A numerically efficient implementation of the expectation maximization algorithm for state space models

Peer reviewedPostprin

Calogero-Sutherland Approach to Defect Blocks

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Euclidean inversion formula for defect correlators.Comment: v2: changes for clarit

Sarcopenia predicts reduced liver growth and reduced resectability in patients undergoing portal vein embolization before liver resection - A DRAGON collaborative analysis of 306 patients

Background: After portal vein embolization (PVE) 30% fail to achieve liver resection. Malnutrition is a modifiable risk factor and can be assessed by radiological indices. This study investigates, if sarcopenia affects resectability and kinetic growth rate (KGR) after PVE. Methods: A retrospective study was performed of the outcome of PVE at 8 centres of the DRAGON collaborative from 2010 to 2019. All malignant tumour types were included. Sarcopenia was defined using gender, body mass and skeletal muscle index. First imaging after PVE was used for liver volumetry. Primary and secondary endpoints were resectability and KGR. Risk factors impacting liver growth were assessed in a multivariable analysis. Results: Eight centres identified 368 patients undergoing PVE. 62 patients (17%) had to be excluded due to unavailability of data. Among the 306 included patients, 112 (37%) were non-sarcopenic and 194 (63%) were sarcopenic. Sarcopenic patients had a 21% lower resectability rate (87% vs. 66%, p &lt; 0.001) and a 23% reduced KGR (p = 0.02) after PVE. In a multivariable model dichotomized for KGR ≥2.3% standardized FLR (sFLR)/week, only sarcopenia and sFLR before embolization correlated with KGR. Conclusion: In this largest study of risk factors, sarcopenia was associated with reduced resectability and KGR in patients undergoing PVE.</p

Defects in Conformal Field Theories

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach tothe relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recentobservation for four-point blocks and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies ofconformal defects. Applications range from several new relations with scalar four-point blocks to a Lorentzian inversion formula for defect correlators

Conformal Blocks for Defects

Non-local operators play an important role in many quantum field theories, e.g. Wilson-loops in gauge theories. In conformal field theories, the kinematical content of correlators is given by conformal blocks and is essential to bootstrap the full correlator. For four-point functions of local operators these are well studied. In this talk I explain a systematic way to obtain the conformal blocks of non-local operators like line-defects in non-supersymmetric theories

A Lorentzian inversion formula for defect CFT

We present a Lorentzian inversion formula valid for any defect CFT that extracts the bulk channel CFT data as an analytic function of the spin variable. This result complements the already obtained inversion formula for the corresponding defect channel, and makes it now possible to implement the analytic bootstrap program for defect CFT, by going back and forth between both channels. A crucial role in our derivation is played by the Calogero-Sutherland description of defect blocks which we review. As first applications we obtain the large-spin limit of bulk CFT data necessary to reproduce the defect identity, and also calculate the bulk data of the twist defect of the $3d$ Ising model to first order in the $\epsilon$-expansion

Assignment of a vibration to a graphical object induced by resonant frequency

PeerReviewe

Joint EEG/fMRI state space model for the detection of directed interactions in human brains—a simulation study

An often addressed challenge in neuroscience research is the assignment of different tasks to specific brain regions. In many cases several brain regions are activated during a single task. Therefore, one is also interested in the temporal evolution of brain activity to infer causal relations between activated brain regions. These causal relations may be described by a directed, task specific network which consists of activated brain regions as vertices and directed edges. The edges describe the causal relations. Inference of the task specific brain network from measurements like electroencephalography (EEG) or functional magnetic resonance imaging (fMRI) is challenging, due to the low spatial resolution of the former and the low temporal resolution of the latter. Here, we present a simulation study investigating a possible combined analysis of simultaneously measured EEG and fMRI data to address the challenge specified above. A nonlinear state space model is used to distinguish between the underlying brain states and the (simulated) EEG/fMRI measurements. We make use of a modified unscented Kalman filter and a corresponding unscented smoother for the estimation of the underlying neural activity. Model parameters are estimated using an expectation-maximization algorithm, which exploits the partial linearity of our model. Inference of the brain network structure is then achieved using directed partial correlation, a measure for Granger causality. The results indicate that the convolution effect of the fMRI forward model imposes a big challenge for the parameter estimation and reduces the influence of the fMRI in combined EEG-fMRI models. It remains to be investigated whether other models or similar combinations of other modalities such as, e.g., EEG and magnetoencephalography can increase the profit of the promising idea of combining various modalities