Dynamic Equations Research Articles

Development of neuronal timescales in human cortical organoids and rat hippocampus dissociated cultures.

To support complex cognition, neuronal circuits must integrate information across multiple temporal scales, ranging from milliseconds to decades. Neuronal timescales describe the duration over which activity within a network persists, posing a putative explanatory mechanism for how information might be integrated over multiple temporal scales. Little is known about how timescales develop in human neural circuits or other model systems, limiting insight into how the functional dynamics necessary for cognition emerge. In our work, we show that neuronal timescales develop in a non-linear fashion in both human cortical organoids and dissociated rat hippocampus cultures. We use spectral parameterization of spiking activity to extract an estimate of neuronal timescale that is unbiased by co-evolving oscillations. Cortical organoid timescales begin to increase around month 6 post-differentiation. We complement these findings with an analysis of timescales in rodent hippocampal dissociated cultures over development and see that timescales decrease from in vitro days 13-23 before stabilizing. We speculate that cortical organoid development over the duration studied here reflects an earlier stage of a generalized developmental timeline in contrast to the rodent hippocampal cultures, potentially accounting for differences in timescale developmental trajectories. The fluctuation of timescales might be an important developmental feature that reflects the changing complexity and information capacity in developing neuronal circuits.

An anageometric time scale calculus and its some basic applications

Anageometric calculus is a branch of non-Newtonian calculus introduced by M. Grossman and R. Katz in 1967, in which changes in functional values are measured by linear differences but arguments are measured by ratios. The theory of time scales was initiated by S. Hilger in 1988 to unify continuous and discrete analysis. In this article, we introduce anageometric time scale calculus to discuss dynamic equations in which the values of the independent variable show non-linear behaviour. This newly introduced calculus will be more applicable than other calculi in atomic reactors, growth models, etc. We shall discuss some applications of anageometric time scale calculus on the geometric real field R(G) with its optimality and better accuracy.

Towards to Theory of the X-ray Diffraction Tomography of Crystals with Nano-Sized Defects

X-ray diffraction tomography is an innovative method that is widely used to obtain 2D-phase-contrast diffraction images and their subsequent 3D-reconstruction of structural defects in crystals. The most frequent objects of research are linear and helical dislocations in a crystal, for which plane wave diffraction images are the most informative, since they do not contain additional interference artifacts unrelated to the images of the defects themselves. In this work the results of modeling and analysis of 2D plane wave diffraction images of a nano-dimensional Coulomb-type defect in a Si(111) thin crystal are presented based on the construction of numerical solutions of the dynamic Takagi-Taupin equations. An adapted physical expression for the elastic displacement field of the point defect, which excludes singularity at the defect location in the crystal, is used. A criterion for evaluating the accuracy of numerical solutions of the Takagi-Taupin equations is proposed and used in calculations. It is shown that in the case of the Coulomb-type defect elastic displacement field, out of the two difference algorithms for solving the Takagi-Taupin equations used in their numerical solution, only the algorithm for solving the Takagi-Taupin equations where the displacement field function enters in exponential form is acceptable in terms of the required accuracy-duration of the calculations.

Effect of Photoperiod on Dry Matter Accumulation and Partitioning in Potato

To explore the effect of the photoperiod on the accumulation and distribution of dry matter in potato, a pot experiment was carried out in 2021 and 2022 with two varieties (Atlantic and Hezuo 88). The varieties were used as the main plot, and light treatments (short-day and long-day) were used as the subplot. The results showed that extended hours of light delayed tuber formation in Hezuo 88, however, the effect was not obvious for the Atlantic. Comprehensive analyses were carried out using the potato developmental process, dynamic equation fitting of the tuber and whole-plant dry matter accumulation, and the dry matter accumulation and distribution rate of each organ of the two varieties under two photoperiods. The two photoperiods had different effects on the parameters of rapid tuber and whole-plant dry matter accumulation: the starting point of the period of the rapid dry matter accumulation (t1), the duration period of the rapid dry matter accumulation (Δt), and the average growth rate of the period of the rapid dry matter accumulation (Vmean). According to comprehensive analysis, tuber dry matter accumulation in Atlantic was the highest under the short-day condition, while Hezuo 88 showed the lowest tuber dry matter accumulation under the long-day condition and was the latest to enter the rapid tuber dry matter accumulation period. The whole-plant dry matter accumulation in Atlantic was the highest under the long-day condition and lowest in Hezuo 88; meanwhile, Hezuo 88 was the latest to enter the rapid whole-plant dry matter accumulation period. In terms of the dry matter accumulation and dry matter partitioning ratio of various organs, Hezuo 88 had the lowest mean tuber dry matter accumulation and partitioning ratio under the long-day condition but the highest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. On the contrary, Atlantic had the highest mean tuber dry matter accumulation and portioning ratio under the short-day condition but the lowest mean stem, leaf, root, underground stem, and stolon dry matter partitioning ratio. It was concluded that different varieties of potato respond differently to the photoperiod. In the case of Hezuo 88, prolonging the photoperiod affected the dynamics and distribution of dry matter accumulation; increased the stem, leaf, root, and underground stem dry matter partitioning ratio; and decreased the tuber dry matter partitioning ratio, which resulted in a decrease in tuber dry matter accumulation and consequently delayed the emergence of the equilibrium period between the aboveground and underground dry matter.

