The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko’s result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov complexity ≤ α to the case of exact dimension. Th...

this paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by topsis method. topsis method is technique for order preference by similarity to ideal solution. topsis is one of the renowned methods for classical multi-criteria decision-making (mcdm) problems that defines the positive ideal solution and negative ideal solution...

We analyze ‘Distribution to Distribution regression’ where one is regressing a mapping where both the covariate (inputs) and response (outputs) are distributions. No parameters on the input or output distributions are assumed, nor are any strong assumptions made on the measure from which input distributions are drawn from. We develop an estimator and derive an upper bound for the L2 risk; also,...

human was created from both the natural and spiritual dimensions and has multimodal functions (e.g., cognitive, behavioral, affective, sensation, interpersonal relationship, and etc.). having one-dimensional impression in life would provide anxiety predisposition for man, but then having an integrated and monotheistic view would result in an assimilated psychological discipline for him/her. the...

Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct representation of the poset, admitting constant response time for queries of the form “is x < y?”. This application motivates looking for stronger notions of dimensi...

In this report, we give a brief survey of various results relating the Teaching Dimension and VC-Dimension. The concept of Teaching Dimension was first introduced by Goldman and Kearns, 1995 and Sinohara and Miyano, 1991. In this model, an algorithm tries to learn the hidden concept c from examples, called the teaching set, which uniquely identifies c from the rest of the concepts in the concep...

‎In this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measures‎. ‎We show that the dimension as a three variables function is an increasing function on observers‎, ‎and decreasing function on the cuts of an observer‎. ‎We find observers with arbitrary non-negative dimensions‎. ‎We show that Caratheodory dimension for obs...

Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...

We introduce a new measure for capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term memory), local herding behavior (information dimension) and uncertainty in the process (entropy). The efficiency measure is then taken as a distance from an ideal efficient market situation. Methodology is applied to a portfolio of 41 stock indices. ...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.