Effect Of Random Fluctuations Research Articles

Dynamical responses for a vertical vibration model of a four-roller cold rolling mill under combined stochastic and harmonic excitations

Considering that random fluctuations can affect the rolling process of cold rolling mills, leading to abnormal cold mill performance and defects in the rolled product. Therefore, it is crucial to study the influence of random fluctuations on the system of cold rolling mills. In this paper, taking a model of the vertical vibration of a four-roller cold rolling mill under harmonic excitation as a prototype class for a real system, the effects of random fluctuations on the system response are analyzed. Firstly, based on the deterministic vertical vibration model of a four-roller cold rolling mill under harmonic excitation, a stochastic vertical vibration model of a four-roller cold rolling mill with random fluctuation as Gaussian white noise is introduced. Subsequently, the vertical vibration model of a four-roller rolling mill is theoretically analyzed by the averaging method and the stochastic averaging method, respectively. The effectiveness of the proposed theoretical method is verified by numerical simulation results, and the influences of harmonic excitation and random excitation on the system response are also investigated in detail. Finally, the results show that the noise induces the occurrence of stochastic transitions and bifurcations, and the steady-state probability density function and time history diagrams are given to further explain the existence of these dynamic phenomena. The related research can provide theoretical guidance for the realization of vibration control and reliability design in the four-roller cold rolling mill system.

Vaccination as an alternative to non-drug interventions to prevent local resurgence of COVID-19

BackgroundWhile a COVID-19 vaccine protects people from serious illness and death, it remains a concern when and how to lift the high-cost and strict non-pharmaceutical interventions (NPIs). This study examined the joint effect of vaccine coverage and NPIs on the control of local and sporadic resurgence of COVID-19 cases.MethodsBetween July 2021 and January 2022, we collected the large-scale testing information and case number of imported COVID-19 patients from the website of the National Health Commission of China. A compartment model was developed to identify the level of vaccine coverage that would allow safe relaxation of NPIs, and vaccination strategies that can best achieve this level of coverage. We applied Monte Carlo simulation 50 000 times to remove random fluctuation effects and obtain fitted/predicted epidemic curve based on various parameters with 95% confidence interval at each time point.ResultsWe found that a vaccination coverage of 50.4% was needed for the safe relaxation of NPIs, if the vaccine effectiveness was 79.3%. The total number of incidence cases under the key groups firstly strategy was 103 times higher than that of accelerated vaccination strategy. It needed 35 months to fully relax NPIs if the key groups firstly strategy was implemented, and 27 months were needed with the accelerated vaccination strategy. If combined the two strategies, only 8 months are needed to achieve the vaccine coverage threshold for the fully relaxation of NPIs. Sensitivity analyses results shown that the higher the transmission rate of the virus and the lower annual vaccine supply, the more difficult the epidemic could be under control. When the transmission rate increased 25% or the vaccination effectiveness rate decreased 20%, 33 months were needed to reduce the number of total incidence cases below 1000.ConclusionsAs vaccine coverage improves, the NPIs can be gradually relaxed. Until that threshold is reached, however, strict NPIs are still needed to control the epidemic. The more transmissible SARS-CoV-2 variant led to higher resurgence probability, which indicates the importance of accelerated vaccination and achieving the vaccine coverage earlier.Graphical

Effect of random fluctuations on minimizing the complexity of universal asynchronous cellular automata

Asynchronous cellular automata (ACAs) are cellular automata (CAs) that allow cells to undergo state transitions independently and randomly. Notwithstanding the unpredictable update timings of each cell, universal computation can be carried out on ACAs via the embedding of logic circuits into cell spaces, like the ACA with von Neumann neighborhood that uses 5 cell states and 55 transition rules (Lee et al. (2003)). Recently, the complexity in terms of the numbers of cell states and rules has been reduced via the use of local configurations representing signals that may fluctuate between moving forward and backward in the cell space. This forms the basis for the implementation of simple circuit elements in ACAs that can exploit signal fluctuations. Nevertheless, universal ACA still appears much more complex than the best synchronous CAs found to date, e.g., the 2-state and 3-rule CA (Banks 1970). This paper aims to propel the fluctuation-based scheme further, by proposing a novel ACA with von Neumann neighborhood which requires merely 3 cell states and 10 rules. The universality of our ACA is shown by implementing a new set of circuit elements that are able to exploit fluctuations, as well as a special circuitry to conduct the crossing of signals in the two-dimensional cell space. The further reduction in the numbers of both cell states and rules demonstrates that random fluctuations may play an important role in pursuing the minimal complexity of universal ACAs.

