The Eurasian grapevine (\textit{Vitis vinifera L.}) is the most widely grown horticultural crop in the world and is important for the economy of many countries. In the wine production chain, grape varieties play an important role, as they directly influence the authenticity and classification of the product. Identifying the different grape varieties is therefore fundamental for quality control and control activities, as well as for regulating production. Currently, ampelography and molecular analysis are the main approaches to identifying grape varieties. However, both methods have limitations. Ampelography is subjective and prone to errors and is experiencing enormous difficulties as ampelographers are increasingly scarce. On the other hand, molecular analyses are very demanding in terms of cost and time. In this scenario, Deep Learning (DL) methods have emerged as a classification alternative to deal with the scarcity of ampelographers and avoid molecular analyses. In this study, the most recent and current methods for identifying grapevine varieties using DL classification-based approaches are presented through a systematic literature review. The steps of the standard DL-based classification pipeline were described for the 18 most relevant studies found in the literature, highlighting their pros and cons. Potential directions for improving this field of research were also presented.

To investigate the differences in cadium (Cd) uptake and translocation among edible rapes and select suitable rape varieties for safe production, a field experiment was carried out with 25 varieties of edible rapes on a farmland polluted with Cd in the central souothern part of Hunan Province. The growing characteristics and Cd contents in rape tissues were measured, and the amount of Cd removed was calculated. The results showed that the growth of 25 rape varieties was not inhibited without withering or inconsistent changes in leaf and so on. The Cd contents in stem-leaf and root of rapes were in the range 0.05-0.26mg·kg-1 and 0.04-0.26mg·kg-1, respectively. Basing on BCF, the stem-leaf showed a greater capacity for Cd transport than root. And the total Cd removed by rape were 0.002-0.016 mg·plant-1. Except for plant height, BCF of soil available Cd from soil to stem-leaf, TCF of Cd from root to stem-leaf and Cd taken away by rape, there was no significant difference among edible rape varieties. Although Cd contents in stem-leaf of 25 rape varieties does not exceed the national safety standards, planting “Lvjin 1”, “Guanyou Qingjing” and “Guanyou brassica” not only reduced soil pollution but also allowed the production of safe leafy rape.

This review examines the categorization of Essentially Derived Varieties (EDV) introduced in the 1991 revision of the Convention of the Union internationale pour la protection des obtentions végétales (UPOV). Challenges in the implementation of the concept and progress made on a crop-by-crop basis to provide greater clarity and more efficient implementation are reviewed. The current approach to EDV remains valid provided i) clarity on thresholds can be achieved including through resource intensive research on an individual crop species basis and ii) that threshold clarity does not lead to perverse incentives to avoid detection of essential derivation. However, technological advances leading to new varieties resulting from the simultaneous introduction or change in expression of more than “a few” genes will so challenge the concept to require a new Convention. Revision could include deletion of the concept of essential derivation and revision on a crop-by-crop basis of the breeder exception. Countries that allow utility patents for individual plant varieties per se should consider removing that possibility unless plant breeders utilize those encouragements for risk taking and investment to broaden the germplasm base upon which the long-term sustainability of plant breeding resides.

