Algorithms and Lower Bounds for De Morgan Formulas of Low-Communication Leaf Gates

The class FORMULA[s]∘G consists of Boolean functions computable by size- s De Morgan formulas whose leaves are any Boolean functions from a class G. We give lower bounds and (SAT, Learning, and pseudorandom generators ( PRG s )) algorithms for FORMULA[n 1.99 ]∘G, for classes G of functions with low communication complexity . Let R (k) G be the maximum k -party number-on-forehead randomized communication complexity of a function in G. Among other results, we show the following: • The Generalized Inner Product function GIP k n cannot be computed in FORMULA[s]° G on more than 1/2+ε fraction of inputs for s=o(n 2 /k⋅4 k ⋅R (k) (G)⋅log⁡(n/ε)⋅log⁡(1/ε)) 2 ). This significantly extends the lower bounds against bipartite formulas obtained by [62]. As a corollary, we get an average-case lower bound for GIP k n against FORMULA[n 1.99 ]∘PTF k −1 , i.e., sub-quadratic-size De Morgan formulas with degree-k-1) PTF ( polynomial threshold function ) gates at the bottom. Previously, it was open whether a super-linear lower bound holds for AND of PTFs. • There is a PRG of seed length n/2+O(s⋅R (2) (G)⋅log⁡(s/ε)⋅log⁡(1/ε)) that ε-fools FORMULA[s]∘G. For the special case of FORMULA[s]∘LTF, i.e., size- s formulas with LTF ( linear threshold function ) gates at the bottom, we get the better seed length O(n 1/2 ⋅s 1/4 ⋅log⁡(n)⋅log⁡(n/ε)). In particular, this provides the first non-trivial PRG (with seed length o(n)) for intersections of n halfspaces in the regime where ε≤1/n, complementing a recent result of [45]. • There exists a randomized 2 n-t #SAT algorithm for FORMULA[s]∘G, where t=Ω(n\√s⋅log 2 ⁡(s)⋅R (2) (G))/1/2. In particular, this implies a nontrivial #SAT algorithm for FORMULA[n 1.99 ]∘LTF. • The Minimum Circuit Size Problem is not in FORMULA[n 1.99 ]∘XOR; thereby making progress on hardness magnification, in connection with results from [14, 46]. On the algorithmic side, we show that the concept class FORMULA[n 1.99 ]∘XOR can be PAC-learned in time 2 O(n/log n) .

Seed Micromorphology of Eleven Species of Pleione (Orchidaceae)

The micromorphological characteristics of the seeds of 11 species of Pleione have been studied, both qualitatively and quantitatively, to establish whether they are useful for systematic studies of the genus. The quantitative characteristics include seed length (0.237–0.626 μm), seed width (0.053–0.133 μm), seed length/width ratio (2.631–7.279), seed ridge thickness (1.4 E-3–4 E-3μm) and seed volume (1.88 E-4–3.06 E-3 μm3). The cluster analysis result agrees well with the results of previous systematic studies. The cluster analysis shows that: P. coronaria, P. forrestii and P. yunnanensis form a group, while the remaining eight species form a second group, with three subgroups, namely: P. limprichtii, P. pleionoides, P. formosana as group I; P. hookeriana and P. bulbocodioides as group II; and P. praecox, P. scopulorum and P. maculata for group III. All the Pleione species of Sect. Pleione and Sect. Humiles show the fusion of adjacent seed coat cells into a network. The shape of the seeds of P. praecox and P. maculata are very similar--being oval, and the mesh walls of their adjacent seed coat cells are not fused. Within these sections no clear pattern can be seen between the species, but the addition of further species might clarify the differences between Sect. Pleione and Sect. Humiles.

Genetic Diversity and Environmental Influence on Growth and Yield Parameters of Bambara Groundnut

