Shortest paths between shortest paths and independent sets

We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even when we know that the sequence has polynomial length. Moreover, we also study reconfiguration of independent sets in three different models and analyze relationships between these models, observing that shortest path reconfiguration is a special case of independent set reconfiguration in perfect graphs, under any of the three models. Finally, we give polynomial results for restricted classes of graphs (even-hole-free and $P_4$-free graphs)

Gravity waves and high-altitude CO2_2 ice cloud formation in the Martian atmosphere

We present the first general circulation model simulations that quantify and reproduce patches of extremely cold air required for CO$_2$ condensation and cloud formation in the Martian mesosphere. They are created by subgrid-scale gravity waves (GWs) accounted for in the model with the interactively implemented spectral parameterization. Distributions of GW-induced temperature fluctuations and occurrences of supersaturation conditions are in a good agreement with observations of high-altitude CO$_2$ ice clouds. Our study confirms the key role of GWs in facilitating CO$_2$ cloud formation, discusses their tidal modulation, and predicts clouds at altitudes higher than have been observed to date.Comment: Accepted for publication in Geophysical Research Letters (GRL

Theoretical analysis of edit distance algorithms: an applied perspective

Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled

Informed and Automated k-Mer Size Selection for Genome Assembly

Genome assembly tools based on the de Bruijn graph framework rely on a parameter k, which represents a trade-off between several competing effects that are difficult to quantify. There is currently a lack of tools that would automatically estimate the best k to use and/or quickly generate histograms of k-mer abundances that would allow the user to make an informed decision. We develop a fast and accurate sampling method that constructs approximate abundance histograms with a several orders of magnitude performance improvement over traditional methods. We then present a fast heuristic that uses the generated abundance histograms for putative k values to estimate the best possible value of k. We test the effectiveness of our tool using diverse sequencing datasets and find that its choice of k leads to some of the best assemblies. Our tool KmerGenie is freely available at: http://kmergenie.bx.psu.edu/Comment: HiTSeq 201

Seasonal Water "Pump" in the Atmosphere of Mars: Vertical Transport to the Thermosphere

We present results of simulations with the Max Planck Institute general circulation model (MPI-MGCM) implementing a hydrological cycle scheme. The simulations reveal a seasonal water "pump" mechanism responsible for the upward transport of water vapor. This mechanism occurs in high latitudes above 60$^\circ$ of the southern hemisphere at perihelion, when the upward branch of the meridional circulation is particularly strong. A combination of the mean vertical flux with variations induced by solar tides facilitates penetration of water across the "bottleneck" at approximately 60 km. The meridional circulation then transports water across the globe to the northern hemisphere. Since the intensity of the meridional cell is tightly controlled by airborne dust, the water abundance in the thermosphere strongly increases during dust storms.Comment: 15 pages, 4 figure