Incompleteness and jump hierarchies Lutz, Patrick; Walsh, James
Proceedings of the American Mathematical Society,
November 1, 2020, 2020-11-00, Letnik:
148, Številka:
11
Journal Article
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This paper is an investigation of the relationship between Gödel's second incompleteness theorem and the well-foundedness of jump hierarchies. It follows from a classic theorem of Spector 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 Gödel'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 )th admissible ordinal. It follows, assuming suitable large cardinal hypotheses, that, on a cone, the rank of X is \omega _1^X.
We correct an error in the statement of a theorem in our paper ``Incompleteness and jump hierarchies'' Proc. Amer. Math. Soc. 148 (2020), pp. 4997-5006.
Polymers that depolymerize back to monomers can be repeatedly chemically recycled, thereby reducing their environmental impact. Polyphthalaldehyde is a metastable polymer that can rapidly and ...quantitatively depolymerize due to its low ceiling temperature. However, the effect of substitution on the physical and chemical properties of polyphthalaldehyde derivatives has not been systematically studied. Herein, we investigate the cationic polymerization of seven o-phthalaldehyde derivatives and demonstrate that judicious choice of substituent results in materials with a wide range of ceiling temperatures (<−60 to 106 °C) and decomposition temperatures (109–196 °C). We anticipate that these new polymers and their derivatives will enable researchers to access degradable materials with tunable thermal, physical, and chemical properties.
Allogeneic stem cell transplantation remains the only curative treatment for sickle cell anemia (SCA), but the place of myeloablative conditioning in the procedure remains to be defined. The aim of ...the present study was to analyze long-term outcomes, including chimerism, SCA-related events and biological data (hemoglobin, reticulocytes, HbS%), and fertility in a French series of 234 SCA patients under 30 years of age who, from 1988 to 2012, received a matched-sibling-donor stem cell transplantation following standardized myeloablative conditioning busulfan, cyclophosphamide and rabbit antithymocyte globulin (ATG). Since the first report of the series (1988-2004), 151 new consecutive patients with SCA have been similarly transplanted. Considering death, non-engraftment or rejection (donor cells <5%) as events, the 5-year event-free survival was 97.9% (95% confidence interval: 95.5-100%), confirming, since the year 2000, an at least 95% chance of cure. In the overall cohort (n=234, median follow up 7.9 years), event-free survival was not associated with age, but chronic-graft-
-host disease (cGvHD) was independently associated with recipient's age >15 years (hazard ratio=4.37;
=0.002) and lower (5-15
20 mg/kg) ATG dose (hazard ratio=4.55;
=0.001). At one year, 44% of patients had mixed chimerism (5-95% donor cells), but those prepared with ATG had no graft rejection. No events related to SCA occurred in patients with mixed chimerism, even those with 15-20% donor cells, but hemolytic anemia stigmata were observed with donor cells <50%. Myeloablative transplantation with matched-sibling donor currently has a higher event-free survival (98%) in patients under 30 years of age than that reported for non-myeloablative conditioning (88%). Nevertheless, the risk of cGvHD in older patients and the need to preserve fertility might be indications for a non-myeloablative conditioning.
