Pointwise Behavior of the Linearized Boltzmann Equation on Torus

We study the pointwise behavior of the linearized Boltzmann equation on torus for non-smooth initial perturbation. The result reveals both the fluid and kinetic aspects of this model. The fluid-like waves are constructed as part of the long-wave expansion in the spectrum of the Fourier mode for the space variable, the time decay rate of the fluid-like waves depends on the size of the domain. We design a Picard-type iteration for constructing the increasingly regular kinetic-like waves, which are carried by the transport equations and have exponential time decay rate. Moreover, the mixture lemma plays an important role in constructing the kinetic-like waves, we supply a new proof of this lemma to avoid constructing explicit solution of the damped transport equation

Mutations in the PKM2 exon-10 region are associated with reduced allostery and increased nuclear translocation.

PKM2 is a key metabolic enzyme central to glucose metabolism and energy expenditure. Multiple stimuli regulate PKM2's activity through allosteric modulation and post-translational modifications. Furthermore, PKM2 can partner with KDM8, an oncogenic demethylase and enter the nucleus to serve as a HIF1α co-activator. Yet, the mechanistic basis of the exon-10 region in allosteric regulation and nuclear translocation remains unclear. Here, we determined the crystal structures and kinetic coupling constants of exon-10 tumor-related mutants (H391Y and R399E), showing altered structural plasticity and reduced allostery. Immunoprecipitation analysis revealed increased interaction with KDM8 for H391Y, R399E, and G415R. We also found a higher degree of HIF1α-mediated transactivation activity, particularly in the presence of KDM8. Furthermore, overexpression of PKM2 mutants significantly elevated cell growth and migration. Together, PKM2 exon-10 mutations lead to structure-allostery alterations and increased nuclear functions mediated by KDM8 in breast cancer cells. Targeting the PKM2-KDM8 complex may provide a potential therapeutic intervention

Embrace Divergence for Richer Insights: A Multi-document Summarization Benchmark and a Case Study on Summarizing Diverse Information from News Articles

Previous research in multi-document news summarization has typically concentrated on collating information that all sources agree upon. However, to our knowledge, the summarization of diverse information dispersed across multiple articles about an event has not been previously investigated. The latter imposes a different set of challenges for a summarization model. In this paper, we propose a new task of summarizing diverse information encountered in multiple news articles encompassing the same event. To facilitate this task, we outlined a data collection schema for identifying diverse information and curated a dataset named DiverseSumm. The dataset includes 245 news stories, with each story comprising 10 news articles and paired with a human-validated reference. Moreover, we conducted a comprehensive analysis to pinpoint the position and verbosity biases when utilizing Large Language Model (LLM)-based metrics for evaluating the coverage and faithfulness of the summaries, as well as their correlation with human assessments. We applied our findings to study how LLMs summarize multiple news articles by analyzing which type of diverse information LLMs are capable of identifying. Our analyses suggest that despite the extraordinary capabilities of LLMs in single-document summarization, the proposed task remains a complex challenge for them mainly due to their limited coverage, with GPT-4 only able to cover less than 40% of the diverse information on average