Variational Integrators Research Articles

Genetic diversity of grain yield traits and identification of a grain weight gene SiTGW6 in foxtail millet.

Agronomic traits were evaluated in 1250 foxtail millet accessions, and a crucial gene SiTGW6 governing grain yield was identified. Elite haplotypes and dCAPS markers developed for SiTGW6 facilitate molecular breeding. A comprehensive evaluation of phenotypic characteristics and genetic diversity in germplasm resources are important for gene discovery and breeding improvements. In this study, we conducted a comprehensive evaluation of 1250 foxtail millet varieties, assessing seven grain yield-related traits and fourteen common agronomic traits over two years. Principal component analysis, correlation analysis, and cluster analysis revealed a strong positive correlation between 1000-grain weight and grain width with grain yield, emphasizing their importance in foxtail millet breeding. Additionally, we found that panicle weight positively correlated with 1000-grain weight but negatively correlated with branch and tiller numbers, indicating selection factors during domestication and breeding. Using this information, we identified 27 germplasm resources suitable for high-yield foxtail millet breeding. Furthermore, through an integration of haplotype variations and phenotype association analysis, we pinpointed a crucial gene, SiTGW6, responsible for governing grain yield in foxtail millet. SiTGW6 encodes an IAA-glucose hydrolase, primarily localized in the cytoplasm and predominantly expressed in flowering panicles. Employing RNAseq analysis, we identified 1439 differentially expressed genes across various SiTGW6 haplotypes. Functional enrichment analysis indicating that SiTGW6 regulates grain yield through the orchestration of auxin and glucan metabolism, as well as plant hormone signaling pathways. Additionally, we have identified elite haplotypes and developed dCAPS markers for SiTGW6, providing valuable technical tools to facilitate molecular breeding efforts in foxtail millet.

A Lie group variational integrator in a closed-loop vector space without a multiplier

Abstract. As a non-tree multi-body system, the dynamics model of four-bar mechanism is a differential algebraic equation. The constraints breach problem leads to many problems for computation accuracy and efficiency. With the traditional method, constructing an ODE-type dynamics equation for it is difficult or impossible. In this exploration, the dynamics model is built with geometry mechanic theory. The kinematic constraint variation relation of a closed-loop system is built in matrix and vector space with Lie group and Lie algebra theory respectively. The results indicate that the attitude variation between the driven body and the follower body has a linear recursion relation, which is the basis for dynamics modelling. With the Lie group variational integrator method, the closed-loop system Lagrangian dynamics model is built in vector space, with Legendre transformation. The dynamics model is reduced to be the Hamilton type. The kinematic model and dynamics model are solved using Newton iteration and the Runge–Kutta method respectively. As a special case of a crank and rocker mechanism, the dynamics character of a parallelogram mechanism is presented to verify the good structure conservation character of the closed-loop geometry dynamics model.

Morphological variation, modularity and integration in the scapula and humerus of Lissotriton newts.

The modular organization of tetrapod paired limbs and girdles, influenced by the expression of Hox genes is one of the primary driving forces of the evolution of animal locomotion. The increased morphological diversification of the paired limbs is correlated with reduced between-limb covariation, while correlation within the elements is usually higher than between the elements. The tailed amphibians, such as Lissotriton newts, have a biphasic lifestyle with aquatic and terrestrial environments imposing different constraints on limb skeleton. By employing the methods of computerized microtomography and 3D geometric morphometrics, we explored the pattern of morphological variation, disparity, modularity and morphological integration in the proximal parts of the anterior limbs of six species of Eurasian small bodied newts. Although the species significantly differ in limb shape, there is a great overlap in morphology of scapula and humerus, and there are no differences in morphological disparity. For the scapula, the shape differences related to the duration of the aquatic period are in length, depth and curvature. The shape of the humerus is not affected by the length of aquatic period, and shape differences between the species are related to robustness of the body. The length of aquatic period has statistically supported phylogenetic signal. The scapula and humerus are structures of varying modularity. For the humerus, the strongest support on the phylogenetic level was for the capitulum/shaft hypothesis, which can also be interpreted as functional modularity. For the scapula, the greatest support was for the antero-posterior hypothesis of modularity in case of Lissotriton vulgaris, which can be explained by different functional roles and muscle insertion patterns, while there was no phylogenetic modularity. The modularity patterns seem to correspond with the general tetrapod pattern, with modularity being more pronounced in the distal structure. The future research should include more salamandrid taxa with different habitat preferences and both adult and larval stages, in order to explore how size, phylogeny and ecology affect the morphology and covariation patterns of limbs.

