Substitution Probabilities Research Articles

Cross-species substitution matrix comparison of Tomato leaf curl New Delhi virus (ToLCNDV) with medicinal plant isolates

The main objective of this study was to estimate and compare substitution matrixes of nucleotide frequencies for Tomato leaf curl New Delhi virus (ToLCNDV) with recently identified begomoviral isolates from two medicinal false daisy (Eclipta prostrata) and tomato (Solanum lycopersicum) plants. The ToLCNDV has become a significant limitation to vegetables production in many countries. A polymerase chain reaction was conducted to conserve the existence of begomoviral infection. The acquired amplicon was amplified using primers appropriate to the sequence in order to retrieve the full genome. The sequence analysis has confirmed the presence of ToLCNDV in symptomatic plants. The complete genome sequence having a 2.6–2.7 kb entire genome of ToLCNDV was obtained. An investigation of the phylogenetic and evolutionary history has verified the connection between this virus and other closely related viruses. The available nucleotide frequencies of codon regions (A, T/U, C, G) with newly isolates revealed 20–28% substitution matrixes. There was a minimal difference of nucleotide frequencies’ with already submitted database of this virus. Substitution matrixes, which quantify the probability of nucleotide substitutions evolving over a period of time, offer valuable information about mutation patterns and the forces driving evolution. This comparative analysis enhanced the comprehension of the genetic diversity of ToLCNDV and its possible consequences on medicinal plants. It also assisted in the formulation of efficient control measures and the preservation of begomoviruses in medicinal plant biodiversity. The information presented here is highly valuable for understanding the ToLCNDV biology and epidemiology, and it would also assist in disease management in the future.

Material Properties ofn‐Type β‐Ga2O3Epilayers with In Situ Doping Grown on Sapphire by Metalorganic Chemical Vapor Deposition

AbstractIn this study, in situ, Si‐doped heteroepitaxial Ga2O3layers are grown onc‐plane sapphire by metalorganic chemical vapor deposition. The X‐ray diffraction peaks of the doped Ga2O3epilayers shows ß‐phase of Ga2O3,and full width at half maximum of Ga2O3crystallinity is decreased at a Tetraethoxysilane (TEOS) molar flow rate of 2.23 × 10−7 mol min−1but increased with higher flow rates. The dopant concentrations of Ga2O3grown at 825 °C with TEOS molar flows of 2.23 × 10−7, 4.47 × 10−7, and 6.69 × 10−7 mol min−1are measured to be 5.5 × 1019, 1.1 × 1020, and 1.4 × 1020 atom cm−3, respectively, using secondary ion mass spectra and Hall measurements revealn‐type nature with carrier concentrations of 6.5 × 1017, 3.2 × 1018, and 3.9 × 1018atom/cm3, respectively. To increase Si dopant activation, Ga2O3growth temperature is raised to 875 °C. The result suggests a higher growth temperature can contribute to a greater probability of Si substitution on Ga lattice sites, which further reduces the resistivity of Ga2O3epilayer. Moreover, results are compared with theoretical Density Functional Theory studies.

The effect of shared e-scooter programs on modal shift: Evidence from Sweden

Fostering sustainable cities necessitates a significant paradigm shift from motorised vehicles to active mobility. However, the impact of emerging transport modes like e-scooters in this transition remains unclear. To explore the potential of this shift, we polled 805 (non)users of e-scooters in Sweden via an online survey to explore (i) who are e-scooter users and (ii) how e-scooter use affects the probability of modal substitution for users. The propensity score matching method was used to obtain unbiased estimates of e-scooter usage impact on modal substitution and to construct an artificial control group, overcoming potential biases present in previous studies that exclusively surveyed e-scooter users. We found that e-scooter users are more likely to have a high-paying job, a driving license, own an e-bike and car, and public transport cards, suggesting diverse travel behaviours. These findings indicate that e-scooter users are more likely to be highly mobile people with a potential for multimodal transport. Furthermore, being an e-scooter user will increase the probability of shifting their short-range trip to an e-scooter by 46 %. Findings provide pivotal insights into e-scooter modal shifts, crucial for ex-ante and ex-post evaluations of e-scooter adoption, the deployment of e-scooter schemes, and contribute to travel demand management.

ARMADiLLO: a web server for analyzing antibody mutation probabilities.

