Search results for: singular perturb

Authors: O. Delage, H. Bencherif, T. Portafaix, A. Bourdier

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The main purpose of time series analysis is to learn about the dynamics behind some time ordered measurement data. Two approaches are used in the literature to get a better knowledge of the dynamics contained in observation data sequences. The first of these approaches concerns time series decomposition, which is an important analysis step allowing patterns and behaviors to be extracted as components providing insight into the mechanisms producing the time series. As in many cases, time series are short, noisy, and non-stationary. To provide components which are physically meaningful, methods such as Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT) or, more recently, Empirical Adaptive Wavelet Decomposition (EAWD) have been proposed. The second approach is to reconstruct the dynamics underlying the time series as a trajectory in state space by mapping a time series into a set of Rᵐ lag vectors by using the method of delays (MOD). Takens has proved that the trajectory obtained with the MOD technic is equivalent to the trajectory representing the dynamics behind the original time series. This work introduces the singular spectrum decomposition (SSD), which is a new adaptive method for decomposing non-linear and non-stationary time series in narrow-banded components. This method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for the analysis and prediction of time series. As the first step of SSD is to constitute a trajectory matrix by embedding a one-dimensional time series into a set of lagged vectors, SSD can also be seen as a reconstruction method like MOD. We will first give a brief overview of the existing decomposition methods (EMD-EWT-EAWD). The SSD method will then be described in detail and applied to experimental time series of observations resulting from total columns of ozone measurements. The results obtained will be compared with those provided by the previously mentioned decomposition methods. We will also compare the reconstruction qualities of the observed dynamics obtained from the SSD and MOD methods.

Keywords: time series analysis, adaptive time series decomposition, wavelet, phase space reconstruction, singular spectrum analysis

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Authors: Szymon Misiek

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The genderqueer (or gender non-binary, both terms referring to those individuals who are identified as neither men nor women) community has been gaining greater visibility over the last few years. This includes legal recognition, representation in popular media, and inclusion of non-binary perspectives in research on transgender issues. Another important aspect of visibility is language. Gender-neutrality, often associated with genderqueer people, is relatively easy to achieve in natural-gender languages such as English. This can be observed in the growing popularity of the 'singular they' pronoun (used specifically with reference to genderqueer individuals) or the gender-neutral title 'Mx.' (as an alternative to 'Ms./Mr.'). 'Singular they' seems to have become a certain standard in the genderqueer community. Grammatical-gender languages, such as Polish, provide for a greater challenge to genderqueer speakers. In Polish, every noun is inherently gendered, while verbs, adjectives, and pronouns inflect for gender. Those who do not wish to settle for using only either masculine or feminine forms (which some genderqueer Polish speakers do choose) have to somehow mix the two, attempt to avoid gendered forms altogether, or turn to non-standard forms, such as neuter (not used for people in standard Polish), plurals (vaguely akin to English 'singular they'), or neologisms (such as verb forms using the '-u-' affix). The following paper presents the results of a survey conducted among genderqueer speakers of Polish regarding their choice of linguistic strategies. As no definitive standard such as 'singular they' has (yet) emerged, it rather seeks to emphasize the diversity of chosen strategies and their relation to a person's specific identity as well as the context an exchange takes place. The findings of the study may offer an insight into how heavily gendered languages deal with non-normatively gendered experiences, and to what extent English influences this process (e.g., the majority of genderqueer poles choose English terms to label their identity), as well as help design good practices aimed at achieving gender-equality in speech.

Keywords: genderqueer, grammatical gender in Polish, non-binary, transgender

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Authors: Reena Behal, D. P. Shukla

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In this paper, we investigate Bulk Viscous Bianchi Type V Cosmological Model with Time dependent gravitational constant and cosmological constant in general Relativity by assuming ξ(t)=ξ_(0 ) p^m where ξ_(0 ) and m are constants. We also assume a variation law for Hubble parameter as H(R) = a (R^(-n)+1), where a>0, n>1 being constant. Two universe models were obtained, and their physical behavior has been discussed. When n=1 the Universe starts from singular state whereas when n=0 the cosmology follows a no singular state. The presence of bulk viscosity increase matter density’s value.

