Robust Bayes-Like Estimation: Rho-Bayes estimation

We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference measure, we consider a density model $\overline S$ for $s$ that we endow with a prior distribution $\pi$ (with support $\overline S$) and we build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around $s$ whenever it belongs to the model $\overline S$. Furthermore, in density estimation, the Hellinger distance between the classical and the robust posterior distributions tends to 0, as the number of observations tends to infinity, under suitable assumptions on the model and the prior, provided that the model $\overline S$ contains the true density $s$. However, unlike what happens with the classical Bayes posterior distribution, we show that the concentration properties of this new posterior distribution are still preserved in the case of a misspecification of the model, that is when $s$ does not belong to $\overline S$ but is close enough to it with respect to the Hellinger distance.Comment: 68 page

Coherent Anti-Stokes Raman Scattering Microspectroscopic Kinetic Study of Fast Hydrogen Bond Formation in Microfluidic Devices

The kinetics of a key noncovalent, hydrogen bonding interaction was studied in situ using coherent anti-stokes Raman scattering (CARS) microspectroscopy in a microfluidic device. The association of model compounds, pyridine and hexafluoroisopropanol, was quantitatively monitored with submicrometer resolution. Lower limits for the very high formation and dissociation rate constants of the model 1:1 pyridine–hexafluoroisopropanol hydrogen bonded complex in dichloromethane-<i>d</i>₂ were determined to be <i>k</i>₁ > 10⁵ M^–1s^–1 and <i>k</i>_–1 > 333.3 s^–1, respectively

Biocompatible Polylactide-<i>block</i>-Polypeptide-<i>block</i>-Polylactide Nanocarrier

Polypeptides are successfully incorporated into poly­(l-lactide) (PLLA) chains in a ring-opening polymerization (ROP) of l-lactide by using them as initiators. The resulting ABA triblock copolymers possess molecular weights up to 11000 g·mol^–1 and polydispersities as low as 1.13, indicating the living character of the polymerization process. In a nonaqueous emulsion, peptide-initiated polymerization of l-lactide leads to well-defined nanoparticles, consisting of PLLA-<i>block</i>-peptide-<i>block</i>-PLLA copolymer. These nanoparticles are easily loaded by dye-encapsulation and transferred into aqueous media without aggregation (average diameter of 100 nm) or significant dye leakage. Finally, internalization of PLLA-<i>block</i>-peptide-<i>block</i>-PLLA nanoparticles by HeLa cells is demonstrated by a combination of coherent anti-Stokes Raman spectroscopy (CARS) and fluorescence microscopy. This demonstrates the promise of their utilization as cargo delivery vehicles