Search results for: Cognitive Complexity Measure

Authors: Md Fazlul Kader, Soo Young Shin

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In this paper, we consider a cognitive relay network (CRN) in which the primary receiver (PR) is protected by peak transmit power ¯PST and/or peak interference power Q constraints. In addition, the interference effect from the primary transmitter (PT) is considered to show its impact on the performance of the CRN. We investigate the outage probability (OP) and outage capacity (OC) of the CRN by deriving closed-form expressions over Rayleigh fading channel. Results show that both the OP and OC improve by increasing the cooperative relay nodes as well as when the PT is far away from the SR.

Keywords: Cognitive relay, outage, interference limited, decode-and-forward (DF).

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Authors: Alawode Kehinde O., Jubril Abimbola M. Komolafe Olusola A.

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This paper solves the environmental/ economic dispatch power system problem using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and its hybrid with a Convergence Accelerator Operator (CAO), called the NSGA-II/CAO. These multiobjective evolutionary algorithms were applied to the standard IEEE 30-bus six-generator test system. Several optimization runs were carried out on different cases of problem complexity. Different quality measure which compare the performance of the two solution techniques were considered. The results demonstrated that the inclusion of the CAO in the original NSGA-II improves its convergence while preserving the diversity properties of the solution set.

Keywords: optimal power flow, multiobjective power dispatch, evolutionary algorithm

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Authors: Zeinabsadat Haghshenas

Abstract:

Bloom’s Taxonomy has been changed during the years. The idea of this writing is about the revision that has happened in both facts and terms. It also contains case studies of using cognitive Bloom’s taxonomy in teaching geometric solids to the secondary school students, affective objectives in a creative workshop for adults and psychomotor objectives in fixing a malfunctioned refrigerator lamp. There is also pointed to the important role of classification objectives in adult education as a way to prevent memory loss.

Keywords: Adult education, affective domain, cognitive domain, memory loss, psychomotor domain.

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Authors: K. Anitha Sheela, J. Tarun Kumar

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HSDPA is a new feature which is introduced in Release-5 specifications of the 3GPP WCDMA/UTRA standard to realize higher speed data rate together with lower round-trip times. Moreover, the HSDPA concept offers outstanding improvement of packet throughput and also significantly reduces the packet call transfer delay as compared to Release -99 DSCH. Till now the HSDPA system uses turbo coding which is the best coding technique to achieve the Shannon limit. However, the main drawbacks of turbo coding are high decoding complexity and high latency which makes it unsuitable for some applications like satellite communications, since the transmission distance itself introduces latency due to limited speed of light. Hence in this paper it is proposed to use LDPC coding in place of Turbo coding for HSDPA system which decreases the latency and decoding complexity. But LDPC coding increases the Encoding complexity. Though the complexity of transmitter increases at NodeB, the End user is at an advantage in terms of receiver complexity and Bit- error rate. In this paper LDPC Encoder is implemented using “sparse parity check matrix" H to generate a codeword at Encoder and “Belief Propagation algorithm "for LDPC decoding .Simulation results shows that in LDPC coding the BER suddenly drops as the number of iterations increase with a small increase in Eb/No. Which is not possible in Turbo coding. Also same BER was achieved using less number of iterations and hence the latency and receiver complexity has decreased for LDPC coding. HSDPA increases the downlink data rate within a cell to a theoretical maximum of 14Mbps, with 2Mbps on the uplink. The changes that HSDPA enables includes better quality, more reliable and more robust data services. In other words, while realistic data rates are only a few Mbps, the actual quality and number of users achieved will improve significantly.

Keywords: AMC, HSDPA, LDPC, WCDMA, 3GPP.

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Authors: Damith Senanayake, Lakmal Muthugama, Laksheen Mendis, Tiroshan Madushanka

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Customer churn prediction is one of the most useful areas of study in customer analytics. Due to the enormous amount of data available for such predictions, machine learning and data mining have been heavily used in this domain. There exist many machine learning algorithms directly applicable for the problem of customer churn prediction, and here, we attempt to experiment on a novel approach by using a cognitive learning based technique in an attempt to improve the results obtained by using a combination of supervised learning methods, with cognitive unsupervised learning methods.

