Movie Reviews- Unfaithful

Okay, so honestly, the fact that this movie was way hot almost outweighed its flaws. Almost...but not quite. So let’s begin with Richard Gere. First of all, I thought his initial reaction was accurate. Well, not accurate, because I can’t really back that up...but handled in what seemed to be a realistic way. His relationship with Diane Lane was logical up to the point where you believed that she cheated because they were just so mismatched. I don’t much see Gere as a romantic lead (even though some casting directors do), so I really could see Lane growing apart. ~excerpt from pros

Unfaithful Glitch Propagation in Existing Binary Circuit Models

We show that no existing continuous-time, binary value-domain model for digital circuits is able to correctly capture glitch propagation. Prominent examples of such models are based on pure delay channels (P), inertial delay channels (I), or the elaborate PID channels proposed by Bellido-D\'iaz et al. We accomplish our goal by considering the solvability/non-solvability border of a simple problem called Short-Pulse Filtration (SPF), which is closely related to arbitration and synchronization. On one hand, we prove that SPF is solvable in bounded time in any such model that provides channels with non-constant delay, like I and PID. This is in opposition to the impossibility of solving bounded SPF in real (physical) circuit models. On the other hand, for binary circuit models with constant-delay channels, we prove that SPF cannot be solved even in unbounded time; again in opposition to physical circuit models. Consequently, indeed none of the binary value-domain models proposed so far (and that we are aware of) faithfully captures glitch propagation of real circuits. We finally show that these modeling mismatches do not hold for the weaker eventual SPF problem.Comment: 23 pages, 15 figure

Geometry of the faithfulness assumption in causal inference

Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for the PC-algorithm and potentially also for other algorithms based on partial correlation testing in the Gaussian case.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1080 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

K(E10), Supergravity and Fermions

We study the fermionic extension of the E10/K(E10) coset model and its relation to eleven-dimensional supergravity. Finite-dimensional spinor representations of the compact subgroup K(E10) of E(10,R) are studied and the supergravity equations are rewritten using the resulting algebraic variables. The canonical bosonic and fermionic constraints are also analysed in this way, and the compatibility of supersymmetry with local K(E10) is investigated. We find that all structures involving A9 levels 0,1 and 2 nicely agree with expectations, and provide many non-trivial consistency checks of the existence of a supersymmetric extension of the E10/K(E10) coset model, as well as a new derivation of the `bosonic dictionary' between supergravity and coset variables. However, there are also definite discrepancies in some terms involving level 3, which suggest the need for an extension of the model to infinite-dimensional faithful representations of the fermionic degrees of freedom.Comment: 50 page