Keywords: Bulk Viscous Bianchi Type V Cosmological Model, hubble constants, gravitational constant, cosmological constants

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Kourosh Modarresi

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The abundance of media channels and devices has given users a variety of options to extract, discover, and explore information in the digital world. Since, often, there is a long and complicated path that a typical user may venture before taking any (significant) action (such as purchasing goods and services), it is critical to know how each node (media channel) in the path of user has contributed to the final action. In this work, the significance of each media channel is computed using statistical analysis and machine learning techniques. More specifically, “Regularized Singular Value Decomposition”, and “Sparse Principal Component” has been used to compute the significance of each channel toward the final action. The results of this work are a considerable improvement compared to the present approaches.

Keywords: multimedia attribution, sparse principal component, regularization, singular value decomposition, feature significance, machine learning, linear systems, variable shrinkage

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Authors: Malay Bhattacharyya, Saparya Suresh

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The Correlation Structure associated with a portfolio is subjected to vary across time. Studying the structural breaks in the time-dependent Correlation matrix associated with a collection had been a subject of interest for a better understanding of the market movements, portfolio selection, etc. The current paper proposes a methodology for testing the change in the time-dependent correlation structure of a portfolio in the high dimensional data using the techniques of generalized inverse, singular valued decomposition and multivariate distribution theory which has not been addressed so far. The asymptotic properties of the proposed test are derived. Also, the performance and the validity of the method is tested on a real data set. The proposed test performs well for detecting the change in the dependence of global markets in the context of high dimensional data.

Keywords: correlation structure, high dimensional data, multivariate distribution theory, singular valued decomposition

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Authors: Olivier Delage, Hassan Bencherif, Alain Bourdier

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Signal decomposition approaches represent an important step in time series analysis, providing useful knowledge and insight into the data and underlying dynamics characteristics while also facilitating tasks such as noise removal and feature extraction. As most of observational time series are nonlinear and nonstationary, resulting of several physical processes interaction at different time scales, experimental time series have fluctuations at all time scales and requires the development of specific signal decomposition techniques. Most commonly used techniques are data driven, enabling to obtain well-behaved signal components without making any prior-assumptions on input data. Among the most popular time series decomposition techniques, most cited in the literature, are the empirical mode decomposition and its variants, the empirical wavelet transform and singular spectrum analysis. With increasing popularity and utility of these methods in wide ranging applications, it is imperative to gain a good understanding and insight into the operation of these algorithms. In this work, we describe all of the techniques mentioned above as well as their ability to denoise signals, to capture trends, to identify components corresponding to the physical processes involved in the evolution of the observed system and deduce the dimensionality of the underlying dynamics. Results obtained with all of these methods on experimental total ozone columns and rainfall time series will be discussed and compared

Keywords: denoising, empirical mode decomposition, singular spectrum analysis, time series, underlying dynamics, wavelet analysis

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Authors: Syamala Krishnannair

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A multivariate statistical process monitoring methodology using dissimilarity scale-based singular spectrum analysis (SSA) is proposed for the detection and diagnosis of process faults in the base metal flotation plant. Process faults are detected based on the multi-level decomposition of process signals by SSA using the dissimilarity structure of the process data and the subsequent monitoring of the multiscale signals using the unified monitoring index which combines T² with SPE. Contribution plots are used to identify the root causes of the process faults. The overall results indicated that the proposed technique outperformed the conventional multivariate techniques in the detection and diagnosis of the process faults in the flotation plant.

Keywords: fault detection, fault diagnosis, process monitoring, dissimilarity scale

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Authors: Qiong Hu, Ming Yue

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Language variation signals the newest usage of language community, which might become the developmental trend of that language. The personal pronoun we is prescribed as a plural pronoun in grammar, but its number value is more flexible in actual use. Based on the homemade Friends corpus, the present research explores the number value of the first person pronoun we in nowadays American spoken English. With consideration of the subjectivity of we, this paper used ‘we+ PCU (Perception-cognation-utterance) verbs’ collocations and ‘we+ plural categories’ as the parameters. Results from corpus data and manual annotation show that: 1) the overall frequency of we has been increasing; 2) we has been increasingly used with other plural categories, indicating a weakening of its plural reference; and 3) we has been increasingly used with PCU (perception-cognition-utterance) verbs of strong subjectivity, indicating a strengthening of its singular reference. All these seem to support our hypothesis that we is undergoing the process of further grammaticalization towards a singular reference, though future evidence is needed to attest the bold prediction.

