Search results for: time path

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

Keywords: Food chain system, periodic solution, time scales, coincidence degree.

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Authors: Mohammad Shoyaib, M. Abdullah-Al-Wadud, Oksam Chae

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Proteomics is one of the largest areas of research for bioinformatics and medical science. An ambitious goal of proteomics is to elucidate the structure, interactions and functions of all proteins within cells and organisms. Predicting Protein-Protein Interaction (PPI) is one of the crucial and decisive problems in current research. Genomic data offer a great opportunity and at the same time a lot of challenges for the identification of these interactions. Many methods have already been proposed in this regard. In case of in-silico identification, most of the methods require both positive and negative examples of protein interaction and the perfection of these examples are very much crucial for the final prediction accuracy. Positive examples are relatively easy to obtain from well known databases. But the generation of negative examples is not a trivial task. Current PPI identification methods generate negative examples based on some assumptions, which are likely to affect their prediction accuracy. Hence, if more reliable negative examples are used, the PPI prediction methods may achieve even more accuracy. Focusing on this issue, a graph based negative example generation method is proposed, which is simple and more accurate than the existing approaches. An interaction graph of the protein sequences is created. The basic assumption is that the longer the shortest path between two protein-sequences in the interaction graph, the less is the possibility of their interaction. A well established PPI detection algorithm is employed with our negative examples and in most cases it increases the accuracy more than 10% in comparison with the negative pair selection method in that paper.

Keywords: Interaction graph, Negative training data, Protein-Protein interaction, Support vector machine.

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.

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Authors: Katleho Daniel Makatjane, Diteboho Lawrence Xaba, Ntebogang Dinah Moroke

Abstract:

The current study investigates the behaviour of time-varying parameters that are based on the score function of the predictive model density at time t. The mechanism to update the parameters over time is the scaled score of the likelihood function. The results revealed that there is high persistence of time-varying, as the location parameter is higher and the skewness parameter implied the departure of scale parameter from the normality with the unconditional parameter as 1.5. The results also revealed that there is a perseverance of the leptokurtic behaviour in stock returns which implies the returns are heavily tailed. Prior to model estimation, the White Neural Network test exposed that the stock price can be modelled by a GAS model. Finally, we proposed further researches specifically to model the existence of time-varying parameters with a more detailed model that encounters the heavy tail distribution of the series and computes the risk measure associated with the returns.

Keywords: Generalized autoregressive score model, stock returns, time-varying.

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Authors: A. Rawangpai, B. Maraungsri, N. Chomnawang

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This paper presents the experimental results on artificial ageing test of 22 kV XLPE cable for distribution system application in Thailand. XLPE insulating material of 22 kV cable was sliced to 60-70 μm in thick and was subjected to ac high voltage at 23 Ôùª C, 60 Ôùª C and 75 Ôùª C. Testing voltage was constantly applied to the specimen until breakdown. Breakdown voltage and time to breakdown were used to evaluate life time of insulating material. Furthermore, the physical model by J. P. Crine for predicts life time of XLPE insulating material was adopted as life time model and was calculated in order to compare the experimental results. Acceptable life time results were obtained from Crine-s model comparing with the experimental result. In addition, fourier transform infrared spectroscopy (FTIR) for chemical analysis and scanning electron microscope (SEM) for physical analysis were conducted on tested specimens.

Keywords: Artificial accelerated ageing test, XLPE cable, distribution system, insulating material, life time, life time model

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Authors: Hun Go, Ji-Su Kim, Dong-Ho Lee

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This study considers the problem of determining operation and maintenance schedules for a containership equipped with components during its sailing according to a pre-determined navigation schedule. The operation schedule, which specifies work time of each component, determines the due-date of each maintenance activity, and the maintenance schedule specifies the actual start time of each maintenance activity. The main constraints are component requirements, workforce availability, working time limitation, and inter-maintenance time. To represent the problem mathematically, a mixed integer programming model is developed. Then, due to the problem complexity, we suggest a heuristic for the objective of minimizing the sum of earliness and tardiness between the due-date and the starting time of each maintenance activity. Computational experiments were done on various test instances and the results are reported.

