Anchored burning bijections on finite and infinite graphs

Let $G$ be an infinite graph such that each tree in the wired uniform spanning forest on $G$ has one end almost surely. On such graphs $G$, we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest on $G$ to recurrent sandpiles on $G$, that we call anchored burning bijections. In the special case of $\mathbb{Z}^d$, $d \ge 2$, we show how the anchored bijection, combined with Wilson's stacks of arrows construction, as well as other known results on spanning trees, yields a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of $\mathbb{Z}^d$. We discuss some open problems related to these findings.Comment: 26 pages; 1 EPS figure. Minor alterations made after comments from refere

Local connectivity and synaptic dynamics in mouse and human neocortex.

We present a unique, extensive, and open synaptic physiology analysis platform and dataset. Through its application, we reveal principles that relate cell type to synaptic properties and intralaminar circuit organization in the mouse and human cortex. The dynamics of excitatory synapses align with the postsynaptic cell subclass, whereas inhibitory synapse dynamics partly align with presynaptic cell subclass but with considerable overlap. Synaptic properties are heterogeneous in most subclass-to-subclass connections. The two main axes of heterogeneity are strength and variability. Cell subclasses divide along the variability axis, whereas the strength axis accounts for substantial heterogeneity within the subclass. In the human cortex, excitatory-to-excitatory synaptic dynamics are distinct from those in the mouse cortex and vary with depth across layers 2 and 3

Human neocortical expansion involves glutamatergic neuron diversification

The neocortex is disproportionately expanded in human compared with mouse1,2, both in its total volume relative to subcortical structures and in the proportion occupied by supragranular layers composed of neurons that selectively make connections within the neocortex and with other telencephalic structures. Single-cell transcriptomic analyses of human and mouse neocortex show an increased diversity of glutamatergic neuron types in supragranular layers in human neocortex and pronounced gradients as a function of cortical depth3. Here, to probe the functional and anatomical correlates of this transcriptomic diversity, we developed a robust platform combining patch clamp recording, biocytin staining and single-cell RNA-sequencing (Patch-seq) to examine neurosurgically resected human tissues. We demonstrate a strong correspondence between morphological, physiological and transcriptomic phenotypes of five human glutamatergic supragranular neuron types. These were enriched in but not restricted to layers, with one type varying continuously in all phenotypes across layers 2 and 3. The deep portion of layer 3 contained highly distinctive cell types, two of which express a neurofilament protein that labels long-range projection neurons in primates that are selectively depleted in Alzheimer’s disease4,5. Together, these results demonstrate the explanatory power of transcriptomic cell-type classification, provide a structural underpinning for increased complexity of cortical function in humans, and implicate discrete transcriptomic neuron types as selectively vulnerable in disease

Author Correction: Human neocortical expansion involves glutamatergic neuron diversification

In the version of this Article initially published, the Acknowledgements statement contained an error. Originally appearing with thanks for support given in part as follows, “R01EY023173 from The National Eye Institute, U01MH105982 from the National Institute of Mental Health and Eunice Kennedy Shriver National Institute of Child Health and Human Development, and R011EY023173 from The National Institute of Allergy and Infectious Disease,” the last number (R011EY023173) was mistakenly added and is not in fact a grant or one provided by the NIAID. The mention has been removed. The changes have been made to the online version of the Article

Human neocortical expansion involves glutamatergic neuron diversification.

The neocortex is disproportionately expanded in human compared with mouse1,2, both in its total volume relative to subcortical structures and in the proportion occupied by supragranular layers composed of neurons that selectively make connections within the neocortex and with other telencephalic structures. Single-cell transcriptomic analyses of human and mouse neocortex show an increased diversity of glutamatergic neuron types in supragranular layers in human neocortex and pronounced gradients as a function of cortical depth3. Here, to probe the functional and anatomical correlates of this transcriptomic diversity, we developed a robust platform combining patch clamp recording, biocytin staining and single-cell RNA-sequencing (Patch-seq) to examine neurosurgically resected human tissues. We demonstrate a strong correspondence between morphological, physiological and transcriptomic phenotypes of five human glutamatergic supragranular neuron types. These were enriched in but not restricted to layers, with one type varying continuously in all phenotypes across layers 2 and 3. The deep portion of layer 3 contained highly distinctive cell types, two of which express a neurofilament protein that labels long-range projection neurons in primates that are selectively depleted in Alzheimer\u27s disease4,5. Together, these results demonstrate the explanatory power of transcriptomic cell-type classification, provide a structural underpinning for increased complexity of cortical function in humans, and implicate discrete transcriptomic neuron types as selectively vulnerable in disease