Bambara groundnut (BGN) is a drought-tolerant crop majorly cultivated in sub-Saharan Africa. Due to a lack of extensive research, marginalization, lack of awareness, and lack of available fund among others, this crop's improvement has been limited. The development of this crop depends on evaluation and selection of unique and stable breeding lines in different environments. This study aims to estimate genetic diversity using morphological traits at different locations in 95 accessions of BGN collected from the Genebank of the International Institute of Tropical Agriculture (IITA), Ibadan. The experiment was carried out in three replicates at IITA experimental sites in two agroecological zones in Ibadan (7°40′19.62″ N, 3°91′73.13″ E) and Ikenne (6°51′00.873″ N, 3°41′48.528″ E) using a randomized complete block design. Ten vegetative growth traits and eight yield traits were scored. The data was subjected to ANOVA, PCA, correlation, and cluster analysis. Estimations of genetic parameters and broad sense heritability were carried out on the traits. ANOVA revealed significant variation in each trait except for days to emergence. Significant variation was also observed for accession and location interactions (genotype x environment interactions) for plant height, leaf length, leaf width, chlorophyll content, number of petioles, germination count, number of pods, number of seeds, seed length, seed width, and yield. PC1 and PC2 show 42.3% of the total variations observed by the PC, with seed thickness contributing more to PC1 and the number of seeds contributing more to PC2. Cluster analysis categorized the accessions into four distinct groups. The number of pods had the highest genotypic coefficient of variation of 32.55% and the phenotypic coefficient of variation of 97.61%, while seed length (0.63), seed width (0.54), and seed thickness (0.58) have high heritability values. The genetic advance was highest in yield (76.15%) and lowest in days to 50% germination (0.21%). This study can be used to predict appropriate agroecological zones for the planting of BGN while the knowledge of the diversity of the accessions based on the traits could serve a guide in selecting the best trait for the improvement of the crop.

Morphometric characteristics and seed germination of Dalbergia granadillo Pittier

Objective: To know the variability and quality of seed in a Dalbergia granadillo Pittier (Fabaceae) population from the Soconusco, Chiapas, Mexico. Design / methodology / approximation: The seed was obtained from six trees during the months of February and March 2020. Two weeks after the seeds were collected, pod and seed variables were determined. Seed length (LS), width (AS), color (CS), weight of 100 seeds (g) (PS) and germination percentage (PG). The results were statistically analysed by analysis of variance using the GLM procedure and the comparison of means by Tukey (P ≤ 0.05) with the SAS 9.0 program. Results: There is wide variation in seed content. The pods registered from 1, 2, 3 and up to four seeds, although pods of one predominated. There are seeds of two colours, dark brown and light brown, and the latter are the most abundant; however, light colored seeds registered higher germination (96%). The weight of 100 seeds registered values ​​of 9.6-9.7 g. Study Limitations / implications: The species has a restricted distribution and presents a low number of individuals in the evaluated populations. Findings / conclusions: The morphometric characteristics of the seeds allowed to identify the variability and quality, mainly in shape, size and coloration of the seeds, as well as the number of seeds per pod.

Genome-wide association studies and genomic selection assays made in a large sample of cacao (Theobroma cacao L.) germplasm reveal significant marker-trait associations and good predictive value for improving yield potential

A genome-wide association study was undertaken to unravel marker-trait associations (MTAs) between SNP markers and yield-related traits. It involved a subset of 421 cacao accessions from the large and diverse collection conserved ex situ at the International Cocoa Genebank Trinidad. An average linkage disequilibrium (r 2 ) of 0.10 at 5.2 Mb was found across several chromosomes. Seventeen significant ( P ≤ 8.17 × 10 -5 (–log10 (p) = 4.088)) MTAs of interest, which accounted for 5 to 17% of the explained phenotypic variation, were identified using a Mixed Linear Model in TASSEL version 5.2.50. The most significant MTAs identified were related to seed number and seed length on chromosome 7 and seed number on chromosome 1. Other significant MTAs involved seed length to width ratio on chromosomes 3 and 5 and seed length on chromosomes 4 and 9. It was noteworthy that several yield-related traits, viz ., seed length, seed length to width ratio and seed number were associated with markers on different chromosomes, indicating their polygenic nature. Approximately 40 candidate genes that encode embryo and seed development, protein synthesis, carbohydrate transport and lipid biosynthesis and transport were identified in this study. A significant association of fruit surface anthocyanin intensity co-localised with MYB-related protein 308 on chromosome 4. Testing of a genomic selection approach revealed good predictive value (GEBV) for economic traits such as seed number (GEBV = 0.611), seed length (0.6199), seed width (0.5435), seed length to width ratio (0.5503), seed/cotyledon mass (0.6014) and ovule number (0.6325). The findings of this study could facilitate genomic selection and marker-assisted breeding of cacao thereby expediting improvement in the yield potential of cacao planting material.

