Partly motivated by the arrow of time problem in cosmology and Weyl curvature hypothesis formulated Roger Penrose, previous works literature have proposed---among other possibilities---the square as being underlying entropy density function black hole entropy, but proposal suffers from a few drawbacks. In this work, we propose new also based solely on curvature, adopting some combinations invar...

Given n discrete random variables = fX1; ; Xng, associated with any subset of f1; 2; ; ng, there is a joint entropy H(X ) where X = fXi: i 2 g. This can be viewed as a function defined on 2 2; ; ng taking values in [0; +1). We call this function the entropy function of . The nonnegativity of the joint entropies implies that this function is nonnegative; the nonnegativity of the conditional join...

We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson [15], we show that growth complexities of the form exp(n) are possible for non-integer α’s. In terminology of [3], such subshifts have entropy dimension α. The class of po...

Identifying diagnostic biomarkers based on genomic features for an accurate disease classification is a problem of great importance for both, basic medical research and clinical practice. In this paper, we introduce quantitative network measures as structural biomarkers and investigate their ability for classifying disease states inferred from gene expression data from prostate cancer. We demon...

The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the turning points of the discussed quantities, establishing the singular character of these points in nuclear phase transition regions between vibrational and rotat...

Abstract We develop a forcing theory of topological entropy for Reeb flows in dimension three. A transverse link L closed contact $3$ -manifold $(Y,\xi )$ is said to force if admits flow with vanishing entropy, and every on realizing as set periodic orbits has positive entropy. Our main results establish conditions , which imply that forces These are formulated terms two Floer theoretical invar...

Given a set K with cardinality ‖K‖ = n, a wedge decomposition of a space Y indexed by K, and a cogroup A, the homotopy group G = [A,Y] is shown, by using Pierce-like idempotents, to have a direct sum decomposition indexed by P(K)−{φ} which is strictly functorial if G is abelian. Given a class ρ : X → Y , there is a Hopf invariant HIρ on [A,Y] which extends Hopf’s definition when ρ is a comultip...