The double slit experiment and the time reversed fire alarm

When both slits of the double slit experiment are open, closing one paradoxically increases the detection rate at some points on the detection screen. Feynman famously warned that temptation to "understand" such a puzzling feature only draws us into blind alleys. Nevertheless, we gain insight into this feature by drawing an analogy between the double slit experiment and a time reversed fire alarm. Much as closing the slit increases probability of a future detection, ruling out fire drill scenarios, having heard the fire alarm, increases probability of a past fire (using Bayesian inference). Classically, Bayesian inference is associated with computing probabilities of past events. We therefore identify this feature of the double slit experiment with a time reversed thermodynamic arrow. We believe that much of the enigma of quantum mechanics is simply due to some variation of time's arrow. In further support of this, we employ a plausible formulation of the thermodynamic arrow to derive an uncertainty in classical mechanics that is reminiscent of quantum uncertainty.Comment: Last two paragraphs of Discussion section are an addendum to the version accepted at Il Nuovo Cimento B

The Supremacy Clause as Structural Safeguard of Federalism: State Judges and International Law in the Post-Erie Era

Against a backdrop of state constitutional and legislative initiatives aimed at limiting judicial use of international law, this Article argues that state judges have, by and large, interpreted treaties and customary international law so as to narrow their effect on state law-making prerogatives. Where state judges have used international law more liberally, they have done so to give effect to state executive and legislative objectives. Not only does this thesis suggest that the trend among state legislatures to limit state judges\u27 use of international law is self-defeating, it also gives substance to a relatively unexplored structural safeguard of federalism: state judges\u27 authority under the Supremacy Clause to harmonize treaties and customary international law with state constitutional, legislative, and common law, and to influence federal jurisprudence on the scope and effect of binding international law. The Supremacy Clause empowers state judges to adapt international law to maximize benefits for--and minimize disruptions to--state policy objectives. As more areas of traditional state authority are displaced by international law, state judicial management of international law may be the strongest structural protection for state interests

Zika, Pregnancy, and the Law

The public health emergency surrounding the spread of the Zika virus has resurrected and brought into sharp relief some of the most vexing questions surrounding the relationship between pregnancy and law: the appropriate circumstances, if any, in which fetal tissue research is permissible; when and how the government may sponsor statements intended to influence reproductive decisions; and how to balance the health and rights of both women and their unborn children when health threats target both

Practical quantitative measurement of graticule misalignment relative to collimator axis of rotation.

We design a practical procedure for measuring translational and rotational misalignment of graticule with collimator axis of rotation and collimator jaws, respectively. The procedure's quantitative results are accurate to less than 0.2 mm (at isocenter) and do not assume alignment of radiation focal spot with collimator axis of rotation. When provided with these quantitative results, the manufacturer can custom-adjust graticules to the purchaser's collimator head

Local Optimality Certificates for LP Decoding of Tanner Codes

We present a new combinatorial characterization for local optimality of a codeword in an irregular Tanner code. The main novelty in this characterization is that it is based on a linear combination of subtrees in the computation trees. These subtrees may have any degree in the local code nodes and may have any height (even greater than the girth). We expect this new characterization to lead to improvements in bounds for successful decoding. We prove that local optimality in this new characterization implies ML-optimality and LP-optimality, as one would expect. Finally, we show that is possible to compute efficiently a certificate for the local optimality of a codeword given an LLR vector

Analysis of the Min-Sum Algorithm for Packing and Covering Problems via Linear Programming

Message-passing algorithms based on belief-propagation (BP) are successfully used in many applications including decoding error correcting codes and solving constraint satisfaction and inference problems. BP-based algorithms operate over graph representations, called factor graphs, that are used to model the input. Although in many cases BP-based algorithms exhibit impressive empirical results, not much has been proved when the factor graphs have cycles. This work deals with packing and covering integer programs in which the constraint matrix is zero-one, the constraint vector is integral, and the variables are subject to box constraints. We study the performance of the min-sum algorithm when applied to the corresponding factor graph models of packing and covering LPs. We compare the solutions computed by the min-sum algorithm for packing and covering problems to the optimal solutions of the corresponding linear programming (LP) relaxations. In particular, we prove that if the LP has an optimal fractional solution, then for each fractional component, the min-sum algorithm either computes multiple solutions or the solution oscillates below and above the fraction. This implies that the min-sum algorithm computes the optimal integral solution only if the LP has a unique optimal solution that is integral. The converse is not true in general. For a special case of packing and covering problems, we prove that if the LP has a unique optimal solution that is integral and on the boundary of the box constraints, then the min-sum algorithm computes the optimal solution in pseudo-polynomial time. Our results unify and extend recent results for the maximum weight matching problem by [Sanghavi et al.,'2011] and [Bayati et al., 2011] and for the maximum weight independent set problem [Sanghavi et al.'2009]