Search results for: Weight Minimization

Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

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Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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Authors: Xijian Wang

Abstract:

This paper is concerned with the numerical minimization of energy functionals in BV ( ) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.

Keywords: finite element method, discontinuous Galerkin method, total variation minimization, inpainting

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Authors: L.Ramesh, S.P.Chowdhury, S.Chowdhury, A.A.Natarajan, C.T.Gaunt

Abstract:

Accurate loss minimization is the critical component for efficient electrical distribution power flow .The contribution of this work presents loss minimization in power distribution system through feeder restructuring, incorporating DG and placement of capacitor. The study of this work was conducted on IEEE distribution network and India Electricity Board benchmark distribution system. The executed experimental result of Indian system is recommended to board and implement practically for regulated stable output.

Keywords: Distribution system, Distributed Generation LossMinimization, Network Restructuring

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Authors: Tarek Aboueldah, Hanan Farag

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Parallel Job Shop Scheduling Problem (JSSP) is a multi-objective and multi constrains NP-optimization problem. Traditional Artificial Intelligence techniques have been widely used; however, they could be trapped into the local minimum without reaching the optimum solution. Thus, we propose a hybrid Artificial Intelligence (AI) model with Discrete Breeding Swarm (DBS) added to traditional AI to avoid this trapping. This model is applied in the cost minimization of the Car Sequencing and Operator Allocation (CSOA) problem. The practical experiment shows that our model outperforms other techniques in cost minimization.

Keywords: Parallel Job Shop Scheduling Problem, Artificial Intelligence, Discrete Breeding Swarm, Car Sequencing and Operator Allocation, cost minimization.

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Authors: I. O. Nascimento, J. T. Manzi

Abstract:

The drying process is an important operation in the chemical industry and it is widely used in the food, grain industry and fertilizer industry. However, for demanding a considerable consumption of energy, such a process requires a deep energetic analysis in order to reduce operating costs. This paper deals with thermodynamic optimization applied to rotary dryers based on the entropy production minimization, aiming at to reduce the energy consumption. To do this, the mass, energy and entropy balance was used for developing a relationship that represents the rate of entropy production. The use of the Second Law of Thermodynamics is essential because it takes into account constraints of nature. Since the entropy production rate is minimized, optimals conditions of operations can be established and the process can obtain a substantial gain in energy saving. The minimization strategy had been led using classical methods such as Lagrange multipliers and implemented in the MATLAB platform. As expected, the preliminary results reveal a significant energy saving by the application of the optimal parameters found by the procedure of the entropy minimization It is important to say that this method has shown easy implementation and low cost.

Keywords: Drying, entropy minimization, modeling dryers, thermodynamic optimization.

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Authors: Dong-Woo Lim, Chang-Jae Chun, Hyung-Myung Kim

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We consider a two-way relay network where two sources exchange information. A relay helps the two sources exchange information using the decode-and-XOR-forward protocol. We investigate the power minimization problem with minimum rate constraints. The system needs two time slots and in each time slot the required rate pair should be achievable. The power consumption is minimized in each time slot and we obtained the closed form solution. The simulation results confirm that the proposed power allocation scheme consumes lower total power than the conventional schemes.

Keywords: Decode-and-XOR-forward, power minimization, two-way relay

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Authors: Amin Eslami, Jafar Bolouri Bazaz

Abstract:

Under active stress conditions, a rigid cantilever retaining wall tends to rotate about a pivot point located within the embedded depth of the wall. For purely granular and cohesive soils, a methodology was previously reported called minimization of moment ratio to determine the location of the pivot point of rotation. The usage of this new methodology is to estimate the rotational stability safety factor. Moreover, the degree of improvement required in a backfill to get a desired safety factor can be estimated by the concept of the shear strength demand. In this article, the accuracy of this method for another type of cantilever walls called Contiguous Bored Pile (CBP) retaining wall is evaluated by using physical modeling technique. Based on observations, the results of moment ratio minimization method are in good agreement with the results of the carried out physical modeling.

Keywords: Cantilever Retaining Wall, Physical Modeling, Minimization of Moment Ratio Method, Pivot Point.

