Monopolization Cases Research Articles

On the virtue and value of ‘little’ monopolization cases

On the virtue and value of ‘little’ monopolization cases

The halo bispectrum multipoles in redshift space

We present the analysis of the halo bispectrum in redshift-space in terms of its multipoles, monopole, quadrupole and hexadecapole, measured from a large set of simulations. We fit such measurements with a tree-level model in perturbation theory that depends on linear and nonlinear bias parameters as well as on the growth rate f of density fluctuations. The likelihood analysis takes advantage of a very large set of mock catalogs, enabling a robust estimation of the covariance properties for all multipoles. We compare the numerical estimate of the covariance matrix to its Gaussian prediction finding discrepancies of 10% or less for all configurations with the sole exception of the squeezed triangles in the monopole case. We find the range of validity of the tree-level model, for the total simulation volume of about 1000 h -3Gpc3, reaches a maximum wavenumber of 0.08 h Mpc-1 for the monopole, while it is limited to 0.06 and 0.045 h Mpc-1 respectively for quadrupole and hexadecapole. Despite this, the addition of the quadrupole to the analysis allows for significant improvements on the determination of the model parameters and specifically on f, similarly to the power spectrum case. Finally, we compare our numerical estimate for the full covariance with its theoretical prediction in the Gaussian approximation and find the latter to work remarkably well in the context of simulation boxes with periodic boundary condition.

Understanding anomalous particle production in massless QED via time-varying θ angle

The Maxwell equations imply that, under the background of non-zero B, varying θ term produces E·B. An interesting example is the Witten effect where a magnetic monopole becomes a dyon which, however, should disappear in the exact massless limit of the fermion. Underlying mechanism of this phenomenon has been understood by Callan by the presence of an effective axion-like degree of freedom around the monopole, which is roughly the phase of the fermions. The configuration of this axion cancels the effect of the θ term. Now, the chiral anomaly implies that non-vanishing E·B induces the chiral charge in the system. The question is whether the chiral charge is generated in the massless limit when we take into account the axion-like degree of freedom in the discussion. The discussion is relevant for the mechanism of baryogenesis under the background of time-dependent θ. We solve the system of the massless QED with time dependent θ by reducing it to the two-dimensional QED. We demonstrate the occurrence of chiral charge generation in the background of static magnetic field for two cases: a magnetic monopole and a uniform magnetic flux. For the monopole case, the chiral charge comes out from the monopole while canceling the Witten effect. For the case of the uniform flux, on the other hand, the effect of the backreaction cannot be ignored, giving a more non-trivial time dependence. We also discuss their implications on baryogenesis.

Enhanced elastodynamic resonance via co-dipole metaclusters

Metamaterials exploit sub-wavelength microstructures to yield novel macroscopic material properties. Recently, the notion of a metacluster has emerged, which is a collection of resonators that interact in order to modify and possibly enhance the resonance. They can also be employed to modify and tune the far-field scattered response. This is particularly important with regard to metamaterial design. In the context of elastodynamics, Cotterill et al. [Proc. R. Soc. A 478(2263), 20220026 (2022)] considered the case of void metaclusters, thus permitting the modification of the so-called giant monopole resonance in elastodynamics. Here, we consider one of the original resonant configurations of metamaterial science in Liu et al. [Science 289, 1734 (2000)]; this structure consists of coated cylinders of circular cross section and gives rise to a strong dipole resonance for sufficiently soft coatings. We consider the nature of the interaction of two such identical resonators in close proximity, which we term the co-dipole metacluster. We show that, contrary to the giant monopole case, the frequency at which the resonance occurs is unchanged as compared to a single resonator. The amplitude of the resonance itself is enhanced significantly, however, by up to 5.7 times the enhancement observed when considering two non-interacting resonators. Furthermore, although the nature of the resonance remains dominated by a dipole response, both the enhancement and the far-field scattered response are now significantly affected by the incidence angle, in contrast to the single resonator.