Effects of Random Migration on the Growth of the Population of a Biological System

The problem under consideration is an example of the anomalous behavior of systems with an explosive pattern of behavior in a random medium. The growth is modeled of a population of microorganisms as a result of their migration into a closed region with favorable conditions for regeneration. The initial number of microorganisms inside the region under consideration can be zero and the number of organisms outside the region is a random quantity. The rate of growth of the population as a result of reproduction is proportional to the squared size of the population, and the rate of extinction of the population is proportional to the population size. The microorganisms arrive inside the region due to diffusion, and the condition for mass transfer is assigned at the region′s boundary. As a result of averaging over the region′s volume, an equation has been obtained for the average size of the population. For a stationary number of microorganisms outside the region, a new class has been obtained of analytical solutions describing the change in the size of the population inside the region depending on the biological characteristics of the system and parameters of migration. The effects of random fluctuations in the number of microorganisms outside the region under consideration are studied on the basis of two approaches. In the first case, a closed-form equation was obtained for the probability density function of a random number of microorganisms inside the region. The effects of random migration on the population′s growth dynamics have been investigated on the basis of a closed system for the first and second moments of the fluctuation in the number of microorganisms. In the second case, direct modeling was implemented of the behavior of a random size of the population inside the region on the basis of solution of a stochastic ordinary differential equation. It has been shown that random fluctuations may result in anomalous growth of the microbiological population size compared to the determinate case.

Effects of random fluctuations in alpha oscillations on orientation detection: an EEG study

Effects of random fluctuations in alpha oscillations on orientation detection: an EEG study

APPLICATION OF SMOOTHING METHODS FOR FORECASTING PRODUCTION VOLUME

The object of the research is the enterprise LLC TPK «Terra» – the leading domestic manufacturer of high-quality protective coatings for industrial use for corrosion protection of metal structures and reinforced concrete structures. Now the company is open to planning future orders, the appropriate use of capacity and the expansion of production capacity. The paper conducted a system analysis of this enterprise by developing a functional model of processes and its decomposition with decomposition to the second level of detail. As a result, the task of forecasting the volume of release of anti-corrosion coatings, preventing the destruction of metal structures and mechanisms. This task is relevant both for the enterprise itself and for meeting the demand in the sales market. The most effective mathematical models that can be used to predict the development of production processes are models based on time series. One of the most common methods for predicting the performance of such series are smoothing methods that are used to reduce the effect of random fluctuations. The problem is solved by the methods of exponential and adaptive smoothing. To check the adequacy of the models obtained, the test of the series (determination of randomness of deviations from the trend), the criterion of the peaks (checking the equality of the mathematical expectation), the R/S criterion (determining the correspondence of the distribution of the residual component to the normal law), the Durbin–Watson criterion (determining the independence of the residual сomponents). The analysis of each prediction model obtained was carried out, and the quality of forecasts was also assessed. Conclusions are made regarding the further manufacture of products based on predicted values. The proposed model has a practical orientation and can be used in tasks related to forecasting in the conditions of industrial enterprises.

Synchronization of complex dynamical networks with random coupling delay and actuator faults

This paper addresses the issue of passivity-based synchronization problem for a family of Markovian jump neutral complex dynamical networks (NCDNs) with coupling delay and actuator faults. Also, by considering the effect of random fluctuation in complex dynamical network systems, the occurrence of coupling delay are taken in terms of a stochastic distribution, which obeys the Bernoulli distribution. To handle the fault effects in actuators of proposed complex network systems, an actuator fault model is considered. The main objective of this paper is to develop a robust state feedback controller such that for all possible actuator failures and random coupling delays, all nodes of the proposed Markovian jump NCDNs is globally asymptotically synchronized to the reference node in mean square sense and guarantee the output strict passivity performance. By developing a suitable Lyapunov–Krasovskii functional and utilizing the Wirtinger-based integral inequality, the required a set of sufficient conditions for the synchronization of proposed system is established in form of linear matrix inequalities. Finally, three numerical examples including a 3-dimensional Lorenz chaotic model are provided to demonstrate the correctness and superiority of the proposed control scheme.