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Authors: Clark Van Dam, Gagan Mirchandani

Abstract:

The Continuously Adaptive Mean-Shift (CamShift) algorithm, incorporating scene depth information is combined with the l1-minimization sparse representation based method to form a hybrid kernel and state space-based tracking algorithm. We take advantage of the increased efficiency of the former with the robustness to occlusion property of the latter. A simple interchange scheme transfers control between algorithms based upon drift and occlusion likelihood. It is quantified by the projection of target candidates onto a depth map of the 2D scene obtained with a low cost stereo vision webcam. Results are improved tracking in terms of drift over each algorithm individually, in a challenging practical outdoor multiple occlusion test case.

Keywords: CamShift, l1-minimization, particle filter, stereo vision, video tracking.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: Syed Muhammad Aqil Burney, Tahseen Ahmed Jilani, C. Ardil

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Minimization methods for training feed-forward networks with Backpropagation are compared. Feedforward network training is a special case of functional minimization, where no explicit model of the data is assumed. Therefore due to the high dimensionality of the data, linearization of the training problem through use of orthogonal basis functions is not desirable. The focus is functional minimization on any basis. A number of methods based on local gradient and Hessian matrices are discussed. Modifications of many methods of first and second order training methods are considered. Using share rates data, experimentally it is proved that Conjugate gradient and Quasi Newton?s methods outperformed the Gradient Descent methods. In case of the Levenberg-Marquardt algorithm is of special interest in financial forecasting.

Keywords: Backpropagation algorithm, conjugacy condition, line search, matrix perturbation

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Authors: Nareelux Suwannobol, JintanaTapin, Khuanchanok Narachan

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The objective of this study was to determine the accuracy to estimation fetal weight by Johnson-s method and compares it with actual birth weight. The sample group was 126 infants delivered in Dan KhunThot hospital from January March 2012. Fetal weight was estimated by measuring fundal height according to Johnson-s method. The information was collected by studying historical delivery records and then analyzed by using the statistics of frequency, percentage, mean, and standard deviation. Finally, the difference was analyzed by a paired t-test.The results showed had an average birth weight was 3093.57 ± 391.03 g (mean ± SD) and 3,455 ± 454.55 g average estimated fetal weight by Johnson-s method higher than average actual birth weight was 384.09 grams. When classifying the infants according to birth weight found that low birth weight (<2500 g) and the appropriate birth weight (2500-3999g) actual birth weight less than estimate fetal weight . But the high birth weight (> 4000 g) actual birth weight was more than estimated fetal weight. The difference was found between actual birth weight and estimation fetal weight of the minimum weight in high birth weight ( > 4000 g) , the appropriate birth weight (2500-3999g) and low birth weight (<2500 g) respectively. The rate of estimates fetal weight within 10% of actual birth weight was 35.7%. Actual birth weight were compared with the found that the difference is statistically significant (p <.000). Employing Johnson-s method to estimate fetal weight can estimate initial fetal weight before passing to special examinations, which may require excessive high cost. A variety of methods should be employed to estimate fetal weight more precisely, which will help plan care for mother-s and infant-s safety.

Keywords: Johnson's method, Fetal weight estimate, Delivery Room, Student nurse.

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Authors: Murat Toren, Mehmet Çelebi

Abstract:

Reducing the weight of transformers while providing good performance, cost reduction and increased efficiency is important. Weight is one of the most significant factors in all electrical machines, and as such, many transformer design parameters are related to weight calculations. This study presents a comparison of the weight of oil type transformers and dry type transformer weight. Oil type transformers are mainly used in industry; however, dry type transformers are becoming more widespread in recent years. MATLAB is typically used for designing transformers and design parameters (rated voltages, core loss, etc.) along with design in ANSYS Maxwell. Similar to other studies, this study presented that the dry type transformer option is limited. Moreover, the commonly-used 50 kVA distribution transformers in the industry are oil type and dry type transformers are designed and considered in terms of weight. Currently, the preference for low-cost oil-type transformers would change if costs for dry-type transformer were more competitive. The aim of this study was to compare the weight of transformers, which is a substantial cost factor, and to provide an evaluation about increasing the use of dry type transformers.

Keywords: Weight, oil-type transformers, dry-type transformers.

