Rank and reverberations in neural networks

Summary In a discrete model of a neural network, from a limitation on the rank of the matrix of “coupling coefficients”, an upper bound for the maximum length of the transients is derived, generalizing the analogue result of Caianiello (1966a) for the case of rank one. A counterexample shows that the limitation found is the best possible involving only the rank of the matrix.     

Pair Rank Set Sampling

Ranked set sampling (RSS) as suggested by McIntyre (1952) may be modified to introduced a new sampling method called pair rank set sampling (PRSS), which might be used in some area of application instead of the RSS to increase the efficiency of the estimators relative to the simple random sampling (SRS) method. Estimators of the population mean are considered. An example using real data is presented to illustrate computations.     

How to Rank Journals

There are now many methods available to assess the relative citation performance of peer-reviewed journals. Regardless of their individual faults and advantages, citation-based metrics are used by researchers to maximize the citation potential of their articles, and by employers to rank academic track records. The absolute value of any particular index is arguably meaningless unless compared to other journals, and different metrics result in divergent rankings. To provide a simple yet more objective way to rank journals within and among disciplines, we developed a κ-resampled composite journal rank incorporating five popular citation indices: Impact Factor, Immediacy Index, Source-Normalized Impact Per Paper, SCImago Journal Rank and Google 5-year h-index; this approach provides an index of relative rank uncertainty. We applied the approach to six sample sets of scientific journals from Ecology (n = 100 journals), Medicine (n = 100), Multidisciplinary (n = 50); Ecology + Multidisciplinary (n = 25), Obstetrics & Gynaecology (n = 25) and Marine Biology & Fisheries (n = 25). We then cross-compared the κ-resampled ranking for the Ecology + Multidisciplinary journal set to the results of a survey of 188 publishing ecologists who were asked to rank the same journals, and found a 0.68–0.84 Spearman’s ρ correlation between the two rankings datasets. Our composite index approach therefore approximates relative journal reputation, at least for that discipline. Agglomerative and divisive clustering and multi-dimensional scaling techniques applied to the Ecology + Multidisciplinary journal set identified specific clusters of similarly ranked journals, with only Nature & Science separating out from the others. When comparing a selection of journals within or among disciplines, we recommend collecting multiple citation-based metrics for a sample of relevant and realistic journals to calculate the composite rankings and their relative uncertainty windows.     

Rank comparisons amongst teenagers and suicidal ideation

We study how competition amongst known peers at the highest-stakes exam in Korea impacts students’ mental health and induces them to express suicidal ideation. Using panel data on Korean students from 2003 to 2007, we exploit a randomization of students’ peers (upon entering middle school) to uncover a relationship between students’ rank at the CSAT (highest-stakes exam in Korea) and their mental health, more particularly their suicidal thoughts. We find that (i) students’ rank amongst peers from middle school affects their suicidal ideation: the farther down in the classification, the more prone to have suicidal thoughts they are; (ii) this association is not capturing the impact of the national ranking at CSAT, which is controlled for in all our specifications; (iii) when reestimating separately our regressions for male and female students, we find all of this association is driven by female students. Male students are more prone to experience other negative feelings such as anxiety or loneliness, but these only appear one year later. Our results confirm that social comparisons with peers matter a lot for individual well-being and mental health. They contribute to building a case against extreme levels of competition at younger ages, as teenagers -especially young girls- suffer deeply from comparing themselves to their peers.     

Generalized Wilcoxon Rank Tests and Sensitivity Curves

In this paper we use the sensitivity curves of TUKEY (1977) and the change of decision point (cdp) (a modified version of the breakdown point of YLVISAKER, 1977), supplemented by simulation studies to acquire knowledge about sensitivity in generalized Wilcoxon rank test statistics. Sensitivity depends on balanced or unbalanced sample size cases, censoring, combinations of failure distributions and sources of errors in the data. It is important to consider the quality of the data, and the results show that cdp and some properties of the sensitivity curves may serve as a hint when selecting a test statistic and when making a decision for a given test statistic.     

