Search results for: generalized topology

Authors: Rana Rimawi, Ayman Baklizi

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Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

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Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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Authors: S. Wakim, M. Nemer, B. Zeghondy, B. Ghannam, C. Bouallou

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Designing the optimal heat exchanger is still an essential objective to be achieved. Parametrical optimization involves the evaluation of the heat exchanger dimensions to find those that best satisfy certain objectives. This method contributes to an enhanced design rather than an optimized one. On the contrary, topology optimization finds the optimal structure that satisfies the design objectives. The huge development in metal additive manufacturing allowed topology optimization to find its way into engineering applications especially in the aerospace field to optimize metal structures. Using topology optimization in 3d heat and mass transfer problems requires huge computational time, therefore coupling it with CFD simulations can reduce this it. However, existed CFD models cannot be coupled with topology optimization. The CFD model must allow creating a uniform mesh despite the initial geometry complexity and also to swap the cells from fluid to solid and vice versa. In this paper, a porous media approach compatible with topology optimization criteria is developed. It consists of modeling the fluid region of the heat exchanger as porous media having high porosity and similarly the solid region is modeled as porous media having low porosity. The switching from fluid to solid cells required by topology optimization is simply done by changing each cell porosity using a user defined function. This model is tested on a plate and fin heat exchanger and validated by comparing its results to experimental data and simulations results. Furthermore, this model is used to perform a material reallocation based on local criteria to optimize a plate and fin heat exchanger under a constant heat duty constraint. The optimized fin uses 20% fewer materials than the first while the pressure drop is reduced by about 13%.

Keywords: computational methods, finite element method, heat exchanger, porous media, topology optimization

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Authors: Yaxiao Zhang, Yangzhou Chen

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This study investigate the formation problem for high-order continuous-time multi-robot with bounded symmetric time-varying delay protocol under switched directed communication topology. By using a linear transformation, the formation problem is transformed to stability analysis of a switched delay system. Under the assumption that each communication topology has a directed spanning tree, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) that the multi-robot system can achieve a desired formation by the trade-off among the pre-exist topologies with the help of the scheme of average dwell time. A numeral example is presented to illustrate the effectiveness of the obtained results.

Keywords: multi-robot systems, formation, switched directed topology, symmetric time-varying delay, average dwell time, linear matrix inequalities (lmis)

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Authors: Voodi Kalandhar, Veera Reddy, Yuva Tejasree

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Researchers have become interested in multilevel inverters (MLI) because of their potential for medium- and high-power applications. MLIs are becoming more popular as a result of their ability to generate higher voltage levels, minimal power losses, small size, and low price. These inverters used in high voltage and high-power applications because the stress on the switch is low. Even though many traditional topologies, such as the cascaded H-bridge MLI, the flying capacitor MLI, and the diode clamped MLI, exist, they all have some drawbacks. A complicated control system is needed for the flying capacitor MLI to balance the voltage across the capacitor and diode clamped MLI requires more no of diodes when no of levels increases. Even though the cascaded H-Bridge MLI is popular in terms of modularity and simple control, it requires more no of isolated DC source. Therefore, a topology with fewer devices has always been necessary for greater efficiency and reliability. A new single-phase MLI topology has been introduced to minimize the required switch count in the circuit and increase output levels. With 3 dc voltage sources, 8 switches, and 13 levels at the output, this new single- phase MLI topology was developed. To demonstrate the proposed converter's superiority over the other MLI topologies currently in use, a thorough analysis of the proposed topology will be conducted.

Keywords: DC-AC converter, multi-level inverter (MLI), diodes, H-bridge inverter, switches

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Authors: Kittipong Tripetch, Nobuhiko Nakano

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Two types of floating active resistors based on a complementary regulated cascode topology with cross-coupled regulated transistors are presented in this paper. The first topology is a high swing complementary regulated cascode active resistor. The second topology is a complementary common gate with a regulated cross coupled transistor. The small-signal input resistances of the floating resistors are derived. Three graphs of the input current versus the input voltage for different aspect ratios are designed and plotted using the Cadence Spectre 0.18-µm Rohm Semiconductor process. The total harmonic distortion graphs are plotted for three different aspect ratios with different input-voltage amplitudes and different input frequencies. From the simulation results, it is observed that a resistance of approximately 8.52 MΩ can be obtained from supply voltage at  ±0.9 V.

Keywords: floating active resistor, complementary common gate, complementary regulated cascode, current mirror

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Authors: Manideepa Saha, Jahnavi Chakrabarty

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Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

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Authors: Mohammed Hussein, Abualseoud Hanani

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In Low Earth Orbit (LEO) satellite constellation system, routing data from the source all the way to the destination constitutes a daunting challenge because LEO satellite constellation resources are spare and the high speed movement of LEO satellites results in a highly dynamic network topology. This situation limits the applicability of traditional routing approaches that rely on exchanging topology information upon change or setup of a connection. Consequently, in recent years, many routing algorithms and implementation strategies for satellite constellation networks with Inter Satellite Links (ISLs) have been proposed. In this article, we summarize and classify some of the most representative solutions according to their objectives, and discuss their advantages and disadvantages. Finally, with a look into the future, we present some of the new challenges and opportunities for LEO satellite constellations in general and routing protocols in particular.

