A NOTE ON AXIOMS FOR INFINITE-GENERIC STRUCTURES (2008)
In this note we give some natural examples of theories T in countable logics L such that the class GT of infinite-generic structures for T is not axiomatizable by a single sentence of LW1> w. The...
FREE ABELIAN LATTICE-ORDERED GROUPS (2008)
Angus Macintyre, Françoise Point
Abstract. Let n be a positive integer and F Aℓ(n) be the free abelian latticeordered group on n generators. We prove that F Aℓ(m) and F Aℓ(n) do not satisfy the same first-order sentences in...
Angus Macintyre, Eduardo D. Sontag
This paper deals with analog circuits. It establishes the finiteness of VC dimension, teaching dimension, and several other measures of sample complexity which arise in learning theory. It also shows...
A Failure of Quantifier Elimination (2007)
Angus Macintyre, David Marker, Let L
uld actually eliminate quantifiers in the language L an [ flogg [ fx q : q 2 Qg. Here we show that although exp and log are interdefinable, log is essential for quantifer elimination. Theorem. Let...
Marek Karpinski, Angus Macintyre, Marek Karpinski (bonn, Angus Macintyre (edinburgh
Using a modification of Wilkie's recent proof of o-minimality for Pfaffian functions, we give an invariant characterization of o-minimal expansions of IR. We apply this to construct the Pfaffian...
Logarithmic-exponential series (2007)
Abstract. We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of "LE-series " (logarithmic-exponential series), which is...
Luc Bélair, Angus Macintyre, Thomas Scanlon
Abstract. We give axiomatizations and prove quantifier elimination theorems for first-order theories of unramified valued fields with an automorphism having a close interaction with the valuation. We...
Model theory of the Frobenius on the Witt vectors (2002)
Luc Bélair, Angus Macintyre, Thomas Scanlon
We give axiomatizations and quantifier eliminations for first-order theories of finitely ramified valued fields with an automorphism having a close interaction with the valuation. We achieve an...
Polynomial bounds for VC dimension of sigmoidal and general pfaffian neural networks (1997)
Marek Karpinski, Angus Macintyre
Abstract. We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension...
Marek Karpinski, Angus Macintyre, Marek Karpinski (bonn, Angus Macintyre (oxford
Using a modification of Wilkie's recent proof of o-minimality for Pfaffian functions, we gave an invariant characterization of o-minimal expansions of IR. We apply this to construct the Pfaffian...
Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks (1996)
By Marek, Marek Karpinski, Angus Macintyre
We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog...
Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks (1995)
Marek Karpinski, Angus Macintyre
. We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of...
Polynomial Bounds for VC Dimension of Sigmoidal Neural Networks (1995)
Marek Karpinski Dept, Marek Karpinski, Angus Macintyre
. We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, the VC Dimension of analog...
VC Dimension of Sigmoidal and General Pfaffian Neural Networks (1995)
Marek Karpinski, Angus Macintyre
We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog...
Polynomial Bounds for VC Dimension of Sigmoidal Neural Networks (1995)
Marek Karpinski, Angus Macintyre
. We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, the VC Dimension of analog...
Bounding VC-Dimension for Neural Networks: Progress and Prospects (1995)
Marek Karpinski, Angus Macintyre
. Techniques from differential topology are used to give polynomial bounds for the VC-dimension of sigmoidal neural networks. The bounds are quadratic in w, the dimension of the space of weights....
Polynomial Bounds for VC Dimension of Sigmoidal Neural Networks (1995)
Marek Karpinski, Angus Macintyre
We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, the VC Dimension of analog...
VC Dimension of Sigmoidal and General Pfaffian Networks (1995)
Marek Karpinski, Angus Macintyre
We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the first time, that the VC Dimension of analog...
Finiteness Results for Sigmoidal "Neural" Networks (1993)
Angus Macintyre, Eduardo D. Sontag
) Angus Macintyre Mathematical Inst., University of Oxford Oxford OX1 3LB, England, UK E-mail: ajm@maths.ox.ac.uk Eduardo D. Sontag 3 Dept. of Mathematics, Rutgers University New Brunswick, NJ 08903...
Thesis (Ph. D.)--University of California, Davis, 1982.
Classifying pairs of real-closed fields. (1967)
Thesis (Ph. D.)--Dept. of Mathematics, Stanford University, 1968.
Logarithmic-Exponential Power Series
. We use generalized power series to construct algebraically a nonstandard model of the theory of the real field with exponentiation. This model enables us to show the undefinability of the zeta...
Logarithmic-Exponential Series
. We extend the eld of Laurent series over the reals in a canonical way to an ordered dierential eld of \LE-series" (logarithmic-exponential series), which is equipped with a well behaved...