Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

Logical stochastic resonance in a cross-bifurcation non-smooth system

This paper investigates logical stochastic resonance(LSR)in a cross-bifurcation non-smooth system driven by Gaussian colored noise.In this system,a bifurcation parameter triggers a transition between monostability,bistability and tristability.By using Novikov's theorem and the unified colored noise approximation method,the approximate Fokker-Planck equation is obtained.Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations.We simulate the logic operation of the system in the bistable and tristable regions respectively.We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter.Furthermore,it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region,since the tristable region is more sensitive to noise than the bistable one.

Target acquisition performance in the presence of JPEG image compression

This paper presents an investigation on the effect of JPEG compression on the similarity between the target image and the background,where the similarity is further used to determine the degree of clutter in the image.Four new clutter metrics based on image quality assessment are introduced,among which the Haar wavelet-based perceptual similarity index,known as HaarPSI,provides the best target acquisition prediction results.It is shown that the similarity between the target and the background at the boundary between visually lossless and visually lossy compression does not change significantly compared to the case when an uncompressed image is used.In future work,through subjective tests,it is necessary to check whether this presence of compression at the threshold of just noticeable differences will affect the human target acquisition performance.Similarity values are compared with the results of subjective tests of the well-known target Search_2 database,where the degree of agreement between objective and subjective scores,measured through linear correlation,reached a value of 90%.

Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.

Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

In this paper, the effect of every parameter （including p, q, r, λ, τ） on the mean first-passage time （MFPT） is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that （1） the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, （2） suppression appears on the curve of the MFPT with small λ （e.g. λ 〈 0.5） but there is a peak on the curve of the MFPT when λ is big （e.g. λ 〉 0.5）, and （3） with different values of r （e.g. r = 0.1, 0.5, 1.5）, the effort of τ on the MFPT is diverse.

Could one single dichotomous noise cause resonant activation for exit time over potential barrier?

This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.

The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

Bayesian Reliability Modeling and Assessment Solution for NC Machine Tools under Small-sample Data

Although Markov chain Monte Carlo（MCMC） algorithms are accurate, many factors may cause instability when they are utilized in reliability analysis; such instability makes these algorithms unsuitable for widespread engineering applications. Thus, a reliability modeling and assessment solution aimed at small-sample data of numerical control（NC） machine tools is proposed on the basis of Bayes theories. An expert-judgment process of fusing multi-source prior information is developed to obtain the Weibull parameters＇ prior distributions and reduce the subjective bias of usual expert-judgment methods. The grid approximation method is applied to two-parameter Weibull distribution to derive the formulas for the parameters＇ posterior distributions and solve the calculation difficulty of high-dimensional integration. The method is then applied to the real data of a type of NC machine tool to implement a reliability assessment and obtain the mean time between failures（MTBF）. The relative error of the proposed method is 5.8020×10-4 compared with the MTBF obtained by the MCMC algorithm. This result indicates that the proposed method is as accurate as MCMC. The newly developed solution for reliability modeling and assessment of NC machine tools under small-sample data is easy, practical, and highly suitable for widespread application in the engineering field; in addition, the solution does not reduce accuracy.

Predicting dynamics of soil organic carbon mineralization with a double exponential model in different forest belts of China

The dynamics of soil organic carbon （SOC） was analyzed by using laboratory incubation and double exponential model that mineralizable SOC was separated into active carbon pools and slow carbon pools in forest soils derived from Changbai and Qilian Mountain areas. By analyzing and fitting the CO2 evolved rates with SOC mineralization, the results showed that active carbon pools accounted tor 1.0% to 8.5% of SOC with an average of mean resistant times （MRTs） for 24 days, and slow carbon pools accounted for 91% to 99% of SOC with an average of MRTs for 179 years. The sizes and MRTs of slow carbon pools showed that SOC in Qilian Mountain sites was more difficult to decompose than that in Changbai Mountain sites. By analyzing the effects of temperature, soil clay content and elevation on SOC mineralization, results indicated that mineralization of SOC was directly related to temperature and that content of accumulated SOC and size of slow carbon pools from Changbai Mountain and Qilian Mountain sites increased linearly with increasing clay content, respectively, which showed temperature and clay content could make greater effect on mineralization of SOC.

