A stochastic approach to unitary coupled cluster.

Unitary coupled cluster (UCC), originally developed as a variational alternative to the popular traditional coupled cluster method, has seen a resurgence as a functional form for use on quantum computers. However, the number of excitors present in the Ansatz often presents a barrier to implementation on quantum computers. Given the natural sparsity of wavefunctions obtained from quantum Monte Carlo methods, we consider here a stochastic solution to the UCC problem. Using the coupled cluster Monte Carlo framework, we develop cluster selection schemes that capture the structure of the UCC wavefunction, as well as its Trotterized approximation, and use these to solve the corresponding projected equations. Due to the fast convergence of the equations with order in the cluster expansion, this approach scales polynomially with the size of the system. Unlike traditional UCC implementations, our approach naturally produces a non-variational estimator for the energy in the form of the projected energy. For unitary coupled cluster singles and doubles (UCCSD) in small systems, we find that this agrees well with the expectation value of the energy and, in the case of two electrons, with full configuration interaction results. For the larger N2 system, the two estimators diverge, with the projected energy approaching the coupled cluster result, while the expectation value is close to results from traditional UCCSD

Multireference Stochastic Coupled Cluster.

We describe a modification of the stochastic coupled cluster algorithm that allows the use of multiple reference determinants. By considering the secondary references as excitations of the primary reference and using them to change the acceptance criteria for selection and spawning, we obtain a simple form of stochastic multireference coupled cluster which preserves the appealing aspects of the single reference approach. The method is able to successfully describe strongly correlated molecular systems using few references and low cluster truncation levels, showing promise as a tool to tackle strong correlation in more general systems. Moreover, it allows simple and comprehensive control of the included references and excitorsthereof, and this flexibility can be taken advantage of to gain insight into some of the inner workings of established electronic structure methods

A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems

The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multi-configurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper we explore the potential of incorporating ideas from conventional MRCC - namely the treatment of the strongly correlated space in a configuration interaction formalism - to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.Comment: 13 pages, 10 figures, 3 table

Focal cortical dysplasia: a practical guide for neurologists

Focal cortical dysplasia (FCD) is a malformation of cortical development characterised by disruption of cortical cytoarchitecture. Classification of FCDs subtypes has initially been based on correlation of the histopathology with relevant clinical, electroencephalographic and neuroimaging features. A recently proposed classification update recommends a multilayered, genotype-phenotype approach, integrating findings from histopathology, genetic analysis of resected tissue and presurgical MRI. FCDs are caused either by single somatic activating mutations in MTOR pathway genes or by double-hit inactivating mutations with a constitutional and a somatic loss-of-function mutation in repressors of the signalling pathway. Mild malformation with oligodendroglial hyperplasia in epilepsy is caused by somatic pathogenic SLC35A2 mutations. FCDs most often present with drug-resistant focal epilepsy or epileptic encephalopathy. Most patients respond to surgical treatment. The use of mechanistic target of rapamycin inhibitors may complement the surgical approach. Treatment approaches and outcomes have improved with advances in neuroimaging, neurophysiology and genetics, although predictors of treatment response have only been determined in part

Multireference Stochastic Coupled Cluster.

We describe a modification of the stochastic coupled cluster algorithm that allows the use of multiple reference determinants. By considering the secondary references as excitations of the primary reference and using them to change the acceptance criteria for selection and spawning, we obtain a simple form of stochastic multireference coupled cluster which preserves the appealing aspects of the single-reference approach. The method is able to successfully describe strongly correlated molecular systems using few references and low cluster truncation levels, showing promise as a tool to tackle strong correlation in more general systems. Moreover, it allows simple and comprehensive control of the included references and excitors thereof, and this flexibility can be taken advantage of to gain insight into some of the inner workings of established electronic structure methods

Structural imaging biomarkers of sudden unexpected death in epilepsy.

Sudden unexpected death in epilepsy is a major cause of premature death in people with epilepsy. We aimed to assess whether structural changes potentially attributable to sudden death pathogenesis were present on magnetic resonance imaging in people who subsequently died of sudden unexpected death in epilepsy. In a retrospective, voxel-based analysis of T1 volume scans, we compared grey matter volumes in 12 cases of sudden unexpected death in epilepsy (two definite, 10 probable; eight males), acquired 2 years [median, interquartile range (IQR) 2.8] before death [median (IQR) age at scanning 33.5 (22) years], with 34 people at high risk [age 30.5 (12); 19 males], 19 at low risk [age 30 (7.5); 12 males] of sudden death, and 15 healthy controls [age 37 (16); seven males]. At-risk subjects were defined based on risk factors of sudden unexpected death in epilepsy identified in a recent combined risk factor analysis. We identified increased grey matter volume in the right anterior hippocampus/amygdala and parahippocampus in sudden death cases and people at high risk, when compared to those at low risk and controls. Compared to controls, posterior thalamic grey matter volume, an area mediating oxygen regulation, was reduced in cases of sudden unexpected death in epilepsy and subjects at high risk. The extent of reduction correlated with disease duration in all subjects with epilepsy. Increased amygdalo-hippocampal grey matter volume with right-sided changes is consistent with histo-pathological findings reported in sudden infant death syndrome. We speculate that the right-sided predominance reflects asymmetric central influences on autonomic outflow, contributing to cardiac arrhythmia. Pulvinar damage may impair hypoxia regulation. The imaging findings in sudden unexpected death in epilepsy and people at high risk may be useful as a biomarker for risk-stratification in future studies

Cortical neuronal hypertrophy and MTOR pathway activation in CAN regions in SUDEP

Objectives: Dysfunctional connectivity and preexisting structural abnormalities of central autonomic network (CAN) regions have been shown on magnetic resonance imaging (MRI) in sudden unexpected death in epilepsy (SUDEP) and may be mechanistically relevant. In a previous postmortem study we reported increased microglia in CAN regions, including the superior temporal gyrus (STG) in SUDEP. In this current study we investigated mammalian target of rapamycin (mTOR) pathway activation and neuronal c-Fos activation in CAN regions in SUDEP compared to control groups. Methods: In a series of 59 postmortem cases (SUDEP, n = 26; epilepsy controls [EPCs], n = 14; and nonepilepsy controls [NECs], n = 19), we quantified pS6-240/4, pS6-235/6 (markers of mTOR activation) and c-Fos neuronal densities and labeling index in the STG, anterior cingulate, insula, frontobasal, and pulvinar regions using immunohistochemistry with whole-slide automated image analysis. Results: Significantly more pS6-positive neurons were present in the STG in cases with a history of recent seizures prior to death and also in SUDEP compared to other cause of death groups. No differences were noted for c-Fos neuronal labeling in any region between cause of death groups. Cortical neuronal hypertrophy in the STG was observed in some SUDEP cases and associated with pS6-240/4 expression. pS6-235/6 highlighted neuronal intranuclear inclusions, mainly in SUDEP cases and in the STG region. Significance: Neuronal labeling for pS6 in the STG correlated with both seizure activity in the period prior to death and SUDEP. Further investigations are required to explore the significance of this region in terms of autonomic network dysfunction that may increase the vulnerability for SUDEP