Satisfying states of triangulations of a convex n-gon

In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a strip of triangles.Comment: 17 pages, 6 figure

Directed cycle double covers: structure and generation of hexagon graphs

Jaeger's directed cycle double cover conjecture can be formulated as a problem of existence of special perfect matchings in a class of graphs that we call hexagon graphs. In this work, we explore the structure of hexagon graphs. We show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig's augmentations.Comment: 20 page

Black hole elasticity and gapped transverse phonons in holography

We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons---the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the translational symmetry breaking. These results provide a new confirmation that the BHs in these models do exhibit solid properties that become more manifest at low temperatures. Also, by the AdS/CFT correspondence, this allows to extend the standard results from the effective field theory for solids to quantum-critical materials.Comment: 28 pages, 7 figures; v3: minor revisions, matching JHEP published versio

Current status of las tablas de daimiel national park wetland and actions required for conservation

Wetlands are complex ecosystems that play multiple roles. ‘Las Tablas de Daimiel National Park’ (TDNP) undoubtedly plays a role in several ecosystem services and provides a connection between nature, farmers, scientists, residents, and other stakeholders. The state of degradation and/or vulnerability of this ecosystem (with a series of socio-economic implications) have led the publication of numerous articles. The work reported here provides a description of the growing importance of this wetland within the rural landscapes of La Mancha and emphasizes its state of degradation, mainly since pedological point of view. In this way, particular attention is required to assure the conservation of the Tablas of Daimiel Wetland; thus, several measures are proposed to improve the conservation of this area as to control and prohibit any dumping of any type of waste in the park or in its vicinityThis Research was funded by Organismo Autonomo Parques Nacionales (Autonomous Organism National Parks) of Spain (OAPN

Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics

An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$, where $q\colon\R\to\R$ and $p\colon\R\to\R$ are bounded and uniformly continuous, is fundamental to explain the absence or occurrence of rate-induced tipping for the differential equation $y' =(y-(2/\pi)\arctan(ct))^2+p(t)$ as the rate $c$ varies on $[0,\infty)$. A classical attractor-repeller pair, whose existence for $c=0$ is assumed, may persist for any $c>0$, or disappear for a certain critical rate $c=c_0$, giving rise to rate-induced tipping. A suitable example demonstrates that this tipping phenomenon may be reversible.Marie Skłodowska-Curie grant agreement No 643073Ministerio de Ciencia, Innovación y Universidades, RTI2018-096523-B-I00Marie Skłodowska-Curie grant agreement No 75446

G-inverses for random walks

Postprint (published version