We present kinematic analyses of the 12 galaxies in the "Survey of H I in Extremely Low-mass Dwarfs" (SHIELD). We use multi-configuration interferometric observations of the H I 21 cm emission line from the Karl G. Jansky Very Large Array (VLA) 22 to produce image cubes at a variety of spatial and spectral resolutions. Both two-and three-dimensional fitting techniques are employed in an attempt to derive inclination-corrected rotation curves for each galaxy. In most cases, the comparable magnitudes of velocity dispersion and projected rotation result in degeneracies that prohibit unambiguous circular velocity solutions. We thus make spatially resolved position-velocity cuts, corrected for inclination using the stellar components, to estimate the circular rotation velocities. We find v circ  30 km s −1 for the entire survey population. Baryonic masses are calculated using singledish H I fluxes from Arecibo and stellar masses derived from HST and Spitzer imaging. Comparison is made with total dynamical masses estimated from the position-velocity analysis. The SHIELD galaxies are then placed on the baryonic Tully-Fisher relation. There exists an empirical threshold rotational velocity, Vrot < 15 km s −1 , below which current observations cannot differentiate coherent rotation from pressure support. The SHIELD galaxies are representative of an important population of galaxies whose properties cannot be described by current models of rotationally dominated galaxy dynamics.

The alignment of S11 to S16, obtained from a lower resolution search of the edge and g parameter space (Fig. DR2A), yields five distinct solutions a 11.1-11.5 (Fig. DR2C). The related 45 synthetic test produced a range of p-values for the average correlation coefficient for which the 46 null hypothesis of no true correlation can be rejected in only one case (Table DR1, g=1). Despite 47

We analyze the relationships between atomic, neutral hydrogen (H I) and star formation (SF) in the 12 low-mass SHIELD galaxies. We compare high spectral (∼0.82 km s −1 ch −1 ) and spatial resolution (physical resolutions of 170 pc -700 pc) H I imaging from the VLA with Hα and far-ultraviolet imaging. We quantify the degree of co-spatiality between star forming regions and regions of high H I column densities. We calculate the global star formation efficiencies (SFE, Σ SFR / Σ H I ), and examine the relationships among the SFE and H I mass, H I column density, and star formation rate (SFR). The systems are consuming their cold neutral gas on timescales of order a few Gyr. While we derive an index for the Kennicutt-Schmidt relation of N ≈ 0.68±0.04 for the SHIELD sample as a whole, the values of N vary considerably from system to system. By supplementing SHIELD results with those from other surveys, we find that HI mass and UV-based SFR are strongly correlated over five orders of magnitude. Identification of patterns within the SHIELD sample allows us to bin the galaxies into three general categories: 1) mainly co-spatial H I and SF regions, found in systems with highest peak H I column densities and highest total H I masses; 2) moderately correlated H I and SF regions, found in systems with moderate H I column densities; and 3) obvious offsets between H I and SF peaks, found in systems with the lowest total H I masses. SF in these galaxies is dominated by stochasticity and random fluctuations in their ISM.

SUMMARY We present and make publicly available a dynamic programming algorithm to simultaneously align the inclination and declination vector directions of sedimentary palaeomagnetic secular variation data. This algorithm generates a library of possible alignments through the systematic variation of assumptions about the relative accumulation rate and shared temporal overlap of two or more time-series. The palaeomagnetist can then evaluate this library of reproducible and objective alignments using available geological constraints, statistical methods and expert knowledge. We apply the algorithm to align previously (visually) correlated medium to high accumulation rate northern North Atlantic Holocene deposits (101–102 cm ka–1) with strong radiocarbon control. The algorithm generates plausible alignments that largely conform with radiocarbon and magnetic acquisition process uncertainty. These alignments illustrate the strengths and limitations of this numerical approach.

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