Search results for: generalization

Authors: O. Z. Jasim

Abstract:

An accuracy digital map must satisfy the users for two main requirements, first, map must be visually readable and second, all the map elements must be in a good representation. These two requirements hold especially true for map generalization which aims at simplifying the representation of cartographic data. Different scales of maps are very important for any decision in any maps with different scales such as master plan and all the infrastructures maps in civil engineering. Cartographer cannot project the data onto a piece of paper, but he has to worry about its readability. The map layout of any geodatabase is very important, this layout is help to read, analyze or extract information from the map. There are many principles and guidelines of generalization that can be find in the cartographic literature. A manual reduction method for generalization depends on experience of map maker and therefore produces incompatible results. Digital generalization, rooted from conventional cartography, has become an increasing concern in both Geographic Information System (GIS) and mapping fields. This project is intended to review the state of the art of the new technology and help to understand the needs and plans for the implementation of digital generalization capability as well as increase the knowledge of production topographic maps.

Keywords: Cartography, digital generalization, mapping, GIS.

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Authors: Naiqin Feng, Fang Wang, Yuhui Qiu

Abstract:

A new approach to promote the generalization ability of neural networks is presented. It is based on the point of view of fuzzy theory. This approach is implemented through shrinking or magnifying the input vector, thereby reducing the difference between training set and testing set. It is called “shrinking-magnifying approach" (SMA). At the same time, a new algorithm; α-algorithm is presented to find out the appropriate shrinking-magnifying-factor (SMF) α and obtain better generalization ability of neural networks. Quite a few simulation experiments serve to study the effect of SMA and α-algorithm. The experiment results are discussed in detail, and the function principle of SMA is analyzed in theory. The results of experiments and analyses show that the new approach is not only simpler and easier, but also is very effective to many neural networks and many classification problems. In our experiments, the proportions promoting the generalization ability of neural networks have even reached 90%.

Keywords: Fuzzy theory, generalization, misclassification rate, neural network.

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Authors: Chengming Li, Yong Yin, Peipei Guo, Xiaoli Liu

Abstract:

Without taking account of the attribute richness of POI (point of interest) data and spatial distribution limited by roads, a POI generalization method considering both attribute information and spatial distribution has been proposed against the existing point generalization algorithm merely focusing on overall information of point groups. Hierarchical characteristic of urban POI information expression has been firstly analyzed to point out the measurement feature of the corresponding hierarchy. On this basis, an urban POI generalizing strategy has been put forward: POIs urban road network have been divided into three distribution pattern; corresponding generalization methods have been proposed according to the characteristic of POI data in different distribution patterns. Experimental results showed that the method taking into account both attribute information and spatial distribution characteristics of POI can better implement urban POI generalization in the mapping presentation.

Keywords: POI, Road network, spatial information expression, selection method, distribution pattern.

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Authors: Ghazi S. Kahmmash

Abstract:

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

Keywords: Generating functions, Recurrences relation and Generalization of the new class matrix polynomial set.

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Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Vadim Vagin, Marina Fomina, Oleg Morosin

Abstract:

This paper contains the description of argumentation approach for the problem of inductive concept formation. It is proposed to use argumentation, based on defeasible reasoning with justification degrees, to improve the quality of classification models, obtained by generalization algorithms. The experiment’s results on both clear and noisy data are also presented.

Keywords: Argumentation, justification degrees, inductive concept formation, noise, generalization.

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Authors: Teerayut Chomchuen, Aiyared Iampan

Abstract:

The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

Keywords: Γ-semiring, bi-Γ-ideal, generalized bi-Γ-ideal.

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Authors: Jānis Zuters

Abstract:

There are a lot of extensions made to the classic model of multi-layer perceptron (MLP). A notable amount of them has been designed to hasten the learning process without considering the quality of generalization. The paper proposes a new MLP extension based on exploiting topology of the input layer of the network. Experimental results show the extended model to improve upon generalization capability in certain cases. The new model requires additional computational resources to compare to the classic model, nevertheless the loss in efficiency isn-t regarded to be significant.

