Persistent current of relativistic electrons on a Dirac ring in presence of impurities

We study the behavior of persistent current of relativistic electrons on a one dimensional ring in presence of attractive/repulsive scattering potentials. In particular, we investigate the persistent current in accordance with the strength as well as the number of the scattering potential. We find that in presence of single scatterer the persistent current becomes smaller in magnitude than the scattering free scenario. This behaviour is similar to the non-relativistic case. Even for a very strong scattering potential, finite amount of persistent current remains for a relativistic ring. In presence of multiple scatterer we observe that the persistent current is maximum when the scatterers are placed uniformly compared to the current averaged over random configurations. However if we increase the number of scatterers, we find that the random averaged current increases with the number of scatterers. The latter behaviour is in contrast to the non-relativistic case.Comment: This is the published versio

Asymptotic Properties of Bayes Risk of a General Class of Shrinkage Priors in Multiple Hypothesis Testing Under Sparsity

Consider the problem of simultaneous testing for the means of independent normal observations. In this paper, we study some asymptotic optimality properties of certain multiple testing rules induced by a general class of one-group shrinkage priors in a Bayesian decision theoretic framework, where the overall loss is taken as the number of misclassified hypotheses. We assume a two-groups normal mixture model for the data and consider the asymptotic framework adopted in Bogdan et al. (2011) who introduced the notion of asymptotic Bayes optimality under sparsity in the context of multiple testing. The general class of one-group priors under study is rich enough to include, among others, the families of three parameter beta, generalized double Pareto priors, and in particular the horseshoe, the normal-exponential-gamma and the Strawderman-Berger priors. We establish that within our chosen asymptotic framework, the multiple testing rules under study asymptotically attain the risk of the Bayes Oracle up to a multiplicative factor, with the constant in the risk close to the constant in the Oracle risk. This is similar to a result obtained in Datta and Ghosh (2013) for the multiple testing rule based on the horseshoe estimator introduced in Carvalho et al. (2009, 2010). We further show that under very mild assumption on the underlying sparsity parameter, the induced decision rules based on an empirical Bayes estimate of the corresponding global shrinkage parameter proposed by van der Pas et al. (2014), attain the optimal Bayes risk up to the same multiplicative factor asymptotically. We provide a unifying argument applicable for the general class of priors under study. In the process, we settle a conjecture regarding optimality property of the generalized double Pareto priors made in Datta and Ghosh (2013). Our work also shows that the result in Datta and Ghosh (2013) can be improved further

Probing pH-triggered self-assembling peptide based tumor imaging contrast agents in blood serum

Poster Division: Engineering, Math, and Physical Sciences: 1st Place (The Ohio State University Edward F. Hayes Graduate Research Forum)Early detection and imaging of cancer is challenging because most of the detection methods are based on specific biomarkers that are heterogeneously expressed on cancer cells leading to missed detection when the receptor is or becomes absent. Developing targeted imaging pharmaceuticals that localize via one of cancer’s broad hallmarks rather than a specific biomarker can have a direct impact on decreasing the number of cancer related deaths. One particularly attractive hallmark target is the acidic extracellular microenvironment of tumor tissue (pHe 6.6−7.4) that arises due to the enhanced rate of glycolysis found in most cancer cells. Creating a material that is nano-sized in blood, but upon reaching the acidic extracellular tumor environment, transforms into a bulky, micro-sized, more slowly diffusing object could serve as a novel mechanism for achieving high accumulation of imaging, drug delivery, or radiotherapeutic agents at the tumor site compared to the bloodstream. Especially for tumors, the heterogeneous matrix and high interstitial fluid pressure should govern blood-tumor diffusion of nano- and micro-particles dependent on their size. Here, we have designed and synthesized self-assembling peptide amphiphile (PA) molecules that transform from isolated molecules or spherical micelles into nanofibers (several microns in length) when the pH is slightly reduced from 7.4 to 6.6, in isotonic salt solutions that simulate the acidic extracellular microenvironment (pHe) of malignant tumor tissue. Our PA molecules consist of four main segments: a hydrophobic tail, a β-sheet-forming peptide sequence, a charged amino acid sequence and a DO3A-Gd Magnetic Resonance imaging (MRI) moiety. The PAs were synthesized via the solid phase technique using Fmoc chemistry, purified by Reverse-phase High Performance Liquid Chromatography (HPLC) and characterized by Mass Spectrometry, analytical HPLC and peptide content analyses. Circular Dichroism spectroscopy, Critical Micellar Concentration measurements and Transmission Electron Microscopy were used to characterize the transition and map a concentration-pH phase diagram. MRI measurements were done to calculate relaxivity values of water protons in presence of the PA and compare the same with a standard control. Finally, Fluorescence Anisotropy (FA) was used to probe self assembly in blood serum. After extensive structure optimization, the particular sequence/molecule Palmitoyl-IAAAEEEEK(DO3A-Gd) was found to transition at pH values closest to our desired physiological conditions. Relaxivity values of water protons in the presence of the PA at pH of 4 (nanofibers) and 10 (nanospheres), were found to be 8.3 and 6.6 mM−1 s−1, respectively. These values were higher than those measured for a Magnevist control standard (4.5 mM−1 s−1) as predicted. Blood serum was found to significantly facilitate formation of the larger fibers as indicated via pH dependent FA measurements. The transition was found to be rapid and reversible in both buffer and serum, indicating the system is in thermodynamic equilibrium.No embarg