Keywords: Containerships, operation and preventive maintenance schedules, integer programming, heuristic

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Authors: Yong-Gyu Lee, Gilwon Yoon

Abstract:

Image processing for capsule endoscopy requires large memory and it takes hours for diagnosis since operation time is normally more than 8 hours. A real-time analysis algorithm of capsule images can be clinically very useful. It can differentiate abnormal tissue from health structure and provide with correlation information among the images. Bleeding is our interest in this regard and we propose a method of detecting frames with potential bleeding in real-time. Our detection algorithm is based on statistical analysis and the shapes of bleeding spots. We tested our algorithm with 30 cases of capsule endoscopy in the digestive track. Results were excellent where a sensitivity of 99% and a specificity of 97% were achieved in detecting the image frames with bleeding spots.

Keywords: bleeding, capsule endoscopy, image processing, real time analysis

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Authors: Ivana Šalinović

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The term gender emerged in the second half of the last century and since then a growing body of research dealing with the topic demonstrates its importance. Primarily, the research and the theories that were addressing the topic were focused on stating the differences between the terms sex and gender, where sex refers to the biological aspect of a person, while gender refers to the socially ascribed roles, attitudes, behaviors, and etc., and on gender discrimination whose visible and invisible repercussions are harming society and one of the agents of change should be educators on all educational levels since they are emotionally sculpting their students, that is why considerable effort should be put into implementing education about this topic into the standard curriculum. Not only educators, but it is also necessary to change the mindset of the younger generations because they will be important agents in the further elimination of gender discrimination, thus causing societal changes. Therefore, it is very important to hear their voices and their experiences and for these reasons, this research has been done, to see what the students of the second year at a private college university Aspira in Croatia have gone through in their educational ladder. The hypothesis was that the findings would most certainly show a huge difference between female and male students’ experiences and effects of gender discrimination, but the results have actually shown a very mixed picture and the original hypothesis was somewhat disapproved. Instead of finding out that girls experienced a lot of gender discrimination, it turned out that it was the boys who believed that in their previous and current education, there was no equal time distribution between genders, they noticed that the language was not gender-sensitive, teaching aids were not adopted to the genders. They were also the ones that pointed out that the discipline path was not the same for everyone, and they were the ones that the teacher’s gender had more influence on and were also the ones that experienced more gender discrimination.

Keywords: Gender, discrimination, elementary school, high school.

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Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin

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The frequency contents of the non-stationary signals vary with time. For proper characterization of such signals, a smart time-frequency representation is necessary. Classically, the STFT (short-time Fourier transform) is employed for this purpose. Its limitation is the fixed timefrequency resolution. To overcome this drawback an enhanced STFT version is devised. It is based on the signal driven sampling scheme, which is named as the cross-level sampling. It can adapt the sampling frequency and the window function (length plus shape) by following the input signal local variations. This adaptation results into the proposed technique appealing features, which are the adaptive time-frequency resolution and the computational efficiency.

Keywords: Level Crossing Sampling, Activity Selection, Adaptive Resolution Analysis, Computational Complexity.

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Authors: Seung Woo Lee, So Jeong Nam, Jai-Kyung Lee

Abstract:

It can be said that the business sector is faced with a range of challenges–a rapidly changing business environment, an increase and diversification of customers- demands and the consequent need for quick response–for having in place flexible management and production info systems. As a matter of fact, many manufacturers have adopted production info management systems such as MES and ERP. Nevertheless, managers are having difficulties obtaining ever-changing production process information in real time, or responding quickly to any change in production related needs on the basis of such information. This is because they rely on poor production info systems which are not capable of providing real-time factory settings. If the manufacturer doesn-t have a capacity for collecting or digitalizing the 4 Ms (Man, Machine, Material, Method), which are resources for production, on a real time basis, it might to difficult to effectively maintain the information on production process. In this regard, this paper will introduce some new alternatives to the existing methods of collecting the 4 Ms in real time, which are currently comprise the production field.