Keywords: LEO satellite constellations, dynamic topology, IP routing, inter-satellite-links

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Authors: Abolfazl Hosseinpour, Javad Marzbanrad

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In this research, the topology and shape optimization of a Macpherson control arm has been accomplished to achieve lighter weight. Present automotive market demands low cost and light weight component to meet the need of fuel efficient and cost effective vehicle. This in turn gives the rise to more effective use of materials for automotive parts which can reduce the mass of vehicle. Since automotive components are under dynamic loads which cause fatigue damage, considering fatigue criteria seems to be essential in designing automotive components. At first, in order to create severe loading condition for control arm, some rough roads are generated through power spectral density. Then, the most critical loading conditions are obtained through multibody dynamics analysis of a full vehicle model. Then, the topology optimization is performed based on fatigue life criterion using HyperMesh software, which resulted to 50 percent mass reduction. In the next step a CAD model is created using CATIA software and shape optimization is performed to achieve accurate dimensions with less mass.

Keywords: topology optimization, shape optimization, fatigue life, MacPherson control arm

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Authors: Zubdahe Noor, Haseeb Athar

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In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

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Authors: Muhammad Zeeshan

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This case study is about a 54 years man named Mr. U, referred to Capital Hospital, Islamabad, with the presenting complaints of Generalized Anxiety Disorder (GAD). Contrary to his complaints, the client reported psychological symptoms such as restlessness, low mood and fear of darkness and fear from closed places from the last 30 days. He also had a fear of death and his existence in the grave. His sleep was also disturbed due to excessive urination due to diabetes. He was also suffering from semantic symptoms such as headache, numbness of feet and pain in the chest and blockage of the nose. A complete history was taken and informal assessment (clinical interview and MSE) and formal testing (BAI) was applied that showed the clear diagnosis of Generalized Anxiety Disorder. CBT, relaxation techniques, prayer chart and behavioural techniques were applied for the treatment purposes.

Keywords: generalized anxiety disorder, presenting complaints, formal and informal assessment, diagnosis

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Authors: Mengxiao Li, Johnson Zhang

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Currently, topology optimization technique is widely used to define the layout design of structures that are presented as truss-like topologies. However, due to the difficulty in combining optimization technique with more realistic material models where their nonlinear properties should be considered, the achieved optimized topologies are commonly unable to apply straight towards the practical design problems. This study presented an optimization procedure of composite structures where different elastic stiffness, yield criteria, and hardening models are assumed for the candidate materials. From the results, it can be concluded that a more explicit modeling has the significant influence on the resulting topologies. Also, the isotropic or kinematic hardening is important for elastoplastic structural optimization design. The capability of the proposed optimization procedure is shown through several cases.

Keywords: topology optimization, material composition, nonlinear modeling, hardening rules

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Authors: Xingyu Pan, Laure Tougne

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For recognizing coins, the graved release date is important information to identify precisely its monetary type. However, reading characters in coins meets much more obstacles than traditional character recognition tasks in the other fields, such as reading scanned documents or license plates. To address this challenging issue in a numismatic context, we propose a training-free approach dedicated to detection and recognition of the release date of the coin. In the first step, the date zone is detected by comparing histogram features; in the second step, a topology-based algorithm is introduced to recognize coin numbers with various font types represented by binary gradient map. Our method obtained a recognition rate of 92% on synthetic data and of 44% on real noised data.

Keywords: coin, detection, character recognition, topology

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Authors: M. A. Islam, P. J. Hazell, J. P. Escobedo, M. Saadatfar

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Quasistatic compression and micro structural characterization of closed cell aluminium foams of different pore size and cell distributions has been carried out. Metallic foams have good potential for lightweight structures for impact and blast mitigation and therefore it is important to find out the optimized foam structure (i.e. cell size, shape, relative density, and distribution) to maximize energy absorption. In this paper, we present results for two different aluminium metal foams of density 0.5 g/cc and 0.7 g/cc respectively that have been tested in quasi-static compression. The influence of cell geometry and cell topology on quasistatic compression behavior has been investigated using computed tomography (micro-CT) analysis. The compression behavior and micro structural characterization will be presented.

