This paper explores using Shannon’s entropy of information to measure linkographs of twelve design sessions which involved six architects in two different experimental conditions. The aim is to find a quantitative tool to interpret the linkographs. This study examines if the differences in the design processes and the design outcomes can be reflected in the entropic interpretations. The results...

A ranked poset is called strongly Sperner if the size of k-family cannot exceed the sum of k-largest Whitney numbers. In the sense of a function ordering, a function f is (weakly) majorized by g if the the sum of k-largest values in f cannot exceed the sum of k-largest values in g. Two definitions arise from different contexts, but they have strong similarities in their own meanings. Furthermor...

We discuss the asymptotic behavior (as n → ∞) of the entropic integrals En = − ∫ 1 −1 log ( p n (x) ) p n (x)w(x) dx , and Fn = − ∫ 1 −1 log ( p n (x)w(x) ) p n (x)w(x) dx, when w is the symmetric Pollaczek weight on [−1, 1] with main parameter λ ≥ 1, and pn is the corresponding orthonormal polynomial of degree n. It is well known that w does not belong to the Szegő class, which implies in part...

We study compact Riemannian manifolds .M;g/ for which the light from any given point x 2 M can be shaded away from any other point y 2 M by finitely many point shades in M . Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat metrics. Using entropy consider...

and Applied Analysis 3

We develop a fine-scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence. The concepts of measure IE-tuples and measure IN-tuples are introduced and studied in analogy with their counterparts in topological dynamics. Local characterizations of the Pinsker von Neumann algebra and its sequence entropy analogue are given in terms of combinatorial i...

We introduce a new approach to characterizing the unobserved portion of a distribution, whichprovides sublinear-sample additive estimators for a class of properties that includes entropy anddistribution support size. Together with the lower bounds proven in the companion paper [29],this settles the longstanding question of the sample complexities of these estimation problems (up...

This paper introduces an entropy approach to measuring market expectations with respect to overnight interest rates in an inter-bank money market. The findings for the Turkish 2000-2001 borrowing crisis suggest that a dynamic, non-extensive entropy framework provides a valuable insight into the degree of aggregate market concerns during the crisis.

This paper deals with a functional equation connected with the Shannon entropy, the entropy of degree fi and others. There are so many algebraic properties which are satisfied by them. Various systems of axioms were used, in literature, to characterize them. Let A„ = {P = (p1, ..., pn)jpi ^ 0, Y,Pt = 1} t> e t n e s e t °f a ' l finite complete discrete probability distributions on a given part...

It is unquestionable that the concept of entropy has played an essential role both in the physical and biological sciences. However, the entropy production, crucial to the second law, has also other features not clearly conceived. We all know that the main difficulty is concerned with its quantification in non-equilibrium processes and consequently its value for some specific cases is limited. ...