Search results for: Binary Integer Linear Programming

Authors: V. Komarova

Abstract:

The main purpose of this research is the calculation of implicit prices of the environmental level of air quality in the city of Moscow on the basis of housing property prices. The database used contains records of approximately 20 thousand apartments and has been provided by a leading real estate agency operating in Russia. The explanatory variables include physical characteristics of the houses, environmental (industry emissions), neighbourhood sociodemographic and geographic data: GPS coordinates of each house. The hedonic regression results for ecological variables show «negative» prices while increasing the level of air contamination from such substances as carbon monoxide, nitrogen dioxide, sulphur dioxide, and particles (CO, NO2, SO2, TSP). The marginal willingness to pay for higher environmental quality is presented for linear and log-log models.

Keywords: Air pollution, environment, hedonic prices, real estate, willingness to pay.

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Authors: J. Sulaiman, M. Othman, M. K. Hasan

Abstract:

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Keywords: MEG iteration, second-order finite difference, weighted parameter.

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Authors: R. Nandikeswari, M. Sambasivam, V. Anandan

Abstract:

In the present study fecundity of Terapon jarbua was estimated for 41 matured females from the Bay of Bengal, Pondicherry. The fecundity (F) was found to range from 13,475 to 115,920 in fishes between 173-278mm Total length (TL) and 65- 298 gm weight respectively. The co-efficient of correlation for F/TL (log F = - 4.821 + 4.146 log TL), F/SL (log F = -3.936 + 3.867 log SL), F/WF (log F = 1.229 + 0.730 log TW) and F/GW (log F = 0.724 + 1.113 log GW) were obtained as 0.474, 0.537, 0.641 and 0.908 respectively. The regression line for the TL, SL, WF and GW of the fishes were found to be linear when they were plotted against their fecundity on logarithmic scales. Highly significant (P<0.01) relationship was obtained for all the variables. Hence Total Length, Standard Length, Weight of Fish and Gonad Weight were found to be the best indicators of the fecundity of Terapon jarbua. Gonadosomatic indices of Terapon jarbua showed that the spawning took place in February to July. The overall sex ratio of male to female is 1.28:1 with chi-square value 5.719, significant at 5% level.

Keywords: Fecundity, Gonadosomatic index, Reproductive biology, spawning, Terapon jarbua.

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Authors: Werner Sandmann, Verena Wolf

Abstract:

Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.

Keywords: Computational Modeling, Biological Networks, Stochastic Models, Markov Chains, Transition Class Models.

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Authors: Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, Roslinda Nazar, Fudziah Ismail, MohamedSuleiman

Abstract:

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.

Keywords: Deformable, Marangoni, Porous, Stability.

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Authors: Caigen Zhou, Haibo Jiang

Abstract:

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

Abstract:

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: L. Sriphong, A. Chaidedgumjorn, K. Chaisuroj

Abstract:

A spectrophotometric method was developed for simultaneous quantification of pseudoephedrine hydrochloride (PSE) triprolidine hydrochloride (TRI) using second derivative method (zero-crossing technique). The second derivative amplitudes of PSE and TRI were measured at 271 and 321 nm, respectively. The calibration curves were linear in the range of 200 to 1,000 g/ml for PSE and 10 to 50 g/ml for TRI. The method was validated for specificity, accuracy, precision, limit of detection and limit of quantitation. The proposed method was applied to the assaying and dissolution of PSE and TRI in commercial tablets without any chemical separation. The results were compared with those obtained by the official USP31 method and statistical tests showed that there is no significant between the methods at 95% confidence level. The proposed method is simple, rapid and suitable for the routine quality control application. KeywordsTriprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

Keywords: Triprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

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Authors: Izzati K. Khalid, Nor Fadzillah M. Mokhtar, Norihan Md. Arifin

Abstract:

The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.

Keywords: Internal heat generation, micropolar fluid, rayleighbenard convection.

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Authors: Kamal K. Bharadwaj, Basheer M. Al-Maqaleh

Abstract:

