The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends the entropy theory for real unimodal maps to complex polynomials: the real segment is replaced by an invariant tree, known as the Hubbard tree, whi...

a 1993 result of j. llibre, and m. misiurewicz, (theorem a [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. also a 1980 result of l.s. block, j. guckenheimer, m. misiurewicz and l.s. young (lemma 1.5 [3]) states that if g is an a-graph of f then h(g) ? h( f ). in this pap...

Laser pulse heating of solid surface and entropy generation during the heating process are considered. Time exponentially decaying pulse is accommodated in the analysis and the laser pulse parameter (b1/b2) resulting in minimum entropy generation rate is computed. Analytical solutions for temperature rise are presented and volumetric entropy generation rate is formulated. Two laser pulses resul...

A fundamental theme in holomorphic dynamics is that the local geometry of parameter space (e.g. the Mandelbrot set) near a parameter reflects the geometry of the Julia set, hence ultimately the dynamical properties, of the corresponding dynamical system. We establish a new instance of this phenomenon in terms of entropy. Indeed, we prove an “entropy formula” relating the entropy of a polynomial...

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFSs. Firstly, we propose a set of entropies on IvIFSs with a parameter λ ∈ [0,+∞), which generalizes the entropy measure defined by Gao, for IvIFSs, and then we prove that the new entropy is an increasing func...

We present a novel binary entropy code called combinatorial coding (CC). The theoretical basis for CC has been described previously under the context of universal coding [1], enumerative coding [2], and minimum description length [3]. The code described in these references works as follows: assume the source data of length M is binary, memoryless, and generated with an unknown parameter θ, the ...

In the previous lecture we defined the notion of a randomness extractor as follows: Definition 1 A function Ext : {0, 1} n ×{0, 1} d → {0, 1} m is a (k,)-extractor if, for every random variable X of range {0, 1} n-which we will call a source-of min-entropy H ∞ (X) ≥ k, the following holds for the statistical difference of Ext(X, U d) and U m : · the min-entropy of a random variable X of a finit...

Abstract: Aimed at the situation that the plan attribute value is a three-parameter interval grey number and that attribute weight is uncertain, a three-parameter interval grey number multi-attribute decision making method based on information entropy is proposed. In this study, we combine the three-parameter interval grey number decision-making problem with information entropy, build the dista...

We study the dynamical response of a system to a sudden change of the tuning parameter starting or ending at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning...

We consider randomness extraction by AC circuits. The main parameter, n, is the length of the source, and all other parameters are functions of it. The additional extraction parameters are the min-entropy bound k = k(n), the seed length r = r(n), the output length m = m(n), and the (output) deviation bound = (n). For k ≤ n/ log n, we show that AC-extraction is possible if and only if mr ≤ 1 + p...