Permutations Containing Many Patterns

It is shown that the maximum number of patterns that can occur in a permutation of length $n$ is asymptotically $2^n$. This significantly improves a previous result of Coleman

Simulation Studies of Nanomagnet-Based Architecture

We report a simulation study on interacting ensembles of Co nanomagnets that can perform basic logic operations and propagate logic signals, where the state variable is the magnetization direction. Dipole field coupling between individual nanomagnets drives the logic functionality of the ensemble and coordinated arrangements of the nanomagnets allow for the logic signal to propagate in a predictable way. Problems with the integrity of the logic signal arising from instabilities in the constituent magnetizations are solved by introducing a biaxial anisotropy term to the Gibbs magnetic free energy of each nanomagnet. The enhanced stability allows for more complex components of a logic architecture capable of random combinatorial logic, including horizontal wires, vertical wires, junctions, fanout nodes, and a novel universal logic gate. Our simulations define the focus of scaling trends in nanomagnet-based logic and provide estimates of the energy dissipation and time per nanomagnet reversal

Synchronization versus stability of the invariant distribution for a class of globally coupled maps

We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant measure (acim), which is furthermore mixing. Interaction arises in the form of diffusive coupling, which involves a function that is discontinuous on the circle. We show that for sufficiently small coupling strength the coupled map system admits a unique absolutely continuous invariant distribution, which depends on the coupling strength $\varepsilon$. Furthermore, the invariant density exponentially attracts all initial distributions considered in our framework. We also show that the dependence of the invariant density on the coupling strength $\varepsilon$ is Lipschitz continuous in the BV norm. When the coupling is sufficiently strong, the limit behavior of the system is more complex. We prove that a wide class of initial measures approach a point mass with support moving chaotically on the circle. This can be interpreted as synchronization in a chaotic state

Ancient Maya Beekeeping (ca. 1000-1520 CE)

Articlehttp://deepblue.lib.umich.edu/bitstream/2027.42/96996/1/UMURJ-Issue07_2010-DMImre.pd

Highly Selective Hydroformylation of the Cinchona Alkaloids

The four naturally occurring cinchona alkaloids were subjected to hydroformylation to create an extra functional group that allows immobilization. Cinchonidine, quinine, and quinidine, could be hydroformylated with virtually complete terminal selectivity, using a rhodium/tetraphosphite catalyst. The cinchonidine aldehyde was reduced to the alcohol and subjected to reductive amination with benzylamine.