Keywords: Learning algorithm, multi-layer perceptron, topology.

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Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: Exponentiated, Inversion Method, Maximum Likelihood Estimation, Transmutation Map.

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Authors: Rafał Adamczak

Abstract:

State-of-the-art methods for secondary structure (Porter, Psi-PRED, SAM-T99sec, Sable) and solvent accessibility (Sable, ACCpro) predictions use evolutionary profiles represented by the position specific scoring matrix (PSSM). It has been demonstrated that evolutionary profiles are the most important features in the feature space for these predictions. Unfortunately applying PSSM matrix leads to high dimensional feature spaces that may create problems with parameter optimization and generalization. Several recently published suggested that applying feature extraction for the PSSM matrix may result in improvements in secondary structure predictions. However, none of the top performing methods considered here utilizes dimensionality reduction to improve generalization. In the present study, we used simple and fast methods for features selection (t-statistics, information gain) that allow us to decrease the dimensionality of PSSM matrix by 75% and improve generalization in the case of secondary structure prediction compared to the Sable server.

Keywords: Secondary structure prediction, feature selection, position specific scoring matrix.

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Mahdiyeh Abbasi, Akbar Golchin

Abstract:

It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we define a generalization of principal weak flatness called GP-Flatness, and will characterize monoids by this property of their right (Rees factor) acts. Also we investigate new classes of monoids called generally regular monoids and generally left almost regular monoids.

Keywords: G-left stabilizing, GP-flatness, generally regular, principal weak flatness.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study some of their main properties. We also analyze a wide range of particular cases found in this generalization such as the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized Minkowski distance, etc. Finally, we give an illustrative example of the new approach where we can see the different results obtained by using different aggregation operators.

Keywords: Aggregation operators, Minkowski distance, OWA operators, Selection of strategies.

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Authors: Wajdi Mohamed Ratemi

Abstract:

The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: Generalized Pascal’s triangle, Pascal’s triangle, polynomial expansion, Sierpinski’s triangle, staircase horizontal vertical method.

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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: Yin Jie, Qin Qiming, Yin Yong

Abstract:

As a tool for human spatial cognition and thinking, the map has been playing an important role. Maps are perhaps as fundamental to society as language and the written word. Economic and social development requires extensive and in-depth understanding of their own living environment, from the scope of the overall global to urban housing. This has brought unprecedented opportunities and challenges for traditional cartography . This paper first proposed the concept of scaleless-map and its basic characteristics, through the analysis of the existing multi-scale representation techniques. Then some strategies are presented for automated mapping compilation. Taking into account the demand of automated map compilation, detailed proposed the software - WJ workstation must have four technical features, which are generalization operators, symbol primitives, dynamically annotation and mapping process template. This paper provides a more systematic new idea and solution to improve the intelligence and automation of the scaleless cartography.

Keywords: scaleless-map, strategy, map generalization, automated compilation, WJ workstation.

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Authors: Yehjune Heo

Abstract:

As biometric systems become widely deployed, the security of identification systems can be easily attacked by various spoof materials. This paper contributes to finding a reliable and practical anti-spoofing method using Convolutional Neural Networks (CNNs) based on the types of loss functions and optimizers. The types of CNNs used in this paper include AlexNet, VGGNet, and ResNet. By using various loss functions including Cross-Entropy, Center Loss, Cosine Proximity, and Hinge Loss, and various loss optimizers which include Adam, SGD, RMSProp, Adadelta, Adagrad, and Nadam, we obtained significant performance changes. We realize that choosing the correct loss function for each model is crucial since different loss functions lead to different errors on the same evaluation. By using a subset of the Livdet 2017 database, we validate our approach to compare the generalization power. It is important to note that we use a subset of LiveDet and the database is the same across all training and testing for each model. This way, we can compare the performance, in terms of generalization, for the unseen data across all different models. The best CNN (AlexNet) with the appropriate loss function and optimizers result in more than 3% of performance gain over the other CNN models with the default loss function and optimizer. In addition to the highest generalization performance, this paper also contains the models with high accuracy associated with parameters and mean average error rates to find the model that consumes the least memory and computation time for training and testing. Although AlexNet has less complexity over other CNN models, it is proven to be very efficient. For practical anti-spoofing systems, the deployed version should use a small amount of memory and should run very fast with high anti-spoofing performance. For our deployed version on smartphones, additional processing steps, such as quantization and pruning algorithms, have been applied in our final model.

