Multi-Lagrangians for Integrable Systems

We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi- Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit $N$-fold first order local Hamiltonian structure can be cast into variational form with $2N-1$ Lagrangians which will be local functionals of Clebsch potentials. This number increases to $3N-2$ when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in $1+1$ dimensions which is a {\it local} functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.Comment: typos corrected and a reference adde

Are stealth scalar fields stable?

Non-gravitating (stealth) scalar fields associated with Minkowski space in scalar-tensor gravity are examined. Analytical solutions for both non-minimally coupled scalar field theory and for Brans-Dicke gravity are studied and their stability with respect to tensor perturbations is assessed using a covariant and gauge-invariant formalism developed for alternative gravity. For Brans-Dicke solutions, the stability with respect to homogeneous perturbations is also studied. There are regions of parameter space corresponding to stability and other regions corresponding to instability.Comment: 10 pages, 1 table, no figures, to appear in Phys. Rev,

Analogies between self-duality and stealth matter source

We consider the problem of a self-interacting scalar field nonminimally coupled to the three-dimensional BTZ metric such that its energy-momentum tensor evaluated on the BTZ metric vanishes. We prove that this system is equivalent to a self-dual system composed by a set of two first-order equations. The self-dual point is achieved by fixing one of the coupling constant of the potential in terms of the nonminimal coupling parameter. At the self-dual point and up to some boundary terms, the matter action evaluated on the BTZ metric is bounded below and above. These two bounds are saturated simultaneously yielding to a vanishing action for configurations satisfying the set of self-dual first-order equations.Comment: 6 pages. To be published in Jour. Phys.

'Square Root' of the Maxwell Lagrangian versus confinement in general relativity

We employ the 'square root' of the Maxwell Lagrangian (i.e. \surd(F_{{\mu}{\nu}}F^{{\mu}{\nu}})), coupled with gravity to search for the possible linear potentials which are believed to play role in confinement. It is found that in the presence of magnetic charge no confining potential exists in such a model. Confining field solutions are found for radial geodesics in pure electrically charged Nariai- Bertotti-Robinson (NBR)-type spacetime with constant scalar curvature. Recently, Guendelman, Kaganovich, Nissimov and Pacheva, [Phys.Lett.B704(2011)230] have shown that superposed square root with standard Maxwell Lagrangians yields confining potentials in spherically symmetric spacetimes with new generalized Reissner-Nordstr\"om-de Sitter / -anti-de Sitter black hole solutions. In NBR spacetimes we show that confining potentials exist even when the standard Maxwell Lagrangian is relaxed.Comment: 5 pages, 0 figures, accepted for publication in Phys. Lett.

Magnetic Branes Supported by Nonlinear Electromagnetic Field

Considering the nonlinear electromagnetic field coupled to Einstein gravity in the presence of cosmological constant, we obtain a new class of $d$-dimensional magnetic brane solutions. This class of solutions yields a spacetime with a longitudinal nonlinear magnetic field generated by a static source. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle $\delta \phi$. We investigate the effects of nonlinearity on the metric function and deficit angle and also find that for the special range of the nonlinear parameter, the solutions are not asymptotic AdS. We generalize this class of solutions to the case of spinning magnetic solutions, and find that when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Then, we use the counterterm method and compute the conserved quantities of these spacetimes. Finally, we obtain a constrain on the nonlinear parameter, such that the nonlinear electromagnetic field is conformally invariant.Comment: 15 pages, one eps figur

BRAF V600E mutations in urine and plasma cell-free DNA from patients with Erdheim-Chester disease.

Erdheim-Chester disease (ECD) is a rare histiocytosis with a high prevalence of BRAF V600E mutation (>50% of patients). Patients with BRAF-mutant ECD can respond to BRAF inhibitors. Unfortunately, the lack of adequate archival tissue often precludes BRAF testing. We hypothesized that cell-free DNA (cfDNA) from plasma or urine can offer an alternative source of biologic material for testing. We tested for BRAF V600E mutation in cfDNA from the plasma and urine of 6 ECD patients. In patients with available archival tissue, the result of BRAF mutation analysis was concordant with plasma and urine cfDNA results in all 3 patients (100% agreement, kappa 1.00). In all 6 patients, BRAF mutation analysis of plasma and urine cfDNA was concordant in 5 of 6 patients (83% agreement, kappa 0.67). Testing for BRAF V600E mutation in plasma and urine cfDNA should be further investigated as an alternative to archival tissue mutation analysis

Validation of risk prediction models applied to longitudinal electronic health record data for the prediction of major cardiovascular events in the presence of data shifts

\ua9 2022 The Author(s). Published by Oxford University Press on behalf of the European Society of Cardiology. Aims: Deep learning has dominated predictive modelling across different fields, but in medicine it has been met with mixed reception. In clinical practice, simple, statistical models and risk scores continue to inform cardiovascular disease risk predictions. This is due in part to the knowledge gap about how deep learning models perform in practice when they are subject to dynamic data shifts; a key criterion that common internal validation procedures do not address. We evaluated the performance of a novel deep learning model, BEHRT, under data shifts and compared it with several ML-based and established risk models. Methods and results: Using linked electronic health records of 1.1 million patients across England aged at least 35 years between 1985 and 2015, we replicated three established statistical models for predicting 5-year risk of incident heart failure, stroke, and coronary heart disease. The results were compared with a widely accepted machine learning model (random forests), and a novel deep learning model (BEHRT). In addition to internal validation, we investigated how data shifts affect model discrimination and calibration. To this end, we tested the models on cohorts from (i) distinct geographical regions; (ii) different periods. Using internal validation, the deep learning models substantially outperformed the best statistical models by 6%, 8%, and 11% in heart failure, stroke, and coronary heart disease, respectively, in terms of the area under the receiver operating characteristic curve. Conclusion: The performance of all models declined as a result of data shifts; despite this, the deep learning models maintained the best performance in all risk prediction tasks. Updating the model with the latest information can improve discrimination but if the prior distribution changes, the model may remain miscalibrated

Hi-BEHRT: Hierarchical Transformer-Based Model for Accurate Prediction of Clinical Events Using Multimodal Longitudinal Electronic Health Records

\ua9 2022 IEEE. Electronic health records (EHR) represent a holistic overview of patients\u27 trajectories. Their increasing availability has fueled new hopes to leverage them and develop accurate risk prediction models for a wide range of diseases. Given the complex interrelationships of medical records and patient outcomes, deep learning models have shown clear merits in achieving this goal. However, a key limitation of current study remains their capacity in processing long sequences, and long sequence modelling and its application in the context of healthcare and EHR remains unexplored. Capturing the whole history of medical encounters is expected to lead to more accurate predictions, but the inclusion of records collected for decades and from multiple resources can inevitably exceed the receptive field of the most existing deep learning architectures. This can result in missing crucial, long-term dependencies. To address this gap, we present Hi-BEHRT, a hierarchical Transformer-based model that can significantly expand the receptive field of Transformers and extract associations from much longer sequences. Using a multimodal large-scale linked longitudinal EHR, the Hi-BEHRT exceeds the state-of-the-art deep learning models 1% to 5% for area under the receiver operating characteristic (AUROC) curve and 1% to 8% for area under the precision recall (AUPRC) curve on average, and 2% to 8% (AUROC) and 2% to 11% (AUPRC) for patients with long medical history for 5-year heart failure, diabetes, chronic kidney disease, and stroke risk prediction. Additionally, because pretraining for hierarchical Transformer is not well-established, we provide an effective end-to-end contrastive pre-training strategy for Hi-BEHRT using EHR, improving its transferability on predicting clinical events with relatively small training dataset