Search results for: linear quadratic Gaussian

Authors: Abraham Castellanos, Christophe Durville, Sophie Echenim

Abstract:

In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling.

Keywords: financial risk, numerical optimization, portfolio management, solvency capital requirement

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Jing Zhao, Yongqing Bai, Qiaofang Shi, Huaihao Zhang

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Advances in software technology enable computational chemistry to be commonly applied in various research fields, especially in pedagogy. Thus, in order to expand and improve experimental instructions of computational chemistry for undergraduates, we designed an introductory experiment—research on acrylamide molecular structure and physicochemical properties. Initially, students construct molecular models of acrylamide and polyacrylamide in Gaussian and Materials Studio software respectively. Then, the infrared spectral data, atomic charge and molecular orbitals of acrylamide as well as solvation effect of polyacrylamide are calculated to predict their physicochemical performance. At last, rheological experiments are used to validate these predictions. Through the combination of molecular simulation (performed on Gaussian, Materials Studio) with experimental verification (rheology experiment), learners have deeply comprehended the chemical nature of acrylamide and polyacrylamide, achieving good learning outcomes.

Keywords: upper-division undergraduate, computer-based learning, laboratory instruction, molecular modeling

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Authors: An Chengrui, Yin Zi, Wu Bingbing, Ma Yuanzhu, Jin Kaixiu, Chen Xiao, Ouyang Hongwei

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Single cell RNA sequence (scRNA-seq) is one of the effective tools to study transcriptomics of biological processes. Recently, similarity measurement of cells is Euclidian distance or its derivatives. However, the process of scRNA-seq is a multi-variate Bernoulli event model, thus we hypothesize that it would be more efficient when the divergence between cells is valued with relative entropy than Euclidian distance. In this study, we compared the performances of Euclidian distance, Spearman correlation distance and Relative Entropy using scRNA-seq data of the early, medial and late stage of limb development generated in our lab. Relative Entropy is better than other methods according to cluster potential test. Furthermore, we developed KL-SNE, an algorithm modifying t-SNE whose definition of divergence between cells Euclidian distance to Kullback–Leibler divergence. Results showed that KL-SNE was more effective to dissect cell heterogeneity than t-SNE, indicating the better performance of relative entropy than Euclidian distance. Specifically, the chondrocyte expressing Comp was clustered together with KL-SNE but not with t-SNE. Surprisingly, cells in early stage were surrounded by cells in medial stage in the processing of KL-SNE while medial cells neighbored to late stage with the process of t-SNE. This results parallel to Heatmap which showed cells in medial stage were more heterogenic than cells in other stages. In addition, we also found that results of KL-SNE tend to follow Gaussian distribution compared with those of the t-SNE, which could also be verified with the analysis of scRNA-seq data from another study on human embryo development. Therefore, it is also an effective way to convert non-Gaussian distribution to Gaussian distribution and facilitate the subsequent statistic possesses. Thus, relative entropy is potentially a better way to determine the divergence of cells in scRNA-seq data analysis.

Keywords: Single cell RNA sequence, Similarity measurement, Relative Entropy, KL-SNE, t-SNE

Procedia PDF Downloads 316

Authors: Yang Yi-Fei, Luo Min-Zhou, Zhang Fu-Chun, He Nai-Bao, Xing Shao-Bang

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This paper presents an electromagnetic finite element model of permanent magnet synchronous linear motor and distortion rate of the air gap flux density waveform is analyzed in detail. By designing the sample space of the parameters, nonlinear regression modeling of the orthogonal experimental design is introduced. We put forward for possible air gap flux density waveform sine electromagnetic scheme. Parameters optimization of the permanent magnet synchronous linear motor is also introduced which is based on chaotic search and adaptation function. Simulation results prove that the pole shifting does not affect the motor back electromotive symmetry based on the structural parameters, it provides a novel way for the optimum design of permanent magnet synchronous linear motor and other engineering.