How bifurcations affect functional connectivity in finite-size neural networks

Understanding how the functional connectivity of a neural network (i.e. the statistical dependencies among different neurons) depends upon its anatomical connectivity and how it is modulated by other network parameters is a central topic in neuroscience [1]. However, only few analytical investigations of functional connectivity in network models have been reported [2]. A difficulty for such analytical studies is that they require in principle characterizing the bifurcation points (i.e. the parameter values at which the network undergoes a sudden change in dynamics) and how functional connectivity changes close to such points. Given that biological networks have a finite number of neurons, it is also important to develop such analytical studies without relying only on large network approximations that neglect finite-size effects. To overcome these difficulties, here we developed a new approach to investigate the dynamics of finite-size networks composed by interconnected inhibitory and excitatory neurons. We applied this approach to a network of neurons described by voltage-based differential equations, with an input to each neuron provided by a deterministic current superimposed to a weak normally distributed stochastic component. To understand the interplay between the deterministic dynamics of the network and the effects of random fluctuations in a finite-size network, we proceeded in two steps. First, we neglected the stochastic component of the input and we performed a complete numerical and analytical bifurcation analysis while varying the deterministic inputs and the strength of the connections. We did this using the MatCont continuation package [3] and the analytical expressions of the Jacobian matrix eigenvalues. We found that our finite-size network displayed standard bifurcations such as saddle-node and Hopf manifolds. Specifically, these manifolds describe the input currents values for which equilibria collide and annihilate to each other, and for which self-sustained oscillations arise, respectively. Moreover, strong inhibition gave rise to additional branch point bifurcations: for highly negative synaptic weights, the system exhibited special multiple solutions characterized by heterogeneous membrane potentials. These particular solutions represent new finite-size effects not captured by large network approximations. Second, we inserted stochastic components into the input and studied the behaviour of the network under the effect of noise. Specifically, we used a new first-order perturbative method where the perturbative parameter is the standard deviation of the noise in the input. This technique allowed the analytical calculation of the cross-correlation between firing rates, and of the Fisher information about the external input carried by the network. Our analytical solutions showed that the neurons become independent when the deterministic component of the input is strong, while they become correlated for smaller current values lying on the saddle-node manifold. The latter is due to a counter-intuitive finite-size effect [4] that can be fully captured by our formalism. Furthermore, in our network strong correlations led to large Fisher information values, thus enhancing the encoding precision of the network with respect to the input variables. This also shows that reducing correlations among neurons activity does not imply an enhancement of the information encoding, as suggested in some studies [5].

The effect of random fluctuations in bottom bathymetry on acoustic coherence in shallow water

The loss of temporal coherence after long range propagation in shallow water is often studied as a consequence of sound speed variability from internal waves. Here, we add the complication of small amplitude and very long wavelength random fluctuations of bottom bathymetry. It is shown that the same range dependent sound speed fluctuations result in markedly different coherence times depending on acoustic wavelength and mode number—a first order effect. A range dependent PE code (MMPE) is used to predict temporal coherence for individual surface reflected-bottom-reflected (SRBR) mode arrivals. Here, a mode coherence calculation is developed and compared for varying RMS bathymetry. Temporal coherence is inferred from mode coherence. We find first order and /or low frequency modes are insensitive to the bottom but when the (sine of the mode angle approaches 1/10 of an acoustic wavelength) the modes structure in amplitude and phase is randomized and the signal decorrelate rapidly in time from just the slightest temporal variations in sound speed. It does not take much; just 1 m in 200 m of range will randomize all but the first mode at mid frequencies (0.5 to 1 kHz). Predictions are in close agreement with SW06 mode coherence measurements.

THE DISORDERING EFFECT ON THE ONE-DIMENSIONAL APPERIODIC OPTICAL SUPER-LATTICE IN MULTI-FREQUENCY SHG

A multi-frequency second harmonic generation (SHG) in one dimensional nonlinear aperiodic optical superlattice in the presence of linear spacers is considered. The effect of random fluctuations in the length of each layer on the output efficiency of SHG process is investigated, and the favorable percentage of fluctuation in the fabrication of aperiodic optical superlattice is obtained. Comparing perfect and fluctuated aperiodic structures, the researcher realized the decrease in the amount of output efficiency with the increase of fluctuation in the linear-nonlinear aperiodic crystals.

