Incompleteness and jump hierarchies

This paper is an investigation of the relationship between G\"odel's second incompleteness theorem and the well-foundedness of jump hierarchies. It follows from a classic theorem of Spector's that the relation $\{(A,B) \in \mathbb{R}^2 : \mathcal{O}^A \leq_H B\}$ is well-founded. We provide an alternative proof of this fact that uses G\"odel's second incompleteness theorem instead of the theory of admissible ordinals. We then derive a semantic version of the second incompleteness theorem, originally due to Mummert and Simpson, from this result. Finally, we turn to the calculation of the ranks of reals in this well-founded relation. We prove that, for any $A\in\mathbb{R}$, if the rank of $A$ is $\alpha$, then $\omega_1^A$ is the $(1 + \alpha)^{\text{th}}$ admissible ordinal. It follows, assuming suitable large cardinal hypotheses, that, on a cone, the rank of $X$ is $\omega_1^X$.Comment: 11 pages. Corrects a mistake in the statements of two result

Dreams from the Podium

This article tells a story about teaching as an act of love, about an instructor who discovered theater as a teaching tool and combined it with working class values and rituals in order to remake the culture of higher education in a classroom of adult learners. The story speaks to the intersection of the arts, Jesuit values of higher education and the person/background of the teacher at just the right time. The story is one of humility

Influence of wolf predation on population momentum of the Nushagak Peninsula caribou herd, southwestern Alaska

We investigated wolf predation as a potential driver of population change in the Nushagak Peninsula caribou herd, southwestern Alaska. We investigated the time budgets of three wolf packs using the peninsula from 2007 through 2012, and thus potentially preying on caribou there, in order to make inferences on their likelihood of serving as an important population modifier for the Nushagak Peninsula caribou herd. We found that only one pack regularly used the peninsula. The pack using the peninsula spent an average of 35% of its time there. Its use of the peninsula was disproportionately high in late summer and fall, disproportionately low in winter, and proportional during the caribou calving season in early summer. Overall wolf use of the Nushagak Peninsula increased in direct response to increasing caribou abundance but was not a primary population driver

Disease activity flares and pain flares in an early rheumatoid arthritis inception cohort; characteristics, antecedents and sequelae

© 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.Background: RA flares are common and disabling. They are described in terms of worsening inflammation but pain and inflammation are often discordant. To inform treatment decisions, we investigated whether inflammatory and pain flares are discrete entities. Methods: People from the Early RA Network (ERAN) cohort were assessed annually up to 11 years after presentation (n = 719, 3703 person-years of follow up). Flare events were defined in 2 different ways that were analysed in parallel; DAS28 or Pain Flares. DAS28 Flares satisfied OMERACT flare criteria of increases in DAS28 since the previous assessment (≥1.2 points if active RA or ≥ 0.6 points if inactive RA). A ≥ 4.8-point worsening of SF36-Bodily Pain score defined Pain Flares. The first documented episode of each of DAS28 and Pain Flare in each person was analysed. Subgroups within DAS28 and Pain Flares were determined using Latent Class Analysis. Clinical course was compared between flare subgroups. Results: DAS28 (45%) and Pain Flares (52%) were each common but usually discordant, with 60% of participants in DAS28 Flare not concurrently in Pain Flare, and 64% of those in Pain Flare not concurrently in DAS28 Flare. Three discrete DAS28 Flare subgroups were identified. One was characterised by increases in tender/swollen joint counts (14.4%), a second by increases in symptoms (13.1%), and a third displayed lower flare severity (72.5%). Two discrete Pain Flare subgroups were identified. One occurred following low disease activity and symptoms (88.6%), and the other occurred on the background of ongoing active disease and pain (11.4%). Despite the observed differences between DAS28 and Pain Flares, each was associated with increased disability which persisted beyond the flare episode. Conclusion: Flares are both common and heterogeneous in people with RA. Furthermore our findings indicate that for some patients there is a discordance between inflammation and pain in flare events. This discrete flare subgroups might reflect different underlying inflammation and pain mechanisms. Treatments addressing different mechanisms might be required to reduce persistent disability after DAS28 and Pain Flares.Peer reviewedFinal Published versio

Single Cell Cryo-Soft X-ray Tomography Shows That Each Chlamydia Trachomatis Inclusion Is a Unique Community of Bacteria

