Parameter estimation method for a linear frequency modulation signal with a Duffing oscillator based on frequency periodicity

In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.

Evolutionary games and spatial periodicity

Spatial interactions are considered an important factor influencing a variety of evolutionary processes that take place in structured populations.It still remains an open problem to fully understand evolutionary game dynamics on networks except for certain limiting scenarios such as weak selection.Here we study the evolutionary dynamics of spatial games under strong selection where strategy evolution of individuals becomes deterministic in a fashion of winners taking all.We show that the long term behavior of the evolutionary process eventually converges to a particular basin of attraction,which is either a periodic cycle or a single fixed state depending on specific initial conditions and model parameters.In particular,we find that symmetric starting configurations can induce an exceedingly long transient phase encompassing a large number of aesthetic spatial patterns including the prominent kaleidoscopic cooperation.Our finding holds for any population structure and a broad class of finite games beyond the Prisoner’s Dilemma.Our work offers insights into understanding evolutionary dynamics of spatially extended systems ubiquitous in biology and ecology.

ANN-Time Varying GARCH Model for Processes with Fixed and Random Periodicity

Financial Time Series Forecasting is an important tool to support both individual and organizational decisions. Periodic phenomena are very popular in econometrics. Many models have been built aiding capture of these periodic trends as a way of enhancing forecasting of future events as well as guiding business and social activities. The nature of real-world systems is characterized by many uncertain fluctuations which makes prediction difficult. In situations when randomness is mixed with periodicity, prediction is even much harder. We therefore constructed an ANN Time Varying Garch model with both linear and non-linear attributes and specific for processes with fixed and random periodicity. To eliminate the need for time series linear component filtering, we incorporated the use of Artificial Neural Networks (ANN) and constructed Time Varying GARCH model on its disturbances. We developed the estimation procedure of the ANN time varying GARCH model parameters using non parametric techniques.

NONLINEAR DYNAMICS MODFLING OF MECHANICAL PERIODICITY OF END DIASTOLIC VOLUME OF LEFT VENTRICLE

The cardiovascular system with a lumped parameter model is treated, in which the Starling model is used to simulate left ventricle and the four-element Burattini & Gnudi model is used in the description of arterial system. Moreover, the feedback action of arterial pressure on cardiac cycle is taken into account. The phenomenon of mechanical periodicity (MP) of end diastolic volume (EDV) of left ventricle is successfully simulated by solving a series of one-dimensional discrete nonlinear dynamical equations. The effects of cardiovascular parameters on MP is also discussed.

THE 152-DAY PERIODICITY OF THE OCCURRENCE RATE OF SOLAR MICROWAVE BURSTS

It has been found for a long time, with analysing the variation of the relative number of sunspot, that there exist the periodicity of 11 years in solar activity. With the deepening research of the varied solar active phenomena, a series of periodicities with different periods have been also found in solar activity. For example, there is the periodicity of about 80 days for the occurrence, rate of proton flares for solar activity cycles 19 and 20 found by Ai and Fan ci:i at 1974. Recently a periodicity of about 152 days of the occurrence rate of solar flares has been proposed by some authors. a3’5】7:i The existence of this periodicity hsa been proved in the various solar flares. In this paper using the data of solar microwave bursts from January 1986 to December 1988, a Fourier analysis of the occurrence rate of solar microwave bursts has been made. There was no periodicity for the occurrence rate of solar microwave bursts of about 152 days found. This is a new result for solar cycle 22 in the first

Detecting Periodicity Associated with the Alpha-Helix Structure Using Fourier Transform

Alpha helix is a common type of secondary structure in the protein structure that consists of repeating helical turns. Patterns in the protein sequences that cause this repetitive pattern in the structure have long been sought. We used the discrete Fourier transform (DFT) to detect the periodicity signals correlated to the helical structure. We studied the distribution of multiple properties along the protein sequence, and found a property that showed strong periodicity correlated with the helical structure. Using a short-time Fourier transform (STFT) method, we investigated the amplitude of the periodical signals at each amino acid position. The results show that residues in the helix structure tend to display higher amplitudes than residues outside of the helices. This tendency is dramatically strengthen when sequence profiles obtained from multiple alignment were used to detect the periodicity. A simple method that predicted helices based on the amplitude yielded overall true positive rate (TPR) of 63%, 49% sensitivity, 72% specificity, and 0.22 Matthews Correlation Coefficient (MCC). The performance seemed to depend on the length of helices that the proteins had.

