An interpolation matched interface and boundary method for elliptic interface problems

AbstractAn interpolation matched interface and boundary (IMIB) method with second-order accuracy is developed for elliptic interface problems on Cartesian grids, based on original MIB method proposed by Zhou et al. [Y. Zhou, G. Wei, On the fictious-domain and interpolation formulations of the matched interface and boundary method, J. Comput. Phys. 219 (2006) 228–246]. Explicit and symmetric finite difference formulas at irregular grid points are derived by virtue of the level set function. The difference scheme using IMIB method is shown to satisfy the discrete maximum principle for a certain class of problems. Rigorous error analyses are given for the IMIB method applied to one-dimensional (1D) problems with piecewise constant coefficients and two-dimensional (2D) problems with singular sources. Comparison functions are constructed to obtain a sharp error bound for 1D approximate solutions. Furthermore, we compare the ghost fluid method (GFM), immersed interface method (IIM), MIB and IMIB methods for 1D problems. Finally, numerical examples are provided to show the efficiency and robustness of the proposed method

Curator: Efficient Indexing for Multi-Tenant Vector Databases

Vector databases have emerged as key enablers for bridging intelligent applications with unstructured data, providing generic search and management support for embedding vectors extracted from the raw unstructured data. As multiple data users can share the same database infrastructure, multi-tenancy support for vector databases is increasingly desirable. This hinges on an efficient filtered search operation, i.e., only querying the vectors accessible to a particular tenant. Multi-tenancy in vector databases is currently achieved by building either a single, shared index among all tenants, or a per-tenant index. The former optimizes for memory efficiency at the expense of search performance, while the latter does the opposite. Instead, this paper presents Curator, an in-memory vector index design tailored for multi-tenant queries that simultaneously achieves the two conflicting goals, low memory overhead and high performance for queries, vector insertion, and deletion. Curator indexes each tenant's vectors with a tenant-specific clustering tree and encodes these trees compactly as sub-trees of a shared clustering tree. Each tenant's clustering tree adapts dynamically to its unique vector distribution, while maintaining a low per-tenant memory footprint. Our evaluation, based on two widely used data sets, confirms that Curator delivers search performance on par with per-tenant indexing, while maintaining memory consumption at the same level as metadata filtering on a single, shared index

On the Socialist Core and Its Modern and Contemporary Values in How the Steel was Tempered from the Perspective of Education

In-depth study of literary appreciation and its educational value for the book "How the Steel was Tempered", interpreted from a pedagogical perspective and in the context of socialist core values. Firstly, starting from the socialist core, the deep relationship between characterization, plot setting and theme is analyzed. Secondly, through the analysis of the growth experience of the hero, Paul Kochagin, the educational significance of his socialist spirit such as adhering to ideals and faiths, unremitting self-improvement and optimism is revealed. Finally, the paper discusses the value of the work in the contemporary content, emphasizing its positive effects on cultivating contemporary youth to take social responsibility, promoting the socialist core values, and upgrading the national moral quality. The research shows that "How the Steel was Tempered", with its profound socialist core and extensive educational value, is of great practical significance for us to deepen the education of socialist core values and guide the youth to establish a correct worldview and values

α-Glucosidase Inhibitors From the Coral-Associated Fungus Aspergillus terreus

Nine novel butenolide derivatives, including four pairs of enantiomers, named (±)-asperteretones A–D (1a/1b–4a/4b), and a racemate, named asperteretone E (5), were isolated and identified from the coral-associated fungus Aspergillus terreus. All the structures were established based on extensive spectroscopic analyses, including HRESIMS and NMR data. The chiral chromatography analyses allowed the separation of (±)-asperteretones A–D, whose absolute configurations were further confirmed by experimental and calculated electronic circular dichroism (ECD) analysis. Structurally, compounds 2–5 represented the first examples of prenylated γ-butenolides bearing 2-phenyl-3-benzyl-4H-furan-1-one motifs, and their crucial biogenetically related metabolite, compound 1, was uniquely defined by an unexpected cleavage of oxygen bridge between C-1 and C-4. Importantly, (±)-asperteretal D and (4S)-4-decarboxylflavipesolide C were revised to (±)-asperteretones B (2a/2b) and D (4), respectively. Additionally, compounds 1a/1b–4a/4b and 5 were evaluated for the α-glucosidase inhibitory activity, and all these compounds exhibited potent inhibitory potency against α-glucosidase, with IC50 values ranging from 15.7 ± 1.1 to 53.1 ± 1.4 μM, which was much lower than that of the positive control acarbose (IC50 = 154.7 ± 8.1 μM), endowing them as promising leading molecules for the discovery of new α-glucosidase inhibitors for type-2 diabetes mellitus treatment

Characterization, Genomic Organization, Abundance, and Chromosomal Distribution of Ty1-copia Retrotransposons in Erianthus arundinaceus