Maize (Zea mays L.) is the most widely grown important crop in mid altitude areas of intensive maize-based cropping system of western Ethiopia. Agronomic management is the most important input for getting potential yield and high net returns in hybrid maize production. A field experiment was carried out on farmers’ field to find out the effect of varieties (four maize) and nitrogen fertilizer rate (55, 110 kg N ha-1) with one control on yield components and nitrogen use efficiency of different maize varieties in 2013 and 2014 cropping season. It was laid with randomized complete block design in factorial arrangement with three replications. Mean grain yield, thousand seed weight, dry biomass and harvest index of maize varieties were significantly differed among farms and varieties of maize. Application of nitrogen fertilizer rates was significantly increased mean grain yield maize varieties. Interaction of maize varieties with nitrogen fertilizer rates was significantly affected all yield components of maize varieties. Application half and full recommended nitrogen fertilizer gave mean grain yield advantages of 31 and 41 % over control maize varieties planted without nitrogen application. Maize varieties producing higher mean grain yield was also giving higher mean dry biomass. Mean nitrogen up take was varied from 225 to 357 kg ha-1 among varieties of maize. Higher agronomic efficiency of all maize varieties was obtained from maize planted with application half recommended nitrogen fertilizer compared to full recommend. Agronomic efficiency was ranged from 18 to 33 produced among maize varieties. Significantly higher nitrogen up take efficiency of maize varieties was achieved from maize planted with full recommended nitrogen fertilizer application. Considerably higher nitrogen use efficiency of maize varieties was realized from all maize varieties planted with application half recommended nitrogen fertilizer. Application of half recommended nitrogen fertilizer was gave 32 % fertilizer N use efficiency advantage as compared to full recommended nitrogen fertilizer. Maize varieties BH-661>BH-660> BH-543>BH-540>BH-140 were desirable varieties for further promotion work and use by smallholder farmers in mid altitude area of western Ethiopia.

While it is generally accepted that food habits established during infancy will track into later childhood, longitudinal analysis of children’s food preferences is rare. This paper examines whether maternal-reported child food preferences at five years of age are the same as that reported at two years; and identifies any patterns of change from two- to five- years. Mothers in the Australian NOURISH trial reported child food preferences at two and five years of age. A four point scale was utilised - ‘like’, ‘neither like or dislike’, ‘dislike’, ‘never tried’. The proportion of children having the same preference at the two time points was calculated (95%CI) for 48 foods (cereals, 4; vegetables, 20; fruit, 14; meat/alternatives, 6; dairy, 4). For foods where ≤50% children had consistent preferences, the pattern of food preference change was determined. For 40/48 foods, more than half of the children were reported to have the same preference at two years of age, and three years later, at age five. Foods for which ≤50% children had the same preference at both ages were high-sugar breakfast cereals, zucchini, mushrooms, eggplant, spinach, lettuce, cabbage and celery. Findings reinforce the importance of promoting a consistent message regarding early and frequent exposure to a variety of healthy foods, particularly during the first 2 years of life, as the preferences established in these early years are likely to be maintained over time.

Seed germination and seedling growth represent two vulnerable stages in a plant life cycle and it is important to determine how they will be affected by environmental changes associated with climate change. This study examines the impact of salinity levels (0, 50, 100, and 150 mM) at each of three temperatures (15, 25, and 35˚C) on seed germination and radicle growth for three dormant and three non-dormant varieties of conventional, glyphosate resistant, or reduced lignin alfalfa. The genetic basis and phenotypic plasticity for seed germination and seedling growth in response to salinity and temperature were determined. Both traits were phenotypically plastic with respect to temperature and salinity. Seed germination was 87.0% ± 1.7 at 25˚C, 0mM (no salinity), but decreased to 33.9% ± 3.9 germination at 35˚C and 150mM. Radicle length went from 36.7 ± 1.5 mm after four days at 25˚C, 0mM, to 10.5 ± 0.7 mm at 35˚C, 150mM. The phenotypic response brought seed germination and radicle length away from their optimum, but we detected standing genetic variation for both seed germination and radicle length. Selection to increase both traits at high temperature and salinity would facilitate alfalfa establishment under climate change.