Keywords: permanent magnet synchronous linear motor, finite element analysis, chaotic search, optimization design

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Authors: A. Didaoui, N. Benhalima, M. Elkeurti, A. Chouaih, F. Hamzaoui

Abstract:

The monomer and dimer structures of the title molecule have been obtained from density functional theory (DFT) B3LYP method with 6-31G (d,p) as basis set calculations. The optimized geometrical parameters obtained by B3LYP/6-31G (d,p) method show good agreement with xperimental X-ray data. The polarizability and first order hyperpolarizabilty of the title molecule were calculated and interpreted. the intermolecular N–H•••O hydrogen bonds are discussed in dimer structure of the molecule. The vibrational wave numbers and their assignments were examined theoretically using the Gaussian 03 set of quantum chemistry codes. The predicted frontier molecular orbital energies at B3LYP/6-31G(d,p) method set show that charge transfer occurs within the molecule. The frontier molecular orbital calculations clearly show the inverse relationship of HOMO–LUMO gap with the total static hyperpolarizability. The results also show that N-(2-Methylphenyl)-2-nitrobenzenesulfonamide molecule may have nonlinear optical (NLO) comportment with non-zero values.

Keywords: DFT, Gaussian 03, NLO, N-(2-Methylphenyl)-2-nitrobenzenesulfonamide

Procedia PDF Downloads 519

Authors: Farhad Ghasemi

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Along with transforming the international system into a complex and chaotic system, the fundamental question arises: how can deterrence be reconstructed conceptually and theoretically in this system model? The deterrence system is much more complex today than it was seven decades ago. This article suggests that the perception of deterrence as a linear system is a fundamental mistake because it does not consider the new dynamics of the international system, including network power dynamics. The author aims to improve this point by focusing on complexity and chaos theories, especially their nonlinearity and cascading failure principles. This article proposes that the perception of deterrence as a linear system is a fundamental mistake, as the new dynamics of the surrounding international system do not take into account. The author recognizes deterrence as a nonlinear system and introduces it as a concept in strategic studies.

Keywords: complexity, international system, deterrence, linear deterrence, nonlinear deterrence

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

Procedia PDF Downloads 443

Authors: A. Didaoui, N. Benhalima, M. Elkeurti, A. Chouaih, F. Hamzaoui

Abstract:

The monomer and dimer structures of the title molecule have been obtained from density functional theory (DFT) B3LYP method with 6-31G(d,p) as basis set calculations. The optimized geometrical parameters obtained by B3LYP/6-31G(d,p) method show good agreement with experimental X-ray data. The polarizability and first order hyperpolarizability of the title molecule were calculated and interpreted. The intermolecular N–H•••O hydrogen bonds are discussed in dimer structure of the molecule. The vibrational wave numbers and their assignments were examined theoretically using the Gaussian 03 set of quantum chemistry codes. The predicted frontier molecular orbital energies at B3LYP/6-31G(d,p) method set show that charge transfer occurs within the molecule. The frontier molecular orbital calculations clearly show the inverse relationship of HOMO–LUMO gap with the total static hyperpolarizability. The results also show that N-(2-Methylphenyl)-2-nitrobenzenesulfonamide molecule may have nonlinear optical (NLO) comportment with non-zero values.

Keywords: DFT, Gaussian 03, NLO, N-(2-Methylphenyl)-2-nitrobenzenesulfonamide, polarizability

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Authors: Qiuxiao Chen, Yan Hou, Ning Wu

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As there are deficiencies of the classic Douglas-Peucker Algorithm (DPA), such as high risks of deleting key nodes by mistake, high complexity, time consumption and relatively slow execution speed, a new Deletion-Cost Based Compression Algorithm (DCA) for linear vector data was proposed. For each curve — the basic element of linear vector data, all the deletion costs of its middle nodes were calculated, and the minimum deletion cost was compared with the pre-defined threshold. If the former was greater than or equal to the latter, all remaining nodes were reserved and the curve’s compression process was finished. Otherwise, the node with the minimal deletion cost was deleted, its two neighbors' deletion costs were updated, and the same loop on the compressed curve was repeated till the termination. By several comparative experiments using different types of linear vector data, the comparison between DPA and DCA was performed from the aspects of compression quality and computing efficiency. Experiment results showed that DCA outperformed DPA in compression accuracy and execution efficiency as well.

