Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

Explicit Solutions of Quadratic FBSDEs Arising From Quadratic Term Structure Models

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107–128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.     

Main Components of Xinjiang Lavender Essential Oil Determined by Partial Least Squares and Near Infrared SpectroscopySCIEI北大核心CSCD

This work was undertaken to establish a quantitative analysis model which can rapid determinate the content of linalool, linalyl acetate of Xinjiang lavender essential oil. Totally 165 lavender essential oil samples were measured by using near infrared absorption spectrum(NIR), after analyzing the near infrared spectral absorption peaks of all samples, lavender essential oil have abundant chemical information and the interference of random noise may be relatively low on the spectral intervals of 7100-4 500 cm(-1). Thus, the PLS models was constructed by using this interval for further analysis. 8 abnormal samples were eliminated. Through the clustering method, 157 lavender essential oil samples were divided into 105 calibration set samples and 52 validation set samples. Gas chromatography mass spectrometry (GC-MS) was used as a tool to determine the content of linalool and linalyl acetate in lavender essential oil. Then the matrix was established with the GC-MS raw data of two compounds in combination with the original NIR data. In order to optimize the model, different pretreatment methods were used to preprocess the raw NIR spectral to contrast the spectral filtering effect, after analysizing the quantitative model results of linalool and linalyl acetate, the root mean square error prediction(RMSEP) of orthogonal signal transformation (OSC) was 0.226, 0.558, spectrally, it was the optimum pretreatment method. In addition, forward interval partial least squares (FiPLS) method was used to exclude the wavelength points which has nothing to do with determination composition or present nonlinear correlation, finally 8 spectral intervals totally 160 wavelength points were obtained as the dataset. Combining the data sets which have optimized by OSC-FiPLS with partial least squares(PLS) to establish a rapid quantitative analysis model for determining the content of linalool and linalyl acetate in Xinjiang lavender essential oil, numbers of hidden variables of two components were 8 in the model. The performance of the model was evaluated according to root mean square error of cross-validation (RMSECV) 9 root mean square error of prediction (RMSEP). In the model, RESECV of linalool and linalyl acetate were 0.170 and 0.416, respectively; RMSEP were 0.188 and 0.364. The results indicated that raw data was pretreated by OSC and FiPLS, the NIR-PLS quantitative analysis model with good robustness, high measurement precision; it could quickly determine the content of linalool and linalyl acetate in lavender essential oil. In addition, the model has a favorable prediction ability. The study also provide a new effective method which could rapid quantitative analysis the major components of Xinjiang lavender essential oil.     

Probabilistic interpretation of a system of quasilinear parabolic PDEs

Using a forward–backward stochastic differential equations (FBSDE) associated to a transmutation process driven by a finite sequence of Poisson processes, we obtain a probabilistic interpretation for a non-degenerate system of quasilinear parabolic partial differential equations (PDEs). The novetly is that the linear second order differential operator is different on each line of the system.     

On solving the forward kinematics of 3RPR planar parallel manipulator using hybrid metaheuristics

Hybrid metaheuristics have been applied with success in solving many real-world problems. This work introduces hybrid metaheuristics to the field of kinematics problem, in particular, for solving the forward kinematics of the 3RPR parallel manipulator. It implements a combination of genetic algorithms and simulated annealing into two popular hybrid metaheuristic techniques. They are combined as teamwork and relay collaborative hybrid metaheuristics and compared to the performance of genetic algorithms and simulated annealing alone. The results show that the meta-heuristic approaches give robust and high quality solutions. Genetic algorithms and teamwork collaborative metaheuristics showed better performance than simulated annealing and relay collaborative metaheuristics. The given metaheuristic methods obtain all the unique solutions and comparisons with algebraic methods show promising results.     