Keywords: Growing Self Organizing Maps, Kernel Methods, Churn Prediction.

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Authors: Hsueh-Chih, Chen, Yau-Ting, Sung, Tsai-Wen, Lin, Hung-Teng, Chou

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It has formed an essential issue that Climate Change, composed of highly knowledge complexity, reveals its significant impact on human existence. Therefore, specific national policies, some of which present the educational aspects, have been published for overcoming the imperative problem. Accordingly, the study aims to analyze as well as integrate the relationship between Climate Change and environmental education and apply the perspective of concept map to represent the knowledge contents and structures of Climate Change; by doing so, knowledge contents of Climate Change could be represented in an even more comprehensive way and manipulated as the tool for environmental education. The method adapted for this study is knowledge conversion model compounded of the platform for experts and teachers, who were the participants for this study, to cooperate and combine each participant-s standpoints into a complete knowledge framework that is the foundation for structuring the concept map. The result of this research contains the important concepts, the precise propositions and the entire concept map for representing the robust concepts of Climate Change.

Keywords: Climate Change, knowledge complexity, concept map.

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Authors: Aliouane Toufik, Hamdi Amine, Bouzid Djamel

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Aspheric optical components are an alternative to the use of conventional lenses in the implementation of imaging systems for the visible range. Spherical lenses are capable of producing aberrations. Therefore, they are not able to focus all the light into a single point. Instead, aspherical lenses correct aberrations and provide better resolution even with compact lenses incorporating a small number of lenses.

Metrology of these components is very difficult especially when the resolution requirements increase and insufficient or complexity of conventional tools requires the development of specific approaches to characterization.

This work is part of the problem existed because the objectives are the study and comparison of different methods used to measure surface rays hybrid aspherical lenses.

Keywords: Aspherical surface, Manufacture of lenses, precision molding, radius of curvature, roughness.

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Authors: Shikha Maheshwari, Amit Srivastava

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In medical investigations, uncertainty is a major challenging problem in making decision for doctors/experts to identify the diseases with a common set of symptoms and also has been extensively increasing in medical diagnosis problems. The theory of cross entropy for intuitionistic fuzzy sets (IFS) is an effective approach in coping uncertainty in decision making for medical diagnosis problem. The main focus of this paper is to propose a new intuitionistic fuzzy cross entropy measure (IFCEM), which aid in reducing the uncertainty and doctors/experts will take their decision easily in context of patient’s disease. It is shown that the proposed measure has some elegant properties, which demonstrates its potency. Further, it is also exemplified in detail the efficiency and utility of the proposed measure by using a real life case study of diagnosis the disease in medical science.

Keywords: Intuitionistic fuzzy cross entropy (IFCEM), intuitionistic fuzzy set (IFS), medical diagnosis, uncertainty.

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Authors: Al Jefferson J. Pabelic, Dennis A. Tarepe

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Bootstrapping has gained popularity in different tests of hypotheses as an alternative in using asymptotic distribution if one is not sure of the distribution of the test statistic under a null hypothesis. This method, in general, has two variants – the parametric and the nonparametric approaches. However, issues on reliability of this method always arise in many applications. This paper addresses the issue on reliability by establishing a reliability measure in terms of quantiles with respect to asymptotic distribution, when this is approximately correct. The test of hypotheses used is Ftest. The simulated results show that using nonparametric bootstrapping in F-test gives better reliability than parametric bootstrapping with relatively higher degrees of freedom.

Keywords: F-test, nonparametric bootstrapping, parametric bootstrapping, reliability measure, tests of hypotheses.

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Authors: Ramesh K. Sunkaria

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The linear methods of heart rate variability analysis such as non-parametric (e.g. fast Fourier transform analysis) and parametric methods (e.g. autoregressive modeling) has become an established non-invasive tool for marking the cardiac health, but their sensitivity and specificity were found to be lower than expected with positive predictive value <30%. This may be due to considering the RR-interval series as stationary and re-sampling them prior to their use for analysis, whereas actually it is not. This paper reviews the non-linear methods of HRV analysis such as correlation dimension, largest Lyupnov exponent, power law slope, fractal analysis, detrended fluctuation analysis, complexity measure etc. which are currently becoming popular as these uses the actual RR-interval series. These methods are expected to highly accurate cardiac health prognosis.

