Anti-dendriform algebras, new splitting of operations and Novikov type algebras

We introduce the notion of anti-dendriform algebras as a new approach of splitting the associativity. They are characterized as the algebras with two operations whose sum is associative and the negative left and right multiplication operators compose the bimodules of the sum associative algebras, justifying the notion due to the comparison with the corresponding characterization of dendriform algebras. The notions of anti-$\mathcal O$-operators and anti-Rota-Baxter operators on associative algebras are introduced to interpret anti-dendriform algebras. In particular, there are compatible anti-dendriform algebra structures on associative algebras with nondegenerate commutative Connes cocycles. There is an important observation that there are correspondences between certain subclasses of dendriform and anti-dendriform algebras in terms of $q$-algebras. As a direct consequence, we give the notion of Novikov-type dendriform algebras as an analogue of Novikov algebras for dendriform algebras, whose relationship with Novikov algebras is consistent with the one between dendriform and pre-Lie algebras. Finally we extend to provide a general framework of introducing the notions of analogues of anti-dendriform algebras, which interprets a new splitting of operations.Comment: 25 page

An extracellular protein expression system in Escherichia coli implies potential application

Escherichia coli is commonly used as a host for the extracellular production of proteins. However, its secretion capacity is often limited to a frustratingly low level compared with other expression hosts, because E. coli has a complex cell envelope with two layers. We recently identified the catalytic domain of a cellulase (Cel-CD) from Bacillus sp. that can be secreted into the medium from recombinant E. coli in large quantities without its native signal peptide. By subcellular location analysis, we verified that the secretion was a two-step process via the SecB-dependent pathway through the inner membrane and an unknown pathway through the outer membrane. However, the N-terminal region of Cel-CD is polar and hydrophilic, which showed no similarities to other typical signal sequences. Random mutagenesis experiment suggested that the N-terminal sequence is a compromising result of transportation through inner and outer membranes. This is the first report that a non-classical signal peptide can guide recombinant proteins out of the cells from cytoplasm. Both the Cel-CD and its N-terminal sequence can serve as carriers for efficient extracellular production of select target proteins with a concentration from 101 to 691 mg/L in flask cultivation. This protein can degrading cellulose efficiently in the culture medium indicating a great potential. Therefore, a recombinant E.coli that can directly utilize cellulose as sole carbon source by fusion Cel-CD with a b-glucosidase was constructed. Recombinant strains were confirmed to use the amorphous cellulose as well as cellobiose as the sole carbon source for growth. Furthermore, both strains were engineered with poly (3-hydroxybutyrate) (PHB) synthesis pathway to demonstrate the production of biodegradable polyesters directly from cellulose materials without exogenously added cellulases. The results suggested that this system has a potential application in lignocellulosic biomass degradation and biochemical biofuel production. These guidelines have been prepared in the format that should be used for the abstract submission. Authors should replace the text of this template in order to prepare their abstracts. Fonts, sizes and spacing should be used as they are used in this document. Page size is US 8.5 inch x 11 inch, top and bottom margin 0.8 inches, left and right margin 0.8 inches. Body text should be written in Arial, 10 pt, single spacing. The Abstract, in English, should introduce the proposed paper’s subject, summarize its contents, explain any unique aspects, and clearly indicate the specific relevance to the themes of the Conference. Do not sub-divide the text into separate sections. References may be included at the bottom. Reference Exploring the N-terminal role of a heterologous protein in secreting out of Escherichia coli, Biotechnol Bioeng. 2016 Dec;113(12):2561-2567. doi: 10.1002/bit.26028. Epub 2016 Jun 14. Construction of cellulose-utilizing Escherichia coli based on a secretable cellulose, Microb Cell Fact. 2015 Oct 9;14:159. doi: 10.1186/s12934-015-0349-7

C3: Zero-shot Text-to-SQL with ChatGPT

This paper proposes a ChatGPT-based zero-shot Text-to-SQL method, dubbed C3, which achieves 82.3\% in terms of execution accuracy on the holdout test set of Spider and becomes the state-of-the-art zero-shot Text-to-SQL method on the Spider Challenge. C3 consists of three key components: Clear Prompting (CP), Calibration with Hints (CH), and Consistent Output (CO), which are corresponding to the model input, model bias and model output respectively. It provides a systematic treatment for zero-shot Text-to-SQL. Extensive experiments have been conducted to verify the effectiveness and efficiency of our proposed method

Phase-locking matter-wave interferometer of vortex states

Matter-wave interferometer of ultracold atoms with different linear momenta has been extensively studied in theory and experiment. The vortex matter-wave interferometer with different angular momenta is applicable as a quantum sensor for measuring the rotation, interatomic interaction, geometric phase, etc. Here we report the first experimental realization of a vortex matter-wave interferometer by coherently transferring the optical angular momentum to an ultracold Bose condensate. After producing a lossless interferometer with atoms only populating the two spin states, we demonstrate that the phase difference between the interferences in the two spin states is locked on $\pi$. We also demonstrate the robustness of this out-of-phase relation, which is independent of the angular-momentum difference between the two interfering vortex states, constituent of Raman optical fields and expansion of the condensate. The experimental results agree well with the calculation from the unitary evolution of wave packet in quantum mechanics. This work opens a new way to build a quantum sensor and measure the atomic correlation in quantum gases.Comment: 5 figure

Expansion dynamics of a spherical Bose-Einstein condensate

We experimentally and theoretically observe the expansion behaviors of a spherical Bose-Einstein condensate. A rubidium condensate is produced in an isotropic optical dipole trap with an asphericity of 0.037. We measure the variation of the condensate size during the expansion process. The free expansion of the condensate is isotropic, which is different from that of the condensate usually produced in the anisotropic trap. The expansion in the short time is speeding and then after a long time the expansion velocity asymptotically approaches a constant value. We derive an analytic solution of the expansion behavior based on the spherical symmetry, allowing a quantitative comparison with the experimental measurement. The interaction energy of the condensate is gradually converted into the kinetic energy at the beginning of the expansion and the kinetic energy dominates after a long-time expansion. We obtain the interaction energy of the condensate in the trap by probing the expansion velocity, which is consistent with the theoretical prediction.Comment: 6 pages, 5 figure