Holomorphic Hartree-Fock Theory: An Inherently Multireference Approach.

We investigate the existence of holomorphic Hartree–Fock solutions using a revised SCF algorithm. We use this algorithm to study the Hartree–Fock solutions for H2 and H42+ and report the emergence of holomorphic solutions at points of symmetry breaking. Finally, we find these holomorphic solutions for H4 and use them as a basis for Non-Orthogonal Configuration Interaction at a range of rectangular geometries and show them to produce energies in good agreement with Full Configuration Interaction.A.J.W.T. thanks the Royal Society for a University Research Fellowship (UF110161), and H.G.A.B. thanks the Royal Society of Chemistry for an Undergraduate Research Bursary.This is the author accepted manuscript. The final version is available from the American Chemical Society via http://dx.doi.org/10.1021/acs.jctc.5b0100

General Approach for Multireference Ground and Excited States Using Nonorthogonal Configuration Interaction.

A balanced description of ground and excited states is essential for the description of many chemical processes. However, few methods can handle cases where static correlation is present, and often these scale very unfavorably with system size. Recently, multiple Hartree-Fock (HF) solutions have been proposed as a basis for nonorthogonal configuration interaction (NOCI) to provide multireference ground- and excited-state energies, although applications across multiple geometries have been limited by the coalescence of HF solutions. Holomorphic HF (h-HF) theory allows solutions to be analytically continued beyond the Coulson-Fischer points at which they vanish, but, until now, this has only been demonstrated for small model systems. In this work, we propose a general protocol for computing NOCI ground- and excited-state energies using multiple HF solutions. To do so, we outline an active space variation of SCF metadynamics that allows a chemically relevant set of HF states to be identified and describe how these states can be routinely traced across all molecular geometries by exploiting the topology of h-HF solutions in the complex plane. Finally, we illustrate our approach using the dissociation of the fluorine dimer and the pseudo-Jahn-Teller distortion of cyclobutadiene, demonstrating its applicability for multireference ground and excited states

Calculating the random guess scores of multiple-response and matching test items

For achievement tests, the guess score is often used as a baseline for the lowest possible grade for score to grade transformations and setting the cut scores. For test item types such as multiple-response, matching and drag-and-drop, determin-ing the guess score requires more elaborate calculations than the more straight-forward calculation of the guess score for True-False and multiple-choice test item formats. For various variants of multiple-response and matching types with respect to dichotomous and polytomous scoring, methods for determining the guess score are presented and illustrated with practical applications. The implica-tions for theory and practice are discussed

Towards a Holomorphic Density Functional Theory.

Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham density-functional theory (KS-DFT) have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parameterized functional that scales between the two representations. Using the hydrogen molecule and a model of electron transfer, we continuously map multiple solutions from the HF potential to a KS-DFT description. We discover that multiple solutions can coalesce and vanish as the functional changes, forming a direct analogy with the disappearance of real HF solutions along a change in molecular structure. To overcome this disappearance of solutions, we develop a complex-analytic extension of DFT-the "holomorphic DFT" approach-that allows every SCF stationary state to be analytically continued across all molecular structures and exchange-correlation functionals.Royal Society Cambridge Trust

Microscopic Marangoni Flows Cannot Be Predicted on the Basis of Pressure Gradients.

A concentration gradient along a fluid-fluid interface can cause flow. On a microscopic level, this so-called Marangoni effect can be viewed as being caused by a gradient in the pressures acting on the fluid elements or as the chemical-potential gradients acting on the excess densities of different species at the interface. If the interface thickness can be ignored, all approaches should result in the same flow profile away from the interface. However, on a more microscopic scale, the different expressions result in different flow profiles, only one of which can be correct. Here we compare the results of direct nonequilibrium molecular dynamics simulations with the flows that are generated by pressure and chemical-potential gradients. We find that the approach based on the chemical-potential gradients agrees with the direct simulations, whereas the calculations based on the pressure gradients do not

Designing and analysing feasibility studies of complex interventions: challenges related to assessing stop/go criteria

Randomised controlled trials (RCTs) are time-consuming and costly so funders often require evidence of feasibility before they will fund large scale trials1. Feasibility studies can provide invaluable evidence relating to the practicalities of conducting large RCTs and can improve their likelihood of success. However, conducting feasibility studies of complex interventions and deciding whether or not to proceed to a full RCT, is not always straightforward. We will present the challenges encountered during the design and analysis of two feasibility studies: OBI (Optimised Behavioural Intervention for avoidant chronic low back pain patients) and MIDSHIPS (Multicentre Intervention Designed for Self-Harm using Interpersonal Problem Solving) and discuss the steps taken to overcome them. Recruiting and treating participants in a limited number of centres, with few therapists, is a complex challenge for both of these feasibility studies and crucial to determining their success; we will present the lessons learnt from our experience. We will also discuss the impact of missing data on our ability to assess stop/go criteria with respect to proof-of-concept. Estimating follow-up questionnaire response rates is an important objective in both studies, hence we will discuss the methods employed to maximise data collection and present our approach for providing robust estimates of response rates for the phase III trials

Complex adiabatic connection: A hidden non-Hermitian path from ground to excited states.