Antibodies are generated by B cells that evolve receptor specificity to pathogens through rounds of mutation and selection in a process called affinity maturation. Somatic hypermutation is mediated by an enzyme with DNA sequence context-dependent targeting and substitution resulting in variable probabilities of amino acid substitutions during affinity maturation. We have previously developed a program called Antigen Receptor Mutation Analyzer for the Detection of Low Likelihood Occurrences (ARMADiLLO) that performs simulations of the somatic hypermutation process to estimate the probabilities of observed antibody mutations. Here we describe the ARMADiLLO web server (https://armadillo.dhvi.duke.edu), an easy-to-use web interface that analyzes input antibody sequences and displays the probability estimates for all possible amino acid changes over the full length of an antibody sequence. The probability of antibody mutations can be used by immunologists studying B cell ontogenies and by vaccine designers that are pursuing strategies to elicit broadly neutralizing antibodies which are enriched with developmentally rate-limiting improbable mutations. The ARMADiLLO web server also contains precomputed results reporting the probability of amino acid substitutions in all human V gene segments and in a collection of HIV broadly neutralizing antibodies.

THE IMPORTANCE OF trnL/trnF IGS REGION IN THE TAXONOMY OF THE GENUS Potentilla L.

This study was performed to determine the phylogenetic relationships in the genus Potentilla L. and to assess the importance of the trnL/trnF intergenic spacer (IGS) region. The selection of DNA barcoding region to provide for more effective, accurate and consistent results in the analysis is one of the most important points in success of the study. For this purpose, 71 Potentilla taxa were examined based on trnL/trnF IGS sequence data of chloroplast DNA acquired from the National Center for Biotechnology Information (NCBI) and a Maximum Parsimony (MP) dendrogram was drawn. The trnL/trnF IGS region has the convenient sequence length for barcoding region, and it is also proposed the use of this region which has highly variable and parsimony informative sites. When the probabilities of substitutions from one base to another base for trnL/trnF IGS region were examined, it was assigned that the rate of transitional substitutions with 57.13% is higher than the transversional substitutions. The MP dendrogram revealed that the studies taxa were placed in six groups as Fragarioides, Reptans, Anserina, Alba, Himalayan and Argentea. Phylogenetic relationships within the Argentea clade, represented by the highest species number in this study, were observed as quite confusing compared to other clades. In order to get the most accurate results, it is necessary to determine the regions giving the best results, and then to use these regions together with as many taxa as possible. In conclusion, the using of trnL/trnF IGS sequence information that have high variable sites and grouping ability for studies taxa is strongly recommended.

Embeddability of centrosymmetric matrices capturing the double-helix structure in natural and synthetic DNA

In this paper, we discuss the embedding problem for centrosymmetric matrices, which are higher order generalizations of the matrices occurring in strand symmetric models. These models capture the substitution symmetries arising from the double helix structure of the DNA. Deciding whether a transition matrix is embeddable or not enables us to know if the observed substitution probabilities are consistent with a homogeneous continuous time substitution model, such as the Kimura models, the Jukes-Cantor model or the general time-reversible model. On the other hand, the generalization to higher order matrices is motivated by the setting of synthetic biology, which works with different sizes of genetic alphabets.

Future of jobs in China under the impact of artificial intelligence

This study presents a new task-based quantification method for constructing Chinese occupational dataset based on the features of US jobs. Furthermore, we estimate the impact of artificial intelligence (AI) on jobs in China by determining substitution probability using a LightGBM-based prediction model. The results show that 54% of jobs in China would be substituted by AI in the following decades. Relatively speaking, unit heads are the safest jobs in China, whereas jobs intensive in perceptive and manipulative tasks are highly susceptible to substitution.

