Search results for: discrete events

Authors: Ashish Ashish

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In the last few decades, the discrete chaos of difference equations has gained a massive attention of academicians and scholars due to its tremendous applications in each and every branch of science, such as cryptography, traffic control models, secure communications, weather forecasting, and engineering. In this article, a generalized logistic discrete map is established and discrete chaos is reported through period doubling bifurcation, period three orbit and Lyapunov exponent. It is interesting to see that the generalized logistic map exhibits superior chaos due to the presence of an extra degree of freedom of an ordered parameter. The period doubling bifurcation and Lyapunov exponent are demonstrated for some particular values of parameter and the discrete chaos is determined in the sense of Devaney's definition of chaos theoretically as well as numerically. Moreover, the study discusses an extended chaos based image encryption and decryption scheme in cryptography using this novel system. Surprisingly, a larger key space for coding and more sensitive dependence on initial conditions are examined for encryption and decryption of text messages, images and videos which secure the system strongly from external cyber attacks, coding attacks, statistic attacks and differential attacks.

Keywords: chaos, period-doubling, logistic map, Lyapunov exponent, image encryption

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Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

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In this paper, a hybrid blind digital watermarking system using Discrete Wavelet Transform (DWT) and Contourlet Transform (CT) has been implemented and tested. The implemented combined digital watermarking system has been tested against five common types of image attacks. The performance evaluation shows improved results in terms of imperceptibility, robustness, and high tolerance against these attacks; accordingly, the system is very effective and applicable.

Keywords: discrete wavelet transform (DWT), contourlet transform (CT), digital image watermarking, copyright protection, geometric attack

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Authors: A. S. Mousa, F. Shoman

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We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: coherent strategy, split strategy, pure strategy, mixed strategy, Nash equilibrium, game theory

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Authors: Samvel H. Sargsyan

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Together with the study of electron-optical properties of nanostructures and proceeding from experiment-based data, the study of the mechanical properties of nanostructures has become quite actual. For the study of the mechanical properties of fullerene, carbon nanotubes, graphene and other nanostructures one of the crucial issues is the construction of their adequate mathematical models. Among all mathematical models of graphene or carbon nano-tubes, this so-called discrete-continuous model is specifically important. It substitutes the interactions between atoms by elastic beams or springs. The present paper demonstrates the construction of the discrete-continual beam model for carbon nanotubes or graphene, where the micropolar beam model based on the theory of moment elasticity is accepted. With the account of the energy balance principle, the elastic moment constants for the beam model, expressed by the physical and geometrical parameters of carbon nanotube or graphene, are determined. By switching from discrete-continual beam model to the continual, the models of micropolar elastic cylindrical shell and micropolar elastic plate are confirmed as continual models for carbon nanotube and graphene respectively.

Keywords: carbon nanotube, discrete-continual, elastic, graphene, micropolar, plate, shell

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Authors: N. Li, Y. M. Cheng

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In this paper, the classical bearing capacity problem is re-considered from discrete element analysis. In the discrete element approach, the bearing capacity problem is considered from the elastic stage to plastic stage to rupture stage (large displacement). The bearing capacity failure mechanism of a strip footing on soil is investigated, and the influence of micro-parameters on the bearing capacity of soil is also observed. It is found that the distinct element method (DEM) gives very good visualized results, and basically coincides well with that derived by the classical methods.

Keywords: bearing capacity, distinct element method, failure mechanism, large displacement

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Babak Kamrani, Nozar Kishi

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Stochastic catalog represents the events module of the earthquake loss estimation models. It includes series of events with different magnitudes and corresponding frequencies/probabilities. For the development of the stochastic catalog, random or uniform sampling methods are used to sample the events from the seismicity model. For covering all the Magnitude Frequency Distribution (MFD), a huge number of events should be generated for the above-mentioned methods. Characteristic Event (CE) method chooses the events based on the interest of the insurance industry. We divide the MFD of each source into bins. We have chosen the bins based on the probability of the interest by the insurance industry. First, we have collected the information for the available seismic sources. Sources are divided into Fault sources, subduction, and events without specific fault source. We have developed the MFD for each of the individual and areal source based on the seismicity of the sources. Afterward, we have calculated the CE magnitudes based on the desired probability. To develop the stochastic catalog, we have introduced uncertainty to the location of the events too.

