We describe a new Hybrid Monte Carlo (HMC) algorithm for dynamical overlap fermions, which improves the rate of topological index changes by adding an additional (intensive) term to the action for the molecular dynamics part of the algorithm. The metropolis step still uses the exact action, so that the Monte Carlo algorithm still generates the correct ensemble. By tuning this new term, we hope ...

The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph G. In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus–Gaddumtype inequalities for the forgotten topological index and coindex...

In this article, a Quantitative structure Toxicity Relationships (QSTR) of twenty five phenol derivatives is presented. The QSTR study is mainly based on topological parameter. The topological parameter has been evaluated by CAChe prosoftware. The calculations of topological parameters have been done by MOPAC 2007. The statistical parameter has been calculated by SSP software. Various QSTR mode...

We study a wide class of free-fermion systems on a hypercubic lattice in spatial dimensions d ≥ 1. When the system is insulating, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analogue ...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and let $d_u$ denote the degree of vertex $u$ in $G$. The Randi'c index of $G$ is defined as${R}(G) =sum_{uvin E(G)} 1/sqrt{d_ud_v}.$In this paper, we investigate the relationships between Randi'cindex and several topological indices.

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network has exactly one density decomposition. The number of nodes in each partition defines a density distribution which we find is measurably similar to the degree...

A proposal is presented for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. Strengths and shortcomings of the method are discussed and it is argued that the approximation – though being crude – shares some qualitative aspects of full QCD which relate to the issue of chiral symmetry breaking.

Let C r ((0; 1]) denote the metric space of C r self-maps of 0; 1] and C s;r ((0; 1]) denote the metric space of C s families of maps in C r ((0; 1]) with the parameter space 0; 1]. Let Hs;r be the unimodal families with non-constant topological entropy in C s;r ((0; 1]). We show that for s 0, r 2, there is an open and dense subset Gs;r of Hs;r such that each family in Gs;r has a map with a hom...