In the recent past, there has been an increasing interest in applying evolutionary methods to Knowledge Discovery in Databases (KDD) and a number of successful applications of Genetic Algorithms (GA) and Genetic Programming (GP) to KDD have been demonstrated. The most predominant representation of the discovered knowledge is the standard Production Rules (PRs) in the form If P Then D. The PRs, however, are unable to handle exceptions and do not exhibit variable precision. The Censored Production Rules (CPRs), an extension of PRs, were proposed by Michalski & Winston that exhibit variable precision and supports an efficient mechanism for handling exceptions. A CPR is an augmented production rule of the form: If P Then D Unless C, where C (Censor) is an exception to the rule. Such rules are employed in situations, in which the conditional statement 'If P Then D' holds frequently and the assertion C holds rarely. By using a rule of this type we are free to ignore the exception conditions, when the resources needed to establish its presence are tight or there is simply no information available as to whether it holds or not. Thus, the 'If P Then D' part of the CPR expresses important information, while the Unless C part acts only as a switch and changes the polarity of D to ~D. This paper presents a classification algorithm based on evolutionary approach that discovers comprehensible rules with exceptions in the form of CPRs. The proposed approach has flexible chromosome encoding, where each chromosome corresponds to a CPR. Appropriate genetic operators are suggested and a fitness function is proposed that incorporates the basic constraints on CPRs. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Censored Production Rule, Data Mining, MachineLearning, Evolutionary Algorithms.

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Authors: Ashok Kumar Goel, Suresh Chandra Saxena, Surekha Bhanot

Abstract:

In this work, a Modified Functional Link Artificial Neural Network (M-FLANN) is proposed which is simpler than a Multilayer Perceptron (MLP) and improves upon the universal approximation capability of Functional Link Artificial Neural Network (FLANN). MLP and its variants: Direct Linear Feedthrough Artificial Neural Network (DLFANN), FLANN and M-FLANN have been implemented to model a simulated Water Bath System and a Continually Stirred Tank Heater (CSTH). Their convergence speed and generalization ability have been compared. The networks have been tested for their interpolation and extrapolation capability using noise-free and noisy data. The results show that M-FLANN which is computationally cheap, performs better and has greater generalization ability than other networks considered in the work.

Keywords: DLFANN, FLANN, M-FLANN, MLP

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Authors: Hong Dongchen, Chen Qiuxiao, Wu Shuang

Abstract:

Systematic Science reveals the complex nonlinear mechanisms of behavior in urban system. However, when confronted with such system, most city planners in China are still utilizing simple linear thinking to learn and understand this open complex giant system. In this paper, the hypercycle theory was introduced, which is one of the basis theories of systematic science. Based on the analysis of the reasons for the failure of current urban planning in China, and in consideration of the nonlinear characteristics of the urban system as well, optimization ideas for urban planning formulation were presented such as the shift from blueprint planning to progressive planning and from the rigid urban planning management control to its dynamically monitor and in time feedback.

Keywords: Systematic science, hypercycle theory, urban planning.

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Authors: M. Ouassaid, A. Nejmi, M. Cherkaoui, M. Maaroufi

Abstract:

The very nonlinear nature of the generator and system behaviour following a severe disturbance precludes the use of classical linear control technique. In this paper, a new approach of nonlinear control is proposed for transient and steady state stability analysis of a synchronous generator. The control law of the generator excitation is derived from the basis of Lyapunov stability criterion. The overall stability of the system is shown using Lyapunov technique. The application of the proposed controller to simulated generator excitation control under a large sudden fault and wide range of operating conditions demonstrates that the new control strategy is superior to conventional automatic voltage regulator (AVR), and show very promising results.

Keywords: Excitation control, Lyapunov technique, non linearcontrol, synchronous generator, transient stability, voltage regulation.

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

Abstract:

In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: Balanced truncation, Clustering, Dominant pole, Hankel norm, Model reduction.

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

Abstract:

In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: Autonomous vehicles, convoy, nonlinear control, nonlinear observer, sliding mode.

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Authors: Hassam Ahmed, Yuanzhi Liu, Yassine Selami, Wei Tao, Hui Zhao

Abstract:

The purpose of this research is to develop a real time axial force measurement system for a smart bearing through the use of strain-gauges, whereby the data acquisition is performed by an Arduino microcontroller due to its easy manipulation and low-cost. The measured signal is acquired and then discretized using a Wheatstone Bridge and an Analog-Digital Converter (ADC) respectively. For bearing monitoring, a real time monitoring system based on Internet of things (IoT) and Bluetooth were developed. Experimental tests were performed on a bearing within a force range up to 600 kN. The experimental results show that there is a proportional linear relationship between the applied force and the output voltage, and the error R squared is within 0.9878 based on the regression analysis.

Keywords: Bearing, force measurement, IoT, strain gauge.

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Authors: Shuh Liang

Abstract:

This article provides empirical evidence on the effect of domestic and international factors on the U.S. current account deficit. Linear dynamic regression and vector autoregression models are employed to estimate the relationships during the period from 1986 to 2011. The findings of this study suggest that the current and lagged private saving rate and foreign current account for East Asian economies have played a vital role in affecting the U.S. current account. Additionally, using Granger causality tests and variance decompositions, the change of the productivity growth and foreign domestic demand are determined to influence significantly the change of the U.S. current account. To summarize, the empirical relationship between the U.S. current account deficit and its determinants is sensitive to alternative regression models and specifications.

