Electronic excitation spectra from time-dependent density functional response theory using plane-wave methods

The time-dependent density functional response theory method for the computation of electronic excitation spectra has been implemented in a plane-wave basis set/pseudo-potential formalism. We compare our test results for N₂ and H₂CO to literature atomic basis set calculations and find good agreement. We also discuss some of the technical complications specific to the use of plane-wave basis sets. As an application, the thermally broadened photoabsorption spectrum of formamide at room temperature is computed by averaging over a number of vibrational configurations sampled from an ab initio molecular dynamics run and compared to experiment.     

Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.     

Empty region graphs

A family of proximity graphs, called Empty Region Graphs (ERG) is presented. The vertices of an ERG are points in the plane, and two points are connected if their neighborhood, defined by a region, does not contain any other point. The region defining the neighborhood of two points is a parameter of the graph. This way of defining graphs is not new, and ERGs include several known proximity graphs such as Nearest Neighbor Graphs, β-Skeletons or Θ-Graphs. The main contribution is to provide insight and connections between the definition of ERG and the properties of the corresponding graphs.We give conditions on the region defining an ERG to ensure a number of properties that might be desirable in applications, such as planarity, connectivity, triangle-freeness, cycle-freeness, bipartiteness and bounded degree. These conditions take the form of what we call tight regions: maximal or minimal regions that a region must contain or be contained in to make the graph satisfy a given property. We show that every monotone property has at least one corresponding tight region; we discuss possibilities and limitations of this general model for constructing a graph from a point set.     

Lipase-Catalyzed Synthesis of Carboxylic Amides: Nitrogen Nucleophiles as Acyl Acceptor

Summary.  The lipase-catalyzed aminolysis of carboxylic esters is a fairly general reaction that has been performed with a wide range of esters and amines, generally in anhydrous organic media to avoid undesirable hydrolysis of the ester. Alternatively, carboxylic amides can be synthesized by lipase mediated condensation of carboxylic acids and amines if an excess of either reactant is avoided. Chiral carboxylic esters have been resolved by lipase-catalyzed aminolysis. In the majority of these resolutions, Candida antarctica lipase B has been employed as the catalyst. A range of chiral amines has been resolved by lipase mediated acylation, using mainly the lipases from C. antarctica (B type) and Pseudomonas species. The enantiorecognition was frequently found to depend critically on the acylating agent and the reaction medium. Received December 20, 1999. Accepted January 1, 2000     

Disentangling the Information in Species Interaction Networks

Shannon’s entropy measure is a popular means for quantifying ecological diversity. We explore how one can use information-theoretic measures (that are often called indices in ecology) on joint ensembles to study the diversity of species interaction networks. We leverage the little-known balance equation to decompose the network information into three components describing the species abundance, specificity, and redundancy. This balance reveals that there exists a fundamental trade-off between these components. The decomposition can be straightforwardly extended to analyse networks through time as well as space, leading to the corresponding notions for alpha, beta, and gamma diversity. Our work aims to provide an accessible introduction for ecologists. To this end, we illustrate the interpretation of the components on numerous real networks. The corresponding code is made available to the community in the specialised Julia package EcologicalNetworks.jl.     

Designing and using professional development resources for inquiry-based learning

This paper describes an attempt to design, analyse and refine professional development (PD) resources that encourage the implementation of inquiry-based learning (IBL). We describe the iterative development of the resources in England with over 100 mathematics teachers from secondary, tertiary and adult education and then analyse the impact these resources had on teachers’ beliefs and practices and the issues arising. This evaluation revealed that teachers had moved away from transmission-based orientations, encouraged by the use of less structured tasks and sample lesson plans, but some found it difficult to adopt IBL pedagogies. The most significant issues for teachers may be summarised as: confusing IBL with ‘discovery’ learning; developing and managing collaborative cultures within the classroom; and planning lessons that adapt to the emerging needs of learners.     

On the Volume of the Intersection of Two Independent Wiener Sausages

The expected volume of intersection of two independent Wiener sausages in ℝ ^m , m ≥ 3, up to time t, and associated to non-polar, compact sets K ₁ and K ₂ respectively, is obtained in the limit of large t.     

On linearizations of the quadratic two-parameter eigenvalue problem

We present several transformations that can be used to solve the quadratic two-parameter eigenvalue problem (QMEP), by formulating an associated linear multiparameter eigenvalue problem. Two of these transformations are generalizations of the well-known linearization of the quadratic eigenvalue problem and linearize the QMEP as a singular two-parameter eigenvalue problem. The third replaces all nonlinear terms by new variables and adds new equations for their relations. The QMEP is thus transformed into a nonsingular five-parameter eigenvalue problem. The advantage of these transformations is that they enable one to solve the QMEP using existing numerical methods for multiparameter eigenvalue problems. We also consider several special cases of the QMEP, where some matrix coefficients are zero