Form discrete- to continuous-time ergodic theorems

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results of interest

Moving up and down in the generic multiverse

We give a brief account of the modal logic of the generic multiverse, which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a ground model of". The fragment of the first relation is called the modal logic of forcing and was studied by us in earlier work. The fragment of the second relation is called the modal logic of grounds and will be studied here for the first time. In addition, we discuss which combinations of modal logics are possible for the two fragments.Comment: 10 pages. Extended abstract. Questions and commentary concerning this article can be made at http://jdh.hamkins.org/up-and-down-in-the-generic-multiverse

Long-Term Follow-Up of Patients Immunized with AN1792: Reduced Functional Decline in Antibody Responders

BACKGROUND: Immunization of patients with Alzheimer's disease (AD) with synthetic amyloid-beta peptide (Abeta(42)) (AN1792) was previously studied in a randomized, double-blind, placebo-controlled phase 2a clinical trial, Study AN1792(QS-21)-201. Treatment was discontinued following reports of encephalitis. One year follow-up revealed that AN1792 antibody responders showed improvements in cognitive measures as assessed by the neuropsychological test battery (NTB) and a decrease in brain volume compared with placebo. METHODS: A follow-up study, Study AN1792(QS-21)-251, was conducted to assess the long-term functional, psychometric, neuroimaging, and safety outcomes of patients from the phase 2a study 4.6 years after immunization with AN1792. The results were analyzed by comparing patients originally identified as antibody responders in the AN1792 phase 2a study with placebo-treated patients. RESULTS: One hundred and fifty-nine patients/caregivers (30 placebo; 129 AN1792) participated in this follow-up study. Of the 129 AN1792-treated patients, 25 were classified in the phase 2a study as antibody responders (anti-AN1792 titers > or = 1:2,200 at any time after the first injection). Low but detectable, sustained anti-AN1792 titers were found in 17 of 19 samples obtained from patients classified as antibody responders in the phase 2a study. No detectable anti-AN1792 antibodies were found in patients not classified as antibody responders in the phase 2a study. Significantly less decline was observed on the Disability Assessment for Dementia scale among antibody responders than placebo-treated patients (p=0.015) after 4.6 years. Significant differences in favor of responders were also observed on the Dependence Scale (p=0.033). Of the small number of patients who underwent a follow-up MRI, antibody responders showed similar brain volume loss during the follow-up period subsequent to the AN1792 phase 2a study compared with placebo-treated patients. CONCLUSIONS: Approximately 4.6 years after immunization with AN1792, patients defined as responders in the phase 2a study maintained low but detectable, sustained anti-AN1792 antibody titers and demonstrated significantly reduced functional decline compared with placebo-treated patients. Brain volume loss in antibody responders was not significantly different from placebo-treated patients approximately 3.6 years from the end of the original study. No further cases of encephalitis were noted. These data support the hypothesis that Abeta immunotherapy may have long-term functional benefits

Northern Hemisphere permafrost map based on TTOP modelling for 2000-2016 at 1 km²scale

Permafrost is a key element of the cryosphere and an essential climate variable in the Global Climate Observing System. There is no remote-sensing method available to reliably monitor the permafrost thermal state. To estimate permafrost distribution at a hemispheric scale, we employ an equilibrium state model for the temperature at the top of the permafrost (TTOP model) for the 2000–2016 period, driven by remotely-sensed land surface temperatures, down-scaled ERA-Interim climate reanalysis data, tundra wetness classes and landcover map from the ESA Landcover Climate Change Initiative (CCI) project. Subgrid variability of ground temperatures due to snow and landcover variability is represented in the model using subpixel statistics. The results are validated against borehole measurements and reviewed regionally. The accuracy of the modelled mean annual ground temperature (MAGT) at the top of the permafrost is ±2 °C when compared to permafrost borehole data. The modelled permafrost area (MAGT 0) is around 21 × 106 km2 (22% of exposed land area), which is approximately 2 × 106 km2 less than estimated previously. Detailed comparisons at a regional scale show that the model performs well in sparsely vegetated tundra regions and mountains, but is less accurate in densely vegetated boreal spruce and larch forests

