Search results for: derive

Authors: Giovanni Merola

Abstract:

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective function. This approach differs from others because it preserves PCA's original optimality: uncorrelatedness of the components and least squares approximation of the data. To identify the best subset of non-zero loadings we propose a branch-and-bound search and an iterative elimination algorithm. This last algorithm finds sparse solutions with large loadings and can be run without specifying the cardinality of the loadings and the number of components to compute in advance. We give thorough comparisons with the existing sparse PCA methods and several examples on real datasets.

Keywords: SPCA, uncorrelated components, branch-and-bound, backward elimination

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Authors: M. Aboalazayem, Essam A. Gouda, Ahmed M. Moussa, Amr E. Flifl

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Field data collecting is considered one of the most difficult work due to the difficulty of accessing large zones such as large lakes. Also, it is well known that the cost of obtaining field data is very expensive. Remotely monitoring of lake water quality (WQ) provides an economically feasible approach comparing to field data collection. Researchers have shown that lake WQ can be properly monitored via Remote sensing (RS) analyses. Using satellite images as a method of WQ detection provides a realistic technique to measure quality parameters across huge areas. Landsat (LS) data provides full free access to often occurring and repeating satellite photos. This enables researchers to undertake large-scale temporal comparisons of parameters related to lake WQ. Satellite measurements have been extensively utilized to develop algorithms for predicting critical water quality parameters (WQPs). The goal of this paper is to use RS to derive WQ indicators in Aswan High Dam Reservoir (AHDR), which is considered Egypt's primary and strategic reservoir of freshwater. This study focuses on using Landsat8 (L-8) band surface reflectance (SR) observations to predict water-quality characteristics which are limited to Turbidity (TUR), total suspended solids (TSS), and chlorophyll-a (Chl-a). ArcGIS pro is used to retrieve L-8 SR data for the study region. Multiple linear regression analysis was used to derive new correlations between observed optical water-quality indicators in April and L-8 SR which were atmospherically corrected by values of various bands, band ratios, and or combinations. Field measurements taken in the month of May were used to validate WQP obtained from SR data of L-8 Operational Land Imager (OLI) satellite. The findings demonstrate a strong correlation between indicators of WQ and L-8 .For TUR, the best validation correlation with OLI SR bands blue, green, and red, were derived with high values of Coefficient of correlation (R2) and Root Mean Square Error (RMSE) equal 0.96 and 3.1 NTU, respectively. For TSS, Two equations were strongly correlated and verified with band ratios and combinations. A logarithm of the ratio of blue and green SR was determined to be the best performing model with values of R2 and RMSE equal to 0.9861 and 1.84 mg/l, respectively. For Chl-a, eight methods were presented for calculating its value within the study area. A mix of blue, red, shortwave infrared 1(SWR1) and panchromatic SR yielded the greatest validation results with values of R2 and RMSE equal 0.98 and 1.4 mg/l, respectively.

Keywords: remote sensing, landsat 8, nasser lake, water quality

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: M. Tiachachat, M. Mihoubi

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The Bell polynomials are special polynomials in combinatorial analysis that have a wide range of applications in mathematics. They have interested many authors. The exponential partial Bell polynomials have been well reduced to some special combinatorial sequences. Numerous researchers had already been interested in the above polynomials, as evidenced by many articles in the literature. Inspired by this work, in this work, we propose a family of special polynomials named after the 2-successive partial Bell polynomials. Using the combinatorial approach, we prove the properties of these numbers, derive several identities, and discuss some special cases. This family includes well-known numbers and polynomials such as Stirling numbers, Bell numbers and polynomials, and so on. We investigate their properties by employing generating functions

Keywords: 2-associated r-Stirling numbers, the exponential partial Bell polynomials, generating function, combinatorial interpretation

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Authors: Hoda Ghavamipoor, S. Alireza Hashemi Golpayegani

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An approach to model the customer interaction with e-commerce websites is presented. Considering the service quality level as a predictive feature, we offer an improved method based on the Customer Behavior Model Graph (CBMG), a state-transition graph model. To derive the Quality of Service sensitive-CBMG (QoS-CBMG) model, process-mining techniques is applied to pre-processed website server logs which are categorized as ‘buy’ or ‘visit’. Experimental results on an e-commerce website data confirmed that the proposed method outperforms CBMG based method.

