# Viktor WitkovskýSlovak Academy of Sciences | SAV · Institute of Measurement Science

Viktor Witkovský

Doctor of Philosophy

## About

125

Publications

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1,157

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Citations since 2017

Introduction

Viktor Witkovský currently works at the Institute of Measurement Science, Slovak Academy of Sciences. Viktor does research in Statistics and Probability Theory and applications in Measurement Science and Metrology. One of his current project is 'CharFunTool: The Characteristic Functions Toolbox.'

Additional affiliations

September 1986 - present

Education

September 1987 - June 1993

September 1981 - July 1986

## Publications

Publications (125)

Measurement uncertainty analysis based on combining the state-of-knowledge distributions requires evaluation of the probability density function (PDF), the cumulative distribution function (CDF), and/or the quantile function (QF) of a random variable reasonably associated with the measurand. This can be derived from the characteristic function (CF)...

Although humans are generally capable of distinguishing single events of pain or touch, recent research suggested that both modalities activate a network of similar brain regions. By contrast, less attention has been paid to which processes uniquely contribute to each modality. The present study investigated the neuronal oscillations that enable a...

Background: One of the main causes of chronic lower back pain is lumbar facet syndrome (LFS). It develops due to the damage of the facet joints and subsequent irritation of the adjacent sensory nerves. The diagnosis of LFS is based on comprehensive clinical examinations of the patient, evaluation of imaging diagnostic studies and nerve blockades un...

We address the problem of linear comparative calibration, a special case of linear calibration where both variables are measured with errors, and the analysis of the uncertainty of the measurement results obtained with the calibrated instrument. The concept is explained in detail using the calibration experiment of the pressure transducer and the s...

Chronic pain diseases are characterised by an ongoing and fluctuating endogenous pain, yet it remains to be elucidated how this is reflected by the dynamics of ongoing functional cortical connections.
Here, we investigated the cortical encoding of 20 chronic back pain patients and 20 chronic migraineurs in four repeated fMRI sessions. A brain parce...

Conflict of Interest
None of the Authors has any financial/commercial conflicts of interest with the published data.
Acknowledgement
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.Herniated lumbar discs are a common cause of low-back pain and decreased quality of life, es...

Probability distributions suitable for modelling measurements and determining their uncertainties are usually based on a standard approximation approach as described in GUM, i.e. the GUM uncertainty framework (GUF), using the law of uncertainty propagation (also known as the delta method) or a more accurate method based on the law of probability pr...

Although we know sensation is continuous, research on long-lasting and continuously changing stimuli is scarce and the dynamic nature of ongoing cortical processing is largely neglected. In a longitudinal study, 38 participants across four sessions were asked to continuously rate the intensity of an applied tonic heat pain for 20 min. Using group-i...

Chronic pain is characterised by an ongoing and fluctuating intensity over time. Here, we investigated how the trajectory of the patients' endogenous pain is encoded in the brain. In repeated functional MRI (fMRI) sessions, 20 patients with chronic back pain and 20 patients with chronic migraine were asked to continuously rate the intensity of thei...

Background
The processing of brief pain and touch stimuli has been associated with an increase of neuronal oscillations in the gamma range (40-90 Hz). However, some studies report divergent gamma effects across single participants.
Methods
In two repeated sessions we recorded gamma responses to pain and touch stimuli using EEG. Individual gamma re...

Analyses of intrinsic network activity have been instrumental in revealing cortical processes that are altered in chronic pain patients. In a novel approach, we aimed to elucidate how intrinsic functional networks evolve in regard to the fluctuating intensity of the experience of chronic pain. In a longitudinal study with 156 fMRI sessions, 20 chro...

We consider methods for numerical evaluation of the probability density function, cumulative distribution function and quantile function of a linear combination of n independent generalized logistic random variables. Here we derive the exact expressions for the probability density function and cumulative distribution function in terms of Fox's H-fu...

Migraine is a complex neurological disorder affecting approximately 12% of the population. The pathophysiology is not yet fully understood, however the clinical features of the disease, such as the cyclic behaviour of attacks and vegetative symptoms, suggest a prominent role of the hypothalamus. Previous research has observed neuronal alterations a...

Background. Chronic pain diseases are characterised by an ongoing and fluctuating endogenous pain, yet it remains to be elucidated how this is reflected by the dynamics of ongoing functional cortical connections. The present study addresses this disparity by taking the individual perspective of pain patients into account, which is the varying inten...