Growth and Yield of Cowpea as Influenced by Different Phosphorus Levels

The experiment was carried out at the research field of the Department of Agronomy of Bangabandhu Sheikh Mujibur Rahman Agricultural University (BSMRAU), Gazipur during December 2016 to April 2017 to investigate the effect of different phosphorus levels (0, 30, 60 and 90 kg P ha-1) on the growth and yield of four selected cowpea genotypes (BARI Felon-1, A-06008, VI046192 and VI034386). The experiment was laid out in a factorial randomized complete block design with three replications. The results indicated that, among the genotype, BARI Felon-1 required minimum days to 1st (96 DAS) and 50% flowering (108 DAS) showing the highest absolute growth rate (0.71 g day-1), crop growth rate (23.69 g m-2 day-1), relative growth rate (0.047 g g-1 day-1), net assimilation rate (1.40 g m-2 day-1), leaf area index (6.68), SPAD value (51.03), seed length (0.71 cm) and breadth (0.54 cm). But the genotype, A-06008 gave the highest grain yield (0.62 t ha-1). Application of phosphorus at 90 kg ha-1 showed the highest leaf area index (6.67), SPAD value (50.98), pod length (14.33 cm), seed length (0.70 cm), seed breadth (0.50 cm) and grain yield (0.34 t ha-1). In terms of growth and yield, the cowpea genotype A-06008 showed the best performance at the phosphorus level of 90 kg ha-1. Bangladesh Agron. J. 2021, 24(1): 25-36

Effects of BrMYC2/3/4 on Plant Development, Glucosinolate Metabolism, and Sclerotinia sclerotiorum Resistance in Transgenic Arabidopsis thaliana

MYC2/3/4, known as a basic helix–loop–helix (bHLH) transcription factor, directly activate the genes involved in diverse plant development and secondary metabolites biosynthesis. In this study, we identified and cloned five MYC paralogs (BrMYC2/3-1/3-2/4-1/4-2) from Chinese cabbage (Brassica rapa ssp. pekinensis). In-silico analyses for the physicochemical properties suggested that BrMYC2/3-1/3-2/4-2/4-3 are unstable hydrophobic and acidic proteins, while BrMYC4-1 is an unstable hydrophobic and basic protein. BrMYC2/3/4 belong to the bHLH superfamily and are closely related to AthMYC2/3/4 orthologs that mediate the regulation of various secondary metabolites. It was demonstrated that BrMYC2/3/4-GFP fusion protein localized in the nucleus and expression levels of five BrMYC2/3/4 homologous genes all elevated relative to control (Ctrl). When expressed in Arabidopsis under the control of 35S promoter, each of the BrMYC2/3-1/3-2/4-1/4-2 transgenes differentially influenced root and shoot elongation, vegetative phase change, flowering time, plant height and tiller number after flowering, and seed production. Despite the variation of phenotypes between the transgenic lines, all the lines except for BrMYC4-2 exhibited shorter seed length, less seed weight, higher accumulation of glucosinolates (GSs), and resistance to Sclerotinia sclerotiorum than Ctrl. Notably, BrMYC2 overexpression (OE) line significantly reduced the lengths of root and hypocotyl, seed length, and weight, along with faster bolting time and strikingly higher accumulation of total GSs. Accumulation of GSs at the highest levels in the BrMYC2OE line conferred the highest resistance to S. sclerotiorum. Unlike BrMYC3OE and BrMYC4OE, BrMYC2OE stimulated the growth of plant height after fluorescence. The results of this study point to the BrMYC2 overexpression that may provide a beneficial effect on plant growth and development via plant resistance to the fungal pathogen.

Evaluation of Traits Associated With Seed Characteristics in Arkansas Restorer Lines

Rice Grain dimension and weight are two critical factors for marketing and increasing yield capacity. Seed shape is measured by its length, width, thickness, and ratio of length-width. In this study, an experiment was conducted in a controlled condition from fall 2017 to 2020 to identify QTL and candidate genes associated with seed dimension and weight using a bi-parental population resulting from two University of Arkansas developed genotypes: a restorer line 367R and an advanced breeding line RU1501139, in Stuttgart, Arkansas. Five seed dimension traits, including seed length, seed width, seed thickness, seed length-width ratio, and 100-seeds weight, were obtained for QTL detection. The study detected a total of 17 QTL. Four QTL associated with seed length were identified, in which two were positioned on chr. 3, one on chr. 7, and one on chr. 11. Two QTL related to seed length-width ratio were detected on chr. 3 and 7. Whereas a total of three QTL were identified for seed thickness, one each on chr. 5, 6, and 8. Eight QTL associated with seed weight were found, of which four QTL were detected on chr. 12, two each on chr. 1 and 10, and one on chr. 3. Of 17 QTL, four QTL originated from RU1501139, while the origin of the other 13 QTL was 367R. Since multiple genes could control the yield and seed physical characteristics, the detected QTL can play a role in introducing superior parental lines for developing conventional and hybrid rice production.

