Action variables for Toda Lattices

This Letter contains constructions of complex action variables for both the full Kostant-Toda Lattice in sl(n, ) and the generalized nonperiodic tridiagonal Toda lattice associated to an arbitrary complex semisimple Lie algebra g. The main tool is the explicit factorization solution for certain Hamiltonian flows. The Letter also contains a generalization of the standard factorization solution theorem necessary for the analysis of the full Kostant-Toda lattice.     

Blow-up results of viriel type for Zakharov equations

We consider the Zakharov equations in ^N (for N=2,N=3). We first establish a viriel identity for such equations and then prove a blow-up result for solutions with a negative energy.     

McKean-Vlasov limit for interacting random processes in random media

We apply large-deviation theory to particle systems with a random mean-field interaction in the McKean-Vlasov limit. In particular, we describe large deviations and normal fluctuations around the McKean-Vlasov equation. Due to the randomness in the interaction, the McKean-Vlasov equation is a collection of coupled PDEs indexed by the state space of the single components in the medium. As a result, the study of its solution and of the finite-size fluctuation around this solution requires some new ingredient as compared to existing techniques for nonrandom interaction.     

Triggering of radial multichannel pseudospark switches by a pulsedhollow cathode discharge

We report on a special trigger discharge for pulsed high-power pseudospark switches. The switch used is a radial three-channel pseudospark switch. For triggering, a cylindrical trigger electrode is inserted into the hollow cathode of the main gap. This electrode acts as a hollow cathode for the dc preionization, while the hollow cathode of the main gap is the anode. A negative high-voltage pulse supplied to the trigger electrode ignites the main discharge. We report the temporal evolution of the trigger discharge observed with a fast camera. This trigger method gives an excellent current distribution among the discharge channels, as can be proven by fast photography. The switch has a delay of 220 ns and a jitter of 15 ns     

Systemic Administration of Polymer‐Coated Nano‐Graphene to Deliver Drugs to Glioblastoma

Graphene—2D carbon—has received significant attention thanks to its electronic, thermal, and mechanical properties. Recently, nano‐graphene (nGr) has been investigated as a possible platform for biomedical applications. Here, a polymer‐coated nGr to deliver drugs to glioblastoma after systemic administration is reported. A biodegradable, biocompatible poly(lactide) (PLA) coating enables encapsulation and controlled release of the hydrophobic anticancer drug paclitaxel (PTX), and a hydrophilic poly(ethylene glycol) (PEG) shell increases the solubility of the nGr drug delivery system. Importantly, the polymer coating mediates the interaction of nGr with U‐138 glioblastoma cells and decreases cytotoxicity compared with pristine untreated nGr. PLA‐PEG‐coated nGr is also able to encapsulate PTX at 4.15 wt% and sustains prolonged PTX release for at least 19 d. PTX‐loaded nGr‐PLA‐PEGs are shown to kill up to 20% of U‐138 glioblastoma cells in vitro. Furthermore, nGr‐PLA‐PEG and CNT‐PLA‐PEG, two carbon nanomaterials with different shapes, are able to kill U‐138 in vitro as well as free PTX at significantly lower doses of drug. Finally, in vivo biodistribution of nGr‐PLA‐PEG shows accumulation of nGr in intracranial U‐138 glioblastoma xenografts and organs of the reticuloendothelial system.     

Geometric Variational Inference

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.     

Characterization of limits of Bayes procedures

For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for the loss function which are more general than squared error. As a corollary it is then stated that the class of procedures with this form is a complete class. The parameter space may be open, and when it is closed, the limits of Bayes procedures are generalized Bayes.     

AC transport and magnetic characterisation of multifilamentary Ag-BSCCO(2223) tapes with different filament arrangements

AC losses in multifilamentary tapes depend on various parameters. Among them, geometrical factors such as overall tape width and thickness as well as the precise arrangement of the filaments are expected to have an important influence. Several theoretical models describe this dependency. In order to study these geometrical effects experimentally, we prepared a series of Bi(2223)/Ag tapes with gradually changing filament arrangements and tape aspect ratio, and characterised them by AC transport and magnetic measurements. The results are compared to model predictions.