The Dead Hand of Cellophane and the Federal Google and Facebook Antitrust Cases: Market Delineation Will Be Crucial

The U.S. Department of Justice (DOJ) and Federal Trade Commission (FTC) monopolization cases against Google and Facebook, respectively, represent the most important federal nonmerger antitrust initiatives since (at least) the 1990s. As in any monopolization case, market delineation will be a central feature of both cases—as it was in the du Pont Cellophane case of sixty-five years ago. Without a delineated market, how can one determine whether a company has engaged in monopolization? Unfortunately, there is currently no accepted market delineation paradigm that can help the courts address this issue for monopolization cases. And this void generally cannot be filled by the market delineation paradigm that is embedded in the DOJ-FTC “Horizontal Merger Guidelines”: although this paradigm has had almost forty years of usage and is now well established and well accepted for merger analysis, this paradigm generally has no applicability for market delineation in monopolization cases. This article expands on this argument and shows the potential difficulties that are likely to arise in this area of market delineation and the consequent problems for both cases. This article also points the way toward a paradigm that offers a sensible approach to dealing with these difficulties.

A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators. Based on the so-called ’t Hooft monopole model, a U(1) Maxwell electromagnetic sub-field is constructed from an SU(2) gauge field, from which arise two types of topological defects, monopoles and merons. We focus on the topological number in the Hall conductance , where C is the Chern number. It is discovered that in the monopole case C is indeterminate, while in the meron case C takes different values, due to a varying on-site energy m. As a typical example, we apply this method to the square lattice and compute the winding numbers (topological charges) of the defects; the C-evaluations we obtain reproduce the results of the usual literature. Furthermore, based on the gauge theory we propose a new model to obtain the high Chern numbers ∣C∣ = 2, 4.

Magnetic field generation from PBH distributions

ABSTRACT We introduce a statistical method for estimating magnetic field fluctuations generated from primordial black hole (PBH) populations. To that end, we consider monochromatic and extended Press–Schechter PBH mass functions, such that each constituent is capable of producing its own magnetic field due to some given physical mechanism. Assuming a linear correlation between magnetic field fluctuations and matter overdensities, our estimates depend on the mass function, the physical field generation mechanism by each PBH constituent, and the characteristic PBH separation. After computing the power spectrum of magnetic field fluctuations, we apply our formalism to study the plausibility that two particular field generation mechanisms could have given rise to the expected seed fields according to current observational constraints. The first mechanism is the Biermann battery and the second one is due to the accretion of magnetic monopoles at PBH formation, constituting magnetic PBHs. Our results show that, for monochromatic distributions, it does not seem to be possible to generate sufficiently intense seed fields in any of the two field generation mechanisms. For extended distributions, it is also not possible to generate the required seed field by only assuming a Biermann battery mechanism. In fact, we report an average seed field by this mechanism of about 10−47 G, at z = 20. For the case of magnetic monopoles, we instead assume that the seed values from the literature are achieved and calculate the necessary number density of monopoles. In this case, we obtain values that are below the upper limits from current constraints.

U.S. v. Google: A Tough Slog; But Maybe an Intriguing Possibility?

In October 2020 the U.S. Department of Justice (DOJ) filed an antitrust suit against Google. It is an alleged monopolization (Sherman Act, Sec. 2) case. In this paper I lay out the main issues in the case and raise an intriguing possibility.

Making Sense of Monopolization: Antitrust and the Digital Economy

For more than a century, courts and scholars have searched without success for a general definition of monopolization. Some proposals rely on elusive ciphers like “predatory conduct” or “competition on the merits”; others depend on nebulous or impractical balancing tests; others make antitrust liability implausible except in the most extreme cases. Our failure to give a clear and principled explanation of what monopolists may not do has daunted enforcers, confounded courts, encouraged bad behavior by powerful firms, and undermined public faith in our antitrust system. In an age of digital dominance, the mounting costs of confusion have fueled calls to replace, or thoroughly reshape, the Sherman Antitrust Act. This Article outlines a course correction, drawing on monopolization’s historical, theoretical, and doctrinal foundations to improve both the vigor and rigor of the law. We can make sense of monopolization by understanding it as an effort to do three separate things: guard against contribution to the dangers of monopoly; protect against a wrong called “exclusion”; and respect a sphere of competitive privilege. This view implies a framework for monopolization cases—which I call the “dangerous exclusion” approach—to replace the conclusory labels of existing law; unify its sprawling array of micro-rules; correct widespread misunderstandings (including mistaken claims that a plaintiff must show actual effects on price, output, or other competitive outcomes); and help navigate real problems. The dangerous-exclusion framework offers a principled and workable middle way between conservative approaches that are unduly preoccupied with the risk of “false positive” interventions and radical proposals that threaten to harm consumers. As a qualitative, court-centric approach, it contrasts sharply with both left-wing calls to entrust the antitrust project to rulemakers and right-wing proposals to delegate it to econometricians. But our imperfect adjudicative tradition is up to the task, in digital markets and beyond. There is plenty of life in the Sherman Act yet.

