Pair Of Rows Research Articles

Row‐Hamiltonian Latin squares and Falconer varieties

AbstractA Latin square is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square is row‐Hamiltonian if the permutation induced by each pair of distinct rows of is a full cycle permutation. Row‐Hamiltonian Latin squares are equivalent to perfect 1‐factorisations of complete bipartite graphs. For the first time, we exhibit a family of Latin squares that are row‐Hamiltonian and also achieve precisely one of the related properties of being column‐Hamiltonian or symbol‐Hamiltonian. This family allows us to construct non‐trivial, anti‐associative, isotopically ‐closed loop varieties, solving an open problem posed by Falconer in 1970.

A Fast Optimal Double-row Legalization Algorithm

In Placement Legalization, it is often assumed that (almost) all standard cells possess the same height and can therefore be aligned in cell rows , which can then be treated independently. However, this is no longer true for recent technologies, where a substantial number of cells of double- or even arbitrary multiple-row height is to be expected. Due to interdependencies between the cell placements within several rows, the legalization task becomes considerably harder. In this article, we show how to optimize squared cell movement for pairs of adjacent rows comprising cells of single- as well as double-row height with a fixed left-to-right ordering in time 𝒪( n · log ( n )), where n denotes the number of cells involved. Opposed to prior works, we do not artificially bound the maximum cell movement and can guarantee to find an optimum solution. Our approach also allows us to include gridding and movebound constraints for the cells. Experimental results show an average percental decrease of over 26% in the total squared movement when compared to a legalization approach that fixes cells of more than single-row height after Global Placement.

Three amazing new species of the genus Chrysolina (Coleoptera: Chrysomelidae: Chrysomelinae) from China

Three new species of the genus Chrysolina Motschulsky, 1860, namely Сh. caspari sp. n., Ch. melchiori sp. n., and Ch. balthazari sp. n. are described from Sichuan and Yunnan Provinces of China. These species have rare or unique features. In Ch. caspari sp. n. the shape of the last maxillary palpomere (it is shorter and narrower than the penultimate one) is a rare case in the genus Chrysolina. Among Chinese species, this shape of maxillary palpi is known only in one species, Ch. pieli Chen, 1936. In Ch. melchiori sp. n. the relief of elytral surface (strongly reticulated irregular funnels bearing a puncture at the bottom, separated by smooth intervals) is unique for the genus Chrysolina. In Ch. balthazari sp. n. the relief of elytra (alternation of wide convex intervals between pairs of rows and very narrow flat or slightly convex intervals between rows of one pair) is well distinguishable from most Chrysolina members. Due to this feature, the new species can only be close to Ch. jinxiaoae Ge in: Daccordi, Ge, Cui, Yang, 2011 from North Sichuan. Photographs of habitus, external characters, and male aedeagi are presented.

Three-level saturated orthogonal arrays with less β-wordlength pattern

Saturated orthogonal array is an important type of fractional factorial designs in experimental design. On the basis of guaranteeing orthogonality, it maximizes the number of factors and saves the cost of experiments. Therefore, it is increasingly used in practical experiment. For quantitative factors, the minimum β-aberration criterion is suitable for selecting good designs under a polynomial model. However, construction methods of designs with less β-aberration have not been fully investigated. In this article, we apply the Rao-Hamming method to construct a class of three-level saturated orthogonal arrays, and perform a special level permutation on the designs of the Rao-Hamming construction, which makes the resultant designs mirror-symmetric ones. Furthermore, we analyze the distribution of elements in each row and among all possible pairs of rows of the mirror-symmetric designs, and discuss some properties of the β-wordlength pattern for three-level mirror-symmetric designs constructed by the Rao-Hamming method. In addition, we provide the explicit expressions of β 3 and β 4 for three-level mirror-symmetric designs, which can reduce the computational complexity of the β-wordlength pattern, and provide an effective idea for finding designs under the minimum β-aberration criterion. Finally, numerical examples are used to illustrate and verify the results.

