New bounds for locally irregular chromatic index of bipartite and subcubic graphs

A graph is locally irregular if the neighbors of every vertex v have degrees distinct from the degree of v. A locally irregular edge-coloring of a graph G is an (improper) edge-coloring such that the graph induced on the edges of any color class is locally irregular. It is conjectured that three colors suffice for a locally irregular edge-coloring. In the paper, we develop a method using which we prove four colors are enough for a locally irregular edge-coloring of any subcubic graph admiting such a coloring. We believe that our method can be further extended to prove the tight bound of three colors for such graphs. Furthermore, using a combination of existing results, we present an improvement of the bounds for bipartite graphs and general graphs, setting the best upper bounds to 7 and 220, respectively.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Comparing the effectiveness of respondent-driven sampling and quota sampling in migration research

We evaluate the effectiveness in empirical migration research of the respondent-driven sampling (RDS) and the quota sampling with regard to four criteria: quality of the data; sociometric diversity of the sample; geographic coverage of the sample; and cost-effectiveness. We review two surveys of ex-USSR migrants, conducted simultaneously in the Warsaw metropolitan area, each undertaken with the use of one of the two sampling methods. We find that although the RDS was considerably costlier, it enabled faster data collection and posed a lower risk of underestimating the cost of the survey. We also find that the RDS generated higher-quality data, and that it was more successful in surveying short-term circular migrants. This comparative evaluation contributes to the literature on social research methods in that it links the sampling methods with the quality and character of the data, and helps assess the usefulness and applicability of RDS in empirical migration studies.     

Discriminant coordinates analysis for multivariate functional data

Abstract

One of the basic statistical methods of dimensionality reduction is analysis of discriminant coordinates given by Fisher (1936 Fisher, R. A. 1936. The use of multiple measurements in taxonomic problem. Annals of Eugenics 7 (2):179–88. doi:10.1111/j.1469-1809.1936.tb02137.x.[Crossref] , [Google Scholar]) and Rao (1948). The space of discriminant coordinates is a space convenient for presenting multidimensional data originating from multiple groups and for the use of various classification methods (methods of discriminant analysis). In the present paper, we adapt the classical discriminant coordinates analysis to multivariate functional data. The theory has been applied to analysis of textural properties of apples of six varieties, measured over a period of 180?days, stored in two types of refrigeration chamber.     

Development of urban behaviour is associated with time since urbanization in a reed-nesting waterbird

Behavioural adaptations are recognized as crucial determinants for successful establishment and persistence of animal populations in a novel urban environment. Here, we examined mechanisms responsible for the development of urban behavioural type in a common waterbird, the Eurasian coot Fulica atra. We compared the behaviour of coots from a rural population and two urban populations that differed in the timing of colonization event (1960s vs. 2000s). We found that some behavioural characters associated with urban life (aggression during nest defence and boldness towards humans during foraging) were more strongly expressed in the older urban population when compared with the recently established urban population. By contrast, coots from the two urban populations showed a similar likelihood of exploiting human-derived food resources, as well as they showed similar levels of physiological stress. Urban coots were generally more aggressive, bolder, and less stressed than their rural conspecifics. Large behavioural and physiological divergence of coots from the recently established urban population and their rural conspecifics suggested that phenotypic plasticity and phenotype sorting may play a key role in the initial stages of urban colonization. On the other hand, increasing expression of boldness and aggression with the time since urbanization may suggest the role of microevolutionary adaptation in response to novel selective forces associated with the urban environment. Our results indicate that a combination of different processes (phenotypic plasticity, phenotype sorting, and microevolution) can determine successful colonization of urban areas by the Eurasian coots, and possibly other bird species.     

Assessing the diversity of the benthic oligochaete communities in urban and woodland ponds in an industrial landscape (Upper Silesia,southern Poland)

Studies were carried out in two mining pond complexes in an industrial landscape. The first complex (consisting of six ponds) was located in an urban area and the second one (consisting of six ponds) in a woodland area. The aims of the study were to assess the diversity of benthic oligochaetes and to evaluate which environmental variables are most important in determining variations in the community structure in ponds of varying location. In total, 21 oligochaete species were recorded (7–11 in the urban ponds, 11–15 in the woodland ponds). Aulodrilus pluriseta, Aulodrilus japonicus and Ophidonais serpentina were only found in the woodland ponds, while Potamothrix bavaricus only occurred in the urban ponds. Limnodrilus hoffmeisteri, Limnodrilus claparedeanus, Chaetogaster diaphanus and Ophidonais serpentina dominated in the woodland ponds, whereas Limnodrilus hoffmeisteri, Limnodrilus claparedeanus, Potamothrix bavaricus and Tubifex tubifex prevailed in the urban ponds. The total density of oligochaetes was higher in the urban ponds thought the values of the diversity indices were higher in the woodland ponds. The local diversity of the ponds was high, while the among-site diversity made only a small contribution to the regional diversity. Nonetheless, a cluster analysis divided all of the ponds into two distinct groups depending on their location. CCA analysis showed that conductivity, pH, total hardness, alkalinity, the concentration of chlorides and the content of organic matter in the bottom sediments were most associated with the distribution of some oligochaete species among the ponds studied.     

An Automatic Test for the Umbrella Alternatives

The paper proposes a new test for detecting the umbrella pattern under a general non‐parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level α on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.