• Title/Summary/Keyword: nonlinear systems

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Automated Finite Element Analyses for Structural Integrated Systems (통합 구조 시스템의 유한요소해석 자동화)

  • Chongyul Yoon
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.37 no.1
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    • pp.49-56
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    • 2024
  • An automated dynamic structural analysis module stands as a crucial element within a structural integrated mitigation system. This module must deliver prompt real-time responses to enable timely actions, such as evacuation or warnings, in response to the severity posed by the structural system. The finite element method, a widely adopted approximate structural analysis approach globally, owes its popularity in part to its user-friendly nature. However, the computational efficiency and accuracy of results depend on the user-provided finite element mesh, with the number of elements and their quality playing pivotal roles. This paper introduces a computationally efficient adaptive mesh generation scheme that optimally combines the h-method of node movement and the r-method of element division for mesh refinement. Adaptive mesh generation schemes automatically create finite element meshes, and in this case, representative strain values for a given mesh are employed for error estimates. When applied to dynamic problems analyzed in the time domain, meshes need to be modified at each time step, considering a few hundred or thousand steps. The algorithm's specifics are demonstrated through a standard cantilever beam example subjected to a concentrated load at the free end. Additionally, a portal frame example showcases the generation of various robust meshes. These examples illustrate the adaptive algorithm's capability to produce robust meshes, ensuring reasonable accuracy and efficient computing time. Moreover, the study highlights the potential for the scheme's effective application in complex structural dynamic problems, such as those subjected to seismic or erratic wind loads. It also emphasizes its suitability for general nonlinear analysis problems, establishing the versatility and reliability of the proposed adaptive mesh generation scheme.

Performance Analysis of the Array Shape Estimation Methods Based on the Nearfield Signal Modeling (근거리 신호 모델링을 기반으로 한 어레이 형상 추정 기법들의 성능 분석)

  • Park, Hee-Young;Lee, Chung-Yong
    • The Journal of the Acoustical Society of Korea
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    • v.27 no.5
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    • pp.221-228
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    • 2008
  • To estimate array shape with reference sources in SONAR systems, nearfield signal modeling is required for the reference sources near a towed array. Array shape estimation method based on the nearfield signal modeling generally exploits the spatial covariance matrix of the received reference sources. Among those method, nearfield eigenvector method uses the eigenvector corresponding to the maximum eigenvalue as a steering vector of the reference source. In this paper, we propose a simplified subspace fitting method based on the nearfield signal modeling with spherical wave modeling. Furthermore, we analyze performance of the array shape estimation methods based on the nearfield signal modeling for various environments. The results of the numerical experiments indicate that the simplified subspace fitting method and the nearfield eigenvector method with single reference source shows almost similar performance. Furthermore, the simplified subspace fitting method with 2 reference sources consistently estimates the shape of the array regardless of the incident angle of the reference sources, whereas the nearfield eigenvector method cannot apply for the case of 2 reference sources.

The Prediction of DEA based Efficiency Rating for Venture Business Using Multi-class SVM (다분류 SVM을 이용한 DEA기반 벤처기업 효율성등급 예측모형)