The Trajectory Prediction of Spacecraft under the Influence of Gyroscopic Effect Generated during Non-Keplerian Motion

Due to perturbation forces and control forces, trajectories of spacecraft around the Earth are usually non-Keplerian orbits, which may result in a gyroscopic effect. To meet the complex demands of space operations in the future, the trajectory prediction of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion needs to be studied in depth. The paper investigated the trajectory of spacecraft under the gyroscopic effect generated during non-Keplerian motion. Firstly, according to the similarity between the spacecraft precession motion and the gyroscopic precession, as well as the definition of the “gyroscopic effect” of high-speed rotating bodies, the “gyroscopic effect” generated during the non-Keplerian motion of spacecraft around the earth was defined. Then, taking a continuous radial thrust orbit as an example, the dynamics equations of spacecraft under the influence of gyroscopic effect were deduced. Through theoretical analysis and numerical simulation, the trajectory of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion was investigated. Finally, the paper simulated the examples and tested the performance of the proposed method. Simulation results show that a large gyroscopic moment may be generated in some non-Keplerian motion of the spacecraft. The greater the rotational angular velocity of the orbital plane, the greater the gyroscopic moment. Due to the gyroscopic effect, there is a significant deviation in the orbit and the orbital elements compared to those without considering the gyroscopic effect, which indicates that the influence of the gyroscopic effect generated during non-Keplerian motion on the orbit of the spacecraft cannot be ignored. It can be seen from the simulation results that the gyroscopic effect has a significant influence on the trajectory of spacecraft. In some special cases, the gyroscopic effect can be utilized reasonably to save fuel and realize low-energy orbit maneuver control technology in actual space missions; but the control should be considered for the spacecraft to bring it back to the desired orbit in most cases. It is necessary to study the trajectory of spacecraft under the influence of gyroscopic effect. The method and conclusions proposed can provide a theoretical reference for spacecraft trajectory prediction and future large-scale fast orbital maneuvers to meet the needs of complex space operations.

Connecting the Dots of Creativity and Curiosity: A Weekly Diary Examination Using Dynamic Structural Equation Modeling

ABSTRACTIn the last decade, research on the connection between curiosity and creativity has surged revealing a positive correlation. However, these findings are primarily based on cross‐sectional studies, which do not establish the direction of the relationship between creativity and curiosity. Is curiosity the driving force behind creativity, or does creativity spark curiosity? The present study addresses this question by examining the potential reciprocal associations between creativity and curiosity within‐persons using state‐of‐the‐art methodology and statistics. Self‐reported data were collected on a weekly basis from a sample of Greek entrepreneurs (N = 195, 49% female) over a 10‐week period. We used the dynamic structural equation modeling (DSEM) framework for data analyses. Results supported the positive relationship between creativity and curiosity within and between individuals. At the within‐person level, creativity and curiosity exhibited significant carry‐over effects from 1 week to the next. However, we did not find consistent evidence for cross‐lagged effects, meaning that curiosity and creativity did not directly cause changes in each other within a 1‐week period. We also found significant random effects underscoring the role of curiosity as a catalyst for creativity, particularly when individuals do not have a strong tendency for their creative levels to persist but do have a strong tendency for their curiosity levels to persist. In such cases, curiosity seems to have a more pronounced impact on shaping creative endeavors. We discuss the implications of our findings for theory and practice and suggest directions for future research.

Excitation of the Secondary Modes by the Broad Spectrum Sound in a Liquid with Relaxation Losses

Features of nonlinear phenomena and, in particular, acoustic excitation of the entropy and relaxation modes in a liquid electrolyte with a chemical reaction are examined. The total range of frequencies of an exciter is considered, and the instantaneous dynamic equations are derived which govern perturbations in the secondary modes. The instantaneous leading-order acoustic forces of the secondary modes are evaluated. Examples of harmonic and nearly harmonic acoustic exciter are considered in detail. The difference in the nonlinear acoustic phenomena in an electrolyte and gases with relaxation mechanisms are specified and discussed.