Keywords: 4M, Acquisition of Data on shop-floor, Real-time machine interface

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Authors: J. Moshtagh, L. Eslami

Abstract:

Various studies have showed that about 90% of single line to ground faults occurred on High voltage transmission lines have transient nature. This type of faults is cleared by temporary outage (by the single phase auto-reclosure). The interval between opening and reclosing of the faulted phase circuit breakers is named “Dead Time” that is varying about several hundred milliseconds. For adjustment of traditional single phase auto-reclosures that usually are not intelligent, it is necessary to calculate the dead time in the off-line condition precisely. If the dead time used in adjustment of single phase auto-reclosure is less than the real dead time, the reclosing of circuit breakers threats the power systems seriously. So in this paper a novel approach for precise calculation of dead time in power transmission lines based on the network equivalencing in time domain is presented. This approach has extremely higher precision in comparison with the traditional method based on Thevenin equivalent circuit. For comparison between the proposed approach in this paper and the traditional method, a comprehensive simulation by EMTP-ATP is performed on an extensive power network.

Keywords: Dead Time, Network Equivalencing, High Voltage Transmission Lines, Single Phase Auto-Reclosure.

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Authors: C. Pacheco, A. Cipriano

Abstract:

A new concept of response system is proposed for filling the gap that exists in reducing vulnerability during immediate response to natural disasters. Real Time Early Response Systems (RTERSs) incorporate real time information as feedback data for closing control loop and for generating real time situation assessment. A review of the state of the art on works that fit the concept of RTERS is presented, and it is found that they are mainly focused on manmade disasters. At the same time, in response phase of natural disaster management many works are involved in creating early warning systems, but just few efforts have been put on deciding what to do once an alarm is activated. In this context a RTERS arises as a useful tool for supporting people in their decision making process during natural disasters after an event is detected, and also as an innovative context for applying well-known automation technologies and automatic control concepts and tools.

Keywords: Disaster management, emergency response system, natural disasters, real time.

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Authors: Anthony Spiteri Staines

Abstract:

This paper examines and compares several of the most common real time methods. These methods are CORE, YSM, MASCOT, JSD, DARTS, RTSAD, ADARTS, CODARTS, HOOD, HRT-HOOD, ROOM, UML, UML-RT. The methods are compared using attributes like i) usability, ii) compositionality and iii) proper RT notations available. Finally some comparison results are given and discussed.

Keywords: Software Engineering Methods, MethodComparison, Real Time Analysis and Design.

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Authors: Prashant P. Bedekar, Sudhir R. Bhide, Vijay S. Kale

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Overcurrent (OC) relays are the major protection devices in a distribution system. The operating time of the OC relays are to be coordinated properly to avoid the mal-operation of the backup relays. The OC relay time coordination in ring fed distribution networks is a highly constrained optimization problem which can be stated as a linear programming problem (LPP). The purpose is to find an optimum relay setting to minimize the time of operation of relays and at the same time, to keep the relays properly coordinated to avoid the mal-operation of relays. This paper presents two phase simplex method for optimum time coordination of OC relays. The method is based on the simplex algorithm which is used to find optimum solution of LPP. The method introduces artificial variables to get an initial basic feasible solution (IBFS). Artificial variables are removed using iterative process of first phase which minimizes the auxiliary objective function. The second phase minimizes the original objective function and gives the optimum time coordination of OC relays.

Keywords: Constrained optimization, LPP, Overcurrent relaycoordination, Two-phase simplex method.

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Authors: Nuray Uçar, Mervin Ölmez, Özge Alptoğa, Nilgün K. Yavuz, Ayşen Önen

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In recent years, research on continuous graphene oxide fibers has been intensified. Therefore, many factors of production stages are being studied. In this study, the effect of exfoliation time and presence of activated carbon particle (ACP) on graphene oxide fiber’s properties has been analyzed. It has been seen that cross-sectional appearance of sample with ACP is harsh and porous because of ACP. The addition of ACP did not change the electrical conductivity. However, ACP results in an enormous decrease of mechanical properties. Longer exfoliation time results to higher crystallinity degree, C/O ratio and less d space between layers. The breaking strength and electrical conductivity of sample with less exfoliation time is some higher than sample with high exfoliation time.

