On a Problem of Burnside

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner. NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

Characterization of harmonic tremor at Santiaguito volcano and its implications for eruption mechanisms

We observed Santiaguito volcano in southwestern Guatemala from March 2008 - March 2010. Seismic and infrasound data collected between January and March of 2009 contain records of many diverse processes occurring at the dacitic dome complex, including the recurrence of short lived (30-200 seconds in duration) harmonic tremor concurrent with ash poor gas emissions from the volcano. We employ several different analytical techniques to examine different portions of the tremor and source mechanisms. We use the parameters derived by this analysis to compare the feasibility of several suggested models of eruption mechanisms, and determine that this type of harmonic tremor is most justifiably generated by the flow of gas through crack networks generated by shear fracture along the magma conduit margin.

Dynamics and kinematics of eruptive activity at Fuego volcano, Guatemala 2005-2009

Volcanoes are the surficial expressions of complex pathways that vent magma and gasses generated deep in the Earth. Geophysical data record at least the partial history of magma and gas movement in the conduit and venting to the atmosphere. This work focuses on developing a more comprehensive understanding of explosive degassing at Fuego volcano, Guatemala through observations and analysis of geophysical data collected in 2005 – 2009. A pattern of eruptive activity was observed during 2005 – 2007 and quantified with seismic and infrasound, satellite thermal and gas measurements, and lava flow lengths. Eruptive styles are related to variable magma flux and accumulation of gas. Explosive degassing was recorded on broadband seismic and infrasound sensors in 2008 and 2009. Explosion energy partitioning between the ground and the atmosphere shows an increase in acoustic energy from 2008 to 2009, indicating a shift toward increased gas pressure in the conduit. Very-long-period (VLP) seismic signals are associated with the strongest explosions recorded in 2009 and waveform modeling in the 10 – 30 s band produces a best-fit source location 300 m west and 300 m below the summit crater. The calculated moment tensor indicates a volumetric source, which is modeled as a dike feeding a SW-dipping (35°) sill. The sill is the dominant component and its projection to the surface nearly intersects the summit crater. The deformation history of the sill is interpreted as: 1) an initial inflation due to pressurization, followed by 2) a rapid deflation as overpressure is explosively release, and finally 3) a reinflation as fresh magma flows into the sill and degasses. Tilt signals are derived from the horizontal components of the seismometer and show repetitive inflation deflation cycles with a 20 minute period coincident with strong explosions. These cycles represent the pressurization of the shallow conduit and explosive venting of overpressure that develops beneath a partially crystallized plug of magma. The energy released during the strong explosions has allowed for imaging of Fuego’s shallow conduit, which appears to have migrated west of the summit crater. In summary, Fuego is becoming more gas charged and its summit centered vent is shifting to the west - serious hazard consequences are likely.

Optimized spectrally selective steady-state free precession sequences for cartilage imaging at ultra-high fields

OBJECT: Fat suppressed 3D steady-state free precession (SSFP) sequences are of special interest in cartilage imaging due to their short repetition time in combination with high signal-to-noise ratio. At low-to-high fields (1.5-3.0 T), spectral spatial (spsp) radio frequency (RF) pulses perform superiorly over conventional saturation of the fat signal (FATSAT pulses). However, ultra-high fields (7.0 T and more) may offer alternative fat suppression techniques as a result of the increased chemical shift. MATERIALS AND METHODS: Application of a single, frequency selective, RF pulse is compared to spsp excitation for water (or fat) selective imaging at 7.0 T. RESULTS: For SSFP, application of a single frequency selective RF pulse for selective water or fat excitation performs beneficially over the commonly applied spsp RF pulses. In addition to the overall improved fat suppression, the application of single RF pulses leads to decreased power depositions, still representing one of the major restrictions in the design and application of many pulse sequences at ultra-high fields. CONCLUSION: The ease of applicability and implementation of single frequency selective RF pulses at ultra-high-fields might be of great benefit for a vast number of applications where fat suppression is desirable or fat-water separation is needed for quantification purposes.

Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

Regulation of mitochondrial function by hypoxia and inflammation in sepsis: A putative role for hypoxia inducible factor

Sepsis-related organ failure is the leading cause of mortality in European intensive care units (ICU). Although the inflammatory cascade of mediators in response to infection is well known, the relationships between regional inflammation, microvascular heterogeneity, hypoxia and hypoxia-inducible gene expression, and finally, organ dysfunction, are unknown. Growing evidence suggests that not only low oxygen supply to the tissues secondary to macrovascular and microvascular alterations, but also altered cellular oxygen utilization is involved in the development of multiorgan dysfunction [1]–[3]. Microbial products and innate and adaptive dysregulated immune response to infection directly affect parenchymal cells of organs and may contribute to multiorgan dysfunction.

Slope stability analysis of the Pacaya Volcano, Guatemala, using limit equilibrium and finite element method

The Pacaya volcanic complex is part of the Central American volcanic arc, which is associated with the subduction of the Cocos tectonic plate under the Caribbean plate. Located 30 km south of Guatemala City, Pacaya is situated on the southern rim of the Amatitlan Caldera. It is the largest post-caldera volcano, and has been one of Central America’s most active volcanoes over the last 500 years. Between 400 and 2000 years B.P, the Pacaya volcano had experienced a huge collapse, which resulted in the formation of horseshoe-shaped scarp that is still visible. In the recent years, several smaller collapses have been associated with the activity of the volcano (in 1961 and 2010) affecting its northwestern flanks, which are likely to be induced by the local and regional stress changes. The similar orientation of dry and volcanic fissures and the distribution of new vents would likely explain the reactivation of the pre-existing stress configuration responsible for the old-collapse. This paper presents the first stability analysis of the Pacaya volcanic flank. The inputs for the geological and geotechnical models were defined based on the stratigraphical, lithological, structural data, and material properties obtained from field survey and lab tests. According to the mechanical characteristics, three lithotechnical units were defined: Lava, Lava-Breccia and Breccia-Lava. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, and strength and deformation characteristics were computed in a specified stress range. Further, the stability of the volcano was evaluated by two-dimensional analysis performed by Limit Equilibrium (LEM, ROCSCIENCE) and Finite Element Method (FEM, PHASE 2 7.0). The stability analysis mainly focused on the modern Pacaya volcano built inside the collapse amphitheatre of “Old Pacaya”. The volcanic instability was assessed based on the variability of safety factor using deterministic, sensitivity, and probabilistic analysis considering the gravitational instability and the effects of external forces such as magma pressure and seismicity as potential triggering mechanisms of lateral collapse. The preliminary results from the analysis provide two insights: first, the least stable sector is on the south-western flank of the volcano; second, the lowest safety factor value suggests that the edifice is stable under gravity alone, and the external triggering mechanism can represent a likely destabilizing factor.

Ultraviolet digital imaging of volcanic plumes : implementation and application to magmatic processes at basaltic volcanoes

Magmatic volatiles play a crucial role in volcanism, from magma production at depth to generation of seismic phenomena to control of eruption style. Accordingly, many models of volcano dynamics rely heavily on behavior of such volatiles. Yet measurements of emission rates of volcanic gases have historically been limited, which has restricted model verification to processes on the order of days or longer. UV cameras are a recent advancement in the field of remote sensing of volcanic SO2 emissions. They offer enhanced temporal and spatial resolution over previous measurement techniques, but need development before they can be widely adopted and achieve the promise of integration with other geophysical datasets. Large datasets require a means by which to quickly and efficiently use imagery to calculate emission rates. We present a suite of programs designed to semi-automatically determine emission rates of SO2 from series of UV images. Extraction of high temporal resolution SO2 emission rates via this software facilitates comparison of gas data to geophysical data for the purposes of evaluating models of volcanic activity and has already proven useful at several volcanoes. Integrated UV camera and seismic measurements recorded in January 2009 at Fuego volcano, Guatemala, provide new insight into the system’s shallow conduit processes. High temporal resolution SO2 data reveal patterns of SO2 emission rate relative to explosions and seismic tremor that indicate tremor and degassing share a common source process. Progressive decreases in emission rate appear to represent inhibition of gas loss from magma as a result of rheological stiffening in the upper conduit. Measurements of emission rate from two closely-spaced vents, made possible by the high spatial resolution of the camera, help constrain this model. UV camera measurements at Kilauea volcano, Hawaii, in May of 2010 captured two occurrences of lava filling and draining within the summit vent. Accompanying high lava stands were diminished SO2 emission rates, decreased seismic and infrasonic tremor, minor deflation, and slowed lava lake surface velocity. Incorporation of UV camera data into the multi-parameter dataset gives credence to the likelihood of shallow gas accumulation as the cause of such events.