Keywords: Douglas-Peucker algorithm, linear vector data, compression, deletion cost

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Authors: Seong-Jin Cho, Jin Ho Kim

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Energy harvesting is the technology which gathers and converts external energies such as light, vibration and heat which are disposed into reusable electrical energy and uses such electrical energy. The vibration energy harvesting is very interesting technology because it produces very high density of energy and unaffected by the climate. Vibration energy can be harvested by the electrostatic, electromagnetic and piezoelectric systems. The electrostatic system has low energy conversion efficiency, and the piezoelectric system is expensive and needs the frequent maintenance because it is made of piezoelectric ceramic. On the other hand, the electromagnetic system has a long life time and high harvesting efficiency, and it is relatively cheap. The electromagnetic harvesting system includes the linear generator and the rotary-type generator. The rotary-type generators require the additional mechanical conversion device if it uses linear motion of vibration. But, the linear generator uses directly linear motion of vibration without a mechanical conversion device, and it has uncomplicated structure and light weight compared with the rotary-type generator. Therefore, the linear electromagnetic generator can be useful in using vibration energy harvesting. The pole transformer systems need electricity sensor system for sending voltage and power information to administrator. Therefore, the battery is essential, and its regular maintenance of replacement is required. In case of the transformer of high location in mountainous areas, the person can’t easily access it resulting in high maintenance cost. To overcome these problems, we designed and developed the linear electromagnetic generator which can replace battery in electricity sensor system for sending voltage and power information of the pole transformer. And, it uses vibration energy of frequency more than 50 Hz by the pole transformer. In order to analyze the electromagnetic characteristics of small linear electric generator, a commercial electromagnetic finite element analysis program "MAXWELL" was used. Then, through the actual production and experiment of linear generator, we confirmed output power of linear generator.

Keywords: energy harvesting, frequency, linear generator, experiment

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

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Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant

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Authors: Vidula Shevade, B. J. Nagare, Sajeev Chacko

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First principles simulation, meaning density functional theory (DFT) calculations with plane waves and pseudopotential, has become a prized technique in condensed matter theory. Nanoparticles (NP) have been known to possess good catalytic activities, especially for molecules such as CO, O₂, etc. Among the metal NPs, Aluminium based NPs are also widely known for their catalytic properties. Aluminium metal is a lightweight, excellent electrical, and thermal abundant chemical element in the earth’s crust. Aluminium NPs, when added to solid rocket fuel, help improve the combustion speed and considerably increase combustion heat and combustion stability. Adding aluminium NPs into normal Al/Al₂O₃ powder improves the sintering processes of the ceramics, with high heat transfer performance, increased density, and enhanced thermal conductivity of the sinter. We used VASP and Gaussian 0₃ package to compute the geometries, electronic structure, and bonding properties of Al₁₂Ni as well as its interaction with O₂ and CO molecules. Several MD simulations were carried out using VASP at various temperatures from which hundreds of structures were optimized, leading to 24 unique structures. These structures were then further optimized through a Gaussian package. The lowest energy structure of Al₁₂Ni has been reported to be a singlet. However, through our extensive search, we found a triplet state to be lower in energy. In our structure, the Ni atom is found to be on the surface, which gives the non-zero magnetic moment. Incidentally, O2 and CO molecules are also triplet in nature, due to which the Al₁₂-Ni cluster is likely to facilitate the oxidation process of the CO molecule. Our results show that the most favourable site for the CO molecule is the Ni atom and that for the O₂ molecule is the Al atom that is nearest to the Ni atom. Al₁₂Ni-O₂ and Al₁₂-Ni-CO structures we extracted using VMD. Al₁₂Ni nanocluster, due to in triplet electronic structure configuration, indicates it to be a potential candidate as a catalyst for oxidation of CO molecules.

Keywords: catalyst, gaussian, nanoparticles, oxidation

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Authors: Graziano Chesi

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The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems.

Keywords: non-linear system, communication constraint, topological entropy

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Authors: Z. Mortezaie, H. Hassanpour, S. Asadi Amiri

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Captured images may suffer from Gaussian blur due to poor lens focus or camera motion. Unsharp masking is a simple and effective technique to boost the image contrast and to improve digital images suffering from Gaussian blur. The technique is based on sharpening object edges by appending the scaled high-frequency components of the image to the original. The quality of the enhanced image is highly dependent on the characteristics of both the high-frequency components and the scaling/gain factor. Since the quality of an image may not be the same throughout, we propose an adaptive unsharp masking method in this paper. In this method, the gain factor is computed, considering the gradient variations, for individual pixels of the image. Subjective and objective image quality assessments are used to compare the performance of the proposed method both with the classic and the recently developed unsharp masking methods. The experimental results show that the proposed method has a better performance in comparison to the other existing methods.