Interplay between charge and spin noise in the near-surface theory of decoherence and relaxation of C3v symmetry qutrit spin-1 centers

Decoherence and relaxation of solid-state defect qutrits near a crystal surface, where they are commonly used as quantum sensors, originate from charge and magnetic field noise. A complete theory requires a formalism for decoherence and relaxation that includes all Hamiltonian terms allowed by the defect's point-group symmetry. This formalism, presented here for the C3v symmetry of a spin-1 defect in a diamond, silicon carbide, or similar host, relies on a Lindblad dynamical equation and clarifies the relative contributions of charge and spin noise to relaxation and decoherence, along with their dependence on the defect spin's depth and resonant frequencies. The calculations agree with the experimental measurements of Sangtawesin [], and corroborate the importance of charge noise. Published by the American Physical Society 2024

New Results on the Quasilinearization Method for Time Scales

We have developed the generalized quasilinearization method (QM) for an initial value problem (IVP) of dynamic equations on time scales by using comparison theorems with a coupled lower solution (LS) and upper solution (US) of the natural type. Under some conditions, we observed that the solutions converged to the unique solution of the problem uniformly and monotonically, and the rate of convergence was investigated.

Coherent interferometric control of strongly-coupled nano-electromechanical resonators

The interferometric control of dissipation in a two-port system is a fruitful concept enabling the enhancement or cancellation of the input amplitudes as a function of their relative phases. Here, beyond the canonical configuration of Coherent Perfect Absorption (CPA), we apply this concept to two simultaneously excited strongly-coupled nanoscale electromechanical resonators submitted to independently controlled phase-shifted excitations. Both subsystems are read simultaneously by optical means allowing us to completely reconstruct the signature of coherent annihilation or amplification on both quadrature. We evidence that the mechanical modes amplitude can be enhanced or inhibited with respect to the case of single port excitation while phase experiences strong variations with the excitation imbalance and phase difference. Meanwhile, phase singularities with opposite topological charges are observed for mechanical normal modes. Close to the phase singularity, we demonstrate that the input of a weak phase modulation induces a large, pure phase modulation of the normal mode. These experimental demonstrations are fully modelled via the mechanical dynamical equations of our system. The interferometric control may open avenues for low-power amplitude controlled phase modulation schemes and vice-versa for potential switches and logical gates.

Dynamic Analysis of Rigid–Flexible Structures with Piezoelectric Actuation and Control

In this paper, the dynamic equation of a rigid body coupled with two flexible beams was established, considering the rotational motion of the rigid body and the elastic deflection of the flexible beams. The coupling effect between the rigid body rotation and flexible beam vibration was studied in detail. The dynamic response of the flexible beam with piezoelectric effect was established based on Hamilton’s principle. Under the premise of ignoring the nonlinear vibration coupling term of flexible beams, only the first two modes of transverse displacement and one directional rotation motion were studied in case studies. It was found that the coupling term caused by rigid body rotation can slightly alter the natural frequency and amplitude of flexible beams, mainly reflected in the first-order mode. With increasing the external excitation on the rigid body, the induced transverse displacement at the tip of the flexible beam increased significantly. Meanwhile, when the flexible beam was under external excitation, the vibration could also induce rigid body rotation. With the inverse piezoelectric effect, one may actively actuate the flexible beam vibration and rigid body rotation or control the undesired motion of the system. The control effect can be adjusted by varying the applied voltage excitation on the piezoelectric patches as well as patch positions. The conclusions drawn from this study can be applied to active precise control of space facilities such as satellites. Based on the dynamic modeling of rigid–flexible multi-body systems, this paper completed the study of the coupling effects of rigid body rotation and flexible body vibration, and proposed an application idea for completing small-angle maneuvers of rigid–flexible multi-body systems through piezoelectric control.

