Exploitation of rank summation index for the selection of 21 maize hybrids for green maize production in South-eastern Nigeria

Green (fresh) maize (Zea mays L.) provides food security and income to farmers especially when other crops are still in the field. However, research on green maize varieties is scarcely reported in the literature or information on suitable genetic material (germplasm) for green maize production. Two local maize landraces collected from south-eastern Nigeria and five improved varieties sourced from the International Institute of Tropical Agriculture (IITA) were used for this experiment. These seven genotypes were crossed in a half diallel mating system in a randomized complete block design (RCBD) with four replications. Data collected were subjected to analysis of variance and those found significant (p = 0.05) were further subjected to diallel analysis using Griffing’s method II and model I for fixed effects. Rank summation index was used for all the traits studied to identify and select the best performer amongst the genotypes. The rank summation index identified and selected the crosses between DTMA-4 X OKA BENDE-WHITE, OKA MBAISE X OKA BENDE-WHITE, PVA SYM 8 F2 X OKA BENDE-WHITE, POOL 66/ACR-91 X OKA BENDE-WHITE and DMR-ESRY X OKA BENDE-WHITE for the production of green maize in south-eastern Nigeria

Enhanced Affinity for Spectral Clustering using Topological Node Features (TNFS)

Data clustering is an active topic of research as it has applications in various fields such as biology, management, statistics, pattern recognition, etc. Spectral Clustering (SC) has gained popularity in recent times due to its ability to handle complex data and ease of implementation. A crucial step in spectral clustering is the construction of the affinity matrix, which is based on a pairwise similarity measure. The varied characteristics of datasets affect the performance of a spectral clustering technique. In this paper, we have proposed an affinity measure based on Topological Node Features (TNFs) viz., Clustering Coefficient (CC) and Summation index (SI) to define the notion of density and local structure. It has been shown that these features improve the performance of SC in clustering the data. The experiments were conducted on synthetic datasets, UCI datasets, and the MNIST handwritten datasets. The results show that the proposed affinity metric outperforms several recent spectral clustering methods in terms of accuracy.

Multivariate Analysis and Selection Indices to Identify Superior Quince Cultivars for Cultivation in the Tropics

Among the fruit species cultivated in subtropical climates, quince has productive cultivars with high horticultural potential. The objectives of this study were to evaluate the genetic divergence among quince cultivars through multivariate procedures and to identify cultivars for cultivation in the tropics through selection indices. Twenty-seven productive quince cultivars were grown in a location with a high-altitude tropical climate. The number of fruit, estimated yield, flowering period, number of buds, number of shoots, number of brindles per shoot, shoot length, average fruit weight, fruit length, and fruit diameter were measured. A multivariate principal component analysis (PCA) associated with the unweighted pair group method with arithmetic means (UPGMA) based on Gower distance and Pearson correlation coefficients was used to evaluate genetic divergence. Superior cultivars were defined by the selection index based on the rank summation index and the Z-index. UPGMA grouping indicated there was genetic variability among cultivars and showed that groups that were more dissimilar [e.g., the cultivars Bereckzy and Champion (distance = 0.69)] had the potential to be used in future stages of quince selection. The estimated yield, shoot length, fruit weight and diameter, and flowering period contributed to the maximum variability among quince cultivars. The selection indices identified cvs. Bereckzy, Alaranjado, and Alongado (30, 68, and 73 rank summation index, respectively) as superior, simultaneously considering the evaluated traits with greater potential for cultivation in the tropics.

The system of powers of conformal mappings and biorthogonal to them systems of the functions

In this article we review the methods of power summation of factors. The degree of factors which are arbitrary powers of summation indices are considered. We show that using the Poisson-Abel method only those series can be summarized the order of member increase of which is proportional to the exponent depending on the summation index. At the same time the Gauss-Weierstrass method and other power factors methods can be also applied to the series the terms of which increase in proportion to the exponential dependence of the indices summation.

A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function

We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.

Non-Terminating Basic Hypergeometric Series and the q-Zeilberger Algorithm

We present a systematic method for proving non-terminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all non-terminating basic hypergeometric summation formulae in the work of Gasper and Rahman. Furthermore, by comparing the recursions and the limit values, we may verify many classical transformation formulae, including the Sears–Carlitz transformation, transformations of the very well-poised 8φ7 series, the Rogers–Fine identity and the limiting case of Watson's formula that implies the Rogers–Ramanujan identities.

Variation of Cold Tolerance among Open-pollinated Sweet Corn Cultivars

Cold tolerance useful for sweet corn improvement may be present in open-pollinated (OP) cultivars. Cold tolerance in sweet corn is the ability to germinate, emerge, and grow under low temperatures. The cold tolerance of 35 open-pollinated sweet corn populations and controls was measured by growing the entries under 14 °C day/10 °C night in growth chambers. The same entries were grown under warm (24 ± 2 °C) conditions in a greenhouse. Traits measured included percent and time to emergence, seedling color, and seedling root and shoot dry mass. Respective repeatability estimates calculated from mean squares were 0.08, 0.33, 0.33, 0.50, and 0.60 for these traits. Entries were ranked separately in each environment based on their performance using a rank-summation index. Differences in cold tolerance existed among the entries. Emergence ranged from 75% to 100% among the entries, with a mean of 90.9%. Time to emergence ranged from 16.2 to 21.9 d, with a mean of 18.2 d. Root and shoot mass ranged from 0.07 to 0.27 g/plot and 0.07 to 0.24 g/plot, respectively. Correlations among the traits measured were favorable, permitting simultaneous improvement. The rankings between the warm and cold environments were significantly correlated (r = 0.67***), indicating that some entries that performed well under low temperatures also performed well under warm conditions.

The Stiles Summation Index Applied to Heterochromatic Brightness Matching

The summation index technique introduced by Stiles has been applied to heterochromatic brightness matching in order to explain individual differences in luminous efficiency functions for brightness. Such functions were obtained for 2-deg and 10-deg fields from twelve subjects, and the difference between the two fields was compared with the macular pigment density tabulated in Wyszecki and Stiles's book. A summation index was obtained for red and green stimuli combinations and the results are expressed in the form of an equation with nonlinear coefficients. The same equation is applied to the brightness luminous efficiency functions and the individual differences in the efficiency function are interpreted as the result of different contributions of opponent chromatic channels to the perception of brightness.