PROTECTING PROPERTY RIGHTS WITH STRICT SCRUTINY: AN ARGUMENT FOR THE SPECIFICALLY AND UNIQUELY ATTRIBUTABLE STANDARD

This article analyzes three levels of scrutiny states have applied to regulatory takings cases. These include \u27judicial deterrence , rational nexus , and specifically and uniquely attributable . The author argues that the first two standards are inefficient and concludes in favor of the specifically and uniquely attributable standard

Super-Linear Gate and Super-Quadratic Wire Lower Bounds for Depth-Two and Depth-Three Threshold Circuits

In order to formally understand the power of neural computing, we first need to crack the frontier of threshold circuits with two and three layers, a regime that has been surprisingly intractable to analyze. We prove the first super-linear gate lower bounds and the first super-quadratic wire lower bounds for depth-two linear threshold circuits with arbitrary weights, and depth-three majority circuits computing an explicit function. $\bullet$ We prove that for all $\epsilon\gg \sqrt{\log(n)/n}$, the linear-time computable Andreev's function cannot be computed on a $(1/2+\epsilon)$-fraction of $n$-bit inputs by depth-two linear threshold circuits of $o(\epsilon^3 n^{3/2}/\log^3 n)$ gates, nor can it be computed with $o(\epsilon^{3} n^{5/2}/\log^{7/2} n)$ wires. This establishes an average-case ``size hierarchy'' for threshold circuits, as Andreev's function is computable by uniform depth-two circuits of $o(n^3)$ linear threshold gates, and by uniform depth-three circuits of $O(n)$ majority gates. $\bullet$ We present a new function in $P$ based on small-biased sets, which we prove cannot be computed by a majority vote of depth-two linear threshold circuits with $o(n^{3/2}/\log^3 n)$ gates, nor with $o(n^{5/2}/\log^{7/2}n)$ wires. $\bullet$ We give tight average-case (gate and wire) complexity results for computing PARITY with depth-two threshold circuits; the answer turns out to be the same as for depth-two majority circuits. The key is a new random restriction lemma for linear threshold functions. Our main analytical tool is the Littlewood-Offord Lemma from additive combinatorics

The Alien \u3ci\u3eHippodamia Variegata\u3c/i\u3e (Coleoptera: Coccinellidae) Quickly Establishes Itself Throughout Wisconsin

(excerpt) Hippodamia variegata (Goeze) (Coleoptera: Coccinellidae) is a Palaearctic species that was first reported to be established in the Nearctic near Montreal, Quebec, in 1984 (Gordon 1987). Since then, this small beetle has been expanding its range in North America, a process summarized by Gardiner and Parsons (2005). It was first reported from Michigan in 2005 (Gardiner and Parsons 2005) and from Ohio in 2007 (Pavuk et al. 2007)

Twisted Alexander Polynomials and Representation Shifts

For any knot, the following are equivalent. (1) The infinite cyclic cover has uncountably many finite covers; (2) there exists a finite-image representation of the knot group for which the twisted Alexander polynomial vanishes; (3) the knot group admits a finite-image representation such that the image of the fundamental group of an incompressible Seifert surface is a proper subgroup of the image of the commutator subgroup of the knot group.Comment: 7 pages, no figure

Coupling QCD-scale axion-like particles to gluons

We present a novel data-driven method for determining the hadronic interaction strengths of axion-like particles (ALPs) with QCD-scale masses. Using our method, it is possible to calculate the hadronic production and decay rates of ALPs, along with many of the largest ALP decay rate to exclusive final states. To illustrate the impact on QCD-scale ALP phenomenology, we consider the scenario where the ALP-gluon coupling is dominant over the ALP coupling to photons, electroweak bosons, and all fermions for $m_{\pi} \lesssim m_a \lesssim 3$ GeV. We emphasize, however, that our method can easily be generalized to any set of ALP couplings to SM particles. Finally, using the approach developed here, we provide calculations for the branching fractions of $\eta_c \to VV$ decays, i.e. $\eta_c$ decays into two vector mesons, which are consistent with the known experimental values.Comment: 19 pages, 7 figures; v3 Fig 4 updated to account for a small change in the limit taken from [1903.03586

Development of a head-mounted, eye-tracking system for dogs

Growing interest in canine cognition and visual perception has promoted research into the allocation of visual attention during free-viewing tasks in the dog. The techniques currently available to study this (i.e. preferential looking) have, however, lacked spatial accuracy, permitting only gross judgements of the location of the dog’s point of gaze and are limited to a laboratory setting. Here we describe a mobile, head-mounted, video-based, eye-tracking system and a procedure for achieving standardised calibration allowing an output with accuracy of 2-3º. The setup allows free movement of dogs; in addition the procedure does not involve extensive training skills, and is completely non-invasive. This apparatus has the potential to allow the study of gaze patterns in a variety of research applications and could enhance the study of areas such as canine vision, cognition and social interactions