Although we know sensation is continuous, research on long-lasting and continuously changing stimuli is scarce and the dynamic nature of ongoing cortical processing is largely neglected.
In a longitudinal study with 152 fMRI sessions, participants were asked to continuously rate the intensity of applied tonic heat pain for 20 minutes. Using group i...

Background
The experience of pain has been dissociated into two interwoven aspects: a sensory-discriminative aspect and an affective-motivational aspect. We aimed to explore which of the pain descriptors is more deeply rooted in the human brain.
Findings
Participants were asked to evaluate applied cold pain. The majority of the trials showed disti...

Analyses of intrinsic network activity have been instrumental in revealing cortical processes that are altered in chronic pain patients. However, such studies have not accounted for variable time courses of network activity and subjective pain experience. In a novel approach, we aimed to elucidate how intrinsic functional networks evolve in regard...

We consider the exact distribution of the best linear unbiased estimator (BLUE) of a linear combination of the unknown model parameters in linear models with possible parameters constraints. Here, we present a method for computing the exact confidence intervals for the considered linear combinations of the model parameters under the assumption that...

Presented is a simple real-data example with analysis of direct pressure measurements by electronic pressure transducer sensors, which illustrates our new method for obtaining exact confidence intervals for the unknown parameters in linear regression models. The method assumes that the errors are expressible as linear combinations of independent ra...

To assess the natural trajectory of brain activity over the migraine cycle, we assessed (1) the cerebral perfusion and (2) the hypothalamic connectivity during spontaneous headache attacks with follow-up recordings towards the next migraine attack. Using pseudo-continuous arterial spin labelling and resting-state functional magnetic resonance imagi...

We investigated how the trajectory of pain patients’ ongoing and fluctuating pain is encoded in the brain. In repeated fMRI sessions, 20 chronic back pain patients and 20 chronic migraineurs were asked to continuously rate the intensity of their endogenous pain. Linear mixed effects models were used to disentangle cortical processes related to pain...

We investigated how the attenuation of pain with cognitive interventions affects brain connectivity using neuroimaging and a whole brain novel analysis approach. While receiving tonic cold pain, 20 healthy participants performed three different pain attenuation strategies during simultaneous collection of functional imaging data at 7 tesla. Partici...

We investigated how the attenuation of pain with cognitive interventions affects brain connectivity using neuroimaging and a whole brain novel analysis approach. While receiving tonic cold pain, 20 healthy participants performed three different pain attenuation strategies during simultaneous collection of functional imaging data at seven tesla. Par...

We investigated how the attenuation of pain with cognitive interventions affects brain connectivity using neuroimaging and a whole brain novel analysis approach. While receiving tonic cold pain, 20 healthy participants performed three different pain attenuation strategies during simultaneous collection of functional imaging data at seven tesla. Par...

Suggested is a non-parametric method and algorithm for estimating the probability distribution of a stochastic sum of independent identically distributed continuous random variables, based on combining and numerically inverting the associated empirical characteristic function (CF) derived from the observed data. This is motivated by classical probl...

Omnia in mensura et numero et pondere disposuisti is a famous Latin phrase from Solomon’s Book of Wisdom , dated to the mid first century BC, meaning that all things were ordered in measure, number, and weight. Naturally, the wisdom is appearing in its relation to man. The Wisdom of Solomon is understood as the perfection of knowledge of the righte...

Background:
Epiduroscopy is a well-established diagnostic and to certain level therapeutic tool in complex situations, where conventional methods such as magnetic resonance imaging (MRI) lack power or resolution to detect pathological changes. Such a situation is primarily failed back surgery syndrome (FBSS) but also radicular pain without surgery...

The perception of pain activates a number of brain regions and processes that are involved in its sensory, emotional, cognitive, and affective aspects; all of which require a flexible functional connectivity between local and distant brain regions. Here, we investigate how the attenuation of pain with cognitive interventions affects the strength of...

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. Howev...

We present application of three alternative approaches for solving the Example S4 from EA-4/02 (Calibration of a gauge block of nominal length 50 mm); see [4]. As a result, application of the alternative approaches validates usage of the standard GUM uncertainty framework; see [1]. In particular, we consider the following alternative approaches to...

Gaseous mixtures of ethanol in nitrogen are prepared by the gravimetric method according to ISO 6142. The liquid component, ethanol, is added into the cylinder by the gas tight syringe. The exact amount of added liquid is determined by weighing the syringes. The exact amount of ethanol is calculated before starting filling the cylinder in accordanc...