Keywords: customer behavior model, electronic commerce, quality of service, customer behavior model graph, process mining

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Authors: Hung-Chi Chang

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For an extended EPQ model with random yield, the existent study revealed that both the disaggregating and consolidating shipment policies for the imperfect quality items are independent of holding cost, and recommended a model with economic benefit by comparing the least total cost for each of the three models investigated. To better capture the real situation, we generalize the existent study to include different holding costs for perfect and imperfect quality items. Through analysis, we show that the above shipment policies are dependent on holding costs. Furthermore, we derive a simple decision rule solely based on the thresholds of problem parameters to select a superior model. The results are illustrated analytically and numerically.

Keywords: consolidating shipments, disaggregating shipments, EPQ, imperfect quality, inventory

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Authors: Viriyavudh Sim, WooYoung Jung

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Damage due to high wind is not limited to load resistance components such as beam and column. The majority of damage is due to breach in the building envelope such as broken roof, window, and door. In this paper, wind fragility of window glass in residential apartment was determined to compare the difference between two window configuration models. Monte Carlo Simulation method had been used to derive damage data and analytical fragilities were constructed. Fragility of window system showed that window located in leeward wall had higher probability of failure, especially those close to the edge of structure. Between the two window models, Model 2 had higher probability of failure, this was due to the number of panel in this configuration.

Keywords: wind fragility, glass window, high rise building, wind disaster

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Authors: Hassan Mahasneh, Abu Sesay

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We propose the use of relay terminals at the cell edge of an LTE-based cellar system. Each relay terminal is equipped with an omni-directional antenna. We refer to this scheme as the Omni-Relay (OR) scheme. The OR scheme coordinates the inter-cell interference (ICI) stemming from adjacent cells and increases the desired signal level at cell-edge regions. To validate the performance of the OR scheme, we derive the average signal-to-interference plus noise ratio (SINR) and the average capacity and compare it with the conventional universal frequency reuse factor (UFRF). The results show that the proposed OR scheme provides higher average SINR and average capacity compared to the UFRF due to the assistance of the distributed relay nodes.

Keywords: the UFRF scheme, the OR scheme, ICI, relay terminals, SINR, spectral efficiency

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Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Bijan Gillani, Roya Gillani

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The purpose of this paper is to propose a pedagogical model where engineering provides the interconnection to integrate the other topics of science, technology, engineering, and mathematics. The author(s) will first present a brief discussion of cognitive theory and then derive an integrated pedagogy to use engineering and technology, such as drones, sensors, camera, iPhone, radio waves as the nexus to an integrated curriculum development for the other topics of STEM. Based on this pedagogy, one example developed by the author(s) called “Drones and Environmental Science,” will be presented that uses a drone and related technology as an appropriate instructional delivery medium to apply Piaget’s cognitive theory to create environments that promote the integration of different STEM subjects that relate to environmental science.

Keywords: cogntive theories, drone, environmental science, pedagogy

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Authors: Jiahau Guo, Yihe Zhang

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This paper proposes solutions for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day one and use the framework of Haug et al. (2003) to value European options on stocks paying discrete dividends. Next, we adopt the fast Fourier transform (FFT) to derive accurate and efficient formulae for American options and further employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed methods is verified by simulations.

Keywords: daily price limit, discrete dividend, early exercise, fast Fourier transform, multi-day density function, Richardson extrapolation

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Authors: Mari Chaikovskaia, Jean-Philippe Gayon, Alain Quilliot

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We consider a fleet of elementary robots that can be connected in different ways to transport loads of different types. For instance, a single robot can transport a small load, and the association of two robots can either transport a large load or two small loads. We seek to determine the optimal number of robots to transport a set of loads in a given time interval, with or without reconfiguration. We show that the problem with reconfiguration is strongly NP-hard by a reduction to the bin-packing problem. Then, we study a special case with unit capacities and derive simple formulas for the minimum number of robots, up to 3 types of loads. For this special case, we compare the minimum number of robots with or without reconfiguration and show that the gain is limited in absolute value but may be significant for small fleets.

