Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm

Empirical Distributions of Log-Returns: Between the Stretched Exponential and the Power Law?

Due to the growing concern on the issues of global warming, climate change, and energy shortage, more rigorous requirements are imposed on the energy conversion process of combustion. Due to the relative safety and convenience in transportation and storage, liquid fuels are commonly used in many practical combustion systems such as diesel engines, gas turbines and industrial furnaces. In these combustion devices, turbulent spray flows are involved. The character of spray dispersion, evaporation, mixing and combustion of fuel droplets strongly determines the performance of these systems with respect to the combustion efficiency, stability, and emissions. Therefore, an improved understanding of turbulent spray combustion and the development of predictive models are needed for a better design of more efficient combustion systems. The present work focuses on the development of a computational methodology based on the transported joint probability density function (PDF) method for the modeling and simulation of two-phase turbulent spray flows without and with chemical reactions. In the non-reacting situation, the dependent variables of the joint PDF include the gas velocity and the mixture fraction. For the simulation of reacting spray flows, a three-variate joint PDF transport equation is derived and modeled in order to account for the pre-vaporization effects and partially premixed regime in turbulent spray flames. The dependent variables include the gas phase mixture fraction, the reaction progress variable and gas enthalpy. Detailed combustion chemistry is considered through an extended spray flamelet model by including a reaction progress variable in addition to the classical formulation. The dilute spray is simulated using a Lagrangian discrete parcel method for the description of droplet motion, heating and evaporation. The infinite conductivity model with consideration of non-equilibrium effects based on the Langmuir-Knudsen law is considered. The spray evolution and flame structures in the frame of the polydisperse reacting spray flows are investigated. Numerical results are compared with experimental data provided by Prof. Masri at the University of Sydney, Australia, and the test cases include three different turbulent non-reacting acetone spray flows in air and turbulent spray flames with the liquid fuel ethanol. For the acetone spray flows, computational results generally show good agreement with experimental data in terms of the droplet size and mean velocity distribution, as well as the liquid volume flux. The results show that the inflow liquid mass loading hardly affects the droplet diameter distribution, whereas the inlet turbulence level has a pronounced effect. The tendency of droplet accumulation near the jet centerline is found with a somewhat overprediction of liquid volume flux at downstream locations. A more sophisticated turbulence model is expected to eliminate this discrepancy. Moreover, the local joint PDF of the gas velocity and the mixture fraction is analyzed. A linear correlation of the gas velocity and the mixture fraction exists close to the nozzle exit outside the main spray jet, and no regions are found where statistical independence prevails. For the simulation of spray flames, computations with the newly developed spray flamelet/progress variable approach and with the previous standard spray flamelet formulation are carried out and compared with the experiments by Prof. Masri at the University of Sydney. A good agreement between the computations with the new formulation and the experiments for gas temperature and droplet size and velocity is achieved. The major spray and combustion properties are correctly captured using this new formulation, which is compared with an unphysically attached flame near the nozzle exit predicted by the previous model. A partially premixed combustion prevails in this piloted turbulent spray flame. Due to the prevaporization of the ethanol droplets near the nozzle exit, a lean premixed gas mixture is found at the inner side of spray jet. Moving downstream, the lean-sided diffusion flame is promoted towards the inner fuel-rich side by heating up the inner premixed core that is controlled by the droplet evaporation. Additionally, it is observed that in the far-field region, the diffusion flame becomes the dominant combustion mode. In summary, an efficient computational model based on the transported joint PDF method is developed to two-phase turbulent spray flows. The combined transported joint PDF and a newly proposed spray flamelet/progress variable approach shows an improved performance in the prediction of complex turbulent spray flames, and new insights on the local flame structure influenced by evaporating sprays are obtained.

