A Bayesian approach to the estimation of maps between riemannian manifolds

Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of the map \gamma we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces \Theta and \Lambda, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of \gamma is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s 31, 41, 4

Formulation and Validation of Nanoparticle Controlled Delivery for Chemotherapeutic Drug Products

Taxol, a formulation of paclitaxel (PTX), is one of the most widely used anticancer drugs, particularly for treating recurring ovarian carcinomas following surgery. Clinically, PTX is used in combination with other drugs such as lapatinib (LAP) to increase treatment efficacy. Delivering drug combinations with nanoparticles has the potential to improve chemotherapy outcomes. In this study, we use Flash NanoPrecipitation, a rapid, scalable process to encapsulate weakly hydrophobic drugs (logP in vitro. Encapsulating either PTX or LAP into nanoparticles increases drug potency. When PTX and LAP are co-loaded in the same nanoparticle, they have a synergistic effect that is greater than treating with two single-drug loaded nanoparticles. Furthermore, we examined in vitro sequential delivery of PTX and LAP encapsulated into polymer nanoparticles on ovarian cancer cells. We observed a sequence-dependent cytotoxic effect. These results are promising for establishing sequential drug delivery with nanoparticles as a method for treating ovarian cancer. Building on this work, we demonstrated the potential of encapsulating a hydrophobic PTX prodrug into pH-responsive nanoparticles as a method to enhance drug efficacy and control drug release. Overall, these findings provide the foundation for developing co-encapsulated nanoparticles with controlled drug release as well as methods for improving the drug efficacy of PTX

Rapid Self-Assembly of Polymer Nanoparticles for Synergistic Codelivery of Paclitaxel and Lapatinib Via Flash Nanoprecipitation

Taxol, a formulation of paclitaxel (PTX), is one of the most widely used anticancer drugs, particularly for treating recurring ovarian carcinomas following surgery. Clinically, PTX is used in combination with other drugs such as lapatinib (LAP) to increase treatment efficacy. Delivering drug combinations with nanoparticles has the potential to improve chemotherapy outcomes. In this study, we use Flash NanoPrecipitation, a rapid, scalable process to encapsulate weakly hydrophobic drugs (logP \u3c 6) PTX and LAP into polymer nanoparticles with a coordination complex of tannic acid and iron formed during the mixing process. We determine the formulation parameters required to achieve uniform nanoparticles and evaluate the drug release in vitro. The size of the resulting nanoparticles was stable at pH 7.4, facilitating sustained drug release via first-order Fickian diffusion. Encapsulating either PTX or LAP into nanoparticles increases drug potency (as indicated by the decrease in IC-50 concentration); we observe a 1500-fold increase in PTX potency and a six-fold increase in LAP potency. When PTX and LAP are co-loaded in the same nanoparticle, they have a synergistic effect that is greater than treating with two single-drug-loaded nanoparticles as the combination index is 0.23 compared to 0.40, respectively

Semiclassical treatment of fusion processes in collisions of weakly bound nuclei

We describe a semiclassical treatment of nuclear fusion reactions involving weakly bound nuclei. In this treatment, the complete fusion probabilities are approximated by products of two factors: a tunneling probability and the probability that the system is in its ground state at the strong absorption radius. We investigate the validity of the method in a schematic two-channel application, where the channels in the continuum are represented by a single resonant state. Comparisons with full coupled-channels calculations are performed. The agreement between semiclassical and quantal calculations isquite good, suggesting that the procedure may be extended to more sophisticated discretizations of the continuum.Comment: 11 pages, 5 figure

Rapid, Single-Step Protein Encapsulation via Flash NanoPrecipitation

Flash NanoPrecipitation (FNP) is a rapid method for encapsulating hydrophobic materials in polymer nanoparticles with high loading capacity. Encapsulating biologics such as proteins remains a challenge due to their low hydrophobicity (logP \u3c 6) and current methods require multiple processing steps. In this work, we report rapid, single-step protein encapsulation via FNP using bovine serum albumin (BSA) as a model protein. Nanoparticle formation involves complexation and precipitation of protein with tannic acid and stabilization with a cationic polyelectrolyte. Nanoparticle self-assembly is driven by hydrogen bonding and electrostatic interactions. Using this approach, high encapsulation efficiency (up to ~80%) of protein can be achieved. The resulting nanoparticles are stable at physiological pH and ionic strength. Overall, FNP is a rapid, efficient platform for encapsulating proteins for various applications

Low temperature dielectric relaxation in ordinary perovskite ferroelectrics: enlightenment from high-energy x-ray diffraction

Ordinary ferroelectrics exhibit a second order phase transition that is characterized by a sharp peak in the dielectric permittivity at a frequency-independent temperature. Furthermore, these materials show a low temperature dielectric relaxation that appears to be a common behavior of perovskite systems. Tetragonal lead zirconate titanate is used here as a model system in order to explore the origin of such an anomaly, since there is no consensus about the physical phenomenon involved in it. Crystallographic and domain structure studies are performed from temperature dependent synchrotron x-ray diffraction measurement. Results indicate that the dielectric relaxation cannot be associated with crystallographic or domain configuration changes. The relaxation process is then parameterized by using the Vogel–Fulcher–Tammann phenomenological equation. Results allow us to hypothesize that the observed phenomenon is due to changes in the dynamic behavior of the ferroelectric domains related to the fluctuation of the local polarization.Postprint (author's final draft

Egoism and Altruism: the "Antagonists" or the "Brothers"?

The article under consideration deals with the theoretical analysis and the practical research of the ratio between the two notions: egoism and altruism. The author shows the inadequacy of the one-sided, morally loaded interpretations of both terms. The scores of two ESM-investigations mostly show the positive correlation between the "egoism" and the "altruism" scales in a person's everyday activity. The results obtained give the opportunity to replace the inadequate view on egoism and altruism as opposites by a more appropriate metaphor of the older and the younger brother. Such an approach removes the idea of antagonism which is usually ascribed to the egoism-altruism interrelation

Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

Coherent optical control of correlation waves of spins in semiconductors

We calculate the dynamical fluctuation spectrum of electronic spins in a semiconductor under a steady-state illumination by light containing polarization squeezing correlations. Taking into account quasi-particle lifetime and spin relaxation for this non-equilibrium situation we consider up to fourth order optical effects which are sensitive to the squeezing phases. We demonstrate the possibility to control the spin fluctuations by optically modulating these phases as a function of frequency, leading to a non-Lorentzian spectrum which is very different from the thermal equilibrium fluctuations in n-doped semiconductors. Specifically, in the time-domain spin-spin correlation can exhibit time delays and sign flips originating from the phase modulations and correlations of polarizations, respectively. For higher light intensity we expect a regime where the squeezing correlations will dominate the spectrum.Comment: 17 pages, 8 figure