Keywords: stochastic catalogue, earthquake loss, uncertainty, characteristic event

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Authors: Harish Krishnamurthy, Anna Lafontant, Ren Yi

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Unidentified Flying Objects (UFOs) have been an interesting topic for most enthusiasts and hence people all over the United States report such findings online at the National UFO Report Center (NUFORC). Some of these reports are a hoax and among those that seem legitimate, our task is not to establish that these events confirm that they indeed are events related to flying objects from aliens in outer space. Rather, we intend to identify if the report was a hoax as was identified by the UFO database team with their existing curation criterion. However, the database provides a wealth of information that can be exploited to provide various analyses and insights such as social reporting, identifying real-time spatial events and much more. We perform analysis to localize these time-series geospatial events and correlate with known real-time events. This paper does not confirm any legitimacy of alien activity, but rather attempts to gather information from likely legitimate reports of UFOs by studying the online reports. These events happen in geospatial clusters and also are time-based. We look at cluster density and data visualization to search the space of various cluster realizations to decide best probable clusters that provide us information about the proximity of such activity. A random forest classifier is also presented that is used to identify true events and hoax events, using the best possible features available such as region, week, time-period and duration. Lastly, we show the performance of the scheme on various days and correlate with real-time events where one of the UFO reports strongly correlates to a missile test conducted in the United States.

Keywords: time-series clustering, feature extraction, hoax prediction, geospatial events

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Authors: Sudhanshu Kumar, Raghvendra Chandrakar, Arun Chakraborty

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In the ocean, the temperature extremes have the potential to devastate marine habitats, ecosystems together with ensuing socioeconomic consequences. In recent years, these extreme events are more frequent and intense globally and their increasing trend is expected to continue in the upcoming decades. It recently attracted public interest, as well as scientific researchers, which motivates us to analyze the current marine heatwave (MHW) events in the Bay of Bengal region. we have isolated 107 MHW events (above 90th percentile threshold) in this region of the Indian Ocean and investigated the variation in duration, intensity, and frequency of MHW events during our test period (1982-2021). Our study reveals that in the study region the average of three MHW events per year with an increasing linear trend of 1.11 MHW events per decade. In the analysis, we found the longest MHW event which lasted about 99 days, which is far greater than an average MHW event duration. The maximum intensity was 5.29°C (above the climatology-mean), while the mean intensity was 2.03°C. In addition, we observed net heat flux accompanied by anticyclonic eddies to be the primary cause of these events. Moreover, we concluded that these events affect sea surface height and oceanic productivity, highlighting the adverse impact of MHWs on marine ecosystems.

Keywords: marine heatwaves, global warming, climate change, sea surface temperature, marine ecosystem

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Authors: Varvara Roubtsova, Mohamed Chekired

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Recent studies on the numerical simulation of geotechnical problems show the importance of considering the soil micro-structure. At this scale, soil is a discrete particle medium where the particles can interact with each other and with water flow under external forces, structure loads or natural events. This paper presents research conducted in a virtual laboratory named SiGran, developed at IREQ (Institut de recherche d’Hydro-Quebec) for the purpose of investigating a broad range of problems encountered in geotechnics. Using Discrete Element Method (DEM), SiGran simulated granular materials directly by applying Newton’s laws to each particle. The water flow was simulated by using Marker and Cell method (MAC) to solve the full form of Navier-Stokes’s equation for non-compressible viscous liquid. In this paper, examples of numerical simulation and their comparisons with real experiments have been selected to show the complexity of geotechnical research at the micro level. These examples describe transient flows into a porous medium, interaction of particles in a viscous flow, compacting of saturated and unsaturated soils and the phenomenon of liquefaction under seismic load. They also provide an opportunity to present SiGran’s capacity to compute the distribution and evolution of energy by type (particle kinetic energy, particle internal elastic energy, energy dissipated by friction or as a result of viscous interaction into flow, and so on). This work also includes the first attempts to apply micro discrete results on a macro continuum level where the Smoothed Particle Hydrodynamics (SPH) method was used to resolve the system of governing equations. The material behavior equation is based on the results of simulations carried out at a micro level. The possibility of combining three methods (DEM, MAC and SPH) is discussed.

