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We derive a spectral sum rule in the shear channel for conformal field theories in general d> 2 dimensions held at finite temperature. The sum rule result from the OPE of the stress tensor at high frequency as well as the hydrodynamic behaviour of the theory at low frequencies. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Maldacena-Hofman variables t_2, t_4 which rely on data which determines the three point function of the stress tensor of the CFT. For theories which admit a two derivative gravity dual this proportionality constant is given by d/2(d+1) . We then use causality constraints and obtain bounds on the sum rule which are valid for any conformal field theory. We illustrate the sum rule by applying it to well studied conformal field theories in d=3, 4, 6. dimensions

Ecosystem responses to climatic droughts range from increased frequency of stomatal closure and declines in carbon assimilation to plant mortality and increased vulnerability to insects/pathogens and fire. Forest thinning is often posited as a management practice that can reduce mitigate these forest drought responses and may have implications for groundwater recharge and streamflow. There are still relatively few field-based studies of thinning impacts on forest water use. Most of these studies focus only on responses in the first 1-2 years following thinning and show substantial cross-site differences in responses. To extend and better understand field-based findings, we utilize a fully coupled model of ecosystem carbon cycling and hydrology to estimate forest water use, carbon sequestration, regrowth rates and indicators of water stress for different thinning densities. We compare results across climate, topography and soils. For the California Sierra, results emphasize the importance of plant accessible subsurface water storage capacity (PAWSC). We find that a first-order control on system response to thinning is the interactions between PAWSC and climate. We also show that a critical information gap is estimates of the degree to which neighboring trees share water. We conclude by suggesting model applications and new measurements that could be used to help guide decision-making with respect to thinning by accounting for how these multiple controls on thinning ecohydrology interact.

Adult mammalian brains show remarkable plasticity in response to deafferentations due to injuries. Lesions of dorsal columns of the spinal cord at cervical levels deafferent sensory inputs from parts of the body below the level of the lesion. Chronic dorsal column injuries in monkeys result in expansion of intact chin inputs into the deafferented hand regions of the primary and secondary somatosensory cortex (area 3 and area S2), ventroposterior lateral nucleus of the thalamus and cuneate nucleus of the brain stem. Our recent evidence suggests that the key plastic change takes place in the brain stem nuclei, perhaps due to axonal growth from the trigeminal nucleus into the cuneate nucleus. This reorganization is then propagated upstream resulting a brain-wide reorganization.