Taxonomic revision and re-description of Ateuchosaurus pellopleurus (Hallowell, 1861) (Reptilia, Squamata, Scincidae) with resurrection of A. okinavensis (Thompson, 1912)

The scincid lizard Ateuchosaurus pellopleurus (Hallowell, 1861) has been recognized as a single species widely distributed in the Osumi, Tokara, Amami, and Okinawa Groups of the Ryukyu Archipelago, southern Japan. However, a recent molecular phylogenetic study suggested that this skink should be divided into two species: one distributed in the Osumi to Amami Groups, and another distributed in the Okinawa Group. For A. pellopleurus, two extant syntypes collected from an island of the Amami Group were confirmed. Therefore, we identified the species in the Osumi to Amami Groups as A. pellopleurus sensu stricto by designating one of the syntypes as the lectotype for this species. For the species in the Okinawa Group, we resurrected A. okinavensis (Thompson, 1912), of which the type locality is on Okinawajima Island in the Okinawa Group. Ateuchosaurus pellopleurus and A. okinavensis can be differentiated by the following characteristics: usually separated frontonasal and frontal, 8–14 subdigital scales on the fourth toe (mode = 11), and usually two or three pairs of dorsal median scale rows with black stripes in A. pellopleurus; usually fused frontonasal and frontal, 10–16 subdigital scales on the fourth toe (mode = 13), and usually no stripe on the dorsal scales or a pair of dorsal median scale rows with black stripes in A. okinavensis.

The sum of hamming distance for some composite graphs relative to vertex-edge incidence matrix

Given C be a vertex-edge incidence matrix of a graph Z. The Hamming distance between two rows C(x, :) and C(y, :) of C is the number of coloumn ℓ such that C (x, ℓ) ≠ C (y, ℓ). In this paper, we discuss the sum of Hamming distances between all pairs of rows of C. We present a formula for the sum of the number of edges and the number of vertices of the graph Z. We then use this formula to determine the sum of Hamming distance for composite graphs such as union of graphs, joint of graphs, corona product of graphs and cartesian product of graphs

The complexity of binary matrix completion under diameter constraints

We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that every pair of rows in the resulting matrix has a Hamming distance within a specified range. We obtain an almost complete picture of the complexity landscape regarding the distance constraints and the maximum number of missing entries in any row. We develop polynomial-time algorithms for maximum diameter three based on Deza's theorem (1973) [11] from extremal set theory. We also prove NP-hardness for diameter at least four. For the number of missing entries per row, we show polynomial-time solvability when there is only one and NP-hardness when there can be at least two. In many of our algorithms, we heavily rely on Deza's theorem to identify sunflower structures. This paves the way towards polynomial-time algorithms which are based on finding graph factors and solving 2-SAT instances.

The oldest gnathostome teeth.

Mandibular teeth and dentitions are features of jawed vertebrates that were first acquired by the Palaeozoic ancestors1-3 of living chondrichthyans and osteichthyans. The fossil record currently points to the latter part of the Silurian period4-7 (around 425 million years ago) as a minimum date for the appearance of gnathostome teeth and to the evolution of growth and replacement mechanisms of mandibular dentitions in the subsequent Devonian period2,8-10. Here we provide, to our knowledge, the earliest direct evidence for jawed vertebrates by describing Qianodus duplicis, a new genus and species of an early Silurian gnathostome based on isolated tooth whorls from Guizhou province, China. The whorls possess non-shedding teeth arranged in a pair of rows that demonstrate a number of features found in modern gnathostome groups. These include lingual addition of teeth in offset rows and maintenance of this patterning throughout whorl development. Our data extend the record of toothed gnathostomes by 14 million years from the late Silurian into the early Silurian (around 439 million years ago) and are important for documenting the initial diversification of vertebrates. Our analyses add to mounting fossil evidence that supports an earlier emergence of jawed vertebrates as part of the Great Ordovician Biodiversification Event (approximately 485-445million years ago).

Mathematical framework for describing multipartite entanglement in terms of rows or columns of coefficient matrices

In this paper, we develop a mathematical framework for describing entanglement quantitatively and qualitatively for multipartite qudit states in terms of rows or columns of coefficient matrices. More specifically, we propose an entanglement measure and separability criteria based on rows or columns of coefficient matrices. This entanglement measure has an explicit mathematical expression by means of exterior products of all pairs of rows or columns in coefficient matrices. It is introduced via our result that the [Formula: see text]-concurrence coincides with the entanglement measure based on two-by-two minors of coefficient matrices. Depending on our entanglement measure, we obtain the separability criteria and maximal entanglement criteria in terms of rows or columns of coefficient matrices. Our conclusions show that just like every two-by-two minor in a coefficient matrix of a multipartite pure state, every pair of rows or columns can also exhibit its entanglement properties, and thus can be viewed as its smallest entanglement contribution unit too. The great merit of our entanglement measure and separability criteria is two-fold. First, they are very practical and convenient for computation compared to other methods. Second, they have clear geometric interpretations.