Keywords: Activated carbon, coagulation by wet spinning, exfoliation, graphene oxide fiber.

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Authors: Miloš Šeda, Tomáš Březina

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In this paper, we focus on the use of knowledge bases in two different application areas – control of systems with unknown or strongly nonlinear models (i.e. hardly controllable by the classical methods), and robot motion planning in eight directions. The first one deals with fuzzy logic and the paper presents approaches for setting and aggregating the rules of a knowledge base. Te second one is concentrated on a case-based reasoning strategy for finding the path in a planar scene with obstacles.

Keywords: fuzzy controller, fuzzification, rule base, inference, defuzzification, genetic algorithm, neural network, case-based reasoning

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Authors: Chunshien Li, Jhao-Wun Hu, Tai-Wei Chiang, Tsunghan Wu

Abstract:

Time series forecasting is an important and widely popular topic in the research of system modeling. This paper describes how to use the hybrid PSO-RLSE neuro-fuzzy learning approach to the problem of time series forecasting. The PSO algorithm is used to update the premise parameters of the proposed prediction system, and the RLSE is used to update the consequence parameters. Thanks to the hybrid learning (HL) approach for the neuro-fuzzy system, the prediction performance is excellent and the speed of learning convergence is much faster than other compared approaches. In the experiments, we use the well-known Mackey-Glass chaos time series. According to the experimental results, the prediction performance and accuracy in time series forecasting by the proposed approach is much better than other compared approaches, as shown in Table IV. Excellent prediction performance by the proposed approach has been observed.

Keywords: forecasting, hybrid learning (HL), Neuro-FuzzySystem (NFS), particle swarm optimization (PSO), recursiveleast-squares estimator (RLSE), time series

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Authors: Xiangbin Zhu

Abstract:

Advances in computing applications in recent years have prompted the demand for more flexible scheduling models for QoS demand. Moreover, in practical applications, partly violated temporal constraints can be tolerated if the violation meets certain distribution. So we need extend the traditional Liu and Lanland model to adapt to these circumstances. There are two extensions, which are the (m, k)-firm model and Window-Constrained model. This paper researches on weakly hard real-time constraints and their combination to support QoS. The fact that a practical application can tolerate some violations of temporal constraint under certain distribution is employed to support adaptive QoS on the open real-time system. The experiment results show these approaches are effective compared to traditional scheduling algorithms.

Keywords: Weakly Hard Real-Time, Real-Time, Scheduling, Quality of Service.

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Authors: B.P. Bezruchko, D.A. Smirnov

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Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the technique is demonstrated in numerical experiments.

Keywords: Nonlinear time series analysis, directional couplings, coupled oscillators.

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Authors: Chao Wang, Yongkun Li

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In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.

Keywords: Discrete-time fuzzy BAM neural networks, ımpulses, global exponential stability, global asymptotical stability, equilibrium point.

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Authors: Kuljit Kaur, Parminder Kaur, Jaspreet Bedi, Hardeep Singh

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Software crisis refers to the situation in which the developers are not able to complete the projects within time and budget constraints and moreover these overscheduled and over budget projects are of low quality as well. Several methodologies have been adopted form time to time to overcome this situation and now in the focus is component based software engineering. In this approach, emphasis is on reuse of already existing software artifacts. But the results can not be achieved just by preaching the principles; they need to be practiced as well. This paper highlights some of the very basic elements of this approach, which has to be in place to get the desired goals of high quality, low cost with shorter time-to-market software products.

Keywords: Component Model, Software Components, SoftwareRepository, Process Models.