The evaluation of the possibility of obtaining dihaploids by the method of anther culture in vitro to accelerate selection for resistance to prolonged flooding of seeded rice with water was carried out. The object of research is rice hybrids F2 of the Rice Breeding and Seed Production Laboratory of the “Donskoy” ASC, obtained as a result of interbreeding the best economically valuable varieties with samples bearing genes of resistance to prolonged flooding with water. Basic nutrient medium with an optimal composition of nutrition elements and growth hormones stimulating callo- and morphogenesis were used. For the induction of callus formation, 12604 anthers were planted, according to 26 hybrid combinations represented by 68 plants, as a result, 716 neoplasms were obtained, including 586 non–morphogenic callus, 130 regenerating plants. Cultivation of anthers revealed large genotypic differences in the samples. According to the responsiveness to neoplasms, 60% of the panicles showed a positive result, the rest did not give callus. The most responsive to the formation of callus were hybrid combinations: 5009/2 – 84 pcs., 5010/2 – 94 pcs., 4565/3 – 85 pcs., 4641/2 – 69 pcs. They also showed the ability to morphogenesis. Androgenic plants were obtained by 14 hybrid combinations, their share was 1.03% of the total number of inoculated anthers. 30 green regenerative lines from four rice hybrids were obtained, differing in visual morphological assessment: 5009/2 - 5 pcs., 5010/2 – 5 pcs., 4565/3 – 2 pcs., 4641/2 – 18 pcs. The isolated lines are characterized by good responsiveness in the culture of anthers in vitro, carry genes for resistance to prolonged flooding, and can be used in rice breeding programs using DG technologies.

Development and deployment of wheat varieties with high yields, wide adaptability, good quality, multiple-resistance to abiotic and biotic stresses, and efficient response to fertilizers have greatly contributed to global wheat sustainable production. The genomic composition of key commercial wheat variety can help understand the genetic basis underlying the development of new variety and permit increased breeding efficiency. In this study, we report the chromosomal and genomic compositions of BN207, presently the leading wheat variety in the southern region of Huang-Huai River Valley, the most important wheat producing area in China through an integrated analysis using fluorescent in situ hybridization (FISH) and wheat 15 K SNP array. Our results showed that BN207 inherited 55.3% and 40.7% of its genome from its male parent BN64 and female parent ZM16, respectively, and generating 64 novel or recombined loci. Besides, we detected nine chromosomal variations in Bn207 and its parents and ten sister lines, and physically mapped two variations, the pericentric inversion of chromosome 6B, and large tandem repeat sequence block at the long arm of 5A, both had positive effects on agronomic traits, by integration of FISH and SNP loci recombination analyses. These results will provide a reference for breeding of high yield wheat varieties as BN207, and the application of founder parents BN64 and ZM16, which are being utilized frequently in wheat breeding programs in Henan Province and surrounding areas.

To ensure consumers can purchase high-quality rice, accurate identification of rice varieties is particularly important. Methods: This article conducts research based on machine learning algorithms from the perspectives of image, spectrum, and spectrogram fusion. Six types of hyperspectral image data of rice were preprocessed using convolutional smoothing (SG) and multiple scatter correction (MSC). Texture information of the images was extracted using gray-level co-occurrence matrix. Spectra, texture, and spectrogram data were fused into a new matrix. Spectral, texture, and spectrogram fusion data were used as inputs for the model, and support vector machines (SVM), logistic regression (LR), and K-nearest neighbors (KNN) classification models were constructed and compared. Results: From the classification results, the spectrogram fusion classification performance was better than classification models using only spectra or texture. Conclusion: The research results showed that the accuracy of SVM and LR classification models exceeded 90%, and the LR model performed the best, effectively classifying rice varieties.

The purpose of the research was to obtain information about the necessity and efficiency of the application of localized irrigation to some qualitative indices of plum trees in the nursery, against the background of different fertilization treatments. The expected results to be obtained by applying differentiated rules of irrigation and fertilization will consist in obtaining a healthy, vigorous fruit tree planting material, increasing production in the nursery. With fruit trees in the nursery, as with all cultivated plants, the growth process depends to the greatest extent on the climate and soil conditions available to them. The use of fertilizers in tree culture becomes necessary to renew the reserve of nutrients consumed by plants or leached in depth, then to improve the physical condition, the chemical composition, and the overall state of fertilization of the soil. It is necessary to intervene every year, in several rounds, with fertilizations that ensure, on the one hand, the achievement of a certain level of production, and on the other hand, a certain level and ratio of nutritional elements by returning the amounts of elements easily accessible nutrients extracted with the harvest to be able to maintain, in this way, the fertility of the soil in accordance with the age of the plantation and the level of production. The two varieties of plum studied were Stanley and Cacanska Lepotica, two valuable varieties for the quality of the fruit. During the research, the fertilization treatments had the highest contribution (34.50 %) on the stem diameter, compared to irrigation (20.67 %) and respectively the variety (5.63 %), considering that the variety did not significantly influence the increase in diameter of the grafted trees.