Keywords: discrete element method, marker and cell method, numerical simulation, multi-scale simulations, smoothed particle hydrodynamics

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Authors: Michalis Linardakis, Vasilis Grammatikopoulos, Athanasios Gregoriadis, Kalliopi Trouli

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Discrete choice models belong to the family of Conjoint analysis that are applied on the preferences of the respondents towards a set of scenarios that describe alternative choices. The scenarios have been pre-designed to cover all the attributes of the alternatives that may affect the choices. In this study, we examine how preschool educators integrate physical activities into their everyday teaching practices through the use of discrete choice models. One of the advantages of discrete choice models compared to other more traditional data collection methods (e.g. questionnaires and interviews that use ratings) is that the respondent is called to select among competitive and realistic alternatives, rather than objectively rate each attribute that the alternatives may have. We present the effort to construct and choose representative attributes that would cover all possible choices of the respondents, and the scenarios that have arisen. For the purposes of the study, we used a sample of 50 preschool educators in Greece that responded to 4 scenarios (from the total of 16 scenarios that the orthogonal design resulted), with each scenario having three alternative teaching practices. Seven attributes of the alternatives were used in the scenarios. For the analysis of the data, we used multinomial logit model with random effects, multinomial probit model and generalized mixed logit model. The conclusions drawn from the estimated parameters of the models are discussed.

Keywords: conjoint analysis, discrete choice models, educational data, multivariate statistical analysis

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Authors: Betty Makena, Tsegaye Tadesse, Mark Svoboda

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Global warming has intensified the frequency and intensity of extreme climate disasters and led to unpredictable weather conditions. Consequently, rapid shifts between drought and floods, known as Drought-Flood Abrupt Alteration (DFAA), have become increasingly common. DFAA results in superimposed impacts of drought and floods within a short period, exacerbating the effects of the floods or drought event. Current disaster management plans often overlook DFAA events, as they primarily focus on either floods or drought. Therefore, effectively identifying DFAA events is crucial for developing effective mitigation strategies. This study aims to identify historical DFAA events in Kenya using the Long Cycle Drought-Flood Abrupt Alteration Index (LDFAI). The research will analyze the spatial distribution, temporal variation, and intensity of DFAA events from 1990 to 2023, as well as their socio-economic impacts. Understanding these events is important to develop more effective strategies to address the impacts of DFAA events. Findings from this study will inform decision making to develop coping strategies to mitigate the adverse effects of DFAA in Kenya.

Keywords: abrupt, alteration, drought, floods

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Authors: Iqbal Felani

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A Coal-Fired Power Plant has some integrated facilities to handle coal from three separated coal yards to eight units power plant’s bunker. But nowadays the facilities are not reliable enough for supporting the system. Management planned to invest some facilities to increase the reliability. They also had a plan to make single spesification of coal used all of the units, called Single Quality Coal (SQC). This simulation would compare before and after improvement with two scenarios i.e First In First Out (FIFO) and Last In First Out (LIFO). Some parameters like stay time, reorder point and safety stock is determined by the simulation. Discrete event simulation based software, Flexsim 5.0, is used to help the simulation. Based on the simulation, Single Quality Coal with FIFO scenario has the shortest staytime with 8.38 days.

Keywords: Coal Yard Management, Discrete event simulation First In First Out, Last In First Out.

