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Mineral classification is an important preparation operation in the process of beneficiation. The classification effect directly affects the production capacity of grinding machines, product quality, subsequent separation of the concentrate grade, and recovery. To improve mineral classification accuracy and provide technical ideas for enriching the separation of fine materials, this paper proposes the use of a trapezoidal inclined channel agitated reflux classifier (TARC) to classify ultra-fine ilmenite. The principle of this separating system is based on a hindered settling effect and fluidization theory. This study focuses on the factors influencing the particle separation through the optimization of different experimental conditions. A satisfactory 10 µm classification efficiency of 67.89% could be obtained when the ore pulp concentration was 15%, the agitation speed was 350 r/min, and the underflow flux was 16 cm3/min. The TARC realized a continuous feeding classification of fine particles within a narrow particle size range, with 10 µm as the limit size, and an effective reduction in the entrainment of fine particles in the underflow and coarse particles in the overflow phenomena, thus achieving improved classification efficiency.

In this paper, for every $��\in \mathbb{Z}$, we introduce an extension of the 2-toroidal Lie algebra by certain derivations. Based on the $��_��$-coordinated modules theory for vertex algebras, we give an explicit realization of a class of irreducible highest weight modules for this extended toroidal Lie algebra. When $��=1$, this affords a realization of certain irreducible modules for the toroidal extended affine Lie algebras first constructed by Billig.

Additional file 1: Suppl_Table 1. The detail of PCR primers and UEP sequence for candidate variants. Suppl_Table 2. Risk analysis for RAD54L2 and GTF2H1 polymorphisms with the susceptibility to lung cancer in different genetic models by logistic regression analysis. Suppl_Table 3. Stratified analysis for the associations between RAD54L2 and GTF2H1 polymorphisms and the risk of lung cancer. Suppl_Table 4. The associations between RAD54L2 and GTF2H1 polymorphisms and the stage and metastasis of lung cancer.

In this paper, we give a unified construction of vertex algebras arising from infinite-dimensional Lie algebras, including the affine Kac-Moody algebras, Virasoro algebras, Heisenberg algebras and their higher rank analogs, orbifolds and deformations. We define a notion of what we call quasi vertex Lie algebra to unify these Lie algebras. Starting from any (maximal) quasi vertex Lie algebra $\mathfrak{g}$, we construct a corresponding vertex Lie algebra ${\mathfrak{g}}_0$, and establish a canonical isomorphism between the category of restricted $\mathfrak{g}$-modules and that of equivariant $\phi$-coordinated quasi $V_{{\mathfrak{g}}_0}$-modules, where $V_{{\mathfrak{g}}_0}$ is the universal enveloping vertex algebra of ${\mathfrak{g}}_0$. This unified all the previous constructions of vertex algebras from infinite-dimensional Lie algebras and shed light on the way to associate vertex algebras with Lie algebras., Comment: 34 pages

Many sequence variants have been linked to complex human traits and diseases1, but deciphering their biological functions remains challenging, as most of them reside in noncoding DNA. Here we have systematically assessed the binding of 270 human transcription factors to 95,886 noncoding variants in the human genome using an ultra-high-throughput multiplex protein-DNA binding assay, termed single-nucleotide polymorphism evaluation by systematic evolution of ligands by exponential enrichment (SNP-SELEX). The resulting 828 million measurements of transcription factor-DNA interactions enable estimation of the relative affinity of these transcription factors to each variant in vitro and evaluation of the current methods to predict the effects of noncoding variants on transcription factor binding. We show that the position weight matrices of most transcription factors lack sufficient predictive power, whereas the support vector machine combined with the gapped k-mer representation show much improved performance, when assessed on results from independent SNP-SELEX experiments involving a new set of 61,020 sequence variants. We report highly predictive models for 94 human transcription factors and demonstrate their utility in genome-wide association studies and understanding of the molecular pathways involved in diverse human traits and diseases.

For any nullity $2$ extended affine Lie algebra $\mathcal{E}$ of maximal type and $\ell\in\mathbb{C}$, we prove that there exist a vertex algebra $V_{\mathcal{E}}(\ell)$ and an automorphism group $G$ of $V_{\mathcal{E}}(\ell)$ equipped with a linear character $��$, such that the category of restricted $\mathcal{E}$-modules of level $\ell$ is canonically isomorphic to the category of $(G,��)$-equivariant $��$-coordinated quasi $V_{\mathcal{E}}(\ell)$-modules. Moreover, when $\ell$ is a nonnegative integer, there is a quotient vertex algebra $L_{\mathcal{E}}(\ell)$ of $V_{\mathcal{E}}(\ell)$ modulo by a $G$-stable ideal, and we prove that the integrable restricted $\mathcal{E}$-modules of level $\ell$ are exactly the $(G,��)$-equivariant $��$-coordinated quasi $L_{\mathcal{E}}(\ell)$-modules., 33 pages

In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $\phi$-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and $\phi$-coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of irreducible modules for the variant Lie algebras.