Grape pomace is one of the main by-products in the wine industry and contains some high added-value compounds such as polysaccharides. Considering the wide application possibilities of polysaccharides in wine and in the food industry, the revalorization of grape pomace to extract polysaccharides presents itself as an opportunity for by-product management. Therefore, the aim of this study was to characterize polysaccharide extracts obtained from pomace by-products of different white grape varieties. The type and content of polysaccharides, proteins and phenols were analyzed. Statistically significant differences were found between the varietal extracts in the types and concentrations of polysaccharides. The extracts obtained from the Verdejo and Puesta en Cruz varieties showed the highest polysaccharide purity and contents, but the type of polysaccharides was different in each case. The Verdejo provided extracts richer in non pectic polysaccharides, while the Puesta en Cruz in pectic polysaccharides. Protein and polyphenol contents were low in all extracts, below 2.5% and 3.7%, respectively. These results open up a new possibility for the revalorization of grape pomace by-products to obtain polysaccharide-rich extracts, although it would be interesting to improve both the yield and the purity of the extracts obtained by studying other extraction techniques or processes.

RNA transcripts play a crucial role as witnesses of gene expression health. Identifying disruptive short sequences in RNA transcription and regulation is essential for potentially treating diseases. Let’s delve into the mathematical intricacies of these sequences. We’ve previously devised a mathematical approach for defining a “healthy” sequence (10.14218/GE.2023.00079). This sequence is characterized by having at most four distinct nucleotides (denoted as nt≤4). It serves as the generator of a group denoted as fp. The desired properties of this sequence are as follows: fp should be close to a free group of rank nt−1, it must be aperiodic, fp should not have isolated singularities within its SL2(C) character variety (specifically within the corresponding Groebner basis). Now, let’s explore the concept of singularities. There are cubic surfaces associated with the character variety of a four-punctured sphere denoted as S24. When we encounter these singularities, we find ourselves dealing with some algebraic solutions of a dynamical second-order differential (and transcendental) equation known as the Painlevé VI equation (10.3390/dynamics4010001). In certain cases, S24 degenerates, in the sense that two punctures collapse, resulting in a “wild” dynamics governed by the Painlevé equations of an index lower than VI. In our paper, we provide examples of these fascinating mathematical structures within the context of miRNAs. Specifically, we find a clear relationship between decorated character varieties of Painlevé equations and the character variety calculated from the seed of oncomirs. These findings should find applications in cancer research.

The article presents research results of the γ-ray and fast neutrons impact on various rice species, in order to obtain mutant forms resistant to salinity (NaCl) and drought factors (sorbitol. They are going to be used as initial forms in synthetic selection when creating varieties, adapted to the stressful conditions of, both, soil and climate in the Kazakhstan Aral Sea. The average lethal doses (LD50) of γ-rays and fast neutrons, as well as the average NaCl and sorbitol lethal concentrations were established. Such environment is best suited for clear manifestation of the mutagenic effect of ionizing radiation and the resistance of rice plants to salinity and drought. A distinct dependence in the effect of ionizing radiation and stress factors on the number of induced resistant mutant forms has been related to the initial rice sort. The largest number of mutant forms was obtained from the local variety Syr Suluy, followed by Leader and AyKerim varieties. From all varieties, the number of mutants obtained from exposure to γ-rays was 43 pieces out of 4500 grains, and from the impact of fast neutrons - 115 pieces out of 2700 grains. M1 mutant plants significantly differ from the initial forms in terms of morphological features – plant height, panicle length, grain size Most plants are characterized by short growth and even dwarfism (˂80 cm). They are lodging tolerant, have short and highly sterile panicles, indicating that they are mutants and resistant to salinity, drought, or both.

