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

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

On the Multiple Access Channel with Asynchronous Cognition

In this paper we introduce the two-user asynchronous cognitive multiple access channel (ACMAC). This channel model includes two transmitters, an uninformed one, and an informed one which knows prior to the beginning of a transmission the message which the uninformed transmitter is about to send. We assume that the channel from the uninformed transmitter to the receiver suffers a fixed but unknown delay. We further introduce a modified model, referred to as the asynchronous codeword cognitive multiple access channel (ACC-MAC), which differs from the ACMAC in that the informed user knows the signal that is to be transmitted by the other user, rather than the message that it is about to transmit. We state inner and outer bounds on the ACMAC and the ACC-MAC capacity regions, and we specialize the results to the Gaussian case. Further, we characterize the capacity regions of these channels in terms of multi-letter expressions. Finally, we provide an example which instantiates the difference between message side-information and codeword side-information.Comment: arXiv admin note: substantial text overlap with arXiv:1402.161

On the non-existence of unbiased estimators in constrained estimation problems

We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then there exists no unbiased estimator.Weaker conditions for the absence of unbiased constrained estimators are also specified. We provide several examples which demonstrate the utility of these conditions