Rank and sequence in Caspar Bauhin's Pinax

CAIN, A. J., 1994. Rank and sequence in Caspar Bauhin's Pinax. Bauhin's consistent use of genera, species and binominals, applauded by historians as anticipating Linnaeus's theory and practice, does not appear on closer examination to be intended as anything of the sort. His use of the terms genus and species is as in Aristotelian logic, with a shifting reference, at all taxonomic levels. His typographical layout, emphasizing (but far from invariably employing) single-word names for effectively generic entities, often qualified by ‘and its species’, gives the impression of Linnaean practice, and coincides with it not infrequently, but not with Linnaean theory. The main entities for which it can be said that Bauhin uses fairly consistently a biverbal binominal name-phrase, like Linnaeus' trivial names, were in fact in Linnaeus's eyes two levels of supraspecific groupings. The main entities in Bauhin which Linnaeus recognized as species, as is shown by his quotations in the Species plantarum, are subdivisions of his biverbally or nearly biverbally named groupings, but themselves have multiverbal names. These correspond closely to Linnaeus's diagnostic specific names, not at all to his biverbal trivial names. Bauhin probably had no conception of the species and genus as ranks in the modern sense, first adumbrated by Tournefort and utilized by Linnaeus. Bauhin certainly tried to group forms by natural affinity, as did Theophrastus before him and Linnaeus afterwards. Not being alerted to the importance of the details of the flower and fruit, he used what characters he could find, notably, but not by any means exclusively, leaf shape. He composed the Pinax as a nomenclatural concordance to earlier authors, notably Dioscorides, Theophrastus and Pliny. He retained the sequence of major groups of Theophrastus (as the greatest authority on plants) but reversed it to start with the best-known plants, grasses. Where Theophrastus gave no help, in the cryptogams, Bauhin inserted as a pendant his own series from ferns down to fungi, using the Aristotelian principles of the gradation of forms. His overall arrangement, therefore, is not a simple progression but a chain with pendants. Bauhin is far closer to earlier authors than to Linnaeus, but his typography, along with other authors, may well have helped to incite Linnaeus to a more rigorous and consistent use of ranked groups and biverbal names.     

An Exact Paired Rank Test

An exact rank test for two dependent samples based on overall mid‐ranks is discussed which can be applied to metric as well as to ordinal data. The exact conditional distribution of the test statistic given the observed vector of rank differences is determined. A recursion formula is given as well as a fast shift algorithm in SAS/IML code. Moreover, it is demonstrated that the paired rank test can be more powerful than other tests for paired samples by means of a simulation study. Finally, the test is applied to a psychiatric trial with longitudinal ordinal data.     

Rank Tests for correlated Random Variables

In this paper we consider the asymptotic distribution of linear rank-statistics allowing certain dependencies between the random variables. General theorems will be given, from which the results contained in SEN (1967a, 1967b, 1968), MEHRA /SEN (1969) and PURI /SEN (1971) can be derived. Applying these theorems we can derive ranktests for the two-sample problem for tied observations, for the two-factor mixed model with random interaction and for a hierarchical design. The distribution of the proposed teststatistics for small sample sizes is considered by Monte-Carlo studies.     

Comparing Survival Curves Using Rank Tests

Survival times of patients can be compared using rank tests in various experimental setups, including the two-sample case and the case of paired data. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author's recent work on a new and simple class of censored rank tests. Various models for tail alternatives are discussed and the relation to censoring is demonstrated.     

Fourth Rank Immobile Nucleic Acid Junctions

Abstract

An immobile nucleic acid junction composed of four dodecanucleotides has been designed according to principles of minimum symmetry aided by equilibrium calculations, and has been synthesized by automated phosphotriester techniques. We can demonstrate its tetrameric character and its 1:1:1:1 stoichiometry by gel electrophoresis. Thermal denaturation monitored by ultraviolet hyperchromism indicates that the complex is stable relative to its component arms. High resolution NMR spectroscopy suggests that this junction exists in more than one conformer at room temperature. The data from this junction are compared with the data from a similar junction composed of four hexadecanucleotides.     

Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H₀ and for arbitrary scores asymptotically a X²-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.