Keywords: Anti-spoofing, CNN, fingerprint recognition, loss function, optimizer.

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Authors: Rameswar Debnath, Haruhisa Takahashi

Abstract:

An evolutionary method whose selection and recombination operations are based on generalization error-bounds of support vector machine (SVM) can select a subset of potentially informative genes for SVM classifier very efficiently [7]. In this paper, we will use the derivative of error-bound (first-order criteria) to select and recombine gene features in the evolutionary process, and compare the performance of the derivative of error-bound with the error-bound itself (zero-order) in the evolutionary process. We also investigate several error-bounds and their derivatives to compare the performance, and find the best criteria for gene selection and classification. We use 7 cancer-related human gene expression datasets to evaluate the performance of the zero-order and first-order criteria of error-bounds. Though both criteria have the same strategy in theoretically, experimental results demonstrate the best criterion for microarray gene expression data.

Keywords: support vector machine, generalization error-bound, feature selection, evolutionary algorithm, microarray data

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Authors: Hadi Firouzi, Majid Nili Ahmadabadi, Babak N. Araabi

Abstract:

Conceptualization strengthens intelligent systems in generalization skill, effective knowledge representation, real-time inference, and managing uncertain and indefinite situations in addition to facilitating knowledge communication for learning agents situated in real world. Concept learning introduces a way of abstraction by which the continuous state is formed as entities called concepts which are connected to the action space and thus, they illustrate somehow the complex action space. Of computational concept learning approaches, action-based conceptualization is favored because of its simplicity and mirror neuron foundations in neuroscience. In this paper, a new biologically inspired concept learning approach based on the probabilistic framework is proposed. This approach exploits and extends the mirror neuron-s role in conceptualization for a reinforcement learning agent in nondeterministic environments. In the proposed method, instead of building a huge numerical knowledge, the concepts are learnt gradually from rewards through interaction with the environment. Moreover the probabilistic formation of the concepts is employed to deal with uncertain and dynamic nature of real problems in addition to the ability of generalization. These characteristics as a whole distinguish the proposed learning algorithm from both a pure classification algorithm and typical reinforcement learning. Simulation results show advantages of the proposed framework in terms of convergence speed as well as generalization and asymptotic behavior because of utilizing both success and failures attempts through received rewards. Experimental results, on the other hand, show the applicability and effectiveness of the proposed method in continuous and noisy environments for a real robotic task such as maze as well as the benefits of implementing an incremental learning scenario in artificial agents.

Keywords: Concept learning, probabilistic decision making, reinforcement learning.

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Authors: Christian H. Sanabria-Montaña, Rodrigo Huerta-Quintanilla

Abstract:

A lattice network is a special type of network in which all nodes have the same number of links, and its boundary conditions are periodic. The most basic lattice network is the ring, a one-dimensional network with periodic border conditions. In contrast, the Cartesian product of d rings forms a d-dimensional lattice network. An analytical expression currently exists for the clustering coefficient in this type of network, but the theoretical value is valid only up to certain connectivity value; in other words, the analytical expression is incomplete. Here we obtain analytically the clustering coefficient expression in d-dimensional lattice networks for any link density. Our analytical results show that the clustering coefficient for a lattice network with density of links that tend to 1, leads to the value of the clustering coefficient of a fully connected network. We developed a model on criminology in which the generalized clustering coefficient expression is applied. The model states that delinquents learn the know-how of crime business by sharing knowledge, directly or indirectly, with their friends of the gang. This generalization shed light on the network properties, which is important to develop new models in different fields where network structure plays an important role in the system dynamic, such as criminology, evolutionary game theory, econophysics, among others.

