Search results for: sigmoid function

Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

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Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs –Sigmoid, ReLU, and Tanh–have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment with multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLUReLU) combination. Our results show that using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: activation function, universal approximation function, neural networks, convergence

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Authors: Dhivyalakshmi Gnanasekaran, Sonali Adole Prasante, Raveendranath Veeramamani, H. Y. Suma

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A rare case of intestinal malrotation with midline descending colon and right sided sigmoid colon was observed in an adult male cadaver aged around 55 years during routine dissection. The descending colon began from the splenic flexure and gradually descended downwards to occupy the midline position and turned to the right side to be continued as sigmoid colon at the level of the fifth lumbar vertebra. In the right iliac fossa some part of loop of sigmoid colon displaced into the right lumbar region before entering into the true pelvis to continue as rectum. This anomalous descending and sigmoid colon was supplied by varying branching pattern of inferior mesenteric artery. It is extremely important to consider this embryological anomaly before any interventional diagnostic procedures like colonoscopy and to enhance the safety of colonic surgery.

Keywords: sigmoid colon, descending colon, hindgut, malrotation

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Authors: Joshua Teo, Leo Phan

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Signet cell carcinoma of the appendix is the rarest and the most aggressive subtype of appendiceal malignancy, typically with non-specific presentations. We describe a case of a 62-year-old male with large bowel obstruction and CT demonstrating dilated large bowels from caecum to proximal sigmoid colon with pneumoperitoneum. Intra-operatively, closed-loop obstruction caused by dense adherence of sigmoid colon to caecum was noted, which had resulted in caecal perforation. Histopathology study indicated primary appendiceal malignancy of signet cell morphology with intra-peritoneal spread to the sigmoid colon. Large bowel obstruction from appendiceal malignancy has rarely been reported, and a similar presentation has not been described in the existing literature. When left-sided large bowel obstruction is suspected to be caused by a malignant stricture, it is essential to consider transperitoneal spread of appendiceal malignancy as potential aetiology, particularly in the elderly.

Keywords: appendiceal carcinoma, large bowel obstruction, signet ring cell cancer, caecal perforation

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Authors: Mahesh Kothari, K. D. Gharde

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The ANN and fuzzy logic (FL) models were developed to predict the runoff and sediment yield for catchment of Kal river, India using 21 years (1991 to 2011) rainfall and other hydrological data (evaporation, temperature and streamflow lag by one and two day) and 7 years data for sediment yield modelling. The ANN model performance improved with increasing the input vectors. The fuzzy logic model was performing with R value more than 0.95 during developmental stage and validation stage. The comparatively FL model found to be performing well to ANN in prediction of runoff and sediment yield for Kal river.

Keywords: transferred function, sigmoid, backpropagation, membership function, defuzzification

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

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Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant

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Authors: Tayo P. Ogundunmade, Adedayo A. Adepoju

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Terrorist attacks in liberal democracies bring about a few pessimistic results, for example, sabotaged public support in the governments they target, disturbing the peace of a protected environment underwritten by the state, and a limitation of individuals from adding to the advancement of the country, among others. Hence, seeking for techniques to understand the different factors involved in terrorism and how to deal with those factors in order to completely stop or reduce terrorist activities is the topmost priority of the government in every country. This research aim is to develop an efficient deep learning-based predictive model for the prediction of future terrorist activities in Nigeria, addressing low-quality prediction accuracy problems associated with the existing solution methods. The proposed predictive AI-based model as a counterterrorism tool will be useful by governments and law enforcement agencies to protect the lives of individuals in society and to improve the quality of life in general. A Heterogeneous Bayesian Neural Network (HETBNN) model was derived with Gaussian error normal distribution. Three primary transfer functions (HOTTFs), as well as two derived transfer functions (HETTFs) arising from the convolution of the HOTTFs, are namely; Symmetric Saturated Linear transfer function (SATLINS ), Hyperbolic Tangent transfer function (TANH), Hyperbolic Tangent sigmoid transfer function (TANSIG), Symmetric Saturated Linear and Hyperbolic Tangent transfer function (SATLINS-TANH) and Symmetric Saturated Linear and Hyperbolic Tangent Sigmoid transfer function (SATLINS-TANSIG). Data on the Terrorist activities in Nigeria gathered through questionnaires for the purpose of this study were used. Mean Square Error (MSE), Mean Absolute Error (MAE) and Test Error are the forecast prediction criteria. The results showed that the HETFs performed better in terms of prediction and factors associated with terrorist activities in Nigeria were determined. The proposed predictive deep learning-based model will be useful to governments and law enforcement agencies as an effective counterterrorism mechanism to understand the parameters of terrorism and to design strategies to deal with terrorism before an incident actually happens and potentially causes the loss of precious lives. The proposed predictive AI-based model will reduce the chances of terrorist activities and is particularly helpful for security agencies to predict future terrorist activities.