Keywords: chaos, nonlinear dynamics, sample entropy, approximate entropy, detrended fluctuation analysis.

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Authors: Michal Natora, Felix Franke, Klaus Obermayer

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Linear convolutive filters are fast in calculation and in application, and thus, often used for real-time processing of continuous data streams. In the case of transient signals, a filter has not only to detect the presence of a specific waveform, but to estimate its arrival time as well. In this study, a measure is presented which indicates the performance of detectors in achieving both of these tasks simultaneously. Furthermore, a new sub-class of linear filters within the class of filters which minimize the quadratic response is proposed. The proposed filters are more flexible than the existing ones, like the adaptive matched filter or the minimum power distortionless response beamformer, and prove to be superior with respect to that measure in certain settings. Simulations of a real-time scenario confirm the advantage of these filters as well as the usefulness of the performance measure.

Keywords: Adaptive matched filter, minimum variance distortionless response, beam forming, Capon beam former, linear filters, performance measure.

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

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Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken.

Keywords: Newton interpolation, Lagrange interpolation, linear complexity.

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Authors: Deon de Jager, Yahya Zweiri, Dimitrios Makris

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The three most important components in the cognitive architecture for cognitive robotics is memory representation, memory recall, and action-selection performed by the executive. In this paper, action selection, performed by the executive, is defined as a memory quantification and optimization process. The methodology describes the real-time construction of episodic memory through semantic memory optimization. The optimization is performed by set-based particle swarm optimization, using an adaptive entropy memory quantification approach for fitness evaluation. The performance of the approach is experimentally evaluated by simulation, where a UAV is tasked with the collection and delivery of a medical package. The experiments show that the UAV dynamically uses the episodic memory to autonomously control its velocity, while successfully completing its mission.

Keywords: Cognitive robotics, semantic memory, episodic memory, maximum entropy principle, particle swarm optimization.

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Authors: Rishi Ruttun

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One of the major features of hypermedia learning is its non-linear structure, allowing learners, the opportunity of flexible navigation to accommodate their own needs. Nevertheless, such flexibility can also cause problems such as insufficient navigation and disorientation for some learners, especially those with Field Dependent cognitive styles. As a result students learning performance can be deteriorated and in turn, they can have negative attitudes with hypermedia learning systems. It was suggested that visual elements can be used to compensate dilemmas. However, it is unclear whether these visual elements improve their learning or whether problems still exist. The aim of this study is to investigate the effect of students cognitive styles and visual elements on students learning performance and attitudes in hypermedia learning environment. Cognitive Style Analysis (CSA), Learning outcome in terms of pre and post-test, practical task, and Attitude Questionnaire (AQ) were administered to a sample of 60 university students. The findings revealed that FD students preformed equally to those of FI. Also, FD students experienced more disorientation in the hypermedia learning system where they depend a lot on the visual elements for navigation and orientation purposes. Furthermore, they had more positive attitudes towards the visual elements which escape them from experiencing navigation and disorientation dilemmas. In contrast, FI students were more comfortable, did not get disturbed or did not need some of the visual elements in the hypermedia learning system.

Keywords: Hypermedia learning, cognitive styles, visual elements, support, learning performance, attitudes and perceptions

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Authors: Johannes Buchmann, Markus Kaiser

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We decribe a formal specification and verification of the Rabin public-key scheme in the formal proof system Is-abelle/HOL. The idea is to use the two views of cryptographic verification: the computational approach relying on the vocabulary of probability theory and complexity theory and the formal approach based on ideas and techniques from logic and programming languages. The analysis presented uses a given database to prove formal properties of our implemented functions with computer support. Thema in task in designing a practical formalization of correctness as well as security properties is to cope with the complexity of cryptographic proving. We reduce this complexity by exploring a light-weight formalization that enables both appropriate formal definitions as well as eficient formal proofs. This yields the first computer-proved implementation of the Rabin public-key scheme in Isabelle/HOL. Consequently, we get reliable proofs with a minimal error rate augmenting the used database. This provides a formal basis for more computer proof constructions in this area.