To give a unified treatment on the association of Lie algebras and vertex algebras, we study $(G,��_��)$-equivariant $��$-coordinated quasi modules for vertex algebras, where $G$ is a group with $��_��$ a linear character of $G$ and $��$ is an associate of the one-dimensional additive formal group. The theory of $(G,��_��)$-equivariant $��$-coordinated quasi modules for nonlocal vertex algebra is established in \cite{JKLT}. In this paper, we concentrate on the context of vertex algebras. We establish several conceptual results, including a generalized commutator formula and a general construction of vertex algebras and their $(G,��_��)$-equivariant $��$-coordinated quasi modules. Furthermore, for any conformal algebra $\mathcal{C}$, we construct a class of Lie algebras $\widehat{\mathcal{C}}_��[G]$ and prove that restricted $\widehat{\mathcal{C}}_��[G]$-modules are exactly $(G,��_��)$-equivariant $��$-coordinated quasi modules for the universal enveloping vertex algebra of $\mathcal{C}$. As an application, we determine the $(G,��_��)$-equivariant $��$-coordinated quasi modules for affine and Virasoro vertex algebras., 31 pages

Delineating the protein network associated with long non-coding RNAs (lncRNAs) is fundamental to understanding the functional mechanisms of lncRNAs. Current methods to identify lncRNA-binding proteins either rely on crosslinking-mediated complex co-precipitation or require extensive molecular engineering, leading to drawbacks such as loss of cellular context and low capture efficiency. Here we describe a CRISPR-Assisted RNA-Protein Interaction Detection method (CARPID), which leverages CRISPR/CasRx-based RNA targeting and proximity labeling, to rapidly capture binding proteins of specific lncRNAs in their native cellular context followed by LC-MS/MS identification. Applied to a variety of lncRNAs of different lengths and subcellular localizations, CARPID is proven to be a reliable and robust tool to discover the binding proteins of lncRNAs inside living cells.

Let $\sigma$ be a character from an abelian group to $\mathbb C^*$, and let $\mathcal R_\sigma$ be the skew Laurent polynomial ring associated to it. In this paper, the fermionic representation of Allison-Faulkner type unitary Lie algebra coordinated by $\mathcal R_\sigma$ is constructed and its irreducible components are determined explicitly.

In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple affine vertex algebra $L_{\widehat{sl_{\infty}}}(\ell,0)$ with $\ell$ a positive integer, and Levi subgroups $G$ of $GL_\ell(\mathbb{C})$. First, we give a canonical isomorphism between the category of integrable restricted $\widehat{sl_N}(\mathbb{C}_q)$-modules of level $\ell$ and that of equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-modules. Second, we classify irreducible $\mathbb{N}$-graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-modules. Third, we establish a duality between irreducible $\mathbb{N}$-graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-modules and irreducible regular $G$-modules on certain fermionic Fock spaces. Fourth, we obtain an explicit realization of every irreducible $\mathbb{N}$-graded equivariant quasi $L_{\widehat{sl_{\infty}}}(\ell,0)$-module. Fifth, we completely determine the following branchings: 1 The branching from $L_{\widehat{sl_{\infty}}}(\ell,0)\otimes L_{\widehat{sl_{\infty}}}(\ell',0)$ to $L_{\widehat{sl_{\infty}}}(\ell+\ell',0)$ for quasi modules. 2 The branching from $\widehat{sl_N}(\mathbb{C}_q)$ to its Levi subalgebras. 3 The branching from $\widehat{sl_N}(\mathbb{C}_q)$ to its subalgebras $\widehat{sl_N}(\mathbb{C}_q[t_0^{\pm M_0},t_1^{\pm M_1}])$., Comment: 54 Pages

A copper-catalyzed diastereoselective [4 + 2] cyclolization of α,β-unsaturated ketoxime acetates and trifluoromethyl ketones affords various 3-trifluoromethylated 3-hydroxy-cylcohexan-1-ones smoothly. This reaction features the selective functionalization of a less acidic C(sp3)-H bond by an internal oxdative C(sp3)-H functionalization strategy. Preliminary investigations revealed that α,β-unsaturated ketoxime acetates were an internal oxidant, and the in situ generated H2O served as the O-source of the carbonyl oxygen in the product.