  • Park, Ji-Young;Hong, Tae-Ho
    • Asia pacific journal of information systems
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    • v.19 no.2
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    • pp.139-155
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    • 2009
  • For the last few decades, many studies have tried to explore and unveil venture companies' success factors and unique features in order to identify the sources of such companies' competitive advantages over their rivals. Such venture companies have shown tendency to give high returns for investors generally making the best use of information technology. For this reason, many venture companies are keen on attracting avid investors' attention. Investors generally make their investment decisions by carefully examining the evaluation criteria of the alternatives. To them, credit rating information provided by international rating agencies, such as Standard and Poor's, Moody's and Fitch is crucial source as to such pivotal concerns as companies stability, growth, and risk status. But these types of information are generated only for the companies issuing corporate bonds, not venture companies. Therefore, this study proposes a method for evaluating venture businesses by presenting our recent empirical results using financial data of Korean venture companies listed on KOSDAQ in Korea exchange. In addition, this paper used multi-class SVM for the prediction of DEA-based efficiency rating for venture businesses, which was derived from our proposed method. Our approach sheds light on ways to locate efficient companies generating high level of profits. Above all, in determining effective ways to evaluate a venture firm's efficiency, it is important to understand the major contributing factors of such efficiency. Therefore, this paper is constructed on the basis of following two ideas to classify which companies are more efficient venture companies: i) making DEA based multi-class rating for sample companies and ii) developing multi-class SVM-based efficiency prediction model for classifying all companies. First, the Data Envelopment Analysis(DEA) is a non-parametric multiple input-output efficiency technique that measures the relative efficiency of decision making units(DMUs) using a linear programming based model. It is non-parametric because it requires no assumption on the shape or parameters of the underlying production function. DEA has been already widely applied for evaluating the relative efficiency of DMUs. Recently, a number of DEA based studies have evaluated the efficiency of various types of companies, such as internet companies and venture companies. It has been also applied to corporate credit ratings. In this study we utilized DEA for sorting venture companies by efficiency based ratings. The Support Vector Machine(SVM), on the other hand, is a popular technique for solving data classification problems. In this paper, we employed SVM to classify the efficiency ratings in IT venture companies according to the results of DEA. The SVM method was first developed by Vapnik (1995). As one of many machine learning techniques, SVM is based on a statistical theory. Thus far, the method has shown good performances especially in generalizing capacity in classification tasks, resulting in numerous applications in many areas of business, SVM is basically the algorithm that finds the maximum margin hyperplane, which is the maximum separation between classes. According to this method, support vectors are the closest to the maximum margin hyperplane. If it is impossible to classify, we can use the kernel function. In the case of nonlinear class boundaries, we can transform the inputs into a high-dimensional feature space, This is the original input space and is mapped into a high-dimensional dot-product space. Many studies applied SVM to the prediction of bankruptcy, the forecast a financial time series, and the problem of estimating credit rating, In this study we employed SVM for developing data mining-based efficiency prediction model. We used the Gaussian radial function as a kernel function of SVM. In multi-class SVM, we adopted one-against-one approach between binary classification method and two all-together methods, proposed by Weston and Watkins(1999) and Crammer and Singer(2000), respectively. In this research, we used corporate information of 154 companies listed on KOSDAQ market in Korea exchange. We obtained companies' financial information of 2005 from the KIS(Korea Information Service, Inc.). Using this data, we made multi-class rating with DEA efficiency and built multi-class prediction model based data mining. Among three manners of multi-classification, the hit ratio of the Weston and Watkins method is the best in the test data set. In multi classification problems as efficiency ratings of venture business, it is very useful for investors to know the class with errors, one class difference, when it is difficult to find out the accurate class in the actual market. So we presented accuracy results within 1-class errors, and the Weston and Watkins method showed 85.7% accuracy in our test samples. We conclude that the DEA based multi-class approach in venture business generates more information than the binary classification problem, notwithstanding its efficiency level. We believe this model can help investors in decision making as it provides a reliably tool to evaluate venture companies in the financial domain. For the future research, we perceive the need to enhance such areas as the variable selection process, the parameter selection of kernel function, the generalization, and the sample size of multi-class.

A Study on the Volatility of Global Stock Markets using Markov Regime Switching model (마코브국면전환모형을 이용한 글로벌 주식시장의 변동성에 대한 연구)

  • Lee, Kyung-Hee;Kim, Kyung-Soo
    • Management & Information Systems Review
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    • v.34 no.3
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    • pp.17-39
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    • 2015
  • This study examined the structural changes and volatility in the global stock markets using a Markov Regime Switching ARCH model developed by the Hamilton and Susmel (1994). Firstly, the US, Italy and Ireland showed that variance in the high volatility regime was more than five times that in the low volatility, while Korea, Russia, India, and Greece exhibited that variance in the high volatility regime was increased more than eight times that in the low. On average, a jump from regime 1 to regime 2 implied roughly three times increased in risk, while the risk during regime 3 was up to almost thirteen times than during regime 1 over the study period. And Korea, the US, India, Italy showed ARCH(1) and ARCH(2) effects, leverage and asymmetric effects. Secondly, 278 days were estimated in the persistence of low volatility regime, indicating that the mean transition probability between volatilities exhibited the highest long-term persistence in Korea. Thirdly, the coefficients appeared to be unstable structural changes and volatility for the stock markets in Chow tests during the Asian, Global and European financial crisis. In addition, 1-Step prediction error tests showed that stock markets were unstable during the Asian crisis of 1997-1998 except for Russia, and the Global crisis of 2007-2008 except for Korea and the European crisis of 2010-2011 except for Korea, the US, Russia and India. N-Step tests exhibited that most of stock markets were unstable during the Asian and Global crisis. There was little change in the Asian crisis in CUSUM tests, while stock markets were stable until the late 2000s except for some countries. Also there were stable and unstable stock markets mixed across countries in CUSUMSQ test during the crises. Fourthly, I confirmed a close relevance of the volatility between Korea and other countries in the stock markets through the likelihood ratio tests. Accordingly, I have identified the episode or events that generated the high volatility in the stock markets for the financial crisis, and for all seven stock markets the significant switch between the volatility regimes implied a considerable change in the market risk. It appeared that the high stock market volatility was related with business recession at the beginning in 1990s. By closely examining the history of political and economical events in the global countries, I found that the results of Lamoureux and Lastrapes (1990) were consistent with those of this paper, indicating there were the structural changes and volatility during the crises and specificly every high volatility regime in SWARCH-L(3,2) student t-model was accompanied by some important policy changes or financial crises in countries or other critical events in the international economy. The sophisticated nonlinear models are needed to further analysis.