Keywords: activation functions, Bayesian neural network, mean square error, test error, terrorism

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Authors: Muhammad Noor Ul Ane, Dong-Soon Kim, Myron P. Zalucki

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Models can be useful to help understand population dynamics of insects under diverse environmental conditions and in developing strategies to manage pest species better. Adult longevity and fecundity of Helicoverpa armigera (Hübner) were evaluated against a wide range of constant temperatures (15, 20, 25, 30, 35 and 37.5ᵒC). The modified Sharpe and DeMichele model described adult aging rate and was used to estimate adult physiological age. Maximum fecundity of H. armigera was 973 egg/female at 25ᵒC decreasing to 72 eggs/female at 37.5ᵒC. The relationship between adult fecundity and temperature was well described by an extreme value function. Age-specific cumulative oviposition rate and age-specific survival rate were well described by a two-parameter Weibull function and sigmoid function, respectively. An oviposition model was developed using three temperature-dependent components: total fecundity, age-specific oviposition rate, and age-specific survival rate. The oviposition model was validated against independent field data and described the field occurrence pattern of egg population of H. armigera very well. Our model should be a useful component for population modeling of H. armigera and can be independently used for the timing of sprays in management programs of this key pest species.

Keywords: cotton bollworm, life table, temperature-dependent adult development, temperature-dependent fecundity

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Authors: Christopher Leung, Assad Zahid

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Mesenteric vasculitis can often mimic abdominal sepsis in a postoperative setting leading to a predicament where steroids could improve mesenteric vasculitis whilst worsening abdominal sepsis. Here this study presents a unique and rare case of perforated sigmoid diverticulitis secondary to systemic vasculitis. A 68-year-old gentleman presented with perforated sigmoid diverticulitis requiring an emergency Hartmann’s procedure. Early in his postoperative course, he had painful and asymmetrical neuropathy that, after a careful history and examination, revealed a patient with mono neuritis multiplex on a background history of longstanding rheumatoid arthritis. On day seven of his postoperative course, he had rising inflammatory markers and a CT abdomen and pelvis showing fluid around the mesentery. Whilst contamination from sigmoid perforation was somewhat congruent with these signs, a diagnosis of polyarteritis nodosa, a common cause of mononeuritis multiplex, is also possible, although involvement of the large bowel in polyarteritis nodosa is extremely rare. The histopathology from the initial Hartmann’s procedure was re-examined, showing medium vessel disease vasculitis. Given his lack of fevers, absence of abdominal pain, and worsening neurology, he was given a provisional diagnosis of polyarteritis nodosa and was treated successfully, not on IV antibiotics but on steroids. Large bowel involvement of polyarteritis nodosa is extremely rare and this is the first case of polyarteritis nodosa causing perforated diverticulitis. The learning point here is to obtain a good clinical picture of a patient to identify mesenteric vasculitis as compared to abdominal sepsis as the treatment of one worsens the other.

Keywords: abdominal sepsis, diverticulitis, mesenteric vasculitis, polyarteritis nodosa

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Authors: M. Sumana, K. S. Hareesha

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Secure computations are essential while performing privacy preserving data mining. Distributed privacy preserving data mining involve two to more sites that cannot pool in their data to a third party due to the violation of law regarding the individual. Hence in order to model the private data without compromising privacy and information loss, secure multiparty computations are used. Secure computations of product, mean, variance, dot product, sigmoid function using the additive and multiplicative homomorphic property is discussed. The computations are performed on vertically partitioned data with a single site holding the class value.

Keywords: homomorphic property, secure product, secure mean and variance, secure dot product, vertically partitioned data

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Authors: Ashutosh Mishra, Nikhil Goyal

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A 3D facial emotion recognition model based on deep learning is proposed in this paper. Two convolution layers and a pooling layer are employed in the deep learning architecture. After the convolution process, the pooling is finished. The probabilities for various classes of human faces are calculated using the sigmoid activation function. To verify the efficiency of deep learning-based systems, a set of faces. The Kaggle dataset is used to verify the accuracy of a deep learning-based face recognition model. The model's accuracy is about 65 percent, which is lower than that of other facial expression recognition techniques. Despite significant gains in representation precision due to the nonlinearity of profound image representations.

