Lower Bound on the Propagation Speed of Gravity from Gravitational Cherenkov Radiation

Recently, interesting 4-D Lorentz violating models have been proposed, in which all particles have a common maximum velocity $c$, but gravity propagates (in the preferred frame) with a different maximum velocity $c_g \neq c$. We show that the case $c_g < c$ is very tightly constrained by the observation of the highest energy cosmic rays. Assuming a galactic origin for the cosmic rays gives a conservative bound of $c-c_g < 2 \times 10^{-15} c$; if the cosmic rays have an extragalactic origin the bound is orders of magnitude tighter, of order $c-c_g < 2 \times 10^{-19} c$.Comment: 8 pages with 1 figure, JHEP style. References added, slight (superficial) change

UV Cascade in Classical Yang-Mills Theory

We study the real-time behavior of classical Yang-Mills theory under initial conditions with nonperturbatively large, infrared field amplitudes. Our lattice study confirms the cascade of energy towards higher momenta and lower occupancy, which occurs via a scaling solution $f[p,t_1] = (t_0/t_1)^{4/7}\, f[p (t_0/t_1)^{1/7},t_0]$. Above a characteristic scale p_{max}, f falls exponentially; below p_{max}, $f[p] \propto p^{-4/3}$. We find no evidence for different infrared exponents or for infrared occupancies in excess of those described by this scaling solution. We also investigate what the fate of large occupancies would be, both in the electric and the magnetic sector.Comment: 24 pages with 13 color figure

Foreword: Reflections on our Founding

Law Journals have been under heavy criticism for as long as we can remember. The criticisms come from all quarters, including judges, law professors, and even commentators at large. In an address at the Fourth Circuit Judicial Conference almost a decade ago, for example, Chief Justice Roberts complained about the “disconnect between the academy and the profession.” More pointedly, he continued, “[p]ick up a copy of any law review that you see, and the first article is likely to be, you know, the influence of Immanuel Kant on evidentiary approaches in 18th Century Bulgaria, or something, which I’m sure was of great interest to the academic that wrote it, but isn’t of much help to the bar.” Similarly, law professors have developed what Lawrence Friedman calls “a literature of invective” against law reviews. Adam Liptak summarized one line of criticism with a question: “[W]hy are law reviews, the primary repositories of legal scholarship, edited by law students?

Race, Federalism, and Voting Rights

In Shelby County v. Holder, the Court struck down an important provision of the Voting Rights Act, section 4, on federalism grounds. The Court argued that Congress no longer had the power to enact section 4 because of the “federalism costs” imposed by the Act and because the Act violated basic principles of federalism. Unfortunately, the Court failed to articulate the costs to federalism imposed by the Act, much less conduct a cost-benefit analysis in order to determine whether the benefits of the Act outweighed its costs. Moreover, the Court failed to discuss whether the Reconstruction Amendments ought to matter at all to the federalism debate. In this Essay, we ask three basic questions in response to Shelby County. First, what does the Court mean by “federalism costs,” and why have these costs undermined the constitutionality of the VRA? Second, does the failure to discuss Reconstruction and the Reconstruction Amendments undermine the Court’s decision in Shelby County? And third, we ask how should we understand the utility of federalism in the context of race and voting. We suggest that if one purpose of federalism is that it enables minorities to engage in self-rule, we should ask whether federalism enables racial minorities to engage in self-rule

Foreword: Reflections on our Founding

Law Journals have been under heavy criticism for as long as we can remember. The criticisms come from all quarters, including judges, law professors, and even commentators at large. In an address at the Fourth Circuit Judicial Conference almost a decade ago, for example, Chief Justice Roberts complained about the “disconnect between the academy and the profession.” More pointedly, he continued, “[p]ick up a copy of any law review that you see, and the first article is likely to be, you know, the influence of Immanuel Kant on evidentiary approaches in 18th Century Bulgaria, or something, which I’m sure was of great interest to the academic that wrote it, but isn’t of much help to the bar.” Similarly, law professors have developed what Lawrence Friedman calls “a literature of invective” against law reviews. Adam Liptak summarized one line of criticism with a question: “[W]hy are law reviews, the primary repositories of legal scholarship, edited by law students?