Chlamydiae are strict intracellular pathogens residing within a specialised membrane-bound compartment called the inclusion. Therefore, each infected cell can, be considered as a single entity where bacteria form a community within the inclusion. It remains unclear as to how the population of bacteria within the inclusion influences individual bacterium. The life cycle of Chlamydia involves transitioning between the invasive elementary bodies (EBs) and replicative reticulate bodies (RBs). We have used cryo-soft X-ray tomography to observe individual inclusions, an approach that combines 40 nm spatial resolution and large volume imaging (up to 16 µm). Using semi-automated segmentation pipeline, we considered each inclusion as an individual bacterial niche. Within each inclusion, we identifyed and classified different forms of the bacteria and confirmed the recent finding that RBs have a variety of volumes (small, large and abnormal). We demonstrate that the proportions of these different RB forms depend on the bacterial concentration in the inclusion. We conclude that each inclusion operates as an autonomous community that influences the characteristics of individual bacteria within the inclusion

Prevalence of the HOXB13 G84E prostate cancer risk allele in men treated with radical prostatectomy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106912/1/bju12522.pd

Impact of Solitary Involved Lymph Node on Outcome in Localized Cancer of the Esophagus and Esophagogastric Junction

Node-positive esophageal cancer is associated with a dismal prognosis. The impact of a solitary involved node, however, is unclear, and this study examined the implications of a solitary node compared with greater nodal involvement and node-negative disease. The clinical and pathologic details of 604 patients were entered prospectively into a database from1993 and 2005. Four pathologic groups were analyzed: node-negative, one lymph node positive, two or three lymph nodes positive, and greater than three lymph nodes positive. Three hundred and fifteen patients (52%) were node-positive and 289 were node-negative. The median survival was 26 months in the node-negative group. Patients (n = 84) who had one node positive had a median survival of 16 months (p = 0.03 vs node-negative). Eighty-four patients who had two or three nodes positive had a median survival of 11 months compared with a median survival of 8 months in the 146 patients who had greater than three nodes positive (p = 0.01). The survival of patients with one node positive [number of nodes (N) = 1] was also significantly greater than the survival of patients with 2–3 nodes positive (N = 2–3) (p = 0.049) and greater than three nodes positive (p < 0001). The presence of a solitary involved lymph node has a negative impact on survival compared with node-negative disease, but it is associated with significantly improved overall survival compared with all other nodal groups

Association between rheumatoid arthritis disease activity, progression of functional limitation and long-term risk of orthopaedic surgery : Combined analysis of two prospective cohorts supports EULAR treat to target DAS thresholds

Objectives: To examine the association between disease activity in early rheumatoid arthritis (RA), functional limitation and long-term orthopaedic episodes. Methods: Health Assessment Questionnaire (HAQ) disability scores were collected from two longitudinal early RA inception cohorts in routine care; Early Rheumatoid Arthritis Study and Early Rheumatoid Arthritis Network from 1986 to 2012. The incidence of major and intermediate orthopaedic surgical episodes over 25 years was collected from national data sets. Disease activity was categorised by mean disease activity score (DAS28) annually between years 1 and 5; remission (RDAS≤2.6), low (LDAS>2.6-3.2), low-moderate (LMDAS≥3.2-4.19), high-moderate (HMDAS 4.2-5.1) and high (HDAS>5.1). Results: Data from 2045 patients were analysed. Patients in RDAS showed no HAQ progression over 5 years, whereas there was a significant relationship between rising DAS28 category and HAQ at 1 year, and the rate of HAQ progression between years 1 and 5. During 27 986 person-years follow-up, 392 intermediate and 591 major surgeries were observed. Compared with the RDAS category, there was a significantly increased cumulative incidence of intermediate surgery in HDAS (OR 2.59 CI 1.49 to 4.52) and HMDAS (OR 1.8 CI 1.05 to 3.11) categories, and for major surgery in HDAS (OR 2.48 CI 1.5 to 4.11), HMDAS (OR 2.16 CI 1.32 to 3.52) and LMDAS (OR 2.07 CI 1.28 to 3.33) categories. There was no significant difference in HAQ progression or orthopaedic episodes between RDAS and LDAS categories. Conclusions: There is an association between disease activity and both poor function and long-term orthopaedic episodes. This illustrates the far from benign consequences of persistent moderate disease activity, and supports European League Against Rheumatism treat to target recommendations to secure low disease activity or remission in all patients.Peer reviewedFinal Published versio

Hubble Space Telescope WFC3 Early Release Science: Emission-Line Galaxies from Infrared Grism Observations

