More security or less insecurity (transcript of discussion)

The purpose of this talk is to explore the possibility of an exploitable analogy between approaches to secure system design and theories of jurisprudence. The prevailing theory of jurisprudence in the West at the moment goes back to Hobbes. It was developed by Immanuel Kant and later by Rousseau, and is sometimes called the contractarian model after Rousseau’s idea of the social contract. It’s not the sort of contract that you look at and think, oh gosh, that might be nice, I might think about opting in to that, it’s more like a pop up licence agreement that says, do you want to comply with this contract, or would you rather be an outlaw. So you don’t get a lot of choice about it. Sometimes the same theory, flying the flag of Immanuel Kant, is called transcendental institutionalism, because the basic approach says, you identify the legal institutions that in a perfect world would govern society, and then you look at the processes and procedures, the protocols that everyone should follow in order to enable those institutions to work, and then you say, right, that can’t be transcended, so therefore there’s a moral imperative for everyone to do it. So this model doesn’t pay any attention to the actual society that emerges, or to the incentives that these processes actually place on various people to act in a particular way. It doesn’t look at any interaction effects, it simply says, well you have to behave in this particular way because that’s what the law says you have to do, and the law is the law, and anybody who doesn’t behave in that way is a criminal, or (in our terms) is an attackerFinal Accepted Versio

Unique Continuation for Quasimodes on Surfaces of Revolution: Rotationally invariant Neighbourhoods

We prove a strong conditional unique continuation estimate for irreducible quasimodes in rotationally invariant neighbourhoods on compact surfaces of revolution. The estimate states that Laplace quasimodes which cannot be decomposed as a sum of other quasimodes have $L^2$ mass bounded below by $C_\epsilon \lambda^{-1 - \epsilon}$ for any $\epsilon>0$ on any open rotationally invariant neighbourhood which meets the semiclassical wavefront set of the quasimode. For an analytic manifold, we conclude the same estimate with a lower bound of $C_\delta \lambda^{-1 + \delta}$ for some fixed $\delta>0$.Comment: 16 pages. Contains summaries of the author's results (with co-authors) from arXiv:1103.3908, arXiv:1303.3309, and arXiv:1303.617

Differentiating through Conjugate Gradient

This is the pre-print version of an article published by Taylor & Francis in Optimization Methods and Software on 6 January 2018, available online at: https://doi.org/10.1080/10556788.2018.1425862.We show that, although the Conjugate Gradient (CG) Algorithm has a singularity at the solution, it is possible to differentiate forward through the algorithm automatically by re-declaring all the variables as truncated Taylor series, the type of active variable widely used in Automatic Differentiation (AD) tools such as ADOL-C. If exact arithmetic is used, this approach gives a complete sequence of correct directional derivatives of the solution, to arbitrary order, in a single cycle of at most n iterations, where n is the number of dimensions. In the inexact case the approach emphasizes the need for a means by which the programmer can communicate certain conditions involving derivative values directly to an AD tool.Peer reviewe

High-frequency resolvent estimates on asymptotically Euclidean warped products

We consider the resolvent on asymptotically Euclidean warped product manifolds in an appropriate 0-Gevrey class, with trapped sets consisting of only finitely many components. We prove that the high-frequency resolvent is either bounded by $C_\epsilon |\lambda|^\epsilon$ for any $\epsilon>0$, or blows up faster than any polynomial (at least along a subsequence). A stronger result holds if the manifold is analytic. The method of proof is to exploit the warped product structure to separate variables, obtaining a one-dimensional semiclassical Schr\"odinger operator. We then classify the microlocal resolvent behaviour associated to every possible type of critical value of the potential, and translate this into the associated resolvent estimates. Weakly stable trapping admits highly concentrated quasimodes and fast growth of the resolvent. Conversely, using a delicate inhomogeneous blowup procedure loosely based on the classical positive commutator argument, we show that any weakly unstable trapping forces at least some spreading of quasimodes. As a first application, we conclude that either there is a resonance free region of size $| \Im \lambda | \leq C_\epsilon | \Re \lambda |^{-1-\epsilon}$ for any $\epsilon>0$, or there is a sequence of resonances converging to the real axis faster than any polynomial. Again, a stronger result holds if the manifold is analytic. As a second application, we prove a spreading result for weak quasimodes in partially rectangular billiards.Comment: 46 pages. Contains summaries of the author's results (with co-authors) from arXiv:1103.3908, arXiv:1303.330