Bela Palancz

• D.Sc.
• Professor Emeritus at Budapest University of Technology and Economics

Model-based glycemic control (GC) protocols are used to treat stress-induced hyperglycaemia in intensive care units (ICUs). The STAR (Stochastic-TARgeted) glycemic control protocol - used in clinical practice in several ICUs in New Zealand, Hungary, Belgium, and Malaysia - is a model-based GC protocol using a patient-specific, model-based insulin s...

The concept of under and over determined systems are introduced. Methods for solution of overdetermined systems like Gauss-Jacobi combinatorical solution, transformation of overdetermined systems into determined ones, extended Newton–Raphson method. Techniques for underdetermined systems like direct minimization, Lagrange method, and method of pena...

Integer programming as a solution of discrete value problems is introduced. We consider typical types of these problems, such as binary programming, i.e. the set-covering problem. Their solution methods, such as binary countdown, branch and bound, are considered. Special techniques like Gröbner basis methods are also discussed. Techniques to solve...

The definition of implicit and explicit parallelism is given and Amdahl’s law is illustrated. Dispatching task and balancing load are demonstrated. Applications of handling tasks in different situations are considered, such as 3D Ranging using the Dixon resultant, reducing colors via color approximation, and photogrammetric position via Gauss-Jacob...

The problem with OLS is demonstrated via Engel’s problem. Concept and definitions of quantiles as well as their connection with other statistical properties are given. Computation of the linear and nonlinear, like B-spline quantile regression are demonstrated. Robustness of QR is investigated. An application example, detecting outliers in cloud poi...

Employing RBF as a function approximation method is introduced. Different types of RBF functions are considered and their effectiveness discussed, especially positive definite RBF. In order to use them in meshless techniques, their generic derivatives are presented. These functions can be employed as an activation function in a neural network for i...

The concept of the genetic algorithm is introduced. The application of the basic algorithm for real value functions is demonstrated. We discuss nonlinear regression, packing spheres of different size, finding roots of non-algebraic systems, and fox-hole problems.

The concept of SVM is introduced. The algorithm to compute the optimal hyperplane for classification and implementation is discussed. The characteristics of the different type of kernels are described and illustrated via numerical examples. SVM regression technique, employing insensitive loss function, wavelet and universal Fourier kernels are demo...

The concept and types of linear and nonlinear homotopy are introduced. Techniques for solving nonlinear equations and systems are discussed, such as regularization and automatic generation of start systems in case of algebraic systems. Their extension for non-polynomial systems and the possibility of parallel computation are discussed. Applications...

Techniques for solution of nonlinear equations where coefficients or parameters are uncertain are considered. An algebraic based nonlinear transformation technique of probability density functions, and a method employing stochastic homotopy are presented. These methods are applied to linear as well as nonlinear systems, even in cases when different...

The concept of robust regression is explained. Different techniques, such as maximum likelihood employing Gröbner basis, Danish algorithm with Gröbner basis, and PCA are introduced and demonstrated via examples. RANSAC algorithm with Gröbner basis is introduced. Combination of RANSAC with SOM is demonstrated via detecting outliers. Application of p...

The meaning of symbolic regression is illustrated via Kepler’s problem. The concept based on computer algebra is explained. Genetic algorithm to find the optimal tree structure is explained. Application of the Pareto-front for selecting optimal model ensuring a trade-off between complexity and precision is discussed. Numerical 1D and 2D examples ar...

The concept of stochastic global optimization, based on the Metropolis algorithm combined with artificial annealing, is introduced. Its application to global minimization of real valued functions is illustrated. Examples are provided, such as the disk packing problem, the traveling salesman problem on the globe, and nonlinear regression.

Comparison of modeling via stochastic differential equation system with parameter estimation to the Nearest Neighbors method as ML technique is illustrated. Machine Learning Differential Equation model is also introduced, employing deep neural network and stochastic differential equations in Ito-form. These methods are applied to image classificati...

