Search results for: variable point spread function

Authors: M. Y. Malik, Farzana Khan

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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.

Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity

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Authors: Constanza A. Barriga, Rafael Bernardi, Amokrane Berdja, Christian D. Guzman

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Most image restoration methods in astronomy rely upon probabilistic tools that infer the best solution for a deconvolution problem. They achieve good performances when the point spread function (PSF) is spatially invariable in the image plane. However, this latter condition is not always satisfied with real optical systems. PSF angular variations cannot be evaluated directly from the observations, neither be corrected at a pixel resolution. We have developed a method for the restoration of images affected by static and anisotropic aberrations using deep neural networks that can be directly applied to sky images. The network is trained using simulated sky images corresponding to the T-80 telescope optical system, an 80 cm survey imager at Cerro Tololo (Chile), which are synthesized using a Zernike polynomial representation of the optical system. Once trained, the network can be used directly on sky images, outputting a corrected version of the image, which has a constant and known PSF across its field-of-view. The method was tested with the T-80 telescope, achieving better results than with PSF deconvolution techniques. We present the method and results on this telescope.

Keywords: aberrations, deep neural networks, image restoration, variable point spread function, wide field images

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Authors: Faisel Eltuhami Alzaalik, Omar Imhemed Alramli, Ahmed Mohamed Elaieb

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The IEEE 802.11 defines two modes of MAC, distributed coordination function (DCF) and point coordination function (PCF) mode. The first sub-layer of the MAC is the distributed coordination function (DCF). A contention algorithm is used via DCF to provide access to all traffic. The point coordination function (PCF) is the second sub-layer used to provide contention-free service. PCF is upper DCF and it uses features of DCF to establish guarantee access of its users. Some papers and researches that have been published in this technology were reviewed in this paper, as well as talking briefly about the distributed coordination function (DCF) technology. The simulation of the PCF function have been applied by using a simulation program called network simulator (NS2) and have been found out the throughput of a transmitter system by using this function.

Keywords: DCF, PCF, throughput, NS2

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Authors: D. S. Palimkar

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Random fixed point theory has received much attention in recent years, and it is needed for the study of various classes of random equations. The study of random fixed point theorems was initiated by the Prague school of probabilistic in the 1950s. The existence and uniqueness of fixed points for the self-maps of a metric space by altering distances between the points with the use of a control function is an interesting aspect in the classical fixed point theory. In a new category of fixed point problems for a single self-map with the help of a control function that alters the distance between two points in a metric space which they called an altering distance function. In this paper, we prove the results of existence of random common fixed point and its uniqueness for a pair of random mappings under weakly contractive condition for generalizing alter distance function in polish spaces using Random Common Fixed Point Theorem for Generalized Weakly Contractions.

Keywords: Polish space, random common fixed point theorem, weakly contractive mapping, altering function

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Authors: Kang-Mo Jung

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The use of regularization for statistical methods has become popular. The least absolute shrinkage and selection operator (LASSO) framework has become the standard tool for sparse regression. However, it is well known that the LASSO is sensitive to outliers or leverage points. We consider a new robust estimation which is composed of the weighted loss function of the pairwise difference of residuals and the adaptive penalty function regulating the tuning parameter for each variable. Rank regression is resistant to regression outliers, but not to leverage points. By adopting a weighted loss function, the proposed method is robust to leverage points of the predictor variable. Furthermore, the adaptive penalty function gives us good statistical properties in variable selection such as oracle property and consistency. We develop an efficient algorithm to compute the proposed estimator using basic functions in program R. We used an optimal tuning parameter based on the Bayesian information criterion (BIC). Numerical simulation shows that the proposed estimator is effective for analyzing real data set and contaminated data.

Keywords: adaptive penalty function, robust penalized regression, variable selection, weighted rank regression

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Authors: Chao-Qing Dai

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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: Lawrence A. Farinola

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Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

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Authors: Srijanani Anurag Prasad

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The Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) was built by combining interpolation data from the Iterated Function System (IFS). The interpolation data in a CHFIS comprises a row and/or column of uncertain values when a single point is entered. Alternatively, a row and/or column of additional points are placed in the given interpolation data to demonstrate the node added CHFIS. There are three techniques for inserting new points that correspond to the row and/or column of nodes inserted, and each method is further classified into four types based on the values of the inserted nodes. As a result, numerous forms of node insertion can be found in a CHFIS.

