It is known that the writhe calculated from any reduced alternating link diagram of same (alternating) has value. That is, it a invariant if we restrict ourselves to diagrams. This due fact diagrams are obtainable each other via flypes and do not change writhe. In this paper, introduce several quantities derived Seifert graphs We prove they “writhe-like” invariants, namely general but invariant...

Previous work introduced two measure-conjugacy invariants: the f-invariant (for actions of free groups) and Σ-entropy (for actions of sofic groups). The purpose of this paper is to show that the f-invariant is essentially a special case of Σ-entropy. There are two applications: the f-invariant is invariant under group automorphisms and there is a uniform lower bound on the f-invariant of a fact...

In this paper, a new  algorithm for computing secondary invariants of  invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants.  The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...

In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These e...

A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) entropy ($\mathcal{K}$), both having attracted attention over past decades, a invariant called concentration ($\mathcal{A}$) introduced in present study. The defined as normalised mean distance between reconstruction vectors, evaluated...

We review some results on the connection among supergravity central charges, BPS states and Bekenstein{Hawking entropy. In particular, N = 2 supergravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N = 8 case when one half of supersymmetry is preserved. We stress the fact that for extremal ...

We study the categorical entropy and counterexamples to Gromov–Yomdin type conjecture via homological mirror symmetry of K3 surfaces established by Sheridan–Smith. introduce asymptotic invariants quasi-endofunctors dg categories, called Hochschild entropy. It is proved that lower bounded Furthermore, motivated Thurston’s classical result, we prove existence a symplectic Torelli mapping class po...

We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D > 5 dimensional supergravities. The scalar flow towards the horizon is described in terms an effective potential given by the superposition of the kinetic energies of all the forms under which the brane is charged. At the horizon active scalars get fixed to the minima of the eff...

Chromosome conformation capture experiments provide a rich set of data concerning the spatial organization of the genome. We use these data along with a maximum entropy approach to derive a least-biased effective energy landscape for the chromosome. Simulations of the ensemble of chromosome conformations based on the resulting information theoretic landscape not only accurately reproduce experi...