Erianthus arundinaceus is an important wild species of the genus Saccharum with many valuable traits. However, the composition and structure of its genome are largely unknown, which have hindered its utilization in sugarcane breeding and evolutionary research. Retrotransposons constitute an appreciable fraction of plant genomes and may have played a significant role in the evolution and sequence organization of genomes. In the current study, we investigate the phylogenetic diversity and genomic abundance of Ty1-copia retrotransposons for the first time and inspect their chromosomal distribution patterns in E. arundinaceus. In total, 70 Ty1-copia reverse transcriptase (RT) sequences with significant levels of heterogeneity were obtained. The phylogenetic analysis revealed these Ty1-copia retrotransposons were classified into four distinct evolutionary lineages (Tork/TAR, Tork/Angela, Retrofit/Ale, and Sire/Maximus). Dot-blot analysis showed estimated the total copy number of Ty1-copia retrotransposons to be about 4.5 × 103 in the E. arundinaceus genome, indicating they were a significant component. Fluorescence in situ hybridization revealed that Ty1-copia retrotransposons from the four lineages had strikingly similar patterns of chromosomal enrichment, being exclusively enriched in the subterminal heterochromatic regions of most E. arundinaceus chromosomes. This is the first clear evidence of the presence of Ty1-copia retrotransposons in the subterminal heterochromatin of E. arundinaceus. Altogether, these results promote the understanding of the diversification of Ty1-copia retrotransposons and shed light on their chromosomal distribution patterns in E. arundinaceus

Automated tooth crown design with optimized shape and biomechanics properties

Despite the large demand for dental restoration each year, the design of crown restorations is mainly performed via manual software operation, which is tedious and subjective. Moreover, the current design process lacks biomechanics optimization, leading to localized stress concentration and reduced working life. To tackle these challenges, we develop a fully automated algorithm for crown restoration based on deformable model fitting and biomechanical optimization. From a library of dental oral scans, a conditional shape model (CSM) is constructed to represent the inter-teeth shape correlation. By matching the CSM to the patient’s oral scan, the optimal crown shape is estimated to coincide with the surrounding teeth. Next, the crown is seamlessly integrated into the finish line of preparation via a surface warping step. Finally, porous internal supporting structures of the crown are generated to avoid excessive localized stresses. This algorithm is validated on clinical oral scan data and achieved less than 2 mm mean surface distance as compared to the manual designs of experienced human operators. The mechanical simulation was conducted to prove that the internal supporting structures lead to uniform stress distribution all over the model

Pathologic complete response of hepatoid adenocarcinoma of the stomach after chemo-immunotherapy: A rare case report and literature review

BackgroundHepatoid adenocarcinoma of the stomach (HAS) is a highly malignant subtype of gastric carcinoma with specific clinicopathological features and extremely poor prognosis. We present an exceedingly rare case of complete response after chemo-immunotherapy.Case DescriptionA 48-year-old woman with highly elevated serum alpha-fetoprotein (AFP) level was found to have HAS verified by pathological examination based on gastroscopy. Computed tomography scan was done and TNM staging of the tumor was T4aN3aMx. Programmed cell death ligand-1 (PD-L1) immunohistochemistry was performed, revealing a negative PD-L1 expression. Chemo-immunotherapy including oxaliplatin plus S-1 and PD-1 inhibitor terelizumab was given to this patient for 2 months until the serum AFP level decreased from 748.5 to 12.9 ng/mL and the tumor shrank. D2 radical gastrectomy was then performed and histopathology of the resected specimen revealed that the cancerous cells had disappeared. Pathologic complete response (pCR) was achieved and no evidence of recurrence has been found after 1 year of follow-up.ConclusionsWe, for the first time, reported an HAS patient with negative PD-L1 expression who achieved pCR from the combined chemotherapy and immunotherapy. Although no consensus has been reached regarding the therapy, it might provide a potential effective management strategy for HAS patient

Genome-wide selection footprints and deleterious variations in young Asian allotetraploid rapeseed

Brassica napus (AACC, 2n=38) is an important oilseed crop grown worldwide. However, little is known about the population evolution of this species, the genomic difference between its major genetic groups, such as European and Asian rapeseed, and the impacts of historical large-scale introgression events on this young tetraploid. In this study, we reported the de novo assembly of the genome sequences of an Asian rapeseed (B. napus), Ningyou 7 and its four progenitors and compared these genomes with other available genomic data from diverse European and Asian cultivars. Our results showed that Asian rapeseed originally derived from European rapeseed but subsequently significantly diverged, with rapid genome differentiation after hybridization and intensive local selective breeding. The first historical introgression of B. rapa dramatically broadened the allelic pool but decreased the deleterious variations of Asian rapeseed. The second historical introgression of the double-low traits of European rapeseed (canola) has reshaped Asian rapeseed into two groups (double-low and double-high), accompanied by an increase in genetic load in the double-low group. This study demonstrates distinctive genomic footprints and deleterious SNP (Single Nucleotide Polymorphism) variants for local adaptation by recent intra- and interspecies introgression events and provides novel insights for understanding the rapid genome evolution of a young allopolyploid cro

DeepSeek LLM: Scaling Open-Source Language Models with Longtermism

The rapid development of open-source large language models (LLMs) has been truly remarkable. However, the scaling law described in previous literature presents varying conclusions, which casts a dark cloud over scaling LLMs. We delve into the study of scaling laws and present our distinctive findings that facilitate scaling of large scale models in two commonly used open-source configurations, 7B and 67B. Guided by the scaling laws, we introduce DeepSeek LLM, a project dedicated to advancing open-source language models with a long-term perspective. To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens and is continuously expanding. We further conduct supervised fine-tuning (SFT) and Direct Preference Optimization (DPO) on DeepSeek LLM Base models, resulting in the creation of DeepSeek Chat models. Our evaluation results demonstrate that DeepSeek LLM 67B surpasses LLaMA-2 70B on various benchmarks, particularly in the domains of code, mathematics, and reasoning. Furthermore, open-ended evaluations reveal that DeepSeek LLM 67B Chat exhibits superior performance compared to GPT-3.5