The Genesis of Prime Numbers—Revealing the Underlying Periodicity of Prime Numbers

Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural numbers with no laws except that of chance. Questions about prime numbers have been perplexing mathematicians over centuries. How to efficiently predict greater prime numbers has been a great challenge for many. Most of the previous studies focus on how many prime numbers there are in certain ranges or patterns of the first or last digits of prime numbers. Honestly, although these patterns are true, they help little with accurately predicting new prime numbers, as a deviation at any digit is enough to annihilate the primality of a number. The author demonstrates the periodicity and inter-relationship underlying all prime numbers that makes the occurrence of all prime numbers predictable. This knowledge helps to fish all prime numbers within one net and will help to speed up the related research.

The Construction of Natural Disaster Database of Alxa and Periodicity Analysis

A compilation of all meaningful historical data of natural-disasters taken place in Alxa of inner-Mongolia is used here for the construction of a 65 Ma high precision database.The data in the database are divided into subsets according to the types

PERIODICITY AND STRICT OSCILLATION FOR GENERALIZED LYNESS EQUATIONS

A generalized Lyness equation is investigated as follows x n+1 =x n(a+bx n )x n-1 , n=0,1,2,…,(*) where a,b∈[0,∞) with a+b>0 and where the initial values x -1 ,x 0 are arbitrary positive numbers. Some new results, mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq(*),are obtained. As an application, the results solve an open problem presented by G.Ladas.

Transverse Vibration Analysis of Concentrated Mass-Loaded Thin Circular Plate Based on Strcutural Circumferential Periodicity

The structural circumferential periodicity of inertial excitation produced by concentrated mass was utilized to establish the mathematical model of thin circular plate carrying eccentric concentrated mass and to analyze its transverse vibration. The fundamental frequency coefficient, natural frequency and mode shape function are determined by this method. A clamped thin circular plate was taken as an example to study the mass effect on the vibrating system.Comparison between the present results and published ones exhibits excellent agreement, which shows that the analytical method in this paper can be used to predict the transverse vibration parameters accurately.

Assessing discharge periodicity in mountain catchments using classified environmental conditions(Tatra Mountains, Poland)

The periodicity of a river expressed in cycles of various lengths(monthly, seasonal,multiannual) is a result of climatic factors and overlapping environmental conditions within its catchment. In uncontrolled or poorly surveyed catchments, it is very difficult to determine the duration of a stream’s hydrological activity. This is especially relevant for catchments with complicated water circulation in karstic rocks. The present study concerns the small catchment of the Str??yski Potok river located in the area of the Tatra National Park, in the Western Tatras. The observation period covered the 2015 hydrological year, which differed hydrologically from average conditions. This study aims to develop a simple method to explain the processes shaping the mountain stream discharge periodicity. The research employed periodic field observations linked with climatic and non-climatic factors. Environmental conditions were assessed as four classes reflecting their influence on appearance or disappearance of mountain stream water. Class boundaries were the values of quartiles. The degree of correspondence between environmental factors and stream field observations was described via the Index DC(Degree Correspondence Index) approach.Complete correspondence(Index DC =0) was found in 23% catchments, a weak relationship between conditions favouring discharge and actual condition(Index DC=-1, +1) was noted within 11 catchments,while in 9 catchments, no such relationship was found(Index DC =-2, +2). The obtained results indicate a correspondence or lack thereof between the environmental potential of the catchment and its discharge periodicity. The discrepancies between the assessment of the influence of climatic and nonclimatic factors and the data collected during field observations provide a basis for more detailed studies.Continuation of these studies based on the proposed classifications will allow for a more complete explanation of water disappearance in river channels and the determination of their short-and long-term discharge periodicity.

