The Large Deviation Principle and Steady-state Fluctuation Theorem for the Entropy Production Rate of a Stochastic Process in Magnetic Fields

Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes have not been rigorously proved yet due to technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Lo\'{e}ve expansion of complex-valued Ornstein-Uhlenbeck process

Non-integrable stable approximation by Stein's method

We develop Stein's method for $\alpha$-stable approximation with $\alpha\in(0,1]$, continuing the recent line of research by Xu \cite{lihu} and Chen, Nourdin and Xu \cite{C-N-X} in the case $\alpha\in(1,2).$ The main results include an intrinsic upper bound for the error of the approximation in a variant of Wasserstein distance that involves the characterizing differential operators for stable distributions, and an application to the generalized central limit theorem. Due to the lack of first moment for the approximating sequence in the latter result, we appeal to an additional truncation procedure and investigate fine regularity properties of the solution to Stein's equation

The Locality and Symmetry of Positional Encodings

Positional Encodings (PEs) are used to inject word-order information into transformer-based language models. While they can significantly enhance the quality of sentence representations, their specific contribution to language models is not fully understood, especially given recent findings that various positional encodings are insensitive to word order. In this work, we conduct a systematic study of positional encodings in \textbf{Bidirectional Masked Language Models} (BERT-style) , which complements existing work in three aspects: (1) We uncover the core function of PEs by identifying two common properties, Locality and Symmetry; (2) We show that the two properties are closely correlated with the performances of downstream tasks; (3) We quantify the weakness of current PEs by introducing two new probing tasks, on which current PEs perform poorly. We believe that these results are the basis for developing better PEs for transformer-based language models. The code is available at \faGithub~ \url{https://github.com/tigerchen52/locality\_symmetry}Comment: Long Paper in Findings of EMNLP2

Simulation and pilot plant measurement for CO2 absorption with mixed amines

AbstractCO2 solubility in an aqueous tertiary amine solution was measured, and thermodynamic models Kent-Eisenberg and Clegg-Pitzer were used to correlate CO2 solubility. Process simulation was also carried out with these models, and simulation results are compared with pilot plant measurement data. The results show that the mixed amine solution of the tertiary amine with MEA could save regeneration energy about 20% compared with 30% MEA aqueous solution

Multivariate stable approximation in Wasserstein distance by Stein's method

We investigate regularity properties of the solution to Stein's equation associated with multivariate integrable $\alpha$-stable distribution for a general class of spectral measures and Lipschitz test functions. The obtained estimates induce an upper bound in Wasserstein distance for the multivariate $\alpha$-stable approximation

Conserved RNA-binding specificity of polycomb repressive complex 2 is achieved by dispersed amino acid patches in EZH2.

Polycomb repressive complex 2 (PRC2) is a key chromatin modifier responsible for methylation of lysine 27 in histone H3. PRC2 has been shown to interact with thousands of RNA species in vivo, but understanding the physiological function of RNA binding has been hampered by the lack of separation-of-function mutants. Here, we use comprehensive mutagenesis and hydrogen deuterium exchange mass spectrometry (HDX-MS) to identify critical residues for RNA interaction in PRC2 core complexes fro

Irreducibility and Asymptotics of Stochastic Burgers Equation Driven by α-stable Processes

The irreducibility, moderate deviation principle and $\psi$-uniformly exponential ergodicity with $\psi(x):=1+\|x\|_0$ are proved for stochastic Burgers equation driven by the $\aa$-stable processes for $\aa\in (1,2),$ where the first two are new for the present model, and the last strengthens the exponential ergodicity under total variational norm derived in \cite{Do-Xu-Zh-14}