Keywords: fractal, interpolation, iterated function system, coalescence, node insertion, knot insertion

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Authors: Manojkumar Sabanayagam

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The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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Authors: Changho Han, Jaemin Lee, Li Hua, Seokkwon Jeong

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Design of membership function ranges in fuzzy logic control (FLC) is presented for robust control of a variable speed refrigeration system (VSRS). The criterion values of the membership function ranges can be carried out from the static experimental data, and two different values are offered to compare control performance. Some simulations and real experiments for the VSRS were conducted to verify the validity of the designed membership functions. The experimental results showed good agreement with the simulation results, and the error change rate and its sampling time strongly affected the control performance at transient state of the VSRS.

Keywords: variable speed refrigeration system, fuzzy logic control, membership function range, control performance

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Authors: Nguyen J. M., Lucas G., Brunner M., Ruan S., Antonioli D.

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Deep learning based on convolutional neural networks (CNN) is a very powerful technique for classifying information from an image. We propose a new method, DeepNic, to transform each variable of a tabular dataset into an image where each pixel represents a set of conditions that allow the variable to make an error-free prediction. The contrast of each pixel is proportional to its prediction performance and the color of each pixel corresponds to a sub-family of NICs. NICs are probabilities that depend on the number of inputs to each neuron and the range of coefficients of the inputs. Each variable can therefore be expressed as a function of a matrix of 2 vectors corresponding to an image whose pixels express predictive capabilities. Our objective is to transform each variable of tabular data into images into an image that can be analysed by CNNs, unlike other methods which use all the variables to construct an image. We analyse the NIC information of each variable and express it as a function of the number of neurons and the range of coefficients used. The predictive value and the category of the NIC are expressed by the contrast and the color of the pixel. We have developed a pipeline to implement this technology and have successfully applied it to genomic expressions on an Affymetrix chip.

Keywords: tabular data, deep learning, perfect trees, NICS

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Authors: Darwin Castillo Huamaní, Francisco A. M. Gomes

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The aim of the multi-material topology optimization (MTO) is to obtain the optimal topology of structures composed by many materials, according to a given set of constraints and cost criteria. In this work, we seek the optimal distribution of materials in a domain, such that the flexibility of the structure is minimized, under certain boundary conditions and the intervention of external forces. In the case we have only one material, each point of the discretized domain is represented by two values from a function, where the value of the function is 1 if the element belongs to the structure or 0 if the element is empty. A common way to avoid the high computational cost of solving integer variable optimization problems is to adopt the Solid Isotropic Material with Penalization (SIMP) method. This method relies on the continuous interpolation function, power function, where the base variable represents a pseudo density at each point of domain. For proper exponent values, the SIMP method reduces intermediate densities, since values other than 0 or 1 usually does not have a physical meaning for the problem. Several extension of the SIMP method were proposed for the multi-material case. The one that we explore here is the ordered SIMP method, that has the advantage of not being based on the addition of variables to represent material selection, so the computational cost is independent of the number of materials considered. Although the number of variables is not increased by this algorithm, the optimization subproblems that are generated at each iteration cannot be solved by methods that rely on second derivatives, due to the cost of calculating the second derivatives. To overcome this, we apply a globally convergent version of the sequential linear programming method, which solves a linear approximation sequence of optimization problems.

Keywords: globally convergence, multi-material design ordered simp, sequential linear programming, topology optimization

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Authors: Sasiporn Rattanasupha, Settapat Chinviriyasit

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The treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals increases and the medical condition is limited. In this paper, the SEIR epidemic model with treatment function is studied to investigate the dynamics of the model due to the effect of treatment. It is assumed that the treatment rate is proportional to the number of infective patients. The stability of the model is analyzed. The model is simulated to illustrate the analytical results and to investigate the effects of treatment on the spread of infection.

