Assessment of the differential entropy of random vectors

Hereby, the features of assessment of differential realization of random vectors for practical use are considered. The question of the stability of the assessment procedure for the presence of anomalous observations in the samples was investigated. The possibility of using differential entropy for samples of random vectors is considered, some components of which are presented in grouped form as discrete quantities. Examples are given of differential entropy assessment with the help of the proposed algorithms.Рассмотрены особенности оценивания дифференциальной реализации случайных векторов для практического использования. Исследован вопрос устойчивости процедуры оценивания к присутствию в выборках аномальных наблюдений. Рассмотрена возможность использования дифференциальной энтропии для выборок случайных векторов, некоторые компоненты которых представлены в сгруппированном виде как дискретные величины. Приведены примеры оценивания дифференциальной энтропии с помощью предложенных алгоритмов.Исследование выполнено при поддержке РФФИ, грант № 17-01-00315а

Three-photon states in nonlinear crystal superlattices

It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly, photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider scheme that involves two parametric processes: $\omega_{0}\rightarrow\omega_{1}+\omega_{2}$, $\omega_{2}\rightarrow\omega_{1}+\omega_{1}$ under pulsed pump and investigate spontaneous creation of photon triplet as well as generation of high-intensity mode in intracavity three-photon splitting. We show preparation of Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II and type-I PDC in framework of consideration dual-grid structure that involves two periodically-poled crystals. We demonstrate the method of compensation of the dispersive effects in non-linear segments by appropriately chosen linear dispersive segments of superlattice for preparation heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on investigation of photon-number distributions, third-order photon-number correlation function as well as the Wigner functions. These quantities are observed both for short interaction time intervals and in over transient regime, when dissipative effects are essential.Comment: 15 pages, 6 figure

Thermal (in)stability of type I collagen fibrils

We measured Young's modulus at temperatures ranging from 20 to 100 ^{\circ}$C for a collagen fibril taken from rat's tendon. The hydration change under heating and the damping decrement were measured as well. At physiological temperatures$25-45^{\circ}$C Young's modulus decreases, which can be interpreted as instability of collagen. For temperatures between$45-80^{\circ}$C Young's modulus first stabilizes and then increases with decreasing the temperature. The hydrated water content and the damping decrement have strong maxima in the interval$70-80^{\circ}$C indicating on complex inter-molecular structural changes in the fibril. All these effects disappear after heat-denaturating the sample at$120^\circ$C. Our main result is a five-stage mechanism by which the instability of a single collagen at physiological temperatures is compensated by the interaction between collagen molecules within the fibril.Comment: 4 pages, 4 figure

The HPS electromagnetic calorimeter

The Heavy Photon Search experiment (HPS) is searching for a new gauge boson, the so-called “heavy photon.” Through its kinetic mixing with the Standard Model photon, this particle could decay into an electron-positron pair. It would then be detectable as a narrow peak in the invariant mass spectrum of such pairs, or, depending on its lifetime, by a decay downstream of the production target. The HPS experiment is installed in Hall-B of Jefferson Lab. This article presents the design and performance of one of the two detectors of the experiment, the electromagnetic calorimeter, during the runs performed in 2015–2016. The calorimeter's main purpose is to provide a fast trigger and reduce the copious background from electromagnetic processes through matching with a tracking detector. The detector is a homogeneous calorimeter, made of 442 lead-tungstate (PbWO4) scintillating crystals, each read out by an avalanche photodiode coupled to a custom trans-impedance amplifier