Limits of end-state planning

Peer reviewedPreprin

A Stable Marriage Requires Communication

The Gale-Shapley algorithm for the Stable Marriage Problem is known to take $\Theta(n^2)$ steps to find a stable marriage in the worst case, but only $\Theta(n \log n)$ steps in the average case (with $n$ women and $n$ men). In 1976, Knuth asked whether the worst-case running time can be improved in a model of computation that does not require sequential access to the whole input. A partial negative answer was given by Ng and Hirschberg, who showed that $\Theta(n^2)$ queries are required in a model that allows certain natural random-access queries to the participants' preferences. A significantly more general - albeit slightly weaker - lower bound follows from Segal's general analysis of communication complexity, namely that $\Omega(n^2)$ Boolean queries are required in order to find a stable marriage, regardless of the set of allowed Boolean queries. Using a reduction to the communication complexity of the disjointness problem, we give a far simpler, yet significantly more powerful argument showing that $\Omega(n^2)$ Boolean queries of any type are indeed required for finding a stable - or even an approximately stable - marriage. Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, (C) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage, and (D) determining whether a proposed marriage is stable or far from stable. In order to analyze "approximately stable" marriages, we introduce the notion of "distance to stability" and provide an efficient algorithm for its computation

Comment on: Abou-Ali, H., El-Azony, H., El-Laithy, H., Haughton, J. and Khandker, S., 2010. Evaluating the impact of Egyptian Social Fund for Development Programmes. Journal of Development Effectiveness, 2 (4), 521–555

PRIFPRI3; ISIDG

Barkhausen noise in the Random Field Ising Magnet Nd2_2Fe14_{14}B

With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a room-temperature realization of the Random Field Ising Model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed in by the transverse field, consistent with theoretical predictions for Barkhausen avalanches in disordered materials. A scaling analysis reveals two regimes of behavior: one at low temperature and high transverse field, where the dynamics are governed by the randomness, and the second at high temperature and low transverse field where thermal fluctuations dominate the dynamics.Comment: 16 pages, 7 figures. Under review at Phys. Rev.

Variational Approach to Gaussian Approximate Coherent States: Quantum Mechanics and Minisuperspace Field Theory

This paper has a dual purpose. One aim is to study the evolution of coherent states in ordinary quantum mechanics. This is done by means of a Hamiltonian approach to the evolution of the parameters that define the state. The stability of the solutions is studied. The second aim is to apply these techniques to the study of the stability of minisuperspace solutions in field theory. For a $\lambda \varphi^4$ theory we show, both by means of perturbation theory and rigorously by means of theorems of the K.A.M. type, that the homogeneous minisuperspace sector is indeed stable for positive values of the parameters that define the field theory.Comment: 26 pages, Plain TeX, no figure

Protecting More than the Front Page: Codifying a Reporter’s Privilege for Digital and Citizen Journalists

This Note will first explain, in Part I, why journalists need to be protected, and detail the history of reporters invoking a reporter’s privilege in court to protect themselves from revealing their sources or information. It will then discuss Branzburg v. Hayes in Section II.A. Section II.B briefly examines circuits’ receptivity to statutory or constitutional protections of reporters. The Supreme Court has stated that Congress could pass a law to protect reporters. However, while multiple federal shield laws have been proposed, none have been passed. The most recent proposal occurred in 2013, and as of December 2013, the Senate version was voted out of committee. Section III.A will address Congress’s attempts at enacting a statutory protection, specifically focusing on who would be covered in proposed bills. Branzburg did not foreclose the possibility of state statutory protections, and thirty-nine states plus the District of Columbia have codified a reporter’s privilege in their shield laws. This Note will briefly examine how states codify reporters’ protections in Section III.B. Section III.C then considers the executive branch’s self-restriction of subpoenaing reporters, which appears in the Code of Federal Regulations. This Note argues that while the constitutional debate surrounding a reporter’s privilege continues, a federal shield law is needed to provide coverage at least until the Supreme Court recognizes First Amendment protection for reporters. A shield law can provide more uniform protections to a broad range of journalists, including digital or citizen journalists, which are critical to any current iteration of a reporter’s privilege. Current state protections are not sufficient because they do not protect reporters being prosecuted under federal law, which is necessary for a more comprehensive coverage that encourages meaningful reporting of nationally relevant material. As discussion over a statutory protection grows, it is important to create a statute that is relevant to the changing media landscape in which digital and citizen journalists are increasingly breaking news and investigating stories. Thus, this Note, in Part IV, addresses the inadequacies of current protections and proposes the solution of a federal shield law, emphasizing the broad number of people, outside of traditional, institutional media, that the shield law should protect. The law should focus on covering those whose actions demonstrate that they are engaging in journalism. The protection should not only be extended to an individual associated with an institutional media entity. The law should cover digital or citizen journalists using Internet news sources, or even social media sites, as vehicles to publish their work. This solution is practical in light of the murky constitutional landscape that does not offer broad enough protection to the growing number of citizen and digital journalists. Although individuals should receive shield law protection from revealing sources in order to encourage investigative journalism, this should not be an absolute protection, but rather a qualified privilege subject to codified exceptions for security and safety issues