Concepts and definitions concerning multiobjective optimization, i.e. Pareto front and Pareto set, are introduced. We consider solution methods like Pareto filter. Techniques of weighted objective are discussed and illustrated. Genetic algorithm filtering dominated solutions are also discussed. As geodetic applications, we consider the solution of...

Algebraic resultant methods to find zeros of polynomials and polynomial systems like Sylvester and Dixon resultant are introduced. Features and applications of the Gröbner basis as a popular tool for reducing multivariate polynomial systems to a higher order univariate polynomial is also discussed. Many geodesical examples are presented, like plana...

Regularization of a simple neural network regression via physical model of glucose-insuline interaction is demostrated. The technique of PINN (Physics Informed Neural Network) is illustrated by employing Mathematica symbolic computation ability.

This presentation is about the combination of Machine Learning and Physical Modeling. Important ideas are discussed and demonstrated in simplified way via toy examples. The applied methods are illustration of the presented ideas.

A variant of the methods for a forecasting stochastic process is introduced. Our technique is based on two steps: 1) The known part of the signal will be used as learning set, applying deep recurrent neural network using Long Short Term Memory Layer, and its forecasting ability is tested on the set of signal of the forecasted part of the data set a...

In the earlier presentation only a single realization of the signal to be forecasted was considered. However frequently we may have more realizations. In this case every realization can be forecasted independently then these single forecasted signals should be agglomerated into a time series with stochastic features. A naive and fast solution can b...

A variant of the methods for a forecasting stochastic process is introduced. Our technique is based on two steps: 1) The known part of the signal will be forecasted, via dynamical neural network using ARX estimator, 2) This forecasted signal is considered as random data and approximated by an assembly of machine learning methods like, Deep neural...

There are several methods for the prediction of future values of a time series, or in general, for the probability density prediction problem. In this paper two neural network prediction models are compared: Mixture Density Network (MDN) and Gated Recurrent Unit (GRU) in the prediction of the insulin sensitivity (SI) of a patient under intensive ca...

The illustration of stochastic modeling of approximation of measured data in differential equation form is presented. The measured data is approximated via deep neural network, then differentiating this network we get differential equation approximation for the measured data. The Ito form of this differential equation can provide a stochastic diffe...

Tight glycaemic control (TGC) is a treatment in the intensive care in order to avoid stress-induced hyperglycaemia. The insulin sensitivity (SI) prediction is an essential step of the best performing, clinically applied so-called STAR (Stochastic-TARgeted) TGC protocol. Previous results showed performance improvement of the SI prediction using arti...

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Many Neural Networks with randomly selected training sets are trained and combined providing conditional probability distribution of the output variable. Parallel computation is employed to accomplish the heavy computation task.

Three Machine Learning Methods: Nearest Neighbors, Decision Tree and Neural Network are combined to form an estimator for computing the density function of conditional probability.

The density functions of the output variables are approximated by a linear combination of more Gaussian Normal Distributions, where their parameters (mean, standard deviation) as well as the weights are computed by deep neural network using loglikelihood function as objective. The dimension of input vectors is reduced to one dimension by dimension...

Multivariate Uncertainty Regression (MUR) requires to compute not only the mean values but the distributions of the conditional probability of the output values, too. In the following notebooks five different techniques are presented. In this first one, the application of the Nearest Neighbors method is demonstrated.

Code for Chapter 5. of book Hibrid Visualization

Codes for the book

Solution of the Global Navigation Satellite Systems (GNSS) phase ambiguity is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. In this paper, three alter-native algorithms are suggested. Two of them are based on local and global linearization via Mc...

Code for chapter 3 of book Hybrid Imaging and Visualization

Web sites of downloadable notebooks of the Dimension Reduction chapter for book Hybrid Imaging and Visualization, Springer, 2019 -2020

Neural network is a special nonlinear model for classification, clustering as well as regression. A single layer network has m input nodes plus a virtual input, called bias, The weighted linear combination of these input values enter into the active node, where it will be transformed by a so called activation function (mostly nonlinear).

In this chapter we shall discuss some important lossy data reduction methods, which are very important in machine learning as well as digital in image processing and visualization.

