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Introduction

## Publications

Publications (229)

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...

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.

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...

Environmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of...

In this paper the insulin sensitivity profile and the diffusion term as stepwise functions were determined for the grey box variant of the ICING (Intensive Control Insulin-Nutrition-Glucose) model used for virtual trial methodology. The suggested technique can separate system noise, which was earlier lumped into the insulin sensitivity profile itse...

Surface reconstruction from point clouds generated by laser scanning technology has become a fundamental task in many fields of geosciences, such as robotics, computer vision, digital photogrammetry, computational geometry, digital building modelling, forest planning and operational activities. Point clouds produced by laser scanning, however, are...

In this paper the stochastic (SDE) version of the ICING (Intensive Control Insulin-Nutrition-Glucose) model has been tested on a cohort data set of 13 patients in a wide range of blood-glucose concentration and handling time period. The suggested technique can separate system noise, which was earlier lumped into the insulin sensitivity profile itse...

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...

In this paper the insulin sensitivity profile and the diffusion term as stepwise functions were determined for the grey box variant of the ICING (Intensive Control Insulin-Nutrition-Glucose) model used for virtual trial methodology. The suggested technique can separate system noise, which was earlier lumped into the insulin sensitivity profile itse...

Traditionally, the least-squares method has been employed as a standard technique for parameter
estimation and regression fitting of models to measured points in data sets in many engineering
disciplines, geoscience fields as well as in geodesy. If the model errors follow the Gaussian distribution
with mean zero in linear models, the least-squares...

In Paláncz et al. (J Geod 84: 79–85, 2009), linear homotopy was introduced and its applications to geodesy presented. Never before had the concept of nonlinear homotopy been used by the geodetic community. This is partly attributed to the complexity of the involved equations and partly due to the computational time required. Recently, however, Nor...

This chapter presents the concepts of ring theory
from a geodetic and geoinformatics perspective. The presentation is such that the mathematical formulations are augmented with examples from the two fields. Ring theory forms the basis upon which polynomial
rings
operate. As we shall see later, exact solution of algebraic nonlinear systems of equati...

This chapter presents the minimization approach known as “Procrustes”
which falls within the multidimensional scaling techniques discussed in Sect. 9.2.2. Procrustes analysis is the technique of matching one configuration into another in-order to produce a measure of match. In adjustment terms, the partial Procrustes problem is formulated as the le...

Since the advent of the Global Navigation Satellite System (GNSS)
, in particular the Global Positioning System (GPS), many fields within geosciences, such as geodesy, geoinformatics, geophysics, hydrology etc., have undergone tremendous changes. GPS satellites have in fact revolutionized operations in these fields and the entire world in ways that...

Throughout history, position determination has been one of the fundamental task undertaken by man on daily basis. Each day, one has to know where one is, and where one is going. To mountaineers, pilots, sailors etc., the knowledge of position is of great importance. The traditional way of locating one’s position has been the use of maps or campus t...

The similarity between resection methods presented in the previous chapter and intersection methods discussed herein is their application of angular observations. The distinction between the two however, is that for resection, the unknown station is occupied while for intersection, the unknown station is observed. Resection uses measuring devices (...

In Chap. 7, we introduced parameter estimation from observational data sample and defined the models applicable to linear and nonlinear cases. In-order for the estimates to be meaningful however.

The 7-parameter datum transformation \(\mathbb{C}_{7}(3)\) problem involves the determination of seven parameters required to transform coordinates from one system to another. The transformation of coordinates is a computational procedure that maps one set of
coordinates in a given system onto another

A fundamental task in geodesy is the solving of systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to the convergence to solutions with no physical meaning, or convergence that requires global...

Symbolic regression (SR) is the process of determining the symbolic function, which describes a data set-effectively developing an analytic model, which summarizes the data and is useful for predicting response behaviors as well as facilitating human insight and understanding. The symbolic regression approach adopted herein is based upon genetic pr...

In some geospatial parametric modeling, the objectives to be minimized are often expressed in different forms, resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may compete in a Pareto sense, namely a small change in the parameters results in the increase of one objective and a...

In geodesy and geoinformatics, most observations are related to unknowns parameters through equations of algebraic (polynomial) type. In cases where the observations are not of polynomial type, as exemplified by the GPS meteorology problem of Chap. 18, they are converted into polynomials. The unknown parameters are then be obtained by solving the r...

In geodesy and geoinformatics, field observations are normally collected with the aim of estimating parameters. Very frequently, one has to handle overdetermined systems
of nonlinear equations. In such cases, there exist more equations than unknowns, therefore “the solution” of the system can be interpreted only in a certain error metric, i.e., lea...

In
Chap. 15, ranging method for positioning was presented where distances were measured to known targets. In this chapter, an alternative positioning technique which uses direction measurements as opposed to distances is presented. This positioning approach is known as the resection. Unlike in ranging where measured distances are affected by atmosp...

In many fields of geosciences such as robotics [413], computer vision [351], digital photogrammetry [538], surface reconstruction [388], computational geometry [336], digital building modelling [48], forest planning and operational activities [386] to list but a few, it is a fundamental task to extract plane features from three-dimensional (3D) poi...

In 1997, the Kyoto protocol to the United Nation’s framework convention on climate change spelt out measures that were to be taken to reduce the greenhouse gas emission that has contributed to global warming.

This chapter presents you the reader with one of the most powerful computer algebra tools, besides the polynomial resultants (discussed in the next chapter), for solving algebraic nonlinear systems of equations which you may encounter. The basic tools that you will require to develop your own algorithms for solving problems requiring closed form (e...

Besides Groebner basis approach discussed in Chap. 4, the other powerful algebraic tools for solving nonlinear systems of equations are the polynomial resultants
approaches. While Groebner basis may require large storage capacity during its computations, polynomial resultants approaches
presented herein offers remedy to users who may not be lucky t...

In Chap. 7, we have seen that overdetermined nonlinear systems are common in geodetic and geoinformatic applications, that is there are frequently more measurements than it is necessary to determine unknown variables, consequently the number of the variables n is less then the number of the equations m. Mathematically, a solution for such systems c...

In establishing a proper reference frame of geodetic point positioning, namely by the Global Positioning System (GPS) – the Global Problem Solver – we are in need to establish a proper model for the Topography
of the Earth, the Moon, the Sun or planets. By the theory of equilibrium figures, we are informed that an ellipsoid, two-axes or three-axes...

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