Keywords: number, PCU verbs, personal pronoun we,

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

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In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: Assma Azeroual, Karim Afdel, Mohamed El Hajji, Hassan Douzi

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Key frame extraction methods select the most representative frames of a video, which can be used in different areas of video processing such as video retrieval, video summary, and video indexing. In this paper we present a novel approach for extracting key frames from video sequences. The frame is characterized uniquely by his contours which are represented by the dominant blocks. These dominant blocks are located on the contours and its near textures. When the video frames have a noticeable changement, its dominant blocks changed, then we can extracte a key frame. The dominant blocks of every frame is computed, and then feature vectors are extracted from the dominant blocks image of each frame and arranged in a feature matrix. Singular Value Decomposition is used to calculate sliding windows ranks of those matrices. Finally the computed ranks are traced and then we are able to extract key frames of a video. Experimental results show that the proposed approach is robust against a large range of digital effects used during shot transition.

Keywords: FSDWT, key frame extraction, shot detection, singular value decomposition

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm

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Authors: Janusz Kwaśniewski, Ireneusz Dominik, Krzysztof Lalik

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The knowledge about rock layers thickness, especially above drilled mining pavements are crucial for workers safety. The measuring systems used nowadays are generally imperfect and there is a strong demand for improvement. The application of a new type of a measurement system called Self-Excited Acoustical System is presented in the paper. The system was applied until now to monitor stress changes in metal and concrete constructions. The change in measurement methodology resulted in possibility of measuring the thickness of the rocks above the tunnels as well as thickness of a singular rock layer. The idea is to find two resonance frequencies of the self-exited system, which consists of a vibration exciter and vibration receiver placed at a distance, which are coupled with a proper power amplifier, and which operate in a closed loop with a positive feedback. The resonance with the higher amplitude determines thickness of the whole rock, whereas the lower amplitude resonance indicates thickness of a singular layer. The results of the laboratory tests conducted on a group of different rock materials are also presented.

Keywords: auto-oscillator, non-destructive testing, rock thickness measurement, geotechnic

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Authors: M. Prema Kumar, P. Rajesh Kumar

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The increasing interest in image fusion (combining images of two or more modalities such as infrared and visible light radiation) has led to a need for accurate and reliable image assessment methods. This paper gives a novel approach of merging the information content from several videos taken from the same scene in order to rack up a combined video that contains the finest information coming from different source videos. This process is known as video fusion which helps in providing superior quality (The term quality, connote measurement on the particular application.) image than the source images. In this technique different sensors (whose redundant information can be reduced) are used for various cameras that are imperative for capturing the required images and also help in reducing. In this paper Image fusion technique based on multi-resolution singular value decomposition (MSVD) has been used. The image fusion by MSVD is almost similar to that of wavelets. The idea behind MSVD is to replace the FIR filters in wavelet transform with singular value decomposition (SVD). It is computationally very simple and is well suited for real time applications like in remote sensing and in astronomy.

Keywords: multi sensor image fusion, MSVD, image processing, monochrome video

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Authors: Mohammad Sahadet Hossain, Shamsil Arifeen, Mehrab Hossian Likhon

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In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives low-rank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems.

Keywords: low-rank cholesky factor alternating directions implicit iteration, LTI Descriptor system, Lyapunov equations, Square-root balanced truncation

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Authors: Qianhua He, Weili Zhou, Aiwu Chen

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A sparse representation speech denoising method based on adapted stopping residue error was presented in this paper. Firstly, the cross-correlation between the clean speech spectrum and the noise spectrum was analyzed, and an estimation method was proposed. In the denoising method, an over-complete dictionary of the clean speech power spectrum was learned with the K-singular value decomposition (K-SVD) algorithm. In the sparse representation stage, the stopping residue error was adaptively achieved according to the estimated cross-correlation and the adjusted noise spectrum, and the orthogonal matching pursuit (OMP) approach was applied to reconstruct the clean speech spectrum from the noisy speech. Finally, the clean speech was re-synthesised via the inverse Fourier transform with the reconstructed speech spectrum and the noisy speech phase. The experiment results show that the proposed method outperforms the conventional methods in terms of subjective and objective measure.