In this paper, we investigate the feasibility of computing DNA patterns on FPGAs by utilising high-performance and parallel computing. In particular, the report analyses and contrasts the FSM -based core implementation of the well-known Smith-Waterman pair-wise sequence alignment algorithm with the dynamic and heuristic alternatives that are currently on the market. In this research project, we investigate the use of parallel and high-performance computing to determine how DNA patterns can be computed on FPGAs. In particular, the report details the findings of a study that compared the FSM -based core implementation of the well-known Smith-Waterman pair-wise sequence alignment algorithm with the algorithm's current dynamic and heuristic programming methods. The study was carried out by comparing these three aspects of the algorithm. The traditional methods of sequence alignment that are software-implied are not adequate to meet the actual data rate requirements. A strategy that is based on the use of hardware makes it possible to process multiple new databases in parallel, which enables a high degree of scalability. A finite state machine serves as the primary data processor in our demonstration of how to organize the sequences of amino acids in a protein (FSM). We also investigate the effectiveness of bit-based sequence alignment algorithms and present the inner stage pipelined FPGA architecture for implementing sequence alignment. Both of these are presented in this paper. Synchronized controllers are utilized in the programming techniques of the algorithm for the purpose of parallel sequence alignment. Inference is the foundation of traditional software-based methods for sequence alignment, but these methods are unable to keep up with the required data rates. A strategy that is based on hardware allows for the processing of parallel tasks with a large number of new databases and provides excellent scalability. Our explanation of the classification of protein sequences is based on a Finite State Machine, which serves as the primary processing unit (FSM). In addition to this, we investigate how well bit-based sequence alignment algorithms work and present the inner stage pipelined Field Programmable Gate Array architecture that can be used to implement sequence alignment. Synchronized controllers are utilized in the process of performing sequence alignment in parallel. The architecture as a whole was made to be scalable and fast, with a small number of computations and the ability to perform parallel processing in hardware using field-programmable gate arrays to compare bits in patterns. Finally, we use FPGA hardware synthesis to show off impressive performance and low resource consumption.

The effects of the subgrid-scale (SGS) turbulence and SGS models on the one-point joint probability density function (JPDF) of resolvable-scale velocity are studied using its transport equation. It is shown that the SGS stress evolves the JPDF through the conditional means of the SGS stress and its production rate conditional on the resolvable-scale velocity, which must be reproduced by the SGS model in order for large-eddy simulation (LES) to reproduce the JPDF. Measurements are conducted in an axisymmetric turbulent jet using an array consisting of three X-wire probes to obtain filtered variables for analysing the conditional means. Data for three filter scales show that both the conditional SGS stress and the conditional SGS stress production rate depend strongly on the resolvable-scale velocity. While the magnitude of the conditional SGS stress decreases with the filter scale, that of the conditional SGS stress production does not, suggesting persistent effects on the resolvable-scale velocity JPDF. Therefore, the SGS model must be able to reproduce the conditional SGS stress production even for inertial-range filter scales. The conditional production of SGS normal stress (energy transfer) has some negative values, indicating conditional backscatter of SGS energy. This provides direct evidence that for LES to reproduce the JPDF it is essential for the SGS models to predict (conditional) backscatter. The Smagorinsky model is capable of predicting the qualitative features of the conditional SGS stress but not those of the conditional SGS stress production, especially the conditional backscatter. The present study links the resolvable-scale statistics to the dynamics of the SGS stress, providing impetus for further study of the SGS dynamics.