Keywords: metal foams, micro-CT, cell topology, quasistatic compression

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Authors: Arya Prakash Padhi, Anupam Chakrabarti, Rajib Chowdhury

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Topology or layout optimization often gives better performing economic structures and is very helpful in the conceptual design phase. But traditionally it is being done in finite element-based optimization schemes which, although gives a good result, is very time-consuming especially in 3D structures. Among other alternatives machine learning, especially deep learning-based methods, have a very good potential in resolving this computational issue. Here convolutional neural network (3D-CNN) based variational auto encoder (VAE) is trained using a dataset generated from commercially available topology optimization code ABAQUS Tosca using solid isotropic material with penalization (SIMP) method for compliance minimization. The encoded data in latent space is then fed to a 3D generative adversarial network (3D-GAN) to generate the outcome in 64x64x64 size. Here the network consists of 3D volumetric CNN with rectified linear unit (ReLU) activation in between and sigmoid activation in the end. The proposed network is seen to provide almost optimal results with significantly reduced computational time, as there is no iteration involved.

Keywords: 3D generative adversarial network, deep learning, structural topology optimization, variational auto encoder

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Authors: Debjit Dutta, P. Roy, O. Panella

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In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

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Authors: Gunasekaran Raja, Ramkumar Jayaraman

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In this paper, we consider CCL-N (Cooperative Cross Layer Network) topology based on the cross layer (both centralized and distributed) environment to form network communities. Various performance metrics related to the IEEE 802.16 networks are discussed to design CCL-N Topology. In CCL-N topology, nodes are classified as master nodes (Master Base Station [MBS]) and serving nodes (Relay Station [RS]). Nodes communities are organized based on the networking terminologies. Based on CCL-N Topology, various simulation analyses for both transparent and non-transparent relays are tabulated and throughput efficiency is calculated. Weighted load balancing problem plays a challenging role in IEEE 802.16 network. CoTS (Concurrent Transmission Scheduling) Scheme is formulated in terms of three aspects – transmission mechanism based on identical communities, different communities and identical node communities. CoTS scheme helps in identifying the weighted load balancing problem. Based on the analytical results, modularity value is inversely proportional to that of the error value. The modularity value plays a key role in solving the CoTS problem based on hop count. The transmission mechanism for identical node community has no impact since modularity value is same for all the network groups. In this paper three aspects of communities based on the modularity value which helps in solving the problem of weighted load balancing and CoTS are discussed.

Keywords: cross layer network topology, concurrent scheduling, modularity value, network communities and weighted load balancing

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Authors: Emmanuel Iyamuremye

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Extreme rainfall events have caused significant damage to agriculture, ecology, and infrastructure, disruption of human activities, injury, and loss of life. They also have significant social, economic, and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur, hence mitigating the consequences. Extreme value theory has been used widely in modeling extreme rainfall and in various disciplines, such as financial markets, the insurance industry, failure cases. Climatic extremes have been analyzed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions, which provides evidence of the importance of modeling extreme rainfall from different regions of the world. In this paper, we focused on Peak Over Thresholds approach, where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research also considers the use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Kigali. The results indicate that the proposed Poisson-GP distribution provides a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. The research also found a slow increase in return levels for maximum monthly rainfall for higher return periods, and further, the intervals are increasingly wider as the return period is increasing.

Keywords: exceedances, extreme value theory, generalized Pareto distribution, Poisson generalized Pareto distribution

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Authors: Amir Bahrami

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In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index or a descriptor index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper some descriptor index (descriptor index) of single-walled carbon nanotubes, is determined.

Keywords: chemical graph theory, molecular topology, molecular descriptor, single-walled carbon nanotubes

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Authors: Elham Kiyani

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In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Silvia Faroni, Olivier Le Courtois, Krzysztof Ostaszewski

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While a lot of research concentrates on the merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on explaining why regulators favor the choice of VaR or TCE in their set of rules. In this paper, we investigate the preferences of regulators with the aim of understanding why, for instance, a VaR with a given confidence level is ultimately retained. Further, this paper provides equivalence rules that explain how a given choice of VaR can be equivalent to a given choice of TCE. Then, we introduce a new risk indicator that extends TCE by providing a more versatile weighting of the constituents of probability distribution tails. All of our results are illustrated using the generalized Pareto distribution.

Keywords: generalized pareto distribution, generalized tail conditional expectation, regulator preferences, risk measure

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Authors: Ines Elouedi, Atef Hammouda

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This paper presents a new fast version of the generalized Multi-Directional Radon Transform method. The new method uses the inverse Fast Fourier Transform to lead to a faster Generalized Radon projections. We prove in this paper that the fast algorithm leads to almost the same results of the eldest one but with a considerable lower time computation cost. The projection end result of the fast method is a parameterized Radon space where a high valued pixel allows the detection of a curve from the original image. The proposed fast inversion algorithm leads to an exact reconstruction of the initial image from the Radon space. We show examples of the impact of this algorithm on the pattern recognition domain.