Keywords: public-key encryption, Rabin public-key scheme, formalproof system, higher-order logic, formal verification.

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Authors: Linnea Stenliden

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The aim of this paper is to understand emerging learning conditions, when a visual analytics is implemented and used in K 12 (education). To date, little attention has been paid to the role visual analytics (digital media and technology that highlight visual data communication in order to support analytical tasks) can play in education, and to the extent to which these tools can process actionable data for young students. This study was conducted in three public K 12 schools, in four social science classes with students aged 10 to 13 years, over a period of two to four weeks at each school. Empirical data were generated using video observations and analyzed with help of metaphors within Actor-network theory (ANT). The learning conditions are found to be distinguished by broad complexity, characterized by four dimensions. These emerge from the actors’ deeply intertwined relations in the activities. The paper argues in relation to the found dimensions that novel approaches to teaching and learning could benefit students’ knowledge building as they work with visual analytics, analyzing visualized data.

Keywords: Analytical reasoning, complexity, data use, problem space, visual analytics, visual storytelling, translation.

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Authors: Mohamed M. Elsherbiny

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Social Avoidance is one of the most important problems that face a good number of disabled students. It results from the negative attitudes of non-disabled students, teachers and others. Some of the past research has shown that non-disabled individuals hold negative attitudes toward persons with disabilities. The present study aims to alleviate Social Avoidance by applying the Cognitive Behavioral Intervention. 24 Blind students aged 19–24 (university students) were randomly chosen we compared an experimental group (consisted of 12 students) who went through the intervention program, with a control group (12 students also) who did not go through such intervention. We used the Social Avoidance and Distress Scale (SADS) to assess social anxiety and distress behavior. The author used many techniques of cognitive behavioral intervention such as modeling, cognitive restructuring, extension, contingency contracts, selfmonitoring, assertiveness training, role play, encouragement and others. Statistically, T-test was employed to test the research hypothesis. Result showed that there is a significance difference between the experimental group and the control group after the intervention and also at the follow up stages of the Social Avoidance and Distress Scale. Also for the experimental group, there is a significance difference before the intervention and the follow up stages for the scale. Results showed that, there is a decrease in social avoidance. Accordingly, cognitive behavioral intervention program was successful in decreasing social avoidance for blind students.

Keywords: Social avoidance, cognitive behavioral intervention, blind disability, disability.

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Authors: Chih-Hsiang Chang, Pei-Shan Kao

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This paper discusses the reaction of investors in the Taiwan stock market to the most probable unknown earnings-related information and the most probable known earnings-related information. As compared with the previous literature regarding the effect of an official announcement of earnings forecast revision, this paper further analyzes investors’ cognitive bias toward the unknown and known earnings-related information, and the role of media during the investors' reactions to the foresaid information shocks. The empirical results show that both the unknown and known earnings-related information provides useful information content for a stock market. In addition, cognitive bias and disposition effect are the behavioral pitfalls that commonly occur in the process of the investors' reactions to the earnings-related information. Finally, media coverage has a remarkable influence upon the investors' trading decisions.

Keywords: Cognitive bias, role of media, disposition effect, earnings-related information, behavioral pitfall.

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Authors: Mahdi Pirmoradian, Olayinka Adigun, Christos Politis

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Cooperative spectrum sensing is a crucial challenge in cognitive radio networks. Cooperative sensing can increase the reliability of spectrum hole detection, optimize sensing time and reduce delay in cooperative networks. In this paper, an efficient central capacity optimization algorithm is proposed to minimize cooperative sensing time in a homogenous sensor network using OR decision rule subject to the detection and false alarm probabilities constraints. The evaluation results reveal significant improvement in the sensing time and normalized capacity of the cognitive sensors.

