Computational Algebraic Geometry and Quantum Mechanics: an Initiative Toward Post Contemporary Quantum Chemistry
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Using Macaulay2 Effectively in Practice
Using Macaulay2 effectively in practice Mike Stillman ([email protected]) Department of Mathematics Cornell 22 July 2019 / IMA Sage/M2 Macaulay2: at a glance Project started in 1993, Dan Grayson and Mike Stillman. Open source. Key computations: Gr¨obnerbases, free resolutions, Hilbert functions and applications of these. Rings, Modules and Chain Complexes are first class objects. Language which is comfortable for mathematicians, yet powerful, expressive, and fun to program in. Now a community project Journal of Software for Algebra and Geometry (started in 2009. Now we handle: Macaulay2, Singular, Gap, Cocoa) (original editors: Greg Smith, Amelia Taylor). Strong community: including about 2 workshops per year. User contributed packages (about 200 so far). Each has doc and tests, is tested every night, and is distributed with M2. Lots of activity Over 2000 math papers refer to Macaulay2. History: 1976-1978 (My undergrad years at Urbana) E. Graham Evans: asked me to write a program to compute syzygies, from Hilbert's algorithm from 1890. Really didn't work on computers of the day (probably might still be an issue!). Instead: Did computation degree by degree, no finishing condition. Used Buchsbaum-Eisenbud \What makes a complex exact" (by hand!) to see if the resulting complex was exact. Winfried Bruns was there too. Very exciting time. History: 1978-1983 (My grad years, with Dave Bayer, at Harvard) History: 1978-1983 (My grad years, with Dave Bayer, at Harvard) I tried to do \real mathematics" but Dave Bayer (basically) rediscovered Groebner bases, and saw that they gave an algorithm for computing all syzygies. I got excited, dropped what I was doing, and we programmed (in Pascal), in less than one week, the first version of what would be Macaulay. -
Luis David Garcıa Puente
Luis David Garc´ıa Puente Department of Mathematics and Statistics (936) 294-1581 Sam Houston State University [email protected] Huntsville, TX 77341–2206 http://www.shsu.edu/ldg005/ Professional Preparation Universidad Nacional Autonoma´ de Mexico´ (UNAM) Mexico City, Mexico´ B.S. Mathematics (with Honors) 1999 Virginia Polytechnic Institute and State University Blacksburg, VA Ph.D. Mathematics 2004 – Advisor: Reinhard Laubenbacher – Dissertation: Algebraic Geometry of Bayesian Networks University of California, Berkeley Berkeley, CA Postdoctoral Fellow Summer 2004 – Mentor: Lior Pachter Mathematical Sciences Research Institute (MSRI) Berkeley, CA Postdoctoral Fellow Fall 2004 – Mentor: Bernd Sturmfels Texas A&M University College Station, TX Visiting Assistant Professor 2005 – 2007 – Mentor: Frank Sottile Appointments Colorado College Colorado Springs, CO Professor of Mathematics and Computer Science 2021 – Sam Houston State University Huntsville, TX Professor of Mathematics 2019 – 2021 Sam Houston State University Huntsville, TX Associate Department Chair Fall 2017 – 2021 Sam Houston State University Huntsville, TX Associate Professor of Mathematics 2013 – 2019 Statistical and Applied Mathematical Sciences Institute Research Triangle Park, NC SAMSI New Researcher fellowship Spring 2009 Sam Houston State University Huntsville, TX Assistant Professor of Mathematics 2007 – 2013 Virginia Bioinformatics Institute (Virginia Tech) Blacksburg, VA Graduate Research Assistant Spring 2004 Virginia Polytechnic Institute and State University Blacksburg, -
Towards a Fully Automated Extraction and Interpretation of Tabular Data Using Machine Learning
UPTEC F 19050 Examensarbete 30 hp August 2019 Towards a fully automated extraction and interpretation of tabular data using machine learning Per Hedbrant Per Hedbrant Master Thesis in Engineering Physics Department of Engineering Sciences Uppsala University Sweden Abstract Towards a fully automated extraction and interpretation of tabular data using machine learning Per Hedbrant Teknisk- naturvetenskaplig fakultet UTH-enheten Motivation A challenge for researchers at CBCS is the ability to efficiently manage the Besöksadress: different data formats that frequently are changed. Significant amount of time is Ångströmlaboratoriet Lägerhyddsvägen 1 spent on manual pre-processing, converting from one format to another. There are Hus 4, Plan 0 currently no solutions that uses pattern recognition to locate and automatically recognise data structures in a spreadsheet. Postadress: Box 536 751 21 Uppsala Problem Definition The desired solution is to build a self-learning Software as-a-Service (SaaS) for Telefon: automated recognition and loading of data stored in arbitrary formats. The aim of 018 – 471 30 03 this study is three-folded: A) Investigate if unsupervised machine learning Telefax: methods can be used to label different types of cells in spreadsheets. B) 018 – 471 30 00 Investigate if a hypothesis-generating algorithm can be used to label different types of cells in spreadsheets. C) Advise on choices of architecture and Hemsida: technologies for the SaaS solution. http://www.teknat.uu.se/student Method A pre-processing framework is built that can read and pre-process any type of spreadsheet into a feature matrix. Different datasets are read and clustered. An investigation on the usefulness of reducing the dimensionality is also done. -
