Business Training, Volume 1, Number 5, August 1914

Newsletter of the Rhode Island Commercial School (RICS) owned by Henry Jacobs. In 1916 RICS merged with Bryant & Stratton when Jacobs bought Bryant. Photos of teachers Gertrude Johnson and Mary Wales appear on page 5. Johnson and Wales left RICS to form Johnson & Wales (now Johnson & Wales University) in 1914

Alternative versions of the Johnson homomorphisms and the LMO functor

Let $\Sigma$ be a compact connected oriented surface with one boundary component and let $\mathcal{M}$ denote the mapping class group of $\Sigma$. By considering the action of $\mathcal{M}$ on the fundamental group of $\Sigma$ it is possible to define different filtrations of $\mathcal{M}$ together with some homomorphisms on each term of the filtration. The aim of this paper is twofold. Firstly we study a filtration of $\mathcal{M}$ introduced recently by Habiro and Massuyeau, whose definition involves a handlebody bounded by $\Sigma$. We shall call it the "alternative Johnson filtration", and the corresponding homomorphisms are referred to as "alternative Johnson homomorphisms". We provide a comparison between the alternative Johnson filtration and two previously known filtrations: the original Johnson filtration and the Johnson-Levine filtration. Secondly, we study the relationship between the alternative Johnson homomorphisms and the functorial extension of the Le-Murakami-Ohtsuki invariant of $3$-manifolds. We prove that these homomorphisms can be read in the tree reduction of the LMO functor. In particular, this provides a new reading grid for the tree reduction of the LMO functor.Comment: 62 pages, several figures. v_2 minor change

Progress in Time-Dependent Density-Functional Theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s, is based upon the idea that the complicated N-electron wavefunction can be replaced with the mathematically simpler 1-electron charge density in electronic struc- ture calculations of the ground stationary state. As such, ordinary DFT is neither able to treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Begin- ning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT has grown, so too has grown our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in this series [Annu. Rev. Phys. Chem. 55: 427 (2004)] left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Since doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis will be placed upon the problem of going beyond or around the TD-DFT adiabatic approximation which limits TD-DFT calculations to nominally singly-excited states. Posted with permission from the Annual Review of Physical Chemistry, Volume 63 \c{opyright} 2012 by Annual Reviews, http://www.annualreviews.org

Hypernetworks for reconstructing the dynamics of multilevel systems

Networks are fundamental for reconstructing the dynamics of many systems, but have the drawback that they are restricted to binary relations. Hypergraphs extend relational structure to multi-vertex edges, but are essentially set-theoretic and unable to represent essential structural properties. Hypernetworks are a natural multidimensional generalisation of networks, representing n-ary relations by simplices with n vertices. The assembly of vertices to make simplices is key for moving between levels in multilevel systems, and integrating dynamics between levels. It is argued that hypernetworks are necessary, if not sufficient, for reconstructing the dynamics of multilevel complex systems

Correction to Metallic 1T Phase, 3d1 Electronic Configuration and Charge Density Wave Order in Molecular-Beam Epitaxy Grown Monolayer Vanadium Ditelluride.

It has been brought to our attention that a mistake exists in the author list. The author “Johnson Goh” in the original article should be “Kuan Eng Johnson Goh”. His primary corresponding email is [email protected]

The Johnson homomorphism and its kernel

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general result that also applies to "subsurface Torelli groups". Using this, we extend Johnson's calculation of the rational abelianization of the Torelli group not only to the subsurface Torelli groups, but also to finite-index subgroups of the Torelli group that contain the kernel of the Johnson homomorphism.Comment: 32 pages, 11 figures; major revision; to appear in J. Reine Angew. Mat