59 research outputs found
On -vectors satisfying the Kruskal-Katona inequalities
We present examples of flag homology spheres whose -vectors satisfy
the Kruskal-Katona inequalities. This includes several families of well-studied
simplicial complexes, including Coxeter complexes and the simplicial complexes
dual to the associahedron and to the cyclohedron. In these cases, we construct
explicit simplicial complexes whose -vectors are the -vectors in
question. In another direction, we show that if a flag -sphere has at
most vertices its -vector satisfies the Kruskal-Katona
inequalities. We conjecture that if is a flag homology sphere then
satisfies the Kruskal-Katona inequalities. This conjecture is
a significant refinement of Gal's conjecture, which asserts that such
-vectors are nonnegative.Comment: 18 pages; Our main result and conjectures have been strengthened.
Also we now have explicit constructions of simplicial complexes whose
-vectors are the -vectors in questio
The Potts Fully Frustrated model: Thermodynamics, percolation and dynamics in 2 dimensions
We consider a Potts model diluted by fully frustrated Ising spins. The model
corresponds to a fully frustrated Potts model with variables having an integer
absolute value and a sign. This model presents precursor phenomena of a glass
transition in the high-temperature region. We show that the onset of these
phenomena can be related to a thermodynamic transition. Furthermore this
transition can be mapped onto a percolation transition. We numerically study
the phase diagram in 2 dimensions (2D) for this model with frustration and {\em
without} disorder and we compare it to the phase diagram of the model with
frustration {\em and} disorder and of the ferromagnetic model.
Introducing a parameter that connects the three models, we generalize the exact
expression of the ferromagnetic Potts transition temperature in 2D to the other
cases. Finally, we estimate the dynamic critical exponents related to the Potts
order parameter and to the energy.Comment: 10 pages, 10 figures, new result
Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020
We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe
Explaining variation in the competitiveness of U.S. Senate elections, 1922–2004
We develop and test predictions about the factors determining the competitiveness of elections to the U.S. Senate. To do so, we deliberately abstract away from candidate-specific conditions that have often been used to study political competitiveness in order to focus on basic structural features of the electoral landscape. In our framework, party-specific constraints on the ideological positioning of local candidates, linked to the national party organization and its contributors, interact with the heterogeneity of state electorates to determine the number of highly competitive Senate contests. Three hypotheses emerge from this model: (1) the greater the diversity of a party’s national legislative delegation, the more highly competitive Senate elections we will observe; (2) states in which the ideological heterogeneity of the electorate is relatively high will exhibit a greater number of highly competitive elections; and (3) highly competitive Senate contests will be more common in states with closed primaries than in states with open primaries. We provide strong evidence in support of the first two hypotheses and some evidence in support of the third
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