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Capacity Comparison of Two Uplink OFDMA Systems Considering Synchronization Error among Multiple Users and Nonlinear Distortion of Amplifiers (사용자간 동기오차와 증폭기의 비선형 왜곡을 동시에 고려한 두 상향링크 OFDMA 기법의 채널용량 비교 분석)

  • Lee, Jin-Hui;Kim, Bong-Seok;Choi, Kwonhue
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.39A no.5
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    • pp.258-270
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    • 2014
  • In this paper, we investigate channel capacity of two kinds of uplink OFDMA (Orthogonal Frequency Division Multiple Access) schemes, i.e. ZCZ (Zero Correlation Zone) code time-spread OFDMA and sparse SC-FDMA (Single Carrier Frequency Division Mmultiple Access) robust to access timing offset (TO) among multiple users. In order to reflect the practical condition, we consider not only access TO among multiple users but also peak to average power ratio (PAPR) which is one of hot issues of uplink OFDMA. In the case with access TO among multiple users, the amplified signal of users by power control might affect a severe interference to signals of other users. Meanwhile, amplified signal by considering distance between user and base station might be distorted due to the limit of amplifier and thus the performance might degrade. In order to achieve the maximum channel capacity, we investigate the combinations of transmit power so called ASF (adaptive scaling factor) by numerical simulations. We check that the channel capacity of the case with ASF increases compared to the case with considering only distance i.e. ASF=1. From the simulation results, In the case of high signal to noise ratio (SNR), ZCZ code time-spread OFDMA achieves higher channel capacity compared to sparse block SC-FDMA. On the other hand, in the case of low SNR, the sparse block SC-FDMA achieves better performance compared to ZCZ time-spread OFDMA.

A Study on Developing a VKOSPI Forecasting Model via GARCH Class Models for Intelligent Volatility Trading Systems (지능형 변동성트레이딩시스템개발을 위한 GARCH 모형을 통한 VKOSPI 예측모형 개발에 관한 연구)

