A Careful Examination of the Live Nation-Ticketmaster Merger

As great admirers of The Boss and as fans of live entertainment, we share in the popular dismay over rising ticket prices for live performances. But we have been asked as antitrust scholars to examine the proposed merger of Live Nation and Ticketmaster, and we do so with the objectivity and honesty called for by The Boss’s quotes above. The proposed merger has been the target of aggressive attacks from several industry commentators and popular figures, but the legal and policy question is whether the transaction is at odds with the nation’s antitrust laws. One primary source of concern to critics is that Ticketmaster and Live Nation are two leading providers of ticket distribution services, and these critics argue that the merged entity would have a combined market share that is presumptively anticompetitive. We observe, however, that this transaction is taking place within a rapidly changing industry. The spread of Internet technologies has transformed the entertainment industry, and along with it the ticket distribution business such that a reliance on market shares based on historical sales is misleading. A growing number of venues, aided by a competitive bidding process that creates moments of focused competition, can now acquire the requisite capabilities to distribute tickets to their own events and can thus easily forgo reliance upon providers of outsourced distribution services. If self-distribution is an available and attractive option for venues, as it appears to be, then it is unlikely that even a monopolist provider of fully outsourced ticketing services could exercise market power. Ultimately, a proper assessment of the horizontal effects of this merger would have to weigh heavily the emerging role of Internet technologies in this dynamic business and the industry-wide trend towards self-distribution. The second category of arguments by critics opposing the merger rests on claims that vertical aspects of the transaction would produce anticompetitive effects. Indeed, Ticketmaster’s and Live Nation’s core businesses are in successive markets, and thus the proposed transaction is primarily a vertical merger, but there is broad agreement among economists and antitrust authorities that vertical mergers rarely introduce competitive concerns and are usually driven by efficiency motivations. This wealth of academic scholarship, which is reflected in current antitrust law, has not - from our vantage point - been properly incorporated into the public dialogue concerning the proposed merger. To the contrary, critics articulate concerns, including the fears that the merger would lead to the leveraging of market power and the foreclosure of downstream competition, that are refuted by accepted scholarship. Moreover, there are a number of specific efficiencies that, consistent with economic and organizational theory, are likely to emerge from a Live Nation-Ticketmaster merger and would be unlikely but for the companies’ integration. For these reasons, we submit this analysis in an effort to inform the debate with current economic and legal scholarship

A New Approximate Min-Max Theorem with Applications in Cryptography

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs

Crystallization of the regulatory and effector domains of the key sporulation response regulator Spo0A

The key response-regulator gene of sporulation, spo0A, has been cloned from Bacillus stearothermophilus and the encoded protein purified. The DNA-binding and phospho-acceptor domains of Spo0A have been prepared by tryptic digestion of the intact protein and subsequently crystallized in forms suitable for X-ray crystallographic studies. The DNA-binding domain has been crystallized in two forms, one of which diffracts X-rays to beyond 2.5 Angstrom spacing. The crystals of the phospho-acceptor domain diffract X-rays beyond 2.0 Angstrom spacing using synchrotron radiation

Secret-Sharing for NP

A computational secret-sharing scheme is a method that enables a dealer, that has a secret, to distribute this secret among a set of parties such that a "qualified" subset of parties can efficiently reconstruct the secret while any "unqualified" subset of parties cannot efficiently learn anything about the secret. The collection of "qualified" subsets is defined by a Boolean function. It has been a major open problem to understand which (monotone) functions can be realized by a computational secret-sharing schemes. Yao suggested a method for secret-sharing for any function that has a polynomial-size monotone circuit (a class which is strictly smaller than the class of monotone functions in P). Around 1990 Rudich raised the possibility of obtaining secret-sharing for all monotone functions in NP: In order to reconstruct the secret a set of parties must be "qualified" and provide a witness attesting to this fact. Recently, Garg et al. (STOC 2013) put forward the concept of witness encryption, where the goal is to encrypt a message relative to a statement "x in L" for a language L in NP such that anyone holding a witness to the statement can decrypt the message, however, if x is not in L, then it is computationally hard to decrypt. Garg et al. showed how to construct several cryptographic primitives from witness encryption and gave a candidate construction. One can show that computational secret-sharing implies witness encryption for the same language. Our main result is the converse: we give a construction of a computational secret-sharing scheme for any monotone function in NP assuming witness encryption for NP and one-way functions. As a consequence we get a completeness theorem for secret-sharing: computational secret-sharing scheme for any single monotone NP-complete function implies a computational secret-sharing scheme for every monotone function in NP

Efficient routing of single photons by one atom and a microtoroidal cavity

Single photons from a coherent input are efficiently redirected to a separate output by way of a fiber-coupled microtoroidal cavity interacting with individual Cesium atoms. By operating in an overcoupled regime for the input-output to a tapered fiber, our system functions as a quantum router with high efficiency for photon sorting. Single photons are reflected and excess photons transmitted, as confirmed by observations of photon antibunching (bunching) for the reflected (transmitted) light. Our photon router is robust against large variations of atomic position and input power, with the observed photon antibunching persisting for intracavity photon number 0.03 \lesssim n \lesssim 0.7

Quantum Lightning Never Strikes the Same State Twice

Public key quantum money can be seen as a version of the quantum no-cloning theorem that holds even when the quantum states can be verified by the adversary. In this work, investigate quantum lightning, a formalization of "collision-free quantum money" defined by Lutomirski et al. [ICS'10], where no-cloning holds even when the adversary herself generates the quantum state to be cloned. We then study quantum money and quantum lightning, showing the following results: - We demonstrate the usefulness of quantum lightning by showing several potential applications, such as generating random strings with a proof of entropy, to completely decentralized cryptocurrency without a block-chain, where transactions is instant and local. - We give win-win results for quantum money/lightning, showing that either signatures/hash functions/commitment schemes meet very strong recently proposed notions of security, or they yield quantum money or lightning. - We construct quantum lightning under the assumed multi-collision resistance of random degree-2 systems of polynomials. - We show that instantiating the quantum money scheme of Aaronson and Christiano [STOC'12] with indistinguishability obfuscation that is secure against quantum computers yields a secure quantum money schem

Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously established result that for all extreme black holes the moduli fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio

On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories

We calculate the energy spectrum of a k=2 flux tube that is closed around a spatial torus, as a function of its length l. We do so for SU(4) and SU(5) gauge theories in 2 space dimensions. We find that to a very good approximation the eigenstates belong to the irreducible representations of the SU(N) group rather than just to its center, Z_N. We obtain convincing evidence that the low-lying states are, for l not too small, very close to those of the Nambu-Goto free string theory (in flat space-time). The correction terms appear to be typically of O(1) in appropriate units, much as one would expect if the bosonic string model were an effective string theory for the dynamics of these flux tubes. This is in marked contrast to the case of fundamental flux tubes where such corrections have been found to be unnaturally small. Moreover we find that these corrections appear to be particularly small when the `phonons' along the string have the same momentum, and large when their momentum is opposite. This provides information about the detailed nature of the interactions in the effective string theory. We have searched for, but not found, extra states that would arise from the excitation of the massive modes presumably associated with the non-trivial structure of the flux tube.Comment: 37 pages, 16 figures, minor changes to text and figure

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure