Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition

Let $\{u(t\,, x)\}_{t >0, x \in\mathbb{R}}$ denote the solution to the parabolic Anderson model with initial condition $\delta_0$ and driven by space-time white noise on $\mathbb{R}_+\times\mathbb{R}$, and let $p_t(x):= (2\pi t)^{-1/2}\exp\{-x^2/(2t)\}$ denote the standard Gaussian heat kernel on the line. We use a non-trivial adaptation of the methods in our companion papers \cite{CKNP,CKNP_b} in order to prove that the random field $x\mapsto u(t\,,x)/p_t(x)$ is ergodic for every $t >0$. And we establish an associated quantitative central limit theorem following the approach based on the Malliavin-Stein method introduced in Huang, Nualart, and Viitasaari \cite{HNV2018}

1,2-Bis[5-(2,2′-dicyano­vinyl)-2-n-pentyl-3-thien­yl]-3,3,4,4,5,5-hexa­fluoro­cyclo­pent-1-ene: a new photochromic diaryl­ethene compound

The title compound, C31H26F6N4S2, is a new photochromic dithienylethene with dicyano­vinyl subsitituents. In the crystal structure, the mol­ecule adopts a photoactive anti­parallel conformation, with two n-pentyl groups located on opposite sides of the cyclo­pentene ring. The cyclo­pentene ring assumes an envelope conformation. The distance between the two reactive C atoms on the thio­phene rings is 3.834 (7) Å. One of the n-pentyl groups is disordered over two positions; the site occupancy factors are ca 0.7 and 0.3

Sudowoodo: a Chinese Lyric Imitation System with Source Lyrics

Lyrics generation is a well-known application in natural language generation research, with several previous studies focusing on generating accurate lyrics using precise control such as keywords, rhymes, etc. However, lyrics imitation, which involves writing new lyrics by imitating the style and content of the source lyrics, remains a challenging task due to the lack of a parallel corpus. In this paper, we introduce \textbf{\textit{Sudowoodo}}, a Chinese lyrics imitation system that can generate new lyrics based on the text of source lyrics. To address the issue of lacking a parallel training corpus for lyrics imitation, we propose a novel framework to construct a parallel corpus based on a keyword-based lyrics model from source lyrics. Then the pairs \textit{(new lyrics, source lyrics)} are used to train the lyrics imitation model. During the inference process, we utilize a post-processing module to filter and rank the generated lyrics, selecting the highest-quality ones. We incorporated audio information and aligned the lyrics with the audio to form the songs as a bonus. The human evaluation results show that our framework can perform better lyric imitation. Meanwhile, the \textit{Sudowoodo} system and demo video of the system is available at \href{https://Sudowoodo.apps-hp.danlu.netease.com/}{Sudowoodo} and \href{https://youtu.be/u5BBT_j1L5M}{https://youtu.be/u5BBT\_j1L5M}.Comment: 7 pages,3 figures, submit to emnlp 2023 demo trac

3-(4-{3,3,4,4,5,5-Hexafluoro-2-[5-(3-methoxy­phen­yl)-2-methyl-3-thien­yl]cyclo­pent-1-en­yl}-5-methyl-2-thien­yl)benzonitrile

The title compound, C29H19F6NOS2, is a new unsymmetrical photochromic diarylethene derivative with different meta-phenyl substituents. The distance between the two reactive (i.e. can be irradiated to form a new chemical bond) C atoms is 3.501 (4) Å; the dihedral angles between the mean plane of the main central cyclo­pentene ring and the thio­phene rings are 47.7 (5) and 45.1 (2)°, and those between the thio­phene rings and the adjacent benzene rings are 29.4 (2) and 28.4 (3)°. The three C atoms and the F atoms of hexa­fuorocyclo­pentene ring are disordered over two positions, with site-occupancy factors of 0.751 (4) and 0.249 (4)

Generation of entangled squeezed states in atomic Bose-Einstein condensates

A method for producing entangled squeezed states (ESSs) for atomic Bose-Einstein condensates (BECs) is proposed by using a BEC with three internal states and two classical laser beams. We show that it is possible to generate two-state and multi-state ESSs under certain circumstances.Comment: 6 pages, 1 figur