Why SAS Programmers Should Learn Python Too Michael Stackhouse, Covance, Inc
PharmaSUG 2018 - Paper AD-12 Why SAS Programmers Should Learn Python Too Michael Stackhouse, Covance, Inc. ABSTRACT Day to day work can often require simple, yet repetitive tasks. All companies have tedious processes that may involve moving and renaming files, making redundant edits to code, and more. Often, one might also want to find or summarize information scattered amongst many different files as well. While SAS programmers are very familiar with the power of SAS, the power of some lesser known but readily available tools may go unnoticed. The programming language Python has many capabilities that can easily automate and facilitate these tasks. Additionally, many companies have adopted Linux and UNIX as their OS of choice. With a small amount of background, and an understanding of Linux/UNIX command line syntax, powerful tools can be developed to eliminate these tedious activities. Better yet, these tools can be written to “talk back” to the user, making them more user friendly for those averse to venturing from their SAS editor. This paper will explore the benefits of how Python can be adopted into a SAS programming world. INTRODUCTION SAS is a great language, and it does what it’s designed to do very well, but other languages are better catered to different tasks. One language in particular that can serve a number of different purposes is Python. This is for a number of reasons. First off, it’s easy. Python has a very spoken-word style of syntax that is both intuitive to use and easy to learn. This makes it a very attractive language for newcomers, but also an attractive language to someone like a SAS programmer. -
An Alternative Algorithm for Computing the Betti Table of a Monomial Ideal 3
AN ALTERNATIVE ALGORITHM FOR COMPUTING THE BETTI TABLE OF A MONOMIAL IDEAL MARIA-LAURA TORRENTE AND MATTEO VARBARO Abstract. In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the way of describing the method, we also prove new constraints on the shape of the possible Betti tables of a monomial ideal. 1. Introduction Since many years syzygies, and more generally free resolutions, are central in purely theo- retical aspects of algebraic geometry; more recently, after the connection between algebra and statistics have been initiated by Diaconis and Sturmfels in [DS98], free resolutions have also become an important tool in statistics (for instance, see [D11, SW09]). As a consequence, it is fundamental to have efficient algorithms to compute them. The usual approach uses Gr¨obner bases and exploits a result of Schreyer (for more details see [Sc80, Sc91] or [Ei95, Chapter 15, Section 5]). The packages for free resolutions of the most used computer algebra systems, like [Macaulay2, Singular, CoCoA], are based on these techniques. In this paper, we introduce a new algorithmic method to compute the minimal graded free resolution of any finitely generated graded module over a polynomial ring such that some (possibly non- minimal) graded free resolution is known a priori. We describe this method and we present the resulting algorithm in the case of monomial ideals in a polynomial ring, in which situ- ation we always have a starting nonminimal graded free resolution. -
Base SAS® Software Flexible and Extensible Fourth-Generation Programming Language Designed for Data Access, Transformation and Reporting
FACT SHEET Base SAS® Software Flexible and extensible fourth-generation programming language designed for data access, transformation and reporting What does Base SAS® software do? Base SAS is a fourth-generation programming language (4GL) for data access, data transformation, analysis and reporting. It is included with the SAS Platform. Base SAS is designed for foundational data manipulation, information storage and retrieval, descrip- tive statistics and report writing. It also includes a powerful macro facility that reduces programming time and maintenance headaches. Why is Base SAS® software important? Base SAS runs on all major operating systems. It significantly reduces programming and maintenance time, while enabling your IT organization to produce the analyses and reports that decision makers need in the format they prefer. For whom is Base SAS® software designed? Base SAS is used by SAS programming experts and power users who prefer to code to manipulate data, produce and distribute ad hoc queries and reports, and/or interpret the results of descriptive data analysis. Many IT organizations