Characterization of Firmiana danxiaensis plastomes and comparative analysis of Firmiana: insight into its phylogeny and evolution

BackgroundFirmiana danxiaensis is a critically endangered and ecologically important tree currently only found in four locations in Danxia or Karst habitats in northern Guangdong Province, China. The specialized habitat preference makes it an ideal model species for study of adaptive evolution. Meanwhile, the phylogenetic relationships of F. danxiaensis in four locations under two landforms are unclear. Therefore, we sequenced its complete chloroplast (cp.) genomes and conducted comprehensive interspecific and intrageneric plastome studies.ResultsThe F. danxiaensis plastomes in four locations showed a typical quadripartite and circular structure that ranged from 160,832 to 161,206 bp in size, with 112 unique genes encoded. Comparative genomics showed that the plastomes of F. danxiaensis were relatively conserved with high similarity of genome organization, gene number, GC content and SSRs. While the genomes revealed higher biased codon preferences in Karst habitat than those in Danxia habitats. Eighteen and 11 divergent hotpots were identified at interspecific and intrageneric levels for species identification and further phylogenetic studies. Seven genes (clpP, accD, ccsA, ndhH, rpl20, rpoC2, and rps4) were under positive selection and may be related to adaptation. Phylogenetic analysis revealed that F. danxiaensis is sister to F. major and F. simplex. However, the interspecific relationships are not consistent with the habitat types.ConclusionsThe characteristics and interspecific relationship of F. danxiaensis plastomes provide new insights into further integration of geographical factors, environmental factors, and genetic variations on the genomic study of F. danxiaensis. Together, our study will contribute to the study of species identification, population genetics, and conservation biology of F. danxiaensis.

An Asynchronous Variational Integrator for Contact Problems Involving Elastoplastic Solids

An Asynchronous Variational Integrator for Contact Problems Involving Elastoplastic Solids

Optimal Control of Mechanical Systems Based on Path-Fitted Variational Integrators

Abstract In view of the crucial importance of optimal control in many application areas and the improved performance of path-fitted variational integrators, the paper links these two aspects and presents a methodology to find optimal control policies for mechanical systems. The main process of the methodology is employing path-fitted variational integrators to discretize the forced mechanical equations and further take the obtained discrete equations as equality constraints for the final optimization problem. Simultaneously, the discretization also provides a reasonable way to approximate the objective function and incorporate the boundary conditions. With the transformation of optimal control problems into nonlinear optimization problems, all the benefits of path-fitted variational integrators are inherited by the presented methodology, mainly expressed in giving more faithful optimizations and thus more accurate solutions, providing a greater possibility of global optimality, as well as conserving computed control efforts. These superiorities, verified by the optimal control of an overhead crane, indicate that the methodology has high potential application in industrial control field.

Exploration of solitons and analytical solutions by sub-ODE and variational integrators to Klein-Gordon model

In this paper, we use the sub-ODE method to analyze soliton solutions for the renowned nonlinear Klein-Gordon model (NLKGM). This method provides a variety of soliton solutions, including three positive solitons, three Jacobian elliptic function solutions, bright solitons, dark solitons, periodic solitons, rational solitons and hyperbolic function solutions. Applications for these solitons can be found in optical communication, fiber optic sensors, plasma physics, Bose-Einstein condensation and other areas. We also study some numerical solutions by using forward, backward, and central difference techniques. Moreover, we discuss variational integrators (VIs) using the projection technique for NLKGM. We develop a numerical solution for NLKGM using the discrete Euler lagrange equation, the Lagrangian and the Euler lagrange equation. At the end, in various dimensions, covering 3D, 2D, and contour, we will also plot several graphs for the obtained NLKGM solutions. A contour plot is a type of graphic representation that displays a three-dimensional surface on a two-dimensional plane by using contour lines. Each contour line in the plotted function represents one of the function's constant values, mapping the function's value across the plane. This model has been studied across multiple soliton solutions using various methods in the open literature, but this model for VIs and finite deference scheme (FDS) is the first time it has been studied. Within the various numerical techniques accessible for solving Hamiltonian systems, variational integrators distinguish themselves because of their symplectic quality. Here are some of the symplectic properties: symplectic orthogonality, energy conservation, area preservation, and structure preservation.