Erythropoietin reduces apoptosis of brain tissue cells in rats after cerebral ischemia/reperfusion injury:a characteristic analysis using magnetic resonance imaging

Some in vitro experiments have shown that erythropoietin （EPO） increases resistance to apoptosis and facilitates neuronal survival follow- ing cerebral ischemia. However, results from in vivo studies are rarely reported. Perfusion-weighted imaging （PWI） and diffusion-weighted imaging （DWI） have been applied successfully to distinguish acute cerebral ischemic necrosis and penumbra in living animals; therefore, we hypothesized that PWI and DWI could be used to provide imaging evidence in vivo for the conclusion that EPO could reduce apoptosis in brain areas injured by cerebral ischemia/reperfusion. To validate this hypothesis, we established a rat model of focal cerebral ischemia/ reperfusion injury, and treated with intra-cerebroventricular injection of EPO （5,000 U/kg） 20 minutes before injury. Brain tissue in the ischemic injury zone was sampled using MRI-guided localization. The relative area of abnormal tissue, changes in PWI and DWI in the ischemic injury zone, and the number of apoptotic cells based on TdT-mediated dUTP-biotin nick end-labeling （TUNEL） were assessed. Our findings demonstrate that EPO reduces the relative area of abnormally high signal in PWI and DWI, increases cerebral blood volume, and decreases the number of apoptotic cells positive for TUNEL in the area injured by cerebral ischemia/reperfusion. The experiment pro- vides imaging evidence in vivo for EPO treating cerebral ischemia/reperfusion injury.

Investigation of Influence of Winding Structure on Reliability of Permanent Magnet Machines

Winding is an important part of the electrical machine and plays a key role in reliability.In this paper,the reliability of multiphase winding structure in permanent magnet machines is evaluated based on the Markov model.The mean time to failure is used to compare the reliability of different windings structure.The mean time to failure of multiphase winding is derived in terms of the underlying parameters.The mean time to failure of winding is affected by the number of phases,the winding failure rate,the fault-tolerant mechanism success probability,and the state transition success probability.The influence of the phase number,winding distribution types,multi three-phase structure,and fault-tolerant mechanism success probability on the winding reliability is investigated.The results of reliability analysis lay the foundation for the reliability design of permanent magnet machines.

Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first- passage time （MFPT） of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kraraers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.

Soil carbon pools of six ecological regions of the United States

Mineralisable soil organic carbon(SOC)pools vary with ecosystem type in response to changes in climate,vegetation and soil properties.Understanding the effect of climate and soil factors on SOC pools is critical for predicting change over time.Surface soil samples from six ecoregions of the United States were analyzed for permanganate oxidizable C(KMnO4-C)and mineralizable C pools.Variations of SOC ranged from 7.9 mg g^-1(Florida site)to 325 mg g^-1(Hawaii site).Mineralisable C pools and KMnO4-C were highest in soils from the Hawaii site.Mean annual precipitation explains SOC and resistant C pool variations.Clay content was related to mineralisable active C pools and bacterial abundance.Mean annual precipitation and clay content are potential variables for predicting changes in SOC pools at large spatial scales.

Reliability analysis of a two-dependent-unit parallel system with a standby unit

A parallel system with two active components and a cold standby unit is studied in this paper. The two simultaneously working components are dependent and the copula function is used to model their dependence. An explicit expression is obtained for the mean time to failure of the system in terms of the copula function and marginal lifetime distributions in two different cases. As an application,numerical calculations are presented corresponding to two different copula functions and marginal lifetime distributions.

