Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are compared to the excitations obtained within $\Delta$SCF and time-dependent density functional theory. We also calculate the excitation energies in perturbation theory using approximate functionals such as the local density approximation and the optimized effective potential method with and without the Colle-Salvetti correlation contribution

On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo

Approximate Bayesian computation (ABC) has gained popularity over the past few years for the analysis of complex models arising in population genetics, epidemiology and system biology. Sequential Monte Carlo (SMC) approaches have become work-horses in ABC. Here we discuss how to construct the perturbation kernels that are required in ABC SMC approaches, in order to construct a sequence of distributions that start out from a suitably defined prior and converge towards the unknown posterior. We derive optimality criteria for different kernels, which are based on the Kullback-Leibler divergence between a distribution and the distribution of the perturbed particles. We will show that for many complicated posterior distributions, locally adapted kernels tend to show the best performance. We find that the added moderate cost of adapting kernel functions is easily regained in terms of the higher acceptance rate. We demonstrate the computational efficiency gains in a range of toy examples which illustrate some of the challenges faced in real-world applications of ABC, before turning to two demanding parameter inference problems in molecular biology, which highlight the huge increases in efficiency that can be gained from choice of optimal kernels. We conclude with a general discussion of the rational choice of perturbation kernels in ABC SMC settings

Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures

In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a "null model" of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets

Energy and variance optimization of many body wave functions

We present a simple, robust and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in flexible Jastrow factors, that include 3-body electron-electron-nucleus correlation terms, for the NO$_2$ and decapentaene (C$_{10}$H$_{12}$) molecules. The basic idea is to add terms to the straightforward expression for the Hessian that are zero when the integrals are performed exactly, but that cancel much of the statistical fluctuations for a finite Monte Carlo sample. The method is compared to what is currently the most popular method for optimizing many-body wave functions, namely minimization of the variance of the local energy. The most efficient wave function is obtained by optimizing a linear combination of the energy and the variance.Comment: 4 pages, 4 figures, minor corrections of inexact statements, missing

Alleviation of the Fermion-sign problem by optimization of many-body wave functions

We present a simple, robust and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wav e function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging C$_2$ molecule to the experimental accuracy of 0.02 eV

Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of the cardiac tissue and its impact in computational models for cardiac electromechanics. We follow a theoretical framework recently proposed in [Cherubini, Filippi, Gizzi, Ruiz-Baier, JTB 2017], in the context of general reaction-diffusion-mechanics systems using multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling using computational tests, conducted using a finite element method. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications

CO2 laser ranging systems study

The conceptual design and error performance of a CO2 laser ranging system are analyzed. Ranging signal and subsystem processing alternatives are identified, and their comprehensive evaluation yields preferred candidate solutions which are analyzed to derive range and range rate error contributions. The performance results are presented in the form of extensive tables and figures which identify the ranging accuracy compromises as a function of the key system design parameters and subsystem performance indexes. The ranging errors obtained are noted to be within the high accuracy requirements of existing NASA/GSFC missions with a proper system design

Early assessment of vestibular function after unilateral cochlear implant surgery

Introduction : Cochlear implantation (CI) has been reported to negatively effect on the vestibular function. The study of the vestibular function has variably been conducted by different types of diagnostic tools. The combined use of modern, rapidly performable diagnostic tools could reveal useful for standardizing the evaluation protocol. Methods: In a group of 28 subjects undergoing CI, the video Head Impulse Test (vHIT), the cervical Vestibular Evoked Myogenic Potentials (cVEMPS) and the short-form of Dizziness Handicap Inventory (DHI) questionnaire were investigated pre-operatively and post-operatively (implant on and off) in both the implanted and the contralateral, non-implanted ear. All surgeries were performed with a round window approach (RWA), except for three otosclerosis cases were the extended RWA (eRWA) was used. Results: The vHIT of the lateral semicircular canal showed a pre-operative vestibular involvement in nearly 50% of the cases, whilst the three canals were contemporarily affected in only 14% of them. In all the hypo-functional subjects, cVEMPs were absent. A low VOR gain in all the investigated SSCC was found in 4 subjects (14%). In those subjects, (21.7%) in whom cVEMPs were pre-operatively present and normal in the operated side, absence of response was post-operatives recorded. Discussion/Conclusion: The vestibular protocol applied for the study showed to be appropriate for distinguishing between the CI operated and the non-operated ear. In this regard, cVEMPs showed to be more sensitive than vHIT for revealing a vestibular sufferance after CI, although without statistical significance. Finally, the use of the RWA surgery was apparently not avoiding signs of vestibular impairment to occur

Simultaneous Contralateral Vestibular Schwannoma and Middle Ear Paraganglioma Tumor

To the best of our knowledge, only 2 cases of a simultaneous contralateral vestibular schwannoma (VS) and middle ear paraganglioma (MEP) have previously been reported in literature. We report the third case observed in a 43-year-old male, who presented with an 11-year history of right-sided hearing loss and a 1-year history of left-sided pulsatile tinnitus. A magnetic resonance imaging (MRI) showed a VS on the right side and computer tomography (CT) identified a Fisch type A1 paraganglioma on the left side. The VS was treated using a translabyrinthine approach and the MEP was kept under radiological observation for 1 year. Due to the growth of the MEP (Fisch type A2), it was treated with excision via a retroauricular approach. Our case was very challenging because there was a different and important pathology on each side, both carrying a risk of deafness as a consequence of the disease and/or the treatments