As pointed out in the previous chapter KNearest Neighbors can be employed for clustering as well as for regression.

KNearest Neighbors Classification is the simplest, purely data-driven algorithm that can be used either for classification or regression tasks. In geosciences literature, it is known as the Voronoi polygons, while in numerical simulations, it is known as Dirichlet cells (Müller and Guido 2017).

The goal of unsupervised learning is to discover the hidden patterns or structures of the data in which no target variable exists to perform either classification or regression methods. Unsupervised learning methods are often more challenging, as the outcomes are subjective and there is no simple goal for the analysis, such as predicting the class...

The book introduces the latest methods and algorithms developed in machine and deep learning (hybrid symbolic-numeric computations, robust statistical techniques for clustering and eliminating data as well as convolutional neural networks) dealing not only with images and the use of computers, but also their applications to visualization tasks gene...

Stress-induced hyperglycaemia is a frequent complication in the intensive therapy that can be safely and efficiently treated by using the recently developed model-based tight glycaemic control (TGC) protocols. The most widely applied TGC protocol is the STAR (Stochastic-TARgeted) protocol which uses the insulin sensitivity (SI) for the assessment o...

Improvements in computational and observational technologies in geoinformatics, e.g., the use of laser scanners that produce huge point cloud data sets, or the proliferation of global navigation satellite systems (GNSS) and unmanned aircraft vehicles (UAVs), have brought with them the challenges of handling and processing this “big data”. These cal...

The model of the human glucose-insulin system plays an important role in several clinical treatment methods and protocols, like tight glycemic control of intensive care patients. The Intensive Control Insulin-Nutrition-Glucose (ICING) model is one of these protocols that was used for the development of the Stochastic Targeted glucose control (STAR)...

In indoor and outdoor navigation, finding the local position of a sphere in mapping space employing a laser scanning technique with low-cost sensors is a very challenging and daunting task. In this contribution, we illustrate how Gröbner basis techniques can be used to solve polynomial equations arising when algebraic and geometric measures for the...

Supplement for the book: Mathematical Geosciences, Hybrid Symbolic - Numeric Methods

Code for solving Over and Underdeterminde Systems

Mathematical Geosciences - Code supplement - Introduction

This book showcases powerful new hybrid methods that combine numerical and symbolic algorithms. Hybrid algorithm research is currently one of the most promising directions in the context of geosciences mathematics and computer mathematics in general. One important topic addressed here with a broad range of applications is the solution of multivari...

Background: Glycaemic control (GC) of critical care patients with abnormal blood glucose (BG) level can reduce mortality and improve clinical outcomes. Model based GC protocol allows personalised and effective control of BG level of the patients. As a part of the protocol the patient's state is predicted by a stochastic model. Improving accuracy of...

In this study, the stochastic version of the Intensive Control Insulin-Nutrition-Glucose model was tested and compared with the original version using a large clinical patient cohort of 60 patients from 3 different countries: Belgium, Hungary and New Zealand. Both models are used to identify the insulin sensitivity profile for each patients, follow...

Introduction of the stochastic noise in the modelling of blood-glucose dynamics becoming more and more acceptable because of the high complexity of the physiological processes. The representation of the stochastic noise term in the phenomenological as well as in data-driven models until now limited to stationary Gaussian process. In this paper the...

A novel RANSAC robust estimation technique is presented as an effiecient method for solving the seven-parameter datum transformation problem in the presence of outliers. RANSAC method, which is frequently employed in geodesy, has two sensitive features: (i) the user adjusts some parameters of the algorithm, making it subjective and a rather difficu...

This paper develops a novel gray-box form of the ICING (Intensive Control Insulin-Nutrition-Glucose) model (Lin et al. (2011)) used both for glycemic control of Intensive Care patients and implementation of virtual trials. The computations of the system trajectories and their statistical features like mean value, standard deviation, and slice distr...

This e-article illustrate how Mathematica can be employed to model stochastic processes via stochastic differential equations to compute trajectories and their statistical features. In addition, we discuss parameter estimation of the model via maximum likelihood method with global optimization. We consider handling modelling error, system noise and...