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

Root research on field grown crops is hindered by the difficulty of estimating root biomass in soil. Root washing, the current standard method is laborious and expensive. Biochemical methods to quantify root biomass in soil, targeting species-specific DNA, have potential as a more efficient assay. We combined an efficient DNA extraction method, designed specifically to extract DNA from soil, with well-established quantitative PCR methods to estimate the root biomass of twenty-two wheat varieties grown in field trials over two seasons. We also developed an assay for estimating root biomass for black-grass, a common weed of wheat cultivation. Two robust qPCR assays were developed to estimate the quantity of plant root DNA in soil samples, one specific to wheat and barley, and a second specific to black-grass. The DNA qPCR method was comparable, with high correlations, with the results of root washing from soil cores taken from winter wheat field trials. The DNA qPCR assay showed both variety and depth as significant factors in the distribution of root biomass in replicated field trials. The results suggest that these DNA qPCR assays are a useful, high throughput tool for investigating the genetic basis of wheat root biomass distribution in field grown crops, and the impact of black-grass root systems on crop production.

The article presents the results of the γ-ray and fast neutrons impact on various rice species, in order to obtain mutant forms resistant to salinity (NaCl) and drought factors (sorbite). They are going to be used as initial forms in synthetic selection when creating varieties, adapted to the stressful conditions of, both, soil and climate in the Kazakhstan Aral Sea. The average lethal doses (LD50) of γ-rays and fast neutrons, as well as, the average NaCl and sorbite lethal concentrations were established. A distinct dependence on the effect of ionizing radiation and stress factors on the number of induced resistant mutant forms has been related to the initial rice variety. The largest number of mutant forms was obtained from the local variety Syr Suluy, followed by Leader and Aikerim varieties. Out of all varieties, only 1% of the initially irradiated by γ-rays seeds survived, while after fast neutron irradiation – 4,3%. M1 mutant plants significantly differ from the initial forms in terms of morphological features – plant height, panicle length, and grain size. They are tolerant to lodging, and have short and highly sterile panicles, indicating that they are mutants.

Microplastic contamination, defined as plastic particles less than 5 mm in size, has become a major global environmental concern. This study synthesizes findings from carefully chosen studies undertaken in a variety of geographical areas and ecosystems, offering light on the multifaceted issues posed by microplastic pollution. These articles show the global prevalence of microplastics in both land and marine ecosystems. Seasonal fluctuations in microplastic abundance highlight the cyclical nature of this pollution, with larger amounts being reported during the summer months. Tourism, industrialization, and urbanization have all been highlighted as significant contributors to microplastic contamination, stressing the impact of man-made influences. Wastewater treatment plants (WWTPs) have been identified as hotspots for microplastic release into aquatic habitats, emphasizing the need for enhanced treatment procedures. Because microplastics can build up in the food chain, it underlines the possible health problems connected with microplastic pollution for both aquatic creatures and human consumers. Longitudinal studies, geographical variety, in-depth health and ecological impact evaluations, standardization, and effective mitigation methods should be prioritized in future studies. To address this worldwide issue, interdisciplinary collaboration among scientists, health professionals, politicians, and industrial stakeholders is required.

We recently proposed that topological quantum computing might be based on $SL(2,\mathbb{C})$ representations of the fundamental group $\pi_1(S^3\setminus K)$ for the complement of a link $K$ in the $3$-sphere. The restriction to links whose associated $SL(2,\mathbb{C})$ character variety $\mathcal{V}$ contains a Fricke surface $\kappa_d=xyz -x^2-y^2-z^2+d$ is desirable due to the connection of Fricke spaces to elementary topology. Taking $K$ as the Hopf link $L2a1$, one of the three arithmetic two-bridge links [the Whitehead link $5_1^2$, the Berge link $6_2^2$, the double-eight link $6_3^2$] or the link $7_3^2$, the $\mathcal{V}$ for those links contains the reducible component $\kappa_4$, the so-called Cayley cubic. In addition, the $\mathcal{V}$ for the later two links contains the irreducible component $\kappa_3$, or $\kappa_2$, respectively. Taking $\rho$ to be a representation with character $\kappa_d$ ($d<4$), with $|x|,|y|,|z| \le 2$, then $\rho(\pi_1)$ fixes a unique point in the hyperbolic space $\mathcal{H}_3$ and is conjugate to a $SU(2)$ representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the $4$-punctured sphere and Painlev\'e VI equation. The $0$-surgery on the $3$ circles of the Borromean rings L6a4 is taken as an example.

