BVR photometry of the resolved dwarf galaxy Ho IX

We present BVR CCD photometry down to limiting magnitude B=23.5 mag for 232 starlike objects and 11 diffuse objects in a 5.4' x 5.4' field of Ho IX. The galaxy is a gas-rich irregular dwarf galaxy possibly very close to M 81, which makes it especially interesting in the context of the evolution of satellite galaxies and the accretion of dwarf galaxies. Investigations of Ho IX were hampered by relatively large contradictions in the magnitude scale between earlier studies. With our new photometry we resolved these discrepancies. The color magnitude diagram (CMD) of Ho IX is fairly typical of a star-forming dwarf irregular, consistent with earlier results. Distance estimates from our new CMD are consistent with Ho IX being very close to M 81 and therefore being a definite member of the M 81 group, apparently in very close physical proximity to M 81.Comment: 9 pages, 8 figures, uses aa.cls, A&A in pres

Remarks on the number of tubulin dimers per neuron and implications for Hameroff-Penrose Orch OR

Stuart Hameroff has wrongly estimated that a typical brain neuron has 10^7^ tubulin dimers and wrongly attributed this result to Yu and Baas, J. Neurosci. 1994; 14: 2818-2829. In this letter we show that Hameroff’s estimate is based on misunderstanding of the results provided by Yu and Baas, who actually measured the total microtubule length in a single axonal projection with length of 56 μm in a differentiating in vitro stage 3 embryonic hippocampal neuron. In order to visualize how big Hameroff’s error is, we have reconstructed two of the studied by Yu and Baas embryonic hippocampal neurons with Neuromantic v1.6.3 and compared them with previously published reconstructions of adult hippocampal neurons. Correct calculations show that an adult differentiated pyramidal neuron in vivo has approximately 1.3×10^9^ tubulin dimers incorporated in cytoskeletal microtubules. This estimate has profound implications for the Hameroff-Penrose Orch OR model, because it sets limitations on the number of quantum coherent neurons and implies that if 100% of the neuronal microtubules are quantum coherent for 25 ms then Hameroff-Penrose Orch OR conscious events should involve only 15 pyramidal neurons

On the lower bound of the inner radius of nodal domains

We discuss the asymptotic lower bound on the inner radius of nodal domains that arise from Laplacian eigenfunctions \varphi _{\lambda} on a closed Riemannian manifold (M, g) . In the real-analytic case, we present an improvement of the currently best-known bounds, due to Mangoubi (Commun Partial Differ Equ 33:1611–1621, 2008; Can Math Bull 51(2):249–260, 2008). Furthermore, using recent results of Hezari (P Am Math Soc, 2016, https://doi.org/10.1090/proc/13766; Anal PDE 11(4):855–871, 2018), we obtain log-type improvements in the case of negative curvature and improved bounds for (M, g) possessing an ergodic geodesic flow