Comparison of Perron and Floquet eigenvalues in age structured cell division cycle models

We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted circadian clocks, known to exert their influence on the cell division cycle. We compare the growth rate of the model controlled by a time-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged coefficients. We firstly derive a delay differential equation which allows us to prove several inequalities and equalities on the growth rates. We also discuss about the necessity to take into account the structure of the cell division cycle for chronotherapy modeling. Numerical simulations illustrate the results.Comment: 26 page

MUSE observations of comet 67P/Churyumov-Gerasimenko:A reference for future comet observations with MUSE

Observations of comet 67P/Churyumov-Gerasimenko were performed with MUSE at large heliocentric distances post-perihelion, between March 3 and 7, 2016. Those observations were part of a simultaneous ground-based campaign aimed at providing large-scale information about comet 67P that complement the ESA/Rosetta mission. We obtained a total of 38 datacubes over 5 nights. We take advantage of the integral field unit (IFU) nature of the instrument to study simultaneously the spectrum of 67P's dust and its spatial distribution in the coma. We also look for evidence of gas emission in the coma. We produce a high quality spectrum of the dust coma over the optical range that could be used as a reference for future comet observations with the instrument. The slope of the dust reflectivity is of 10%$/100$ nm over the 480-900 nm interval, with a shallower slope towards redder wavelengths. We use the $\mathrm{Af\rho}$ to quantify the dust production and measure values of 65$\pm$4 cm, 75$\pm$4 cm, and 82$\pm$4 cm in the V, R, and I bands respectively. We detect several jets in the coma, as well as the dust trail. Finally, using a novel method combining spectral and spatial information, we detect the forbidden oxygen emission line at 630 nm. Using this line we derive a water production rate of $1.5\pm0.6 \times 10^{26} \mathrm{molec./s}$, assuming all oxygen atoms come from the photo-dissociation of water.Comment: Accepted for publication in Astronomy and Astrophysic

Characterization of the Subsurface of 67P/Churyumov-Gerasimenko's Abydos Site

We investigate the structure of the subsurface of the Abydos site using a cometary nucleus model with parameters adapted to comet 67P/Churyumov-Gerasimenko and the Abydos landing site. We aim to compare the production rates derived from our model with those of the main molecules measured by Ptolemy. This will allow us to retrieve the depths at which the different molecules still exist in solid form

High-fidelity CCRZ(ϕ)CCR_Z(\phi) gates via RF-induced F\"{o}rster resonances

Registers of trapped neutral atoms, excited to Rydberg states to induce strong long-distance interactions, are extensively studied for direct applications in quantum computing. In this regard, new effective approaches to the creation of multiqubit quantum gates arise high interest. Here, we present a novel gate implementation technique based on RF-induced few-body F\"{o}rster resonances. External radio frequency (RF) control field allows us to manipulate the phase and population dynamics of many-atom system, thus enabling the realization of universal $CCR_{Z}(\phi)$ quantum gates. We numerically demonstrate RF-induced resonant interactions, as well as high-precision three-qubit gates. The extreme controllability of interactions provided by RF makes it possible to implement gates for a wide range of parameters of the atomic system, and significantly facilitates their experimental implementation. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction ($\sim 99.7\%$) using reasonable experimental parameters.Comment: 6 pages, 3 figures, 1 tabl

Exploring out-of-equilibrium quantum magnetism and thermalization in a spin-3 many-body dipolar lattice system

Understanding quantum thermalization through entanglement build-up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 spins prepared in a pure coherent spin state, tilted compared to the magnetic field, under the effect of magnetic dipole-dipole interactions. The experiment uses a unit filled array of 104 chromium atoms in a three dimensional optical lattice, realizing the spin-3 XXZ Heisenberg model. The buildup of quantum correlation during the dynamics, especially as the angle approaches pi/2, is supported by comparison with an improved numerical quantum phase-space method and further confirmed by the observation that our isolated system thermalizes under its own dynamics, reaching a steady state consistent with the one extracted from a thermal ensemble with a temperature dictated from the system's energy. This indicates a scenario of quantum thermalization which is tied to the growth of entanglement entropy. Although direct experimental measurements of the Renyi entropy in our macroscopic system are unfeasible, the excellent agreement with the theory, which can compute this entropy, does indicate entanglement build-up.Comment: 12 figure

