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Tensor representations of discrete data
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Polynomial constraints on representing entangled qubits as matrix product states
with
Jason Morton (2012).
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Binary hidden Markov models and varieties
(2012), to appear in the Journal of Algebraic Statistics
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A note on the proportionality between some consistency indices in the AHPwith
Matteo Brunelli and
Michele Fedrizzi
(2010), in Applied Mathematics and Computation.
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Pushing the limit (generalized limits and limit extrema in topology)
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Resolving the Banach-Tarski paradox: inseparability of rigid bodies
Papers
We represent discrete random variables as tensors in a way that allows us to treat any discrete random vector essentially like a binary vector. This enables us to generalize certain known results on the geometry of binary models for arbitrary discrete models.
@misc{CM12,
author="Andrew J. Critch and Jason Morton",
title = "{Polynomial constraints on representing entangled qubits as matrix product states}",
year = {2012},
howpublished = "{arXiv:1210.2812}",
}
@misc{Cri12,
author="{Andrew J. Critch}",
title = "{Binary hidden Markov models and varieties}",
year = {2012},
howpublished = "{arXiv:1206.0500}",
}
@misc{BCF10,
author="Matteo Brunelli and Andrew J. Critch and Michele Fedrizzi",
title = "{A note on the proportionality between some consistency indices in the AHP}",
year = {2010},
howpublished = "{arXiv:1203.6431v1}",
}
@article{Cri06a,
author="{Andrew J. Critch}",
title="{Generalized limits and limit extrema}",
journal="Atlantic Electronic Journal of Mathematics",
year={2006},
volume={1},
number={1},
pages={47 - 55},
}
@misc{Cri06b,
author="{Andrew J. Critch}",
title = "{Resolving the Banach-Tarski paradox: inseparability of rigid bodies}",
year = {2006},
howpublished = "{B.Sc. Honors thesis, Memorial University of Newfoundland}",
}
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Tensors.m2 – a Macaulay2 package for studying varieties of tensors and tensor networks.
with Claudiu Raicu (2012), began at the WFU2012 Macaulay2 developers workshop.
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Credence – a game using information-theoretic scoring to calibrate players’ subjective belief strengths to more accurately match their success rates.
Software
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Algebraic constraints on MPS-entangled qubits
(September, 2012) in the RTG workshop on Tensors and their Geometry in High Dimensions at UC Berkeley
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Causality and algebraic geometry
(September, 2012) in the Queen’s Algebraic Geometry Seminar
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A new parametrization for binary hidden Markov models
(June, 2012) at Algebraic Statistics in the Alleghenies, Pennsylvania State University
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Computing examples in algebraic geometry
(January, 2012) in the Student Algebraic Geometry Seminar, UC Berkeley
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What causality is (stats for mathematicians)
(August, 2011) in the Berkeley Algebraic Statistics Seminar
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Picard group of the moduli stack of elliptic curves
(an introduction to stacks by example)
(March, 2011) in the Student Algebraic Geometry Seminar, UC Berkeley
Selected talks
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Berkeley Student Algebraic Geometry Seminar
(Spring 2011 – Spring 2012) Co-organized the seminar, first with Charley Crissman, and later with Andrew Dudzik.
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COGS Causal Inference Symposium
(February, 2012) Co-organized the symposium with Mike Pacer.
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Berkeley Algebraic Statistics Seminar
(Fall 2011) Co-organized the seminar with Shaowei Lin.
In preparation, with
Shaowei Lin,
Luca Weihs, and
Piotr Zwiernik.