Effects of Holes Arrangement on the Superposition Characteristics of Film Cooling Effectiveness

The purpose of the current research is to test and analyze the applicability of the Sellers model in different arrangements and configurations of film cooling holes and then to modify the Sellers model to improve the accuracy of the superposition prediction. The film cooling effectiveness distributions at different blowing ratios are obtained using the infrared thermometry technology. The flat plate experiments are completed in a low-speed closed-loop wind tunnel facility. The mainstream Reynolds number based on the film hole diameter is 6300, and the blowing ratios range from 0.8 to 1.8. The superposition characteristics are described in three different cases: double rows of cylindrical holes in an inline arrangement, double rows of cylindrical holes in a staggered arrangement, and double rows of compound angle holes in an inline arrangement. The results indicate that the Sellers model cannot accurately predict the film cooling effectiveness in certain conditions, which is mainly attributed to the interaction between counter-rotating vortex pairs of the adjacent rows and the increasing momentum of mainstream near the wall surface. For all cases, the corresponding modified superposition prediction methods are given in this paper.

Multi-scale affinities with missing data: Estimation and applications.

Many machine learning algorithms depend on weights that quantify row and column similarities of a data matrix. The choice of weights can dramatically impact the effectiveness of the algorithm. Nonetheless, the problem of choosing weights has arguably not been given enough study. When a data matrix is completely observed, Gaussian kernel affinities can be used to quantify the local similarity between pairs of rows and pairs of columns. Computing weights in the presence of missing data, however, becomes challenging. In this paper, we propose a new method to construct row and column affinities even when data are missing by building off a co-clustering technique. This method takes advantage of solving the optimization problem for multiple pairs of cost parameters and filling in the missing values with increasingly smooth estimates. It exploits the coupled similarity structure among both the rows and columns of a data matrix. We show these affinities can be used to perform tasks such as data imputation, clustering, and matrix completion on graphs.

Productivity and competitive ability of rabi maize and legumes intercropping system

The intercropping system involves two or more crops coexist for some period of their cycles and ensure multifaceted benefits. As maize is a widely spaced crop, it offers enough scope for adoption of intercropping and legumes are known as good companions in intercropping. Considering the facts, an experiment was carried out at Bagusala Farm of Centurion University of Technology and Management on intercropping maize (Zea mays L.) with legumes, namely, groundnut (Arachis hypogaea L.) and green gram (Vigna radiata L.). Paired row maize was sown during first week of January 2020 and in between two pairs of maize rows, one, two and three rows of groundnut and green gram seeds were sown. The results revealed that the grain and straw yields of maize were not influenced significantly by intercropping system. However, total biomass yield was differed among the treatments and maize + groundnut (2: 3) produced maximum biomass yield and it was closely followed by maize + groundnut (2: 2) and maize + green gram (2: 3). The land equivalent ratio (LER) clearly showed advantages of intercropping and maximum LER was obtained with maize + groundnut (2: 1) and it was followed by maize + green gram (2: 3). But maximum area time equivalent ratio (ATER) was noted with maize + groundnut (2: 3). Aggressivity values indicated that maize was more aggressive compared to legumes. Maize equivalent yield (MEY) was maximum with maize + groundnut (2: 3) and it was followed by maize + groundnut (2: 2). The results suggest that intercropping of maize + groundnut either in 2: 2 or 2: 3 proportions can be adopted under south Odisha conditions for greater productivity than pure stand of maize.

Spatial Arrangements on Growth and Yield of Cowpea (<em>Vigna unguiculata L. Walp.</em>) in Intercropping

This experiment was conducted at the Crop Farm of Eastern University, Sri Lanka to evaluate the effect of different spatial arrangements on growth and yield of cowpea (Vigna unguiculata L. Walp) under okra (Abelmoschus esculentus L.) cowpea intercropping in sandy regosol. The experiment was laid out in a Randomized Complete Block Design (RCBD) having monocropping and different intercropping patterns. The results revealed that there was a significant difference (P<0.05) among treatments for plant height, root length, leaf area, leaf area index, pod length, number of total and effective nodules per plant, dry weight of effective nodules and total pod yield of cowpea. However, seeds per pod was not significantly different (P>0.05) with different plating patterns. The study concluded that 60 cm between two rows with 150 cm between two pairs of rows of okra with three rows of cowpea in between paired rows would be the most suitable planting system to get maximum growth and yield of cowpea.

