Related papers: Distances between formal theories
We lift metrics over words to metrics over word-to-word transductions, by defining the distance between two transductions as the supremum of the distances of their respective outputs over all inputs. This allows to compare transducers…
Let $|A|$ denote the cardinality of a finite set $A$. For any real number $x$ define $t(x)=x$ if $x\geq1$ and 1 otherwise. For any finite sets $A,B$ let $\delta(A,B)$ $=$ $\log_{2}(t(|B\cap\bar{A}||A|))$. We define {This appears as…
Let \({\mathbb K}\) be any field, let \(X\subset {\mathbb P}^{k-1}\) be a set of \(n\) distinct \({\mathbb K}\)-rational points, and let \(a\geq 1\) be an integer. In this paper we find lower bounds for the minimum distance \(d(X)_a\) of…
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…
Spacetime is conventionally viewed as a stage on which actors, in the form of fields, move. Here, we explore what may lie beyond this picture. The starting point is the observation that quantum fluctuations of fields are the more strongly…
The rapid development of such natural language processing tasks as style transfer, paraphrase, and machine translation often calls for the use of semantic similarity metrics. In recent years a lot of methods to measure the semantic…
We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…
Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
We consider general structures where formulas have truth values in the real unit interval as in continuous model theory, but whose predicates and functions need not be uniformly continuous with respect to a distance predicate. Every general…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…
The distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the distance into what is today known as a metric. In this…
The concept of distance rationalizability of social choice rules has been explored in recent years by several authors. We deal here with several foundational questions, and unify, correct, and generalize previous work. For example, we study…
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
Beyond the new results mentioned hereafter, this article aims at familiarizing researchers working in applied fields -- such as physics or economics -- with notions or formulas that they use daily without always identifying all their…
Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical…
Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm…
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued…
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…