A statistical methodology for estimating dataset size requirements for classifying microarray data using learning curves is introduced. The goal is to use existing classification results to estimate dataset size requirements for future classification experiments and to evaluate the gain in accuracy and significance of classifiers built with additional data. The method is based on fitting inverse power-law models to construct empirical learning curves. It also includes a permutation test procedure to assess the statistical significance of classification performance for a given dataset size. This procedure is applied to several molecular classification problems representing a broad spectrum of levels of complexity.

Saturn’s moon Titan is the only extraterrestrial body known to host stable lakes and a hydrological cycle. Titan’s lakes predominantly contain liquid methane, ethane, and nitrogen, with methane evaporation driving its hydrological cycle. Molecular interactions between these three species lead to nonideal behavior that causes Titan’s lakes to behave differently than Earth’s lakes. Here, we numerically investigate how methane evaporation and nonideal interactions affect the physical properties, structure, dynamics, and evolution of shallow lakes on Titan. We find that, under certain temperature regimes, methane-rich mixtures are denser than relatively ethane-rich mixtures. This allows methane evaporation to stratify Titan’s lakes into ethane-rich upper layers and methane-rich lower layers, separated by a strong compositional gradient. At temperatures above 86 K, lakes remain well mixed and unstratified. Between 84 and 86 K, lakes can stratify episodically. Below 84 K, lakes permanently stratify and develop very methane-depleted epilimnia. Despite small seasonal and diurnal deviations (<5 K) from typical surface temperatures, Titan’s rain-filled ephemeral lakes and “phantom lakes” may nevertheless experience significantly larger temperature fluctuations, resulting in polymictic or even meromictic stratification, which may trigger ethane ice precipitation.

A combination band due to a mechanism whereby a photon excites two or more vibrational modes (e.g. a bend and a stretch) of an individual molecule is commonly seen in laboratory and astronomical spectroscopy. Here, we present evidence of a much less commonly seen combination band − one where a photon simultaneously excites two adjacent molecules in an ice. In particular, we present nearinfrared spectra of laboratory CO/N 2 ice samples where we identify a band at 4467.5 cm −1 (2.239 µm) that results from single photons exciting adjacent pairs of CO and N 2 molecules. We also present a near-infrared spectrum of Neptune's largest satellite Triton taken with the Gemini-South 8.1 meter telescope and the Immersion Grating Infrared Spectrograph (IGRINS) that shows this 4467.5 cm −1 (2.239 µm) CO-N 2 combination band. The existence of the band in a spectrum of Triton indicates that CO and N 2 molecules are intimately mixed in the ice rather than existing as separate regions of pure CO and pure N 2 deposits. Our finding is important because CO and N 2 are the most volatile species on Triton and so dominate seasonal volatile transport across its surface. Our result will place constraints on the interaction between the surface and atmosphere of Triton.

On Titan, methane (CH4) and ethane (C2H6) are the dominant species found in the lakes and seas. In this study, we have combined laboratory work and modeling to refine the methane–ethane binary phase diagram at low temperatures and probe how the molecules interact at these conditions. We used visual inspection for the liquidus and Raman spectroscopy for the solidus. Through these methods, we determined a eutectic point of 71.15 ± 0.5 K at a composition of 0.644 ± 0.018 methane–0.356 ± 0.018 ethane mole fraction from the liquidus data. Using the solidus data, we found a eutectic isotherm temperature of 72.2 K with a standard deviation of 0.4 K. In addition to mapping the binary system, we looked at the solid–solid transitions of pure ethane and found that, when cooling, the transition of solid I–III occurred at 89.45 ± 0.2 K. The warming sequence showed transitions of solid III–II occurring at 89.85 ± 0.2 K and solid II–I at 89.65 ± 0.2 K. Ideal predictions were compared with molecular dynamics simulations to reveal that the methane–ethane system behaves almost ideally, and the largest deviations occur as the mixing ratio approaches the eutectic composition.