The classical origin of modern mathematics

The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database includes a large number (N~200K) of advisor-student relationships, with affiliations and keywords on their research topic, over several centuries, from the 14th century until today. We focus on two different topics, the evolving importance of countries and of the research disciplines over time. Moreover we study the database at three levels, its global statistics, the mesoscale networks connecting countries and disciplines, and the genealogical level

ROOT - A C++ Framework for Petabyte Data Storage, Statistical Analysis and Visualization

ROOT is an object-oriented C++ framework conceived in the high-energy physics (HEP) community, designed for storing and analyzing petabytes of data in an efficient way. Any instance of a C++ class can be stored into a ROOT file in a machine-independent compressed binary format. In ROOT the TTree object container is optimized for statistical data analysis over very large data sets by using vertical data storage techniques. These containers can span a large number of files on local disks, the web, or a number of different shared file systems. In order to analyze this data, the user can chose out of a wide set of mathematical and statistical functions, including linear algebra classes, numerical algorithms such as integration and minimization, and various methods for performing regression analysis (fitting). In particular, ROOT offers packages for complex data modeling and fitting, as well as multivariate classification based on machine learning techniques. A central piece in these analysis tools are the histogram classes which provide binning of one- and multi-dimensional data. Results can be saved in high-quality graphical formats like Postscript and PDF or in bitmap formats like JPG or GIF. The result can also be stored into ROOT macros that allow a full recreation and rework of the graphics. Users typically create their analysis macros step by step, making use of the interactive C++ interpreter CINT, while running over small data samples. Once the development is finished, they can run these macros at full compiled speed over large data sets, using on-the-fly compilation, or by creating a stand-alone batch program. Finally, if processing farms are available, the user can reduce the execution time of intrinsically parallel tasks - e.g. data mining in HEP - by using PROOF, which will take care of optimally distributing the work over the available resources in a transparent way

Methods For Fuzzy Demand Assessment For IT Specialties

The rapid development of information technologies and their penetration into various spheres of human activity cause a sharply increased demand for IT specialists, in many countries of the world far exceeding the supply on them. High rates of technological transformation contribute to the diversification of the IT segment of the labor market, on the one hand, stimulate the disappearance of some and the emergence of new IT specialties, on the other. This creates a discrepancy between the structure of IT-related education and the labor market demand for IT specialists of the required profile and determines the relevance of developing methods for assessing the demand for IT specialties.This article is devoted to the study and solution of the problem of identifying the demand for IT specialties in the absence of accurate and complete information about the situation in the IT market segment. For the assessment of IT specialties and their ranking by the degree of demand in the labor market, the tasks of making individual and group decisions in the context of fuzzy initial information are formulated and solved. The methodological basis of the tasks posed is multi-criteria decision support methods based on fuzzy relations of expert preferences.The proposed approach as a mathematical tool for minimizing the structural imbalance of supply and demand for IT specialties is one of the components of the system of intellectual management of the labor market of IT specialists. The latter is designed to support the adoption of scientifically based management decisions to eliminate the mismatch of supply and demand in the IT segment of the labor market in professional, quantitative and qualitative sections

Explicit and spontaneous breaking of SU(3) into its finite subgroups

We investigate the breaking of SU(3) into its subgroups from the viewpoints of explicit and spontaneous breaking. A one-to-one link between these two approaches is given by the complex spherical harmonics, which form a complete set of SU(3)-representation functions. An invariant of degrees p and q in complex conjugate variables corresponds to a singlet, or vacuum expectation value, in a (p,q)-representation of SU(3). We review the formalism of the Molien function, which contains information on primary and secondary invariants. Generalizations of the Molien function to the tensor generating functions are discussed. The latter allows all branching rules to be deduced. We have computed all primary and secondary invariants for all proper finite subgroups of order smaller than 512, for the entire series of groups \Delta(3n^2), \Delta(6n^2), and for all crystallographic groups. Examples of sufficient conditions for breaking into a subgroup are worked out for the entire T_{n[a]}-, \Delta(3n^2)-, \Delta(6n^2)-series and for all crystallographic groups \Sigma(X). The corresponding invariants provide an alternative definition of these groups. A Mathematica package, SUtree, is provided which allows the extraction of the invariants, Molien and generating functions, syzygies, VEVs, branching rules, character tables, matrix (p,q)_{SU(3)}-representations, Kronecker products, etc. for the groups discussed above.Comment: 62 pages, 5 figures; the corresponding software package SUtree can be downloaded from http://theophys.kth.se/~amerle/SUtree/SUtree.html New in v2: Nice figure added, references added, explicit transformation matrices between different embeddings calculated, software package update