The oligodendrocyte transcription factor Olig2 plays a crucial role in the neurogenesis of both spinal cord and brain. In the cerebellum, deletion of both Olig2 and Olig1 results in impaired genesis of Purkinje cells (PCs) and Pax2+ interneurons. Here, we perform an independent study to show that Olig2 protein is transiently expressed in the cerebellar ventricular zone (VZ) during a period when PCs are specified. Further analyses demonstrate that Olig2 is expressed in both cerebellar VZ progenitors and early-born neurons. In addition, unlike in the ganglionic eminence of the embryonic forebrain where Olig2 is mostly expressed in proliferating progenitors, Olig2+ cells in the cerebellar VZ are in the process of leaving the cell cycle and differentiating into postmitotic neurons. Functionally, deletion of Olig2 alone results in a preferential reduction of PCs in the cerebellum, which is likely mediated by decreased neuronal generation from their cerebellar VZ progenitors. Furthermore, our long-term lineage tracing experiments show that cerebellar Olig gene-expressing progenitors produce PCs but rarely Pax2+ interneurons in the developing cerebellum, which opposes the “temporal identity transition” model of the cerebellar VZ progenitors stating that majority of Pax2+ interneuron progenitors are transitioned from Olig2+ PC progenitors.

No abstract

No abstract

This paper addresses the stabilization of fractional‐order nonlinear lower triangular systems and applies the obtained results to the synchronization of fractional‐order chaotic systems (FOCSs). Three cases are considered as follows: (i) FOCSs have a lower triangular structure themselves. (ii) FOCSs can be converted into the form in full by appropriate nonsingular coordinate transformations. (iii) FOCSs can be transformed into the structure in part by the conversions. It is shown that the above three cases combining with back‐stepping approach are useful for the control of FOCSs. Different from the previous literature, the system structure studied is more concise with more applications. A numerical example is presented to show the validity of the proposed results.

No abstract