Keywords: facial recognition, computational intelligence, convolutional neural network, depth map

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Authors: Aysun Pınarbaşı, Béla Vizvári

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The countries are the units that procure the vaccines during the COVID-19 pandemic. The delivered quantities are huge. The countries must bear the inventory holding cost according to the variation of stock quantities. This cost depends on the speed of the vaccination in the country. This speed is time-dependent. The vaccinated portion of the population can be approximated by the cumulative distribution function of the Cauchy distribution. A model is provided for determining the minimal-cost inventory policy, and its optimality conditions are provided. The model is solved for 20 countries for different numbers of procurements. The results reveal the individual behavior of each country. We provide an inventory policy for the pandemic period for the countries. This paper presents a deterministic model for vaccines with a demand rate variable over time for the countries. It is aimed to provide an analytical model to deal with the minimization of holding cost and develop inventory policies regarding this aim to be used for a variety of perishable products such as vaccines. The saturation process is introduced, and an approximation of the vaccination curve of the countries has been discussed. According to this aspect, a deterministic model for inventory policy has been developed.

Keywords: covid-19, vaccination, inventory policy, bounded total demand, inventory holding cost, cauchy distribution, sigmoid function

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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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: Shatha S. Alhily

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The purpose of this research paper is to show all the possible values of the pth power of the integrable function which make the integral means of the derivative of univalent function existing and finite.

Keywords: derivative, integral means, self conformal maps, univalent function

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang

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A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.

Keywords: beta function, compressor map, interpolation error, map optimization tool

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Authors: Mehrdad Shahrbanozadeh, Gholam Abbas Barani, Saeed Shojaee

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In this study, a finite element (Seep3D model) and an artificial neural network (ANN) model were developed to simulate flow through dam foundation. Seep3D model is capable of simulating three-dimensional flow through a heterogeneous and anisotropic, saturated and unsaturated porous media. Flow through the Shahid Abbaspour dam foundation has been used as a case study. The FEM with 24960 triangular elements and 28707 nodes applied to model flow through foundation of this dam. The FEM being made denser in the neighborhood of the curtain screen. The ANN model developed for Shahid Abbaspour dam is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning. The water level elevations of the upstream and downstream of the dam have been used as input variables and the piezometric heads as the target outputs in the ANN model. The two models are calibrated and verified using the Shahid Abbaspour’s dam piezometric data. Results of the models were compared with those measured by the piezometers which are in good agreement. The model results also revealed that the ANN model performed as good as and in some cases better than the FEM.

Keywords: seepage, dam foundation, finite element method, neural network, seep 3D model

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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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: Maryam Kheirollahpour, Mahmoud Danaee, Amir Faisal Merican, Asma Ahmad Shariff

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Background: The presence of nonlinearity among the risk factors of eating behavior causes a bias in the prediction models. The accuracy of estimation of eating behaviors risk factors in the primary prevention of obesity has been established. Objective: The aim of this study was to explore the potential of a hybrid model of structural equation modeling (SEM) and Artificial Neural Networks (ANN) to predict eating behaviors. Methods: The Partial Least Square-SEM (PLS-SEM) and a hybrid model (SEM-Artificial Neural Networks (SEM-ANN)) were applied to evaluate the factors affecting eating behavior patterns among university students. 340 university students participated in this study. The PLS-SEM analysis was used to check the effect of emotional eating scale (EES), body shape concern (BSC), and body appreciation scale (BAS) on different categories of eating behavior patterns (EBP). Then, the hybrid model was conducted using multilayer perceptron (MLP) with feedforward network topology. Moreover, Levenberg-Marquardt, which is a supervised learning model, was applied as a learning method for MLP training. The Tangent/sigmoid function was used for the input layer while the linear function applied for the output layer. The coefficient of determination (R²) and mean square error (MSE) was calculated. Results: It was proved that the hybrid model was superior to PLS-SEM methods. Using hybrid model, the optimal network happened at MPLP 3-17-8, while the R² of the model was increased by 27%, while, the MSE was decreased by 9.6%. Moreover, it was found that which one of these factors have significantly affected on healthy and unhealthy eating behavior patterns. The p-value was reported to be less than 0.01 for most of the paths. Conclusion/Importance: Thus, a hybrid approach could be suggested as a significant methodological contribution from a statistical standpoint, and it can be implemented as software to be able to predict models with the highest accuracy.