Our recent work has focused on the application of infinite group theory and related algebraic geometric tools in the context of transcription factors and microRNAs. We were able to differentiate between “healthy" nucleotide sequences and disrupted sequences that may be associated with various diseases. In this paper, we extend our efforts to the study of messenger RNA metabolism, showcasing the power of our approach. We investigate (i) mRNA translation in prokaryotes and eukaryotes, (ii) polyadenylation in eukaryotes, which is crucial for nuclear export, translation, stability, and splicing of mRNA, (iii) miRNAs involved in RNA silencing and post-transcriptional regulation of gene expression, and (iv) the identification of disrupted sequences that could lead to potential illnesses. To achieve this, we employ (a) infinite (finitely generated) groups fp, with generators representing the r+1 distinct nucleotides and a relation between them [e.g., the consensus sequence in the mRNA translation (i), the poly(A) tail in item (ii), and the miRNA seed in item (iii)], (b) aperiodicity theory, which connects “healthy groups" fp to free groups Fr of rank r and their profinite completion F^r, and (c) the representation theory of groups fp over the space-time-spin group SL2(C), highlighting the role of surfaces with isolated singularities in the character variety. Our approach could potentially contribute to the understanding of the molecular mechanisms underlying various diseases and help develop new diagnostic or therapeutic strategies.

Plants significantly shape root-associated microbiota, making rhizosphere microbes useful environmental indicator organisms for safety assessment. Here, we report the pyrosequencing of the bacterial 16S ribosomal RNA in rhizosphere soil samples collected from transgenic cry1Ab/cry1Ac Bt rice Huahui No. 1 (GM crop) and its parental counterpart, Minghui63. We identified a total of 2,579 quantifiable bacterial operational taxonomic units (OTUs). Many treatment-enriched microbial OTUs were identified, including 14 NonGM-enriched OTUs and 10 GM-enriched OTUs. The rhizosphere microbiota communities were influenced more strongly by growth in the field than by rice varieties. Furthermore, Huahui No. 1 transgenic Bt rice had a greater impact on the rhizosphere bacterial communities than Minghui63. Early developmental stages of the transgenic Bt rice had a significant impact on many Bacillaceae communities. While soil chemical properties were not significantly altered by the presence of transgenic Bt rice, we found peak expression level of Bt proteins during the seedling stage, which may be an intriguing factor for bacterial diversity variations. Based on these findings, we conclude that transgenic Bt rice has a significant impact on root-associated bacteria. This information may be leveraged in future environmental safety assessments of transgenic Bt rice varieties.

The symmetries of a Riemann surface $\Sigma \setminus \{a_i\}$ with $n$ punctures $a_i$ are encoded in its fundamental group $\pi_1(\Sigma)$. Further structure may be described through representations (homomorphisms) of $\pi_1$ over a Lie group $G$ as globalized by the character variety $\mathcal{C}=\mbox{Hom} (\pi_1,G)/G$. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the $4$-punctured Riemann sphere $\Sigma=S_2^{(4)}$ and the \lq space-time-spin' group $G=SL_2(\mathbb{C})$. In such a situation, $\mathcal{C}$ possesses remarkable properties (i) a representation is described by a $3$-dimensional cubic surface $V_{a,b,c,d}(x,y,z)$ with $3$ variables and $4$ parameters, (ii) the automorphisms of the surface satisfy the dynamical (non linear and transcendental) Painlev\'e VI equation (or $P_{VI}$), (iii) there exists a finite set of $1$ (\mbox{Cayley-Picard})+$3$ (\mbox{continuous platonic})+$45$ (\mbox{icosahedral}) solutions of $P_{VI}$. In this paper we feature on the parametric representation of some solutions of $P_{VI}$, (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups $f_p$ encountered in TQC or DNA/RNA sequences are proposed.

