Modeling network traffic using generalized Cauchy process

Processes with long-range dependence (LRD) have gained wide applications in many fields of science and technologies ranging from hydrology to network traffic. Two key properties of such processes are LRD that is characterized by the Hurst parameter H and self-similarity (SS) that is measured by the fractal dimension D. However, in the popular traffic model using fractional Gaussian noise (fGn), these two parameters are linearly related. This may be regarded as a limitation of fGn in traffic modeling from the point of view of either accurately fitting real traffic or appropriately explaining the particular multi-fractal phenomena of traffic. In this paper, we discuss recent results in traffic modeling from a view of the generalized Cauchy (GC) process. The GC process is indexed by two parameters D and H. The parameter D in the GC model is independent of H. Hence, it provides a more flexible way to describe the multi-fractal phenomena of traffic in addition to accurately modeling traffic for both short-term lags and long-term ones.     

On the continuing relevance of Mandelbrot’s non-ergodic fractional renewal models of 1963 to 1967

The problem of “1∕f” noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot’s very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, “1∕f” noise and LRD, concepts which are often treated as equivalent.     

Performance Study on Priority Stratgegies for WDM Packet Switches under Long-Range Dependent Traffic

The impact of long-range dependent (LRD) traffic on the buffer management schemes for WDM packet switches is studied by simulation. The different priority strategies are compared. The principles of efficient strategy design are also presented.     

Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series

The detection of long range dependence (LRD) is an important task in time series analysis. LRD is often summarized by the well-known Hurst parameter (or exponent) H∈[0,1], which can be estimated by a number of methods. Some of these techniques are designed to be applied to signals behaving as a stationary fractional Gaussian noise (fGn), whereas others imply that the analyzed time series behave as a non-stationary fractional Brownian motion (fBm). Moreover, some estimators do not yield the Hurst parameter but indexes related to H and ranging outside the unit interval. Therefore, the fGn or fBm nature of the studied time series has to be preliminarily analyzed before applying any estimation method, and the relationships between H and the indexes resulting from the analyses have to be taken into account to obtain coherent results. Since fGn-like series represent the increments of fBm-like processes and both the signals are characterized by the same H value by definition, estimators designed for fGn-like series can be applied to fBm-like sequences after preventive differentiation, and conversely estimators designed for fBm-like processes can be applied to fGn-like series after preventive integration. The signal characterization is particularly important when H is estimated on financial time series because the returns represent the first difference of price time series, which are often assumed to behave like self-affine sequences. The analysis of simulated fGn and fBm time series shows that all the considered methods yield comparable H values when properly applied. The reanalysis of several market price time series already studied in the literature points out that a correct application of the estimators (supported by a preventive signal classification) yields homogeneous H values allowing for a useful cross-validation of results reported in different works. Moreover, some conclusions reported in the literature about the anti-persistence of some financial series are shown to be incorrect because of the inappropriate application of the estimation methods.     

一种推广伊辛自旋模型的实空间重正化群理论

本文提出了一种推广的伊辛自旋模型。它包括了伊辛自旋模型、Schofield和Bowers提出的混合自旋模型以及一种特殊的格点稀释伊辛自旋模型作为特例。运用实空间重正化群得到了这个推广模型的相变流图和三个非平庸不动点(一个伊辛不动点,一个三相不动点和一个一级相变不动点)。结果表明:混合自旋模型和伊辛模型属于同一普适类。证实了Schofield和Bowers通过直接对混合自旋模型临界指数的计算所做的结论。 关键词：     

Modeling NMR Lineshapes Using Logspline Density Functions

Distortions in the FID and spin echo due to magnetic field inhomogeneity are proved to have a representation as the characteristic function of some probability distribution. In the special case that the distribution is Cauchy, the model reduces to the conventional Lorentzian model. A more general and flexible representation is presented using the Fourier transform of a logspline density. An algorithm for fitting the model is described, the performance of the model and algorithm is investigated in applications to real and simulated data sets, and the logspline approach is compared to a previous Hermitian spline approach and to the Lorentzian model. The logspline model is more parsimonious than the Hermitian spline model, provides a better fit to real data, and is much less biased than the Lorentzian model.     

The dynamic evolutions of the generalized Hobbit model and structure formation

In this paper a more general phenomenological model is proposed on the basis of the Hobbit model in Cardone et al. (Phys Rev D 69:083517, 2004). The main purpose of constructing our model is to make this model can not only mimic the ΛCDM model, but also describe a four-phase smooth transition of the universe, namely the inflationary phase, a radiation-dominated phase, a matter-dominated phase and a de Sitter-like phase. In order to check whether this model is a viable one, the evolutions of the universe are respectively discussed in the two cases, and the possible physical interpretations for this model are also respectively shown by using the scalar fields. Finally, the structure formations in our model are simply discussed for the both cases, and the results given by us reconfirm that our model can be regarded as a fit to the ΛCDM model, if we choose the proper conditions.     