Keywords: basic reproduction number, local stability, SEIR epidemic model, treatment function

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Authors: Ya-Mei Chang

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This research is intended to apply spatio-temporal point process methods to the dengue fever data in Tainan. The spatio-temporal intensity function of the dataset is assumed to be separable. The kernel estimation is a widely used approach to estimate intensity functions. The intensity function is very helpful to study the relation of the spatio-temporal point process and some covariates. The covariate effects might be nonlinear. An nonparametric smoothing estimator is used to detect the nonlinearity of the covariate effects. A fitted parametric model could describe the influence of the covariates to the dengue fever. The correlation between the data points is detected by the K-function. The result of this research could provide useful information to help the government or the stakeholders making decisions.

Keywords: dengue fever, spatial point process, kernel estimation, covariate effect

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

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

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Authors: Shokrya Saleh A. Alshqaq, Abdullah Ali H. Ahmadini

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The Schwarz information criterion (SIC) is a popular tool for selecting the best variables in regression datasets. However, SIC is defined using an unbounded estimator, namely, the least-squares (LS), which is highly sensitive to outlying observations, especially bad leverage points. A method for robust variable selection based on SIC for linear regression models is thus needed. This study investigates the robustness properties of SIC by deriving its influence function and proposes a robust SIC based on the MM-estimation scale. The aim of this study is to produce a criterion that can effectively select accurate models in the presence of vertical outliers and high leverage points. The advantages of the proposed robust SIC is demonstrated through a simulation study and an analysis of a real dataset.

Keywords: influence function, robust variable selection, robust regression, Schwarz information criterion

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Authors: Meng Wu

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Unmanned aerial vehicle (UAV) landing technology is a common task that is required to be fulfilled by fly robots. In this paper, the crazyflie2.0 is located by ultra-wideband (UWB) localization system that contains 4 UWB anchors. Another UWB anchor is introduced and installed on a stationary platform. One cost function is designed to find the minimum distance between crazyflie2.0 and the anchor installed on the stationary platform. The coordinates of the anchor are unknown in advance, and the goal of the cost function is to define the location of the anchor, which can be considered as an optimal landing point. When the cost function reaches the minimum value, the corresponding coordinates of the UWB anchor fixed on the stationary platform can be calculated and defined as the landing point. The simulation shows the effectiveness of the method in this paper.

Keywords: UAV landing, UWB localization system, UWB anchor, cost function, stationary platform

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Authors: Valerii Dashuk

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The usage of the confidence intervals in economics and econometrics is widespread. To be able to investigate a random variable more thoroughly, joint tests are applied. One of such examples is joint mean-variance test. A new approach for testing such hypotheses and constructing confidence sets is introduced. Exploring both the value of the random variable and its deviation with the help of this technique allows checking simultaneously the shift and the probability of that shift (i.e., portfolio risks). Another application is based on the normal distribution, which is fully defined by mean and variance, therefore could be tested using the introduced approach. This method is based on the difference of probability density functions. The starting point is two sets of normal distribution parameters that should be compared (whether they may be considered as identical with given significance level). Then the absolute difference in probabilities at each 'point' of the domain of these distributions is calculated. This measure is transformed to a function of cumulative distribution functions and compared to the critical values. Critical values table was designed from the simulations. The approach was compared with the other techniques for the univariate case. It differs qualitatively and quantitatively in easiness of implementation, computation speed, accuracy of the critical region (theoretical vs. real significance level). Stable results when working with outliers and non-normal distributions, as well as scaling possibilities, are also strong sides of the method. The main advantage of this approach is the possibility to extend it to infinite-dimension case, which was not possible in the most of the previous works. At the moment expansion to 2-dimensional state is done and it allows to test jointly up to 5 parameters. Therefore the derived technique is equivalent to classic tests in standard situations but gives more efficient alternatives in nonstandard problems and on big amounts of data.