Topological defects and confinement with machine learning: The case of monopoles in compact electrodynamics

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained.

A Retrospective on U.S. v. Microsoft: Why Does It Resonate Today?

The U.S. v. Microsoft case was filed in 1998, the District Court filed its opinion in 2000, and the D.C. Circuit’s opinion came down in 2001. This article explains why the case continues to stand as an important Sherman Act, Section 2 monopolization case. Moreover, if restated and reviewed as a two-sided market case in light of Ohio v. Am. Express Co., the outline would be unchanged.

Investigation on acoustic reflection logging of LWD using a flexible finite difference technique

ABSTRACTAcoustic reflection logging while drilling (LWD) measurement has overwhelming advantages in detecting reflectors outside the borehole, making it a prominent technology in geosteering during LWD operations. This paper carries out a comprehensive numerical investigation into the acoustic reflection logging responses in LWD environments by combining the analytical real axis integration (RAI) solution and an exquisitely improved finite difference method (FDM). Mutual validation of these two methods using typical and well-known cases ensures the reliability of the modelling methodology. Numerical studies on LWD and wireline acoustic reflection logging reveal that a ring source rather than four azimuthally orthogonal point sources can excite acoustic LWD monopole waves without interference from higher order wave modes. Lower order spatial differential operators are more efficient for FDM simulations of LWD cases when variance in the medium is obvious. Compared with the wireline monopole case, LWD monopole reflection acoustic logging can obtain higher quality reflected waves and has a superior ability to identify the azimuth of a geological reflector away from the borehole.

Monopole production via photon fusion and Drell\u2013Yan processes: MadGraph implementation and perturbativity via velocity-dependent coupling and magnetic moment as novel features

In this work we consider point-like monopole production via photon-fusion and Drell–Yan processes in the framework of an effective U(1) gauge field theory obtained from conventional models describing the interaction of spin magnetically-charged fields with ordinary photons, upon electric-magnetic dualisation. We present arguments based on such dualities which support the conjecture of an effective monopole-velocity-dependent magnetic charge. For the cases of spin- and spin-1 monopoles, we also include a magnetic-moment term kappa , which is treated as a new phenomenological parameter and, together with the velocity-dependent coupling, allows for a perturbative treatment of the cross-section calculation. We discuss unitarity issues within these effective field theories, in particular we point out that in the spin-1 monopole case only the value kappa =1 may restore unitarity. However from an effective-field-theory point of view, this lack of unitarity should not be viewed as an impediment for the phenomenological studies and experimental searches of generic spin-1 monopoles, given that the potential appearance of new degrees of freedom in the ultraviolet completion of such models might restore it. The second part of the paper deals with an appropriate implementation of photon-fusion and Drell–Yan processes based on the above theoretical scenarios into MadGraph UFO models, aimed to serve as a useful tool in interpretations of monopole searches at colliders such as LHC, especially for photon fusion, given that it has not been considered by experimental collaborations so far. Moreover, the experimental implications of such perturbatively reliable monopole searches have been laid out.

Android - Is There a Viable Monopolization Case?

This paper considers the viability of a Sherman Act § 2 enforcement action in respect of Google’s Android operating system. It discusses the applicability of the D.C. Circuit’s 2001 Microsoft opinion in which Microsoft was found to have engaged in anticompetitive conduct to maintain its Windows operating system monopoly. The paper explains why, despite some superficial similarities, the facts that gave rise to liability in Microsoft are different in crucial respects from those pertaining to Android. The paper concludes 1) that Google lacks monopoly power in a properly defined market in which Android competes; and 2) that Google has not engaged in the type of anticompetitive conduct condemned in Microsoft. The facts underlying Microsoft and the D.C. Circuit’s reasoning strongly suggest that an enforcement action in the United States is unlikely to succeed notwithstanding the European Commission’s July 2018 Android decision.

