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.
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.
Abstract: One-way functions are functions that are easy to
compute but hard to invert. Their existence is an open conjecture; it
would imply the existence of intractable problems (i.e. NP-problems
which are not in the P complexity class).
If true, the existence of one-way functions would have an impact
on the theoretical framework of physics, in particularly, quantum
mechanics. Such aspect of one-way functions has never been shown
before.
In the present work, we put forward the following.
We can calculate the microscopic state (say, the particle spin in the
z direction) of a macroscopic system (a measuring apparatus
registering the particle z-spin) by the system macroscopic state (the
apparatus output); let us call this association the function F. The
question is: can we compute the function F in the inverse direction?
In other words, can we compute the macroscopic state of the system
through its microscopic state (the preimage F -1)?
In the paper, we assume that the function F is a one-way function.
The assumption implies that at the macroscopic level the Schrödinger
equation becomes unfeasible to compute. This unfeasibility plays a
role of limit of the validity of the linear Schrödinger equation.
Abstract: If a possibility distribution and a probability distribution
are describing values x of one and the same system or process
x(t), can they relate to each other? Though in general the possibility
and probability distributions might be not connected at all, we
can assume that in some particular cases there is an association linked
them.
In the presented paper, we consider distributions of bloodstream
concentrations of physiologically active substances and propose that
the probability to observe a concentration x of a substance X can be
produced from the possibility of the event X = x .
The proposed assumptions and resulted theoretical distributions
are tested against the data obtained from various panel studies of the
bloodstream concentrations of the different physiologically active
substances in patients and healthy adults as well.