Estimation of the number of necessary beds for tuberculosis patients, in Japan

To estimate the number of necessary beds for tuberculosis patients in Japan from the view point of isolation of the source of infection. We calculated the number of necessary beds for tuberculosis cases separately for the initial phase and for the chronic excreters. For the initial phase we calculated by multiplying the number of detected tuberculosis cases and the duration of hospitalization. The number of detected cases is based on the figures in 2002 and the duration of hospitalization is assumed to be 90 days for sputum smear positive cases and 60 days for sputum smear negative cases. We calculated the number of necessary beds using the Monte Carlo simulation for each prefecture on the assumption that the incidence and the duration of diseases will be under the effect of random fluctuation with the Poisson's distribution for the number of cases and with the log normal distribution for the duration of hospitalization. We also considered the seasonal fluctuation. Our calculation revealed that around 6,413 beds would be necessary for the initial phase and 200-400 beds for chronic excreters in Japan. There are several prefectures which only requires less than 30 beds. Currently, Japan has around 17,000 beds secured for tuberculosis patients. Our calculation showed that this was much more than needed. In many areas, one ward will provide more than sufficient number of tuberculosis beds. Specialist consultation system must be improved because of the reduction in the number of TB cases treated at hospitals with TB wards and TB specialists. For the treatment of non-infectious TB, ambulatory DOT system, TB shelter and nursing care facilities would be necessary to guarantee compliance to treatment.

A Continuous-Time, Discrete-State Method for Simulating the Dynamics of Biochemical Systems

Computational systems biology is largely driven by mathematical modeling and simulation of biochemical networks, via continuous deterministic methods or discrete event stochastic methods. Although the deterministic methods are efficient in predicting the macroscopic behavior of a biochemical system, they are severely limited by their inability to represent the stochastic effects of random molecular fluctuations at lower concentration. In this work, we have presented a novel method for simulating biochemical networks based on a deterministic solution with a modification that permits the incorporation of stochastic effects. To demonstrate the feasibility of our approach, we have tested our method on three previously reported biochemical networks. The results, while staying true to their deterministic form, also reflect the stochastic effects of random fluctuations that are dominant as the system transitions into a lower concentration. This ability to adapt to a concentration gradient makes this method particularly attractive for systems biology-based applications.

Temporal Sequence Parameters in Isodistributional Surrogate Data: Model and Exact Expressions

In this paper, a set of formulae for the temporal spontaneous baroreceptor reflex (sBRR) sequence parameters in isodistributional (ID) surrogate data is derived. This is facilitated by representing successive positive or negative amplitude changes as a Markov chain model. The obtained analytical tool measures the effect of random fluctuations on the overall number of sequences, estimated from the original biomedical time series. The formulae are tested using ID surrogates of systolic blood pressure and pulse-interval signals recorded from 13 healthy male Wistar rats at baseline conditions.

Influence of Imperfect Internal Waves on Long-Range Underwater Acoustic Propagation

This work presents a numerical analysis of the effect of random fluctuations of internal waves on the chaotic dynamics of ray trajectories in ocean acoustics. The Eikonal equation is considered in a form of the second order, nonlinear ordinary differential equation. Random phase modulations in the form of zero mean Gaussian white noise are considered for modeling an imperfectly periodic single mode internal wave. It is shown that in the presence of random fluctuations the intersection of acoustic rays with the ocean surface occurs sooner and becomes more frequent than predicted by deterministic ocean models.

Influence of Uncertain Source Parameters on Strong Ground Motion Simulation with the Empirical Green's Function Method

A combined stochastic and Green's function approach was developed to simulate strong ground motions in Southwest Western Australia (SWWA) in a previous study. Although it was demonstrated that adopting the source parameters derived from other regions yielded reasonable simulation of ground motions in SWWA as compared with a few available strong motion records, the effect of source parameter variations on simulated ground motions was not known. This article performs a statistical study of the effects of random fluctuations of the seismic source parameters on simulated strong ground motions. The uncertain source parameters, i.e., stress drop ratio, rupture velocity, and rise time corresponding to the empirical source models are assumed to be the respective mean value of the parameter and normally distributed with an assumed coefficient of variation. The Rosenblueth's point estimate method [Rosenblueth, 1981] is used to calculate the statistics of the simulate ground motion parameters corresponding to different magnitudes and epicentral distances. The accuracy of the Rosenblueth's point estimate method in estimating the mean and standard deviation of ground motion PGA, PGV, and response spectrum is proven by simulating the ground motions from an ML6.0 and epicentral distance 100 km event with both the Rosenblueth's point estimate method and the Monte Carlo simulation method. A sensitivity analysis is preformed to investigate the effect of random fluctuations of each source parameters on strong ground motion simulation. A coefficient of variation model for ground motion parameters is developed based on the simulated data as a function of the variations of the three source parameters and earthquake magnitude, which can be used in probabilistic predictions of earthquake ground motions with uncertain source parameters.

