Faster all-pairs shortest paths via circuit complexity

We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary edge weights. On the real RAM, where additions and comparisons of reals are unit cost (but all other operations have typical logarithmic cost), the algorithm runs in time $$\frac{n^3}{2^{\Omega(\log n)^{1/2}}}$$ and is correct with high probability. On the word RAM, the algorithm runs in $n^3/2^{\Omega(\log n)^{1/2}} + n^{2+o(1)}\log M$ time for edge weights in $([0,M] \cap {\mathbb Z})\cup\{\infty\}$. Prior algorithms used either $n^3/(\log^c n)$ time for various $c \leq 2$, or $O(M^{\alpha}n^{\beta})$ time for various $\alpha > 0$ and $\beta > 2$. The new algorithm applies a tool from circuit complexity, namely the Razborov-Smolensky polynomials for approximately representing ${\sf AC}^0[p]$ circuits, to efficiently reduce a matrix product over the $(\min,+)$ algebra to a relatively small number of rectangular matrix products over ${\mathbb F}_2$, each of which are computable using a particularly efficient method due to Coppersmith. We also give a deterministic version of the algorithm running in $n^3/2^{\log^{\delta} n}$ time for some $\delta > 0$, which utilizes the Yao-Beigel-Tarui translation of ${\sf AC}^0[m]$ circuits into "nice" depth-two circuits.Comment: 24 pages. Updated version now has slightly faster running time. To appear in ACM Symposium on Theory of Computing (STOC), 201

Who Owns the Law? Why We Must Restore Public Ownership of Legal Publishing

Each state has its own method for officially publishing the law. This article looks at the history of legal publishing for the fifty states before looking at how legal publishing even in moving to electronic publishing may not ensure public access to the law. The article addresses barriers to free access to the law in electronic publishing including copyright, contract law, and potentially, the Computer Fraud and Abuse Act. The article concludes with prescriptions for how different actors, including state governments, publishers, libraries, and others can ensure robust public access to the law moving forward

Growth or decline in the Church of England during the decade of Evangelism: did the Churchmanship of the Bishop matter?

The Decade of Evangelism occupied the attention of the Church of England throughout the 1990s. The present study employs the statistics routinely published by the Church of England in order to assess two matters: the extent to which these statistics suggest that the 43 individual dioceses finished the decade in a stronger or weaker position than they had entered it and the extent to which, according to these statistics, the performance of dioceses led by bishops shaped in the Evangelical tradition differed from the performance of dioceses led by bishops shaped in the Catholic tradition. The data demonstrated that the majority of dioceses were performing less effectively at the end of the decade than at the beginning, in terms of a range of membership statistics, and that the rate of decline varied considerably from one diocese to another. The only exception to the trend was provided by the diocese of London, which experienced some growth. The data also demonstrated that little depended on the churchmanship of the diocesan bishop in shaping diocesan outcomes on the performance indicators employed in the study

A Search for Planets Transiting the M Dwarf Debris Disk Host, AU Microscopii

We present high cadence, high precision multi-band photometry of the young, M1Ve, debris disk star, AU Microscopii. The data were obtained in three continuum filters spanning a wavelength range from 4500\AA to 6600\AA, plus H$\alpha$, over 28 nights in 2005. The lightcurves show intrinsic stellar variability due to starspots with an amplitude in the blue band of 0.051 magnitudes and a period of 4.847 days. In addition, three large flares were detected in the data which all occur near the minimum brightness of the star. We remove the intrinsic stellar variability and combine the lightcurves of all the filters in order to search for transits by possible planetary companions orbiting in the plane of the nearly edge-on debris disk. The combined final lightcurve has a sampling of 0.35 minutes and a standard deviation of 6.8 millimags (mmag). We performed Monte Carlo simulations by adding fake transits to the observed lightcurve and find with 95% significance that there are no Jupiter mass planets orbiting in the plane of the debris disk on circular orbits with periods, P $\le 5$ days. In addition, there are no young Neptune-like planets (with radii 2.5$\times$ smaller than the young Jupiter) on circular orbits with periods, P $\le 3$ days.Comment: accepted to MNRA

NASA Innovative Advanced Concepts (NIAC) Phase 1 Final Report: Venus Landsailer Zephyr

Imagine sailing across the hot plains of Venus! A design for a craft to do just this was completed by the COncurrent Multidisciplinary Preliminary Assessment of Space Systems (COMPASS) Team for the NASA Innovative Advanced Concepts (NIAC) project. The robotic craft could explore over 30 km of surface of Venus, driven by the power of the wind

The Dalradian rocks of Scotland: an introduction

The Dalradian Supergroup and its basement rocks, together with younger plutons, underpin most of the Grampian Highlands and the islands of the Inner Hebrides between the Highland Boundary and Great Glen faults. The Dalradian is a mid-Neoproterozoic to early-Ordovician sequence of largely clastic metasedimentary rocks, with some volcanic units, which were deformed and metamorphosed to varying degrees during the Early Palaeozoic Caledonian Orogeny. Sedimentation of the lower parts of the Dalradian Supergroup, possibly commencing about 730 million years ago, took place initially in fault-bounded rift basins, within the supercontinent of Rodinia and adjacent to sectors of continental crust that were later to become the foundations of North America, Greenland and Scandinavia. Later sedimentation reflected increased instability, culminating between 600 and 570 million years ago in continental rupture, volcanicity and the development of the Iapetus Ocean. This left the crustal foundations of Scotland, together with those of North America and Greenland, on a laterally extensive passive margin to the new continent of Laurentia, where turbiditic sedimentation continued for about 85 million years. Later plate movements led to closure of the Iapetus Ocean and the multi-event Caledonian Orogeny. Most of the deformation and metamorphism of the Dalradian strata peaked at about 470 million years ago, during the mid-Ordovician Grampian Event, which has been attributed to the collision of an oceanic arc with Laurentia. The later, mid-Silurian Scandian Event, attributed to the collision of the continent of Baltica with Laurentia and the final closure of the Iapetus Ocean, apparently had little effect on the Dalradian rocks but marked the start of late-orogenic uplift and extensive magmatism in the Grampian Highlands that continued until Early Devonian times. The Dalradian rocks thus record a wide range of sedimentary environments (alluvial, tidal, deltaic, shallow marine, turbiditic, debris flow) and a complex structural and metamorphic history. In areas of low strain, original sedimentary and volcanic structures are well preserved, even at relatively high metamorphic grades. There is convincing evidence for glacial episodes of worldwide importance and economic deposits of stratiform barium minerals are unique. The Grampian Highlands include two of the World's type-areas for metamorphic zonation, Barrovian and Buchan, with spectacular examples of the key metamorphic minerals, and various stages of migmatite development. Polyphase folding is widespread on all scales and gives rise to a range of associated cleavages and lineations. Regional dislocations, both ductile and brittle, are associated with a range of shear fabrics, breccias, clay gouges and veining