Keywords: confidence set, cumulative distribution function, hypotheses testing, normal distribution, probability density function

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Authors: Arafat Husain

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The lubricants are one of the most used resource in today’s world. Lot of the superpowers are dependent on the lubricant resource for their country to function. To see that the lubricants are not adulterated we need to develop some efficient ways and to see which fluid has been added to the lubricant. So to observe the these malpractices in the lubricant we need to develop a method. We take a elastic ball and through it at probability circle in the submerged in the lubricant at a fixed force and see the distance of pitching and the point of fall. Then we the ratio of distance of falling to the distance of pitching and if the measured ratio is greater than one the fluid is less viscous and if the ratio is lesser than the lubricant is viscous. We will check the falling point of pure lubricant at fixed force and every pure lubricant would have a fixed falling point. After that we would adulterate the lubricant and note the falling point and if the falling point is less than the standard value then adulterate is solid and if the adulterate is liquid the falling point will be more than the standard value. Hence the comparison with the standard falling point will give the efficiency of the lubricant.

Keywords: falling point of lubricant, falling point ratios, probability circle, octane number

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Authors: Getu Hailu, Catelynn Hettick, Niklas Pieper, Paul Kim, Augustine Hamner

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Airborne transmission is a problem that all viral respiratory diseases have in common. In late 2019, a disease outbreak, now known as SARS-CoV-2, suddenly expanded across China and the rest of the world in a matter of months. Research on the spread and transmission of SARS-CoV-2 airborne particles is ongoing, as well as the development of strategies for the prevention of the spread of these pathogens using indoor air quality (IAQ) methods. By evaluating the surface area of pollutants on the surface of a mannequin in a mock-based clinic room, this study aims to better understand how altering temperature and relative humidity affect aerosol spread and contamination. Four experiments were carried out at a constant temperature of 70 degrees Fahrenheit but with four different humidity levels of 0%, 30%, 45 percent, and 60%. The mannequin was placed in direct aerosol flow since it was discovered that this was the position with the largest exposed surface area. The findings demonstrate that as relative humidity increased while the temperature remained constant, the amount of surface area infected by virus particles decreased. These findings point to approaches to reduce the spread of viral particles, such as SARS-CoV-2 and emphasize the significance of IAQ controls in enclosed environments.

Keywords: IAQ, ventilation, COVID-19, humidity, temperature

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Authors: Yungtai Lo

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Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a continuous right-skewed distribution for positive values. We review methods proposed in the literature for analyzing data with excess zeros. A two-part logit-log-normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.

Keywords: two-part model, semi-continuous variable, truncated normal, gamma regression, skew normal, Pearson residual, receiver operating characteristic curve

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Authors: Alev Atak

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We study the endogeneity in the cryptocurrency market over the branching ratio of the Hawkes process and evaluate the movement of self-excitability in the financial markets. We consider a semi-parametric self-exciting point process regression model where the excitation function is assumed to be smooth and decreasing but otherwise unspecified, and the baseline intensity is assumed to be a linear function of the regressors. We apply the empirical analysis to the three largest crypto assets, i.e. Bitcoin - Ethereum - Ripple, and provide a comparison with other financial assets such as SP500, Gold, and the volatility index VIX observed from January 2015 to December 2020. The results depict variable and high levels of endogeneity in the basket of cryptocurrencies under investigation, underlining the evidence of a significant role of endogenous feedback mechanisms in the price formation process.

Keywords: hawkes process, cryptocurrency, endogeneity, reflexivity

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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: Jianqin Qu

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This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: covariant point, point matching, dimension free, rigid registration

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Authors: L. Totladze

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The role of financial sector in supporting economic growth and development is well acknowledged. The term spread (the difference between the yields on long-term and short-term Treasury securities) has been found useful for predicting economic variables as output growth, inflation, industrial production, consumption. The temp spread is one of the leading economic indicators according to NBER methodology. Leading economic indicators are widely used in forecasting of economic activity. Many empirical studies find that the term spread predicts future economic activity. The article shortly explains how the term spread might predict future economic activity. This paper analyses the dynamics of the spread between short and long-term interest rates in countries with transition economies. The research paper analyses term spread dynamics in Georgia and compare it with post-communist countries and transition economies spread dynamics. In Georgia, the banking sector plays an important and dominant role in the financial sector, especially with respect to the mobilization of savings and provision of credit and may impact on economic activity. For this purpose, we study the impact of the term spread on economic growth in Georgia.