Keywords: Cooperative networks, normalized capacity, sensing time.

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Authors: Cheng-Chieh Chiang, Yi-Chia Chan, Greg C. Lee

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This paper proposes a video-based framework for face recognition to identify which faces appear in a video sequence. Our basic idea is like a tracking task - to track a selection of person candidates over time according to the observing visual features of face images in video frames. Hence, we employ the state-space model to formulate video-based face recognition by dividing this problem into two parts: the likelihood and the transition measures. The likelihood measure is to recognize whose face is currently being observed in video frames, for which two-dimensional linear discriminant analysis is employed. The transition measure estimates the probability of changing from an incorrect recognition at the previous stage to the correct person at the current stage. Moreover, extra nodes associated with head nodes are incorporated into our proposed state-space model. The experimental results are also provided to demonstrate the robustness and efficiency of our proposed approach.

Keywords: 2DLDA, face recognition, state-space model, likelihood measure, transition measure.

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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Authors: Maryam Gallab, Hafida Bouloiz, Youness Chater, Mohamed Tkiouat

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The aim of this paper is to present a model based on multi-agent systems in order to manage the maintenance activities and to ensure the reliability and availability of machines just with the required resources (operators, tools). The interest of the simulation is to solve the complexity of the system and to find results without cost or wasting time. An implementation of the model is carried out on the AnyLogic platform to display the defined performance indicators.

Keywords: Maintenance, complexity, simulation, multi-agent systems, AnyLogic platform.

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Authors: Nurul Diyana, A., Zainul Abidin, N.

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Social cognitive theory explains the power to inaugurate change is determined by the mutual influence of personal proclivity and social factors which will shape ones- motivations and expectations. In construction industry, green concept offers an opportunity to leave a lighter footprint on the environment. This opportunity, however, has not been fully grasped by many countries. As such, venturing into green construction for many practitioners would be their maiden experience. Decision to venture into new practice such as green construction will be influenced by certain drivers. This paper explores these drivers which is further expanded into motivational factors and later becomes the platform upon which expectation for green construction stands. This theoretical concept of motivation and expectations, which is adapted from social cognitive theory, focus on developers- view because of their crucial role in green application. This conceptual framework, which serves as the basis for further research, will benefit the industry as it elucidate cognitive angles to attract more new entrants to green business.

Keywords: Developers, Green Construction, Motivation, Expectation, Social Cognitive Theory.

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Authors: J.Partanen

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Complexity, as a theoretical background has made it easier to understand and explain the features and dynamic behavior of various complex systems. As the common theoretical background has confirmed, borrowing the terminology for design from the natural sciences has helped to control and understand urban complexity. Phenomena like self-organization, evolution and adaptation are appropriate to describe the formerly inaccessible characteristics of the complex environment in unpredictable bottomup systems. Increased computing capacity has been a key element in capturing the chaotic nature of these systems. A paradigm shift in urban planning and architectural design has forced us to give up the illusion of total control in urban environment, and consequently to seek for novel methods for steering the development. New methods using dynamic modeling have offered a real option for more thorough understanding of complexity and urban processes. At best new approaches may renew the design processes so that we get a better grip on the complex world via more flexible processes, support urban environmental diversity and respond to our needs beyond basic welfare by liberating ourselves from the standardized minimalism. A complex system and its features are as such beyond human ethics. Self-organization or evolution is either good or bad. Their mechanisms are by nature devoid of reason. They are common in urban dynamics in both natural processes and gas. They are features of a complex system, and they cannot be prevented. Yet their dynamics can be studied and supported. The paradigm of complexity and new design approaches has been criticized for a lack of humanity and morality, but the ethical implications of scientific or computational design processes have not been much discussed. It is important to distinguish the (unexciting) ethics of the theory and tools from the ethics of computer aided processes based on ethical decisions. Urban planning and architecture cannot be based on the survival of the fittest; however, the natural dynamics of the system cannot be impeded on grounds of being “non-human". In this paper the ethical challenges of using the dynamic models are contemplated in light of a few examples of new architecture and dynamic urban models and literature. It is suggested that ethical challenges in computational design processes could be reframed under the concepts of responsibility and transparency.