Transcriptomic and epigenomic remodeling occurs during vascular cambium periodicity in Populus tomentosa

Trees in temperate regions exhibit evident seasonal patterns,which play vital roles in their growth and development.The activity of cambial stem cells is the basis for regulating the quantity and quality of wood,which has received considerable attention.However,the underlying mechanisms of these processes have not been fully elucidated.Here we performed a comprehensive analysis of morphological observations,transcriptome profiles,the DNA methylome,and miRNAs of the cambium in Populus tomentosa during the transition from dormancy to activation.Anatomical analysis showed that the active cambial zone exhibited a significant increase in the width and number of cell layers compared with those of the dormant and reactivating cambium.Furthermore,we found that differentially expressed genes associated with vascular development were mainly involved in plant hormone signal transduction,cell division and expansion,and cell wall biosynthesis.In addition,we identified 235 known miRNAs and 125 novel miRNAs.Differentially expressed miRNAs and target genes showed stronger negative correlations than other miRNA/target pairs.Moreover,global methylation and transcription analysis revealed that CG gene body methylation was positively correlated with gene expression,whereas CHG exhibited the opposite trend in the downstream region.Most importantly,we observed that the number of CHH differentially methylated region(DMR)changes was the greatest during cambium periodicity.Intriguingly,the genes with hypomethylated CHH DMRs in the promoter were involved in plant hormone signal transduction,phenylpropanoid biosynthesis,and plant–pathogen interactions during vascular cambium development.These findings improve our systems-level understanding of the epigenomic diversity that exists in the annual growth cycle of trees.

RBF-FD Method for Some Dispersive Wave Equations and Their Eventual Periodicity

In this paper,we approximate the solution and also discuss the periodic behavior termed as eventual periodicity of solutions of(IBVPs)for some dispersive wave equations on a bounded domain corresponding to periodic forcing.The constructed numerical scheme is based on radial kernels and local in nature like finite difference method.The temporal variable is executed through RK4 scheme.Due to the local nature and sparse differentiation matrices our numerical scheme efficiently recovers the solution.The results achieved are validated and examined with other methods accessible in the literature.

Periodicity and Solution of Rational Recurrence Relation of Order Six

Difference equations or discrete dynamical systems is diverse field whose impact almost every branch of pure and ap- plied mathematics. Every dynamical system an+1=f(an) determines a difference equation and vise versa. We ob-tain in this paper the solution and periodicity of the following difference equation. xn+1=(xnxn-2xn-4)/(xn-1xn-3xn-5, (1) n=0,1,... where the initial conditions x-5,x-4,x-3,x-2,x-1 and x0 are arbitrary real numbers with x-1,x-3 and x-5 not equal to be zero. On the other hand, we will study the local stability of the solutions of Equation (1). Moreover, we give graphically the behavior of some numerical examples for this difference equation with some initial conditions.

Trend and Periodicity of Temperature Time Series in Ontario

The trends and periodicities in the annual and seasonal temperature time series at fifteen weather stations within Ontario Great Lakes Basins have been analyzed, for the period 1941-2005, using the statistical analyses (Fourier series analysis, t-test, and Mann-Kendall test). The stations were spatially divided into three regions: northwest (NW), southwest (SW), and southeast (SE) to evaluate spatial variability in temperature. The results of the study reveal that the annual maximum mean temperature showed increasing trend for NW, and mixed trends for SW and SE regions. The variability was found to be more for northern stations as compared to southern stations for annual extreme minimum temperature. In addition, the trend slope per 100 years for the average annual extreme minimum temperature increased within the range of -0.8°C (Stratford) to 15°C (Porcupine). The seasonal analysis demonstrated that extreme maximum temperature has an increasing trend and maximum mean temperature has a decreasing trend during summer and winter. The extreme minimum temperature for winter illustrated an increasing trend (90%) with 22% statistically significant for NW region. For the SW region, the trend is also increasing (80%) for most of the temperature variables and 25% of temperature data were significantly increased in the SW region. The SE region stations showed overall very clear increasing trends (95%) for all the temperature variables. The data also showed that 47% of data were statistically significant in the SE region. The analysis of variance accounted for by trend, significant periodicities, and random component show that the pattern is similar for the percent of variance accounted for periodicities, and random component contribute dominantly for the four temperature variables and frost free days (FFD) for all three regions. Overall, the study reveals that the extreme minimum temperature is increasing annually and seasonally, with statistically significant at many stations.

Asymptotic Periodicity in the Fecally-Orally Epidemic Model in a Heterogeneous Environment

To understand the influence of seasonal periodicity and environmental heterogeneity on the transmission dynamics of an infectious disease, we consider asymptotic periodicity in the fecally-orally epidemic model in a heterogeneous environment. By using the next generation operator and the related eigenvalue problems, the basic reproduction number is introduced and shows that it plays an important role in the existence and non-existence of a positive T-periodic solution. The sufficient conditions for the existence and non-existence of a positive T-periodic solution are provided by applying upper and lower solutions method. Our results showed that the fecally-orally epidemic model in a heterogeneous environment admits at least one positive T-periodic solution if the basic reproduction number is greater than one, while no T-periodic solution exists if the basic reproduction number is less than or equal to one. By means of monotone iterative schemes, we construct the true positive solutions. The asymptotic behavior of periodic solutions is presented. To illustrate our theoretical results, some numerical simulations are given. The paper ends with some conclusions and future considerations.

