpath analysis revealed that a three-stage processing model was supported: (1) find desired data dimension, (2) find its datapoint, and (3) map the datapoint to its value. Mapping a datapoint to its value was slower on radial than linear graphs, probably because eyes need to follow a circular, as opposed to a linear path. Finding a datapoint within a dimension was harder using line and area graphs than bar and scatter graphs, possibly due to visual confusion of the line representing a data series. Although few errors were made, eye tracking was also used here to classify error strategies. As a result of these analyses, guidelines are proposed for the design of radial and linear graphs.