Meta-Tree Random Forest: Probabilistic Data-Generative Model and Bayes Optimal Prediction

This paper deals with a prediction problem of a new targeting variable corresponding to a new explanatory variable given a training dataset. To predict the targeting variable, we consider a model tree, which is used to represent a conditional probabilistic structure of a targeting variable given an explanatory variable, and discuss statistical optimality for prediction based on the Bayes decision theory. The optimal prediction based on the Bayes decision theory is given by weighting all the model trees in the model tree candidate set, where the model tree candidate set is a set of model trees in which the true model tree is assumed to be included. Because the number of all the model trees in the model tree candidate set increases exponentially according to the maximum depth of model trees, the computational complexity of weighting them increases exponentially according to the maximum depth of model trees. To solve this issue, we introduce a notion of meta-tree and propose an algorithm called MTRF (Meta-Tree Random Forest) by using multiple meta-trees. Theoretical and experimental analyses of the MTRF show the superiority of the MTRF to previous decision tree-based algorithms.     

Portfolio Optimization with a Mean–Absolute Deviation–Entropy Multi-Objective Model

Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model.     

A dual model strategy to transfer multivariate calibration models for near-infrared spectral analysis

A dual-model method is proposed for correcting the calibration model. In the method, a primary calibration model is built using the spectra of a primary instrument and a correction model is established to describe the ratios between the predicted results from the spectra of different instruments. The prediction for the spectra of secondary instrument can be achieved by correcting the prediction of the primary model. A mathematical proof is described for the existence of the correction model, and the model is investigated using a near-infrared spectroscopic dataset of plant leaf samples measured on two instruments. The results show that a precise correction model is obtained and the model can be used to correct the predictions of the primary model. The correlation coefficients between the predicted and the reference ratios are above 0.9, and the prediction error after the correction is at the same level of the primary model.     

Fractional differential models for anomalous diffusion

In this study, we investigate three kinds of fractional differential models (distributed-order model, variable-order model and random-order model) for characterization of anomalous diffusion. The characteristics, physical advantages and potential applications of each model are highlighted. The numerical simulations also validate our analytical and comparison results. Furthermore, a generalized distributed-variable-order model and a more generalized distributed-variable-random-order model are proposed to combine the advantages of distributed-order model, variable-order model and random-order model.     

Micro-vibration model and parameter estimation method of a reaction wheel assembly

Reaction wheel assemblies (RWAs) are a source of disturbance in satellites, and they are regarded as the largest jitter contributor in optical payloads. In order to ensure a stringent jitter requirement, the wheel disturbance effects on spacecraft should be predicted precisely prior to launch through analytical or experimental approaches. For this purpose, the wheel disturbance should be identified and modeled accurately. In the present study, a micro-vibration model of the RWA is introduced through coupling an analytical wheel model and an empirical disturbance model; furthermore, a parameter estimation process of the coupled model from the micro-vibration disturbance data is proposed. In order to verify the modeling and estimation techniques, a micro-vibration model of a numerical RWA is established and its estimation error is validated. Then, the micro-vibration model is extended to consider an axial disturbance and a measurement offset effect. Finally, the micro-vibration model is applied to a commercial RWA and the model parameters are extracted from the disturbance test data of the RWA using the parameter estimation process. The analytical and experimental results demonstrate that the proposed micro-vibration model and parameter estimation process are effective in the dynamic disturbance modeling of RWAs.     

Mirror Symmetry in Two Steps: A–I–B

We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A–model). The second theory is an intermediate model, which we call the I–model. The equivalence between the A–model and the I–model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T–duality. On the other hand, the I–model is closely related to the twisted Landau-Ginzburg model (the B–model) that is mirror dual to the A–model. Thus, the mirror symmetry is realized in two steps, via the I–model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I–model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Partially supported by the DARPA grant HR0011-04-1-0031 and the NSF grant DMS-0303529.Partially supported by the Federal Program 40.052.1.1.1112, by the Grants INTAS 03-51-6346, NSh-1999/2003.2 and RFFI-04-01- 00637.     