Keywords: fast generalized multi-directional Radon transform, curve, exact reconstruction, pattern recognition

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Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

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‎In this article‎, ‎sequential order statistics (SOS) censoring type II samples coming from the generalized Pareto distribution are considered‎. ‎Maximum likelihood (ML) estimators of the unknown parameters are derived on the basis of the available multiple SOS data‎. ‎Necessary conditions for existence and uniqueness of the derived ML estimates are given‎. Due to complexity in the proposed likelihood function‎, ‎a useful re-parametrization is suggested‎. ‎For illustrative purposes‎, ‎a Monte Carlo simulation study is conducted and an illustrative example is analysed‎.

Keywords: bayesian estimation‎, generalized pareto distribution‎, ‎maximum likelihood estimation‎, sequential order statistics

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Authors: Riccardo Zanni, Maria Galvez-Llompart, Ramon Garcia-Domenech, Jorge Galvez

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Biopesticides, such as naturally occurring chemicals, pheromones, fungi, bacteria and insect predators are often a winning choice in crop protection because of their environmental friendly profile. They are considered to have lower toxicity than traditional pesticides. After almost a century of pesticides use, resistances to traditional insecticides are wide spread, while those to bioinsecticides have raised less attention, and resistance management is frequently neglected. This seems to be a crucial mistake since resistances have already occurred for many marketed biopesticides. With an eye to the future, we present here a selection of new natural occurring chemicals as potential bioinsecticides. The molecules were selected using a consolidated mathematical paradigm called molecular topology. Several QSAR equations were depicted and subsequently applied for the virtual screening of hundred thousands molecules of natural origin, which resulted in the selection of new potential bioinsecticides. The most innovative aspect of this work does not only reside in the importance of the identification of new molecules overcoming biopesticides’ resistances, but on the possibility to promote shared knowledge in the field of green chemistry through this unique in silico discipline named molecular topology.

Keywords: green chemistry, QSAR, molecular topology, biopesticide

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Authors: Hichem Ramoul

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In this work, we introduce a new type of contractive maps and we establish a new fixed point theorem for the class of almost θ-contractions (more general than the class of almost contractions) in a complete generalized metric space. The major novelty of our work is to prove a new fixed point result by weakening some hypotheses imposed on the function θ which will change completely the classical technique used in the literature review to prove fixed point theorems for almost θ-contractions in a complete generalized metric space.

Keywords: almost contraction, almost θ-contraction, fixed point, generalized metric space

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Authors: Wei Feilong

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In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment

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Authors: Vinod Kumar Jaysaval, Prateek Agarwal

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Performance prediction of airborne radar is a challenging and cumbersome task in clutter scenario for different types of targets. A generalized model requires to predict the performance of Radar for air targets as well as ground moving targets. In this paper, we propose a generalized model to bring out the performance of airborne radar for different Pulsed Repetition Frequency (PRF) as well as different type of targets. The model provides a platform to bring out different subsystem parameters for different applications and performance requirements under different types of clutter terrain.

Keywords: airborne radar, blind zone, clutter, probability of detection

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Authors: Mbida Mohamed, Ezzati Abdellah

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A strong challenge in the wireless sensor networks (WSN) is to save the energy and have a long life time in the network without having a high rate of loss information. However, topology control (TC) protocols are designed in a way that the network is divided and having a standard system of exchange packets between nodes. In this article, we will propose a clustering based and centralized routing table protocol of TC (CBCRT) which delegates a leader node that will encapsulate a single routing table in every cluster nodes. Hence, if a node wants to send packets to the sink, it requests the information's routing table of the current cluster from the node leader in order to root the packet.

Keywords: mobile wireless sensor networks, routing, topology of control, protocols

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Authors: Retius Chifurira

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Logistic regression model is the most used regression model to predict meteorological drought probabilities. When the dependent variable is extreme, the logistic model fails to adequately capture drought probabilities. In order to adequately predict drought probabilities, we use the generalized linear model (GLM) with the quantile function of the generalized extreme value distribution (GEVD) as the link function. The method maximum likelihood estimation is used to estimate the parameters of the generalized extreme value (GEV) regression model. We compare the performance of the logistic and the GEV regression models in predicting drought probabilities for Zimbabwe. The performance of the regression models are assessed using the goodness-of-fit tests, namely; relative root mean square error (RRMSE) and relative mean absolute error (RMAE). Results show that the GEV regression model performs better than the logistic model, thereby providing a good alternative candidate for predicting drought probabilities. This paper provides the first application of GLM derived from extreme value theory to predict drought probabilities for a drought-prone country such as Zimbabwe.

Keywords: generalized extreme value distribution, general linear model, mean annual rainfall, meteorological drought probabilities

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Authors: Wikanda Phaphan

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Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.

Keywords: conjugate gradient method, quasi-Newton method, EM-algorithm, generalized gamma distribution, length biased generalized gamma distribution, maximum likelihood method

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