struggle with functionality, including direct access to familiar Python interface using the SAS problems arising from complex and distrib- standardized data sources and advanced pipefitter package, fostering consis- uted data, spending excessive time synchro- statistical analysis. tency of code in the organization. nizing and reformatting data for various • Simplify reporting and delivery to applications. Producing accurate and visually Key Benefits mobile devices. Base SAS provides appealing reports often requires dispropor- maximum reporting flexibility. Easily • Integrate data across environments. tionate programming resources. Addition- create reports in formats such as RTF, Available with the SAS Platform, Base ally, IT often must manage a plethora of PDF, Microsoft PowerPoint, HTML and SAS integrates into any computing software packages that only support a e-books that can be read on many environment infrastructure, unifying specific demand. -
Computations in Algebraic Geometry with Macaulay 2
Computations in algebraic geometry with Macaulay 2 Editors: D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels Preface Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re- cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith- mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv- ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi- mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. -
A Simplified Introduction to Virus Propagation Using Maple's Turtle Graphics Package
E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package A simplified introduction to virus propagation using Maple's Turtle Graphics package Eugenio Roanes-Lozano Instituto de Matemática Interdisciplinar & Departamento de Didáctica de las Ciencias Experimentales, Sociales y Matemáticas Facultad de Educación, Universidad Complutense de Madrid, Spain Carmen Solano-Macías Departamento de Información y Comunicación Facultad de CC. de la Documentación y Comunicación, Universidad de Extremadura, Spain Eugenio Roanes-Macías Departamento de Álgebra, Universidad Complutense de Madrid, Spain [email protected] ; [email protected] ; [email protected] Partially funded by the research project PGC2018-096509-B-100 (Government of Spain) 1 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package 1. INTRODUCTION: TURTLE GEOMETRY AND LOGO • Logo language: developed at the end of the ‘60s • Characterized by the use of Turtle Geometry (a.k.a. as Turtle Graphics). • Oriented to introduce kids to programming (Papert, 1980). • Basic movements of the turtle (graphic cursor): FD, BK RT, LT. • It is not based on a Cartesian Coordinate system. 2 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package • Initially robots were used to plot the trail of the turtle. http://cyberneticzoo.com/cyberneticanimals/1969-the-logo-turtle-seymour-papert-marvin-minsky-et-al-american/ 3 E. Roanes-Lozano, C. Solano-Macías & E. Roanes-Macías.: A simplified introduction to virus propagation using Maple's Turtle Graphics package • IBM Logo / LCSI Logo (’80) 4 E. -
Clinical Trial Laboratory Data Management Using the SAS ® System
Clinical Trial Laboratory Data Management using the SAS® System Marianne Hack, Covance, Inc., Princeton NJ ABSTRACT In terms of volume, for many clinical trials laboratory process lab data, these standard agreements are data comprises a very large portion of all data collected. adhered to whenever possible on any studies that Add to that the fact that laboratory data is inherently utilize these laboratories. complex, and the management of the data acquisition (electronic and/or data entry), cleaning (synchronization Given that we know what to expect when receiving data of databases), and reporting (unit conversions, files from a particular laboratory data vendor, we can character to numeric conversions, result flagging, etc.) then build standard SAS modules to import and processes can be overwhelming. This paper discusses reformat the vendor data. The end result is that a SAS an approach to building and using an arsenal of data set (see example B) containing data from Vendor specialized SAS program modules in order to A will be very similar to a SAS data set containing data standardize the various processes involved in from Vendor B. These SAS data sets are then ready managing and reporting clinical laboratory data. for the data cleaning stage. DATA CLEANING INTRODUCTION Data review and cleaning of vendor data requires As a CRO (Contract Research Organization), we are additional steps over and above what one might required to be able to work with data from a multitude of ordinarily do to review data-entered laboratory data. sources. Clinical laboratory data is usually integrated Commonly called ‘header cleaning’, this involves into the clinical database via direct data entry or reconciling the patient identifiers from the vendor through importation of electronic data files. -
What Can Computer Algebraic Geometry Do Today?
