We generalize our results on Deligne’s conjecture to prove the statement that the normalized Hochschild co–chains of a finite–dimensional associative algebra with a non–degenerate, symmetric, invariant inner product are an algebra over a chain model of the framed little discs operad which is given by cacti. In particular, in characteristic zero they are a BV algebra up to homotopy and the Hochs...

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 design space exploration of the off-chip IO along with the DRAM and cache parameters. We describe the models added to CACTI-IO that help include the off-chip impact to the tradeoffs betwee...

The original CACTI tool was released in 1994 to give computer architects a fast tool to model SRAM caches. It has been widely adopted and used since. Two new versions were released to add area and active power modeling to CACTI. This new version adds a model for leakage power and updates the basic circuit structure and device parameters to better reflect the advances in scaling semiconductors w...

Many plants produce structural defenses to deter feeding by herbivores. However, many previous studies testing whether spines are eff ective at defending against mammalian herbivores have produced equivocal results. Th ese ambiguous results are hypothesized to be due to herbivore counter-adaptations. We investigated potential counter-adaptations in a population of white-throated woodrats Neotom...

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let G (n, r) be the set of cacti of order n and with r cycles, ξ(2n, r) the set of cacti of order 2n with a perfect matching and r cycles. In this paper, we give the sharp upper bounds of t...

Major diseases in grafted cacti have been reported and Fusarium oxysporum, Bipolaris cactivora, Phytophthora spp. and Collectotrichum spp. are known as causal pathogens. These pathogens can lead to plant death after infection. Therefore, some European countries have quarantined imported cacti that are infected with specific fungal pathogens. Consequently, we developed PCR detection methods to i...

Motivated by the second author’s construction of a classifying space for the group of pure symmetric automorphisms of a free product, we introduce and study a family of topological operads, the operads of based cacti, defined for every pointed simplicial set .Y;p/ . These operads also admit linear versions, which are defined for every augmented graded cocommutative coalgebra C . We show that th...

Abstract In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n–gon–trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so–called clique–forest–like graphs are chromatically equivalent.

Cactaceae represents one of the most species-rich families of succulent plants native to arid and semi-arid ecosystems, yet the associations Cacti establish with microorganisms and the rules governing microbial community assembly remain poorly understood. We analyzed the composition, diversity, and factors influencing above- and below-ground bacterial, archaeal, and fungal communities associate...