Keywords: Clustering coefficient, criminology, generalized, regular network d-dimensional.

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Authors: Dakshina Ranjan Kisku, Hunny Mehrotra, Jamuna Kanta Sing, Phalguni Gupta

Abstract:

Identity verification of authentic persons by their multiview faces is a real valued problem in machine vision. Multiview faces are having difficulties due to non-linear representation in the feature space. This paper illustrates the usability of the generalization of LDA in the form of canonical covariate for face recognition to multiview faces. In the proposed work, the Gabor filter bank is used to extract facial features that characterized by spatial frequency, spatial locality and orientation. Gabor face representation captures substantial amount of variations of the face instances that often occurs due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to face images of rotated profile views produce Gabor faces with high dimensional features vectors. Canonical covariate is then used to Gabor faces to reduce the high dimensional feature spaces into low dimensional subspaces. Finally, support vector machines are trained with canonical sub-spaces that contain reduced set of features and perform recognition task. The proposed system is evaluated with UMIST face database. The experiment results demonstrate the efficiency and robustness of the proposed system with high recognition rates.

Keywords: Biometrics, Multiview face Recognition, Gaborwavelets, LDA, SVM.

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Authors: Rohitash Chandra, Christian W. Omlin

Abstract:

We present a hybrid architecture of recurrent neural networks (RNNs) inspired by hidden Markov models (HMMs). We train the hybrid architecture using genetic algorithms to learn and represent dynamical systems. We train the hybrid architecture on a set of deterministic finite-state automata strings and observe the generalization performance of the hybrid architecture when presented with a new set of strings which were not present in the training data set. In this way, we show that the hybrid system of HMM and RNN can learn and represent deterministic finite-state automata. We ran experiments with different sets of population sizes in the genetic algorithm; we also ran experiments to find out which weight initializations were best for training the hybrid architecture. The results show that the hybrid architecture of recurrent neural networks inspired by hidden Markov models can train and represent dynamical systems. The best training and generalization performance is achieved when the hybrid architecture is initialized with random real weight values of range -15 to 15.

Keywords: Deterministic finite-state automata, genetic algorithm, hidden Markov models, hybrid systems and recurrent neural networks.

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Authors: Omessaad Hamdi, Ammar Bouallegue, Sami Harari

Abstract:

In [4], Kipnis and Shamir have cryptanalised a version of HFE of degree 2. In this paper, we describe the generalization of this attack of HFE of degree more than 2. We are based on Fourier Transformation to acheive partially this attack.

Keywords: Public, cryptosystem, cryptanalisis, HFE.

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Authors: Hamza A. Ali, Waleed A. J. Rasheed

Abstract:

The use of neural networks for recognition application is generally constrained by their inherent parameters inflexibility after the training phase. This means no adaptation is accommodated for input variations that have any influence on the network parameters. Attempts were made in this work to design a neural network that includes an additional mechanism that adjusts the threshold values according to the input pattern variations. The new approach is based on splitting the whole network into two subnets; main traditional net and a supportive net. The first deals with the required output of trained patterns with predefined settings, while the second tolerates output generation dynamically with tuning capability for any newly applied input. This tuning comes in the form of an adjustment to the threshold values. Two levels of supportive net were studied; one implements an extended additional layer with adjustable neuronal threshold setting mechanism, while the second implements an auxiliary net with traditional architecture performs dynamic adjustment to the threshold value of the main net that is constructed in dual-layer architecture. Experiment results and analysis of the proposed designs have given quite satisfactory conducts. The supportive layer approach achieved over 90% recognition rate, while the multiple network technique shows more effective and acceptable level of recognition. However, this is achieved at the price of network complexity and computation time. Recognition generalization may be also improved by accommodating capabilities involving all the innate structures in conjugation with Intelligence abilities with the needs of further advanced learning phases.

Keywords: Classification, Recognition, Neural Networks, Pattern Recognition, Generalization.