Regularized Kalb-Ramond magnetic monopole with finite energy

In a previous work we suggested a self-gravitating electromagnetic monopole solution in a string-inspired model involving global spontaneous breaking of a SO(3) internal symmetry and Kalb-Ramond (KR) axions, stemming from an antisymmetric tensor field in the massless string multiplet. These axions carry a charge, which, in our model, also plays the role of the magnetic charge. The resulting geometry is close to that of a Reissner-Nordstr\"om (RN) black hole with charge proportional to the KR-axion charge. We proposed the existence of a thin shell structure surrounding a (large inner) core as the dominant mass contribution to the energy functional. Although the resulting energy was finite, and proportional to the KR-axion charge, the size of the shell was not determined and left as a phenomenological parameter. In the current article, we propose a new way to calculate the size of the thin shell: string theory considerations suggest that the short-distance physics inside the inner core may be dominated by a positive cosmological constant term proportional to the scale of the spontaneous symmetry breaking of SO(3). The size of the shell is estimated by matching the RN metric of the shell to the de Sitter metric inside the core. The matching entails the Israel junction conditions for the metric and its first derivatives at the inner boundary of the shell, and determines the inner mass-shell radius. The axion charge plays an important role in guaranteeing the positivity of the ``mass coefficient'' of the gravitational potential term appearing in the metric; so, the KR electromagnetic monopole shows normal attractive gravitational effects. This is to be contrasted with the axion-less global monopole case where such a matching is known to yield a negative ``mass coefficient'' (and, hence, a repulsive gravitational effect). The total energy of our monopole within the shell is calculated. As a result of the violation of Birkhoff's theorem (due to the formal divergence of the energy functional in the absence of a large distance cutoff), the total energy does not have to equal the mass coefficient. However, for phenomenologically relevant sets of parameters, the ratio of the total energy and the mass coefficient in the shell is close to 1. The gravitational ``effective mass coefficient'' in the shell can be made equal to the total energy outside the core by a small decrease in the cosmological constant in the de Sitter region. This is achieved through a dilaton potential which is suitably negative inside the de-Sitter region, but vanishes outside that region.

Should We Be Concerned About Data-opolies?

With the rise of a progressive antitrust movement, the power of Google, Apple, Facebook, and Amazon is now topical. This article explores some of the potential harms from data-opolies. Data-opolies, in contrast to the earlier monopolies, are unlikely to exercise their power by charging higher prices to consumers. But this does not mean they are harmless. Data-opolies can raise other significant concerns, including less privacy, degraded quality, a transfer of wealth from consumers to data-opolies, less innovation and dynamic disruption in markets in which they dominate, and political and social concerns. Data-opolies can also be more durable than some earlier monopolies. Moreover, data-opolies at times can more easily avoid antitrust scrutiny when they engage in anticompetitive tactics to attain or maintain their dominance. The United States Department of Justice has brought only one monopolization case under Section 2 of the Sherman Act in the past decade. This abdication is not justifiable going forward, given the risks posed by these data-opolies, whose abuses can affect not only our wallets, but also our privacy, autonomy, democracy, and well-being.

Innovation and Competition Policy, Chap. 4: Competition Policy and the Patent System

This book of CASES AND MATERIALS ON INNOVATION AND COMPETITION POLICY is intended for educational use. The book is free for all to use subject to an open source license agreement. It considers numerous sources of competition policy in addition to antitrust, including those that emanate from the intellectual property laws themselves, and also related issues such as the relationship between market structure and innovation, the competitive consequences of regulatory rules governing technology competition such as net neutrality and interconnection, misuse, the first sale doctrine, and the Digital Millennium Copyright Act (DMCA). Chapters will be updated frequently. The author uses this casebook for a three-unit class in Innovation and Competition Policy taught at the University of Iowa College of Law and available to first year law students as an elective.This document is the second edition of Chapter Four, which focuses on antitrust and the patent system, including the Walker Process doctrine and other issues relating to unreasonable enforcement, measurement of market power in patent monopolization cases, consumer standing to challenge improper patent exclusions, unreasonable and exclusionary uses of patent continuations and related devices. It also covers pay for delay settlements in cases involving pharmaceutical patents and the Hatch-Waxman Act, including the Supreme Court's 2013 Actavis decision, together with several notes and comments.