Keywords: fleet sizing, reconfigurability, robots, transportation

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Authors: Mahbube Eghtesad

Abstract:

For a number of years, the problem of simultaneous detection and tracking of a target has been one of the most relevant and challenging issues in a wide variety of military and civilian systems. We develop methods for detecting and tracking a target using an orthogonal frequency division multiplexing (OFDM) based radar. As a preliminary step we introduce the target trajectory and Gaussian noise model in discrete time form. Then resorting to match filter and Kalman filter we derive a detector and target tracker. After that we propose an OFDM radar in order to achieve further improvement in tracking performance. The motivation for employing multiple frequencies is that the different scattering centers of a target resonate differently at each frequency. Numerical examples illustrate our analytical results, demonstrating the achieved performance improvement due to the OFDM signaling method.

Keywords: matched filter, target trashing, OFDM radar, Kalman filter

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Authors: Rong-Tsorng Wang

Abstract:

In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: catastrophe equity put options, compound distributions, nonhomogeneous Poisson process, pricing model

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Authors: Ulrike Dowie, Ralph Grothmann

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Rational planning decisions are based upon forecasts. Precise forecasting has, therefore, a central role in business. The prediction of customer demand is a prime example. This paper introduces recurrent neural networks to model customer demand and combines the forecast with uncertainty measures to derive decision support of the demand planning department. It identifies and describes the keys to the successful implementation of an AI-based solution: bringing together data with business knowledge, AI methods, and user experience, and applying agile software development practices.

Keywords: agile software development, AI project success factors, deep learning, demand forecasting, forecast uncertainty, neural networks, supply chain management

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Authors: Jeryes Danial, Yosi Ben Asher

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Algorithms for controlling a swarm of robots is an active research field, out of which cattle herding is one of the most complex problems to solve. In this paper, we derive an independent herding algorithm that is specifically designed for a swarm of quadcopters. The algorithm works by devising flight trajectories that cause the cows to run-away in the desired direction and hence herd cows that are distributed in a given field towards a common gathering point. Unlike previously proposed swarm herding algorithms, this algorithm does not use a flocking model but rather stars each cow separately. The effectiveness of this algorithm is verified experimentally using a simulator. We use a special set of experiments attempting to demonstrate that the herding times of this algorithm correspond to field diameter small constant regardless of the number of cows in the field. This is an optimal result indicating that the algorithm groups the cows into intermediate groups and herd them as one forming ever closing bigger groups.

Keywords: swarm, independent, distributed, algorithm

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Authors: Yi-Fei Yang, Nai-Bao He, Shao-Bang Xing

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This study investigates the permanent magnet synchronous linear motor (PMSLM) chaotic motion under the specific physical parameters, the stability and the security of motor-driven system will be unavoidably influenced. Therefore, it is really necessary to investigate the methods of controlling or suppressing chaos in PMSLM. Firstly, we derive a chaotic model of PMSLM in the closed-loop system. Secondly, in order to realize the local asymptotic stabilization of the mechanical subsystem and the global stabilization of the motor-driven system including electrical subsystem, we propose an improved uniting control lyapunov functions by introducing backstepping approach. Finally, an illustrated example is also given to show the electiveness of the obtained results.

Keywords: linear motor, lyapunov functions, chao control, hybrid controller

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Authors: Adel Mohsen

Abstract:

A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Shunichi Ohmori, Sirawadee Arunyanart, Kazuho Yoshimoto

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We consider a periodic review inventory control problem of minimizing production cost, inventory cost, and lost-sales under demand uncertainty, in which product demands are not specified exactly and it is only known to belong to a given uncertainty set, yet the constraints must hold for possible values of the data from the uncertainty set. We propose a robust optimization formulation for obtaining lowest cost possible and guaranteeing the feasibility with respect to range of order quantity and inventory level under demand uncertainty. Our formulation is based on the adaptive robust counterpart, which suppose order quantity is affine function of past demands. We derive certainty equivalent problem via second-order cone programming, which gives 'not too pessimistic' worst-case.

