MAT1509HS: Mathematical and Computational Linguistics
Winter 2019: University of Toronto, BA6180, Tuesday 4-6 pm and Wednesday 4-5pm
(Alexander Calder, "Four Red Systems", 1960)
Brief Course Description
The class will cover mathematical and computational models of
acquisition and evolution of natural languages. We will discuss
learnability questions, Markov chain models, population dynamics
models, evolutionary behavior, communicative efficiency and fitness,
We will focus in particular on the Principles and Parameters model
of linguistics and we will discuss the use of mathematical methods,
involving algebraic geometry, topology, and statistical physics, to
describe the evolution of natural languages. Specific examples from
historical linguistics will be revisited from a mathematical and
Slides of Lectures
Links to articles and reading suggestions for presentations:
Noam Chomsky, "Three models for the description of Language"
pdf C.E.Shannon, "Prediction and Entropy of Printed English"
D.Link, "Traces of the Mouth: Andrei Andreyevich Markov's mathematization
- pdf R.C.Berwick, "Mind the Gap"
- pdf Partha Niyogi, Robert C. Berwick, "A dynamical systems model for
L.Pacher, B.Sturmfels, "The Mathematics of Phylogenomics"
pdf G. Longobardi, C. Guardiano, G. Silvestri, A. Boattini, A. Ceolin,
"Towards a syntactic phylogeny of modern Indo-European languages"
- pdf G. Longobardi, C. Guardiano, "Evidence for syntax
as a signal of historical relatedness"
K.Ehret, B.Szmrecsanyi, "An information-theoretic approach to
assess linguistic complexity"
M.Bane, "Quantifying and measuring Morphological Complexity"
A.Kaltchenko, "Algorithms for estimating information distance with
applications to bioinformatics and linguistics"
M.Belkin, P.Niyogi, "Towards a theoretical foundation for Laplacian-based
- pdf P.Breiding, S.Kalisnik, B.Sturmfels, M.Weinstein, "Learning algebraic varieties from samples"
- pdf A.Auffinger, A.Lerario, E.Lundberg, "Topologies of random
geometric complexes on Riemannian manifolds in the thermodynamic limit"
R.Clark, "Kolmogorov complexity and the information content of parameters"
A.K.Zvonkin, L.A.Levin, "The complexity of finite objects and the
development of the concepts of information and randomness by means of the
theory of algorithms"
pdf R.Sproat, M.Yarmohammadi, I.Shafran, B.Roark,
- pdf E.P.Stabler, "Computational perspectives on minimalism"
- pdf T.Hunter, C.Dyer, "Distributions on Minimalist Grammar Derivations"
- pdf P.beim Graben, S.Gerth, "Geometric representations for minimalist grammars"
S.Giraudo, J.G.Luque, L.Mignot, F.Nicart, "Operads, quasiorders and
pdf T.Ceccherini-Silberstein, W.Woess, "Growth and Ergodicity
of Context-free Languages"
- pdf J.Shallit, "Number Theory and Formal Languages"
Eibe Frank, "Formal Languages and Automata", Chapter 6
- pdf L.Sennhauser, R.C.Berwick, "Evaluating the Ability of LSTMs to Learn Context-Free Grammars"
Schedule of Final Presentations
- Tuesday April 2 (class time)
- Laurestine Bradford, "Applications
of Lexicographic Semirings to Problems in Speech and Language Processing"
- Gal Gross, "Algebraic languages and polyominoes enumeration"
- Amjad Mobayed, "Traces of The Mouth: Andrei Anderyevich Markov's
Mathematization of Writing"
- Tuesday April 9 (class time)
- Shuyang Shen, "Number theory and formal languages"
- Sitanshu Gakkhar, "Computational neurolinguistics"
- David Ledvinka, "Monad Transformers for Natural Language: Combining
Monads to Model Effect Interaction"
- Feodor Kogan, "Operads and formal grammar"
- Wednesday April 10 (class time)
- Suleiman Motasem, "Arabic computational linguistics"
- Jesse Frolich and Andrew Wilson, "toki pun-a: a computational
approach to jokes (i.e. syntactic ambiguity)"