The pruning method developed earlier by one of the authors (K.B.) combined with the operator method is shown to yield powerful recursive relations for generating functions for dimer statistics and characteristic polynomials of cacti graphs and cacti lattices. The method developed is applied to linear cacti, Bethe cacti of any length containing rings of any size, and cyclic cacti of any length a...

We consider four operads which are different varieties of the cacti operad. These are cacti without local zeros (or spines) and cacti proper as well as both varieties with fixed constant size one of the constituting loops. We show that both types of cacti are a semi–direct products as operads of their normalized versions with a re–scaling operad based on R>0 which are homotopic to direct produc...

The purpose of this paper is to enumerate various classes of cyclically colored m-gonal plane cacti, called m-ary cacti. This combinatorial problem is motivated by the topological classiication of complex polynomials having at most m critical values, studied by Zvonkin and others. We obtain explicit formulae for both labelled and unlabelled m-ary cacti, according to i) the number of polygons, i...

We enumerate cyclically colored m-gonal plane cacti (called m-ary cacti) according to the degree distribution of vertices of each color. This combinatorial problem is motivated by the topological classification of complex polynomials having at most m critical values, studied by Zvonkin and others. The corresponding problem for rooted m-ary cacti has been solved by Goulden and Jackson in connect...

We give a new direct proof of Deligne’s conjecture on the Hochschild cohomology. For this we use the cellular chain operad of normalized spineless cacti as a model for the chains of the little discs operad. Previously, we had shown that the operad of spineless cacti is homotopy equivalent to the little discs operad. Moreover, we also showed that the quasi–operad of normalized spineless cacti is...

in this paper we present explicit formulas for the eccentric connectivity index of three classesof chain hexagonal cacti. further, it is shown that the extremal chain hexagonal cacti withrespect to the eccentric connectivity index belong to one of the considered types. some openproblems and possible directions of further research are mentioned in the concluding section.

There is a growing need for accurate power models at the higher levels of design hierarchy. CACTI is a micro-architecture level tool widely used (i) to estimate power dissipation in caches and (ii) to determine the cache configuration that best meets the desired optimization criterion. However, we observed several limitations in CACTI that lead to inaccuracies in cache power estimates especiall...

 CACTI-IO Technical Report Norman P. Jouppi, Andrew B. Kahng, Naveen Muralimanohar, Vaishnav Srinivas HP Laboratories HPL-2013-79 IO; Interconnect; SERDES; PHY; Memory bus; DDR; LPDDR We describe CACTI-IO, an extension to CACTI that includes power, area and timing models for the IO and PHY of the off-chip memory interface for various server and mobile configurations. CACTI-IO enables quick des...

Columnar cacti occur naturally in many habitats and environments in the Americas but are conspicuously dominant in very dry desert regions. These majestic plants are widely regarded for their cultural, economic, and ecological value and, in many ecosystems, support highly diverse communities of pollinators, seed dispersers, and frugivores. Massive amounts of water and other resources stored in ...