Chapter 1 describes methods and algorithms, based on using the classical regression approach used for the errors-in-variable model and applied it for the comparative calibration with the generalized polynomial calibration function. The present approach is based on strictly metrologist considerations. The inputs quantities are fully characterized by...

Proper uncertainty analysis in metrology frequently requires using model with a nonlinear measurement equation Y = f(X), where X = (X1, ... ,XN), and non-trivial joint multivariate distribution of the input quantities X. This is exactly the situation suitable for application of the approach suggested in the GUM Supplements 1 and 2. In this paper we...

The paper builds the comparative calibration model with a polynomial calibration function. The model allows to consider possibly correlated data and combines the type A as well as type B unceranities of measurements. From statistical point of view the model after linearization could be represented by the linear errors-in-variables model (EIV).

Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions. Typically, distribution of many estimators and test statistics can be structur...

Poster presented at CMStatistics 2017, University of London, UK, December 16-18, 2017. CharFunTool is a MATLAB repository of characteristic functions and tools for their combinations and numerical inversion. The Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algori...

The basic working tool in measurement uncertainty analysis, as advocated in recent discussions related to the possible revision of the Guide to the expression of uncertainty in measurement (GUM), and in particular by its Supplements, is the state-of-knowledge distribution about the quantity derived based on the currently available information. The...

The exact (statistical) inference frequently require evaluation of the probability density function (PDF), the cumulative distribution function (CDF), and/or the quantile function (QF) of a random ariable from its (known) characteristic function (CF), which is defined as a Fourier transform of its probability distribution function. Working with CFs...

Although the Heydemann correction is widely used to demodulate the phase of quadrature homodyne interferometer and encoder signals, the related measurement uncertainty is considered only in a few publications. The statistical uncertainty of the phase, which is the contribution of the high-frequency noise in the input signals, due to the use of a si...

We consider a problem of constructing the exact and/or approximate coverage intervals for the common mean of several independent distributions. In a metrological context, this problem is closely related to evaluation of the interlabo-ratory comparison experiments, and in particular, to determination of the reference value (estimate) of a measurand...

The measurement signals of the quadrature homodyne interferometers (say x and
y, usually called Sine/Cosine signals and/or quadrature signals) typically exhibit offsets, unequal
amplitudes and a phase difference that is not exactly 90 degree as would be expected in
the ideal/theoretical case. Moreover, frequently there is a significant component of...

Under physiological conditions, momentary pain serves vital protective functions. Ongoing pain in chronic pain states, on the other hand, is a pathological condition that causes widespread suffering and whose treatment remains unsatisfactory. The brain mechanisms of ongoing pain are largely unknown. In this study, we applied tonic painful heat stim...

We introduce a class of logarithmic Lambert W random variables for a specific family of distributions. In particular, we characterize the log-Lambert W random variables for chi-squared distributions which naturally appear in the likelihood based inference of normal random variables.

HPMIXED fits the linear mixed effects models (LME models) of the form: y = X*b + Z*u + e, and with a simple variance covariance structure (VC: variance components), by solving the Henderson's mixed model equations.

Optical interferometers are widely used in dimensional metrology applications. Among them are many quadrature homodyne interferometers. These exhibit two sinusoidal interference signals shifted, in the ideal case, by 90 degree to allow a direction sensitive detection of the motion responsible for the actual phase change. But practically encountered...

A suite of Matlab functions with implemented algorithms for computing CDF, PDF, quantiles, convolutions, etc., for the class of random variables distributed according to the logarithmic Lambert W x chi2 distribution.
See also http://www.mathworks.com/matlabcentral/fileexchange/46754-lambertwchi2.

EllipseFit4HC is an ellipse fitting algorithm based on first order Taylor expansion (linearization) of the originally nonlinear model. EllipseFit4HC is suggested for uncertainty evaluation of the estimated phases and/or displacements, based on quadrature homodyne interferometer measurements (with the Heydemann Correction applied). See also http://w...

Statistical tolerance intervals are another tool for making statistical inference on an unknown population. The tolerance interval is an interval estimator based on the results of a calibration experiment, which can be asserted with stated confidence level $1-\alpha$, for example $0.95$, to contain at least a specified proportion $1-\gamma$, for ex...

The noncentral $t$-distribution is a generalization of the Student's
$t$-distribution. In this paper we suggest an alternative approach for
computing the cumulative distribution function (CDF) of the noncentral
$t$-distribution which is based on a direct numerical integration of a well
behaved function. With a double-precision arithmetic, the algor...

