Related papers: Distances between formal theories
A generalized view of Duality is offered as a bridge between physical sciences and the more abstract philosophical dimensions bordering on mysticism. To that end several examples of duality are first cited from from conventional physics…
This paper uses an axiomatic foundation to create a new measure for the cost of learning that allows for multiple perceptual distances in a single choice environment so that some events can be harder to differentiate between than others.…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
The huge amount of information stored in text form makes methods that deal with texts really interesting. This thesis focuses on dealing with texts using compression distances. More specifically, the thesis takes a small step towards…
This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low…
This paper presents a new approach for measuring semantic similarity/distance between words and concepts. It combines a lexical taxonomy structure with corpus statistical information so that the semantic distance between nodes in the…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are:…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
We recall the main concepts of the Le Cam theory of statistical experiments , especially the notion of Le Cam distance and its properties. We also review classical tools for bounding such a distance before presenting some examples. A proof…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
The paper defends the thesis that it's possible to maintain some conceptual preconditions of overcoming of relativistic intentions in modern philosophy of science ("there are no any general foundations in philosophy of science"). We found…
The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…
The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information…
The newly discovered principle of maximum force makes it possible to summarize special relativity, quantum theory\se, and general relativity in one fundamental limit principle each. The three principles fully contain the three theories and…
In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model's output. We first show…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…