On the minimal sum of Betti numbers of an almost complex manifold

We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex structures, and infinitely many which do not. We then show that if a closed almost complex manifold has sum of Betti numbers three, then its dimension must be a power of two.     

基于持续同调的边坡土颗粒应力链失稳分析

采用颗粒离散元方法和持续同调理论,研究了内排土场堆叠至不同高度时的边坡稳定性。为便于研究,现采用一水平金属板向下施加压力,代替不同厚度土层的重力荷载,对边坡在竖向荷载作用下的失稳破坏过程进行了颗粒离散元模拟。研究了二维边坡土颗粒速度总矢量、边坡失稳破坏时滑移开裂面的角度以及边坡坡顶y方向的平均速度等宏观响应过程,并构建了自然堆积下边坡堆积体颗粒的法向力链无向网络模型。最后,用持续同调方法对边坡坡顶颗粒接触力链网络的拓扑特征进行分析,获得条码图,建立了岩体结构持续同调特征与失稳演化的关系。本文为研究边坡失稳拓扑识别提供了一种新方法,从而可以有效预测边坡的失稳破坏。     

Wedge Operations and Doubling Operations of Real Toric Manifolds

This paper deals with two things.First,the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G.Second,the author focuses on a specific canonical extensions called doublings and presents their various properties.They include existence of infinitely many real topological toric manifolds admitting complex structures,and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover,some questions about real topological toric manifolds related to Halperin's toral rank conjecture are presented.     

On the vanishing of homology in random Čech complexes

We compute the homology of random ?ech complexes over a homogeneous Poisson process on the d‐dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erd?s ‐Rényi phase transition, where the ?ech complex becomes connected. The second transition is where all the other homology groups are computed correctly (almost simultaneously). Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14–51, 2017     

Hochschild and cyclic (co)homology of superadditive categories

We define the Hochschild and cyclic (co)homology groups for superadditive categories and show that these (co)homology groups are graded Morita invariants. We also show that the Hochschild and cyclic homology are compatible with the tensor product of superadditive categories.     

Glutamine: fructose-6-phosphate amidotransferase (GFAT): homology modelling and designing of new inhibitors using pharmacophore and docking based hierarchical virtual screening protocol

Glutamine: fructose-6-phosphate amidotransferase (GFAT), also termed GFPT1 and GFAT1, catalyzes the first committed step of the hexosamine biosynthesis pathway in mammals and consequently plays an important role in type 2 diabetes. In the present study, a combination of pharmacophore modelling, homology modelling, and molecular docking analysis was performed to design new glutamine competitive inhibitors of human GFAT, and to investigate important interaction details of inhibitor molecules. A pharmacophore model of GFAT inhibitors was developed, subsequently validated, and utilized for the screening by the PHASE database to identify new molecules. Afterwards, homology modelling was performed to construct the glutamine-binding site of the GFAT protein. The modelled active site was utilized to dock the studied molecules to investigate important receptor-ligand interactions and to scrutinize database-screened molecules on the basis of essential interactions. This systematic in silico protocol helped us to identify new molecules that would be explored for the treatment of type 2 diabetes and its complications.     

On homotopy groups of quandle spaces and the quandle homotopy invariant of links

For a quandle X, the quandle space BX is defined, modifying the rack space of Fenn, Rourke and Sanderson (1995) [13], and the quandle homotopy invariant of links is defined in Z[π₂(BX)], modifying the rack homotopy invariant of Fenn, Rourke and Sanderson (1995) [13]. It is known that the cocycle invariants introduced in Carter et al. (2005) [3], Carter et al. (2003) [5], Carter et al. (2001) [6] can be derived from the quandle homotopy invariant.In this paper, we show that, for a finite quandle X, π₂(BX) is finitely generated, and that, for a connected finite quandle X, π₂(BX) is finite. It follows that the space spanned by cocycle invariants for a finite quandle is finitely generated. Further, we calculate π₂(BX) for some concrete quandles. From the calculation, all cocycle invariants for those quandles are concretely presented. Moreover, we show formulas of the quandle homotopy invariant for connected sum of knots and for the mirror image of links.     

Homology Modeling of Cyt2Ca1 of Bacillus thuringiensis and Its Molecular Docking with Inositol Monophosphate

Cyt2Ca1 is an insecticidal crystal protein produced by Bacillus thuringiensis ET29 during its stationary phase, and this δ‐endotoxin demonstrates remarkable insecticidal activity against not only insects of the order Coleoptera, but also against fleas, and in particular the larvae of the cat flea, Ctenocephalides felis. The first theoretical model of the three‐dimensional structure of Cyt2Ca1 was predicted and compared with Cyt2Aa, which is lethal to insect larvae. The three‐dimensional structure of the Cyt2Ca1 was obtained by homology modeling on the structures of the Cyt2Aa protein. The deduced model resembles previously reported Cyt2Aa toxin. A binding mode of inositol monophosphate as a polar head group of the putative membrane phospholipid ligand to Cyt2Ca1 was presented using molecular docking. The residues of Leu9, Glu21, Tyr23 and Gln110 of the Cyt2Ca1 toxin are responsible for the interactions with inositol monophosphate via eight hydrogen bonds. Those residues could be important for receptor recognition. This binding simulation will be helpful for the design of mutagenesis experiments aimed at the improvement of toxicity, and lead to a deep understanding of the mechanism of action of Cyt toxins.