Keywords: hybrid model, structural equation modeling, artificial neural networks, eating behavior patterns

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Authors: Naga Velamakuri, Jyothi K. Reddy

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Quality must be designed into a product and not inspected has become the main motto of all the companies globally. Due to the rapidly increasing technology in the past few decades, the nature of demands from the consumers has become more sophisticated. To sustain this global revolution of innovation in production systems, companies have to take steps to accommodate this technology growth. In this process of understanding the customers' expectations, all the firms globally take steps to deliver a perfect output. Most of these techniques also concentrate on the consistent development and optimization of the product to exceed the expectations. Quality Function Deployment(QFD) and Modular Function Deployment(MFD) are such techniques which rely on the voice of the customer and help deliver the needs. In this paper, Quality Function Deployment and Modular Function Deployment techniques which help in converting the quantitative descriptions to qualitative outcomes are discussed. The area of interest would be to understand the scope of each of the techniques and the application range in product development when these are applied together to any problem. The research question would be mainly aimed at comprehending the limitations using modularity in product development.

Keywords: quality function deployment, modular function deployment, house of quality, methodology

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Authors: Andrew N. Saylor, James R. Peters

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Scoliosis is a complex 3D deformity of the thoracic and lumbar spines, clinically diagnosed by measurement of a Cobb angle of 10 degrees or more on a coronal X-ray. The Cobb angle is the angle made by the lines drawn along the proximal and distal endplates of the respective proximal and distal vertebrae comprising the curve. Traditionally, Cobb angles are measured manually using either a marker, straight edge, and protractor or image measurement software. The task of measuring the Cobb angle can also be represented by a function taking the spine geometry rendered using X-ray imaging as input and returning the approximate angle. Although the form of such a function may be unknown, it can be approximated using artificial neural networks (ANNs). The performance of ANNs is affected by many factors, including the choice of activation function and network architecture; however, the effects of these parameters on the accuracy of scoliotic deformity measurements are poorly understood. Therefore, the objective of this study was to systematically investigate the effect of ANN architecture and activation function on Cobb angle measurement from the coronal X-rays of scoliotic subjects. The data set for this study consisted of 609 coronal chest X-rays of scoliotic subjects divided into 481 training images and 128 test images. These data, which included labeled Cobb angle measurements, were obtained from the SpineWeb online database. In order to normalize the input data, each image was resized using bi-linear interpolation to a size of 500 × 187 pixels, and the pixel intensities were scaled to be between 0 and 1. A fully connected (dense) ANN with a fixed cost function (mean squared error), batch size (10), and learning rate (0.01) was developed using Python Version 3.7.3 and TensorFlow 1.13.1. The activation functions (sigmoid, hyperbolic tangent [tanh], or rectified linear units [ReLU]), number of hidden layers (1, 3, 5, or 10), and number of neurons per layer (10, 100, or 1000) were varied systematically to generate a total of 36 network conditions. Stochastic gradient descent with early stopping was used to train each network. Three trials were run per condition, and the final mean squared errors and mean absolute errors were averaged to quantify the network response for each condition. The network that performed the best used ReLU neurons had three hidden layers, and 100 neurons per layer. The average mean squared error of this network was 222.28 ± 30 degrees2, and the average mean absolute error was 11.96 ± 0.64 degrees. It is also notable that while most of the networks performed similarly, the networks using ReLU neurons, 10 hidden layers, and 1000 neurons per layer, and those using Tanh neurons, one hidden layer, and 10 neurons per layer performed markedly worse with average mean squared errors greater than 400 degrees2 and average mean absolute errors greater than 16 degrees. From the results of this study, it can be seen that the choice of ANN architecture and activation function has a clear impact on Cobb angle inference from coronal X-rays of scoliotic subjects.