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Authors: Chris K. Y. Lo, Andy C. L. Yeung, T. C. Edwin Cheng

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ISO 9000 is the most popular and widely adopted meta-standard for quality and operational improvements. However, only limited empirical research has been conducted to examine the impact of ISO 9000 on operational performance based on objective and longitudinal data. To reveal any causal relationship between the adoption of ISO 9000 and operational performance, we examined the timing and magnitude of change in time-based performance as a result of ISO 9000 adoption. We analyzed the changes in operating cycle, inventory days, and account receivable days prior and after the implementation of ISO 9000 in 695 publicly listed manufacturing firms. We found that ISO 9000 certified firms shortened their operating cycle time by 5.28 days one year after the implementation of ISO 9000. In the long-run (3 years after certification), certified firms showed continuous improvement in time-based efficiency, and experienced a shorter operating cycle time of 11 days than that of non-certified firms. There was an average of 6.5% improvement in operating cycle time for ISO 9000 certified firms. Both inventory days and account receivable days showed similar significant improvements after the implementation of ISO 9000, too.

Keywords: ISO 9000, Operating Cycle, Time-based efficiency.

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Authors: Katleho D. Makatjane, Kalebe M. Kalebe

Abstract:

The present paper used time-varying parameters which are based on the score function of a probability density at time t to model volatility of saving rate. We used a scaled likelihood function to update the parameters of the model overtime. Our results revealed high diligence of time-varying since the location parameter is greater than zero. Furthermore, we discovered a leptokurtic condition on saving rate’s distribution. Kapetanios, Shin-Shell Nonlinear Augmented Dickey-Fuller (KSS-NADF) test showed that the saving rate has a nonlinear unit root; therefore, it can be modeled by a generalised autoregressive score (GAS) model. Additionally, value at risk (VaR) and conditional tail expectation (CTE) indicate that 99% of the time people in Lesotho are saving more than spending. This puts the economy in high risk of not expanding. Therefore, the monetary policy committee (MPC) of Lesotho should revise their monetary policies towards this high saving rates risk.

Keywords: Generalized autoregressive score, time-varying, saving rate, Lesotho.

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Authors: Zhongzhen Luo, Saeid Habibi, Martin v. Mohrenschildt

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Self-driving vehicle require a high level of situational awareness in order to maneuver safely when driving in real world condition. This paper presents a LiDAR based real time perception system that is able to process sensor raw data for multiple target detection and tracking in dynamic environment. The proposed algorithm is nonparametric and deterministic that is no assumptions and priori knowledge are needed from the input data and no initializations are required. Additionally, the proposed method is working on the three-dimensional data directly generated by LiDAR while not scarifying the rich information contained in the domain of 3D. Moreover, a fast and efficient for real time clustering algorithm is applied based on a radially bounded nearest neighbor (RBNN). Hungarian algorithm procedure and adaptive Kalman filtering are used for data association and tracking algorithm. The proposed algorithm is able to run in real time with average run time of 70ms per frame.

Keywords: LiDAR, real-time system, clustering, tracking, data association.

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Authors: Long Jye Sheu, Horng-Shing Chiou, Wei Ching Chen

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We propose a new perspective on speech communication using blind source separation. The original speech is mixed with key signals which consist of the mixing matrix, chaotic signals and a random noise. However, parts of the keys (the mixing matrix and the random noise) are not necessary in decryption. In practice implement, one can encrypt the speech by changing the noise signal every time. Hence, the present scheme obtains the advantages of a One Time Pad encryption while avoiding its drawbacks in key exchange. It is demonstrated that the proposed scheme is immune against traditional attacks.

Keywords: one time pad, blind source separation, independentcomponent analysis, speech encryption.

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Authors: Zhang Xiaodong, Tang Zixin, Liu Xin

Abstract:

In order to avoid self-collision of space manipulators during operation process, a real-time detection method is proposed in this paper. The manipulator is fitted into a cylinder-enveloping surface, and then, a kind of detection algorithm of collision between cylinders is analyzed. The collision model of space manipulator self-links can be detected by using this algorithm in real-time detection during the operation process. To ensure security of the operation, a safety threshold is designed. The simulation and experiment results verify the effectiveness of the proposed algorithm for a 7-DOF space manipulator.

Keywords: Space manipulator, Collision detection, Self-collision, the real-time collision detection.