Broadacre Crop Yield Estimation Using Imaging Spectroscopy from Unmanned Aerial Systems (UAS): A Field-Based Case Study with Snap Bean

Accurate, precise, and timely estimation of crop yield is key to a grower’s ability to proactively manage crop growth and predict harvest logistics. Such yield predictions typically are based on multi-parametric models and in-situ sampling. Here we investigate the extension of a greenhouse study, to low-altitude unmanned aerial systems (UAS). Our principal objective was to investigate snap bean crop (Phaseolus vulgaris) yield using imaging spectroscopy (hyperspectral imaging) in the visible to near-infrared (VNIR; 400–1000 nm) region via UAS. We aimed to solve the problem of crop yield modelling by identifying spectral features explaining yield and evaluating the best time period for accurate yield prediction, early in time. We introduced a Python library, named Jostar, for spectral feature selection. Embedded in Jostar, we proposed a new ranking method for selected features that reaches an agreement between multiple optimization models. Moreover, we implemented a well-known denoising algorithm for the spectral data used in this study. This study benefited from two years of remotely sensed data, captured at multiple instances over the summers of 2019 and 2020, with 24 plots and 18 plots, respectively. Two harvest stage models, early and late harvest, were assessed at two different locations in upstate New York, USA. Six varieties of snap bean were quantified using two components of yield, pod weight and seed length. We used two different vegetation detection algorithms. the Red-Edge Normalized Difference Vegetation Index (RENDVI) and Spectral Angle Mapper (SAM), to subset the fields into vegetation vs. non-vegetation pixels. Partial least squares regression (PLSR) was used as the regression model. Among nine different optimization models embedded in Jostar, we selected the Genetic Algorithm (GA), Ant Colony Optimization (ACO), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) and their resulting joint ranking. The findings show that pod weight can be explained with a high coefficient of determination (R2 = 0.78–0.93) and low root-mean-square error (RMSE = 940–1369 kg/ha) for two years of data. Seed length yield assessment resulted in higher accuracies (R2 = 0.83–0.98) and lower errors (RMSE = 4.245–6.018 mm). Among optimization models used, ACO and SA outperformed others and the SAM vegetation detection approach showed improved results when compared to the RENDVI approach when dense canopies were being examined. Wavelengths at 450, 500, 520, 650, 700, and 760 nm, were identified in almost all data sets and harvest stage models used. The period between 44–55 days after planting (DAP) the optimal time period for yield assessment. Future work should involve transferring the learned concepts to a multispectral system, for eventual operational use; further attention should also be paid to seed length as a ground truth data collection technique, since this yield indicator is far more rapid and straightforward.

Influence of parental nitrogen : phosphorus stoichiometry on seed characteristics and performance of Holcus lanatus L. and Parnassia palustris L.

Nitrogen (N) and phosphorus (P) availability affect plant sexual reproduction performance. Seed as the main product of sexual reproduction is expected to be affected by N and P availability in parent plant. We experimentally test how parental N:P stoichiometry affected seed characteristics and performance of two grassland species. Seeds of a common species (Holcus lanatus) and an endangered species (Parnassia palustris) were collected from parent plants under two different N:P ratio growth conditions in a grassland reserve in the Netherlands. We measured the following traits of the two species from the two parental N:P ratio growth conditions: seed N concentration and content, seed P concentration and content, seed length, seed area, seed weight, seed germination, and offspring survival. No significant inter-location difference was found in seed weight of the collected seeds for either of the two species. However, the stronger P-limited conditions at the locations of the parent plants affected seed length and seed area negatively in H. lanatus and positively in P. palustris. Stronger P-limited conditions also decreased seed P concentration and content and increased seed N:P ratio of H. lanatus, but no inter-location nutrient difference was found in seeds of P. palustris. Surprisingly, contrary to what could be expected from seed P concentration and content there was no inter-location difference in seed germination for H. lanatus. For P. palustris, stronger P-limited conditions in the parental environment significantly enhanced seed germination, whereas stronger P-limited conditions in the offspring environment decreased offspring survival, suggesting that P limitation may negatively affect P. palustris rejuvenation. Our results suggest the possibility of different influences of parental N:P ratio and especially of P limitation on seed characteristics and performance of a common and an endangered species.