PRACTICAL APPROACHES TO ORGANIZING SECURE DATA TRANSFER VIA TLS PROTOCOL USING OPENSSL MEANS

Information protection during message transmission is one of the most important tasks in the modern world. The workstations of a particular organization can be well protected using different software and hardware means, but when information is transferred to an open unprotected space, there is a high probability of data leakage, interception, and substitution. In most cases, the use of insufficiently effective security measures causes the loss of personal data of citizens, data of an enterprise or organization that is a commercial secret, information with limited access or even state secrets of the critical infrastructure sector. In this case, it is considered appropriate to use modern cryptographic methods to organize secure data transmission. Considering the ever-growing statistics of cyberattacks on information and telecommunication networks, after in-depth analysis and development of this issue, the authors of the article highlighted the current directions of protection of information and telecommunication networks and security solutions in information and telecommunication networks. The authors have comprehensively covered and investigated the basic principles of the modern state of data transmission security and the organization of information protection during its transmission using the TLS protocol, which made it possible to determine the directions for solving or modernizing existing information security means. Also, attention is paid to the development of a software implementation of the module for secure data transmission in the information and telecommunications network using the improved TLS protocol by means of OpenSSL, which made it possible to establish connections using digital signature algorithms. The authors are planning a series of scientific and technical solutions for the development and implementation of effective cryptographic methods to ensure the security of information and telecommunications networks

Manage Inventories with Learning on Demands and Buy-up Substitution Probability

Problem Definition: This paper considers a setting in which an airline company sells seats periodically, and each period consists of two selling phases, an early-bird discount phase and a regular-price phase. In each period, when the early-bird discount seat is stocked out, an early-bird customer who comes for the discounted seat either purchases the regular-price seat as a substitute (called buy-up substitution) or simply leaves. Methodology/Results: The optimal inventory level of the discounted seats reserved for the early-bird sale is a critical decision for the airline company to maximize its revenue. The airline company learns about the demands for both discounted and regular-price seats and the buy-up substitution probability from historical sales data, which, in turn, are affected by past inventory allocation decisions. In this paper, we investigate two information scenarios based on whether lost sales are observable, and we provide the corresponding Bayesian updating mechanism for learning about demand parameters and substitution probability. We then construct a dynamic programming model to derive the Bayesian optimal inventory level decisions in a multiperiod setting. The literature finds that the unobservability of lost sales drives the inventory manager to stock more (i.e., the Bayesian optimal inventory level should be kept higher than the myopic inventory level) to observe and learn more about demand distributions. Here, we show that when the buy-up substitution probability is known, one may stock less, because one can infer some information about the primary demand for the discounted seat from the customer substitution behavior. We also find that to learn about the unknown buy-up substitution probability drives the inventory manager to stock less so as to induce more substitution trials. Finally, we develop a SoftMax algorithm to solve our dynamic programming problem. We show that the obtained stock more (less) result can be utilized to speed up the convergence of the algorithm to the optimal solution. Managerial Implications: Our results shed light on the airline seat protection level decision with learning about demand parameters and buy-up substitution probability. Compared with myopic optimization, Bayesian inventory decisions that consider the exploration-exploitation tradeoff can avoid getting stuck in local optima and improve the revenue. We also identify new driving forces behind the stock more (less) result that complement the Bayesian inventory management literature. Funding: Z. Luo acknowledges the financial support by the Internal Start-up Fund of The Hong Kong Polytechnic University [Grant P0039035]. P. Guo acknowledges the financial support from the Research Grants Council of Hong Kong [Grant 15508518]. Y. Wang’s work was supported by the Research Grants Council of Hong Kong [Grant 15505318] and the National Natural Science Foundation of China [Grant 71971184]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1169 .

Mode substitution and carbon emission impacts of electric bike sharing systems

This paper presents a quantitative analysis of the mode substitution and usage-phase carbon emission impacts of the electric bike-sharing system (EBSS) on urban transportation using self-administrated survey data and EBSS operating data. The substitution probabilities of a given EBSS trip for different transport modes is determined using the Bayesian inference method. Emission impact is measured by comparing the current emissions to those generated by other transport modes without the EBSS. Remarkably, the partial-trip substitution impact of the EBSS on car travel is investigated, where the EBSS serves as a connection to public transit. The results show that the EBSS barely generates new trips; most short-distance EBSS trips were transferred from walking and conventional bike-sharing, and most long-distance trips were shifted from cars, buses, and the subway. Around 5% of EBSS trips less than 2 km were transferred from the car by integrating with public transit while accounting for over half of the emission reduction. Based on our method, the CO2 emissions per km of EBSS are 19.47 g, with 6.91 g generated by e-bikes due to electricity consumption and 12.56 g by trucks for battery swapping and bike relocation. The studied EBSS has saved 75.52% of CO2 emissions that other transport modes could have generated.

