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Abstract. Sufficient conditions have been given for the convergence in norm and a.e. of the ergodic Hilbert transform ([11], [5], [6]). Here we apply these conditions to the rotated ergodic Hilbert transform ∑∞ n=1 λn n T nf, where λ is a complex number of modulus 1. When T is a contraction in a Hilbert space, we show that the logarithmic Hausdorff dimension of the set of λ’s for which this series does not converge is at most 2 and give examples where this bound is attained

Two for the Price of One: A Neuroprotective Chaperone Kit within NAD Synthase Protein NMNAT2

One of the most fascinating properties of the brain is the ability to function smoothly across decades of a lifespan. Neurons are nondividing mature cells specialized in fast electrical and chemical communication at synapses. Often, neurons and synapses operate at high levels of activity through sophisticated arborizations of long axons and dendrites that nevertheless stay healthy throughout years. On the other hand, aging and activity-dependent stress strike onto the protein machineries turning proteins unfolded and prone to form pathological aggregates associated with neurodegeneration. How do neurons protect from those insults and remain healthy for their whole life? Ali and colleagues now present a molecular mechanism by which the enzyme nicotinamide mononucleotide adenylyltransferase 2 (NMNAT2) acts not only as a NAD synthase involved in axonal maintenance but as a molecular chaperone helping neurons to overcome protein unfolding and protein aggregation