Collective photon emission in solid state environments: Concatenating non-Markovian and Markovian dynamics

Collective light emission and multiqubit dynamics of solid-state quantum emitters are affected both by their coupling to the light field and to lattice vibrations. The effect of phonons on quantum emitters is twofold: polaron formation is described by ultrafast non-Markovian dynamics, while slower dephasing is well described by exponential decay. Of the two temperature-dependent processes, the effect of the former on the collective emission and the entanglement decay of emitters is usually not modeled, and also the latter is sometimes neglected. Here we propose and compare two methods that are efficient also for several emitters: the first method concatenates the fast and slow phonon dynamics, and the second is the polaron method. For a single quantum emitter, we show that the dynamical equations are identical in both methods, while predictions for two or more emitters also agree very well. Both of our methods incorporate non-Markovian dynamics due to phonons demonstrating the temperature sensitivity of the collective photon emission. Utilizing a simplified Markovian model instead may not be accurate enough especially for quantum information applications: for example, we show how the Markovian model may considerably overestimate the two-emitter concurrence, except at very low temperatures. Our concatenation and polaron methods can be applied to an arbitrary number and type of quantum emitters, and beyond the bulk GaAs environment that we consider here. Especially the concatenation method can take phonon effects into account at the same computational cost as modeling the emitter-photon interaction alone. Finally, we present approximate analytical expressions for the collective emission spectrum for N emitters on a one-dimensional chain. Published by the American Physical Society 2024

Matter–curvature effects upon the dissipative viscous collapse of massive stellar object

This paper investigates the evolutionary phases of a collapsing dissipative star cluster in the presence of dark matter. For this purpose, the minimal coupling model of [Formula: see text] gravity is used as a candidate for exotic matter in star cluster. The collapse equation is derived from generalized dynamical equations which show the total conservation of energy within the cluster. In this context, the approach of Misner and Sharp is applied to study the phenomenon and differentiate between homologous as well as non-homologous gravitational collapse. The generalized dynamical equations are also connected to modified heat transport equations related to heat flux, viscosity and shear, which deals with Israel–Stewart theory (without removing the thermodynamics heat/viscous coupling coefficients). It is found that shear-free and non-dissipative fluid give homologous collapse. The dissipation of collapsing star cluster provides a relation between tidal forces and density inhomogeneity. It is theoretically predicted that the presence of exotic matter controlled the collapsing mechanism.

Inferring dynamical models from time-series biological data using an interpretable machine learning method based on weighted expression trees

Abstract The growing time-series data make it possible to glimpse the hidden dynamics in various fields. However, developing a computational toolbox with high interpretability to unveil the interaction dynamics from data remains a crucial challenge. Here, we propose a new computational approach called Automated Dynamical Model Inference based on Expression Trees (ADMIET), in which the machine learning algorithm, the numerical integration of ordinary differential equations and the interpretability from prior knowledge are embedded into the symbolic learning scheme to establish a general framework for revealing the hidden dynamics in time-series data. ADMIET takes full advantage of both machine learning algorithm and expression tree. Firstly, we translate the prior knowledge into constraints on the structure of expression tree, reducing the search space and enhancing the interpretability. Secondly, we utilize the proposed adaptive penalty function to ensure the convergence of gradient descent algorithm and the selection of the symbols. Compared to gene expression programming, ADMIET exhibits its remarkable capability in function fitting with higher accuracy and broader applicability. Moreover, ADMIET can better fit parameters in nonlinear forms compared to regression methods. Furthermore, we apply ADMIET to two typical biological systems and one real data with different prior knowledge to infer the dynamical equations. The results indicate that ADMIET can not only discover the interaction relationships but also provide accurate estimates of the parameters in the equations. These results demonstrate ADMIET's superiority in revealing interpretable dynamics from time-series biological data.

Divergent evolution of NLR genes in the genus Glycine: impacts of annuals and perennials’ life history strategies

Within the family Fabaceae, the genus Glycine is composed of two subgenera annuals (2n=40) and perennials. This life strategy transition may have differentially affected the evolution of various gene families. Its cultivated species G. max has high level of susceptibility to major pathogens including viruses, bacteria and fungi. Understanding nucleotide-binding domain leucine-rich repeat (NLR) genes evolution in soybean is of paramount importance due to their central role in plant immunity and their potential in improving disease resistance in soybean cultivars. In this study, we investigated the significance of this annual-perennial transition on the macroevolution of NLR genes in the genus Glycine. Our results reveal a remarkable distinction between annual species such as Glycine max and Glycine soja, which exhibit an expanded NLRome compared to perennial species (G. cyrtoloba, G. stenophita, G. dolichocarpa, G. falcata, G. syndetika, G. latifolia and G. tomentella). Our evolutionary timescale analysis pinpoints recent accelerated gene duplication events for this expansion, which occurred between 0.1 and 0.5 million years ago, driven predominantly by lineage-specific and terminal duplications. In contrast, perennials initially experienced significant contraction during the diploidisation phase following the Glycine-specific whole-genome duplication event (~10 million years ago). Despite the reduction in the NLRome, perennial lineages exhibit a unique and highly diversified repertoire of NLR genes with limited interspecies synteny. The investigation of gene gain and loss ratios revealed that this diversification resulted from the birth of novel genes following individual speciation events. Among perennials, G. latifolia, a well-known resistance resource, has the highest ratio of these novel genes in the tertiary gene pool. Our study suggests evolutionary mechanisms, including recombination and transposition, as potential drivers for the emergence of these novel genes. This study also provides evidence for the unbalanced expansion of the NLRome in the Dt subgenome compared with the At subgenome in the young allopolyploid G. dolichocarpa. To the best of our knowledge, this is the first study to investigate the effect of annuality and perenniality life transition on the evolution of NLR genes in the genus Glycine to identify its genomics resources for improving the resistance of soybean crop with global importance on the economy and food security.