Capacitated assortment planning of a multi-location system under transshipments

We analyze a joint assortment optimization problem for multiple locations of a firm, where each of those locations has an assortment capacity. When one location does not keep a product in its assortment, it transships the requested product from another location when needed. If this is not possible, then demand may be fulfilled by a substitutable (second choice) product from the current location or another demand location through transshipment. We show that the resulting assortment planning problem is NP-complete. We provide structural properties of the optimal assortments that would simplify and speed up the search for the optimal solution. We specifically obtain the optimal product assortment in polynomial time when no substitutions are present. When both transshipments and substitutions are considered, the products adopted by all locations form a common assortment that includes the most popular products among customers, i.e., a popular set, which may not be valid for the individual assortment of each location. We derive an upper limit on customers' substitution probability for each location, such that at optimality, the location's capacity is utilized in full when the substitution probability is below this threshold value. Moreover, we show that when all locations have the same assortment capacity, utilizing theirs to the maximum reduces costly transshipment opportunities. Extensive numerical analyses are also conducted that illustrate the sensitivity of the optimal assortments to system characteristics and the benefits of allowing transshipment and demand substitution in multi-location assortment planning.

Scientific approach to probabilistic assessment of information protection against imposing false messages in telecommunication systems

To date, in all economically developed countries of the world, multibillion-dollar scientific and exploratory research is being carried out on the problems of building quantum-resistant cryptographic systems. In particular, work is being carried out on the analysis, development and research of models, methods and computational algorithms for post-quantum cryptographic transformations, their possible standardization and implementation. At the same time, it is necessary to have an objective, scientifically based approach for assessing the level of information security, which can be guaranteed when implementing one or another protection mechanism. This paper presents formulated scientific approaches, derived expressions making it possible to evaluate the strength of MAC codes as mechanisms for ensuring the authenticity, integrity, and authenticity of messages. It is shown that it is necessary to use the statistics of joint message distributions for accurate calculation of the MAC codes simulation and collision stability. It is proved that the lower limits for the probabilities of imitation and substitution ignore the statistical properties of authenticators arrays. They are based on the pseudo-randomness model of f(x) function and determine the minimum requirements for the key space size and the MAC values space. The upper bounds for the imitation and substitution probabilities are related to combinatorial properties of the MAC arrays and evaluate the value of collisions in the space of MAC values f(x) and messages for the worst case choice of keys and messages. Collision characteristics of MAC codes are considered. The derived equations make it possible to solve accurately the problem of determining the number of experiments indispensable to create a collision with a certain probability on a set of MAC code values. The MAS stability estimates for one of the types of hash functions are obtained using the derived equations.

Study on Correlation Characteristics of PCDD/Fs Isomers Generation during the Coal-Combustion Process with Sludge Mixing

The 17 toxic polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) isomers as a persistent and refractory organic pollutant are one of the pollutants produced in solid fuel (including pulverized coal and mixed fuel) combustion, and regulating their distribution characteristics is an important aspect of effectively reducing their toxic equivalent. In this study, a correlation model of PCDD/Fs toxic equivalent was proposed to quantitatively analyze the correlation between HCl and SO2 concentrations in the reaction atmosphere, meanwhile, a pathway-diagnosis method of PCDD/Fs isomers transformation was adopted to analyze the PCDD/Fs distribution characteristics of coal combustion and that mixed with 10% sludge. The results show that the inflection point for the derivative of the relationship between HCl concentration and SO2 concentration moves towards the direction of lower SO2 concentration and higher HCl concentration with the increase of PCDD/Fs toxic equivalent. Besides, the functional pathways of mixing sludge on PCDD/Fs generation in coal combustion were obtained by calculating chlorine substitution probability. It has been deduced that five transformation pathways were improved by mixing sludge. Next, the critical pathways of the influence from mixing sludge on the distribution characteristics of PCDD/Fs isomers in coal combustion were analyzed by drawing the percentage content migration diagram of PCDD/Fs isomers and the average toxic equivalent migration diagram that combined with the toxic equivalent of PCDD/Fs isomers. The results showed that the main reasons for mixing sludge to further reduce the average toxic equivalent of PCDD/Fs isomers in coal combustion were the increased chlorine substitution probability at the 4-position of 12378 Pentachlorodibenzo-p-dioxin (12378-PeCDD), the decreased chlorine substitution probability at the 4-position of 2378 Tetrachlorodibenzo-p-furan (2378-TeCDF), and the increased total chlorine substitution probability of 23478 Pentachlorodibenzo-p-furan (23478-PeCDF), 123478-Hexachlorodibenzofuran (123478-HxCDF) and 123678-HxCDF respectively. Finally, the functional pathway diagram of PCDD/Fs isomers generated from coal combustion with sludge mixing was drawn.

