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2022 ◽  
Vol 23 (1) ◽  
Johannes Hettich ◽  
J. Christof M. Gebhardt

Abstract Background The temporal progression of many fundamental processes in cells and organisms, including homeostasis, differentiation and development, are governed by gene regulatory networks (GRNs). GRNs balance fluctuations in the output of their genes, which trace back to the stochasticity of molecular interactions. Although highly desirable to understand life processes, predicting the temporal progression of gene products within a GRN is challenging when considering stochastic events such as transcription factor–DNA interactions or protein production and degradation. Results We report a method to simulate and infer GRNs including genes and biochemical reactions at molecular detail. In our approach, we consider each network element to be isolated from other elements during small time intervals, after which we synchronize molecule numbers across all network elements. Thereby, the temporal behaviour of network elements is decoupled and can be treated by local stochastic or deterministic solutions. We demonstrate the working principle of this modular approach with a repressive gene cascade comprising four genes. By considering a deterministic time evolution within each time interval for all elements, our method approaches the solution of the system of deterministic differential equations associated with the GRN. By allowing genes to stochastically switch between on and off states or by considering stochastic production of gene outputs, we are able to include increasing levels of stochastic detail and approximate the solution of a Gillespie simulation. Thereby, CaiNet is able to reproduce noise-induced bi-stability and oscillations in dynamically complex GRNs. Notably, our modular approach further allows for a simple consideration of deterministic delays. We further infer relevant regulatory connections and steady-state parameters of a GRN of up to ten genes from steady-state measurements by identifying each gene of the network with a single perceptron in an artificial neuronal network and using a gradient decent method originally designed to train recurrent neural networks. To facilitate setting up GRNs and using our simulation and inference method, we provide a fast computer-aided interactive network simulation environment, CaiNet. Conclusion We developed a method to simulate GRNs at molecular detail and to infer the topology and steady-state parameters of GRNs. Our method and associated user-friendly framework CaiNet should prove helpful to analyze or predict the temporal progression of reaction networks or GRNs in cellular and organismic biology. CaiNet is freely available at

2022 ◽  
pp. 133-155
Giulio Ferro ◽  
Riccardo Minciardi ◽  
Luca Parodi ◽  
Michela Robba

The relevance of electric vehicles (EVs) is increasing along with the relative issues. The definition of smart policies for scheduling the EVs charging process represents one of the most important problems. A discrete-event approach is proposed for the optimal scheduling of EVs in microgrids. This choice is due to the necessity of limiting the number of the decision variables, which rapidly grows when a small-time discretization step is chosen. The considered optimization problem regards the charging of a series of vehicles in a microgrid characterized by renewable energy source, a storage element, the connection to the main grid, and a charging station. The objective function to be minimized results from the weighted sum of the cost for purchasing energy from the external grid, the weighted tardiness of the services provided, and a cost related to the occupancy of the socket. The approach is tested on a real case study.

2021 ◽  
Frederick Law ◽  
Antoine J Cerfon ◽  
Benjamin Peherstorfer

Abstract In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.

2021 ◽  
pp. 002224372110708
Rouven E. Haschka

This paper proposes a panel data generalization for a recently suggested IVfree estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common GLS transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor-error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to GMM-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.

2021 ◽  
Surath Ghosh ◽  
Snehasis Kundu ◽  
Sunil Kumar

Abstract In this study, the effects of time-memory on the mixing and nonequilibrium transportation of particles in an unsteady turbulent flow are investigated. The memory effect of particles is captured through a time-fractional advection-dispersion equation rather than a traditional advection-dispersion equation. The time-fractional derivative is considered in Caputo sense which includes a power-law memory kernel that captures the power-law jumps of particles. The time-fractional model is solved using the Chebyshev collocation method. To make the solution procedure more robust three different kinds of Chebyshev polynomials are considered. The time-fractional derivative is approximated using the finite difference method at small time intervals and numerical solutions are obtained in terms of Chebyshev polynomials. The model solutions are compared with existing experimental data of traditional conditions and satisfactory results are obtained. Apart from this, the effects of time-memory are analyzed for bottom concentration and transient concentration distribution of particles. The results show that for uniform initial conditions, bottom concentration increases with time as the order of fractional derivative decreases. In the case of transient concentration, the value of concentration initially decreases when $T<1$ and thereafter increases throughout the flow depth. The effects of time-memory \textcolor{green}{are} also analyzed under steady flow conditions. Results show that under steady conditions, transient concentration is more sensitive for linear, parabolic, and parabolic-constant models \textcolor{green}{of} sediment diffusivity rather than the constant model.