Keywords: forecasting, leading economic indicators, term spread, transition economies

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Authors: Hudson Akewe

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This research presents complementary results with wider applications on convergence and rate of convergence of classical fixed point theory in Banach spaces to the world of the theory of fixed points of mappings defined in classes of spaces of measurable functions, known in the literature as modular function spaces. The study gives a comprehensive survey of various iterative fixed point results for the classes of multivalued ρ-contractive-like, ρ-quasi-contractive-like, ρ-quasi-contractive, ρ-Zamfirescu and ρ-contraction mappings in the framework of modular function spaces. An example is presented to demonstrate the applicability of the implicit-type iterative schemes to the system of ordinary differential equations. Furthermore, numerical examples are given to show the rate of convergence of the various explicit Kirk-type and implicit Kirk-type iterative schemes under consideration. Our results complement the results obtained on normed and metric spaces in the literature. Also, our methods of proof serve as a guide to obtain several similar improved results for nonexpansive, pseudo-contractive, and accretive type mappings.

Keywords: implicit Kirk-type iterative schemes, multivalued mappings, convergence results, fixed point

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Authors: Jacky Liu

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This paper develops a team sports outcome prediction system with potential for wide-ranging applications across various disciplines. Despite significant advancements in predictive analytics, existing studies in sports outcome predictions possess considerable limitations, including insufficient feature engineering and underutilization of advanced machine learning techniques, among others. To address these issues, we extend the Sports Cross Industry Standard Process for Data Mining (SRP-CRISP-DM) framework and propose a unique, comprehensive predictive system, using National Basketball Association (NBA) data as an example to test this extended framework. Our approach follows a holistic methodology in feature engineering, employing both Time Series and Non-Time Series Data, as well as conducting Explanatory Data Analysis and Feature Selection. Furthermore, we contribute to the discourse on target variable choice in team sports outcome prediction, asserting that point spread prediction yields higher profits as opposed to game-winner predictions. Using machine learning algorithms, particularly XGBoost, results in a significant improvement in predictive accuracy of team sports outcomes. Applied to point spread betting strategies, it offers an astounding annual return of approximately 900% on an initial investment of $100. Our findings not only contribute to academic literature, but have critical practical implications for sports betting. Our study advances the understanding of team sports outcome prediction a burgeoning are in complex system predictions and pave the way for potential profitability and more informed decision making in sports betting markets.

Keywords: machine learning, team sports, game outcome prediction, sports betting, profits simulation

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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Authors: Selvakumar Ulaganathan, Ivo Couckuyt, Francesco Ferranti, Tom Dhaene, Eric Laermans

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Variable-fidelity surrogate modelling offers an efficient way to approximate function data available in multiple degrees of accuracy each with varying computational cost. In this paper, a Kriging-based variable-fidelity surrogate modelling approach is introduced to approximate such deterministic data. Initially, individual Kriging surrogate models, which are enhanced with gradient data of different degrees of accuracy, are constructed. Then these Gradient enhanced Kriging surrogate models are strategically coupled using a recursive CoKriging formulation to provide an accurate surrogate model for the highest fidelity data. While, intuitively, gradient data is useful to enhance the accuracy of surrogate models, the primary motivation behind this work is to investigate if it is also worthwhile incorporating gradient data of varying degrees of accuracy.

Keywords: Kriging, CoKriging, Surrogate modelling, Variable- fidelity modelling, Gradients

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Authors: Kaouther Selmi, Alaeddine Sridi, Mohamed Bouallegue, Kais Bouallegue

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Neurons are the fundamental units of the brain and the nervous system. The variable structure model of neurons consists of a system of differential equations with various parameters. By optimizing these parameters, we can create a unique model that describes the dynamic behavior of a single neuron. We introduce a neural network based on neurons with multiple dendrites employing an activation function with a variable structure. In this paper, we present a model for heart behavior. Finally, we showcase our successful simulation of the heart's ECG diagram using our Variable Structure Neuron Model (VSMN). This result could provide valuable insights into cardiology.

Keywords: neural networks, neuron, dendrites, heart behavior, ECG

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