Blood Brain Barrier (BBB) breakdown is a secondary form of brain injury which has yet to be fully elucidated mechanistically. Existing research suggests that breakdown of tight junction proteins ...between endothelial cells is a primary driver of increased BBB permeability following injury, and intercellular signaling between primary cells of the neurovascular unit: endothelial cells, astrocytes, and pericytes; contribute to tight junction restoration. To expound upon this body of research, we analyzed the effects of severely injured patient plasma on each of the cell types in monoculture and together in a triculture model for the transcriptional and translational expression of the tight junction proteins Claudins 3 and 5, (CLDN3, CLDN5) and Zona Occludens 1 (ZO-1). Conditioned media transfer studies were performed to illuminate the cell type responsible for differential tight junction expression. Our data show that incubation with 5% human ex vivo severely injured patient plasma is sufficient to produce a differential response in endothelial cell tight junction mRNA and protein expression. Endothelial cells in monoculture produced a significant increase of CLDN3 and CLDN5 mRNA expression, (3.98 and 3.51 fold increase vs. control respectively, p<0.01) and CLDN5 protein expression, (2.58 fold change vs. control, p<0.01), whereas in triculture, this increase was attenuated. Our triculture model and conditioned media experiments suggest that conditioned media from astrocytes and pericytes and a triculture of astrocytes, pericytes and endothelial cells are sufficient in attenuating the transcriptional increases of tight junction proteins CLDN3 and CLDN5 observed in endothelial monocultures following incubation with severely injured trauma plasma. This data suggests that inhibitory molecular signals from astrocytes and pericytes contributes to prolonged BBB breakdown following injury via tight junction transcriptional and translational downregulation of CLDN5.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The synthesis, processing, and galvanic exchange of three heterostructured nanoparticle systems is described. The surface accessibility and redox potential of a Au/Pd-Ag dumbbell nanoparticle, where ...a Au/Pd core/shell region, and a silver region make up the domains, was used to prepare the new nanostructures with controlled composition, morphology, and microstructure. Results indicate that the silver domain was particularly susceptible to galvanic displacement, and was exchanged to Au/Pd-M (M = Au, Pd, Pt). Interestingly, the dumbbell morphology remained after exchange, and the silver region was transformed to hollow, parachute, or concentric domains respectively. The morphology and microstructure change was visualized via TEM and HRTEM, and the composition changes were probed via STEM-EDS imaging and XPS. The electrocatalytic activity of the Au/Pd-M towards methanol oxidation was studied, with results indicating that the Au/Pd-Pt nanoparticles had high activity attributed to the porous nature of the platinum domains.
Rhodium-catalyzed intramolecular carboacylation of alkenes, achieved using quinolinyl ketones containing tethered alkenes, proceeds via the activation and functionalization of a carbon–carbon single ...bond. This transformation has been demonstrated using RhCl(PPh3)3 and Rh(C2H4)2Cl2 catalysts. Mechanistic investigations of these systems, including determination of the rate law and kinetic isotope effects, were utilized to identify a change in mechanism with substrate. With each catalyst, the transformation occurs via rate-limiting carbon–carbon bond activation for species with minimal alkene substitution, but alkene insertion becomes rate-limiting for more sterically encumbered substrates. Hammett studies and analysis of a series of substituted analogues provide additional insight into the nature of these turnover-limiting elementary steps of catalysis and the relative energies of the carbon–carbon bond activation and alkene insertion steps.
To evaluate the efficacy of vinblastine for relapsed/refractory anaplastic large-cell lymphoma (ALCL).
Data were reviewed on all 36 patients included prospectively in the French database for ...pediatric ALCL who were treated with vinblastine (6 mg/m(2)/wk) for resistant primary disease (one), a first relapse (15), or subsequent relapses (20). Fifteen patients had undergone hematopoietic stem-cell transplantation (HSCT) for a previous relapse.
Six patients were not evaluable for response, 25 (83%) of 30 evaluable patients achieved a complete remission (CR), and five experienced progressive disease. Among the 31 patients who achieved a CR with vinblastine or before its initiation, six patients were treated with HSCT and 25 with vinblastine alone (median duration, 14 months). Overall, nine of 25 patients treated with vinblastine alone have remained in CR (median, 7 years since the end of treatment), and 16 patients have relapsed. Vinblastine was still efficient for subsequent relapses. With a median follow-up of 9.2 years, 12 patients have died (four as a result of toxicity after HSCT and eight as a result of disease), and 24 patients are alive (15 following treatment with single-agent vinblastine for the last event). Five-year overall survival is 65% (95% CI, 48% to 79%), and 5-year event-free survival is 30% (95% CI, 17% to 47%).
Vinblastine is highly efficient in relapsed ALCL and may produce durable remissions. The optimal treatment duration still has to be assessed. These results should be borne in mind when designing future phase II studies with the targeted therapies directed against anaplastic lymphoma kinase.
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