Evolution of the subsurface of 67P/Churyumov-Gerasimenko’s Abydos Site

On November 12, 2014, Rosetta's descent module Philae landed on the Abydos site of comet 67P/Churyumov-Gerasimenko (67P). Here we investigate the structure of the subsurface of the Abydos site by making use of a cometary nucleus model [1] employing an updated set of thermodynamic parameters relevant for 67P and an appropriated parameterization of the illumination of the Abydos site. The model considers an initially homogeneous sphere composed of a predefined porous mixture of crystalline ices (H2O, CO and CO2) and dust in specified proportions, and uses parameters derived from recent 67P studies [2], [3] and [4]. The comparison of the production rates derived from our model with those of the main molecules measured by Ptolemy (the mass spectrometer performing the analysis of several samples collected from the surface and atmosphere of the comet) should allow us to place important constraints on the structure (layering and composition) of the subsurface of Philae’s landing site

Entrepreneurs’ age, institutions, and social value creation goals: a multi-country study

This study explores the relationship between an entrepreneur's age and his/her social value creation goals. Building on the lifespan developmental psychology literature and institutional theory, we hypothesize a U-shaped relationship between entrepreneurs’ age and their choice to create social value through their ventures, such that younger and older entrepreneurs create more social value with their businesses while middle age entrepreneurs are relatively more economically and less socially oriented with their ventures. We further hypothesize that the quality of a country’s formal institutions in terms of economic, social, and political freedom steepen the U-shaped relationship between entrepreneurs’ age and their choice to pursue social value creation as supportive institutional environments allow entrepreneurs to follow their age-based preferences. We confirm our predictions using multilevel mixed-effects linear regressions on a sample of over 15,000 entrepreneurs (aged between 18 and 64 years) in 45 countries from Global Entrepreneurship Monitor data. The findings are robust to several alternative specifications. Based on our findings, we discuss implications for theory and practice, and we propose future research directions

Non-local double-path Casimir phase in atom interferometers

We present a quantum open system theory of atom interferometers evolving in the quantized electromagnetic field bounded by an ideal conductor. Our treatment reveals an unprecedented feature of matter-wave propagation, namely the appearance of a non-local double-path phase coherence. Such a non-local phase arises from the coarse-graining over the quantized electromagnetic field and internal atomic degrees of freedom, yielding a non-Hamiltonian evolution of the atomic waves moving in presence of correlated quantum dipole and field fluctuations. We develop a diagrammatic interpretation of this phase, and estimate it for realistic experimental parameters.Comment: 5 pages, 1 figure. Final version, published in the Europhysics Letter

The Classical Harmonic Vibrations of the Atomic Centers of Mass with Micro Amplitudes and Low Frequencies Monitored by the Entanglement between the Two Two-level Atoms in a Single mode Cavity

We study the entanglement dynamics of the two two-level atoms coupling with a single-mode polarized cavity field after incorporating the atomic centers of mass classical harmonic vibrations with micro amplitudes and low frequencies. We propose a quantitative vibrant factor to modify the concurrence of the two atoms states. When the vibrant frequencies are very low, we obtain that: (i) the factor depends on the relative vibrant displacements and the initial phases rather than the absolute amplitudes, and reduces the concurrence to three orders of magnitude; (ii) the concurrence increases with the increase of the initial phases; (iii) the frequency of the harmonic vibration can be obtained by measuring the maximal value of the concurrence during a small time. These results indicate that even the extremely weak classical harmonic vibrations can be monitored by the entanglement of quantum states.Comment: 10 pages, 3 figure