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Authors: Mohamed Hassan Abdullahi

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Decomposition is used as a synthesis tool in several physical systems. It can also be used for tearing and restructuring, which is large-scale system analysis. On the other hand, the commutativity of series-connected systems has fascinated the interest of researchers, and its advantages have been emphasized in the literature. The presentation looks into the necessary conditions for decomposing any third-order discrete-time linear time-varying system into a commutative pair of first- and second-order systems. Additional requirements are derived in the case of nonzero initial conditions. MATLAB simulations are used to verify the findings. The work is unique and is being published for the first time. It is critical from the standpoints of synthesis and/or design. Because many design techniques in engineering systems rely on tearing and reconstruction, this is the process of putting together simple components to create a finished product. Furthermore, it is demonstrated that regarding sensitivity to initial conditions, some combinations may be better than others. The results of this work can be extended for the decomposition of fourth-order discrete-time linear time-varying systems into lower-order commutative pairs, as two second-order commutative subsystems or one first-order and one third-order commutative subsystems.

Keywords: commutativity, decomposition, discrete time-varying systems, systems

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Authors: Anders Schou Simonsen, Thomas Condra, Kim Sørensen

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Various processes are modelled using a discrete phase, where particles are seeded from a source. Such particles can represent liquid water droplets, which are affecting the continuous phase by exchanging thermal energy, momentum, species etc. Discrete phases are typically modelled using parcel, which represents a collection of particles, which share properties such as temperature, velocity etc. When coupling the phases, the exchange rates are integrated over the cell, in which the parcel is located. This can cause spikes and fluctuating exchange rates. This paper presents an alternative method of coupling a discrete and a continuous plug flow phase. This is done using triangular parcels, which span between nodes following the dynamics of single droplets. Thus, the triangular parcels are propagated using the corner nodes. At each time step, the exchange rates are spatially integrated over the surface of the triangular parcels, which yields a smooth continuous exchange rate to the continuous phase. The results shows that the method is more stable, converges slightly faster and yields smooth exchange rates compared with the steam tube approach. However, the computational requirements are about five times greater, so the applicability of the alternative method should be limited to processes, where the exchange rates are important. The overall balances of the exchanged properties did not change significantly using the new approach.

Keywords: CFD, coupling, discrete phase, parcel

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Authors: Raed Alnajjar, Mohd Zakree, Ahmad Nazri

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In this study, we apply Discrete Group Search Optimizer (DGSO) for solving Traveling Salesman Problem (TSP). The DGSO is a nature inspired optimization algorithm that imitates the animal behavior, especially animal searching behavior. The proposed DGSO uses a vector representation and some discrete operators, such as destruction, construction, differential evolution, swap and insert. The TSP is a well-known hard combinatorial optimization problem, which seeks to find the shortest path among numbers of cities. The performance of the proposed DGSO is evaluated and tested on benchmark instances which listed in LIBTSP dataset. The experimental results show that the performance of the proposed DGSO is comparable with the other methods in the state of the art for some instances. The results show that DGSO outperform Ant Colony System (ACS) in some instances whilst outperform other metaheuristic in most instances. In addition to that, the new results obtained a number of optimal solutions and some best known results. DGSO was able to obtain feasible and good quality solution across all dataset.

Keywords: discrete group search optimizer (DGSO); Travelling salesman problem (TSP); Variable neighborhood search(VNS)

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Authors: Saleem Abuleil, Khalid S. Alsamara

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Events represent a significant source of information on the web; they deliver information about events that occurred around the world in all kind of subjects and areas. These events can be collected and organized to provide valuable and useful information for decision makers, researchers, as well as any person seeking knowledge. In this paper, we discuss an ongoing research to target stock markets domain to observe and record changes (events) when they happen, collect them, understand the meaning of each one of them, and organize the information along with meaning in a well-structured format. By using Semantic Role Labeling (SRL) technique, we identified four factors for each event in this paper: verb of action and three roles associated with it, entity name, attribute, and attribute value. We have generated a set of rules and techniques to support our approach to analyze and understand the meaning of the events taking place in stock markets.

Keywords: natuaral language processing, Arabic language, event extraction and understanding, sematic role labeling, stock market

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Authors: Ozden Saygili, Eser Cakti

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Mosques and minarets can be severely damaged as a result of earthquakes. Non-linear behavior of minarets of Mihrimah Sultan and Süleymaniye Mosques and the minaret of St. Sophia are analyzed to investigate seismic response, damage and failure mechanisms of minarets during earthquake. Selected minarets have different height and diameter. Discrete elements method was used to create the numerical minaret models. Analyses were performed using sine waves. Two parameters were used for evaluating the results: the maximum relative dislocation of adjacent drums and the maximum displacement at the top of the minaret. Both parameters were normalized by the drum diameter. The effects of minaret geometry on seismic behavior were evaluated by comparing the results of analyses.