A. M. Davie

AbstractWe develop an asymptotic expansion for small time of the density of the solution of a non-degenerate system of stochastic differential equations with smooth coefficients, and apply this to the stepwise approximation of solutions. The asymptotic expansion, which takes the form of a multivariate Edgeworth-type expansion, is obtained from the Kolmogorov forward equation using some standard PDE results. To generate one step of the approximation to the solution, we use a Cornish–Fisher type expansion derived from the Edgeworth expansion. To interpret the approximation generated in this way as a strong approximation we use couplings between the (normal) random variables used and the Brownian path driving the SDE. These couplings are constructed using techniques from optimal transport and Vaserstein metrics. The type of approximation so obtained may be regarded as intermediate between a conventional strong approximation and a weak approximation. In principle approximations of any order can be obtained, though for higher orders the algebra becomes very heavy. In order 1/2 the method gives the usual Euler approximation; in order 1 it gives a variant of the Milstein method, but which needs only normal variables to be generated. However the method is somewhat limited by the non-degeneracy requirement.

2021 ◽  
Vol 932 ◽  
G.E. Elsinga ◽  
T. Ishihara ◽  
J.C.R. Hunt

The Richardson-scaling law states that the mean square separation of a fluid particle pair grows according to t3 within the inertial range and at intermediate times. The theories predicting this scaling regime assume that the pair separation is within the inertial range and that the dispersion is local, which means that only eddies at the scale of the separation contribute. These assumptions ignore the structural organization of the turbulent flow into large-scale shear layers, where the intense small-scale motions are bounded by the large-scale energetic motions. Therefore, the large scales contribute to the velocity difference across the small-scale structures. It is shown that, indeed, the pair dispersion inside these layers is highly non-local and approaches Taylor dispersion in a way that is fundamentally different from the Richardson-scaling law. Also, the layer's contribution to the overall mean square separation remains significant as the Reynolds number increases. This calls into question the validity of the theoretical assumptions. Moreover, a literature survey reveals that, so far, t3 scaling is not observed for initial separations within the inertial range. We propose that the intermediate pair dispersion regime is a transition region that connects the initial Batchelor- with the final Taylor-dispersion regime. Such a simple interpretation is shown to be consistent with observations and is able to explain why t3 scaling is found only for one specific initial separation outside the inertial range. Moreover, the model incorporates the observed non-local contribution to the dispersion, because it requires only small-time-scale properties and large-scale properties.

2021 ◽  
Vol 15 ◽  
pp. 23-26
Marwa A. El-Diwiny ◽  
Abou-Hashema M. El-Sayed

This paper handle a new terminology of the field of the unmanned aerial vehicle is Auto-self defensive UAV, by using new configuration of x-band Doppler surface distribution. The aim of this research is to make UAV can avoid any directed missiles at small time delay before the collision. The intelligent control will process the data of the hypothetical missiles by using supercomputing and send it to the inertial navigation system to correct the path of UAV every sample time against the missile. The goal is to make intelligent UAV that can maneuver the missile and never collide with it.

А. Н. Нарожный

A possible component of dark matter is considered. Astronomer began to talk about this matter for a long time, when the speed of movement of galaxies in the clusters was coordinated with classical mechanics. Subsequently, the idea of dark matter became used in the dynamics of stars and lineling phenomena. The observational data of astronomy and astrophysics indicate another path, which leads to the idea of the existence of dark matter, if these data are considered through the prism of the main principles and laws of natural science. On this path, the component of dark matter (DM) appears as an environment in the universe necessary to ensure the life of galaxies. The origin of the dark matter and the functions performed by it are binding to star electromagnetic radiation (SER). Features of the interaction of a two-component system - DM and SER - the basis of all further conclusions. First of all, the outer space is considered filled with subtle forms of matter. It is assumed that DM belongs to them. The presence of two giant material objects distributed over the entire space of the Universe, DM and SER - means their interaction among themselves. First, it follows from dialectic, arguing about the relationship of phenomena in nature. Secondly, from the interpretation of the results of measurements of cosmic microwave radiation obtained by the Arcade system (NASA, 2006). A two-component environment - DM and SER - contains all the baryon matter of the universe, ranging from elementary particles and ending with galactic clusters. Support for "life" of baryon matter is carried out through a number of functions performed by this medium. It is assumed that the star radiation, spreading the space, gives its energy to the dark component. The photons shifted into the microwave region are capable of pairing unaging among themselves in counter courses and small sighting distances. Appearing bosons particles correlate with dark matter. These particles have zero spin or two. Their spectrum of mass turns out to be continuous, the maximum mass of the particle is given. The assumption of energy transmission by a quantum dissemination environment and the microwave hypothesis is consistently explained by many observation results. First of all, it is a red shift in galaxies spectra and the presence of a large cosmic microwave background with its intensity variations at relatively small time intervals. DM particles due to the gravitational interaction return the energy back to its baryonic sources. At the same time, the dark component additionally fills the central supermassive object of the galaxy, which in the quasar phase conducts utilization of star waste with hydrogen regeneration. It is DM that provides large energies allocated by quasars. Given the small part of the star matter, turning into the SER, it is shown that the particles of DM are a medium with a relatively low temperature. It is concluded that DM and SER are a comprehensive dynamic environment in which the baryon matter of the universe lives and develops. Through this two-component "ocean" of matter, all major metabolic processes supporting the "life" of galaxies are carried out.

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