Numerical investigation of the effect of transitory strand opening on mixing in a multistrand tundish

In a multistrand,the outlet near the inlet produces short circuiting flow.This leads to the formation of dead zones inside the tundish,and consequently,the mean residence time decreases.In the present study,numerical investigation of mixing inside a delta shaped tundish with sloping boundaries was carried out by solving the Navier-Stokes equation and employing the standard turbulence model.To decrease the dead zone volume inside the tundish,the effect of closing the outlet near the inlet for a small amount of time and further opening it on the mixing behavior of the tundish was studied.The outlets near the inlet were closed for varying amount of time,and the transient analysis of fluid flow and the tracer dispersion study were carried out to find the mixing parameters of the tundish,namely,mean residence time and the ratio of mixed to dead volume of the tundish.An optimum closure time of the near outlet has been found,which yields best mixing inside the tundish.The numerical code was validated against the experimental observation by performing the tracer dispersion study inside a multistrand tundish and the reasonably good match between the experimental and numerical results in terms of residence time distribution （RTD） curves.The results obtained from the present study confirm the strong role of choosing the right time for opening and closing the outlets to get improved characteristics for the fluid flow and mixing behavior of the tundish.The educational version of computational fluid dynamics （CFD） software PHOENICS was used to solve the governing equations and interpret the results in different forms.

MP-RAID: Mirroring and parity protected disk array

Redundant array of inexpensive disk （RAID）10 is known as the most reliable disk array architecture to tolerate up to half of total disk failures, but failure of two disks in the same mirror set still results in data loss. In this paper, we propose a new disk array architecture, mirroring and parity protected RAID （MP-RAID）, which combines both mirroring and parity techniques to further improve reliability of disk arrays. The main idea behind MP-RAID is to protect the data by both mirroring and parity techniques： keep two copies of data in the same mirror set and update the parity block in the log disk within the same parity groups. Reliability analysis shows that the reliability of MP-RAID, in terms of mean time to data loss （MTTDL）, is much better than RAID10 and RAID5.

Study of Asymmetric Polling System with Two Message Classes

A novel mixed polling system with multiple stations is considered. Each station produces two classes of messages served with different disciplines. The real time message served with exhaustive service discipline and the unreal time message served with gated service discipline. Using an iterative method, the exact mean waiting times for both message classes are derived. The influence of the gate location of the message class served by the gated service discipline on the mean waiting time is also analyzed. The analytical results are verified with simulation method and agree well with simulation results.

Random walks in generalized delayed recursive trees

Recently a great deal of effort has been made to explicitly determine the mean first-passage time （MFPT） between two nodes averaged over all pairs of nodes on a fractal network. In this paper, we first propose a family of generalized delayed recursive trees characterized by two parameters, where the existing nodes have a time delay to produce new nodes. We then study the MFPT of random walks on this kind of recursive tree and investigate the effect of the time delay on the MFPT. By relating random walks to electrical networks, we obtain an exact formula for the MFPT and verify it by numerical calculations. Based on the obtained results, we further show that the MFPT of delayed recursive trees is much shorter, implying that the efficiency of random walks is much higher compared with the non-delayed counterpart. Our study provides a deeper understanding of random walks on delayed fractal networks.

A Simple and Practical Algorithm for Calculating MTBF of Complex Systems

It is often difficult to calculate the failure rate of a complex system. For a complex system, therefore, the value of mean time between failures (MTBF) is also difficult to obtain with formula M=1/λ. The authors introduce a simple and practical algorithm, which can be easily used to obtain the value of MTBF of a complex system with M=∫∞0R(t)dt. The time axis is divided into lots of small intervals with step Δt, and lots of small trapezoids under the curve R(t) are obtained. By summing up all the areas of the trapezoids, a close approximation to MTBF of the system is obtained.

Quantum intelligence on protein folding pathways

We study the protein folding problem on the base of our quantum approach by considering the model of protein chain with nine amino-acid residues.We introduce the concept of distance space and its projections on a XY-plane,and two characteristic quantities,one is called compactness of protein structure and another is called probability ratio involving shortest path.The concept of shortest path enables us to reduce the 388×388 density matrix to a 2×2 one from which the von Neumann entropy reflecting certain quantum coherence feature is naturally defined.We observe the time evolution of average distance and compactness solved from the classical random walk and quantum walk,we also compare the features of the time-dependence of Shannon entropy and von Neumann entropy.All the results not only reveal the fast quantum folding time but also unveil the existence of quantum intelligence hidden behind in choosing protein folding pathways.