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

Моральна свідомість та релігійна віра в перспективі філософії Іммануїла Канта

У статті розкриваються головні ідеї та логічна структура філософії релігії Іммануїла Канта у її зв’язку з практичною філософією. Обґрунтовано тезу про те, що розуміння Кантом головних релігійних ідей – особистого безсмертя та Бога − було дуже неортодоксальним і наближає його філософію до індійської релігійно-філософської традиції.В статье раскрываются главные идеи и логическая структура философии религии Иммануила Канта в связи с его практической философией. Обосновывается тезис о том, что понимание Кантом главных религиозных идей – личного бессмертия и Бога − было очень неортодоксальным и сближает его философию с индийской религиозно-философской традицией.The article explains main ideas and logical structure of Immanuel Kant’s philosophy of religion in its connection with practical philosophy. It argues that Kant’s views of main religious ideas – personal immortality and God − were very unorthodox and congenial with Indian religious-philosophical tradition

Box traps on an atom chip for one-dimensional quantum gases

We present the implementation of tailored trapping potentials for ultracold gases on an atom chip. We realize highly elongated traps with box-like confinement along the long, axial direction combined with conventional harmonic confinement along the two radial directions. The design, fabrication and characterization of the atom chip and the box traps is described. We load ultracold ($\lesssim1 \mu$K) clouds of $^{87}$Rb in a box trap, and demonstrate Bose-gas focusing as a means to characterize these atomic clouds in arbitrarily shaped potentials. Our results show that box-like axial potentials on atom chips are very promising for studies of one-dimensional quantum gases.Comment: 9 pages 4 figure

Three-dimensional character of atom-chip-based rf-dressed potentials

We experimentally investigate the properties of radio-frequency-dressed potentials for Bose-Einstein condensates on atom chips. The three-dimensional potential forms a connected pair of parallel waveguides. We show that rf-dressed potentials are robust against the effect of small magnetic-field variations on the trap potential. Long-lived dipole oscillations of condensates induced in the rf-dressed potentials can be tuned to a remarkably low damping rate. We study a beam-splitter for Bose-Einstein condensates and show that a propagating condensate can be dynamically split in two vertically separated parts and guided along two paths. The effect of gravity on the potential can be tuned and compensated for using a rf-field gradient.Comment: 9 pages, 7 figure

Two-dimensional spatiotemporal monitoring of temperature in photothermal therapy using hybrid photoacoustic-ultrasound transmission tomography

Recently, we presented an add-on to a photoacoustic (PA) computed tomography imager that permits the simultaneous imaging of ultrasound (US) transmission parameters such as the speed of sound (SOS), without additional measurements or instruments. This method uses strong absorbers positioned outside the object in the path of light for producing laser-induced US to interrogate the object in a conventional PA imager. Here, we investigate the feasibility of using this approach, first with PA to pin-point the location of photothermal therapeutic agents and then with serial SOS tomograms to image and monitor the resulting local temperature changes when the agents are excited with continuous wave (CW) light. As the object we used an agar-based tissue-mimicking cylinder carrying beads embedded with different concentrations of gold nanospheres. PA and SOS tomograms were simultaneously acquired as the gold nanospheres were photothermally heated using a 532-nm CW laser. In a first approximation, using the relation between SOS of water and temperature, the SOS tomograms were converted into temperature maps. The experimental results were verified using simulations: Monte Carlo modeling of light propagation through a turbid medium and using the obtained absorbed energy densities in heat diffusion modeling for spatial temperature distributio

Yang-Yang thermodynamics on an atom chip

We investigate the behavior of a weakly interacting nearly one-dimensional (1D) trapped Bose gas at finite temperature. We perform in situ measurements of spatial density profiles and show that they are very well described by a model based on exact solutions obtained using the Yang-Yang thermodynamic formalism, in a regime where other, approximate theoretical approaches fail. We use Bose-gas focusing [Shvarchuck etal., Phys. Rev. Lett. 89, 270404 (2002)] to probe the axial momentum distribution of the gas, and find good agreement with the in situ results.Comment: extended introduction and conclusions, and minor changes throughout; accepted for publication in Phys. Rev. Let

Конституційно-правова природа Ради Міністрів Автономної Республіки Крим: дискусійні питання теорії та практики

У статті розкриваються особливості конституційно-правової природи Ради міністрів Автономної Республіки Крим. Показане місце Ради міністрів Автономної Республіки Крим серед інших органів публічної влади. Ключові слова: Рада міністрів Автономної Республіки Крим, Автономна Республіка Крим, уряд, автономія.В статье раскрываются особенности конституционно-правовой природы Совета министров Автономной Республики Крым. Показано место Совета министров Автономной Республики Крым среди других органов публичной власти. Ключевые слова: Совет министров Автономной Республики Крым, Автономная Республика Крым, правительство, автономия.In the article the features of constitutional and legal status of the Rada of Ministry of the Autonomous Republic of Crimea are analyzed. The place of the Rada of Ministry of the Autonomous Republic of Crimea between others organs of public power is defined. Key words: the Rada of Ministry of the Autonomous Republic of Crimea, the Autonomous Republic of Crimea, government, autonomy

The percutaneous assessment of regional and acute coronary hot unstable plaques by thermographic evaluation (PARACHUTE) study: A prospective reproducibility and prognostic clinical study using thermography to predict future ischemic cardiac events

Intravascular thermography is currently being considered as a valuable tool in assessing macrophage-rich plaques. Since it is unknown what the prognostic value is of non-obstructive atherosclerotic plaques showing temperature heterogeneity, we designed the PARACHUTE study, a prospective, reproducibility, and prognostic clinical study using thermography in patients presenting with an unstable coronary syndrome. The primary endpoint of the study is the predictive value of temperature heterogeneity towards the occurrence of ischemic coronary events and hospitalization for ischemia and/or angina. The secondary endpoints are the predictive value of high-risk plaques associated with the development of future cardiac events, assessmen

Thermoluminescence of zircon: a kinetic model

The mineral zircon, ZrSiO4, belongs to a class of promising materials for geochronometry by means of thermoluminescence (TL) dating. The development of a reliable and reproducible method for TL dating with zircon requires detailed knowledge of the processes taking place during exposure to ionizing radiation, long-term storage, annealing at moderate temperatures and heating at a constant rate (TL measurements). To understand these processes one needs a kinetic model of TL. This paper is devoted to the construction of such amodel. The goal is to study the qualitative behaviour of the system and to determine the parameters and processes controlling TL phenomena of zircon. The model considers the following processes: (i) Filling of electron and hole traps at the excitation stage as a function of the dose rate and the dose for both (low dose rate) natural and (high dose rate) laboratory irradiation. (ii) Time dependence of TL fading in samples irradiated under laboratory conditions. (iii) Short time annealing at a given temperature. (iv) Heating of the irradiated sample to simulate TL experiments both after laboratory and natural irradiation. The input parameters of the model, such as the types and concentrations of the TL centres and the energy distributions of the hole and electron traps, were obtained by analysing the experimental data on fading of the TL-emission spectra of samples from different geological locations. Electron paramagnetic resonance (EPR) data were used to establish the nature of the TL centres. Glow curves and 3D TL emission spectra are simulated and compared with the experimental data on time-dependent TL fading. The saturation and annealing behaviour of filled trap concentrations has been considered in the framework of the proposed kinetic model and comparedwith the EPR data associated with the rare-earth ions Tb3+ and Dy3+, which play a crucial role as hole traps and recombination centres. Inaddition, the behaviour of some of the SiOmn− centres has been compared with simulation results.