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Authors: N. Arulanand, P. M. Ananth

Abstract:

Quality of Service (QoS) attributes as part of the service description is an important factor for service attribute. It is not easy to exactly quantify the weight of each QoS conditions since human judgments based on their preference causes vagueness. As web services selection requires optimization, evolutionary computing based on heuristics to select an optimal solution is adopted. In this work, the evolutionary computing technique Particle Swarm Optimization (PSO) is used for selecting a suitable web services based on the user’s weightage of each QoS values by optimizing the QoS weight vector and thereby finding the best weight vectors for best services that is being selected. Finally the results are compared and analyzed using static inertia weight and deterministic inertia weight of PSO.

Keywords: QoS, Optimization, Particle Swarm Optimization (PSO), weight vector, web services, web service selection.

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Authors: Wojciech Rejchel

Abstract:

The problem of ranking (rank regression) has become popular in the machine learning community. This theory relates to problems, in which one has to predict (guess) the order between objects on the basis of vectors describing their observed features. In many ranking algorithms a convex loss function is used instead of the 0-1 loss. It makes these procedures computationally efficient. Hence, convex risk minimizers and their statistical properties are investigated in this paper. Fast rates of convergence are obtained under conditions, that look similarly to the ones from the classification theory. Methods used in this paper come from the theory of U-processes as well as empirical processes.

Keywords: Convex loss function, empirical risk minimization, empirical process, U-process, boosting, euclidean family.

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Authors: Deependra Singh, Devender Singh, K. S. Verma

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This paper addresses a novel technique for placement of distributed generation (DG) in electric power systems. A GA based approach for sizing and placement of DG keeping in view of system power loss minimization in different loading conditions is explained. Minimal system power loss is obtained under voltage and line loading constraints. Proposed strategy is applied to power distribution systems and its effectiveness is verified through simulation results on 16, 37-bus and 75-bus test systems.

Keywords: Distributed generation (DG), Genetic algorithms (GA), optimal sizing and placement, Power loss.

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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Authors: H. Zare Aliabadi

Abstract:

The equilibrium chemical reactions taken place in a converter reactor of the Khorasan Petrochemical Ammonia plant was studied using the minimization of Gibbs free energy method. In the minimization of the Gibbs free energy function the Davidon– Fletcher–Powell (DFP) optimization procedure using the penalty terms in the well-defined objective function was used. It should be noted that in the DFP procedure along with the corresponding penalty terms the Hessian matrices for the composition of constituents in the Converter reactor can be excluded. This, in fact, can be considered as the main advantage of the DFP optimization procedure. Also the effect of temperature and pressure on the equilibrium composition of the constituents was investigated. The results obtained in this work were compared with the data collected from the converter reactor of the Khorasan Petrochemical Ammonia plant. It was concluded that the results obtained from the method used in this work are in good agreement with the industrial data. Notably, the algorithm developed in this work, in spite of its simplicity, takes the advantage of short computation and convergence time.

Keywords: Gibbs free energy, converter reactors, Chemical equilibrium

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Authors: Nurnadiah Z., Lazim A.

Abstract:

The design of weight is one of the important parts in fuzzy decision making, as it would have a deep effect on the evaluation results. Entropy is one of the weight measure based on objective evaluation. Non--probabilistic-type entropy measures for fuzzy set and interval type-2 fuzzy sets (IT2FS) have been developed and applied to weight measure. Since the entropy for (IT2FS) for decision making yet to be explored, this paper proposes a new objective weight method by using entropy weight method for multiple attribute decision making (MADM). This paper utilizes the nature of IT2FS concept in the evaluation process to assess the attribute weight based on the credibility of data. An example was presented to demonstrate the feasibility of the new method in decision making. The entropy measure of interval type-2 fuzzy sets yield flexible judgment and could be applied in decision making environment.

Keywords: Objective weight, entropy weight, multiple attributedecision making, type-2 fuzzy sets, interval type-2 fuzzy sets

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Authors: Sujing Wang, Song Wang, Jian Zhang, Qiang Xu

Abstract:

