Lattice initial segments of the hyperdegrees

We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, $\mathcal{D}_{h}$. In fact, we prove that every sublattice of any hyperarithmetic lattice (and so, in particular, every countable locally finite lattice) is isomorphic to an initial segment of $\mathcal{D}_{h}$. Corollaries include the decidability of the two quantifier theory of $$ and the undecidability of its three quantifier theory. The key tool in the proof is a new lattice representation theorem that provides a notion of forcing for which we can prove a version of the fusion lemma in the hyperarithmetic setting and so the preservation of $\omega _{1}^{CK}$. Somewhat surprisingly, the set theoretic analog of this forcing does not preserve $\omega _{1}$. On the other hand, we construct countable lattices that are not isomorphic to an initial segment of $\mathcal{D}_{h}$

The toggle group, homomesy, and the Razumov-Stroganov correspondence

The Razumov-Stroganov correspondence, an important link between statistical physics and combinatorics proved in 2011 by L. Cantini and A. Sportiello, relates the ground state eigenvector of the O(1) dense loop model on a semi-infinite cylinder to a refined enumeration of fully-packed loops, which are in bijection with alternating sign matrices. This paper reformulates a key component of this proof in terms of posets, the toggle group, and homomesy, and proves two new homomesy results on general posets which we hope will have broader implications.Comment: 14 pages, 10 figures, final versio

Improving social game engagement on Facebook through enhanced socio-contextual information

In this paper we describe the results of a controlled study of a social game, Magpies, which was built on the Facebook Online Social Network (OSN) and enhanced with contextual social information in the form of a variety of social network indices. Through comparison with a concurrent control trial using an identical game without the enhanced social information, it was shown that the additional contextual data increased the frequency of social activity between players engaged in the game. Despite this increase in activity, there was little increase in growth of the player-base when compared to the control condition. These findings corroborate previous work that showed how socio-contextual enhancement can increase performance on task-driven games, whilst also suggesting that it can increase activity and engagement when provided as context for non task-driven game environments

Path diversity improves the identification of influential spreaders

Identifying influential spreaders in complex networks is a crucial problem which relates to wide applications. Many methods based on the global information such as $k$-shell and PageRank have been applied to rank spreaders. However, most of related previous works overwhelmingly focus on the number of paths for propagation, while whether the paths are diverse enough is usually overlooked. Generally, the spreading ability of a node might not be strong if its propagation depends on one or two paths while the other paths are dead ends. In this Letter, we introduced the concept of path diversity and find that it can largely improve the ranking accuracy. We further propose a local method combining the information of path number and path diversity to identify influential nodes in complex networks. This method is shown to outperform many well-known methods in both undirected and directed networks. Moreover, the efficiency of our method makes it possible to be applied to very large systems.Comment: 6 pages, 6 figure

Towards a Sustainable FTAA: DOes Latin America Meet the Necessary Financial Preconditions?

This paper focuses on identifying preconditions that will ensure the sustainability of a Free Trade Area of the Americas (FTAA). It argues that the macro, micro, and political conditions advanced in the literature to measure a country's ability to compete internationally, while necessary, are not sufficient to ensure the success and permanence of a free trade agreement. Instead, two additional financial conditions are needed. The first is that each partner in the free trade area needs to have sustainable public debts as determined by the achievement of credible and sustainable structural fiscal balances. The second is that exchange rate regimes across trading partners should be compatible in the sense that adverse shocks in one country do not generate a policy dilemma in other partners between abandoning their exchange rate system or the free trade area. A preliminary analysis of the evidence in the Latin American and Caribbean region shows the importance of these two preconditions. An analysis of debt sustainability reveals that there are a number of countries in the region that need to deal with potential solvency problems before reaching the status of credible partners in a regional trade arrangement. Argentina is already deemed insolvent, and countries such as Ecuador and Venezuela rank high on the list of countries where the issue of debt sustainability can become a serious problem. Not resolving this before reaching a regional trade agreement can threaten its long-term stability. The examination of the compatibility of exchange rate systems across trading partners is also very revealing. Part of the success of NAFTA since the late 1990s and the "impasse" of Mercosur during 1999-2001 had to do with the choices of exchange rate regimes. In both trade areas the share of trade among the partners is very high, and in NAFTA, this includes significant financial transactions. While Mexico was able to use the flexibility of the exchange rate to improve competitiveness following the sharp decline of portfolio flows from US investors into Mexico following the Asian and Russian crises, Argentina had no mechanisms to deal with an adverse shock from Brazil (such as a depreciation of the real in 1999). From this perspective, the recent move of Argentina towards a more flexible exchange rate system is good news for a sustainable free trade area.

Connected Coalition Formation and Voting Power in the Council of the European Union: An Endogenous Policy Approach. EIPA Working Paper 99/W/05

Resorting to political economy approaches, this paper attempts to associate the industrial structure in the European Union (EU) to the coalition formation process between European member states. Using a well-known measure of relative voting power, the (normalized) Banzhaf power index, we relax the common assumption that coalitions form randomly. Instead, we adopt the standard interest group model and look at the structure of European industry, mainly in terms of industrial concentration in the EU, as an indicator of its lobbying influence on domestic politics and governments’ preferences. This, in turn, influences the political stance, and thus the coalition building process, of the different member states in the Council. We derive estimates on members’ relative influence within the Council for different policy areas in the broader framework of industry and trade, on the basis of both weighted votes and likely patterns of coalition-formation in the Council