Keywords: speech denoising, sparse representation, k-singular value decomposition, orthogonal matching pursuit

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Authors: Kyoung-Jae Kim

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Collaborative Filtering (CF) is a popular technique for the personalization in the E-commerce domain to reduce information overload. In general, CF provides recommending items list based on other similar users’ preferences from the user-item matrix and predicts the focal user’s preference for particular items by using them. Many recommender systems in real-world use CF techniques because it’s excellent accuracy and robustness. However, it has some limitations including sparsity problems and complex dimensionality in a user-item matrix. In addition, traditional CF does not consider the emotional interaction between users. In this study, we propose recommender systems using social network and singular value decomposition (SVD) to alleviate some limitations. The purpose of this study is to reduce the dimensionality of data set using SVD and to improve the performance of CF by using emotional information from social network data of the focal user. In this study, we test the usability of hybrid CF, SVD and social network information model using the real-world data. The experimental results show that the proposed model outperforms conventional CF models.

Keywords: recommender systems, collaborative filtering, social network information, singular value decomposition

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Authors: Marwan Jarrah

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This research paper provides two pieces of phonological and syntactic evidence from Arabic for biolinguistics perspective of language processing. The first piece of evidence concerns the instances where a singular noun is converted to a plural noun in Arabic. Based on the findings of several research papers, this study shows that a singular word does not lose any of its moras when it is pluralized either regularly or irregularly. This mora conservation principle complies with the general physical law of the conservation of mass which states that mass is neither created nor destroyed but changed from one form into another. The second piece of evidence concerns the observation that when the object in some Arabic dialects including Jordanian Arabic and Najdi Arabic is a topic and positioned in situ (i.e. after the verb), the verb agrees with it, something that generates an agreeing inflection marker of the verb that agrees in Number, Person, and Gender with the in-situ topicalized object. This interaction between the verb and the object in such cases is invoked because of the extra feature the object bears, i.e. TOPIC feature. We suggest that such an interaction complies with the general natural law that elements become active when they, e.g., get an additional electron, when the mass number is not equal to the atomic number.

Keywords: biolinguistics, Arabic, physics, interaction

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Authors: Fatemah A. Alqallaf, Debasis Kundu

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The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

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Authors: Natalia Wojarnik

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The paper aims to present the analysis of a Reddit confessions corpus. The interpretation focuses on the use of emotional language, in particular emotive verbs, in the context of personal pronouns. The analysis of the linguistic properties answers the question of what the Reddit users confess about and who is the subject of confessions. The study reveals that the specific language patterns used in Reddit confessions reflect the language of depression and the language used by patients during different stages of their psychotherapy sessions. The paper concludes that Reddit users are more willing to confess about their own experiences, not rarely very private and intimate, extensively using the first person singular pronoun I. It indicates that the Reddit users use the language of depression and the language used by psychotherapy patients. The language they use is very emotionally impacted and includes many emotive verbs such as want, feel, need, hate, love. This finding in Reddit confessions correlates with the extensive use of stative affective verbs in the first stages of the psychotherapy sessions. Lastly, the paper refers to the positive and negative lexicon and helps determine how online posts can serve as a depression detector and “talking cure” for the users.

Keywords: confessions, emotional language, emotive verbs, pronouns, first person pronoun, language of depression, depression detection, psychotherapy language

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Authors: Amir Hadi Ziaie

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In the present work, we revisit the collapse process of a spherically symmetric homogeneous scalar field (in FRW background) minimally coupled to gravity, when the phase-space deformations are taken into account. Such a deformation is mathematically introduced as a particular type of noncommutativity between the canonical momenta of the scale factor and of the scalar field. In the absence of such deformation, the collapse culminates in a spacetime singularity. However, when the phase-space is deformed, we find that the singularity is removed by a non-singular bounce, beyond which the collapsing cloud re-expands to infinity. More precisely, for negative values of the deformation parameter, we identify the appearance of a negative pressure, which decelerates the collapse to finally avoid the singularity formation. While in the un-deformed case, the horizon curve monotonically decreases to finally cover the singularity, in the deformed case the horizon has a minimum value that this value depends on deformation parameter and initial configuration of the collapse. Such a setting predicts a threshold mass for black hole formation in stellar collapse and manifests the role of non-commutative geometry in physics and especially in stellar collapse and supernova explosion.