Lewis Carroll and the Red Hot Potato: A graph theoretic approach to a linear algebraic identity

The Lewis Carroll Identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns. Using the matrix tree theorem, we can convert this into an equivalent identity involving sums over pairs of forests. Unlike the Lewis Carroll Identity, the Forest Identity involves no minus signs. In 2011, Vlasev and Yeats (2012) suggested that such a Forest Identity could be proven using edge transfers similar to Zeilberger’s 1997 matrix proof. However, until now, such an algorithm has not yet been developed. In this paper, we provide this edge transfer algorithm and a bijective proof for both the Lewis Carroll Identity and Forest Identity. This bijection is implemented by the Red Hot Potato algorithm, so called because the way edges get tossed back and forth between the two forests is reminiscent of the children’s game of hot potato.

Two-row and two-column mixed-integer presolve using hashing-based pairing methods

In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.

Refining invariants for computing autotopism groups of partial Latin rectangles

Prior to using computational tools that find the autotopism group of a partial Latin rectangle (its stabilizer group under row, column and symbol permutations), it is beneficial to find partitions of the rows, columns and symbols that are invariant under autotopisms and are as fine as possible. We look at the lattices formed by these partitions and introduce two invariant refining maps on these lattices. The first map generalizes the strong entry invariant in a previous work. The second map utilizes some bipartite graphs, introduced here, whose structure is determined by pairs of rows (or columns, or symbols). Experimental results indicate that in most cases (ordinarily 99%+), the combined use of these invariants gives the theoretical best partition of the rows, columns and symbols, outperforms the strong entry invariant, which only gives the theoretical best partitions in roughly 80% of the cases.

Evaluation of Cotton Establishment Strategies Using Subsurface Drip Irrigation (SDI) in the Southern High Plains of Texas

Abstract.HighlightsPlanting date and crop row distance from SDI laterals affect final cotton plant population, lint yield and water use.Cotton rows directly above 2.03-m spaced SDI laterals should only be used late within the cotton planting window.Positioning pairs of rows nearer to 2.03-m spaced SDI laterals increased yield compared to evenly spaced rows.SDI laterals spaced 1.02 m versus 2.03 m apart increased cotton yield by 5% and water use efficiency by 7%. In the Texas High Plains (THP), water table declines in the Ogallala Aquifer and the high evaporative environment have helped motivate the transition from surface and center pivot irrigation to subsurface drip irrigation (SDI). A major challenge to wider adoption of SDI in the region is inconsistent cotton seed germination and plant establishment due to dry overwinter conditions, the difficulty of “pushing” irrigation water upward into the seed germination zone, and the high evaporative environment during the optimum cotton planting period. To evaluate strategies for improving cotton establishment using SDI in the Southern High Plains (SHP) of Texas, a field experiment having five crop row/ SDI lateral configurations, each with two planting dates, was conducted from 2013 to 2018 at the Texas A&M AgriLife Research Center in Halfway, Texas. Differences in final plant stands, cotton yields, cotton fiber qualities, and water productivities were determined. Averaged over planting dates and years, planting directly over 1.02-m spaced SDI laterals (Every-Row configuration) increased final plant stand by 9.5%, cotton yield by 5.1%, irrigation water use efficiencies (IWUE) by 6.7%, and irrigation value (IValue) by 6.1% over planting pairs of 1.02-m spaced rows equidistant and parallel to 2.03-m spaced laterals (Traditional configuration). Compared to the Traditional configuration, planting pairs of cotton rows 0.76 m apart with both rows closer to 2.03-m spaced SDI laterals (30-50 configuration) increased final plant stand by 9.5% and yield by 3.0%. Considering additional treatments with 2.03-m spaced cotton rows planted directly over 2.03-m spaced SDI laterals (Skip-Row configuration) and 1.02-m spaced cotton rows having one row directly over 2.03-m spaced laterals and one row “not irrigated” (Skip-Row Plus configuration), early plantings resulted in five-year yields of 1400 and 1600 kg ha-1, respectively. However, these yields were less than those from the late planted, Traditional treatment at 1620 kg ha-1. Also, IValues and IWUEs of both Skip-Row treatments were significantly lower (p<0.05) than those of the Traditional treatment. Based on these results, the Skip-Row or Skip-Row Plus configurations should only be used late in the cotton planting period when soil water is not available for plant establishment using the Traditional or 30-50 configurations. Advantages of Every-Row and 30-50 over the Traditional configuration must be weighed against their increased costs. Keywords: Cotton, Germination, Irrigation, Southern High Plains, Subsurface drip irrigation (SDI).

