Revisiting two-sided stability constraints

We show that previous filtering propositions on two-sided stability problems do not enforce arc consistency (AC), however they maintain Bound(D) Consistency (BC(D)). We propose an optimal algorithm achieving BC(D) with O(L) time complexity where L is the length of the preference lists. We also show an adaptation of this filtering approach to achieve AC. Next, we report the first polynomial time algorithm for solving the hospital/resident problem with forced and forbidden pairs. Furthermore, we show that the particular case of this problem for stable marriage can be solved in O(n2) which improves the previously best complexity by a factor of n2. Finally, we present a comprehensive set of experiments to evaluate the filtering propositions

Revisiting Event Horizon Finders

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time to be most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only {\em some} of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision

The Causes of Political Integration: An Application to School Districts

This paper examines the forces behind political integration through the lens of school district consolidations, which reduced the number of school districts in the United States from around 130,000 in 1930 to under 15,000 at present. Despite this large observed decline, many districts resisted consolidation before ultimately merging and others never merged, choosing to remain at enrollment levels that nearly any education cost function would deem inefficiently small. Why do some districts voluntarily integrate while others remain small, and how do those districts that do merge choose with which of their neighbors to do so? In addressing these questions, we empirically examine the role of potential economies and diseconomies of scale, heterogeneity between merger partners, and the role of state governments. We first develop a simulation-based estimator that is rooted in the economics of matching and thus accounts for three important features of typical merger protocol: two-sided decision making, multiple potential partners, and spatial interdependence. We then apply this methodology to a wave of school district mergers in the state of Iowa during the 1990s. Our results highlight the importance of economies of scale, diseconomies of scale, state financial incentives for consolidation, and a variety of heterogeneity measures.

Fiscal and Monetary Interaction: The Role of Asymmetries of the Stability and Growth Pact in EMU

The paper builds a simplified model describing the economy of a currency union with decentralised national fiscal policy, where the main features characterising the policy-making are similar to those in EMU. National governments choose the size of deficit taking into account the two main rules of the Stability and Growth Pact on public finance. Unlike previous literature the asymmetric working of those rules is explicitly modelled in order to identify its impact on the Nash equilibrium of deficits arising from a game of strategic interaction between fiscal authorities in the union.Stability and Growth Pact, EMU, asymmetric fiscal rules, decentralised fiscal policy

Mechanical systems subjected to generalized nonholonomic constraints

We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit formula to obtain the ``post-impact'' momentum in terms of the ``pre-impact'' momentum.Comment: 24 pages, no figure

FIDE Congress 2020 - EU Competition Law and the Digital Economy: United Kingdom Report

This report was prepared for the 29th biennial Congress of the International Federation of European Law (FIDE) to be held in The Hague in May 2020. It is the national report for the United Kingdom in response to Topic 3 of the 2020 FIDE Congress, titled ‘EU Competition Law and the Digital Economy’. This report offers an overview of UK competition enforcement in digital economy markets by answering twelve questions organised into four sections. Part A summarises key UK antitrust and merger decisions, agency publications, priorities and goals of enforcement in digital economy markets. Part B focuses upon the definition of markets and conceptualisation of market power by UK authorities in digital economy cases in light of their challenges and particularities. Part C offers a detailed overview of the issues underpinning UK antitrust and merger scrutiny in this field: the types of conduct investigated, relevant factors and concepts, theories of harm, efficiency justifications and remedies in digital economy cases. Finally, Part D identifies the potential for incoherent enforcement in this field from two different sources: the overlap between UK competition law and ex ante regulatory regimes (e.g. consumer protection, data protection); and the overlap between the powers of various UK competition decision-makers (e.g. sectoral regulators, the Competition Appeal Tribunal, and the courts)

Correlating Cell Behavior with Tissue Topology in Embryonic Epithelia

Measurements on embryonic epithelial tissues in a diverse range of organisms have shown that the statistics of cell neighbor numbers are universal in tissues where cell proliferation is the primary cell activity. Highly simplified non-spatial models of proliferation are claimed to accurately reproduce these statistics. Using a systematic critical analysis, we show that non-spatial models are not capable of robustly describing the universal statistics observed in proliferating epithelia, indicating strong spatial correlations between cells. Furthermore we show that spatial simulations using the Subcellular Element Model are able to robustly reproduce the universal histogram. In addition these simulations are able to unify ostensibly divergent experimental data in the literature. We also analyze cell neighbor statistics in early stages of chick embryo development in which cell behaviors other than proliferation are important. We find from experimental observation that cell neighbor statistics in the primitive streak region, where cell motility and ingression are also important, show a much broader distribution. A non-spatial Markov process model provides excellent agreement with this broader histogram indicating that cells in the primitive streak may have significantly weaker spatial correlations. These findings show that cell neighbor statistics provide a potentially useful signature of collective cell behavior.Comment: PLoS one 201