Keywords: gravitational collapse, non-commutative geometry, spacetime singularity, black hole physics

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Authors: Marek Dlapa

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The algebraic approach is applied to the control of the HiMAT (Highly Maneuverable Aircraft Technology). The objective is to find a robust controller which guarantees robust stability and decoupled control of longitudinal model of a scaled remotely controlled vehicle version of the advanced fighter HiMAT. Control design is performed by decoupling the nominal MIMO (multi-input multi-output) system into two identical SISO (single-input single-output) plants which are approximated by a 4th order transfer function. The algebraic approach is then used for pole placement design, and the nominal closed-loop poles are tuned so that the peak of the µ-function is minimal. As an optimization tool, evolutionary algorithm Differential Migration is used in order to overcome the multimodality of the cost function yielding simple controller with decoupling for nominal plant which is compared with the D-K iteration through simulations of standard longitudinal manoeuvres documenting decoupled control obtained from algebraic approach for nominal plant as well as worst case perturbation.

Keywords: algebraic approach, evolutionary computation, genetic algorithms, HiMAT, robust control, structured singular value

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: S. J. Bindhu, Edwina G. Rodrigues, Jijo Balakrishnan

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A grid-connected photovoltaic (PV) micro inverter with good performance properties is proposed in this paper. The proposed inverter with a quadrupler, having more efficiency and less voltage stress across the diodes. The stress that come across the diodes that use in the inverter section is considerably low in the proposed converter, also the protection scheme that we provided can eliminate the chances of the error due to fault. The proposed converter is implemented using perturb and observe algorithm so that the fluctuation in the voltage can be reduce and can attain maximum power point. Finally, some simulation and experimental results are also presented to demonstrate the effectiveness of the proposed converter.

Keywords: DC-DC converter, MPPT, quadrupler, PV panel

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Authors: Qiong Hu

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From old English to modern English, the gender category has changed from grammatical gender system to natural gender system. The word classes that reflected gender has changed from pronouns, adjectives, and numerals in old English to only pronouns in modern English. In present-day English, the third person singular pronouns are the only paradigm that keeps an intact gender. 'He' and 'they' used as epicene pronouns are one of the two commonest phenomena of gender disagreement (the other being those against the natural gender). Considering the convenience of corpus concordance, epicene pronoun usage is selected in this study in which the anaphors are restricted to possessives (eg. his, their), and the antecedents are restricted to compound indefinite pronouns (eg. someone, somebody). Factors like writing form (eg. someone vs. some one), the semantics of the prefixes (eg. some- vs. any-), and suffixes (eg. -one vs. -body), as well as frequency, are taken into consideration. Statistics indicate that 'their' is increasingly used as the epicene pronoun compared with the decline of 'his' (when both writing forms are considered). This is influenced by social factors such as feminist movement, as well as the semantics and frequency of antecedents. Their (plural) used in anaphoric reference to various indefinite pronouns (singular in form) can also be treated as number variation in third person pronouns, and the trend that 'their' in place of his can also be treated as a change in number category. Among different candidates for the gender-neutral function, 'their' is proven to be the most promising one based on the diachronic data. This does not reject any new competitors in the future which still remains to be seen.

Keywords: language variation and change, epicene pronouns, gender, number

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Authors: Zerzouri Nora

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In this paper, author presented the generalities of a photovoltaic system study and simulation. Author inserted the DC-DC converter to raise the voltage level and improve the operation of the PV panel by continuing the operating point at maximum power by using the Perturb and Observe technique (P&O). The connection to the network is made by inserting a three-phase voltage inverter allowing synchronization with the network the inverter is controlled by a PWM control. The simulation results allow the author to visualize the operation of the different components of the system, as well as the behavior of the system during the variation of meteorological values.