Keywords: urban planning, architecture, dynamic modeling, ethics, complexity theory.

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Authors: Rajkumar Verma, Bhu Dev Sharma

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In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy.

Keywords: fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.

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Authors: Rui Antunes, Fernando V. Coito

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This article presents the development of a neural network cognitive model for the classification and detection of different frequency signals. The basic structure of the implemented neural network was inspired on the perception process that humans generally make in order to visually distinguish between high and low frequency signals. It is based on the dynamic neural network concept, with delays. A special two-layer feedforward neural net structure was successfully implemented, trained and validated, to achieve minimum target error. Training confirmed that this neural net structure descents and converges to a human perception classification solution, even when far away from the target.

Keywords: Neural Networks, Signal Classification, Adaptative Filters, Cognitive Neuroscience

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Authors: Cesar Hernández, Diego Giral, Fernando Santa

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Spectrum handover is a significant topic in the cognitive radio networks to assure an efficient data transmission in the cognitive radio user’s communications. This paper proposes a comparison between three spectrum handover models: VIKOR, SAW and MEW. Four evaluation metrics are used. These metrics are, accumulative average of failed handover, accumulative average of handover performed, accumulative average of transmission bandwidth and, accumulative average of the transmission delay. As a difference with related work, the performance of the three spectrum handover models was validated with captured data of spectrum occupancy in experiments performed at the GSM frequency band (824 MHz - 849 MHz). These data represent the actual behavior of the licensed users for this wireless frequency band. The results of the comparison show that VIKOR Algorithm provides a 15.8% performance improvement compared to SAW Algorithm and, it is 12.1% better than the MEW Algorithm.

Keywords: Cognitive radio, decision making, MEW, SAW, spectrum handover, VIKOR.

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Authors: Rizwan Asghar, Dake Liu

Abstract:

A hardware efficient, multi mode, re-configurable architecture of interleaver/de-interleaver for multiple standards, like DVB, WiMAX and WLAN is presented. The interleavers consume a large part of silicon area when implemented by using conventional methods as they use memories to store permutation patterns. In addition, different types of interleavers in different standards cannot share the hardware due to different construction methodologies. The novelty of the work presented in this paper is threefold: 1) Mapping of vital types of interleavers including convolutional interleaver onto a single architecture with flexibility to change interleaver size; 2) Hardware complexity for channel interleaving in WiMAX is reduced by using 2-D realization of the interleaver functions; and 3) Silicon cost overheads reduced by avoiding the use of small memories. The proposed architecture consumes 0.18mm2 silicon area for 0.12μm process and can operate at a frequency of 140 MHz. The reduced complexity helps in minimizing the memory utilization, and at the same time provides strong support to on-the-fly computation of permutation patterns.

Keywords: Hardware interleaver implementation, WiMAX, DVB, block interleaver, convolutional interleaver, hardwaremultiplexing.

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Authors: Fanqiang Kong, Jindong Zhang, Daiyin Zhu

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Space-time adaptive processing (STAP) techniques have been motivated as a key enabling technology for advanced airborne radar applications. In this paper, the notion of cognitive radar is extended to STAP technique, and cognitive STAP is discussed. The principle for improving signal-to-clutter ratio (SCNR) based on slow-time coding is given, and the corresponding optimization algorithm based on cyclic and power-like algorithms is presented. Numerical examples show the effectiveness of the proposed method.

Keywords: Space-time adaptive processing (STAP), signal-to-clutter ratio, slow-time coding.

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Authors: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. However, most of the option pricing models have no analytical solution. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, we solve the American option under jump diffusion models by using efficient time-dependent numerical methods. several techniques are integrated to reduced the overcome the computational complexity. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). Partial fraction decomposition technique is applied to rational approximation schemes to overcome the complexity of inverting polynomial of matrices. The proposed method is easy to implement on serial or parallel versions. Numerical results are presented to prove the accuracy and efficiency of the proposed method.

Keywords: Integral differential equations, American options, jump–diffusion model, rational approximation.

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