Linear forms and quadratic uniformity for functions on ZN\mathbb{Z}_N

A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that quasirandomness can often be measured by means of certain easily described norms, known as uniformity norms. However, determining which uniformity norms work for which structures turns out to be a surprisingly hard question. In [GW09a] and [GW09b, GW09c] we gave a complete answer to this question for groups of the form $G=\mathbb{F}_p^n$, provided $p$ is not too small. In $\mathbb{Z}_N$, substantial extra difficulties arise, of which the most important is that an "inverse theorem" even for the uniformity norm $\|.\|_{U^3}$ requires a more sophisticated (local) formulation. When $N$ is prime, $\mathbb{Z}_N$ is not rich in subgroups, so one must use regular Bohr neighbourhoods instead. In this paper, we prove the first non-trivial case of the main conjecture from [GW09a].Comment: 66 page

Inter- and intraobserver reliability of the MTM-classification for proximal humeral fractures: A prospective study

<p>Abstract</p> <p>Background</p> <p>A precise modular topographic-morphological (MTM) classification for proximal humeral fractures may address current classification problems. The classification was developed to evaluate whether a very detailed classification exceeding the analysis of fractured parts may be a valuable tool.</p> <p>Methods</p> <p>Three observers classified plain radiographs of 22 fractures using both a simple version (fracture displacement, number of parts) and an extensive version (individual topographic fracture type and morphology) of the MTM classification. Kappa-statistics were used to determine reliability.</p> <p>Results</p> <p>An acceptable reliability was found for the simple version classifying fracture displacement and fractured main parts. Fair interobserver agreement was found for the extensive version with individual topographic fracture type and morphology.</p> <p>Conclusion</p> <p>Although the MTM-classification covers a wide spectrum of fracture types, our results indicate that the precise topographic and morphological description is not delivering reproducible results. Therefore, simplicity in fracture classification may be more useful than extensive approaches, which are not adequately reliable to address current classification problems.</p

Northern Hemisphere permafrost map based on TTOP modelling for 2000–2016 at 1 km2 scale

Permafrost is a key element of the cryosphere and an essential climate variable in the Global Climate Observing System. There is no remote-sensing method available to reliably monitor the permafrost thermal state. To estimate permafrost distribution at a hemispheric scale, we employ an equilibrium state model for the temperature at the top of the permafrost (TTOP model) for the 2000–2016 period, driven by remotely- sensed land surface temperatures, down-scaled ERA-Interim climate reanalysis data, tundra wetness classes and landcover map from the ESA Landcover Climate Change Initiative (CCI) project. Subgrid variability of ground temperatures due to snow and landcover variability is represented in the model using subpixel statistics. The results are validated against borehole measurements and reviewed regionally. The accuracy of the modelled mean annual ground temperature (MAGT) at the top of the permafrost is ±2 °C when compared to permafrost borehole data. The modelled permafrost area (MAGT 0) is around 21 × 106 km2 (22% of exposed land area), which is approximately 2 × 106 km2 less than estimated previously. Detailed comparisons at a regional scale show that the model performs well in sparsely vegetated tundra regions and mountains, but is less accurate in densely vegetated boreal spruce and larch forests

The rice NLR pair Pikp-1/Pikp-2 initiates cell death through receptor cooperation rather than negative regulation

Plant NLR immune receptors are multidomain proteins that can function as specialized sensor/helper pairs. Paired NLR immune receptors are generally thought to function via negative regulation, where one NLR represses the activity of the second and detection of pathogen effectors relieves this repression to initiate immunity. However, whether this mechanism is common to all NLR pairs is not known. Here, we show that the rice NLR pair Pikp-1/Pikp-2, which confers resistance to strains of the blast pathogen Magnaporthe oryzae (syn. Pyricularia oryzae) expressing the AVR-PikD effector, functions via receptor cooperation, with effector-triggered activation requiring both NLRs to trigger the immune response. To investigate the mechanism of Pikp-1/Pikp-2 activation, we expressed truncated variants of these proteins, and made mutations in previously identified NLR sequence motifs. We found that any domain truncation, in either Pikp-1 or Pikp-2, prevented cell death in the presence of AVR-PikD, revealing that all domains are required for activity. Further, expression of individual Pikp-1 or Pikp-2 domains did not result in cell death. Mutations in the conserved P-loop and MHD sequence motifs in both Pikp-1 and Pikp-2 prevented cell death activation, demonstrating that these motifs are required for the function of the two partner NLRs. Finally, we showed that Pikp-1 and Pikp-2 associate to form homo- and hetero-complexes in planta in the absence of AVR-PikD; on co-expression the effector binds to Pikp-1 generating a tri-partite complex. Taken together, we provide evidence that Pikp-1 and Pikp-2 form a fine-tuned system that is activated by AVR-PikD via receptor cooperation rather than negative regulation