The MATLAB algorithm NCTCDFVW is suggested for computing the extreme tail probabilities of the noncentral T distribution with large noncentrality parameter, say delta. The CDF is computed by the GAUSS-KRONOD (non-adaptive) quadrature.
P = NCTCDFVW(X,NU,NCP,TAIL) returns the cummulative distribution function (CDF) of the noncentral T distribution w...

ToleranceFactorGK computes (by the Gauss-Kronod quadrature) the exact tolerance factor k for the two-sided (optionally for the one-sided) p-content and (1-alpha)-confidence tolerance interval TI = [Xmean - k * S, Xmean + k * S], where Xmean = mean(X) and S = std(X), are based on X = [X_1,...,X_n], a random sample of size n from the distribution N(m...

We consider the comparative calibration problem in the case when linear relationship is assumed between two considered measuring devices with possibly different units and precisions. The first method for obtaining the approximate confidence region for unknown parameters of the calibration line applies the maximum likelihood estimators of the unknow...

We present a brief overview of the methods for making statistical inference (testing statistical hypotheses, construction of confi-dence and/or prediction intervals and regions) about linear functions of the fixed effects and/or about the fixed and random effects simultaneously, in conventional simple linear mixed model. The presented approach is b...

Linear models with variance-covariance components are used in a wide variety of applications. In most situations it is possible to partition the response vector into a set of independent subvectors, such as in longitudinal models where the response is observed repeatedly on a set of sampling units (see, e.g., Laird & Ware 1982). Often the objective...

We propose an implementation of the straight-line fit algorithm to evaluate data obtained as part of measurements of line structures, e.g. a grating line, which allows us to determine, at a conventional threshold value, the coordinates of the edges, the position and the width of its photometric profile as well as the related standard uncertainty co...

Pain signals threat and initiates motor responses to avoid harm. The transformation of pain into a motor response is thus an essential part of pain. Here, we investigated the neural mechanisms subserving the sensorimotor transformation of pain at the cortical level by using electroencephalography. In a simple reaction time experiment, brief painful...

TDIST Computes the distribution of a linear combination of independent Student's T random variables (with small degrees of freedom, df<=100) and/or standard Normal Z random variables.

Professor Lubomír Kubáček has provided exceptional contributions to mathematical statistics and its applications. Because of his excellent knowledge in mathematical statistics as well as in the different fields of natural and especially technical sciences, he contributed to solution of a large number of real world problems. The continuation of Prof...

Proton Transfer Reaction Mass Spectrometry (PTR-MS) is a chemical ionization mass spectrometric technique which allows to measure trace gases as, for example, in exhaled human breath. The quantification of compounds at low concentrations is desirable for medical diagnostics. Typically, an increase of measuring accuracy can be achieved if the durati...

We consider the problem of making statistical inference about the mean of a normal distribution based on a random sample of quantized (digitized) observations. This problem arises, for example, in a measurement process with errors drawn from a normal distribution and with a measurement device or process with a known resolution, such as the resoluti...

A software system Gel Analysis System for Epo (GASepo) has been developed within an international WADA project. As recent
WADA criteria of rEpo positivity are based on identification of each relevant object (band) in Epo images, development of
suitable methods of image segmentation and object classification were needed for the GASepo system. In the...

The present study was performed to determine the variations of breath acetone concentrations with age, gender and body-mass index (BMI). Previous investigations were based on a relatively small cohort of subjects (see Turner et al 2006 Physiol. Meas. 27 321–37). Since exhaled breath analysis is affected by considerable variation, larger studies are...

In this paper we present an exact likelihood ratio test (LRT) for testing the simple null hypothesis on all parameters of the linear regression model with normally distributed errors. In particular, we consider the simultaneous test for the regression parameters, β, and the error standard deviation, σ. The critical values of the LRT are presented f...

This paper deals with variability issues connected with the proton transfer reaction-mass spectrometry (PTR-MS) measurements of isoprene concentration. We focus on isoprene as an abundant and widely studied compound in human breath. The variability caused by the measurement process is described by the within-sample distribution. Thus, based on the...

This study was performed to clarify variations in breath isoprene concentrations with age, gender, body mass index (BMI) and total serum cholesterol. Our cohort consisted of 205 adult volunteers of different smoking background without health complaints. Total cholesterol in blood serum was measured in 79 of these volunteers.
Mixed expiratory exhale...

We discuss the problem of evaluating measurement results from interlaboratory comparisons in metrology. Here we permit the laboratories to have systematic errors that are assumed to be uniformly distributed. Two approaches for modeling the measurement results are introduced and compared, and the associated problems connected with estimation of the...