Flaring emissions during abnormal operating conditions such as plant start-ups, shut-downs, and upsets in chemical process industries (CPI) are usually significant. Flare minimization can help to save raw material and energy for CPI plants, and to improve local environmental sustainability. In this paper, a systematic methodology based on plant-wide dynamic simulation is presented for CPI plant flare minimizations under abnormal operating conditions. Since off-specification emission sources are inevitable during abnormal operating conditions, to significantly reduce flaring emission in a CPI plant, they must be either recycled to the upstream process for online reuse, or stored somewhere temporarily for future reprocessing, when the CPI plant manufacturing returns to stable operation. Thus, the off-spec products could be reused instead of being flared. This can be achieved through the identification of viable design and operational strategies during normal and abnormal operations through plant-wide dynamic scheduling, simulation, and optimization. The proposed study includes three stages of simulation works: (i) developing and validating a steady-state model of a CPI plant; (ii) transiting the obtained steady-state plant model to the dynamic modeling environment; and refining and validating the plant dynamic model; and (iii) developing flare minimization strategies for abnormal operating conditions of a CPI plant via a validated plant-wide dynamic model. This cost-effective methodology has two main merits: (i) employing large-scale dynamic modeling and simulations for industrial flare minimization, which involves various unit models for modeling hundreds of CPI plant facilities; (ii) dealing with critical abnormal operating conditions of CPI plants such as plant start-up and shut-down. Two virtual case studies on flare minimizations for start-up operation (over 50% of emission savings) and shut-down operation (over 70% of emission savings) of an ethylene plant have been employed to demonstrate the efficacy of the proposed study.

Keywords: Flare minimization, large-scale modeling and simulation, plant shut-down, plant start-up.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai

Abstract:

One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.

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Authors: Muhammad Naeem, Asif Hussain Bhatti, Muhammad Fahad Nouman

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115 samples of Labeo calbasu ranged 8.0-17.9cm length with mean11.90±1.96 and 4.9-68.5g weight with mean 22.25±12.54 from the River Chenab, Southern Punjab, Pakistan were analyzed to investigate length-weight relationships (LWR) of fish in relation to condition factor (K). Standard length (SL), fork length (FL), head length (HL) head width (HW), body girth (BG), dorsal fin length (DFL), dorsal fin base (DFB), pectoral fin length (PcFL), pelvic fin length (PvFL) and anal fin length (AFL) are found to be highly correlated with increasing total length and wet body weight (r > 0.500). Wet body weight has positive (r=0.540) and total length has no correlation (r=0.344) with calculated Condition factor (K). The slope “b" in the relationship is 3.27 and intercepts -2.2258.

Keywords: Labeo calbasu, Length-weight relationship, Body weight, condition factor

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Authors: Zheng-Yan Ruan, Chien-Hao Wang, Hong-Jen Lin, Chien-Peng Huang, Ying-Hao Chen, En-Cheng Yang, Chwan-Lu Tseng, Joe-Air Jiang

Abstract:

Bees play a vital role in pollination. This paper focuses on the weighing process of honey. Honey is usually stored at the comb in a hive. Bee farmers brush bees away from the comb and then collect honey, and the collected honey is weighed afterward. However, such a process brings strong negative influences on bees and even leads to the death of bees. This paper therefore presents an Internet of Things-based weight monitoring system which uses weight sensors to measure the weight of honey and simplifies the whole weighing procedure. To verify the system, the weight measured by the system is compared to the weight of standard weights used for calibration by employing a linear regression model. The R² of the regression model is 0.9788, which suggests that the weighing system is highly reliable and is able to be applied to obtain actual weight of honey. In the future, the weight data of honey can be used to find the relationship between honey production and different ecological parameters, such as bees’ foraging behavior and weather conditions. It is expected that the findings can serve as critical information for honey production improvement.

Keywords: Internet of Things, weight, honey, bee.

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Authors: Bahareh Amirjabbari, Nadia Bhuiyan

Abstract:

In recent decades, the lean methodology, and the development of its principles and concepts have widely been applied in supply chain management. One of the most important strategies of being lean is having efficient inventory within the chain. On the other hand, managing inventory efficiently requires appropriate management of safety stock in order to protect against increasing stretch in the breaking points of the supply chain, which in turn can result in possible reduction of inventory. This paper applies a safety stock cost minimization model in a manufacturing company. The model results in optimum levels and locations of safety stock within the company-s supply chain in order to minimize total logistics costs.

