The Price of Order

We present tight bounds on the spanning ratio of a large family of ordered $\theta$-graphs. A $\theta$-graph partitions the plane around each vertex into $m$ disjoint cones, each having aperture $\theta = 2 \pi/m$. An ordered $\theta$-graph is constructed by inserting the vertices one by one and connecting each vertex to the closest previously-inserted vertex in each cone. We show that for any integer $k \geq 1$, ordered $\theta$-graphs with $4k + 4$ cones have a tight spanning ratio of $1 + 2 \sin(\theta/2) / (\cos(\theta/2) - \sin(\theta/2))$. We also show that for any integer $k \geq 2$, ordered $\theta$-graphs with $4k + 2$ cones have a tight spanning ratio of $1 / (1 - 2 \sin(\theta/2))$. We provide lower bounds for ordered $\theta$-graphs with $4k + 3$ and $4k + 5$ cones. For ordered $\theta$-graphs with $4k + 2$ and $4k + 5$ cones these lower bounds are strictly greater than the worst case spanning ratios of their unordered counterparts. These are the first results showing that ordered $\theta$-graphs have worse spanning ratios than unordered $\theta$-graphs. Finally, we show that, unlike their unordered counterparts, the ordered $\theta$-graphs with 4, 5, and 6 cones are not spanners

Windiness spells in SW Europe since the last glacial maximum

Dunefields have a great potential to unravel past regimes of atmospheric circulation as they record direct traces of this component of the climate system. Along the Portuguese coast, transgressive dunefields represent relict features originated by intense and frequent westerly winds that largely contrast with present conditions, clearly dominated by weaker northwesterly winds. Optical dating and subsurface stratigraphy document three age clusters indicating main episodes of dune mobilization during: the last termination (20-11.6 ka), Middle Holocene (5.6 ka), and Late Holocene (1.2-0.98 and 0.4-0.15 ka).We find reconstructed windfields to be analogous during all episodes and dominated by strong westerlies. Yet, larger grain size diameters and dune volumes documented for the last termination support amplified patterns compatible with a southward shift and intensification of the North Atlantic westerlies during winters. Conversely, dunes deposited after the Middle Holocene are compatible with more variable windfields and weakened patterns controlled by interannual shifts towards low values of the North Atlantic Oscillation (NAO).This work demonstrates that present windfield regimes in southern Europe are not compatible with past aeolian activity. Indeed, present day analogs indicate that wind intensities compatible with past aeolian activity are rare at present (sediment transport potentials below estimates in the aeolian record), but can occur if the jet stream is diverted to the south (i.e. 30 degrees N with negative NAO index) or if very deep cyclones anchor around 50 degrees N, extending their influence to the western Portuguese coast (relatively low NAO index). However, these conditions represent temporary patterns lasting around one day, while we suggest that the identified episodes of aeolian activity may represent semi-permanent conditions. (C) 2016 Elsevier B.V. All rights reserved

Sensitivity of discharge and flood frequency to twenty-first century and late Holocene changes in climate and land use (River Meuse, northwest Europe)

We used a calibrated coupled climate–hydrological model to simulate Meuse discharge over the late Holocene (4000–3000 BP and 1000–2000 AD). We then used this model to simulate discharge in the twenty-first century under SRES emission scenarios A2 and B1, with and without future land use change. Mean discharge and medium-sized high-flow (e.g. Q99) frequency are higher in 1000–2000 AD than in 4000–3000 BP; almost all of this increase can be attributed to the conversion of forest to agriculture. In the twentieth century, mean discharge and the frequency of medium-sized high-flow events are higher than in the nineteenth century; this increase can be attributed to increased (winter half-year) precipitation. Between the twentieth and twenty-first centuries, anthropogenic climate change causes a further increase in discharge and medium-sized high-flow frequency; this increase is of a similar order of magnitude to the changes over the last 4,000 years. The magnitude of extreme flood events (return period 1,250-years) is higher in the twenty-first century than in any preceding period of the time-slices studied. In contrast to the long-term influence of deforestation on mean discharge, changes in forest cover have had little effect on these extreme floods, even on the millennial timescale

Routing on the Visibility Graph

We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of non-crossing line segments whose endpoints are in $P$. We present two deterministic 1-local $O(1)$-memory routing algorithms that are guaranteed to find a path of at most linear size between any pair of vertices of the \emph{visibility graph} of $P$ with respect to a set of constraints $S$ (i.e., the algorithms never look beyond the direct neighbours of the current location and store only a constant amount of additional information). Contrary to {\em all} existing deterministic local routing algorithms, our routing algorithms do not route on a plane subgraph of the visibility graph. Additionally, we provide lower bounds on the routing ratio of any deterministic local routing algorithm on the visibility graph.Comment: An extended abstract of this paper appeared in the proceedings of the 28th International Symposium on Algorithms and Computation (ISAAC 2017). Final version appeared in the Journal of Computational Geometr

Major Δ14C excursions during the late glacial and early Holocene: changes in ocean ventilation or solar forcing of climate change?

The atmospheric 14C record during the Late Glacial and the early Holocene shows sharp increases simultaneous with cold climatic phases. These increases in the atmospheric 14C content are usually explained as the effect of reduced oceanic CO2 ventilation after episodic outbursts of large meltwater reservoirs into the North Atlantic. In this hypothesis the stagnation of the thermohaline circulation is the cause of both climate change as well as an increase in atmospheric 14C: As an alternative hypothesis we propose that changes in 14C production give an indication for the cause of the recorded climate shifts: changes in solar activity cause fluctuations in the solar wind, which modulate the cosmic ray intensity and related 14C production. Two possible mechanisms amplifying the changes in solar activity may result in climate change. In the case of a temporary decline in solar activity: (1) reduced solar UV intensity may cause a decline of stratospheric ozone production and cooling as a result of less absorption of sunlight. This might influence atmospheric circulation patterns (extension of Polar Cells and equatorward relocation of mid-latitude storm tracks), with effects on oceanic circulation, and (2) increased cosmic ray intensity may stimulate cloud formation and precipitation, while 14C production increases.