We explore the relationship between grand canonical (GC) ensemble and charge equilibration (CE), also known as electronegativity equalization, theories for describing charge flow in molecules. We introduce a new unifying approach to classical charge transfer theories based on valence bond (VB) theory and the maximum entropy (ME) method, which we call MEVB. We show how MEVB reduces to GC and CE ...

Given a fuzzy variable, what is the degree of difficulty of predicting the specified value that the fuzzy variable will take? Entropy provides a measure to characterize the fuzziness. Given some constraints, there are usually multiple compatible membership functions. Which membership function shall we take? The maximum entropy principle attempts to select the membership function that maximizes ...

Entropy methods enable a convenient general approach to providing a probability distribution with partial information. The minimum cross-entropy principle selects the distribution that minimizes the Kullback–Leibler divergence subject to the given constraints. This general principle encompasses a wide variety of distributions, and generalizes other methods that have been proposed independently....

Thermodynamic fluctuation among many electronic states in systems with ‘itinerant-electron’ magnetism is addressed with a first-principles formulation of the Helmholtz energy. The Ce γ –α phase transition is used as an illustrative case. The kB ln(2J + 1) form for the magnetic entropy that is commonly found in the literature is replaced with an expression that is derived from configurational fl...

The cell envelope (CE) is a specialized structure that is important for barrier function in terminally differentiated stratified squamous epithelia. The CE is formed inside the plasma membrane and becomes insoluble as a result of cross-linking of constituent proteins by isopeptide bonds formed by transglutaminases. To investigate the earliest stages of assembly of the CE, we have studied human ...

A new theoretical model to predict bubble frequencies and weeping rates at a submerged ori%ce with liquid cross-(ow has been developed. The model predicts a signi%cant in(uence of liquid cross-(ow velocity on bubble formation frequency, and especially on liquid weeping. Simulated values of weeping rates for di7erent ori%ce diameters, gas (owrates and liquid cross-(ow velocities show good agreem...

Thegeodesic flowof theflatmetric on a torus isminimizing the polynomial entropy among all geodesic flows on this torus. We prove here that this properties characterises the flat metric on the two torus. Résumé Leflot géodésique desmétriques plates sur un toreminimise l’entropie polynomiale parmi tous les flots géodésique sur ce tore. On montre ici que cette propriété caractérise les métriques p...

Double Refined IndeterminacyNeutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache [1], which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indete...

We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illust...

Capsule endoscopy (CE) has revolutionized the diagnosis and monitoring of small bowel Crohn's disease (CD). The procedure is patient friendly and noninvasive, and compared to cross-sectional imaging, CE allows a direct and detailed evaluation of the entire small bowel mucosa with a high sensitivity for the earliest lesions of CD. Today, CE is the leading modality for visualizing the small bowel...