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Authors: Payam Mousavi, Andrew L. Stewart, Huiwen You, Aryeh F. G. Fayerman

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We present a decision-support tool to assist an operator in the detection and tracking of a suspect vehicle traveling to an unknown target destination. Multiple data sources, such as traffic cameras, traffic information, weather, etc., are integrated and processed in real-time to infer a suspect’s intended destination chosen from a list of pre-determined high-value targets. Previously, we presented our work in the detection and tracking of vehicles using traffic and airborne cameras. Here, we focus on the fusion and processing of that information to predict a suspect’s behavior. The network of cameras is represented by a directional graph, where the edges correspond to direct road connections between the nodes and the edge weights are proportional to the average time it takes to travel from one node to another. For our experiments, we construct our graph based on the greater Los Angeles subset of the Caltrans’s “Performance Measurement System” (PeMS) dataset. We propose a Bayesian approach where a posterior probability for each target is continuously updated based on detections of the suspect in the live video feeds. Additionally, we introduce the concept of ‘soft interventions’, inspired by the field of Causal Inference. Soft interventions are herein defined as interventions that do not immediately interfere with the suspect’s movements; rather, a soft intervention may induce the suspect into making a new decision, ultimately making their intent more transparent. For example, a soft intervention could be temporarily closing a road a few blocks from the suspect’s current location, which may require the suspect to change their current course. The objective of these interventions is to gain the maximum amount of information about the suspect’s intent in the shortest possible time. Our system currently operates in a human-on-the-loop mode where at each step, a set of recommendations are presented to the operator to aid in decision-making. In principle, the system could operate autonomously, only prompting the operator for critical decisions, allowing the system to significantly scale up to larger areas and multiple suspects. Once the intended target is identified with sufficient confidence, the vehicle is reported to the authorities to take further action. Other recommendations include a selection of road closures, i.e., soft interventions, or to continue monitoring. We evaluate the performance of the proposed system using simulated scenarios where the suspect, starting at random locations, takes a noisy shortest path to their intended target. In all scenarios, the suspect’s intended target is unknown to our system. The decision thresholds are selected to maximize the chances of determining the suspect’s intended target in the minimum amount of time and with the smallest number of interventions. We conclude by discussing the limitations of our current approach to motivate a machine learning approach, based on reinforcement learning in order to relax some of the current limiting assumptions.

Keywords: Autonomous surveillance, Bayesian reasoning, decision-support, interventions, patterns-of-life, predictive analytics, predictive insights.

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Authors: Udeni Jayasinghe, Anuja Dharmaratne

Abstract:

Each year many people are reported missing in most of the countries in the world owing to various reasons. Arrangements have to be made to find these people after some time. So the investigating agencies are compelled to make out these people by using manpower. But in many cases, the investigations carried out to find out an absconding for a long time may not be successful. At a time like that it may be difficult to identify these people by examining their old photographs, because their facial appearance might have changed mainly due to the natural aging process. On some occasions in forensic medicine if a dead body is found, investigations should be held to make sure that this corpse belongs to the same person disappeared some time ago. With the passage of time the face of the person might have changed and there should be a mechanism to reveal the person-s identity. In order to make this process easy, we must guess and decide as to how he will look like by now. To address this problem this paper presents a way of synthesizing a facial image with the aging effects.

Keywords: Cranio-facial growth model, eigenfaces, eigenvectors, Face Anthropometry.

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Authors: S.K.Ayyaswamy, S.Balachandran

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The Detour matrix (DD) of a graph has for its ( i , j) entry the length of the longest path between vertices i and j. The DD-eigenvalues of a connected graph G are the eigenvalues for its detour matrix, and they form the DD-spectrum of G. The DD-energy EDD of the graph G is the sum of the absolute values of its DDeigenvalues. Two connected graphs are said to be DD- equienergetic if they have equal DD-energies. In this paper, the DD- spectra of a variety of graphs and their DD-energies are calculated.

Keywords: Detour eigenvalue (of a graph), detour spectrum(of a graph), detour energy(of a graph), detour - equienergetic graphs.

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