Critical Pebbling Numbers of Graphs

We define three new pebbling parameters of a connected graph $G$, the $r$-, $g$-, and $u$-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $n$ and the diameter $d$ of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the $r$-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the $r$-critical pebbling number is $2^d$.Comment: 26 page

Rational combinations of Betti diagrams of complete intersections

We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-S\"oderberg theory. That is, given a Betti diagram, we determine if it is possible to decompose it into the Betti diagrams of complete intersections. To do so, we determine the extremal rays of the cone generated by the diagrams of complete intersections and provide a rudimentary algorithm for decomposition.Comment: This research was conducted at the Willamette Mathematics Consortium RE

The Effect of Inheritance Receipt on Retirement

This paper uses the receipt of an inheritance to measure the effect of wealth shocks on retirement. Using the Health and Retirement Study (HRS), we first document that inheritance receipt is common among older workers %u2013 one in five households receives an inheritance over an eight-year period, with a median value of about $30,000. We find that inheritance receipt is associated with a significant increase in the probability of retirement. In particular, we find that receiving an inheritance increases the probability of retiring earlier than expected by 4.4 percentage points, or 12 percent relative to the baseline retirement rate, over an eight-year period. Importantly, this effect is stronger when the inheritance is unexpected and thus more likely to represent an exogenous shock to wealth.

Interactive manipulation of microparticles in an octagonal sonotweezer

An ultrasonic device for micro-patterning and precision manipulation of micrometre-scale particles is demonstrated. The device is formed using eight piezoelectric transducers shaped into an octagonal cavity. By exciting combinations of transducers simultaneously, with a controlled phase delay between them, different acoustic landscapes can be created, patterning micro-particles into lines, squares, and more complex shapes. When operated with all eight transducers the device can, with appropriate phase control, manipulate the two dimensional acoustic pressure gradient; it thus has the ability to position and translate a single tweezing zone to different locations on a surface in a precise and programmable manner

GaAs monolithic frequency doublers with series connected varactor diodes

GaAs monolithic frequency doublers using series connected varactor diodes have been fabricated for the first time. Output powers of 150 mW at 36.9 GHz with 24% efficiency and 300 mW at 24.8 GHz with 18% efficiency have been obtained. Peak efficiencies of 35% at output power levels near 100 mW have been achieved at both frequencies. Both K-band and Ka-band frequency doublers are derived from a lower power, single-diode design by series connection of two diodes and scaling to achieve different power and frequency specifications. Their fabrication was accomplished using the same process sequence

Polycistronic Delivery of IL-10 and NT-3 Promotes Oligodendrocyte Myelination and Functional Recovery in a Mouse Spinal Cord Injury Model.

One million estimated cases of spinal cord injury (SCI) have been reported in the United States and repairing an injury has constituted a difficult clinical challenge. The complex, dynamic, inhibitory microenvironment postinjury, which is characterized by proinflammatory signaling from invading leukocytes and lack of sufficient factors that promote axonal survival and elongation, limits regeneration. Herein, we investigated the delivery of polycistronic vectors, which have the potential to coexpress factors that target distinct barriers to regeneration, from a multiple channel poly(lactide-co-glycolide) (PLG) bridge to enhance spinal cord regeneration. In this study, we investigated polycistronic delivery of IL-10 that targets proinflammatory signaling, and NT-3 that targets axonal survival and elongation. A significant increase was observed in the density of regenerative macrophages for IL-10+NT-3 condition relative to conditions without IL-10. Furthermore, combined delivery of IL-10+NT-3 produced a significant increase of axonal density and notably myelinated axons compared with all other conditions. A significant increase in functional recovery was observed for IL-10+NT-3 delivery at 12 weeks postinjury that was positively correlated to oligodendrocyte myelinated axon density, suggesting oligodendrocyte-mediated myelination as an important target to improve functional recovery. These results further support the use of multiple channel PLG bridges as a growth supportive substrate and platform to deliver bioactive agents to modulate the SCI microenvironment and promote regeneration and functional recovery. Impact statement Spinal cord injury (SCI) results in a complex microenvironment that contains multiple barriers to regeneration and functional recovery. Multiple factors are necessary to address these barriers to regeneration, and polycistronic lentiviral gene therapy represents a strategy to locally express multiple factors simultaneously. A bicistronic vector encoding IL-10 and NT-3 was delivered from a poly(lactide-co-glycolide) bridge, which provides structural support that guides regeneration, resulting in increased axonal growth, myelination, and subsequent functional recovery. These results demonstrate the opportunity of targeting multiple barriers to SCI regeneration for additive effects

PLG Bridge Implantation in Chronic SCI Promotes Axonal Elongation and Myelination.

Spinal cord injury (SCI) is a devastating condition that may cause permanent functional loss below the level of injury, including paralysis and loss of bladder, bowel, and sexual function. Patients are rarely treated immediately, and this delay is associated with tissue loss and scar formation that can make regeneration at chronic time points more challenging. Herein, we investigated regeneration using a poly(lactide-co-glycolide) multichannel bridge implanted into a chronic SCI following surgical resection of necrotic tissue. We characterized the dynamic injury response and noted that scar formation decreased at 4 and 8 weeks postinjury (wpi), yet macrophage infiltration increased between 4 and 8 wpi. Subsequently, the scar tissue was resected and bridges were implanted at 4 and 8 wpi. We observed robust axon growth into the bridge and remyelination at 6 months after initial injury. Axon densities were increased for 8 week bridge implantation relative to 4 week bridge implantation, whereas greater myelination, particularly by Schwann cells, was observed with 4 week bridge implantation. The process of bridge implantation did not significantly decrease the postinjury function. Collectively, this chronic model follows the pathophysiology of human SCI, and bridge implantation allows for clear demarcation of the regenerated tissue. These data demonstrate that bridge implantation into chronic SCI supports regeneration and provides a platform to investigate strategies to buttress and expand regeneration of neural tissue at chronic time points

Research review: young people leaving care

This paper reviews the international research on young people leaving care. Set in the context of a social exclusion framework, it explores young people's accelerated and compressed transitions to adulthood, and discusses the development and classification of leaving care services in responding to their needs. It then considers the evidence from outcome studies and argues that adopting a resilience framework suggests that young people leaving care may fall into three groups: young people 'moving on', 'survivors' and 'victims'. In concluding, it argues that these three pathways are associated with the quality of care young people receive, their transitions from care and the support they receive after care

Hundred photon microwave ionization of Rydberg atoms in a static electric field

We present analytical and numerical results for the microwave excitation of nonhydrogenic atoms in a static electric field when up to 1000 photons are required to ionize an atom. For small microwave fields, dynamical localization in photon number leads to exponentially small ionization while above quantum delocalization border ionization goes in a diffusive way. For alkali atoms in a static field the ionization border is much lower than in hydrogen due to internal chaos.Comment: revtex, 4 pages, 5 figure