Design Considerations for PD/SOI SRAM: Impact of Gate Leakage and Threshold Voltage Variation

We present a critical study of the impact of gate tunneling currents on the yield of 65-nm partially depleted/silicon-on-insulator (PD/SOI) SRAM designs. A new gate leakage monitor structure is developed to obtain device-specific gate leakage characteristics of the SRAM cells. This allows us to explore the design space accurately with reliable process information at an early stage. By relying on supply voltage-dependent analysis, it is shown that the gate-leakage impact on the cell yield can be nonmonotonic and substantial even for nondefective devices. It is also shown that design optimizations such as increased operating voltages or shorter hierarchical bitline architecture can help alleviate the gate-leakage impact on yield. Mixture importance sampling is used to estimate yield in terms of cell writability and stability. Threshold voltage variations to model random fluctuation effects are extrapolated from hardware results.

Four-wave mixing in fibers with randomly varying zero-dispersion wavelength

The effect of random fluctuations in the zero-dispersion wavelength is considered for fiber four-wave mixing. Theoretical expressions for average parametric gain, phase-conjugation conversion efficiency, and gain bandwidth are obtained and found to be in good agreement with experiments. Possible limitations on the noise figure in phase-sensitive amplifiers based on fiber four-wave mixing are also discussed.

Do random fluctuations in daily ration affect the growth rate of juvenile three‐spined sticklebacks?

The effect of random fluctuations in daily ration on the growth performance of individual juvenile three‐spined sticklebacks Gasterosteus aculeatus was studied in experiments lasting 21 days at 14°C and a photoperiod of 10L:14D. Two mean ration levels were used: a maintenance ration of 2%, and a high ration of 6% of initial body weight per day. For experimental fish, the daily ration varied randomly about the required mean value with a coefficient of variation of 33%. The controls received a constant daily ration. The experiment was replicated in winter (Dec.‐Jan.) and spring (Mar.‐Apr.). At a given ration, there was no significant difference between the specific growth rates of fish receiving constant or varying ration. Neither the final dry weight, final body water content nor final lipid content (% dry weight) differed significantly. As expected, ration had a significant effect on growth rate, final dry weight and body lipid and water content. There was a significant difference in mean growth rate between the winter and spring replicates. The growth rates observed in these experiments were compared with those predicted from a previously described empirical growth model developed for sticklebacks fed constant rations. The model underestimated mean growth rates.

Do random fluctuations in daily ration affect the growth rate of juvenile three-spined sticklebacks?

The effect of random fluctuations in daily ration on the growth performance of individual juvenile three-spined sticklebacks Gasterosteus aculeatus was studied in experiments lasting 21 days at 14°C and a photoperiod of 10L:14D. Two mean ration levels were used: a maintenance ration of 2%, and a high ration of 6% of initial body weight per day. For experimental fish, the daily ration varied randomly about the required mean value with a coefficient of variation of 33%. The controls received a constant daily ration. The experiment was replicated in winter (Dec.-Jan.) and spring (Mar.-Apr.). At a given ration, there was no significant difference between the specific growth rates of fish receiving constant or varying ration. Neither the final dry weight, final body water content nor final lipid content (% dry weight) differed significantly. As expected, ration had a significant effect on growth rate, final dry weight and body lipid and water content. There was a significant difference in mean growth rate between the winter and spring replicates. The growth rates observed in these experiments were compared with those predicted from a previously described empirical growth model developed for sticklebacks fed constant rations. The model underestimated mean growth rates.

Effect of coupling strength fluctuations on soliton switching in nonlinear couplers

We numerically analyse the effect of coupling strength random fluctuations on both dynamic and static soliton switching in symmetric nonlinear couplers. As in the cw case, the effect is generally found to be strong only near the switching regions. In the dynamical switching regime, the effect appears to increase with the length of the coupler at a rate twice as large for odd multiples of the linear coupling length, π/2, than for even ones. In the static case, the region of bistability shows the greatest change in the effect of random fluctuations, with a maximum at exactly the first bifurcation point. The solitons also appear to be quite stable against the random fluctuations in the sense that no pulse distortion or emission of dispersive radiation was detected.