Rational incorporation of any unnatural amino acid into proteins by machine learning on existing experimental proofs

The unnatural amino acid (UAA) incorporation technique through genetic code expansion has been extensively used in protein engineering for the last two decades. Mutations into UAAs offer more dimensions to tune protein structures and functions. However, the huge library of optional UAAs and various circumstances of mutation sites on different proteins urge rational UAA incorporations guided by artificial intelligence. Here we collected existing experimental proofs of UAA-incorporated proteins in literature and established a database of known UAA substitution sites. By program designing and machine learning on the database, we showed that UAA incorporations into proteins are predictable by the observed evolutional, steric and physiochemical factors. Based on the predicted probability of successful UAA substitutions, we tested the model performance using literature-reported and freshly-designed experimental proofs, and demonstrated its potential in screening UAA-incorporated proteins. This work expands structure-based computational biology and virtual screening to UAA-incorporated proteins, and offers a useful tool to automate the rational design of proteins with any UAA.

Biofuel feedstock contract attributes, substitutability and tradeoffs in sugarcane production for ethanol in the Brazilian Cerrado: A stated choice approach

Biofuel expansion may entail elaborate contractual relationships between processors and farmers. Past studies have been limited to explaining choices between single contracts or standard land fixed rental versus crop share contracts. Little is known about how changes in contract attributes affect the probability of farmers' switching between contracts, if given the choice. Contract choice in turn, has implications for biofuel market structure and farmer welfare. Sugarcane expansion into the Brazilian Cerrado provides an optimal setting to investigate farmers’ willingness to enter into contractual arrangements with biofuel processors. The study design involves a hypothetical stated choice experiment conducted with farmers and landowners in the Cerrado. Respondents choose between three contract types (land rental, agricultural partnership, and supply) or to opt-out. A novel two-opt opt model was applied to better model the opt out decision. Data is analyzed using a random parameter mixed logit model. Willingness to pay for contract attributes highlight farmer preference for shorter contracts with higher revenues. Direct and cross-attribute elasticities results provide unique insight into how market competition and farmer welfare can be affected by the substitution between contract options. They show a larger probability of substitution from more autonomous (e.g. supply) to less autonomous (e.g. land rental) contracts. Farmer contract preferences can motivate vertical integration in the emerging biofuel market, potentially resulting in consequences for farmer welfare and long-run sustainability of biofuel production. Our findings provide guidance for countries seeking to expand biofuel production in areas with enrooted agricultural production systems.

Low temperature magnetic study and first principle calculation in ‘Mo’ doped CoFe2O4 for magnetic information storage applications

Structural and low temperature magnetic properties of CoFe2−xMoxO4 (x = 0.01, 0.03 and 0.05) were studied in the present work. Rietveld refinement of XRD patterns of CoFe2−xMoxO4 (x = 0.01, 0.03 and 0.05) confirm the pure phase cubic crystal structure in Fd3m space group. The decrease in lattice parameters (a contraction of the lattice) has been observed with doping, which confirms the probability of substitution of ‘Mo’ at the octahedral site of parental CoFe2O4 (CFO). The micro-strain via W-H plots was found to be enhanced for CoFe1.95Mo0.05O4 (CMFO5) sample which confirms the incorporation of ‘Mo’ atoms at Fe-site and subsequently reducing impurities as observed from refined patterns. The low temperature (2K) magnetic parameters were found to be greatly enhanced with ‘Mo’ substitution. We observed the decrease in anisotropy constant of Co2+ ions with ‘Mo’ doping and Mo6+ ions concentration at the tetrahedral site of CFO, increases the magnetization of the samples. Both M-H and ZFC-FC measurements confirm the ferrimagnetic behavior of all the samples. The maximum value of information storage parameter ‘S’ achieved around 0.442 for x = 0.03 sample at 2K. The structural parameters, electronic (density of states and band structure) and magnetic properties of pure CFO have also been investigated via computational first principle based density functional theory (DFT) calculations. The computational results are in good agreement with the experimental outputs.