Hadamard-Type Matrices on Finite Fields and Complete Complementary Codes

Hadamard matrix is defined as a square matrix where any components are -1 or +1, and where any pairs of rows are mutually orthogonal. In this work, we consider the similar matrix on finite field GF(p) where p is an odd prime. In such a matrix, every component is one of the integers on GF(p)\{0}, that is, {1,2,...,p-1}. Any additions and multiplications should be executed under modulo p. In this paper, a method to generate such matrices is proposed. In addition, the paper includes the applications to generate n-shift orthogonal sequences and complete complementary codes. The generated complete complementary code is a family of multi-valued sequences on GF(p)\{0}, where the number of sequence sets, the number of sequences in each sequence set and the sequence length depend on the various divisors of p-1. Such complete complementary codes with various parameters have not been proposed in previous studies.

Two new species of Helicopsyche Siebold 1856 (Insecta: Trichoptera: Helicopsychidae) from Pará State, northern Brazil.

Two new species of Helicopsychidae from Pará State, Brazil, are described and illustrated: male of Helicopsyche (Feropsyche) carajas n. sp. is characterized by segment X having 8 pairs of subequal megasetae distributed in a pair of longitudinal rows; the primary branch of each gonocoxite, in lateral view, with its basal half nearly as broad as its median part and parallel-sided, its posterior apex directed slightly ventrad and slender and strongly pointed; the dorsal lobes of the endotheca posteriorly protruding, and the lateral lobes of the endotheca well developed. Helicopsyche (Feropsyche) inflata n. sp. is characterized by the hind wings each having very long fringes along the anal border; the primary branch of each gonocoxite having a pointed apex in lateral view and its basimesal lobe being triangular in lateral and ventral views and bearing eight megasetae; and the dorsal lobe of the endotheca being very well developed in lateral view.

Growth and development of energy willow plantations of different density for the introduction of nitrogen fertilizers on the leached chernozems of the Central Forest-Steppe

Purpose. Determine the optimal density and nitrogen fertilization rates to ensure the intensive growth and high productivity of energy plantations of some willow varieties under the conditions of the Central Forest-Steppe. Methods. The object of the study was the exploration of plantations of two willow varieties ( Salix viminalis L.), namely ‘Tora’ and ‘Ternopilska’, created under the conditions of the northern part of the Central Forest-Steppe of Ukraine in the spring of 2015. Willow twigs of 20 cm were planted in two pairs of rows with a distance between them 0.75 m for two variants of row spacing: 1.50 and 2.50 m. The planting density was 12, 15 and 18 thousand plant/ha. Results. After two years of growing willow, the average height of plants ranged from 339 to 493 cm. After the third year (2017), the height increase was less than the previous year. For planting schemes 0.75×1.50×0.75 m in ‘Tora’ variety, higher plants were in the variant with a planting density of 12 thousand plants/ha (553 cm), and for widths spaced 2.50 m at 18 thousand plants/ha (588 cm). In ‘Ternopilska’ variety, under both planting schemes, plant height was higher at the density of 18,000 plant/ha (452 and 414 cm, respectively). Before the beginning of the fourth vegetation period (2018), three years of the aboveground mass of willow was cut and ammoniac saltpeter was added to the part of the area in the amount of 35 and 70 kg a.i./ha. In both varieties, new coppice formed, which was characterized by a much larger number of shoots per bush, from 4.8 to 6.6 in ‘Tora’ and from 3.5 to 8.8 in ‘Ternopilska’. Their height after the first vegetation period was 398–477 and 283–425 cm respectively, that is approximately at the height of plants after the first two years of vegetation. There was a tendency to reduce the number of shoots in the bush and their height for increasing the density of plantings. The conducted researches indicate the positive influence of the introduction of ammonium nitrate in the norm of 70 kg a.i./ha on plant height and biomass productivity. Conclusions. Among the two used varieties of willow on the leached chernozem of the Central Forest-Steppe of Ukraine, ‘Tora’ variety was marked by more intensive growth and higher productivity. Better planting design for both varieties was 0.75×1.50×0.75 m. Since the density options selected for research yielded roughly identical results, the smaller ones should be considered suitable for use, i.e. 12 and 15 thousand plants per hectare. Used rates of ammonium nitrate, especially N 70 , contributed to the increase in the height of annual voluntary growth and biomass productivity.