Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts

We study the analytic behavior of the restriction of a Siegel modular form to $\mathbb{H} \times \mathbb{H}$ in the case that the Siegel form is a Saito-Kurokawa lift. A formula of Ichino links this behavior to a family of $GL_3 \times GL_2$ $L$-functions.Comment: 28 page

Modelling Safety-Related Driving Behaviour - the Impact of Parameter Values

Traffic simulation models make assumptions about the safety-related behaviour of drivers. These assumptions may or may not replicate the real behaviour of those drivers who adopt seemingly unsafe behaviour, for example running red lights at signalised intersections or too closely following the vehicles in front. Such behaviour results in the performance of the system that we observe but will often result in conflicts and very occasionally in accidents. The question is whether these models should reflect safe behav- iour or actual behaviour. Good design should seek to enhance safety, but is the safety of a design neces- sarily enhanced by making unrealistically optimistic assumptions about the safety of drivers behaviour? This paper explores the questions associated with the choice of values for safety-related parameters in simulation models. The paper identifies the key parameters of traffic simulation models and notes that sev- eral of them have been derived from theory or informed guesswork rather than observation of real behav- iour and that, even where they are based on observations, these may have been conducted in circumstances quite different to those which now apply. Tests with the micro-simulation model DRACULA demonstrate the sensitivity of model predictions—and perhaps policy decisions—to the value of some of the key param- eters. It is concluded that, in general, it is better to use values that are realistic-but-unsafe than values that are safe-but-unrealistic. Although the use of realistic-but-unsafe parameter values could result in the adop- tion of unsafe designs, this problem can be overcome by paying attention to the safety aspects of designs. The possibility of using traffic simulation models to culties involved in doing so are discussed

On the Capacity Region for Secure Index Coding

We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region