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. In this paper, we describe the algebraic geometry of both TFs and miRNAs thanks to group theory. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group $\pi$, we compute the $SL(2,\mathbb{C})$ character variety, where $SL(2,\mathbb{C})$ is simultaneously a \lq space-time' (a Lorentz group) and a \lq quantum' (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when $\pi$ looks like a free group $F_r$ ($r =1$ to $3$) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis $\mathcal{G}$ of the variety. A surface with simple singularities (like the well known Cayley cubic) within $\mathcal{G}$ is a signature of a potential disease even when $G$ looks like a free group $F_r$ in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA/RNA bases in $\{A,T/U,G,C\}$. Several human TFs and miRNAs are investigated in detail thanks to our approach.

This paper combines the Good Regulator Theorem with the Law of Requisite Variety and seven other requisites that are necessary and sufficient for a cybernetic regulator to be effective and ethical. The resulting Ethical Regulator Theorem provides a basis for systematically evaluating and improving the adequacy of existing or proposed designs for systems that make decisions that can have ethical consequences; regardless of whether the regulators are human, machines, cyberanthropic hybrids, organizations, corporations, or government institutions. The theorem is then used to define an ethical design process that has potentially far-reaching implications for society. A six-level framework is proposed for classifying cybernetic and superintelligent systems, which highlights the existence of a possibility-space bifurcation in our future time-line. The implementation of “super-ethical” systems is identified as an urgent imperative for humanity to avoid the danger that superintelligent machines might lead to a technological dystopia. Third-order cybernetics is defined as the cybernetics of ethical systems. Concrete actions, a grand challenge, and a vision of a super-ethical society are proposed to help steer the future of the human race and our wonderful planet towards a realistically achievable minimum viable cyberanthropic utopia.

Revealing the time structure of physical or biological objects is usually performed thanks to the tools of signal processing like the fast Fourier transform, Ramanujan sum signal processing and many other techniques. For space-time topological objects in physics and biology, we propose a type of algebraic processing based on schemes in which the discrimination of singularities within objects is based on the space-time-spin group SL(2,C). Such topological objects possess an homotopy structure encoded in their fundamental group and the related SL(2,C) multivariate polynomial character variety contains a plethora of singularities somehow analogous to the frequency spectrum in time structures. Our approach is applied to an Akbulut cork in exotic R4, to an hyperbolic model of topological quantum computing based on algebraic surfaces and to microRNAs in genetics. Such diverse topics reveal the manifold of possibilities of using the concept of a scheme spectrum.

Nitrogen use efficiency (NUE) in maize (Zea mays L.) is an important trait to maximize yield with minimal input of nitrogen (N) fertilizer. Expired Plant Variety Protection (ex-PVP) Act-certified germplasm may be an important genetic resource for public breeding sectors. The objectives of this research were to evaluate the genetic variation of N-use traits and to characterize maize ex-PVP inbreds adapted to the U.S. Corn Belt for NUE performance. Eighty-nine ex-PVP inbreds [36 stiff stalk synthetic (SSS), and 53 non-stiff stalk synthetic (NSSS)] were genotyped using 26,769 single-nucleotide polymorphisms, then 263 single-cross maize hybrids derived from these inbreds were grown in eight environments from 2011 to 2015 at two N fertilizer rates (0 and 252 kg N ha⁻¹) and three replications. Genetic utilization and the yield response to N fertilizer were stable across environments and were highly correlated with yield under low and high N conditions, respectively. Cluster analysis identified inbreds with desirable NUE performance. However, only one inbred (PHK56) was ranked in the top 10% for yield under both N-stress and high N conditions. Broad-sense heritability across 12 different N-use traits ranged from 0.11 to 0.77, but was not associated with breeding value accuracy. Nitrogen-stress tolerance was negatively correlated with the yield increase from N fertilizer.

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.