Deconvolution for an atomic distribution: rates of convergence

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are unobservable and that $Y=AV,$ where $A$ and $V$ are independent, $A$ has a Bernoulli distribution with probability of success equal to $1-p$ and $V$ has a distribution function $F$ with density $f.$ Let the random variable $Z$ have a known distribution with density $k.$ Based on a sample $X_1,...,X_n,$ we consider the problem of nonparametric estimation of the density $f$ and the probability $p.$ Our estimators of $f$ and $p$ are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of $f$ and $p$ we show that our estimators are rate-optimal in these cases.Comment: 27 page

Regulation of cargo transfer between ESCRT-0 and ESCRT-I complexes by flotillin-1 during endosomal sorting of ubiquitinated cargo

Ubiquitin-dependent sorting of membrane proteins in endosomes directs them to lysosomal degradation. In the case of receptors such as the epidermal growth factor receptor (EGFR), lysosomal degradation is important for the regulation of downstream signalling. Ubiquitinated proteins are recognised in endosomes by the endosomal sorting complexes required for transport (ESCRT) complexes, which sequentially interact with the ubiquitinated cargo. Although the role of each ESCRT complex in sorting is well established, it is not clear how the cargo is passed on from one ESCRT to the next. We here show that flotillin-1 is required for EGFR degradation, and that it interacts with the subunits of ESCRT-0 and -I complexes (hepatocyte growth factor-regulated tyrosine kinase substrate (Hrs) and Tsg101). Flotillin-1 is required for cargo recognition and sorting by ESCRT-0/Hrs and for its interaction with Tsg101. In addition, flotillin-1 is also required for the sorting of human immunodeficiency virus 1 Gag polyprotein, which mimics ESCRT-0 complex during viral assembly. We propose that flotillin-1 functions in cargo transfer between ESCRT-0 and -I complexes

Quantum mechanical Carnot engine

A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.Comment: 10 page