Divergent evolution of NLR genes in the genus Glycine: impacts of annuals and perennials’ life history strategies

Within the family Fabaceae, the genus Glycine is composed of two subgenera annuals (2n=40) and perennials. This life strategy transition may have differentially affected the evolution of various gene families. Its cultivated species G. max has high level of susceptibility to major pathogens including viruses, bacteria and fungi. Understanding nucleotide-binding domain leucine-rich repeat (NLR) genes evolution in soybean is of paramount importance due to their central role in plant immunity and their potential in improving disease resistance in soybean cultivars. In this study, we investigated the significance of this annual-perennial transition on the macroevolution of NLR genes in the genus Glycine. Our results reveal a remarkable distinction between annual species such as Glycine max and Glycine soja, which exhibit an expanded NLRome compared to perennial species (G. cyrtoloba, G. stenophita, G. dolichocarpa, G. falcata, G. syndetika, G. latifolia and G. tomentella). Our evolutionary timescale analysis pinpoints recent accelerated gene duplication events for this expansion, which occurred between 0.1 and 0.5 million years ago, driven predominantly by lineage-specific and terminal duplications. In contrast, perennials initially experienced significant contraction during the diploidisation phase following the Glycine-specific whole-genome duplication event (~10 million years ago). Despite the reduction in the NLRome, perennial lineages exhibit a unique and highly diversified repertoire of NLR genes with limited interspecies synteny. The investigation of gene gain and loss ratios revealed that this diversification resulted from the birth of novel genes following individual speciation events. Among perennials, G. latifolia, a well-known resistance resource, has the highest ratio of these novel genes in the tertiary gene pool. Our study suggests evolutionary mechanisms, including recombination and transposition, as potential drivers for the emergence of these novel genes. This study also provides evidence for the unbalanced expansion of the NLRome in the Dt subgenome compared with the At subgenome in the young allopolyploid G. dolichocarpa. To the best of our knowledge, this is the first study to investigate the effect of annuality and perenniality life transition on the evolution of NLR genes in the genus Glycine to identify its genomics resources for improving the resistance of soybean crop with global importance on the economy and food security.

Modeling and Optimal Control of Infectious Diseases

We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained.

Modeling and Optimal Control of Infectious Diseases

We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained.

Modeling and optimization of costs associated with the development of clustered organizational management structures in construction companies

The article aims to examine models and methods of cost optimization associated with the development of clustered organizational structures in construction companies. The research methodology involved an analysis of existing approaches, simulation modeling, and econometric equation analysis. As a result, different approaches to cost estimation and optimization applied in the construction sphere are presented. Particular attention is paid to the development of complex models and their optimization under the conditions of uncertainty through simulation modeling of various scenarios of cluster organizational structures in construction companies. The analysis also includes an assessment of the advantages and disadvantages of econometric semi-linear dynamic equations and the feasibility of their application. The discussion section emphasizes the importance of integrating different optimization methods to achieve the most optimal outcome in the management of construction companies. Further research directions are outlined. The results can be relevant when formulating development strategies and making investment decisions in the construction sphere. The research conclusions confirm the significance of applying modern cost optimization methods to improve the management efficiency of construction companies and their competitiveness in the market of construction services.

A noncommutative Bianchi I model with radiation

In this work, we study the dynamical evolution of a homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to a homogeneous and isotropic NC Friedmann–Robertson–Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor [Formula: see text] and the two parameters [Formula: see text], which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables’ transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model in which the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe. Based on that result, we can speculate that the solutions may represent an initial anisotropic stage of our Universe, that later, due to the expansion, became isotropic.