Keywords: unsharp masking, blur image, sub-region gradient, image enhancement

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Authors: Yunwei Zhang, Qiaochu Tang, Yao Zhang, Jiabin Wang, Ulrich Stimming, Alpha Lee

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Forecasting the state of health and remaining useful life of Li-ion batteries is an unsolved challenge that limits technologies such as consumer electronics and electric vehicles. Here we build an accurate battery forecasting system by combining electrochemical impedance spectroscopy (EIS) -- a real-time, non-invasive and information-rich measurement that is hitherto underused in battery diagnosis -- with Gaussian process machine learning. We collect over 20,000 EIS spectra of commercial Li-ion batteries at different states of health, states of charge and temperatures -- the largest dataset to our knowledge of its kind. Our Gaussian process model takes the entire spectrum as input, without further feature engineering, and automatically determines which spectral features predict degradation. Our model accurately predicts the remaining useful life, even without complete knowledge of past operating conditions of the battery. Our results demonstrate the value of EIS signals in battery management systems.

Keywords: battery degradation, machine learning method, electrochemical impedance spectroscopy, battery diagnosis

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Authors: I. F. Ejim, F. L. Kamen

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Aims: In this experiment, algae oil extraction with a combination of n-hexane and ethanol was investigated. The effects of extraction solvent concentration, extraction time and temperature on the yield and quality of oil were studied using Response Surface Methodology (RSM). Experimental Design: Optimization of algae oil extraction using Box-Behnken design was used to generate 17 experimental runs in a three-factor-three-level design where oil yield, specific gravity, acid value and saponification value were evaluated as the response. Result: In this result, a minimum oil yield of 17% and maximum of 44% was realized. The optimum values for yield, specific gravity, acid value and saponification value from the overlay plot were 40.79%, 0.8788, 0.5056 mg KOH/g and 180.78 mg KOH/g respectively with desirability of 0.801. The maximum point prediction was yield 40.79% at solvent concentration 66.68 n-hexane, temperature of 40.0°C and extraction time of 4 hrs. Analysis of Variance (ANOVA) results showed that the linear and quadratic coefficient were all significant at p<0.05. The experiment was validated and results obtained were with the predicted values. Conclusion: Algae oil extraction was successfully optimized using RSM and its quality indicated it is suitable for many industrial uses.

Keywords: algae oil, response surface methodology, optimization, Box-Bohnken, extraction

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Authors: Guillermo Manuel Flores Figueroa, Juan Alejandro Vazquez Feijoo, Jose Navarro Antonio

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A continuous nonlinear system response may be obtained by an infinite sum of the so-called Volterra operators. Each operator is obtained from multidimensional convolution of nth-order between the nth-order Volterra kernel and the system input. These operators can also be obtained from the Associated Linear Equations (ALEs) that are linear models of subsystems which inputs and outputs are of the same nth-order. Each ALEs produces a particular nth-Volterra operator. As linear models a unitary impulse response can be obtained from them. This work shows the relationship between this unitary impulse responses and the corresponding order Volterra kernel.

Keywords: Volterra series, frequency response functions FRF, associated linear equations ALEs, unitary response function, Voterra kernel

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: single-degree-of-freedom system (SDOF), linear acceleration method, nonlinear excited system, equivalent displacement method, equivalent energy method

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: C. V. Pietreanu, S. E. Zaharia, C. Dinu

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The present research is built on three major pillars, commencing by making some considerations on accident investigation methods and pointing out both defining aspects and differences between linear and non-linear analysis. The traditional linear focus on accident analysis describes accidents as a sequence of events, while the latest systemic models outline interdependencies between different factors and define the processes evolution related to a specific (normal) situation. Linear and non-linear accident analysis methods have specific limitations, so the second point of interest is mirrored by the aim to discover the drawbacks of systemic models which becomes a starting point for developing new directions to identify risks or data closer to the cause of incidents/accidents. Since communication represents a critical issue in the interaction of human factor and has been proved to be the answer of the problems made by possible breakdowns in different communication procedures, from this focus point, on the third pylon a new error-modeling instrument suitable for risk assessment/accident analysis will be elaborated.