On the discrete equivalence of Lagrangian, Hamiltonian and mixed finite element formulations for linear wave phenomena

It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit a Hamiltonian structure when written in mixed form. In this contribution, the discrete equivalence of Lagrangian, symplectic Hamiltonian and mixed formulations is investigated for linear wave propagation phenomena. Under compatibility conditions between the finite elements, the Lagrangian and mixed formulations are indeed equivalent. For the time discretization the leapfrog scheme and the implicit midpoint rule are considered. In mixed methods applied to wave problems the primal variable (e.g. the displacement in mechanics or the magnetic potential in electromagnetism) is not an unknown of the problem and is reconstructed a posteriori from its time derivative. When this reconstruction is performed via the trapezoidal rule, then these time-discretization methods lead to equivalent formulations.

Variational Integrators for Stochastic Mechanical Hybrid Systems

This paper introduces stochastic variational impact integrators for the class of hybrid mechanical systems that incorporate random noise. The governing equations are obtained by the application of the variational principle to the stochastic action integral, where both the continuous-time dynamics as well as the discrete transitions are considered. Furthermore, structure-preserving geometric integrators are derived through the discretization of the stochastic variational principle. This ensures the consistency in comparison to the continuous versions of the Euler-Lagrange or Hamilton’s equations. The effectiveness of the proposed methods in capturing the long-term energy behavior of a stochastic mechanical hybrid system is illustrated by numerical examples.

ANALYSIS OF VERTICAL INTEGRATION OF RICE MARKET IN SOUTH KALIMANTAN PROVINCE

Vertical integration is important to know to see whether changes in rice prices in the reference market (consumers) are followed by changes in rice prices in the follower market (producers) which will have an impact on the effectiveness of the Government's policies in stabilizing rice prices. This study aims to determine the price variation and vertical integration of local and superior rice markets in South Kalimantan Province. This study uses local and superior rice price data at the producer (milling) and consumer (retailer) levels from January 2014 to March 2024. The data used was sourced from the Central Statistics Agency and the South Kalimantan Provincial Agriculture and Food Security Office. The Coefficient of Variation is used to see price variations in local and superior rice. VAR/VECM analysis is used to identify vertical integration relationships between local and superior rice markets at the producer and consumer levels. The results of the study show that the highest coefficient of variation in local and superior rice prices occurred in the year of the Covid-19 pandemic. The coefficient of variation in local rice prices of producers was highest in 2020 and 2022 at 10.96% and 15.68%. The coefficient of variation in the price of superior rice for the highest producers in 2022 and 2023 is 16.23% and 12.48%. The results of the study also show that there is a vertical integration of a long-term equilibrium relationship between the consumer and producer of local and superior rice market. In the integration of the long-term equilibrium relationship, when the price of local and superior rice at the consumer level increases, the price of local and superior rice at the producer level also increases. The vertical integration of the short-term equilibrium relationship in the local rice market is full integration because both the consumer and producer markets influence each other but in opposite directions of price transmission. If prices in the consumer market rise, prices in the producer market will fall. The vertical integration of the short-term equilibrium relationship in the superior rice market is not complete because the producer market affects the consumer market but the consumer market does not significantly affect the producer market.

Variational integrators for dynamics of a flexible beam undergoing large overall motion

Variational integrators for dynamics of a flexible beam undergoing large overall motion

Multisymplectic variational integrators for free boundary barotropic fluid models with constraints

Multisymplectic variational integrators for free boundary barotropic fluid models with constraints

"Sonny’s Blues": The Dream Variation and Cultural Integration through Music

“Sonny’s Blues” is a chronicle of racial prejudice, diverse dreams, suffering, redemption, and reconciliation. As a tale of conflicting relationships between two brothers in Harlem society, it narrates the narrative of life, liberty and the pursuit of happiness on two opposite sides that the brothers are situated in: the legacy of African-American cultural and mainstream dreams. It is against this background dichotomy that the suffering of Sonny, the African-American protagonist, engendered due to his latent desire to be a jazz musician, is shown. This paper discourses on the existential narrative and its manifestation on society through an individual and answers different questions: why would characters go through extreme familial tension? What aspires them to embody two dissimilar legacies? How does music amidst racism produce a therapeutic effect? How are human predicaments resolved and why do characters go back to their original niche, which their ancestors had created? Hence, this paper aims at how music outcasts the barriers and welcomes avenues of resilience by removing the thundering cloud of stillness and darkness in the blue sky of Harlem.