包含液相扩散方程简化的锂离子电池电化学模型

锂离子电池的电化学模型对于电池特性分析和电池管理具有重要意义,但是准二维(P2D)模型复杂度太高,为了在保证模型精度的基础上尽量降低复杂度,本文提出了一种包含液相简化的P2D (LSP2D)模型,该模型首先基于电化学平均动力学将电池端电压化简成为仅耦合固相Li+浓度c_s和液相Li+浓度c_e的方程,然后进一步对表达c_s和c_e演化规律的偏微分方程进行抛物线近似化简,使得最终的模型由多项式组成.COMSOL仿真表明在放电倍率为1C时该模型与单粒子(SP)模型的估算精度和速度相当,但在放电倍率为3C时,该模型的估算时间比P2D模型减少了99.73%,与SP模型相当,估算精度相比SP模型有大幅度提升.     

Analytical model for nanoscale viscoelastic properties characterization using dynamic nanoindentation

In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin–Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin–Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin–Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model.     

Calibration of the Pseudo-Reaction-Zone model for detonation wave propagation

An approach for the calibration of an advanced programmed burn (PB) model for detonation performance calculations in high explosive systems is detailed. Programmed burn methods split the detonation performance calculation into two components: timing and energy release. For the timing, the PB model uses a Detonation Shock Dynamics (DSD) surface propagation model, where the normal surface speed is a function of local surface curvature. For the energy release calculation and subsequent hydrodynamic flow evolution, a Pseudo-Reaction-Zone (PRZ) model is used. The PRZ model is similar to a reactive burn model in that it converts reactants into products at a finite rate, but it has a reaction rate dependent on the normal surface speed derived from the DSD calculation. The PRZ reaction rate parameters must be calibrated in such a way that the rate of energy release due to reaction in multi-dimensional geometries is consistent with the timing calculation provided by the DSD model. Our strategy for achieving this is to run the PRZ model in a detonation shock-attached frame in a compliant 2D planar slab geometry in an equivalent way to a reactive burn model, from which we can generate detonation front shapes and detonation phase speed variations with slab thickness. In this case, the D _n field used by the PRZ model is then simply the normal detonation shock speed rather than the DSD surface normal speed. The PRZ rate parameters are then iterated on to match the equivalent surface front shapes and surface phase speed variations with slab thickness derived from the target DSD model. For the purposes of this paper, the target DSD model is fitted to the performance properties of an idealised condensed-phase reactive burn model, which allows us to compare the detonation structure of the calibrated PRZ model to that of the originating idealised-condensed phase model.     

An Improvement to Conformer-Based Model for High-Accuracy Speech Feature Extraction and Learning

Owing to the loss of effective information and incomplete feature extraction caused by the convolution and pooling operations in a convolution subsampling network, the accuracy and speed of current speech processing architectures based on the conformer model are influenced because the shallow features of speech signals are not completely extracted. To solve these problems, in this study, we researched a method that used a capsule network to improve the accuracy of feature extraction in a conformer-based model, and then, we proposed a new end-to-end model architecture for speech recognition. First, to improve the accuracy of speech feature extraction, a capsule network with a dynamic routing mechanism was introduced into the conformer model; thus, the structural information in speech was preserved, and it was input to the conformer blocks via sequestered vectors; the learning ability of the conformed-based model was significantly enhanced using dynamic weight updating. Second, a residual network was added to the capsule blocks, thus, the mapping ability of our model was improved and the training difficulty was reduced. Furthermore, the bi-transformer model was adopted in the decoding network to promote the consistency of the hypotheses in different directions through bidirectional modeling. Finally, the effectiveness and robustness of the proposed model were verified against different types of recognition models by performing multiple sets of experiments. The experimental results demonstrated that our speech recognition model achieved a lower word error rate without a language model because of the higher accuracy of speech feature extraction and learning using our model architecture with a capsule network. Furthermore, our model architecture benefited from the advantage of the capsule network and the conformer encoder, and also has potential for other speech-related applications.     

Application of the conditional source-term estimation model for turbulence–chemistry interactions in a premixed flame

Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model.     

一个高效的离散Boltzmann爆轰模型

构建一个适用于爆轰过程模拟的离散Boltzmann模型.该模型由一个离散Boltzmann方程和一个唯象反应率方程构成;在物理建模上,它等效于一个传统Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.与传统流体模型相比,它能够提供更多的动力学和动理学信息.该模型采用16个离散速度,相比于使用33个离散速度的模型具有更高的运算效率,模型中引入了额外自由度,通过调节额外自由度的数目,可以模拟各种不同比热比的爆轰.采用爆轰问题中的一些经典算例对所建立的模型进行数值验证.结果表明：该模型不仅对传统流体模型所能模拟的爆轰问题有效,而且能够用于一些传统流体模型不能描述的非平衡过程,有利于对爆轰问题的深入研究.     

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.