# Arkady Bolotin

## Publications

##### 4 The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances

**Authors:**
Arkady Bolotin

**Abstract:**

**Keywords:**
Possibility distributions,
possibility-probability relationship

##### 3 Fuzzy Logic Approach to Robust Regression Models of Uncertain Medical Categories

**Authors:**
Arkady Bolotin

**Abstract:**

Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cut-off point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cut-off point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.

**Keywords:**
Robustness,
Categorization,
Uncertain medical categories,
Binomial regression model,
Fuzzy dependent variable

##### 2 Impact of the Existence of One-Way Functionson the Conceptual Difficulties of Quantum Measurements

**Authors:**
Arkady Bolotin

**Abstract:**

**Keywords:**
One-way functions,
P versus NP problem,
quantummeasurements

##### 1 The Possibility Distribution for the Controlled Bloodstream Concentrations of Any Physiologically Active Substance

**Authors:**
Arkady Bolotin

**Abstract:**

In many ways, biomedical analysis is analogous to possibilistic reasoning. In spite of that, there are hardly any applications of possibility theory in biology or medicine. The aim of this work is to demonstrate the use of possibility theory in an epidemiological study. In the paper, we build the possibility distribution for the controlled bloodstream concentrations of any physiologically active substance through few approximate considerations. This possibility distribution is tested later against the empirical histograms obtained from the panel study of the eight different physiologically active substances in 417 individuals.

**Keywords:**
Possibility distributions,
physiologically activesubstances,
bloodstream concentrations