Keywords: Current account deficit, productivity growth, foreign demand, vector autoregression.

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Authors: A. Alghanim, J. Benedikt, P. J. Tasker

Abstract:

The increasing demand for higher data rates in wireless communication systems has led to the more effective and efficient use of all allocated frequency bands. In order to use the whole bandwidth at maximum efficiency, one needs to have RF power amplifiers with a higher linear level and memory-less performance. This is considered to be a major challenge to circuit designers. In this thesis the linearity and memory are studied and examined via the behavior of the intermodulation distortion (IMD). A major source of the in-band distortion can be shown to be influenced by the out-of-band impedances presented at either the input or the output of the device, especially those impedances terminated the low frequency (IF) components. Thus, in order to regulate the in-band distortion, the out of-band distortion must be controllable. These investigations are performed on a 12W LDMOS device characterised at 2.1 GHz within a purpose built, high-power measurement system.

Keywords: Low Frequency Memory, IntermodulationDistortion (IMD).

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Dali Zhang, Baoqun Yin, Hongsheng Xi

Abstract:

In this paper, we propose a single sample path based algorithm with state aggregation to optimize the average rewards of singularly perturbed Markov reward processes (SPMRPs) with a large scale state spaces. It is assumed that such a reward process depend on a set of parameters. Differing from the other kinds of Markov chain, SPMRPs have their own hierarchical structure. Based on this special structure, our algorithm can alleviate the load in the optimization for performance. Moreover, our method can be applied on line because of its evolution with the sample path simulated. Compared with the original algorithm applied on these problems of general MRPs, a new gradient formula for average reward performance metric in SPMRPs is brought in, which will be proved in Appendix, and then based on these gradients, the schedule of the iteration algorithm is presented, which is based on a single sample path, and eventually a special case in which parameters only dominate the disturbance matrices will be analyzed, and a precise comparison with be displayed between our algorithm with the old ones which is aim to solve these problems in general Markov reward processes. When applied in SPMRPs, our method will approach a fast pace in these cases. Furthermore, to illustrate the practical value of SPMRPs, a simple example in multiple programming in computer systems will be listed and simulated. Corresponding to some practical model, physical meanings of SPMRPs in networks of queues will be clarified.

Keywords: Singularly perturbed Markov processes, Gradient of average reward, Differential reward, State aggregation, Perturbed close network.

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Authors: Siliang Wang, Minghui Wang

Abstract:

Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, time-varying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that the problem of route choice in stochastic, time-varying networks can be formulated as a minimum cost hyperpath problem, and it also can be solved in linear time. We finally demonstrate the significant computational advantages of the introduced methods.

Keywords: Markov decision processes (MDPs), stochastictime-varying networks, hypergraphs, route choice.

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Authors: A. M. Maqableh

Abstract:

Modelling techniques for a fluid coupling taken from published literature have been extended to include the effects of the filling and emptying of the coupling with oil and the variation in losses when the coupling is partially full. In the model, the fluid flow inside the coupling is considered to have two principal velocity components; one circumferentially about the coupling axis (centrifugal head) and the other representing the secondary vortex within the coupling itself (vortex head). The calculation of liquid mass flow rate circulating between the two halves of the coupling is based on: the assumption of a linear velocity variation in the circulating vortex flow; the head differential in the fluid due to the speed difference between the two shafts; and the losses in the circulating vortex flow as a result of the impingement of the flow with the blades in the coupling and friction within the passages between the blades.

Keywords: Fluid Coupling, Mathematical Modelling, partially filled.

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Authors: H. K. Hwang, Zekeriya Aliyazicioglu, Solomon Wu, Hung Lu, Nick Wilkins, Daniel Kerr

Abstract:

Multiple-input multiple-output (MIMO) radar has received increasing attention in recent years. MIMO radar has many advantages over conventional phased array radar such as target detection,resolution enhancement, and interference suppression. In this paper, the results are presented from a simulation study of MIMO uniformly-spaced linear array (ULA) antennas. The performance is investigated under varied parameters, including varied array size, pseudo random (PN) sequence length, number of snapshots, and signal to noise ratio (SNR). The results of MIMO are compared to a traditional array antenna.

Keywords: Multiple-input multiple-output (MIMO) radar, phased array antenna, target detection, radar signal processing.