The strong fuzzy variational Henstock multiple integral on n-dimensional fuzzy number space

In this paper, we define strongly fuzzy variational Henstock multiple integral and fuzzy Henstock integral by support functions on n-dimensional fuzzy number space. And we prove these two types of integrals are equivalent. After that, we propose the support-based derivative for strongly fuzzy variational Henstock integral functions and obtain the necessary and sufficient conditions for this differential. By the properties of ACGδ⁎⁎, we use the concepts of inner small variation and singular point covering to derive some characterization theorems of the primitives for strongly fuzzy variational Henstock integral. Finally, the Dominated Convergence Theorem for SFVH integral is obtained in the sense of UACGδ⁎⁎.

Geometric Methods for Adjoint Systems

Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or differential-algebraic equations. In this paper, we explore the geometric properties and develop methods for such adjoint systems. In particular, we utilize symplectic and presymplectic geometry to investigate the properties of adjoint systems associated with ordinary differential equations and differential-algebraic equations, respectively. We show that the adjoint variational quadratic conservation laws, which are key to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems. We discuss various additional geometric properties of adjoint systems, such as symmetries and variational characterizations. For adjoint systems associated with a differential-algebraic equation, we relate the index of the differential-algebraic equation to the presymplectic constraint algorithm of Gotay et al. (J Math Phys 19(11):2388–2399, 1978). As an application of this geometric framework, we discuss how the adjoint variational quadratic conservation laws can be used to compute sensitivities of terminal or running cost functions. Furthermore, we develop structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators (Leok and Zhang in IMA J. Numer. Anal. 31(4):1497–1532, 2011) which admit discrete analogues of these quadratic conservation laws. We additionally show that such methods are natural, in the sense that reduction, forming the adjoint system, and discretization all commute, for suitable choices of these processes. We utilize this naturality to derive a variational error analysis result for the presymplectic variational integrator that we use to discretize the adjoint DAE system. Finally, we discuss the application of adjoint systems in the context of optimal control problems, where we prove a similar naturality result.

Continuity of limit surfaces of locally uniform random permutations

A locally uniform random permutation is generated by sampling n points independently from some absolutely continuous distribution ρ on the plane and interpreting them as a permutation by the rule that i maps to j if the ith point from the left is the jth point from below. As n tends to infinity, decreasing subsequences in the permutation will appear as curves in the plane, and by interpreting these as level curves, a union of decreasing subsequences gives rise to a surface. In a recent paper by the author it was shown that, for any r≥0, under the correct scaling as n tends to infinity, the surface of the largest union of ⌊rn⌋ decreasing subsequences approaches a limit in the sense that it will come close to a maximizer of a specific variational integral (and, under reasonable assumptions, that the maximizer is essentially unique). In the present paper we show that there exists a continuous maximizer, provided that ρ has bounded density and support.The key ingredient in the proof is a new theorem about real functions of two variables that are increasing in both variables: We show that, for any constant C, any such function can be made continuous without increasing the diameter of its image or decreasing anywhere the product of its partial derivatives clipped by C, that is the minimum of the product and C.

