Designing software to maximize learning1

This paper starts from the assumption that any evaluation of educational software should focus on whether or not, and the extent to which, it maximizes learning. It is particularly concerned with the impact of software on the quality of learning. The paper reviews key texts in the literature on learning, including some which relate directly to software development, and suggests ways in which a range of learning theories can inform the process of software design. The paper sets out to make a contribution to both the design and the evaluation of educational software

A General Formula for the Mismatch Capacity

The fundamental limits of channels with mismatched decoding are addressed. A general formula is established for the mismatch capacity of a general channel, defined as a sequence of conditional distributions with a general decoding metrics sequence. We deduce an identity between the Verd\'{u}-Han general channel capacity formula, and the mismatch capacity formula applied to Maximum Likelihood decoding metric. Further, several upper bounds on the capacity are provided, and a simpler expression for a lower bound is derived for the case of a non-negative decoding metric. The general formula is specialized to the case of finite input and output alphabet channels with a type-dependent metric. The closely related problem of threshold mismatched decoding is also studied, and a general expression for the threshold mismatch capacity is obtained. As an example of threshold mismatch capacity, we state a general expression for the erasures-only capacity of the finite input and output alphabet channel. We observe that for every channel there exists a (matched) threshold decoder which is capacity achieving. Additionally, necessary and sufficient conditions are stated for a channel to have a strong converse. Csisz\'{a}r and Narayan's conjecture is proved for bounded metrics, providing a positive answer to the open problem introduced in [1], i.e., that the "product-space" improvement of the lower random coding bound, $C_q^{(\infty)}(W)$, is indeed the mismatch capacity of the discrete memoryless channel $W$. We conclude by presenting an identity between the threshold capacity and $C_q^{(\infty)}(W)$ in the DMC case

Phase-matchable nonlinear optical interactions in periodic thin films

A proposal for a new method of phase matching in nonlinear optical interactions is made. A periodic perturbation of the surface of a thin-film waveguide generates space harmonics with new propagation constants which can be phase matched. An analysis of this proposal shows it to be particularly interesting for a class of thin-film nonlinear devices using the cubic optically isotropic semiconductors (such as GaAs, GaP, etc.) which possess high nonlinear optical coefficients but are not phase matchable by the conventional birefringent techniques