We present grism spectra of emission-line galaxies (ELGs) from 0.6-1.6 microns from the Wide Field Camera 3 on the Hubble Space Telescope. These new infrared grism data augment previous optical Advanced Camera for Surveys G800L 0.6-0.95 micron grism data in GOODS-South from the PEARS program, extending the wavelength covereage well past the G800L red cutoff. The ERS grism field was observed at a depth of 2 orbits per grism, yielding spectra of hundreds of faint objects, a subset of which are presented here. ELGs are studied via the Ha, [OIII], and [OII] emission lines detected in the redshift ranges 0.2<z<1.4, 1.2<z<2.2 and 2.0<z<3.3 respectively in the G102 (0.8-1.1 microns; R~210) and G141 (1.1-1.6 microns; R~130) grisms. The higher spectral resolution afforded by the WFC3 grisms also reveals emission lines not detectable with the G800L grism (e.g., [SII] and [SIII] lines). From these relatively shallow observations, line luminosities, star-formation rates, and grism spectroscopic redshifts are determined for a total of 48 ELGs to m(AB)~25 mag. Seventeen GOODS-South galaxies that previously only had photometric redshifts now have new grism-spectroscopic redshifts, in some cases with large corrections to the photometric redshifts (Delta(z)~0.3-0.5). Additionally, one galaxy had no previously-measured redshift but now has a secure grism-spectroscopic redshift, for a total of 18 new GOODS-South spectroscopic redshifts. The faintest source in our sample has a magnitude m(AB)=26.9 mag. The ERS grism data also reflect the expected trend of lower specific star formation rates for the highest mass galaxies in the sample as a function of redshift, consistent with downsizing and discovered previously from large surveys. These results demonstrate the remarkable efficiency and capability of the WFC3 NIR grisms for measuring galaxy properties to faint magnitudes and redshifts to z>2.Comment: Accepted for publication in AJ. Updated to include referee comments. Updated sample using improved reduction contains 23 new galaxies (Table 1; Figures 2 & 3

Eddy-resolving simulation of plankton ecosystem dynamics in the California Current System

Author Posting. © Elsevier B.V., 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part I: Oceanographic Research Papers 53 (2006): 1483-1516, doi:10.1016/j.dsr.2006.06.005.We study the dynamics of the planktonic ecosystem in the coastal upwelling zone within the California Current System using a three-dimensional, eddy-resolving circulation model coupled to an ecosystem/biogeochemistry model. The physical model is based on the Regional Oceanic Modeling System (ROMS), configured at a resolution of 15 km for a domain covering the entire U.S. West Coast, with an embedded child grid covering the central California upwelling region at a resolution of 5 km. The model is forced with monthly mean boundary conditions at the open lateral boundaries as well as at the surface. The ecological/biogeochemical model is nitrogen based, includes single classes for phytoplankton and zooplankton, and considers two detrital pools with different sinking speeds. The model also explicitly simulates a variable chlorophyll-to-carbon ratio. Comparisons of model results with either remote sensing observations (AVHRR, SeaWiFS) or in situ measurements from the CalCOFI program indicate that our model is capable of replicating many of the large-scale, time averaged features of the coastal upwelling system. An exception is the underestimation of the chlorophyll levels in the northern part of the domain, perhaps because of the lack of short-term variations in the forcing from the atmosphere. Another shortcoming is that the modeled thermocline is too diffuse, and that the upward slope of the isolines toward the coast is too small. Detailed time-series comparisons with observations from Monterey Bay reveal similar agreements and discrepancies. We attribute the good agreement between the modeled and observed ecological properties in large part to the accuracy of the physical fields. In turn, many of the discrepancies can be traced back to our use of monthly mean forcing. Analysis of the ecosystem structure and dynamics reveal that the magnitude and pattern of phytoplankton biomass in the nearshore region are determined largely by the balance of growth and zooplankton grazing, while in the offshore region, growth is balanced by mortality. The latter appears to be inconsistent with in situ observations and is a result of our consideration of only one zooplankton size class (mesozooplankton), neglecting the importance of microzooplankton grazing in the offshore region. A comparison of the allocation of nitrogen into the different pools of the ecosystem in the 3-D results with those obtained from a box model configuration of the same ecosystem model reveals that only a few components of the ecosystem reach a local steady-state, i.e. where biological sources and sinks balance each other. The balances for the majority of the components are achieved by local biological source and sink terms balancing the net physical divergence, confirming the importance of the 3-D nature of circulation and mixing in a coastal upwelling system.Most of this work has been made possible by two grants from NASA. Additional support is acknowledged from NSF’s ITR program