Uniform Big Bang–Chaotic Big Crunch optimization

This study proposes methods to improve the convergence of the novel optimization method, Big Bang–Big Crunch (BB–BC). Uniform population method has been used to generate uniformly distributed random points in the Big Bang phase. Chaos has been utilized to rapidly shrink those points to a single representative point via a center of mass in the Big Crunch phase. The proposed algorithm has been named as Uniform Big Bang–Chaotic Big Crunch (UBB–CBC). The performance of the UBB–CBC optimization algorithm demonstrates superiority over the BB–BC optimization for the benchmark functions.     

Big rational surfaces

We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of \mathbbP²{\mathbb{P}^2} at distinct points lying on a (possibly reducible) cubic.     

Big Mathematical Systems

In the first volume of the treatise “éléments de Mathématique,” N. Bourbaki has given one of the possible rigorous definitions of a mathematical structure. However, it turned out that this definition leads to considerable conceptual difficulties in defining a general notion of a mathematical system, because structures in Bourbaki's sense possess a bracket division, which means a definite order of priority in assignment of constituent partial structures (such as addition, order, norm, topology, etc.). In this paper, a conception of a mathematical system is presented that includes as partial cases both the bracket conception of a mathematical system in the Bourbaki-Semadeni sense and the indexed conception of an axiomatizable algebraic system in the Birkhoff-Tarski sense and that is suitable for the assignment of big mathematical systems, such as big common categories, ordered proper classes, and so on. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15, 2000.     

CFO的大数据时代

在大数据时代．无论是管理会计战略预算,还是流程梳理、成本控制．CFO都必须考虑量级远远超过传统数据库的非结构化数据,他们发现太多改变：集群特征比样本分析重要．相关关系比因果关系重要,未来趋势比具体问题重要。这让那些习惯每一个数字都准确到小数点的传统财务高管们产生了很多迷茫与不适。     

大数据冲击银行业

“在目前的银行业内,只有一小部分的从业人员能够真正理解IT和数据对银行的影响和作用。但在未来,大数据会推动整个金融业的深刻变革。”     

什么是随机动力系统

微生物组学大数据在生态环境、人类健康和疾病研究方面都起到了重要作用。通过数学、统计等数据挖掘方法,从高维复杂数据中提取有用信息,是微生物组学大数据建模和分析的关键问题。本文分析了微生物组学大数据的特点,对当前数据分析和计算研究中存在的热点和难点进行了探讨分析,并综述了当前微生物组学大数据模式挖掘、网络重建与分析的研究概况。     

Big Cohen-Macaulay algebras and seeds

In this article, we delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big Cohen-Macaulay algebra. We will also strengthen Hochster and Huneke's ``weakly functorial" existence result for big Cohen-Macaulay algebras by showing that the seed property is stable under base change between complete local domains of positive characteristic. We also show that every seed over a positive characteristic ring maps to a balanced big Cohen-Macaulay -algebra that is an absolutely integrally closed, -adically separated, quasilocal domain.

     

微生物组学的大数据研究

微生物组学大数据在生态环境、人类健康和疾病研究方面都起到了重要作用。通过数学、统计等数据挖掘方法,从高维复杂数据中提取有用信息,是微生物组学大数据建模和分析的关键问题。本文分析了微生物组学大数据的特点,对当前数据分析和计算研究中存在的热点和难点进行了探讨分析,并综述了当前微生物组学大数据模式挖掘、网络重建与分析的研究概况。     

Filter-正则序列与BalancedBigFilter-模

通过对 filter-正则元及 filter-正则序列的研究 ,利用 Cousin复形 ,局部上同调等一些用于研究banlanced big Cohen-Macaulay模的工具及思想方法 ,给出了关于 balanced big filter-模的一些等价刻划 .     

A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation

A novel computer aided method is presented that yields Linear Time Invariant Reduced Order System (LTI-ROS). This is accomplished by using the combined benefits of Big Bang Big Crunch (BBBC) optimization and Routh Approximation (RA) method. The applicability of the proposed method for both Single Input Single Output (SISO) and Multiple Input Multiple Output (MIMO) Linear Time Invariant (LTI) systems is verified by solving numerical examples. Furthermore, the results show that the realized LTI-ROS retain stability and steady state conditions of original system. The reduced order system also exhibits lower Integral Square Error (ISE) values.     

Big elements in irreducible linear groups

Let V be a linear space over a field K of dimension n > 1, and let \({G \leq {\rm GL}(V)}\) be an irreducible linear group. In this paper we prove that the group G contains an element g such that rank \({(g - \alpha E_{n}) \geq \frac{n}{2}}\) for every \({\alpha \in K}\) , where E _n is the identity operator on V. This estimate is sharp for any \({n = 2^{m}}\) . The existence of such an element implies that the conjugacy class of G in GL(V) intersects the big Bruhat cell \({B\dot{w}_{0}B}\) of GL(V) non-trivially (here B is a fixed Borel subgroup of G). The latter fact is equivalent to the existence of a complete flag \({\mathfrak{F}}\) such that the flags \({g(\mathfrak{F}), \mathfrak{F}}\) are in general position for some g ∈ G.     

团队中枢节点的效率模型

集团性是社会网络的显著特征.团队作为一个小规模的社会网络,也存在网络结构的非均匀性以及中枢节点.在阐述团队网络的集团性和中枢节点导致网络的两面性等结构特征的基础上,运用小世界模型的局部效率和集聚系数等指标,建立了团队中枢节点的效率模型,并通过网络结构的调整(如加键和断键重连)研究了网络结构对中枢节点的效率的影响.     

Big Hankel operators of higher weight

Known results concerning the smoothness and boundedness of «big» Hankel operators (Hankel operators in the sense of Axler) are generalized to the case of higher weight (in the sense of representation theory). The key result is a certain estimate for thes-numbers of a particular such operator, involving a combinatorial sum.     

Generalized Big Picard Theorem for pseudo-holomorphic maps

We show how an appropriate choice for affine connections in the target manifold allows the pseudo-holomorphic curves to be realized as harmonic maps. As an application, we present a generalized Big Picard Theorem for pseudo-holomorphic maps between manifolds with almost complex structures.