Efficient Construction of Probabilistic Tree Embeddings

In this paper we describe an algorithm that embeds a graph metric $(V,d_G)$ on an undirected weighted graph $G=(V,E)$ into a distribution of tree metrics $(T,D_T)$ such that for every pair $u,v\in V$, $d_G(u,v)\leq d_T(u,v)$ and ${\bf{E}}_{T}[d_T(u,v)]\leq O(\log n)\cdot d_G(u,v)$. Such embeddings have proved highly useful in designing fast approximation algorithms, as many hard problems on graphs are easy to solve on tree instances. For a graph with $n$ vertices and $m$ edges, our algorithm runs in $O(m\log n)$ time with high probability, which improves the previous upper bound of $O(m\log^3 n)$ shown by Mendel et al.\,in 2009. The key component of our algorithm is a new approximate single-source shortest-path algorithm, which implements the priority queue with a new data structure, the "bucket-tree structure". The algorithm has three properties: it only requires linear time in the number of edges in the input graph; the computed distances have a distance preserving property; and when computing the shortest-paths to the $k$-nearest vertices from the source, it only requires to visit these vertices and their edge lists. These properties are essential to guarantee the correctness and the stated time bound. Using this shortest-path algorithm, we show how to generate an intermediate structure, the approximate dominance sequences of the input graph, in $O(m \log n)$ time, and further propose a simple yet efficient algorithm to converted this sequence to a tree embedding in $O(n\log n)$ time, both with high probability. Combining the three subroutines gives the stated time bound of the algorithm. Then we show that this efficient construction can facilitate some applications. We proved that FRT trees (the generated tree embedding) are Ramsey partitions with asymptotically tight bound, so the construction of a series of distance oracles can be accelerated

The toxic sheep collar for control of sheep-killing coyotes: A progress report

The toxic sheep collar is the most selective method known for killing coyotes that prey on domestic sheep. The concept dates back to the early 1900's and has been studied at the Denver Wildlife Research Center (DWRC) since 1974. Field tests with sodium cyanide (NaCN) in 1975 were unsuccessful due to repellent properties of the toxicant and to the apparent reluctance of coyotes to attack tethered lambs wearing bulky collars. Coyotes attacked one or more tethered, collared lambs in 7 of the 19 test pastures. In all, 14 collared lambs were attacked. Eight of the collars were punctured but no dead coyotes were recovered. A smaller collar containing diphacinone was field tested in 1976. The diphacinone-filled collars were readily accepted by coyotes and lethal to them, but the slow action (5-16 days between dosing and death) of diphacinone made it difficult to assess the effectiveness of these collars under field conditions. Target flocks containing 1 to 12 collared lambs plus uncollared ewes were placed in 15 fenced pastures from which the larger ranch flocks had been removed after repeated coyote predation. One or more collared lambs were attacked in 11 of the 15 tests. An unknown number of coyotes were killed, and in most tests the subsequent incidence of predation was lower than that before the test. Captive coyotes continued to kill sheep for 4 or 5 days after they received a lethal dose of diphacinone; therefore a faster-acting toxicant is needed. This research has shown that problem coyotes can be killed with toxic collars, but further studies are needed to determine the feasibility of this approach compared with traditional means of control. In most tests to date the frequency of coyote predation has been too low and too irregular to permit effective use of the collar; target flocks were in the field for an average of 10 days before being attacked. The known disadvantages of the method include the need to sacrifice live lambs, the human hazards associated with the use of toxicants under field conditions, and the costs of managing target flocks and other sheep in the problem areas

Negative Differential Spin Conductance by Population Switching

An examination of the properties of many-electron conduction through spin-degenerate systems can lead to situations where increasing the bias voltage applied to the system is predicted to decrease the current flowing through it, for the electrons of a particular spin. While this does not necessarily constitute negative differential conductance (NDC) per se, it is an example of negative differential conductance per spin (NDSC) which to our knowledge is discussed here for the first time. Within a many-body master equation approach which accounts for charging effects in the Coulomb Blockade regime, we show how this might occur.Comment: 6 page, 2 figure