Ambient but not local lactate underlies neuronal tolerance to prolonged glucose deprivation

Neurons require a nearly constant supply of ATP. Glucose is the predominant source of brain ATP, but the direct effects of prolonged glucose deprivation on neuronal viability and function remain unclear. In sparse rat hippocampal microcultures, neurons were surprisingly resilient to 16 h glucose removal in the absence of secondary excitotoxicity. Neuronal survival and synaptic transmission were unaffected by prolonged removal of exogenous glucose. Inhibition of lactate transport decreased microculture neuronal survival during concurrent glucose deprivation, suggesting that endogenously released lactate is important for tolerance to glucose deprivation. Tandem depolarization and glucose deprivation also reduced neuronal survival, and trace glucose concentrations afforded neuroprotection. Mass cultures, in contrast to microcultures, were insensitive to depolarizing glucose deprivation, a difference attributable to increased extracellular lactate levels. Removal of local astrocyte support did not reduce survival in response to glucose deprivation or alter evoked excitatory transmission, suggesting that on-demand, local lactate shuttling is not necessary for neuronal tolerance to prolonged glucose removal. Taken together, these data suggest that endogenously produced lactate available globally in the extracellular milieu sustains neurons in the absence of glucose. A better understanding of resilience mechanisms in reduced preparations could lead to therapeutic strategies aimed to bolster these mechanisms in vulnerable neuronal populations

FAST TCP: Motivation, Architecture, Algorithms, Performance

We describe FAST TCP, a new TCP congestion control algorithm for high-speed long-latency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties which the current TCP implementation has at large windows. We describe the architecture and summarize some of the algorithms implemented in our prototype. We characterize its equilibrium and stability properties. We evaluate it experimentally in terms of throughput, fairness, stability, and responsiveness

A monad measure space for logarithmic density

We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $A\subseteq \mathbb{N}$ has positive Banach logarithmic density, then $A$ contains an approximate geometric progression of any length. We also prove that if $A,B\subseteq \mathbb{N}$ have positive Banach logarithmic density, then there are arbitrarily long intervals whose gaps on $A\cdot B$ are multiplicatively bounded, a multiplicative version Jin's sumset theorem. The main technical tool is the use of a quotient of a Loeb measure space with respect to a multiplicative cut.Comment: 26 page

High density piecewise syndeticity of product sets in amenable groups

M. Beiglb\"ock, V. Bergelson, and A. Fish proved that if $G$ is a countable amenable group and $A$ and $B$ are subsets of $G$ with positive Banach density, then the product set $AB$ is piecewise syndetic. This means that there is a finite subset $E$ of $G$ such that $EAB$ is thick, that is, $EAB$ contains translates of any finite subset of $G$. When $G=\mathbb{Z}$, this was first proven by R. Jin. We prove a quantitative version of the aforementioned result by providing a lower bound on the density (with respect to a F\o lner sequence) of the set of witnesses to the thickness of $$. When $G=\mathbb{Z}^d$, this result was first proven by the current set of authors using completely different techniques.Comment: 7 pages; the proof of the main result has been simplified and sharpened by removing a technical assumption; also, a lower density version has been adde