Solving a class of matrix minimization problems by linear variational inequality approaches

AbstractA class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg–Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising

Improving Factual Error Correction by Learning to Inject Factual Errors

Factual error correction (FEC) aims to revise factual errors in false claims with minimal editing, making them faithful to the provided evidence. This task is crucial for alleviating the hallucination problem encountered by large language models. Given the lack of paired data (i.e., false claims and their corresponding correct claims), existing methods typically adopt the mask-then-correct paradigm. This paradigm relies solely on unpaired false claims and correct claims, thus being referred to as distantly supervised methods. These methods require a masker to explicitly identify factual errors within false claims before revising with a corrector. However, the absence of paired data to train the masker makes accurately pinpointing factual errors within claims challenging. To mitigate this, we propose to improve FEC by Learning to Inject Factual Errors (LIFE), a three-step distantly supervised method: mask-corrupt-correct. Specifically, we first train a corruptor using the mask-then-corrupt procedure, allowing it to deliberately introduce factual errors into correct text. The corruptor is then applied to correct claims, generating a substantial amount of paired data. After that, we filter out low-quality data, and use the remaining data to train a corrector. Notably, our corrector does not require a masker, thus circumventing the bottleneck associated with explicit factual error identification. Our experiments on a public dataset verify the effectiveness of LIFE in two key aspects: Firstly, it outperforms the previous best-performing distantly supervised method by a notable margin of 10.59 points in SARI Final (19.3% improvement). Secondly, even compared to ChatGPT prompted with in-context examples, LIFE achieves a superiority of 7.16 points in SARI Final.Comment: Accepted to AAAI 202

Kinking of a Crack Out of an Interface,”

Kinking of a plane strain crack out of the interface between two dissimilar isotropi

Artemisia anomala extracts enhance the viability and antioxidation capacity of human keratinocytes

Purpose: To investigate the effect of extracts of Artemisia anomala S. Moore tissues on viability, apoptosis and antioxidant capacity of human keratinocytes.Methods: Human keratinocyte cell line HaCaT were treated with extracts of A. anomala for 12 h or 24 h. Cell viability, level of reactive oxygen species (ROS), and incidence of apoptosis were measured by flow cytometry. Levels of mRNA and key proteins in the mitogen-activated protein kinase (MAPK) pathway were determined by quantitative reverse-transcription polymerase chain reaction (qRT-PCR). Key proteins of caspase pathways were assessed by western blot. The influence of the extract on the MAPK pathway was further probed by treating cells with MAPK activator in the presence and absence of the extract.Results: Treatment of cells with extracts of A. anomala enhanced viability and reduced apoptosis in a time-dependent manner, and increased ROS level, compared with control. mRNA and protein expressions of c-Jun N-terminal kinase (JNK), extracellular regulated protein kinase (ERK), and p38 MAPK decreased in extract-treated cells. The extracts also reversed the inhibitory effects of the MAPK pathway activator, actinomycin, on cell viability and ROS, and inhibited protein-cleaved caspase-8 and cleaved caspase-3.Conclusion: A. anomala extract increases cell viability and antioxidant capacity via inactivation of MAPK pathway, and also inhibits cell apoptosis via inactivation of caspase pathways. Hence, the extract may serve as a promising drug for the treatment of psoriasis.Keywords: Artemisia anomala, MAPK pathway, Anti-oxidation, Keratinocyte, Psoriasi

(25R)-5a-Spiro­stane-3,12-dione

The title compound, C27H40O4, was obtained from the oxidation of (25R)-3b-hydr­oxy-5a-spiro­stan-12-one (Hecogenin) by Jone’s reagent. The mol­ecule contains six alicyclic and heterocyclic rings, all trans-fused, among which four six-membered rings adopt similar chair conformations while two five-membered rings assume an envelope conformation