Why Michigan v. EPA Requires that the Meaning of the Cost/Rationality Nexus Be Clarified

This article examines the recent decision in Michigan v. EPA, in which the U.S. Supreme Court held that the EPA acted unreasonably in not considering costs at the listing phase of the regulation of power plants’ emissions under a specific provision of the Clear Air Act (CAA). In Michigan, the Court interpreted the applicable statutory provision based on the principles of rational administrative decision-making, thereby establishing a connection between cost consideration by administrative agencies and the principles of reasonable exercise of administrative discretion. We contend that Michigan failed to properly appreciate the logical and axiological connection between cost consideration and administrative rationality (i.e., the cost/rationality nexus). More specifically, the Court failed to distinguish between two independent steps of cost consideration: cost determination and cost quantification. Cost determination considers that one set of relevant interests must be made a cost upon someone else, and decides how to allocate rights between competing interests. This decision rests on political considerations and moral factors that are independent of the concept of cost. Cost quantification requires deliberating to what extent one set of interests should be made a cost upon someone else. Unlike cost determination, cost quantification is logically based on the concept of cost. Cost quantification assumes cost determination in order to function. The failure to appreciate this distinction led to illogical reasoning by the Court and to a decision that is inconsistent with Congress’ cost determination. This paper contributes to the legal-economic literature on cost-benefit analysis (CBA) by outlining a functional dimension of cost consideration by administrative agencies that is frequently overlooked in legal-economic literature. While CBA proponents often note that cost consideration provides agencies with a method for promoting social welfare maximization, we emphasize that cost consideration enhances the rationality of administrative action by ensuring a transparent and accountable definition of the set of relevant interests that underpins the definition of costs and benefits

Jet Observables Without Jet Algorithms

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet clustering algorithm, they incorporate a jet radius parameter and a transverse momentum cut. Three of the ubiquitous jet-based observables---jet multiplicity, summed scalar transverse momentum, and missing transverse momentum---have event shape counterparts that are closely correlated with their jet-based cousins. Due to their "local" computational structure, these jet-like event shapes could potentially be used for trigger-level event selection at the LHC. Intriguingly, the jet multiplicity event shape typically takes on non-integer values, highlighting the inherent ambiguity in defining jets. By inverting jet multiplicity, we show how to characterize the transverse momentum of the n-th hardest jet without actually finding the constituents of that jet. Since many physics applications do require knowledge about the jet constituents, we also build a hybrid event shape that incorporates (local) jet clustering information. As a straightforward application of our general technique, we derive an event-shape version of jet trimming, allowing event-wide jet grooming without explicit jet identification. Finally, we briefly mention possible applications of our method for jet substructure studies.Comment: v2 - 31 pages, 18 figures; update to JHEP version, section 3.2 expanded, reference to FastJet contrib updated, results unchange

TASI 2012: Super-Tricks for Superspace

These lectures from the TASI 2012 summer school outline the basics of supersymmetry (SUSY) in 3+1 dimensions. Starting from a ground-up development of superspace, we develop all of the tools necessary to construct SUSY lagrangians. While aimed at an introductory level, these lectures incorporate a number of "super-tricks" for SUSY aficionados, including SUSY-covariant derivatives, equations of motion in superspace, background field methods, and non-linear realizations of goldstinos.Comment: 75 pages, 4 figures, 1 table. v2: formatting improved, hyperlinks added, references update

Pileup Per Particle Identification

We propose a new method for pileup mitigation by implementing "pileup per particle identification" (PUPPI). For each particle we first define a local shape $\alpha$ which probes the collinear versus soft diffuse structure in the neighborhood of the particle. The former is indicative of particles originating from the hard scatter and the latter of particles originating from pileup interactions. The distribution of $\alpha$ for charged pileup, assumed as a proxy for all pileup, is used on an event-by-event basis to calculate a weight for each particle. The weights describe the degree to which particles are pileup-like and are used to rescale their four-momenta, superseding the need for jet-based corrections. Furthermore, the algorithm flexibly allows combination with other, possibly experimental, probabilistic information associated with particles such as vertexing and timing performance. We demonstrate the algorithm improves over existing methods by looking at jet $p_T$ and jet mass. We also find an improvement on non-jet quantities like missing transverse energy.Comment: v2 - 23 pages, 10 figures; update to JHEP version, minor revisions throughout, results unchange

The Trispectrum in the Effective Field Theory of Large Scale Structure

We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for general wavenumber configurations of the trispectrum. We consistently incorporate vorticity and non-locality in time into the EFT counterterms and lay out a complete basis of building blocks for the stress tensor. We show predictions for the one-loop SPT trispectrum and the EFT contributions, focusing on configurations which have particular relevance for using LSS to constrain primordial non-Gaussianity.Comment: 25+3 pages, 7 figure

Non-Gaussian Covariance of the Matter Power Spectrum in the Effective Field Theory of Large Scale Structure

We compute the non-Gaussian contribution to the covariance of the matter power spectrum at one-loop order in Standard Perturbation Theory (SPT), and using the framework of the effective field theory (EFT) of large scale structure (LSS). The complete one-loop contributions are evaluated for the first time, including the leading EFT corrections that involve seven independent operators, of which four appear in the power spectrum and bispectrum. We compare the non-Gaussian part of the one-loop covariance computed with both SPT and EFT of LSS to two separate simulations. In one simulation, we find that the one-loop prediction from SPT reproduces the simulation well to $k_i + k_j \sim$ 0.25 h/Mpc, while in the other simulation we find a substantial improvement of EFT of LSS (with one free parameter) over SPT, more than doubling the range of $k$ where the theory accurately reproduces the simulation. The disagreement between these two simulations points to unaccounted for systematics, highlighting the need for improved numerical and analytic understanding of the covariance.Comment: v2 - 10+9 pages, 6 figures; minor changes + data analysis and conclusions updated. Version accepted for publication in PR

Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders

We introduce a method to compute one-loop soft functions for exclusive $N$-jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the $N$-jettiness hemisphere decomposition of [Jouttenus 2011] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti-$k_T$, XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in $pp \to L + 1$ jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius $R$. We find that the small-$R$ results, including corrections up to $\mathcal{O}(R^2)$, accurately capture the full behavior over a large range of $R$.Comment: 33 pages + appendices, 17 figures, v2: journal version, v3: fixed typo in eq.(4.37

Accuracy of Rats in Discriminating Visual Objects Is Explained by the Complexity of Their Perceptual Strategy

Despite their growing popularity as models of visual functions, it remains unclear whether rodents are capable of deploying advanced shape-processing strategies when engaged in visual object recognition. In rats, for instance, pattern vision has been reported to range from mere detection of overall object luminance to view-invariant processing of discriminative shape features. Here we sought to clarify how refined object vision is in rodents, and how variable the complexity of their visual processing strategy is across individuals. To this aim, we measured how well rats could discriminate a reference object from 11 distractors, which spanned a spectrum of image-level similarity to the reference. We also presented the animals with random variations of the reference, and processed their responses to these stimuli to derive subject-specific models of rat perceptual choices. Our models successfully captured the highly variable discrimination performance observed across subjects and object conditions. In particular, they revealed that the animals that succeeded with the most challenging distractors were those that integrated the wider variety of discriminative features into their perceptual strategies. Critically, these strategies were largely preserved when the rats were required to discriminate outlined and scaled versions of the stimuli, thus showing that rat object vision can be characterized as a transformation-tolerant, feature-based filtering process. Overall, these findings indicate that rats are capable of advanced processing of shape information, and point to the rodents as powerful models for investigating the neuronal underpinnings of visual object recognition and other high-level visual functions