Keywords: scoliosis, artificial neural networks, cobb angle, medical imaging

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Authors: Myunggon Yoon, Jung-Ho Moon

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In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: combustor, dynamics, thermoacoustics, transfer function

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Authors: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Medet K. Khamitov, Marat M. Ospanov, Vasiliy M. Lozovoy, Zhenis N. Sakuov, Dastan Z. Rustemov

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With a high rectosigmoid transitional zone in children with Hirschsprung’s disease, the upper rectal, sigmoid, left colon arteries are ligated during the pull-through of the descending part of the colon. As a result, the inferior mesenteric artery ceases to participate in the blood supply to the descending part of the colon. As a result, the reduced colon is supplied with blood only by the middle colon artery, which originates from the superior mesenteric artery. Insufficiency of blood supply to the reduced colon is the cause of the development of chronic hypoxia of the intestinal wall or necrosis of the reduced descending colon. Some surgeons prefer to preserve the left colon artery. However, it is possible to stretch the mesentery, which can lead to bowel retraction to anastomotic leaks and stenosis. Chronic hypoxia of the reduced colon, in turn, is the cause of acquired (secondary) aganglionosis. The highest frequency of anastomotic leaks is observed in children older than five years. The purpose is to reduce the risk of complications in the pull-through procedure of the descending part of the colon in patients with Hirschsprung’s disease by ensuring its sufficient mobility and maintaining blood supply to the lower mesenteric artery. Methodology and events. Two children aged 5 and 7 years with Hirschsprung’s disease were operated under the conditions of the hospital in Nur-Sultan. The diagnosis was made using x-ray contrast enema and histological examination. Operational technique. After revision of the left part of the colon and assessment of the architectonics of its blood vessels, parietal mobilization of the affected sigmoid and rectum was performed on laparotomy access, while maintaining the arterial and venous terminal arcades of the sigmoid vessels. Then, the descending branch of the left colon artery was crossed (if there is an insufficient length of the reduced intestine, the left colonic artery itself may also be crossed). This manipulation provides additional mobility of the pull-through descending part of the colon. The resulting "windows" in the mesentery of the reduced intestine were sutured to prevent the development of an internal hernia. Formed a full-blooded, sufficiently long transplant from the transverse loops of the splenic angle and the descending parts of the colon with blood supply from the upper and lower mesenteric artery, freely, without tension, is reduced to the rectal zone with the coloanal anastomosis 1.5 cm above the dentate line. Results. The postoperative period was uneventful. Patients were discharged on the 7th day. The observation was carried out for six months. In no case, there was a bowel retraction, anastomotic leak, anastomotic stenosis, or other complications. Conclusion. The presented technique of mobilization of the colon for the pull-through procedure in a high transitional rectosigmoid zone of Hirschsprung’s disease allows to maintain normal blood supply to the distal part of the colon and to avoid the tension of the colon. The technique allows reducing the risk of anastomotic leak, bowel necrosis, chronic ischemia, to exclude colon retraction and anastomotic stenosis.

Keywords: blood supply, children, colon mobilization, Hirschsprung's disease, pull-through

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Selim M. Khan

Abstract:

Indoor air quality is strongly influenced by the presence of radioactive radon (222Rn) gas. Indeed, exposure to high 222Rn concentrations is unequivocally linked to DNA damage and lung cancer and is a worsening issue in North American and European built environments, having increased over time within newer housing stocks as a function of as yet unclear variables. Indoor air radon concentration can be influenced by a wide range of environmental, structural, and behavioral factors. As some of these factors are quantitative while others are qualitative, no single statistical model can determine indoor radon level precisely while simultaneously considering all these variables across a complex and highly diverse dataset. The ability of AI- machine (deep) learning to simultaneously analyze multiple quantitative and qualitative features makes it suitable to predict radon with a high degree of precision. Using Canadian and Swedish long-term indoor air radon exposure data, we are using artificial deep neural network models with random weights and polynomial statistical models in MATLAB to assess and predict radon health risk to human as a function of geospatial, human behavioral, and built environmental metrics. Our initial artificial neural network with random weights model run by sigmoid activation tested different combinations of variables and showed the highest prediction accuracy (>96%) within the reasonable iterations. Here, we present details of these emerging methods and discuss strengths and weaknesses compared to the traditional artificial neural network and statistical methods commonly used to predict indoor air quality in different countries. We propose an artificial deep neural network with random weights as a highly effective method for assessing and predicting indoor radon.

Keywords: radon, radiation protection, lung cancer, aI-machine deep learnng, risk assessment, risk prediction, Europe, North America

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Authors: Rogelio Luck, Yucheng Liu

Abstract:

This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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