What can computer Algebraic Geometry do today? Gregory G. Smith Wolfram Decker Mike Stillman 14 July 2015 Essential Questions ̭ What can be computed? ̭ What software is currently available? ̭ What would you like to compute? ̭ How should software advance your research? Basic Mathematical Types ̭ Polynomial Rings, Ideals, Modules, ̭ Varieties (affine, projective, toric, abstract), ̭ Sheaves, Divisors, Intersection Rings, ̭ Maps, Chain Complexes, Homology, ̭ Polyhedra, Graphs, Matroids, ̯ Established Geometric Tools ̭ Elimination, Blowups, Normalization, ̭ Rational maps, Working with divisors, ̭ Components, Parametrizing curves, ̭ Sheaf Cohomology, ঠ-modules, ̯ Emerging Geometric Tools ̭ Classification of singularities, ̭ Numerical algebraic geometry, ̭ ैक़௴Ь, Derived equivalences, ̭ Deformation theory,Positivity, ̯ Some Geometric Successes ̭ GEOGRAPHY OF SURFACES: exhibiting surfaces with given invariants ̭ BOIJ-SÖDERBERG: examples lead to new conjectures and theorems ̭ MODULI SPACES: computer aided proofs of unirationality Some Existing Software ̭ GAP,Macaulay2, SINGULAR, ̭ CoCoA, Magma, Sage, PARI, RISA/ASIR, ̭ Gfan, Polymake, Normaliz, 4ti2, ̭ Bertini, PHCpack, Schubert, Bergman, an idiosyncratic and incomplete list Effective Software ̭ USEABLE: documented examples ̭ MAINTAINABLE: includes tests, part of a larger distribution ̭ PUBLISHABLE: Journal of Software for Algebra and Geometry; www.j-sag.org ̭ CITATIONS: reference software Recent Developments in Singular Wolfram Decker Janko B¨ohm, Hans Sch¨onemann, Mathias Schulze Mohamed Barakat TU Kaiserslautern July 14, 2015 Wolfram Decker (TU-KL) Recent Developments in Singular July 14, 2015 1 / 24 commutative and non-commutative algebra, singularity theory, and with packages for convex and tropical geometry. It is free and open-source under the GNU General Public Licence. -
Introduction to SAS
1 Introduction to SAS How to Get SAS® The University has a license agreement with SAS® for individual use for $35 a year. You can buy and download the software package at: https://software.ucdavis.edu/index.cfm. If you can have the software installed on your laptop and bring it with you to the seminar, we can work through the examples and exercises together. SAS will run in Windows® Vista, 7, 8, and 10, and on UNIX. To run SAS on a Mac® you can run SAS University, which is a limited version that is free and runs virtually on OS X http://www.sas.com/en_us/software/university-edition/download-software.html#os-x or you will need to log in remotely to a Windows or UNIX system or use a desktop virtualization program such as Parallels®. Your department can purchase a license for Parallels® using the link above for a discount. You can get a free 14 day trial of Parallels at: http://trial.parallels.com/?lang=en&terr=us. What is SAS®? SAS is an integrated software system that enables you to perform a variety of tasks. For the purposes of this seminar series, we will be focusing on: 1) Data entry, retrieval, and management 2) Tables and graphics 3) Statistical analysis For this session held on Sept 14 and 21 we will mainly discuss (1) and (2) as a start. The future seminars will discuss (3) in detail in the context of statistical analysis methods covered. SAS stands for Statistical Analysis Software, but now we just use SAS as the registered trademark for the software package. -
IBM SPSS Modeler Premium
IBM Software IBM SPSS Modeler Premium IBM SPSS Modeler Premium Improve model accuracy with unstructured data IBM® SPSS® Modeler Premium helps you achieve superior outcomes Highlights by basing your business decisions on predictive intelligence. Predictive intelligence creates more effective strategies because it allows Solve business problems faster with organizations not only to evaluate trends and benchmarking results, analytical techniques that deliver deeper insight. plans and performance, but also to look into the future by evaluating likely outcomes and understanding how the interplay of factors affects • Easily access, prepare and integrate structured data and text, web and survey those outcomes. data. With SPSS Modeler Premium, you can solve any business problem • Quickly identify and extract sentiments from text in more than 30 languages. faster using powerful, proven analytical techniques that deliver deeper insight into your customers or constituents. However, because the • Extend access to text stored in legacy majority of data is trapped in unstructured or textual form – in systems, such as mainframes, through support for IBM Classic Federation Server comments, files or on the web – modeling with structured data alone and IBM® zDB2® data stores. may provide an incomplete view into your business processes and outcomes. • Easily perform in-database analytics and mining for IBM® Netezza®*. SPSS Modeler Premium enables organizations to tap into the • Broaden visibility into the full customer predictive intelligence held in all forms of data. It goes beyond the view with the ability to export to IBM® Cognos® Business Intelligence directly analysis of structured numerical data and includes information from from the interface. unstructured data, such as web activity, blog content, customer feedback, emails, articles and more to discover relationships between • Add more deployment options through zLinux, SuSE Linux Enterprise Server and concepts and sentiments and create the most accurate predictive models inclusion in IBM Smart Analytics System possible.