Keywords: robust optimization, inventory control, supply chain managment, second-order programming

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Authors: Taehyun Kim, Taehyun Kim, Hyunjoo Park

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Photovoltaic facility occurs conflicts and disputes over environmental issues such as soil runoff, landscapes damage, and ecosystems damage. Because of these problems, huge social and economic cost occurred. The purpose of this study is to analyze resident‘s acceptability and conflict factors on the location of PV facilities, and suggest ways to promote resident’s acceptability and solutions for conflicts. Literature review, cases analysis, and expert interview on the acceptance and conflict factors related to the location of PV facilities are used to derive results. The results of this study are expected to contribute to the minimization of environmental impact and social conflict due to the development of renewable energy in the future.

Keywords: acceptance factor, conflict factor, factor analysis, photovoltaic facility

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Authors: Rafik Djemili, Hocine Bourouba, M. C. Amara Korba

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In this paper, we present a method in order to classify EEG signals for Brain-Computer Interfaces (BCI). EEG signals are first processed by means of spectral estimation methods to derive reliable features before classification step. Spectral estimation methods used are standard periodogram and the periodogram calculated by the Welch method; both methods are compared with Logarithm of Band Power (logBP) features. In the method proposed, we apply Linear Discriminant Analysis (LDA) followed by Support Vector Machine (SVM). Classification accuracy reached could be as high as 85%, which proves the effectiveness of classification of EEG signals based BCI using spectral methods.

Keywords: brain-computer interface, motor imagery, electroencephalogram, linear discriminant analysis, support vector machine

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Authors: Rodrigo S. Piera, Jailson Sales Ara´ujo, Gabriela B. Lemos, Matthew B. Weiss, John B. DeBrota, Gabriel H. Aguilar, Jacques L. Pienaar

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The Born rule was historically viewed as an independent axiom of quantum mechanics until Gleason derived it in 1957 by assuming the Hilbert space structure of quantum measurements [1]. In subsequent decades there have been diverse proposals to derive the Born rule starting from even more basic assumptions [2]. In this work, we demonstrate that a simple reinforcement-learning algorithm, having no pre-programmed assumptions about quantum theory, will nevertheless converge to a behaviour pattern that accords with the Born rule, when tasked with predicting the output of a quantum optical implementation of a symmetric informationally-complete measurement (SIC). Our findings support a hypothesis due to QBism (the subjective Bayesian approach to quantum theory), which states that the Born rule can be thought of as a normative rule for making decisions in a quantum world [3].

Keywords: quantum Bayesianism, quantum theory, quantum information, quantum measurement

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Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Mohsen Farshad

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Information and force definition has been intertwined with the concept of entropy for many years. The displacement information of degrees of freedom with Brownian motions at a given temperature in space emerges as an entropic force between species. Here, we use this concept of entropy to understand the underlying physics behind the formation of attractive and repulsive forces by imagining that space is filled with free Brownian degrees of freedom. We incorporate the radius of bodies and the distance between them into entropic force relation systematically. Using this modified gravitational entropic force, we derive the attractive entropic force between bodies without considering their spin. We further hypothesize a possible mechanism for the formation of the repulsive force between two bodies. We visually elaborate that the repulsive entropic force will be manifested through the rotation of degrees of freedom around the spinning particles.

Keywords: entropy, information, force, Brownian Motions

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Authors: N. Kaewpraek, W. Assawinchaichote

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This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: h-infinity fuzzy control, an LMI approach, Takagi-Sugano (TS) fuzzy system, the photovoltaic systems

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Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Nivedita Ghosh

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This paper undertakes an analysis of permissions that are required by documentary filmmakers in order to access the locations and respondents that they desire to film. The attempt is to bring out the manner in which the practice of documentary filmmaking becomes embedded within complex social structures and relationships within/around which the film is being made. These social relationships may not only influence the direction that the film takes with respect to its final story, but may also impact the very method of filmmaking undertaken by the filmmaker. The following essay presents four types of filmmaking permissions, each revealing the specific social dynamics between the filmmaker and the filmed, and intra social dynamics between those who are intended to be filmed. The analysis shows how documentary filmmaking permissions derive from the community norms and values of the respondents. The paper is based on fieldwork carried out amongst documentary filmmakers filming in Delhi and Gujarat in India and Sardinia, Italy.

Keywords: documentary film, documentary film shooting, India, permissions

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

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New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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