Splittings of Non-Finitely Generated Groups.

In geometric group theory one uses group actions on spaces to gain information about groups. One natural space to use is the Cayley graph of a group. The Cayley graph arguments that one encounters tend to require local niteness, and hence finite generation of the group. In this paper, I take the theory of intersection numbers of splittings of finitely generated groups (as developed by Scott, Scott-Swarup, and Niblo-Sageev-Scott-Swarup), and rework it to remove finite generation assumptions. I show that when working with splittings, instead of using the Cayley graph, one can use Bass-Serre trees.Ph.D.MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91432/1/lassonde_1.pd

Laser-assisted guiding of electric discharges around objects

Electric breakdown in air occurs for electric fields exceeding 34 kV/cm and results in a large current surge that propagates along unpredictable trajectories. Guiding such currents across specific paths in a controllable manner could allow protection against lightning strikes and high-voltage capacitor discharges. Such capabilities can be used for delivering charge to specific targets, for electronic jamming, or for applications associated with electric welding and machining. We show that judiciously shaped laser radiation can be effectively used to manipulate the discharge along a complex path and to produce electric discharges that unfold along a predefined trajectory. Remarkably, such laser-induced arcing can even circumvent an object that completely occludes the line of sight

Demonstration of the synchrotron-type spectrum of laser-produced Betatron radiation

Betatron X-ray radiation in laser-plasma accelerators is produced when electrons are accelerated and wiggled in the laser-wakefield cavity. This femtosecond source, producing intense X-ray beams in the multi kiloelectronvolt range has been observed at different interaction regime using high power laser from 10 to 100 TW. However, none of the spectral measurement performed were at sufficient resolution, bandwidth and signal to noise ratio to precisely determine the shape of spectra with a single laser shot in order to avoid shot to shot fluctuations. In this letter, the Betatron radiation produced using a 80 TW laser is characterized by using a single photon counting method. We measure in single shot spectra from 8 to 21 keV with a resolution better than 350 eV. The results obtained are in excellent agreement with theoretical predictions and demonstrate the synchrotron type nature of this radiation mechanism. The critical energy is found to be Ec = 5.6 \pm 1 keV for our experimental conditions. In addition, the features of the source at this energy range open novel perspectives for applications in time-resolved X-ray science.Comment: 5 pages, 4 figure

2018 Scholars at Work Conference Program

Program for the 2018 Scholars at Work Conference at Minnesota State University, Mankato on March 30, 2018

2019 Scholars at Work Conference Program

Program for the 2019 Scholars at Work Conference at Minnesota State University, Mankato on March 29, 2019

Metabolic changes in concussed American football players during the acute and chronic post-injury phases

<p>Abstract</p> <p>Background</p> <p>Despite negative neuroimaging findings many athletes display neurophysiological alterations and post-concussion symptoms that may be attributable to neurometabolic alterations.</p> <p>Methods</p> <p>The present study investigated the effects of sports concussion on brain metabolism using ¹H-MR Spectroscopy by comparing a group of 10 non-concussed athletes with a group of 10 concussed athletes of the same age (mean: 22.5 years) and education (mean: 16 years) within both the acute and chronic post-injury phases. All athletes were scanned 1-6 days post-concussion and again 6-months later in a 3T Siemens MRI.</p> <p>Results</p> <p>Concussed athletes demonstrated neurometabolic impairment in prefrontal and motor (M1) cortices in the acute phase where NAA:Cr levels remained depressed relative to controls. There was some recovery observed in the chronic phase where Glu:Cr levels returned to those of control athletes; however, there was a pathological increase of m-I:Cr levels in M1 that was only present in the chronic phase.</p> <p>Conclusions</p> <p>These results confirm cortical neurometabolic changes in the acute post-concussion phase as well as recovery and continued metabolic abnormalities in the chronic phase. The results indicate that complex pathophysiological processes differ depending on the post-injury phase and the neurometabolite in question.</p

Developmental malformation of the corpus callosum: a review of typical callosal development and examples of developmental disorders with callosal involvement

This review provides an overview of the involvement of the corpus callosum (CC) in a variety of developmental disorders that are currently defined exclusively by genetics, developmental insult, and/or behavior. I begin with a general review of CC development, connectivity, and function, followed by discussion of the research methods typically utilized to study the callosum. The bulk of the review concentrates on specific developmental disorders, beginning with agenesis of the corpus callosum (AgCC)—the only condition diagnosed exclusively by callosal anatomy. This is followed by a review of several genetic disorders that commonly result in social impairments and/or psychopathology similar to AgCC (neurofibromatosis-1, Turner syndrome, 22q11.2 deletion syndrome, Williams yndrome, and fragile X) and two forms of prenatal injury (premature birth, fetal alcohol syndrome) known to impact callosal development. Finally, I examine callosal involvement in several common developmental disorders defined exclusively by behavioral patterns (developmental language delay, dyslexia, attention-deficit hyperactive disorder, autism spectrum disorders, and Tourette syndrome)

Anterior and posterior commissures in agenesis of the corpus callosum: alternative pathways for attention processes?

Developmental absence (agenesis) of the corpus callosum (AgCC) is a congenital brain malformation resulting from disruption of corpus callosum formation, a structure that is crucial for the transfer and integration of information, including attention processes, across the brain. This study aimed to investigate previously proposed candidates for alternative inter-hemispheric pathways in AgCC by examining (1) white matter volume and microstructure of the anterior and posterior commissures in children with AgCC compared to typically developing controls (TDC), and (2) in children with AgCC, examine the associations of white matter volume and microstructure of the anterior and posterior commissures and any remaining corpus callosum with attention processes. Participants were 21 children with AgCC (13 complete, 8 partial) recruited from The Royal Children's Hospital, Melbourne, and 30 TDC aged 8–17 years. T1-and diffusion-weighted MR sequences were used to calculate volume and microstructural parameters. Neuropsychological testing assessed attention processes. We found the anterior commissure was significantly larger in volume in children with AgCC than TDC (p = .027), with reduced mean FA (p = .001) associated with increased mean RD (p < .001). In children with AgCC, we found microstructural properties of the anterior commissure associated with attentional processes, specifically, mean FA of the anterior commissure was associated with better divided attention (p = .03), and the association between alerting attention and mean AD and RD was found to be moderated by age (p = .027, p = .008) and the degree of corpus callosum agenesis (p = .025, p = .016). Furthermore, in partial AgCC, larger posterior commissure volume was associated with better orienting attention (p = .035). In conclusion, we provide evidence that the volume and microstructure of the anterior commissure are altered in children with AgCC, and this neuroplastic response might have an influence on attention processes