BACKGROUND To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. METHODS Thirteen he...

This paper considers the problem of estimating the power consumption at logic and register transfer levels of design from an information theoretical point of view. In particular, it is demonstrated that the average switching activity in the circuit can be calculated using either entropy or informational energy averages. For control circuits and random logic, the output entropy (informational en...

We consider the problem of optimal quantization with norm exponent r > 0 for Borel probability measures on R under constrained Rényi-αentropy of the quantizers. If the bound on the entropy becomes large, then sharp asymptotics for the optimal quantization error are well-known in the special cases α = 0 (memory-constrained quantization) and α = 1 (Shannon-entropy-constrained quantization). In th...

After generalization of Shannon‘s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon‘s entropy measure. What is the role of the parameter(s) from application point of view? In the pre...

This paper considers the problem of estimating the power consumption at logic and register transfer levels of design from an information theoretical point of view. In particular, it is demonstrated that the average switching activity in the circuit can be calculated using either entropy or informational energy averages. For control circuits and random logic, the output entropy (informational en...

In the present paper, we construct a simple, consistent and powerful test for qualitative spatial independence, called the TG test, by using symbolic dynamics and symbolic entropy as a measure of spatial dependence. We also give a standard asymptotic distribution of an affine transformation of the symbolic entropy under the null hypothesis of independence in the spatial qualitative process. Giv...

The zero-entropy-density conjecture states that the entropy density defined as s ≔ lim N→∞ S N /N vanishes for all translation-invariant pure states on the spin chain. Or equivalently, S N , the von Neumann entropy of such a state restricted to N consecutive spins, is sublinear. In this paper it is proved that this conjecture cannot be sharpened, i.e translation-invariant states give rise to ar...

The entropy loss due to the formation of one or multiple loops in circular and linear DNA chains is calculated from a scaling approach in the limit of long chain segments. The analytical results allow us to obtain a fast estimate for the entropy loss for a given configuration. Numerical values obtained for some examples suggest that the entropy loss encountered in loop closure in typical geneti...

The zero-entropy-density conjecture states that the entropy density defined as s ≔ lim N→∞ S N /N vanishes for all translation-invariant pure states on the spin chain. Or equivalently, S N , the von Neumann entropy of such a state restricted to N consecutive spins, is sublinear. In this paper it is proved that this conjecture cannot be sharpened, i.e translation-invariant states give rise to ar...