On Donkin's Tilting Module Conjecture II: Counterexamples

In this paper we produce infinite families of counterexamples to Jantzen's question posed in 1980 on the existence of Weyl $p$-filtrations for Weyl modules for an algebraic group and Donkin's Tilting Module Conjecture formulated in 1990. New techniques to exhibit explicit examples are provided along with methods to produce counterexamples in large rank from counterexamples in small rank. Counterexamples can be produced via our methods for all groups other than when the root system is of type $\rm{A}_{n}$ or $\rm{B}_{2}$

Developmental changes in spinal neuronal properties, motor network configuration, and neuromodulation at free-swimming stages of Xenopus tadpoles

We describe a novel preparation of the isolated brainstem and spinal cord from pro-metamorphic tadpole stages of the South African clawed frog (Xenopus laevis) that permits whole cell patch-clamp recordings from neurons in the ventral spinal cord. Previous research on earlier stages of the same species has provided one of the most detailed understandings of the design and operation of a CPG circuit. Here we have addressed how development sculpts complexity from this more basic circuit. The preparation generates bouts of fictive31 swimming activity either spontaneously or in response to electrical stimulation of the optic tectum, allowing an investigation into how the neuronal properties, activity patterns and neuromodulation of locomotor rhythm generation change during development. We describe an increased repertoire of cellular responses compared to younger larval stages and investigate the cellular level effects of nitrergic neuromodulation as well as the development of a sodium pump-mediated ultra-slow afterhyperpolarisation (usAHP) in these free-swimming larval animals.PostprintPeer reviewe

Studies on the Weak Itinerant Ferromagnet SrRuO3 under High Pressure to 34 GPa

The dependence of the Curie temperature Tc on nearly hydrostatic pressure has been determined to 17.2 GPa for the weak itinerant ferromagnetic SrRuO3 in both polycrystalline and single-crystalline form. Tc is found to decrease under pressure from 162 K to 42.7 K at 17.2 GPa in nearly linear fashion at the rate dTc/dP = -6.8 K/GPa. No superconductivity was found above 4 K in the pressure range 17 to 34 GPa. Room-temperature X-ray diffraction studies to 25.3 GPa reveal no structural phase transition but indicate that the average Ru-O-Ru bond angle passes through a minimum near 15 GPa. The bulk modulus and its pressure derivative were determined to be B =192(3) GPa and B' = 5.0(3), respectively. Parallel ac susceptibility studies on polycrystalline CaRuO3 at 6 and 8 GPa pressure found no evidence for either ferromagnetism or superconductivity above 4 K