Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...

We investigate how information leakage reduces computational entropy of a random variable X. Recall that HILL and metric computational entropy are parameterized by quality (how distinguishable is X from a variable Z that has true entropy) and quantity (how much true entropy is there in Z). We prove an intuitively natural result: conditioning on an event of probability p reduces the quality of m...

We investigate how information leakage reduces computational entropy of a random variable X. Recall that HILL and metric computational entropy are parameterized by quality (how distinguishable is X from a variable Z that has true entropy) and quantity (how much true entropy is there in Z). We prove an intuitively natural result: conditioning on an event of probability p reduces the quality of m...

A concept of entropy production associated with continuous topolog-ical evolution is deduced (without statistics) from the fact that Cartan-Hilbert 1-form of Action defines a non-equilibrium symplectic system of Pfaff Topological dimension 2n+2. The differential entropy, dS, is composed of the interior product of the non-canonical components of momentum with the components of the differential v...

Introduction and Aims: Alzheimer’s disease is the most prevalent neurodegenerative disorder and a type of dementia. 80% of dementia in older adults is because of Alzheimer’s disease. According to multiple research articles, Alzheimer's has several changes in EEG signals such as slowing of rhythms, reduction in complexity and reduction in functional associations, and disordered functional commun...

String theory is used to compute the microscopic entropy for several examples of black holes in compactifications with N = 2 supersymmetry. Agreement with the Bekenstein-Hawking entropy and the moduli-independent N = 2 area formula is found in all cases.

The information entropy of the harmonic oscillator potential V (x) = 1 2 x 2 in both position and momentum spaces can be expressed in terms of the so-called \entropy of Hermite polynomials", i.e. the quantity S n (H) := R +1 ?1 H 2 n (x) log H 2 n (x)e ?x 2 dx. These polynomials are instances of the poly-nomials orthogonal with respect to the Freud weights w(x) = exp(?jxj m), m > 0. Here, rstly...

wear is a complicated phenomenon caused by the relative movement of two contacting surfaces compressed together by a normal force. prediction of the wear, in most cases, requires various experiments and microstructural characterization of the contacting surfaces. mathematical models based on physical concepts could provide considerable help in understanding the physical behavior and hence the p...

We consider the task of deriving a key with high HILL entropy (i.e., being computationally indistinguishable from a key with high min-entropy) from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was indistinguishable from having min-entropy was via pseudorandomness, for example by Goldreich-Levin (GL) hardcore bits. This approach...