Keywords: accident analysis, multi-factorial error modeling, risk, systemic methods

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Authors: Aouiche Abdelaziz, Soudani Mouhamed Salah, Aouiche El Moundhe

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The present paper addresses the utilization of Artificial Neural Networks (ANNs) and Fuzzy Inference Systems (FISs) for the identification and control of dynamical systems with some degree of uncertainty. Because ANNs and FISs have an inherent ability to approximate functions and to adapt to changes in input and parameters, they can be used to control systems too complex for linear controllers. In this work, we show how ANNs and FISs can be put in order to form nets that can learn from external data. In sequence, it is presented structures of inputs that can be used along with ANNs and FISs to model non-linear systems. Four systems were used to test the identification and control of the structures proposed. The results show the ANNs and FISs (Back Propagation Algorithm) used were efficient in modeling and controlling the non-linear plants.

Keywords: non-linear systems, fuzzy set Models, neural network, control law

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.

Keywords: nonlinear, stability, buckling, modified newmark method

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: Timothée Bligny, Clément Codron, Antoine Estruch, Nicolas Girodet, Clément Ginet

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Collateralized Debt Obligations are not as widely used nowadays as they were before 2007 Subprime crisis. Nonetheless there remains an enthralling challenge to optimize cash flows associated with synthetic CDOs. A Gaussian-based model is used here in which default correlation and unconditional probabilities of default are highlighted. Then numerous simulations are performed based on this model for different scenarios in order to evaluate the associated cash flows given a specific number of defaults at different periods of time. Cash flows are not solely calculated on a single bought or sold tranche but rather on a combination of bought and sold tranches. With some assumptions, the simplex algorithm gives a way to find the maximum cash flow according to correlation of defaults and maturities. The used Gaussian model is not realistic in crisis situations. Besides present system does not handle buying or selling a portion of a tranche but only the whole tranche. However the work provides the investor with relevant elements on how to know what and when to buy and sell.

Keywords: synthetic collateralized debt obligation (CDO), credit default swap (CDS), cash flow optimization, probability of default, default correlation, strategies, simulation, simplex

Procedia PDF Downloads 243

Authors: Saeed Ur Rahman, Naveed Ullah, Muhammad Irshad Khan, Quensheng Cao, Niaz Muhammad Khan

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In this paper the optimization performance of non-uniform linear antenna array is presented. The Particle Swarm Optimization (PSO) algorithm is presented to minimize Side Lobe Level (SLL) and Half Power Beamwidth (HPBW). The purpose of using the PSO algorithm is to get the optimum values for inter-element spacing and excitation amplitude of linear antenna array that provides a radiation pattern with minimum SLL and HPBW. Various design examples are considered and the obtain results using PSO are confirmed by comparing with results achieved using other nature inspired metaheuristic algorithms such as real coded genetic algorithm (RGA) and biogeography (BBO) algorithm. The comparative results show that optimization of linear antenna array using the PSO provides considerable enhancement in the SLL and HPBW.

Keywords: linear antenna array, minimum side lobe level, narrow half power beamwidth, particle swarm optimization

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Authors: Merve Begum Terzi, Orhan Arikan, Adnan Abaci, Mustafa Candemir

