Physical Sciences and Mathematics Commons^™

Search Under Uncertainty Should Be Randomized: A Lesson From The 2021 Nobel Prize In Medicine, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, we know that one of several objects has the desired property, but we do not know which one. To find the desired object, we need to test these objects one by one. In situations when we have no additional information, there is no reason to prefer any testing order and thus, a usual recommendation is to test them in any order. This is usually interpreted as ordering the objects in the increasing value of some seemingly unrelated quantity. A possible drawback of this approach is that it may turn out that the selected quantity is correlated …

Why Physical Power Laws Usually Have Rational Exponents, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many physical dependencies are described by power laws y=A*xa, for some exponent a. This makes perfect sense: in many cases, there are no preferred measuring units for the corresponding quantities, so the form of the dependence should not change if we simply replace the original unit with a different one. It is known that such invariance implies a power law. Interestingly, not all exponents are possible in physical dependencies: in most cases, we have power laws with rational exponents. In this paper, we explain the ubiquity of rational exponents by taking into account that in many case, there is also …

Can Physics Attain Its Goals: Extending D'Agostino's Analysis To 21st Century And Beyond, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In his 2000 seminal book, Silvo D'Agostino provided the detailed overview of the history of ideas underlying 19th and 20th century physics. Now that we are two decades into the 21st century, a natural question is: how can we extend his analysis to the 21st century physics -- and, if possible, beyond, to try to predict how physics will change? To perform this analysis, we go beyond an analysis of what happened and focus more on why para-digm changes happened in the history of physics. To better understand these paradigm changes, we analyze now only what were the main ideas …

Why Sine Membership Functions, Sofia Holguin, Javier Viaña, Kelly Cohen, Anca Ralescu, Vladik Kreinovich

Departmental Technical Reports (CS)

In applications of fuzzy techniques to several practical problems -- in particular, to the problem of predicting passenger flows in the airports -- the most efficient membership function is a sine function; to be precise, a portion of a sine function between the two zeros. In this paper, we provide a theoretical explanation for this empirical success.

Need To Combine Interval And Probabilistic Uncertainty: What Needs To Be Computed, What Can Be Computed, What Can Be Feasibly Computed, And How Physics Can Help, Julio Urenda, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical situations, the quantity of interest is difficult to measure directly. In such situations, to estimate this quantity, we measure easier-to-measure quantities which are related to the desired one by a known relation, and we use the results of these measurement to estimate the desired quantity. How accurate is this estimate?

Traditional engineering approach assumes that we know the probability distributions of measurement errors; however, in practice, we often only have partial information about these distributions. In some cases, we only know the upper bounds on the measurement errors; in such cases, the only thing we know about …

Macrocausality Implies Lorenz Group: A Physics-Related Comment On Guts's Results, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, in the space-time of Special Relativity, causality implies Lorenz group, i.e., if we know which events can causally influence each other, then, based on this information, we can uniquely reconstruct the affine structure of space-time. When the two events are very close, quantum effects, with their probabilistic nature, make it difficult to detect causality. So, the following question naturally arises: can we uniquely reconstruct the affine structure if we only know causality for events which are sufficiently far away from each other? Several positive answers to this question were provided in a recent paper by Alexander …

Towards Optimal Techniques Intermediate Between Interval And Affine, Affine And Taylor, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In data processing, it is important to gauge how input uncertainty affects the results of data processing. Several techniques have been proposed for this gauging, from interval to affine to Taylor techniques. Some of these techniques result in more accurate estimates but require longer computation time, others' results are less accurate but can be obtained faster. Sometimes, we do not have enough time to use more accurate (but more time-consuming) techniques, but we have more time than needed for less accurate ones. In such cases, it is desirable to come up with intermediate techniques that would utilize the available additional …

Discrete Causality Implies Lorenz Group: Case Of 2-D Space-Times, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that for Minkowski space-times of dimension larger than 2, any causality-preserving transformation is linear. It is also known that in a 2-D space-time, there are many nonlinear causality-preserving transformations. In this paper, we show that for 2-D space-times, if we restrict ourselves to discrete space-times, then linearity is retained: only linear transformation preserve causality.

How To Elicit Complex-Valued Fuzzy Degrees, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the traditional fuzzy logic, an expert's degree of certainty in a statement is described by a single number from the interval [0,1]. However, there are situations when a single number is not sufficient: e.g., a situation when we know nothing and a situation in which we have a lot of arguments for a given statement and an equal number of arguments against it are both described by the same number 0.5. Several techniques have been proposed to distinguish between such situations. The most widely used is interval-valued technique, where we allow the expert to describe his/her degree of certainty …