A resource-saving decoding scheme of the orthogonally concatenated codes for optical transport networks in FPGA

A decoding scheme of the orthogonally concatenated codes with low resource utilizations is proposed. In the optical transport networks (OTN), forward error-correction (FEC) techniques are used to reduce the errors which occur in transmissions. Two-orthogonal-concatenated (TOC) codes are widely used in FEC techniques for their powerful error-correction capabilities based on the iterative decoding procedure. However, the framing structure is complex so the decoding procedure is more difficult than the decoding of in–out concatenated codes. And the powerful error-correction capability relies on the multi-iterative decoding processing, thus how to effectively utilize the hardware resources is a very important problem. Especially when the decoding procedure is implemented in the field programmable gate array (FPGA) devices, effective optimizations are required for the limited resources. In this paper we present an iterative decoding scheme in FPGA with low resource utilizations. As an example, an actual engineering application under the G.975.1 recommendation is given to show the efficiency of the proposed design.     

Weak solutions of the forward problem in EEG for different conductivity values

The potential distribution on the scalp produced by current sources in the brain can be measured by an EEG recorder. The relationship between these sources and the scalp potential distribution may be described by a well-known mathematical model where some simplifications are usually introduced. The head is modeled as a multicompartment nested set and the conductivity of the different tissues is approximated by a positive piecewise constant function. This simplified model is used to solve the forward problem (FP), i.e., to calculate the scalp potential for a current source configuration. In this work, we prove that the weak solutions of the FP are continuous with respect to the conductivity values, that is, the difference between the scalp potentials is small if the conductivity values are closed enough. We present numerical examples that illustrates this property.     

A General Stochastic Calculus Approach to Insider Trading

The purpose of this paper is to present a general stochastic calculus approach to insider trading. We consider a market driven by a standard Brownian motion $B(t)$ on a filtered probability space $\displaystyle (\Omega,\F,\left\{\F\right\}_{t\geq 0},P)$ where the coefficients are adapted to a filtration ${\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$, with $\F_t\subset\G_t$ for all $t\in [0,T]$, $T>0$ being a fixed terminal time. By an {\it insider} in this market we mean a person who has access to a filtration (information) $\displaystyle{\Bbb H}=\left\{\H_t\right\}_{0\leq t\leq T}$ which is strictly bigger than the filtration $\displaystyle{\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$. In this context an insider strategy is represented by an $\H_t$-adapted process $\phi(t)$ and we interpret all anticipating integrals as the forward integral defined in [23] and [25]. We consider an optimal portfolio problem with general utility for an insider with access to a general information $\H_t \supset\G_t$ and show that if an optimal insider portfolio $\pi^*(t)$ of this problem exists, then $B(t)$ is an $\H_t$-semimartingale, i.e. the enlargement of filtration property holds. This is a converse of previously known results in this field. Moreover, if $\pi^*$ exists we obtain an explicit expression in terms of $\pi^*$ for the semimartingale decomposition of $B(t)$ with respect to $\H_t$. This is a generalization of results in [16], [20] and [2].     

Effect of flow history on the structure of a non-polar polymer/clay nanocomposite model system

The effect of flow history on the linear and non-linear viscoelastic properties of non-polar polymer nanocomposites (PNCs) has been investigated by means of a suitable model system based on a Newtonian matrix. The structural recovery of this model suspension after cessation of different pre-shear rates was monitored by measuring its linear viscoelastic properties while its structural evolution under shear flow was followed by using stepwise changes in shear rate including flow reversal measurements. To assess the kinetics of the structural evolution at rest and under flow, empirical relations of stretched exponential form were used. It is shown that for different pre-shear rates, different equilibrium structures were reached at rest but with a similar kinetics of recovery. As a result, the low frequency behaviour was typical of solid-like or weak gel material, strongly dependent on the flow history. After any given shear rate under steady state, only one reversible equilibrium structure was reached after a kinetics that was dependent on the pre-shear history. Finally, typical flow reversal responses as observed for PNCs are reported and interpreted in light of the microstructure evolution under flow. This paper was presented at the Annual Meeting of the European Society of Rheology, Hersonisos, Greece April 2006.