Laboratoire Paul Painlevé

Correction for 'Reversible and reusable compartmentalized thermoplastic chip for coculture of dorsal root ganglion neurons' by Solène Moreau et al., Lab Chip, 2025, 25, 6741-6755, https://doi.org/10.1039/d5lc00666j.

Abstract Quantum technology advances crucially depend on the scaling up of essential quantum resources. Their ideal multiplexing offers more significant gains in applications; however, the scaling of the nonidentical, fragile and varying resources is neither theoretically nor experimentally known. For bosonic systems, multimode interference is an essential tool already widely exploited to develop quantum technology. Here, we analyze, predict and compare essential scaling laws for a constructive interference of multiplexed nonclassical Gaussian states carrying information by displacement with weakly fluctuating squeezing in different multimode interference architectures. The signal-to-noise ratio quantifies the increase in displacement relative to the noise. We introduce the gain-toinstability ratio to numerically estimate the effect of unexplored resource instabilities in a large scale interference scheme. The use of the gain-to-instability ratio to quantify the scaling laws opens steps for extensive theoretical investigation of other bosonic resources and follow-up feasible experimental verification necessary for further development of these platforms.

Abstract We prove a joint value equidistribution statement for Hecke–Maaß cusp forms on the hyperbolic three‐space . This supports the conjectural statistical independence of orthogonal cusp forms.

For every $n\ge 2$, we construct a body $U_n$ of constant width $2$ in $\mathbb{E}^n$ with small volume and symmetries of a regular $n$-simplex. $U_2$ is the Reuleaux triangle. To the best of our knowledge, $U_3$ was not previously constructed, and its volume is smaller than the volume of other three-dimensional bodies of constant width with tetrahedral symmetries. While the volume of $U_3$ is slightly larger than the volume of Meissner's bodies of width $2$, it exceeds the latter by less than $0.137\%$. For all large $n$, the volume of $U_n$ is smaller than the volume of the ball of radius $0.891$.

Abstract We show that Lasso and Bayesian Lasso are very close when the sparsity is large and the noise is small. We propose to solve Bayesian Lasso using multivalued stochastic differential equation. We derive four discretization algorithms, and present highly efficient multilevel Monte Carlo (MLMC) simulations. Additionally, we perform a numerical comparison of the Monte Carlo (MC), MLMC and proximal Markov chain Monte Carlo algorithm (PMALA).