Every Boolean function can be uniquely represented as a multilinear polynomial. The entropy and the total influence are two ways to measure the concentration of its Fourier coefficients, namely the monomial coefficients in this representation: the entropy roughly measures their spread, while the total influence measures their average level. The Fourier Entropy/Influence conjecture of Friedgut a...

One of the advantages of the Discrete Wavelet Transform (DWT) compared to Fourier Transform (e.g. Discrete Cosine Transform DCT) is its ability to provide both spatial and frequency localization of image energy. However, WT coefficients, like DCT coefficients, are defined by magnitude as well as sign. While algorithms exist for the coding of wavelet coefficients magnitude, there are no efficien...

A new interpretation of transform coding is developed that downplays quantization and emphasizes entropy coding, allowing a comparison of entropy coding methods with different memory requirements. With conventional transform coding, based on computing Karhunen–Loève transform coefficients and then quantizing them, vector entropy coding can be replaced by scalar entropy coding without an increas...

We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between t...

Elementary model of intracellular (or intra-organellar) pattern formation: Belousov – Zhabotinsky reaction in a Petri dish. The Belousov – Zhabotinsky reaction (Belousov 1958) was devised as a primitive model of citric acid cycle. To the surprise of the authors, it brought about the phenomenon of chemical clock (in mixed systems) or spontaneous pattern formation (in still compartments). We use ...

We consider the maximum entropy extention of a partially specified autocovariance sequence of a periodically correlated process. The sequence may be specified on a non-contiguous set. We give a method which solves the problem completely—it gives the positive definite solution when it exists and reports that it does not exist otherwise. The method is numerically reliable even when the solution i...

Lorenz curves of bubble size distributions and their Gini coefficients characterize demixing processes. Through a systematic size classification, bubble size histograms are generated and investigated concerning their statistical entropy. It turns out that the temporal development of the entropy is preserved although characteristics of the histograms like number of size classes and modality are ...

Multispectral geospatial image sets retain the scene’s spatial and spectral information. To jointly use both of them for analysis purposes, we propose to extend the concept of wavelet packets, by introducing a new integrated multispectral entropy function. Each spectral band is individually decomposed by the wavelet packets transform, and then the entropy term is jointly guided by information f...

in this article, multichannel eeg signals of artists and nonartists were analyzed during the performances of visual perception and mental imagery of paintings using cepstrum coefficients. each of the calculated cepstrum coefficients and their parameters such as energy, average, standard deviation and entropy were separately used for distinguishing the two groups. it was also found that a distin...