  • Kim, Sun-Woong
    • Journal of Intelligence and Information Systems
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    • v.16 no.2
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    • pp.19-32
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    • 2010
  • Volatility plays a central role in both academic and practical applications, especially in pricing financial derivative products and trading volatility strategies. This study presents a novel mechanism based on generalized autoregressive conditional heteroskedasticity (GARCH) models that is able to enhance the performance of intelligent volatility trading systems by predicting Korean stock market volatility more accurately. In particular, we embedded the concept of the volatility asymmetry documented widely in the literature into our model. The newly developed Korean stock market volatility index of KOSPI 200, VKOSPI, is used as a volatility proxy. It is the price of a linear portfolio of the KOSPI 200 index options and measures the effect of the expectations of dealers and option traders on stock market volatility for 30 calendar days. The KOSPI 200 index options market started in 1997 and has become the most actively traded market in the world. Its trading volume is more than 10 million contracts a day and records the highest of all the stock index option markets. Therefore, analyzing the VKOSPI has great importance in understanding volatility inherent in option prices and can afford some trading ideas for futures and option dealers. Use of the VKOSPI as volatility proxy avoids statistical estimation problems associated with other measures of volatility since the VKOSPI is model-free expected volatility of market participants calculated directly from the transacted option prices. This study estimates the symmetric and asymmetric GARCH models for the KOSPI 200 index from January 2003 to December 2006 by the maximum likelihood procedure. Asymmetric GARCH models include GJR-GARCH model of Glosten, Jagannathan and Runke, exponential GARCH model of Nelson and power autoregressive conditional heteroskedasticity (ARCH) of Ding, Granger and Engle. Symmetric GARCH model indicates basic GARCH (1, 1). Tomorrow's forecasted value and change direction of stock market volatility are obtained by recursive GARCH specifications from January 2007 to December 2009 and are compared with the VKOSPI. Empirical results indicate that negative unanticipated returns increase volatility more than positive return shocks of equal magnitude decrease volatility, indicating the existence of volatility asymmetry in the Korean stock market. The point value and change direction of tomorrow VKOSPI are estimated and forecasted by GARCH models. Volatility trading system is developed using the forecasted change direction of the VKOSPI, that is, if tomorrow VKOSPI is expected to rise, a long straddle or strangle position is established. A short straddle or strangle position is taken if VKOSPI is expected to fall tomorrow. Total profit is calculated as the cumulative sum of the VKOSPI percentage change. If forecasted direction is correct, the absolute value of the VKOSPI percentage changes is added to trading profit. It is subtracted from the trading profit if forecasted direction is not correct. For the in-sample period, the power ARCH model best fits in a statistical metric, Mean Squared Prediction Error (MSPE), and the exponential GARCH model shows the highest Mean Correct Prediction (MCP). The power ARCH model best fits also for the out-of-sample period and provides the highest probability for the VKOSPI change direction tomorrow. Generally, the power ARCH model shows the best fit for the VKOSPI. All the GARCH models provide trading profits for volatility trading system and the exponential GARCH model shows the best performance, annual profit of 197.56%, during the in-sample period. The GARCH models present trading profits during the out-of-sample period except for the exponential GARCH model. During the out-of-sample period, the power ARCH model shows the largest annual trading profit of 38%. The volatility clustering and asymmetry found in this research are the reflection of volatility non-linearity. This further suggests that combining the asymmetric GARCH models and artificial neural networks can significantly enhance the performance of the suggested volatility trading system, since artificial neural networks have been shown to effectively model nonlinear relationships.

Corporate Default Prediction Model Using Deep Learning Time Series Algorithm, RNN and LSTM (딥러닝 시계열 알고리즘 적용한 기업부도예측모형 유용성 검증)

  • Cha, Sungjae;Kang, Jungseok
    • Journal of Intelligence and Information Systems
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    • v.24 no.4
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    • pp.1-32
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    • 2018
  • In addition to stakeholders including managers, employees, creditors, and investors of bankrupt companies, corporate defaults have a ripple effect on the local and national economy. Before the Asian financial crisis, the Korean government only analyzed SMEs and tried to improve the forecasting power of a default prediction model, rather than developing various corporate default models. As a result, even large corporations called 'chaebol enterprises' become bankrupt. Even after that, the analysis of past corporate defaults has been focused on specific variables, and when the government restructured immediately after the global financial crisis, they only focused on certain main variables such as 'debt ratio'. A multifaceted study of corporate default prediction models is essential to ensure diverse interests, to avoid situations like the 'Lehman Brothers Case' of the global financial crisis, to avoid total collapse in a single moment. The key variables used in corporate defaults vary over time. This is confirmed by Beaver (1967, 1968) and Altman's (1968) analysis that Deakins'(1972) study shows that the major factors affecting corporate failure have changed. In Grice's (2001) study, the importance of predictive variables was also found through Zmijewski's (1984) and Ohlson's (1980) models. However, the studies that have been carried out in the past use static models. Most of them do not consider the changes that occur in the course of time. Therefore, in order to construct consistent prediction models, it is necessary to compensate the time-dependent bias by means of a time series analysis algorithm reflecting dynamic change. Based on the global financial crisis, which has had a significant impact on Korea, this study is conducted using 10 years of annual corporate data from 2000 to 2009. Data are divided into training data, validation data, and test data respectively, and are divided into 7, 2, and 1 years respectively. In order to construct a consistent bankruptcy model in the flow of time change, we first train a time series deep learning algorithm model using the data before the financial crisis (2000~2006). The parameter tuning of the existing model and the deep learning time series algorithm is conducted with validation data including the financial crisis period (2007~2008). As a result, we construct a model that shows similar pattern to the results of the learning data and shows excellent prediction power. After that, each bankruptcy prediction model is restructured by integrating the learning data and validation data again (2000 ~ 2008), applying the optimal parameters as in the previous validation. Finally, each corporate default prediction model is evaluated and compared using test data (2009) based on the trained models over nine years. Then, the usefulness of the corporate default prediction model based on the deep learning time series algorithm is proved. In addition, by adding the Lasso regression analysis to the existing methods (multiple discriminant analysis, logit model) which select the variables, it is proved that the deep learning time series algorithm model based on the three bundles of variables is useful for robust corporate default prediction. The definition of bankruptcy used is the same as that of Lee (2015). Independent variables include financial information such as financial ratios used in previous studies. Multivariate discriminant analysis, logit model, and Lasso regression model are used to select the optimal variable group. The influence of the Multivariate discriminant analysis model proposed by Altman (1968), the Logit model proposed by Ohlson (1980), the non-time series machine learning algorithms, and the deep learning time series algorithms are compared. In the case of corporate data, there are limitations of 'nonlinear variables', 'multi-collinearity' of variables, and 'lack of data'. While the logit model is nonlinear, the Lasso regression model solves the multi-collinearity problem, and the deep learning time series algorithm using the variable data generation method complements the lack of data. Big Data Technology, a leading technology in the future, is moving from simple human analysis, to automated AI analysis, and finally towards future intertwined AI applications. Although the study of the corporate default prediction model using the time series algorithm is still in its early stages, deep learning algorithm is much faster than regression analysis at corporate default prediction modeling. Also, it is more effective on prediction power. Through the Fourth Industrial Revolution, the current government and other overseas governments are working hard to integrate the system in everyday life of their nation and society. Yet the field of deep learning time series research for the financial industry is still insufficient. This is an initial study on deep learning time series algorithm analysis of corporate defaults. Therefore it is hoped that it will be used as a comparative analysis data for non-specialists who start a study combining financial data and deep learning time series algorithm.