Sun, Earth, radioactive ore: Common periodicity

The study of natural radioactivity of objects which are able to change their temporal timing feature is presented. It is of interest to compare the latest data on the activity of the Sun and the periodicity of solar neutrinos and the temporal characteristics of the radioactive source. That is, to conduct a search for the possible influence of external sources for radioactivity. There are cycles 5 min, 18 min and 53 min found in solar physics. The cycle of 27 days corresponds to the activity of the Sun. During of the solar activeity these temporal pulsations are lost in a strong variation of solar wind (Neugebauer, NASA). The Stanford University scientists (P. Starrek, G. Valter and M. Vitlend) have found the cycle of 28.4 days as pulsations of the solar neutrinos. Neutrinos come from the depths of the Sun and they tell about the frequency of oscillations of solar bowels. It is also seen online: Kostyantynivska L. V. Solar activity. Search experiment is better to have a known but modified experiment. Experiments on monitoring natural radioactivity and the possible influence from the Sun were previously carried out by measuring the variations of the gamma-ray sample of ore from the TransBaikal uranium deposit;the characteristics of the sample are known. The spectrum of temporal variations in the activity of the sample Zabaikalskaya radioactive ore contains peaks which coincide with the period of natural oscillations of the Sun. The capture cross section of the radioactive heavy deformed nucleus in time decay increases in many orders and is able to interact with the stream of solar neutrinos which are modulated by own oscillations of the Sun. The picks of spectrum of long-period oscillations of the Earth exceed its own contain peaks that match the value with an accuracy of 1% 3% with peaks of its own oscillations of the Sun. The mechanism of excitation of these oscillations is similar to the nature of variations in the activity of a radioactive sample of ore. These effects are included in the mechanisms of interaction of the Earth—the Sun systems and impact on seismicity;search problem of existing natural nuclear reactor inside Earth core.

Diurnal Periodicity of the Expression of Genes Involved in Monolignol Biosynthesis in Differentiating Xylem of Cryptomeria japonica

The cell wall in wood is mainly composed of three components: cellulose, hemicellulose and lignin. According to electron microscopy observations of the innermost surface of cell walls in the tracheids of Cryptomeria japonica , cellulose microfibrils are deposited during the day and a matrix containing hemicellulose is deposited at night. This indicates that the deposition of cell wall components exhibits diurnal periodicity. To gain new insights into the diurnal periodicity of lignin deposition not revealed by microscopic observations, we examined diurnal fluctuations in the expression of genes involved in monolignol biosynthesis in C. japonica saplings grown in the field and in growth chambers under a 12 h light/dark cycle. In the field experiment, two gene expression peaks were observed daily, at dusk and dawn. In the growth chamber experiment, two daily peaks were observed 0 h and 6 - 9 h after the light switched on.

The Proof of Riemann Hypothesis, the Key to the Door Is the Periodicity

The Riemann hypothesis is a well-known mathematical problem that has been in suspense for 162 years. Its difficulty lies in the fact that it is involved in an infinite integral which includes infinite series with complex variables. To detour this is in vain, since all the messages are hid in it. To unscramble them, there is a totally new idea, that is, the “periodicity”! By investigating the numerical approximate values of zero points, an explicit distribution law on the critical line was found. To accord with this, a periodic form for the real part of Xi function was constructed and rigidly proved. The Riemann hypothesis can be divided into three progressive propositions. The first proposition (the number of zero points in the critical strip satisfies a certain estimation) had been proved in 1905. The second proposition (the number of zero points on the critical line satisfies the same estimation as in the critical strip) is ever in suspense. It can be solved perfectly with the newly found “periodicity”. The third proposition (all the nontrivial zero points are on the critical line), that is, the Riemann hypothesis, is also true. The proof is a combination of the symmetry, monotonicity, periodicity of the Xi function and the extremum principle of the harmonic functions. It is the moment to draw full stop for this suspending problem.

Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.