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

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

Semantic Sentiment Analysis of Twitter Data

Internet and the proliferation of smart mobile devices have changed the way information is created, shared, and spreads, e.g., microblogs such as Twitter, weblogs such as LiveJournal, social networks such as Facebook, and instant messengers such as Skype and WhatsApp are now commonly used to share thoughts and opinions about anything in the surrounding world. This has resulted in the proliferation of social media content, thus creating new opportunities to study public opinion at a scale that was never possible before. Naturally, this abundance of data has quickly attracted business and research interest from various fields including marketing, political science, and social studies, among many others, which are interested in questions like these: Do people like the new Apple Watch? Do Americans support ObamaCare? How do Scottish feel about the Brexit? Answering these questions requires studying the sentiment of opinions people express in social media, which has given rise to the fast growth of the field of sentiment analysis in social media, with Twitter being especially popular for research due to its scale, representativeness, variety of topics discussed, as well as ease of public access to its messages. Here we present an overview of work on sentiment analysis on Twitter.Comment: Microblog sentiment analysis; Twitter opinion mining; In the Encyclopedia on Social Network Analysis and Mining (ESNAM), Second edition. 201

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

Combining estimates of interest in prognostic modelling studies after multiple imputation: current practice and guidelines

Background: Multiple imputation (MI) provides an effective approach to handle missing covariate data within prognostic modelling studies, as it can properly account for the missing data uncertainty. The multiply imputed datasets are each analysed using standard prognostic modelling techniques to obtain the estimates of interest. The estimates from each imputed dataset are then combined into one overall estimate and variance, incorporating both the within and between imputation variability. Rubin's rules for combining these multiply imputed estimates are based on asymptotic theory. The resulting combined estimates may be more accurate if the posterior distribution of the population parameter of interest is better approximated by the normal distribution. However, the normality assumption may not be appropriate for all the parameters of interest when analysing prognostic modelling studies, such as predicted survival probabilities and model performance measures. Methods: Guidelines for combining the estimates of interest when analysing prognostic modelling studies are provided. A literature review is performed to identify current practice for combining such estimates in prognostic modelling studies. Results: Methods for combining all reported estimates after MI were not well reported in the current literature. Rubin's rules without applying any transformations were the standard approach used, when any method was stated. Conclusion: The proposed simple guidelines for combining estimates after MI may lead to a wider and more appropriate use of MI in future prognostic modelling studies

Analysis of four studies in a comparative framework reveals: health linkage consent rates on British cohort studies higher than on UK household panel surveys

Background: A number of cohort studies and longitudinal household panel studies in Great Britain have asked for consent to link survey data to administrative health data. We explore commonalities and differences in the process of collecting consent, achieved consent rates and biases in consent with respect to socio-demographic, socio-economic and health characteristics. We hypothesise that British cohort studies which are rooted within the health sciences achieve higher consent rates than the UK household longitudinal studies which are rooted within the social sciences. By contrast, the lack of a specific health focus in household panel studies means there may be less selectivity in consent, in particular, with respect to health characteristics. Methods: Survey designs and protocols for collecting informed consent to health record linkage on two British cohort studies and two UK household panel studies are systematically compared. Multivariate statistical analysis is then performed on information from one cohort and two household panel studies that share a great deal of the data linkage protocol but vary according to study branding, survey design and study population. Results: We find that consent is higher in the British cohort studies than in the UK household panel studies, and is higher the more health-focused the study is. There are no systematic patterns of consent bias across the studies and where effects exist within a study or study type they tend to be small. Minority ethnic groups will be underrepresented in record linkage studies on the basis of all three studies. Conclusions: Systematic analysis of three studies in a comparative framework suggests that the factors associated with consent are idiosyncratic to the study. Analysis of linked health data is needed to establish whether selectivity in consent means the resulting research databases suffer from any biases that ought to be considered

A new modality of treatment for non-united fracture of the humerus in a patient with osteopetrosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Osteopetrosis introduces technical limitations to the traditional treatment of fracture management that may be minimised with specific pre-operative planning. Extreme care and caution are required when drilling, reaming, or inserting implants in patients with osteopetrosis. Caution must be exercised throughout the postoperative course when these patients are at greatest risk for device failure or further injury.</p> <p>Case presentation</p> <p>We present our experience of treating such a fracture where a patient presented with a non-united fracture of the humerus. The bone was already osteoporotic. We successfully used a new technique which has not been described in the literature before. This included the use of a high-speed drill to prepare the bone for screw fixation. Bone healing was augmented with bone morphogenic protein.</p> <p>Conclusion</p> <p>This technique can give invaluable experience to surgeons who are involved in treating these types of fracture.</p

Listeners form average-based representations of individual voice identities.

Models of voice perception propose that identities are encoded relative to an abstracted average or prototype. While there is some evidence for norm-based coding when learning to discriminate different voices, little is known about how the representation of an individual's voice identity is formed through variable exposure to that voice. In two experiments, we show evidence that participants form abstracted representations of individual voice identities based on averages, despite having never been exposed to these averages during learning. We created 3 perceptually distinct voice identities, fully controlling their within-person variability. Listeners first learned to recognise these identities based on ring-shaped distributions located around the perimeter of within-person voice spaces - crucially, these distributions were missing their centres. At test, listeners' accuracy for old/new judgements was higher for stimuli located on an untrained distribution nested around the centre of each ring-shaped distribution compared to stimuli on the trained ring-shaped distribution

Error Rates, Decisive Outcomes and Publication Bias with Several Inferential Methods

Correction to this article published Hopkins, W.G. & Batterham, A.M. Sports Med (2016) 46: 923. doi:10.1007/s40279-016-0530-