Keywords: discrete element method, earthquake safety, nonlinear analysis, masonry structures

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Authors: Y. P. Raghavendra Babu

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Electrocution is a common cause of morbidity and mortality as electricity is an indispensible part of today’s World. Deaths due to electrocution which are witnessed do not pose a problem at the manner and cause of death. However un-witnessed deaths can raise suspicion of manner of death. A case of fatal electrocution is reported here which was diagnosed to be accidental in manner with the help of reconstruction of events by proper investigation.

Keywords: electrocution, manner of death, reconstruction of events, health information

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Authors: Hongyu Chen, Li Jiang

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Ubiquitous anomalies endanger the security of our system con- stantly. They may bring irreversible damages to the system and cause leakage of privacy. Thus, it is of vital importance to promptly detect these anomalies. Traditional supervised methods such as Decision Trees and Support Vector Machine (SVM) are used to classify normality and abnormality. However, in some case, the abnormal status are largely rarer than normal status, which leads to decision bias of these methods. Generative adversarial network (GAN) has been proposed to handle the case. With its strong generative ability, it only needs to learn the distribution of normal status, and identify the abnormal status through the gap between it and the learned distribution. Nevertheless, existing GAN-based models are not suitable to process data with discrete values, leading to immense degradation of detection performance. To cope with the discrete features, in this paper, we propose an efficient GAN-based model with specifically-designed loss function. Experiment results show that our model outperforms state-of-the-art models on discrete dataset and remarkably reduce the overhead.

Keywords: GAN, discrete feature, Wasserstein distance, multiple intermediate layers

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Authors: Kennedy Efosa Ehimwenma, Sujatha Krishnamoorthy, Safiya Al‑Sharji

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The probability computation of events is in the interval of [0, 1], which are values that are determined by the number of outcomes of events in a sample space S. The probability Pr(A) that an event A will never occur is 0. The probability Pr(B) that event B will certainly occur is 1. This makes both events A and B a certainty. Furthermore, the sum of probabilities Pr(E₁) + Pr(E₂) + … + Pr(Eₙ) of a finite set of events in a given sample space S equals 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. This paper first discusses Bayes, the complement of probability, and the difference of probability for occurrences of learning-events before applying them in the prediction of learning objects in student learning. Given the sum of 1; to make a recommendation for student learning, this paper proposes that the difference of argMaxPr(S) and the probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates i) the probability of skill-set events that have occurred that would lead to higher-level learning; ii) the probability of the events that have not occurred that requires subject-matter relearning; iii) accuracy of the decision tree in the prediction of student performance into class labels and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning.

Keywords: complement of probability, Bayes’ rule, prediction, pre-assessments, computational education, information theory

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Authors: H. El-Kamchouchi, Heba Gaber, Fatma Ahmed, Dalia H. El-Kamchouchi

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A digital signature is an electronic signature form used by an original signer to sign a specific document. When the original signer is not in his office or when he/she travels outside, he/she delegates his signing capability to a proxy signer and then the proxy signer generates a signing message on behalf of the original signer. The two parties must be able to authenticate one another and agree on a secret encryption key, in order to communicate securely over an unreliable public network. Authenticated key agreement protocols have an important role in building a secure communications network between the two parties. In this paper, we present a secure proxy signature scheme over an efficient and secure authenticated key agreement protocol based on factoring and discrete logarithm problem.