A detailed analysis of stochastic models applied to temporal gravity field recovery with GRACE observations

Summary In this study, we analyzed the impacts of errors in background force models and observed non-gravitational forces on the pseudo-observations (pre-fits) during gravity field recovery based on the GRACE satellite gravity mission. To reduce these effects, we introduced the stochastic parameters into the functional model of the variational equation integration approach to absorb this type of noise contribution. Simultaneously, the prior variances of observed orbits and K-Band range rates used in traditional method are re-estimated with least-square variance component estimation (LS-VCE) after considering these stochastic parameters. To improve the computing efficiency, a modified method of the calculation of sensitivity matrices related to the introduced stochastic parameters is proposed. Compared to the method of variation of constants widely used in the precise orbit determination and gravity field recovery, the modified method decreases the computational time of these matrices by about four times. Furthermore, an efficient LS-VCE algorithm is derived in a more generalized case. The efficient algorithm only costs 1% of the time of the unoptimized method. With the GRACE data, we analyzed the benefits of these refinements in gravity field recovery, and the results show that these improvements can mitigate the impacts of errors in background force models and accelerometer data on recovered gravity field models, especially in the high degree signals. Furthermore, the quality of results has less dependence on parameterization.

Variational integrators and graph-based solvers for multibody dynamics in maximal coordinates

Multibody dynamics simulators are an important tool in many fields, including learning and control in robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to unsuitable integrators with bad energy behavior and problematic constraint violations, for example in contact interactions. Variational integrators are numerical discretization methods that can reduce physical inaccuracies when simulating mechanical systems, and formulating the dynamics in maximal coordinates allows for easy and numerically robust incorporation of constraints such as kinematic loops or contacts. Therefore, this article derives a variational integrator for mechanical systems with equality and inequality constraints in maximal coordinates. Additionally, efficient graph-based sparsity-exploiting algorithms for solving the integrator are provided and implemented as an open-source simulator. The evaluation of the simulator shows improved physical accuracy due to the variational integrator and the advantages of the sparse solvers. Comparisons to minimal-coordinate algorithms show improved numerical robustness, and application examples of a walking robot and an exoskeleton with explicit constraints demonstrate the necessity and capabilities of maximal coordinates.

Integrating Temporal Fluctuations in Crop Growth with Stacked Bidirectional LSTM and 3D CNN Fusion for Enhanced Crop Yield Prediction

Optimizing farming methods and guaranteeing a steady supply of food depend critically on accurate predictions of crop yields. The dynamic temporal changes that occur during crop growth are generally ignored by conventional crop growth models, resulting in less precise projections. Using a stacked bidirectional Long Short-Term Memory (LSTM) structure and a 3D Convolutional Neural Network (CNN) fusion, we offer a novel neural network model that accounts for temporal oscillations in the crop growth process. The 3D CNN efficiently recovers spatial and temporal features from the crop development data, while the bidirectional LSTM cells capture the sequential dependencies and allow the model to learn from both past and future temporal information. Our model's prediction accuracy is improved by combining the LSTM and 3D CNN layers at the top, which better captures temporal and spatial patterns. We also provide a novel label-related loss function that is optimized for agricultural yield forecasting. Because of the relevance of temporal oscillations in crop development and the dynamic character of crop growth, a new loss function has been developed. This loss function encourages our model to learn and take advantage of the temporal trends, which improves our ability to estimate crop yield. We perform comprehensive experiments on real-world crop growth datasets to verify the efficacy of our suggested approach. The outcomes prove that our unified strategy performs far better than both baseline crop growth prediction algorithms and cutting-edge applications of deep learning. Improved crop yield prediction accuracy is achieved with the integration of temporal variations via the merging of bidirectional LSTM and 3D CNN and a unique loss function. This study helps move the science of estimating crop yields forward, which is important for informing agricultural policy and ensuring a steady supply of food.

Adapting crop production to climate change and air pollution at different scales.

Air pollution and climate change are tightly interconnected and jointly affect field crop production and agroecosystem health. Although our understanding of the individual and combined impacts of air pollution and climate change factors is improving, the adaptation of crop production to concurrent air pollution and climate change remains challenging to resolve. Here we evaluate recent advances in the adaptation of crop production to climate change and air pollution at the plant, field and ecosystem scales. The main approaches at the plant level include the integration of genetic variation, molecular breeding and phenotyping. Field-level techniques include optimizing cultivation practices, promoting mixed cropping and diversification, and applying technologies such as antiozonants, nanotechnology and robot-assisted farming. Plant- and field-level techniques would be further facilitated by enhancing soil resilience, incorporating precision agriculture and modifying the hydrology and microclimate of agricultural landscapes at the ecosystem level. Strategies and opportunities for crop production under climate change and air pollution are discussed.