Keywords: Cost, efficient inventory, optimization, safety stock, supply chain

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Authors: Grigoris Giannarakis, Despina Galani, Charitoudi Georgia, Nikolaos Litinas

Abstract:

The Corporate Social Responsibility (CSR) performance has garnered significant interest during the last two decades as numerous methodologies are proposed by Social Responsible Investment (SRI) indexes. The weight of each indicator is a crucial component of the CSR measurement procedures. Based on a previous study, the appropriate weight of each proposed indicator for the Greek telecommunication sector is specified using the rank reciprocal weighting. The Kendall-s Coefficient of Concordance and Spearman Correlation Coefficient non-parametric tests are adopted to determine the level of consensus among the experts concerning the importance rank of indicators. The results show that there is no consensus regarding the rank of indicators in most of stakeholders- domains. The equal weight for all indicators could be proposed as a solution for the lack of consensus among the experts. The study recommends three different equations concerning the adopted weight approach.

Keywords: Corporate Social Responsibility, Indicator, Weight.

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Authors: Yasuhiko Okuma, Yuichi Suzuki, Takahiro Murakami, Yoshihisa Ishida

Abstract:

In this paper, an extended method of the directionally constrained minimization of power (DCMP) algorithm for broadband signals is proposed. The DCMP algorithm is one of the useful techniques of extracting a target signal from observed signals of a microphone array system. In the DCMP algorithm, output power of the microphone array is minimized under a constraint of constant responses to directions of arrival (DOAs) of specific signals. In our algorithm, by limiting the directional constraint to the perpendicular direction to the sensor array system, the calculating time is reduced.

Keywords: Beamformer, directionally constrained minimizationof power, direction of arrival, microphone array.

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Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We study different types of aggregation operators and the decision making process with minimization of regret. We analyze the original work developed by Savage and the recent work developed by Yager that generalizes the MMR method creating a parameterized family of minimal regret methods by using the ordered weighted averaging (OWA) operator. We suggest a new method that uses different types of geometric operators such as the weighted geometric mean or the ordered weighted geometric operator (OWG) to generalize the MMR method obtaining a new parameterized family of minimal regret methods. The main result obtained in this method is that it allows to aggregate negative numbers in the OWG operator. Finally, we give an illustrative example.

Keywords: Decision making, Regret, Aggregation operators, OWA operator, OWG operator.

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Authors: Shubhajit Roy Chowdhury, Aritra Banerjee, Aniruddha Roy, Hiranmay Saha

Abstract:

The paper proposes the novel design of a 3T XOR gate combining complementary CMOS with pass transistor logic. The design has been compared with earlier proposed 4T and 6T XOR gates and a significant improvement in silicon area and power-delay product has been obtained. An eight transistor full adder has been designed using the proposed three-transistor XOR gate and its performance has been investigated using 0.15um and 0.35um technologies. Compared to the earlier designed 10 transistor full adder, the proposed adder shows a significant improvement in silicon area and power delay product. The whole simulation has been carried out using HSPICE.

Keywords: XOR gate, full adder, improvement in speed, area minimization, transistor count minimization.

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Authors: L. Abdelmalek, M. Zerikat, M. Rahli

Abstract:

In this paper, we present a comparative study of the genetic algorithms and Hessian-s methods for optimal research of the active powers in an electric network of power. The objective function which is the performance index of production of electrical energy is minimized by satisfying the constraints of the equality type and inequality type initially by the Hessian-s methods and in the second time by the genetic Algorithms. The results found by the application of AG for the minimization of the electric production costs of power are very encouraging. The algorithms seem to be an effective technique to solve a great number of problems and which are in constant evolution. Nevertheless it should be specified that the traditional binary representation used for the genetic algorithms creates problems of optimization of management of the large-sized networks with high numerical precision.

Keywords: Genetic algorithm, Flow of optimum loadimpedances, Hessians method, Optimal distribution.

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

Abstract:

The present study investigates the length-weight relationship of Terapon jarbua from Puducherry (East coast of India). A total of 370 individuals of different sizes were collected from Puducherry landings centre. Length-weight relationships were calculated for all specimens sampled. The length weight relationship equations are W = 0.0050 L3.2742; W = 0.0035 L3.3616; W = 0.0736 L2.4076; W = 0.0098 L3.0807; W = 0.0088 L3.0914; W = 0.0038 L3.3776 for immature male, immature female, matured male, matured female, total male, and total female respectively. The growth exponential (b) values were found to be positively allometric for all the stages except matured male.

Keywords: Allometry, Length weight relationship, Puducherry waters, Terapon jarbua.

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Authors: César Garza

Abstract:

In supervised binary classification and regression problems, it is well-known that learnability is equivalent to uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: Statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization.

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