Processes related to electronically excited states are central in many areas of science; however, accurately determining excited-state energies remains a major challenge in theoretical chemistry. Recently, higher energy stationary states of non-linear methods have themselves been proposed as approximations to excited states, although the general understanding of the nature of these solutions remains surprisingly limited. In this letter, we present an entirely novel approach for exploring and obtaining excited stationary states by exploiting the properties of non-Hermitian Hamiltonians. Our key idea centres on performing analytic continuations of conventional quantum chemistry methods. Considering Hartree-Fock theory as an example, we analytically continue the electron-electron interaction to expose a hidden connectivity of multiple solutions across the complex plane, revealing a close resemblance between Coulson-Fischer points and non-Hermitian degeneracies. Finally, we demonstrate how a ground-state wave function can be morphed naturally into an excited-state wave function by constructing a well-defined complex adiabatic connection

Rotation Curves of Spiral Galaxies

Rotation curves of spiral galaxies are the major tool for determining the distribution of mass in spiral galaxies. They provide fundamental information for understanding the dynamics, evolution and formation of spiral galaxies. We describe various methods to derive rotation curves, and review the results obtained. We discuss the basic characteristics of observed rotation curves in relation to various galaxy properties, such as Hubble type, structure, activity, and environment.Comment: 40 pages, 6 gif figures; Ann. Rev. Astron. Astrophys. Vol. 39, p.137, 200

A gene-based SNP resource and linkage map for the copepod Tigriopus californicus

<p>Abstract</p> <p>Background</p> <p>As yet, few genomic resources have been developed in crustaceans. This lack is particularly evident in Copepoda, given the extraordinary numerical abundance, and taxonomic and ecological diversity of this group. <it>Tigriopus californicus </it>is ideally suited to serve as a genetic model copepod and has been the subject of extensive work in environmental stress and reproductive isolation. Accordingly, we set out to develop a broadly-useful panel of genetic markers and to construct a linkage map dense enough for quantitative trait locus detection in an interval mapping framework for <it>T. californicus--</it>a first for copepods.</p> <p>Results</p> <p>One hundred and ninety Single Nucleotide Polymorphisms (SNPs) were used to genotype our mapping population of 250 F₂larvae. We were able to construct a linkage map with an average intermarker distance of 1.8 cM, and a maximum intermarker distance of 10.3 cM. All markers were assembled into linkage groups, and the 12 linkage groups corresponded to the 12 known chromosomes of <it>T. californicus</it>. We estimate a total genome size of 401.0 cM, and a total coverage of 73.7%. Seventy five percent of the mapped markers were detected in 9 additional populations of <it>T. californicus</it>. Of available model arthropod genomes, we were able to show more colocalized pairs of homologues between <it>T. californicus </it>and the honeybee <it>Apis mellifera</it>, than expected by chance, suggesting preserved macrosynteny between Hymenoptera and Copepoda.</p> <p>Conclusions</p> <p>Our study provides an abundance of linked markers spanning all chromosomes. Many of these markers are also found in multiple populations of <it>T. californicus</it>, and in two other species in the genus. The genomic resource we have developed will enable mapping throughout the geographical range of this species and in closely related species. This linkage map will facilitate genome sequencing, mapping and assembly in an ecologically and taxonomically interesting group for which genomic resources are currently under development.</p

Longer fixation duration while viewing face images

The spatio-temporal properties of saccadic eye movements can be influenced by the cognitive demand and the characteristics of the observed scene. Probably due to its crucial role in social communication, it is argued that face perception may involve different cognitive processes compared with non-face object or scene perception. In this study, we investigated whether and how face and natural scene images can influence the patterns of visuomotor activity. We recorded monkeys’ saccadic eye movements as they freely viewed monkey face and natural scene images. The face and natural scene images attracted similar number of fixations, but viewing of faces was accompanied by longer fixations compared with natural scenes. These longer fixations were dependent on the context of facial features. The duration of fixations directed at facial contours decreased when the face images were scrambled, and increased at the later stage of normal face viewing. The results suggest that face and natural scene images can generate different patterns of visuomotor activity. The extra fixation duration on faces may be correlated with the detailed analysis of facial features