no code implementations • 10 Nov 2023 • Matilde Marcolli, Robert C. Berwick, Noam Chomsky
We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface.
no code implementations • 8 Sep 2023 • Vasiliki Liontou, Matilde Marcolli
We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the manifold signal.
no code implementations • 17 Jun 2023 • Matilde Marcolli, Robert C. Berwick, Noam Chomsky
In this paper we compare some old formulations of Minimalism, in particular Stabler's computational minimalism, and Chomsky's new formulation of Merge and Minimalism, from the point of view of their mathematical description in terms of Hopf algebras.
no code implementations • 29 May 2023 • Matilde Marcolli, Noam Chomsky, Robert Berwick
The syntactic Merge operation of the Minimalist Program in linguistics can be described mathematically in terms of Hopf algebras, with a formalism similar to the one arising in the physics of renormalization.
no code implementations • 8 Jan 2022 • Matilde Marcolli
The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.
no code implementations • 3 Nov 2021 • Vasiliki Liontou, Matilde Marcolli
We analyze the interplay between contact geometry and Gabor filters signal analysis in geometric models of the primary visual cortex.
1 code implementation • 17 Apr 2021 • Sitanshu Gakkhar, Matilde Marcolli
We study phylogenetic signal present in syntactic information by considering the syntactic structures data from Longobardi (2017b), Collins (2010), Ceolin et al. (2020) and Koopman (2011).
no code implementations • 12 Mar 2019 • Alexander Port, Taelin Karidi, Matilde Marcolli
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages.
no code implementations • 26 Mar 2018 • Andrew Ortegaray, Robert C. Berwick, Matilde Marcolli
We compute clustering coefficients and their variance.
no code implementations • 5 Dec 2017 • Kevin Shu, Andrew Ortegaray, Robert Berwick, Matilde Marcolli
Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures.
no code implementations • 2 Oct 2016 • Kevin Shu, Matilde Marcolli
We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters.
no code implementations • 10 Jul 2016 • Kevin Shu, Sharjeel Aziz, Vy-Luan Huynh, David Warrick, Matilde Marcolli
In this paper we identify several serious problems that arise in the use of syntactic data from the SSWL database for the purpose of computational phylogenetic reconstruction.
no code implementations • 13 May 2016 • Yuri Manin, Matilde Marcolli
In particular, in this paper we consider the Vector Space Model of semantics based on frequency matrices, as used in Natural Language Processing.
no code implementations • 21 Oct 2015 • Jeong Joon Park, Ronnel Boettcher, Andrew Zhao, Alex Mun, Kevin Yuh, Vibhor Kumar, Matilde Marcolli
We propose a new method, based on Sparse Distributed Memory (Kanerva Networks), for studying dependency relations between different syntactic parameters in the Principles and Parameters model of Syntax.
1 code implementation • 31 Jul 2015 • Karthik Siva, Jim Tao, Matilde Marcolli
Using the SSWL database of syntactic parameters of world languages, and the MIT Media Lab data on language interactions, we construct a spin glass model of language evolution.
no code implementations • 18 Jul 2015 • Alexander Port, Iulia Gheorghita, Daniel Guth, John M. Clark, Crystal Liang, Shival Dasu, Matilde Marcolli
We study the persistent homology of the data set of syntactic parameters of the world languages.
no code implementations • 26 Jul 2014 • Matilde Marcolli
The code parameters of the resulting code can be compared with some classical bounds in coding theory: the asymptotic bound, the Gilbert-Varshamov bound, etc.