Characterizing Amino Acid Substitution with Complete Linkage of Sites on a Lineage.

Amino acid substitution models are commonly used for phylogenetic inference, for ancestral sequence reconstruction, and for the inference of positive selection. All commonly used models explicitly assume that each site evolves independently, an assumption that is violated by both linkage and protein structural and functional constraints. We introduce two new models for amino acid substitution which incorporate linkage between sites, each based on the (population-genetic) Moran model. The first model is a generalized population process tracking arbitrarily many sites which undergo mutation, with individuals replaced according to their fitnesses. This model provides a reasonably complete framework for simulations but is numerically and analytically intractable. We also introduce a second model which includes several simplifying assumptions but for which some theoretical results can be derived. We analyze the simplified model to determine conditions where linkage is likely to have meaningful effects on sitewise substitution probabilities, as well as conditions under which the effects are likely to be negligible. These findings are an important step in the generation of tractable phylogenetic models that parameterize selective coefficients for amino acid substitution while accounting for linkage of sites leading to both hitchhiking and background selection.

Prediction of the Probability of Job Loss due to Digitalization and Comparison by Industry: Using Machine Learning Methods

Purpose – The essential purpose of this study is to analyze the possibility of substitution of an individual job resulting from technological development represented by the 4th Industrial Resolution, considering the different effects of digital transformation on the labor market. Design/methodology – In order to estimate the substitution probability, this study used two data sets which the job characteristics data for individual occupations provided by KEIS and the information on occupational status of substitution provided by Frey and Osborne(2013). In total, 665 occupations were considered in this study. Of these, 80 occupations had data with labels of substitution status. The primary goal of estimation was to predict the degree of substitution for 607 of 665 occupations (excluding 58 with markers). It utilized three methods a principal component analysis, an unsupervised learning methodology of machine learning, and Ridge and Lasso from supervised learning methodology. After extracting significant variables based on the three methods, this study carried out logistics regression to estimate the probability of substitution for each occupation. Findings – The probability of substitution for other occupational groups did not significantly vary across individual models, and the rank order of the probabilities across occupational groups were similar across models. The mean of three methods of substitution probability was analyzed to be 45.3%. The highest value was obtained using the PCA method, and the lowest value was derived from the LASSO method. The average substitution probability of the trading industry was 45.1%, very similar to the overall average. Originality/value – This study has a significance in that it estimates the job substitution probability using various machine learning methods. The results of substitution probability estimation were compared by industry sector. In addition, This study attempts to compare between trade business and industry sector.

MixChannel: Advanced Augmentation for Multispectral Satellite Images

Usage of multispectral satellite imaging data opens vast possibilities for monitoring and quantitatively assessing properties or objects of interest on a global scale. Machine learning and computer vision (CV) approaches show themselves as promising tools for automatizing satellite image analysis. However, there are limitations in using CV for satellite data. Mainly, the crucial one is the amount of data available for model training. This paper presents a novel image augmentation approach called MixChannel that helps to address this limitation and improve the accuracy of solving segmentation and classification tasks with multispectral satellite images. The core idea is to utilize the fact that there is usually more than one image for each location in remote sensing tasks, and this extra data can be mixed to achieve the more robust performance of the trained models. The proposed approach substitutes some channels of the original training image with channels from other images of the exact location to mix auxiliary data. This augmentation technique preserves the spatial features of the original image and adds natural color variability with some probability. We also show an efficient algorithm to tune channel substitution probabilities. We report that the MixChannel image augmentation method provides a noticeable increase in performance of all the considered models in the studied forest types classification problem.

Three Authentication Schemes without Secrecy over Finite Fields and Galois Rings

We provide three new authentication schemes without secrecy. The first two on finite fields and Galois rings, using Gray map for this link. The third construction is based on Galois rings. The main achievement in this work is to obtain optimal impersonation and substitution probabilities in the schemes. Additionally, in the first and second scheme, we simplify the source space and obtain a better relationship between the size of the message space and the key space than the one given in a recent paper. Finally, we provide a third scheme on Galois rings.