Modeling of Sensorineural Hearing Loss for the Evaluation of Digital Hearing Aid Algorithms (디지털 보청기 알고리즘 평가를 위한 감음신경성 난청의 모델링)

  • 김동욱;박영철
    • Journal of Biomedical Engineering Research
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    • v.19 no.1
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    • pp.59-68
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    • 1998
  • Digital hearing aids offer many advantages over conventional analog hearing aids. With the advent of high speed digital signal processing chips, new digital techniques have been introduced to digital hearing aids. In addition, the evaluation of new ideas in hearing aids is necessarily accompanied by intensive subject-based clinical tests which requires much time and cost. In this paper, we present an objective method to evaluate and predict the performance of hearing aid systems without the help of such subject-based tests. In the hearing impairment simulation(HIS) algorithm, a sensorineural hearing impairment medel is established from auditory test data of the impaired subject being simulated. Also, the nonlinear behavior of the loudness recruitment is defined using hearing loss functions generated from the measurements. To transform the natural input sound into the impaired one, a frequency sampling filter is designed. The filter is continuously refreshed with the level-dependent frequency response function provided by the impairment model. To assess the performance, the HIS algorithm was implemented in real-time using a floating-point DSP. Signals processed with the real-time system were presented to normal subjects and their auditory data modified by the system was measured. The sensorineural hearing impairment was simulated and tested. The threshold of hearing and the speech discrimination tests exhibited the efficiency of the system in its use for the hearing impairment simulation. Using the HIS system we evaluated three typical hearing aid algorithms.

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Development and Adult Life Span of Aphidoletes aphidimyza (Rondani) (Diptera: Cecidomyiidae) Fed on the Melon Aphid, Aphis gossypii Glover or the Green Peach Aphid, Myzus persicae($S\"{u}lzer$) (Homoptera: Aphididae) (목화진딧물(Aphis gossypii)과 복숭아혹진딧물(Myzus persicae) (Homoptera: Aphididae)을 먹이로 한 진디혹파리[Aphidoletes aphidimyza (Rondani)] (Diptera: Cecidomyiidae)의 발육 및 성충수명)