Keywords: discrete logarithm, factoring, proxy signature, key agreement

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Authors: Liang-Ta Cheng, Ching-Yu Yang

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Based on fast discrete cosine transform (FDCT), the authors present a high capacity and high perceived quality method for electrocardiogram (ECG) signal. By using a simple adjusting policy to the 1-dimentional (1-D) DCT coefficients, a large volume of secret message can be effectively embedded in an ECG host signal and be successfully extracted at the intended receiver. Simulations confirmed that the resulting perceived quality is good, while the hiding capability of the proposed method significantly outperforms that of existing techniques. In addition, our proposed method has a certain degree of robustness. Since the computational complexity is low, it is feasible for our method being employed in real-time applications.

Keywords: data hiding, ECG steganography, fast discrete cosine transform, 1-D DCT bundle, real-time applications

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Authors: N. Mathew, A. Qureshi, D. C. Khakha, R. Sagar

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Adolescents in India, account for one-fifth of the total population and are a significant human resource. Present study was conducted to find out various life stressors of adolescents, coping strategies adopted by them and the impact of stress on adolescent mental health. A descriptive, cross sectional study conducted on schools in the south zone of Delhi, capital city of the country. Data was collected on 360 adolescents between the age group of 13-17 years on socio-demographic profile, Adolescent life event stress scale, brief cope and youth self report for ages 11-18. Adolescents had significantly higher stress on uncontrollable events such as family events, relocation events, accident events and ambiguous events as compared to controllable events such as sexual events, deviance events and autonomy events (p<0.01).Adolescent stress was significantly correlated with various demographic variables in the study. The most frequently used coping strategies by the adolescents were positive reframing, planning, active coping, and instrumental support. It has also been found that the stress has a significant impact on adolescent mental health in the form of either internalizing problems such as anxious, withdrawn and somatic problems or externalizing problems such as rule breaking and aggressive behaviors. Out of the total sample of 360 adolescents 150 were identified as having psycho-social morbidity, including 59 borderline cases and 91 high-risk cases Study pointed out the need for mental health screening among the adolescents and also indicated the need for mental health inputs in educational institutions.

Keywords: adolecents, stress, coping, mental health

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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In this paper we study that the catastrophic events arrive independently at the service facility according to a Poisson process with rate λ. The nature of a catastrophic event is that upon its arrival at a service station, it destroys all the customers there waiting and in the service. We will derive the net profit associated with queuing system and obtain its probability of the busy period.

Keywords: queueing system, net-profit, busy period, catastrophical events

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Authors: Mwafak Shakoor

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The purpose of this study was to reduce patient waiting times, improve system throughput and improve resources utilization in radiology department. A discrete event simulation model was developed using Arena simulation software to investigate different alternatives to improve the overall system delivery based on adding resource scenarios due to the linkage between patient waiting times and resource availability. The study revealed that there is no addition investment need to procure additional scanner but hospital management deploy managerial tactics to enhance machine utilization and reduce the long waiting time in the department.

Keywords: discrete event simulation, radiology department, arena, waiting time, healthcare modeling, computed tomography

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Authors: F. J. Ma, A. K. H. Kwan

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Crack caused by shrinkage movement of concrete is a serious problem especially when restraint is provided. It may cause severe serviceability and durability problems. The existing prediction methods for crack width of concrete due to shrinkage movement are mainly numerical methods under simplified circumstances, which do not agree with each other. To get a more unified prediction method applicable to more sophisticated circumstances, finite element crack width analysis for shrinkage effect should be developed. However, no existing finite element analysis can be carried out to predict the crack width of concrete due to shrinkage movement because of unsolved reasons of conventional finite element analysis. In this paper, crack width analysis implemented by finite element analysis is presented with pseudo-discrete crack model, which combines traditional smeared crack model and newly proposed crack queuing algorithm. The proposed pseudo-discrete crack model is capable of simulating separate and single crack without adopting discrete crack element. And the improved finite element analysis can successfully simulate the stress redistribution when concrete is cracked, which is crucial for predicting crack width, crack spacing and crack number.

Keywords: crack queuing algorithm, crack width analysis, finite element analysis, shrinkage effect

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Authors: Tomoaki Hashimoto

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Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition.

Keywords: computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems

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Authors: Tomoaki Hashimoto

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Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.

Keywords: optimal control, stochastic systems, random dither, quantization

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

Procedia PDF Downloads 123