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Authors: Yehjune Heo

Abstract:

Fingerprint Anti-Spoofing approaches have been actively developed and applied in real-world applications. One of the main problems for Fingerprint Anti-Spoofing is not robust to unseen samples, especially in real-world scenarios. A possible solution will be to generate artificial, but realistic fingerprint samples and use them for training in order to achieve good generalization. This paper contains experimental and comparative results with currently popular GAN based methods and uses realistic synthesis of fingerprints in training in order to increase the performance. Among various GAN models, the most popular StyleGAN is used for the experiments. The CNN models were first trained with the dataset that did not contain generated fake images and the accuracy along with the mean average error rate were recorded. Then, the fake generated images (fake images of live fingerprints and fake images of spoof fingerprints) were each combined with the original images (real images of live fingerprints and real images of spoof fingerprints), and various CNN models were trained. The best performances for each CNN model, trained with the dataset of generated fake images and each time the accuracy and the mean average error rate, were recorded. We observe that current GAN based approaches need significant improvements for the Anti-Spoofing performance, although the overall quality of the synthesized fingerprints seems to be reasonable. We include the analysis of this performance degradation, especially with a small number of samples. In addition, we suggest several approaches towards improved generalization with a small number of samples, by focusing on what GAN based approaches should learn and should not learn.

Keywords: Anti-spoofing, CNN, fingerprint recognition, GAN.

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Authors: Somayeh Komeylian

Abstract:

The direction of arrival (DoA) estimation is the crucial aspect of the radar technologies for detecting and dividing several signal sources. In this scenario, the antenna array output modeling involves numerous parameters including noise samples, signal waveform, signal directions, signal number, and signal to noise ratio (SNR), and thereby the methods of the DoA estimation rely heavily on the generalization characteristic for establishing a large number of the training data sets. Hence, we have analogously represented the two different optimization models of the DoA estimation; (1) the implementation of the decision directed acyclic graph (DDAG) for the multiclass least-squares support vector machine (LS-SVM), and (2) the optimization method of the deep neural network (DNN) radial basis function (RBF). We have rigorously verified that the LS-SVM DDAG algorithm is capable of accurately classifying DoAs for the three classes. However, the accuracy and robustness of the DoA estimation are still highly sensitive to technological imperfections of the antenna arrays such as non-ideal array design and manufacture, array implementation, mutual coupling effect, and background radiation and thereby the method may fail in representing high precision for the DoA estimation. Therefore, this work has a further contribution on developing the DNN-RBF model for the DoA estimation for overcoming the limitations of the non-parametric and data-driven methods in terms of array imperfection and generalization. The numerical results of implementing the DNN-RBF model have confirmed the better performance of the DoA estimation compared with the LS-SVM algorithm. Consequently, we have analogously evaluated the performance of utilizing the two aforementioned optimization methods for the DoA estimation using the concept of the mean squared error (MSE).

Keywords: DoA estimation, adaptive antenna array, Deep Neural Network, LS-SVM optimization model, radial basis function, MSE.

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Authors: Ruigang Zhang, Wuyungaowa, Xingchen Ma

Abstract:

In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

Keywords: Generating functions, operators sequence group, Riordan arrays, R. G operator group, combinatorial identities.

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Authors: Donglan Zha, Jiansong Si

Abstract:

Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: Bias of technical change, CES production function, elasticity of substitution, energy input.

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Authors: Sathinee Malee, Ronnason Chinram

Abstract:

The notion of k-fuzzy ideals of semirings was introduced by Kim and Park in 1996. In 2003, Dutta and Kar introduced a notion of ternary semirings. This structure is a generalization of ternary rings and semirings. The main purpose of this paper is to introduce and study k-fuzzy ideals in ternary semirings analogous to k-fuzzy ideals in semirings considered by Kim and Park.

Keywords: k-ideals, k-fuzzy ideals, fuzzy k-ideals, ternarysemirings

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Authors: Abdullah E. Al-Mazrooei

Abstract:

In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real measurements is introduced to illustrate the efficiency of the proposed algorithm.

Keywords: Bilinear systems, state space model, Kalman filter.

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