Efficient biological sequence (proteins or DNA) alignment is an important and challenging task in bioinformatics. It is similar to string matching in the context of biological data and is used to infer the evolutionary relationship between a set of protein or DNA sequences. An accurate alignment can provide valuable information for experimentation on the newly found sequences. It is indispensable in basic research as well as in practical applications such as pharmaceutical development, drug discovery, disease prevention and criminal forensics. Many algorithms and methods, such as, dot plot (Gibbs & McIntyre, 1970),Needleman-Wunsch (N-W) (Needleman & Wunsch, 1970), Smith-Waterman (S-W) (Smith & Waterman, 1981), FASTA (Pearson & Lipman, 1985), BLAST (Altschul et al., 1990), HMMER (Eddy, 1998) and ClustalW (Thompson et al., 1994) have been proposed to perform and accelerate sequence alignment activities. An overview of these methods is given in (Hasan et al., 2007). Out of these, S-W algorithm is an optimal sequence alignment method, but its computational cost makes it inappropriate for practical purposes. To develop efficient and optimal sequence alignment solutions, the S-W algorithm has recently been implemented on emerging accelerator platforms such as Field Programmable Gate Arrays (FPGAs), Cell Broadband Engine (Cell/B.E.) and Graphics Processing Units (GPUs) (Buyukkur & Najjar, 2008; Hasan et al., 2010; Liu et al., 2009; 2010; Lu et al., 2008). This chapter aims at providing a broad overview of sequence alignment in general with particular emphasis on the classification and discussion of available methods and their comparison. Further, it reviews in detail the acceleration approaches based on implementations on different platforms and provides a comparison considering different parameters. This chapter is organized as follows: The remainder of this section gives a classification, discussion and comparison of the available methods and their hardware acceleration. Section 2 introduces the S-W algorithm which is the focus of discussion in the succeeding sections. Section 3 reviews CPU-based acceleration. Section 4 provides a review of FPGA-based acceleration. Section 5 overviews GPU-based acceleration. Section 6 presents a comparison of accelerations on different platforms, whereas Section 7 concludes the chapter.

Clustering large financial time series data enables pattern extraction that facilitates risk management. The knowledge gathered from unsupervised learning is useful for improving portfolio optimization and making stock trading recommendations. Most methods available in the literature for clustering financial time series are based on exploiting linear relationships between time series. However, prices of different assets (stocks) may have non‐linear relationships which may be quantified using information based measures such as mutual information (MI). To estimate the empirical mutual information between time series of stock returns, we employ a novel kernel density estimator (KDE) based jackknife mutual information estimation (JMI), and compare it with the widely‐used binning method. We then propose an average distance gradient change algorithm and an algorithm based on the average silhouette criterion that use pairwise and groupwise MI of high‐frequency financial stock returns. Through numerical studies, we provide insights into the impact of the clustering on asset allocation and risk management based on the nonlinear information structure of the US stock market.

Pairwise optimal alignments between three or more sequences are not necessarily consistent as a whole, but consistent and inconsistent residues are usually distributed in clusters. An efficient method has been developed for locating consistent regions when each pairwise alignment is given in the form of a "skeletal representation" (Bull. math. Biol. 52, 359-373). This method is further extended so that the combination of pairwise alignments that gives the greatest consistency is found when possibly many alignments are equally optimal for each pairwise comparison. A method for acceleration of simultaneous multiple sequence alignment is proposed in which consistent regions serve as "anchor points" limiting application of direct multi-way alignment to the rest of "inconsistent" regions.

Environmental noise energy can be effectively captured by an energy harvester (EH) and then converted into usable electricity for low-powered monitoring sensors in aerospace vehicles. It is important to investigate the influence of potential well parameters on the energy harvesting performance under random excitation. Therefore, this paper theoretically derives the marginal probability density function (PDF), the joint PDF, and the averaging output power of the decoupled bistable energy harvester driven by the Gaussian white noise. First, the bistable energy harvester is linearized using the statistical linearization method, which is advantageous in obtaining coarse mean square values of outputs for further analysis. Second, the dimension of Fokker–Planck–Kolmogorov (FPK) equations is reduced by the state-space-split (SSS) method. Then, the approximate marginal and joint PDF can be obtained. Third, the influence of potential well width and height on PDFs and the averaging output power are, respectively, analyzed and discussed, respectively. Finally, the theoretical derivation is successfully validated by Monte Carlo simulations. Results show that the large potential well width can improve the averaging output power of the bistable EH under random excitation.

