Affine differential geometry analysis of human arm movements

Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the “two-thirds power law” which connects path curvature with velocity, and “local isochrony” which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan’s moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants—equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production

RADVAN: a randomised phase 2 trial of WBRT plus vandetanib for melanoma brain metastases - results and lessons learnt

BACKGROUND: Brain metastases occur in up to 75% of patients with advanced melanoma. Most are treated with whole-brain radiotherapy (WBRT), with limited effectiveness. Vandetanib, an inhibitor of vascular endothelial growth factor receptor, epidermal growth factor receptor and rearranged during transfection tyrosine kinases, is a potent radiosensitiser in xenograft models. We compared WBRT with WBRT plus vandetanib in the treatment of patients with melanoma brain metastases. METHODS: In this double-blind, multi-centre, phase 2 trial patients with melanoma brain metastases were randomised to receive WBRT (30 Gy in 10 fractions) plus 3 weeks of concurrent vandetanib 100 mg once daily or placebo. The primary endpoint was progression-free survival in brain (PFS brain). The main study was preceded by a safety run-in phase to confirm tolerability of the combination. A post-hoc analysis and literature review considered barriers to recruiting patients with melanoma brain metastases to clinical trials. RESULTS: Twenty-four patients were recruited, six to the safety phase and 18 to the randomised phase. The study closed early due to poor recruitment. Median PFS brain was 3.3 months (90% confidence interval (CI): 1.6-5.6) in the vandetanib group and 2.5 months (90% CI: 0.2-4.8) in the placebo group (P=0.34). Median overall survival (OS) was 4.6 months (90% CI: 1.6-6.3) and 2.5 months (90% CI: 0.2-7.2), respectively (P=0.54). The most frequent adverse events were fatigue, alopecia, confusion and nausea. The most common barrier to study recruitment was availability of alternative treatments. CONCLUSIONS: The combination of WBRT plus vandetanib was well tolerated. Compared with WBRT alone, there was no significant improvement in PFS brain or OS, although we are unable to provide a definitive result due to poor accrual. A review of barriers to trial accrual identified several factors that affect study recruitment in this difficult disease area

A Census of Sub-kiloparsec Resolution Metallicity Gradients in Star-forming Galaxies at Cosmic Noon from HST Slitless Spectroscopy

We present the hitherto largest sample of gas-phase metallicity radial gradients measured at sub-kpc resolution in star-forming galaxies in the redshift range of z ∈ [1.2, 2.3]. These measurements are enabled by the synergy of slitless spectroscopy from the Hubble Space Telescope near-infrared channels and the lensing magnification from foreground galaxy clusters. Our sample consists of 76 galaxies with stellar mass ranging from 107 to 1010 M⊙, an instantaneous star formation rate in the range of [1, 100] M⊙ yr-1, and global metallicity [1/12 ,2] of solar. At a 2σ confidence level, 15/76 galaxies in our sample show negative radial gradients, whereas 7/76 show inverted gradients. Combining ours and all other metallicity gradients obtained at a similar resolution currently available in the literature, we measure a negative mass dependence of Δlog(O/H)/Δ r [dex kpc-1] = (-0.020 ± 0.007) + (-0.016 ± 0.008), with the intrinsic scatter being σ = 0.060 ± 0.006 over 4 orders of magnitude in stellar mass. Our result is consistent with strong feedback, not secular processes, being the primary governor of the chemostructural evolution of star-forming galaxies during the disk mass assembly at cosmic noon. We also find that the intrinsic scatter of metallicity gradients increases with decreasing stellar mass and increasing specific star formation rate. This increase in the intrinsic scatter is likely caused by the combined effect of cold-mode gas accretion and merger-induced starbursts, with the latter more predominant in the dwarf mass regime of M∗ ≤ 109 M⊙