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Acute myocardial infarction is a major cause of death in the world. Therefore, its fast and reliable diagnosis is a major clinical need. ECG is the most important diagnostic methodology which is used to make decisions about the management of the cardiovascular diseases. In patients with acute myocardial ischemia, temporary chest pains together with changes in ST segment and T wave of ECG occur shortly before the start of myocardial infarction. In this study, a technique which detects changes in ST/T sections of ECG is developed for the early diagnosis of acute myocardial ischemia. For this purpose, a database of real ECG recordings that contains a set of records from 75 patients presenting symptoms of chest pain who underwent elective percutaneous coronary intervention (PCI) is constituted. 12-lead ECG’s of the patients were recorded before and during the PCI procedure. Two ECG epochs, which are the pre-inflation ECG which is acquired before any catheter insertion and the occlusion ECG which is acquired during balloon inflation, are analyzed for each patient. By using pre-inflation and occlusion recordings, ECG features that are critical in the detection of acute myocardial ischemia are identified and the most discriminative features for the detection of acute myocardial ischemia are extracted. A classification technique based on support vector machine (SVM) approach operating with linear and radial basis function (RBF) kernels to detect ischemic events by using ST-T derived joint features from non-ischemic and ischemic states of the patients is developed. The dataset is randomly divided into training and testing sets and the training set is used to optimize SVM hyperparameters by using grid-search method and 10fold cross-validation. SVMs are designed specifically for each patient by tuning the kernel parameters in order to obtain the optimal classification performance results. As a result of implementing the developed classification technique to real ECG recordings, it is shown that the proposed technique provides highly reliable detections of the anomalies in ECG signals. Furthermore, to develop a detection technique that can be used in the absence of ECG recording obtained during healthy stage, the detection of acute myocardial ischemia based on ECG recordings of the patients obtained during ischemia is also investigated. For this purpose, a Gaussian mixture model (GMM) is used to represent the joint pdf of the most discriminating ECG features of myocardial ischemia. Then, a Neyman-Pearson type of approach is developed to provide detection of outliers that would correspond to acute myocardial ischemia. Neyman – Pearson decision strategy is used by computing the average log likelihood values of ECG segments and comparing them with a range of different threshold values. For different discrimination threshold values and number of ECG segments, probability of detection and probability of false alarm values are computed, and the corresponding ROC curves are obtained. The results indicate that increasing number of ECG segments provide higher performance for GMM based classification. Moreover, the comparison between the performances of SVM and GMM based classification showed that SVM provides higher classification performance results over ECG recordings of considerable number of patients.

Keywords: ECG classification, Gaussian mixture model, Neyman–Pearson approach, support vector machine

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Authors: S. Zenhari, M. R. Hematiyan, A. Khosravifard, M. R. Feizi

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The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains.

Keywords: boundary element method, method of fundamental solutions, elasticity, potential problem, convex domain, concave domain

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Authors: Barbara Kilosanidze, George Kakauridze, Levan Nadareishvili, Yuri Mshvenieradze

Abstract:

A new method for determining the distribution of birefringence and linear dichroism in optical polymer materials is presented. The method is based on the use of polarization-holographic diffraction grating that forms an orthogonal circular basis in the process of diffraction of probing laser beam on the grating. The intensities ratio of the orders of diffraction on this grating enables the value of birefringence and linear dichroism in the sample to be determined. The distribution of birefringence in the sample is determined by scanning with a circularly polarized beam with a wavelength far from the absorption band of the material. If the scanning is carried out by probing beam with the wavelength near to a maximum of the absorption band of the chromophore then the distribution of linear dichroism can be determined. An appropriate theoretical model of this method is presented. A laboratory setup was created for the proposed method. An optical scheme of the laboratory setup is presented. The results of measurement in polymer films with two-dimensional gradient distribution of birefringence and linear dichroism are discussed.

Keywords: birefringence, linear dichroism, graded oriented polymers, optical polymers, optical anisotropy, polarization-holographic grating

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Authors: Alla Levina, Sergey Taranov

Abstract:

The classical approach to the providing noise immunity and integrity of information that process in computing devices and communication channels is to use linear codes. Linear codes have fast and efficient algorithms of encoding and decoding information, but this codes concentrate their detect and correct abilities in certain error configurations. To protect against any configuration of errors at predetermined probability can robust codes. This is accomplished by the use of perfect nonlinear and almost perfect nonlinear functions to calculate the code redundancy. The paper presents the error-correcting coding scheme using biorthogonal wavelet transform. Wavelet transform applied in various fields of science. Some of the wavelet applications are cleaning of signal from noise, data compression, spectral analysis of the signal components. The article suggests methods for constructing linear codes based on wavelet decomposition. For developed constructions we build generator and check matrix that contain the scaling function coefficients of wavelet. Based on linear wavelet codes we develop robust codes that provide uniform protection against all errors. In article we propose two constructions of robust code. The first class of robust code is based on multiplicative inverse in finite field. In the second robust code construction the redundancy part is a cube of information part. Also, this paper investigates the characteristics of proposed robust and linear codes.

Keywords: robust code, linear code, wavelet decomposition, scaling function, error masking probability

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