◮ In most programming languages, variables are mutable — i.e., a variable provides both ◮ a name that refers to a previously calculated value, and ◮ the possibility of overwriting this value with another (which will be referred to by the same name) ◮ In some languages (e.g., OCaml), these features are separate: ◮ variables are only for naming — the binding between a variable and its value is immutable ◮ introduce a new class of mutable values (called reference cells or references) ◮ at any given moment, a reference holds a value (and can be dereferenced to obtain this value) ◮ a new value may be assigned to a reference We choose OCaml’s style, which is easier to work with formally. So a variable of type T in most languages (except OCaml) will correspond to a Ref T (actually, a Ref(Option T)) here.

variables are mutable — i.e., a variable provides both I a name that refers to a previously calculated value, and I the possibility of overwriting this value with another (which will be referred to by the same name) I In some languages (e.g., OCaml), these features are separate: I variables are only for naming — the binding between a variable and its value is immutable I introduce a new class of mutable values (called reference cells or references) I at any given moment, a reference holds a value (and can be dereferenced to obtain this value) I a new value may be assigned to a reference We choose OCaml’s style, which is easier to work with formally. So a variable of type T in most languages (except OCaml) will correspond to a Ref T (actually, a Ref(Option T)) here.

Abstract not found

Abstract not found

I want most of all to thank Joe Harris for introducing me to the beautiful geometry of algebraic curves and for guiding me through the process of writing a thesis. I could not have written this thesis without your patient and clear explanations of so many topics. You were always available to answer my questions, and I always left your office excited to continue my work. I am indebted to many members of the Harvard Mathematics Department who have taught and advised me in the past four years, especially Curtis McMullen, Michael Hopkins and Barry Mazur. Thanks also to Thomas Garrity, who introduced me to mathematical research at Williams College. Finally, thanks to my parents and my sister for encouraging me to pursue mathe-matics and remaining supportive whenever I encountered difficulties. 1

We have used information-theoretic ideas to derive a class of practical and nearly optimal schemes for adapting the size of a neural network. By removing unimportant weights from a network, several improvements can be expected: better generalization, fewer training examples required, and improved

Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, data-flow graphs, Petri nets

algorithms are available that make a bounded number of mistakes, with the bound independent of the number of examples seen by the learner. We present one such algorithm that learns disjunctive Boolean functions, along with variants for learning other classes of Boolean functions. The basic method can

the object has all coefficients nonzero, but the coefficients obey an `p bound, for some p ∈ (0, 1]. These experiments show that the basic inequalities behind the CS method seem to involve reasonable constants. We next consider synthetic examples modelling problems in spectroscopy and image pro-

the probabilistic and ofttimes incorrect world models generated by learning processes. Execution is fully reactive in the sense that no planning intervenes between perception and action. Dyna relies on machine learning methods for learning from examples--these are among the basic building blocks making up