Reliable assessment of topological modifications in UWB antennas by means of multi‐objective optimization

AbstractIn this letter, the problem of systematic and rigorous assessment of effects of topological modifications on the performance of miniaturized UWB antennas has been addressed. The primary assessment tool is fast multi‐objective optimization, here, realized using a recent sequential domain patching algorithm. Identification of the Pareto front for an antenna structure, ie, the set of designs representing the best possible tradeoffs between conflicting objectives (here, reflection characteristic and the antenna footprint) allows for conclusive comparison of antenna performance and suitability for space‐limited applications. Here, we are interested in the effect of seemingly small topological modifications, the importance of which cannot be detected using parameters sweeps because of heavy interactions between such modifications and the remaining parameters of the structure. An UWB monopole case study demonstrates that small topological amendments may lead to considerable improvement of antenna performance and reduction of its size. Numerical results are supported by experimental validation of the fabricated antenna prototypes.

Dependence of the black-body force on spacetime geometry and topology

In this paper we compute the corrections to the black-body force (BBF) potential due to spacetime geometry and topology. This recently discovered attractive force on neutral atoms is caused by the thermal radiation emitted from black bodies and here we investigate it in relativistic gravitational systems with spherical and cylindrical symmetries. For some astrophysical objects we find that the corrected BBF potential is greater than the flat case, showing that this kind of correction can be quite relevant when curved spaces are considered. Then we consider four cases: The Schwarzschild spacetime, the global monopole, the non-relativistic infinity cylinder and the static cosmic string. For the spherically symmetric case of a massive body, we find that two corrections appear: One due to the gravitational modification of the temperature and the other due to the modification of the solid angle subtended by the atom. We apply the found results to a typical neutron star and to the Sun. For the global monopole, the modification in the BBF potential is of topological nature and it is due to the central solid angle deficit that occurs in the spacetime generated by that object. In the cylindrical case, which is locally flat, no gravitational correction to the temperature exists, as in the global monopole case. However, we find the curious fact that the BBF depends on the topology of the spacetime through the modification of the azimuthal angle and therefore of the solid angle. For the static cosmic string we find that the force is null for the zero thickness case.

The Rule of Reason

Antitrust’s rule of reason was born out of a thirty year (1897-1927) division among Supreme Court Justices about the proper way to assess multi-firm restraints on competition. By the late 1920s the basic contours of the rule for restraints among competitors was roughly established. Antitrust policy toward vertical restraints remained much more unstable, however, largely because their effects were so poorly understood.This article provides a litigation field guide for antitrust claims under the rule of reason – or more precisely, for situations when application of the rule of reason is likely. At the time pleadings are drafted and even up to the point of summary judgment, the parties are often uncertain whether a court will apply the rule of reason. Because the choice of rule presents a question of law, it is generally established prior to trial. The first section examines pleading and summary judgment rules, including the role of stare decisis, arguing that stare decisis should apply to a mode of analysis rather than to a specific class of restraints. Then it discusses numerous problems surrounding the burden of proof and the quality of evidence needed to shift the burden or get to a jury. I argue that the plaintiff’s burden for a prima facie case should be relatively stringent for the market power requirement, but relatively light for proof of an anticompetitive act.I also show why a consumer welfare standard for antitrust violations is the only manageable one for evaluating practices under the rule of reason. The alternative, general welfare standard requires that all consumer losses be quantified and compared with producer efficiency gains, as well as likely effects on others. Aside from any substantive reasons for preferring a consumer welfare standard, a general welfare standard is impossible to apply in any but the most obvious cases. The consumer welfare standard queries only whether output will be higher or lower (or prices lower or higher) under the restraint. This query can be difficult enough but is nevertheless much simpler than the proof requirements for a general welfare standard. Finally, this section examines the possibility of truncated, or “quick look,” analysis as an alternative to both the rule of reason and the per se rule, arguing against recognition of any categorical “quick look.” I conclude with a brief discussion of “balancing,” and why the rule of reason’s staged set of queries is designed so that courts can avoid balancing whenever possible.The next section considers how to identify the types of conduct to which antitrust’s rule of reason should be applied. It also examines the question of appropriate remedies, particularly when the basic features of joint activity are either unchallenged or conceded to be competitive, but a specific provision or practice threatens competition. Then it turns briefly to the special case of antitrust restraints in markets for intellectual property rights. A final section examines the market structure requirements for antitrust rule of reason cases, including vertical agreements as well as agreements that have both horizontal and vertical elements. For rule of reason cases involving collaborative conduct generally, market power requirements should be less than those for single firm conduct. The principal exception is vertical exclusionary agreements (mainly, tying and exclusive dealing), where power requirements should be equivalent to those used in monopolization cases.