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Authors: A. Salmanpour, Sh. Mohammad Nejad

Abstract:

One of the methods for detecting the target position error in the laser tracking systems is using Four Quadrant (4Q) detectors. If the coordinates of the target center is yielded through the usual relations of the detector outputs, the results will be nonlinear, dependent on the shape, target size and its position on the detector screen. In this paper we have designed an algorithm with using neural network that coordinates of the target center in laser tracking systems is calculated by using detector outputs obtained from visual modeling. With this method, the results except from the part related to the detector intrinsic limitation, are linear and dependent from the shape and target size.

Keywords: four quadrant detector, laser tracking system, rangefinder, tracking sensor

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Authors: Shuhe Shao

Abstract:

This article provides partial evaluation index and its standard of sports aerobics, including the following 12 indexes: health vitality, coordination, flexibility, accuracy, pace, endurance, elasticity, self-confidence, form, control, uniformity and musicality. The three-layer BP artificial neural network model including input layer, hidden layer and output layer is established. The result shows that the model can well reflect the non-linear relationship between the performance of 12 indexes and the overall performance. The predicted value of each sample is very close to the true value, with a relative error fluctuating around of 5%, and the network training is successful. It shows that BP network has high prediction accuracy and good generalization capacity if being applied in sports aerobics performance evaluation after effective training.

Keywords: BP neural network, sports aerobics, performance, evaluation.

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Authors: Thanh-Phong Dao, Shyh-Chour Huang

Abstract:

This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.

Keywords: Vibration isolator, quasi-zero stiffness, flexure-based spring mechanisms, compliant mechanism.

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Authors: N. Ojaroudi Parchin, H. Jahanbakhsh Basherlou, Y. Al-Yasir, A. M. Abdulkhaleq, R. A. Abd-Alhameed, P. S. Excell

Abstract:

A compact design of multi-sector patch antenna array for 60 GHz applications is presented and discussed in details. The proposed design combines five 1x8 linear patch antenna arrays, referred to as sectors, in a multi-sector configuration. The coaxial-fed radiation elements of the multi-sector array are designed on 0.2 mm Rogers RT5880 dielectrics. The array operates in the frequency range of 58-62 GHz and provides switchable directional/omnidirectional radiation beams with high gain and high directivity characteristics. The designed multi-sector array exhibits good performances and could be used in the fifth generation (5G) cellular networks.

Keywords: MM-wave communications, multi-sector array, patch antenna, small cell networks.

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Authors: Marina Velikova, Hennie Daniels, Ad Feelders

Abstract:

In many applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. Here we consider partially monotone problems, where the target variable depends monotonically on some of the predictor variables but not all. We propose an approach to build partially monotone models based on the convolution of monotone neural networks and kernel functions. The results from simulations and a real case study on house pricing show that our approach has significantly better performance than partially monotone linear models. Furthermore, the incorporation of partial monotonicity constraints not only leads to models that are in accordance with the decision maker's expertise, but also reduces considerably the model variance in comparison to standard neural networks with weight decay.

Keywords: Mixture models, monotone neural networks, partially monotone models, partially monotone problems.

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Authors: Harish Kumar, Hussein Yahia, Oriol Pont, Michel Haissaguerre, Nicolas Derval, Meleze Hocini

Abstract:

The analysis to detect arrhythmias and life-threatening conditions are highly essential in today world and this analysis can be accomplished by advanced non-linear processing methods for accurate analysis of the complex signals of heartbeat dynamics. In this perspective, recent developments in the field of multiscale information content have lead to the Microcanonical Multiscale Formalism (MMF). We show that such framework provides several signal analysis techniques that are especially adapted to the study of heartbeat dynamics. In this paper, we just show first hand results of whether the considered heartbeat dynamics signals have the multiscale properties by computing local preticability exponents (LPEs) and the Unpredictable Points Manifold (UPM), and thereby computing the singularity spectrum.

Keywords: Microcanonical Multiscale Formalism (MMF), UnpredictablePoints Manifold (UPM), Heartbeat Dynamics.

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Authors: Moung Young Lee, Chul Gyu Song

Abstract:

Photoacoustic imaging is the imaging technology that combines the optical imaging and ultrasound. This provides the high contrast and resolution due to optical imaging and ultrasound imaging, respectively. We developed the real-time photoacoustic tomography (PAT) system using linear-ultrasound transducer and digital acquisition (DAQ) board. There are two types of algorithm for reconstructing the photoacoustic signal. One is back-projection algorithm, the other is FFT algorithm. Especially, we used the non-uniform FFT algorithm. To evaluate the performance of our system and algorithms, we monitored two wires that stands at interval of 2.89 mm and 0.87 mm. Then, we compared the images reconstructed by algorithms. Finally, we monitored the two hairs crossed and compared between these algorithms.

Keywords: Back-projection, image comparison, non-uniform FFT, photoacoustic tomography.

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