  • Kim Tae-Heung;Kim Ji-Soo
    • Korean journal of applied entomology
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    • v.43 no.4 s.137
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    • pp.297-304
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    • 2004
  • The development of Aphidoletes aphidimyza, an aphidophagous gall midge, was studied at various constant temperatures ranging from 15 to $35^{\circ}C$, with $65{\pm}5\%$ RH, and a photo-period of 16L:8D. When A. aphidimyra was fed either on Aphis gossypii or Myzus persicae, it took 43.9 and 44.5 days, respectively, to develop from egg to pupa at $15^{\circ}C$, whereas at $25^{\circ}C$, 14.3 and 15.8 days. The developmental zero was 10.7 and $10.0^{\circ}C$, respectively, while the effective accumuative temperatures were 210.8 and 245.5 day-degrees. The nonlinear shape of temperature-dependent development, shown by A. aphidimyza when fed on either species of the aphids, was well described by the modified Sharpe and DeMichele model. When distribution model of completion time of development for each growth stage was expressed as physiological age and fitted to the Weibull fuction, the completion time of development gradually shortened from egg to larva, and to pupa. In addition, the coefficient of determination $r^2$ ranged between 0.86-0.93 and 0.85-0.94, respectively providing a good approximation of cumulative developmental rates. The life span of adult was 8.7 and 9.2 days at $15^{\circ}C$, and 3.1 and 2.7 days at $30^{\circ}C$, respectively. Egg incubation period was relatively short at $35^{\circ}C$ but hatchability was less than $50\%$ and the mortality of the larva at $35^{\circ}C$ reached $100\%$. At $30^{\circ}C$, the time of development lengthened and the adult longevity was short suggesting ill effect of high temperatures. Even though the life span of adults at $15^{\circ}C$ was relatively long, none moved freely in the rearing cage and no oviposition occurred. Accordingly, in case A. aphidimyza is adopted to suppress phytophagus aphid populations, it could be applicable to cropping systems with ambient temperatures above $20^{\circ}C$ and below $30^{\circ}C$. Within this range, A. aphidimyza adults was observed to be active and oviposit fully.

A digital Audio Watermarking Algorithm using 2D Barcode (2차원 바코드를 이용한 오디오 워터마킹 알고리즘)

  • Bae, Kyoung-Yul
    • Journal of Intelligence and Information Systems
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    • v.17 no.2
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    • pp.97-107
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    • 2011
  • Nowadays there are a lot of issues about copyright infringement in the Internet world because the digital content on the network can be copied and delivered easily. Indeed the copied version has same quality with the original one. So, copyright owners and content provider want a powerful solution to protect their content. The popular one of the solutions was DRM (digital rights management) that is based on encryption technology and rights control. However, DRM-free service was launched after Steve Jobs who is CEO of Apple proposed a new music service paradigm without DRM, and the DRM is disappeared at the online music market. Even though the online music service decided to not equip the DRM solution, copyright owners and content providers are still searching a solution to protect their content. A solution to replace the DRM technology is digital audio watermarking technology which can embed copyright information into the music. In this paper, the author proposed a new audio watermarking algorithm with two approaches. First, the watermark information is generated by two dimensional barcode which has error correction code. So, the information can be recovered by itself if the errors fall into the range of the error tolerance. The other one is to use chirp sequence of CDMA (code division multiple access). These make the algorithm robust to the several malicious attacks. There are many 2D barcodes. Especially, QR code which is one of the matrix barcodes can express the information and the expression is freer than that of the other matrix barcodes. QR code has the square patterns with double at the three corners and these indicate the boundary of the symbol. This feature of the QR code is proper to express the watermark information. That is, because the QR code is 2D barcodes, nonlinear code and matrix code, it can be modulated to the spread spectrum and can be used for the watermarking algorithm. The proposed algorithm assigns the different spread spectrum sequences to the individual users respectively. In the case that the assigned code sequences are orthogonal, we can identify the watermark information of the individual user from an audio content. The algorithm used the Walsh code as an orthogonal code. The watermark information is rearranged to the 1D sequence from 2D barcode and modulated by the Walsh code. The modulated watermark information is embedded into the DCT (discrete cosine transform) domain of the original audio content. For the performance evaluation, I used 3 audio samples, "Amazing Grace", "Oh! Carol" and "Take me home country roads", The attacks for the robustness test were MP3 compression, echo attack, and sub woofer boost. The MP3 compression was performed by a tool of Cool Edit Pro 2.0. The specification of MP3 was CBR(Constant Bit Rate) 128kbps, 44,100Hz, and stereo. The echo attack had the echo with initial volume 70%, decay 75%, and delay 100msec. The sub woofer boost attack was a modification attack of low frequency part in the Fourier coefficients. The test results showed the proposed algorithm is robust to the attacks. In the MP3 attack, the strength of the watermark information is not affected, and then the watermark can be detected from all of the sample audios. In the sub woofer boost attack, the watermark was detected when the strength is 0.3. Also, in the case of echo attack, the watermark can be identified if the strength is greater and equal than 0.5.