Some things i've made, most of which involve a combination of mathematics, programming, data analysis, and visualization.
An open-source Python package to model radio signal propagation. A project for NZRS. [Image excerpted from the Wikipedia article on dipole antenna.]
A visualization of scheduled transit flows in Auckland, New Zealand. A project for MRCagney.
Python toolkit for analyzing General Transit Feed Specification (GTFS) data. A project for MRCagney.
A web application to analyze and visualize transit data in the form of General Transit Feed Specification (GTFS) feeds. A project for MRCagney.
A fast-food, grain-free, vegetarian cookbook. [Image excerpted from Carl Warner's Vegehead.]
Python/Sage code for running graph dynamics experiments. A social networks project for Mark C. Wilson and Patrick Girard at the University of Auckland.
A Python 3 package implementing a new discrete global grid system (DGGS) based on NASA's HEALPix projection. Designed to underlie SCENZ-Grid, an open-source geographic analysis system for worldwide scientific collaboration. See the rHEALPix article below for more background. A project for Landcare Research.
Asymptotics of Multivariate Generating Functions
Python/Sage code to compute asymptotics of coefficients of multivariate generating functions. To be incorporated into the Sage codebase; see Sage ticket #10519. Update 2016-02: Finally incorporated into Sage!
Most of the publications below are journal articles but typeset without the journal house styles and with minor typos corrected.
- Location affordability in New Zealand cities: an intra-urban and comparative perspective, Saeid Adli, Geoff Cooper, Stuart Donovan, Peter Nunns, and Alexander Raichev, presented at the Annual Conference of the New Zealand Association of Economists, July 2014.
- The rHEALPix discrete global grid system, Robert Gibb, Alexander Raichev, and Michael Speth, in preparation.
- New software for computing asymptotics of multivariate generating functions, Alexander Raichev, ACM Communications in Computer Algebra, Volume 45 Issue 3/4, September/December 2011, pages 183–185.
- Asymptotics of coefficients of multivariate generating functions: improvements for multiple points. Alexander Raichev and Mark C. Wilson, Online Journal of Analytic Combinatorics, Issue 6, 2011. As printed in the Online Journal of Analytic Combinatorics and elsewhere online, Theorem 3.4 of this paper contains a typo. Its hypotheses should be strengthened to require that α lies in the interior of the critical cone of p. Indeed, 1) in our proof of Theorem 3.4 we actually used the interior of the cone when considering the integrals Ij, r; 2) for α in the critical cone of p and on its boundary, asymptotics can differ from our formula in Theorem 3.4, e.g. the leading term coefficient can be half of what our formula states, as shown in [PeWi2010] Lemma 4.7, where [PeWi2010] is the article "Asymptotic expansions of oscillatory integrals with complex phase" in Algorithmic Probability and Combinatorics, AMS Contemporary Mathematics series, vol. 520, pages 221--240, 2010.
- Asymptotics of coefficients of multivariate generating functions: improvements for smooth points. Alexander Raichev and Mark C. Wilson, Electronic Journal of Combinatorics, Vol. 15 (2008), R89.
- A new method for computing asymptotics of diagonal coefficients of multivariate generating functions. Alexander Raichev and Mark C. Wilson, Discrete Mathematics & Theoretical Computer Science Proceedings, Conference on Analysis of Algorithms 2007.
- Relative randomness via rK-reducibility, Alexander Raichev, Ph.D. dissertation, University of Wisconsin–Madison, 2006.
- A minimal rK-degree. Alexander Raichev and Frank Stephan, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 15 (2008), 261--269.
- Model completeness for trivial, uncountably categorical theories of Morley rank 1. Alfred Dolich, Michael C. Laskowski, and Alexander Raichev, Archive for Mathematical Logic, Jul 2006, 1--15.
- Relative randomness and real closed fields. Alexander Raichev, Journal of Symbolic Logic, 70 (2005), no. 1, 319--330. Were i to write this paper and the corresponding section in my thesis again, i would use the standard notion of a computable real function instead of introducing the new notion of a weakly computable real function, and then use computable locally Lipschitz functions. The theorems all go through with only minor modifications.
- Relative randomness and real closed fields (extended abstract). Alexander Raichev, Proceedings of the 6th Workshop on Computability and Complexity in Analysis (CCA 2004), 135--143, Electron. Notes Theor. Comput. Sci., 120, Elsevier, Amsterdam, 2005.