New, exact expressions for the probability density and distribution functions of a bivariate Hoyt (Nakagami-q) process with arbitrary correlation pattern in a nonstationary environment are derived, a solution to a longstanding unsolved problem. More specifically, the following are obtained: joint probability density function, joint cumulative distribution function, power and envelope correlation coefficients, and some statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability and probability density function. The exact expressions are given in infinite series form, but are mathematically tractable, easy to evaluate, and flexible enough to accommodate a myriad of correlation scenarios, useful in the analysis of a more general fading environment. The power correlation coefficient is found in an exact, simple, closed-form formula, whereas the envelope one, also exact, is more mathematically elaborate. Approximate, simple closed-form expressions for the joint distribution are also obtained that yield (i) excellent results for small to medium correlation coefficients and (ii) reasonable ones for high correlation coefficient.

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.

A flamelet-based Eulerian transported PDF method for the modeling and simulation of supersonic combustion

This paper derives closed-form formulas for the joint statistics of two correlated Weibull variates. In particular, the joint probability density function, the general joint moments, and the general correlation coefficient are obtained in terms of well-known fading physical parameters.

The three-condition version of the uniform conditional state combustion model makes use of the mixture fraction, progress variable, and normalized total enthalpy as conditioning variables to build a three-dimensional conditional manifold for chemistry. In order to map the solution in conditional space into the flow domain, the joint Probability Density Function (PDF) of the conditioning variables needs to be modeled. In simulations, presumed functions (i.e., β-PDF for the mixture fraction and progress variable and δ-PDF for total enthalpy) are often used for modeling the marginal PDFs. In this work, the measurements from the Cambridge/Sandia burner are employed to obtain the marginal PDFs for the conditioning variables at various points in the reacting domain. The measurements are then combined from all positions in space to form conditional PDFs of the normalized total enthalpy for various values of the other two variables. In the vicinity of the flame brush, the marginal PDF of the normalized total enthalpy resembles a bimodal Gaussian distribution; nonetheless, the conditional PDFs for this variable are nearly Gaussian distributions. The correlation coefficients between the conditioning variables are also investigated, and the assumption of their statistical independence is examined. To consider the association between the conditioning variables for modeling, the copula concept is introduced, and the performances of three different copulas are tested. Furthermore, the statistical moments of the conditioning variables are computed from the experimental data at different points and are utilized for modeling the joint PDF of the conditioning variables from two different approaches that are compared.

A modulated synchronous doubly stochastic flow under conditions of a fixed dead time is considered. After each registered event there is a time of fixed duration T (dead time), during which another flow events are inaccessible for observation. When duration of the dead time period finishes, the first happened event creates the dead time period of duration T again and etc. An explicit form of a probability density function of interval duration between two adjacent events of modulated synchronous doubly stochastic flow under conditions of a fixed dead time is derived. Also an explicit form of a joint probability density function for modulated synchronous flow interval duration is obtained. A recurrent conditions for modulated synchronous flow as well as some probabilistic characteristics of the flow are obtained using the formula for a joint probability density function.

We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the Neyman-Pearson setting are based on likelihood ratio tests (LRT), which, in this set-up, evaluate the quotient between the probability density functions (PDF) of the measurements when the source signal is present and absent. When the source is present, the computation of the joint PDF of the energy measurements at the nodes is a challenging problem. This is due to the statistical dependence introduced to the received signals by the propagation through fading channels of the radio signal emitted by the source. We deal with this problem using the characteristic function of the (intractable) joint PDF, and proposing an approximation to it. We derive bounds for the approximation error in two wireless propagation scenarios, slow and fast fading, and show that the proposed approximation is exponentially tight with the number of nodes when the time-bandwidth product is sufficiently high. The approximation is used as a substitute of the exact joint PDF for building an approximate LRT, which performs better than other well-known detectors, as verified by Monte Carlo simulations.