Lieb-Thirring inequalities for Schr\"odinger operators with complex-valued potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\"odinger operator with a complex-valued potential.Comment: 9 pages; typos correcte

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

On inductive biases for the robust and interpretable prediction of drug concentrations using deep compartment models

Conventional pharmacokinetic (PK) models contain several useful inductive biases guiding model convergence to more realistic predictions of drug concentrations. Implementing similar biases in standard neural networks can be challenging, but might be fundamental for model robustness and predictive performance. In this study, we build on the deep compartment model (DCM) architecture by introducing constraints that guide the model to explore more physiologically realistic solutions. Using a simulation study, we show that constraints improve robustness in sparse data settings. Additionally, predicted concentration–time curves took on more realistic shapes compared to unconstrained models. Next, we propose the use of multi-branch networks, where each covariate can be connected to specific PK parameters, to reduce the propensity of models to learn spurious effects. Another benefit of this architecture is that covariate effects are isolated, enabling model interpretability through the visualization of learned functions. We show that all models were sensitive to learning false effects when trained in the presence of unimportant covariates, indicating the importance of selecting an appropriate set of covariates to link to the PK parameters. Finally, we compared the predictive performance of the constrained models to previous relevant population PK models on a real-world data set of 69 haemophilia A patients. Here, constrained models obtained higher accuracy compared to the standard DCM, with the multi-branch network outperforming previous PK models. We conclude that physiological-based constraints can improve model robustness. We describe an interpretable architecture which aids model trust, which will be key for the adoption of machine learning-based models in clinical practice.</p

Incorporating self-reported health measures in risk equalization through constrained regression

Most health insurance markets with premium-rate restrictions include a risk equalization system to compensate insurers for predictable variation in spending. Recent research has shown, however, that even the most sophisticated risk equalization systems tend to undercompensate (overcompensate) groups of people with poor (good) self-reported health, confronting insurers with incentives for risk selection. Self-reported health measures are generally considered infeasible for use as an explicit ‘risk adjuster’ in risk equalization models. This study examines an alternative way to exploit this information, namely through ‘constrained regression’ (CR). To do so, we use administrative data (N = 17 m) and health survey information (N = 380 k) from the Netherlands. We estimate five CR models and compare these models with the actual Dutch risk equalization model of 2016 which was estimated by ordinary least squares (OLS). In the CR models, the estimated coefficients are restricted, such that t

Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.Comment: First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimensions at least 3, with a new and simplyfied proof of finiteness of the two-component spanning tree. Second revision: LaTeX; 32 page

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials

Search for new physics indirect effects in e+e−→W+W−e^+e^-\to W^+W^- at linear colliders with polarized beams

We discuss the potential of a $0.5\hskip 2pt TeV$ linear collider to explore manifestations of extended (or alternative) electroweak models of current interest, through measurements of the reaction $e^+e^-\to W^+W^-$ with both initial and final states polarization. Specifically, we consider the possibility to put stringent constraints on lepton mixing (or extended lepton couplings) and $Z-Z^\prime$ mixing, showing in particular the usefulness of polarization in order to disentangle these effects.Comment: 12 pages, latex, seven figures (available from [email protected]

On the possibility of P-violation at finite baryon-number densities

We show how the introduction of a finite baryon density may trigger spontaneous parity violation in the hadronic phase of QCD. Since this involves strong interaction physics in an intermediate energy range we approximate QCD by a \sigma model that retains the two lowest scalar and pseudoscalar multiplets. We propose a novel mechanism based on interplay between lightest and heavy meson states which cannot be realized solely in the Goldstone boson (pion) sector and thereby is unrelated to the one advocated by Migdal some time ago. Our approach is relevant for dense matter in an intermediate regime of few nuclear densities where quark percolation does not yet play a significant role.Comment: 9 pages, reduced to publish in Phys.Lett.B, a relevant ref. is added and the title is changed as compared to previous version