Pseudomonas aeruginosa DN1 strain and Bacillus subtilis QHQ110 strain were chosen as rhamnolipid and lipopeptide producer respectively, to evaluate the efficiency of exogenous inoculants on enhancing oil recovery (EOR) and to explore the relationship between injected bacteria and indigenous bacterial community dynamics in long-term filed pilot of Hujianshan low permeability water-flooded reservoir for 26 months. Core-flooding tests showed that the oil displacement efficiency increased by 18.46% with addition of exogenous consortia. Bacterial community dynamics using quantitative PCR and high-throughput sequencing revealed that the exogenous inoculants survived and could live together with indigenous bacterial populations. They gradually became the dominant community after the initial activation, while their comparative advantage weakened continually after 3 months of the first injection. The bacterial populations did not exert an observable change in the process of the second injection of exogenous inoculants. On account of facilitating oil emulsification and accelerating bacterial growth with oil as the carbon source by the injection of exogenous consortia, γ-proteobacteria was finally the prominent bacterial community at class level varying from 25.55 to 32.67%, and the dominant bacterial populations were increased by 2-3 orders of magnitude during the whole processes. The content of organic acids and rhamnolipids in reservoir were promoted with the change of bacterial community diversity, respectively. Cumulative oil increments reached 26,190 barrels for 13 months after the first injection, and 55,947 barrels of oil had been accumulated in all of A20 wells block through two rounds of bacterial consortia injection. The performance of EOR has a cumulative improvement by the injection of exogenous inoculants without observable inhibitory effect on the indigenous bacterial populations, demonstrating the application potential in low permeability water-flooded reservoirs.

The capacity to induce a rapid and controlled healing of bone defects is critical for a bone substitute. Previous studies have reported hydrothermal transformation (HT) of aragonite from cuttlebone (CB) to cuttlebone hydroxyapatite (CBHA). However, the biocompatibility and in vivo characteristic of CBHA have not been fully investigated. We fabricated CBHA via the in situ HT of aragonite from CB. This CBHA exhibited a highly porous structure and nanoscaled surface morphology with a significantly higher protein adsorption rate than CB. Marrow mesenchymal stem cells (MSCs) were seeded and cultured on the CBHA and CB to evaluate their influence on cell proliferation and differentiation. According to scanning electronic microscopy observation and MTT assay, the MSCs adhered and proliferated well on both the CBHA and CB. Compared with the cells on the CB, the MSCs on CBHA exhibited enhanced alkaline phosphatase activity and osteocalcin levels after 13 days of culture. In vivo testing revealed that CBHA could induce ectopic bone formation after implantation, while no bone formation being observed in the CB. These findings demonstrated that a nanoscaled and osteoinductive bone substitute could be produced by hydrothermally transforming an aragonite of CB into a hydroxyapatite.

The capacity to induce a rapid and controlled healing of bone defects is critical for a bone substitute. Previous studies have reported hydrothermal transformation (HT) of aragonite from cuttlebone (CB) to cuttlebone hydroxyapatite (CBHA). However, the biocompatibility and in vivo characteristic of CBHA have not been fully investigated. We fabricated CBHA via the in situ HT of aragonite from CB. This CBHA exhibited a highly porous structure and nanoscaled surface morphology with a significantly higher protein adsorption rate than CB. Marrow mesenchymal stem cells (MSCs) were seeded and cultured on the CBHA and CB to evaluate their influence on cell proliferation and differentiation. According to scanning electronic microscopy observation and MTT assay, the MSCs adhered and proliferated well on both the CBHA and CB. Compared with the cells on the CB, the MSCs on CBHA exhibited enhanced alkaline phosphatase activity and osteocalcin levels after 13 days of culture. In vivo testing revealed that CBHA could induce ectopic bone formation after implantation, while no bone formation being observed in the CB. These findings demonstrated that a nanoscaled and osteoinductive bone substitute could be produced by hydrothermally transforming an aragonite of CB into a hydroxyapatite.

Let $��$ be a generic subgroup of the multiplicative group $\mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $��$, called twisted $��$-Lie algebras, which is a natural generalization of the twisted affine Lie algebras. Starting from an arbitrary even sublattice $Q$ of $\mathbb Z^N$ and an arbitrary finite order isometry of $\mathbb Z^N$ preserving $Q$, we construct a family of twisted $��$-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted $��$-Lie algebras. As application, this recovers a number of known vertex operator realizations for infinite dimensional Lie algebras, such as twisted affine Lie algebras, extended affine Lie algebras of type $A$, trigonometric Lie algebras of series $A$ and $B$, unitary Lie algebras, and $BC$-graded Lie algebras.