Keywords: photovoltaic generator PV, boost converter, P&O MPPT, PWM inverter, three phase grid

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Linyu Wang, Mingjun Zhu, Jianhong Xiang, Hanyu Jiang

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Aiming at the problem that the spectral efficiency of hybrid precoding (HP) is too low in the current millimeter wave (mmWave) massive multiple input multiple output (MIMO) system, this paper proposes a digital joint equivalent channel hybrid precoding algorithm, which is based on the introduction of digital encoding matrix iteration. First, the objective function is expanded to obtain the relation equation, and the pseudo-inverse iterative function of the analog encoder is derived by using the pseudo-inverse method, which solves the problem of greatly increasing the amount of computation caused by the lack of rank of the digital encoding matrix and reduces the overall complexity of hybrid precoding. Secondly, the analog coding matrix and the millimeter-wave sparse channel matrix are combined into an equivalent channel, and then the equivalent channel is subjected to Singular Value Decomposition (SVD) to obtain a digital coding matrix, and then the derived pseudo-inverse iterative function is used to iteratively regenerate the simulated encoding matrix. The simulation results show that the proposed algorithm improves the system spectral efficiency by 10~20%compared with other algorithms and the stability is also improved.

Keywords: mmWave, massive MIMO, hybrid precoding, singular value decompositing, equivalent channel

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Authors: Ophir Nave

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In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system.

Keywords: polydisperse spray, model reduction, asymptotic analysis, multi-scale systems

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Authors: Olga Hernán-Vega, Patricia López-Rodríguez, David Escot-Bocanegra, Raúl Fernández-Recio, Ignacio Bravo

Abstract:

Non-Cooperative Target Identification has become a key research domain in the Defense industry since it provides the ability to recognize targets at long distance and under any weather condition. High Resolution Range Profiles, one-dimensional radar images where the reflectivity of a target is projected onto the radar line of sight, are widely used for identification of flying targets. According to that, to face this problem, an approach to Non-Cooperative Target Identification based on the exploitation of Singular Value Decomposition to a matrix of range profiles is presented. Target Identification based on one-dimensional radar images compares a collection of profiles of a given target, namely test set, with the profiles included in a pre-loaded database, namely training set. The classification is improved by using Singular Value Decomposition since it allows to model each aircraft as a subspace and to accomplish recognition in a transformed domain where the main features are easier to extract hence, reducing unwanted information such as noise. Singular Value Decomposition permits to define a signal subspace which contain the highest percentage of the energy, and a noise subspace which will be discarded. This way, only the valuable information of each target is used in the recognition process. The identification algorithm is based on finding the target that minimizes the angle between subspaces and takes place in a transformed domain. Two metrics, F1 and F2, based on Singular Value Decomposition are accomplished in the identification process. In the case of F2, the angle is weighted, since the top vectors set the importance in the contribution to the formation of a target signal, on the contrary F1 simply shows the evolution of the unweighted angle. In order to have a wide database or radar signatures and evaluate the performance, range profiles are obtained through numerical simulation of seven civil aircraft at defined trajectories taken from an actual measurement. Taking into account the nature of the datasets, the main drawback of using simulated profiles instead of actual measured profiles is that the former implies an ideal identification scenario, since measured profiles suffer from noise, clutter and other unwanted information and simulated profiles don't. In this case, the test and training samples have similar nature and usually a similar high signal-to-noise ratio, so as to assess the feasibility of the approach, the addition of noise has been considered before the creation of the test set. The identification results applying the unweighted and weighted metrics are analysed for demonstrating which algorithm provides the best robustness against noise in an actual possible scenario. So as to confirm the validity of the methodology, identification experiments of profiles coming from electromagnetic simulations are conducted, revealing promising results. Considering the dissimilarities between the test and training sets when noise is added, the recognition performance has been improved when weighting is applied. Future experiments with larger sets are expected to be conducted with the aim of finally using actual profiles as test sets in a real hostile situation.

Keywords: HRRP, NCTI, simulated/synthetic database, SVD

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