A renormalization fixed point for Lorenz maps

A Lorenz map is a Poincar\'e map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a hyperbolic fixed point. The proof is computer assisted and we include a detailed exposition on how to make rigorous estimates using a computer as well as the implementation of the estimates.Comment: 29 pages, 2 figure

Raman spectroscopy reveals new insights into the zonal organization of native and tissue-engineered articular cartilage

Tissue architecture is intimately linked with its functions, and loss of tissue organization is often associated with pathologies. The intricate depth-dependent extracellular matrix (ECM) arrangement in articular cartilage is critical to its biomechanical functions. In this study, we developed a Raman spectroscopic imaging approach to gain new insight into the depth-dependent arrangement of native and tissue-engineered articular cartilage using bovine tissues and cells. Our results revealed previously unreported tissue complexity into at least six zones above the tidemark based on a principal component analysis and k-means clustering analysis of the distribution and orientation of the main ECM components. Correlation of nanoindentation and Raman spectroscopic data suggested that the biomechanics across the tissue depth are influenced by ECM microstructure rather than composition. Further, Raman spectroscopy together with multivariate analysis revealed changes in the collagen, glycosaminoglycan and water distributions in tissue-engineered constructs over time. These changes were assessed using simple metrics that promise to instruct efforts towards the regeneration of a broad range of tissues with native zonal complexity and functional performance

Impacts of Atmospheric Nitrogen Deposition on Surface Waters of the Western North Atlantic Mitigated by Multiple Feedbacks

The impacts of atmospheric nitrogen deposition (AND) on the chlorophyll and nitrogen dynamics of surface waters in the western North Atlantic (25 degrees N-45 degrees N, 65 degrees W-80 degrees W) are examined with a biogeochemical ocean model forced with a regional atmospheric chemistry model (Community Multiscale Air Quality, CMAQ). CMAQ simulations with year-specific emissions reveal the existence of a hot spot of AND over the Gulf Stream. The impact of the hot spot on the oceanic biogeochemistry is mitigated in three ways by physical and biogeochemical processes. First, AND significantly contributes to surface oceanic nitrogen concentrations only during the summer period, when the stratification is maximal and the background nitrogen inventories are minimal. Second, the increase in summer surface nitrate concentrations is accompanied by a reduction in upward nitrate diffusion at the base of the surface layer. This negative feedback partly cancels the nitrogen enrichment from AND. Third, gains in biomass near the surface force a shoaling of the euphotic layer and a reduction of about 5% in deep primary production and biomass on the continental shelf. Despite these mitigating processes, the impacts of AND remain substantial. AND increases surface nitrate concentrations in the Gulf Stream region by 14% during the summer (2% on average over the year). New primary production increases by 22% in this region during summer (8% on average). Although these changes may be difficult to distinguish from natural variability in observations, the results support the view that AND significantly enhances local carbon export

Bioenergetic-active materials enhance tissue regeneration by modulating cellular metabolic state

Cellular bioenergetics (CBE) plays a critical role in tissue regeneration. Physiologically, an enhanced metabolic state facilitates anabolic biosynthesis and mitosis to accelerate regeneration. However, the development of approaches to reprogram CBE, towards the treatment of substantial tissue injuries, hasbeen limited thus far. Here, we show that induced repair in a rabbit model of weight-bearing bone defects is greatly enhanced using a bioenergetic-active material (BAM) scaffold, compared to commercialized poly (lactic acid) and calcium phosphate ceramic scaffolds. This material was composed of energy-active units that can be released in a sustained degradation-mediated fashion once implanted. By establishing an intramitochondrial metabolic bypass, the internalized energy-active units significantly elevatemitochondria membrane potential (ΔΨm) to supply increased bioenergetic levels and accelerate bone formation. The ready-to-use material developed here represents a highly efficient and easy-to-implement therapeutic approach toward tissue regeneration, withpromise for bench-to-bedside translation

Mixed methods, materialism and the micropolitics of the research-assemblage

We assess the potential for mixing social research methods, based upon a materialist and micropolitical analysis of the research-assemblage and of what individual research techniques and methods do in practice. Applying a DeleuzoGuattarian toolkit of assemblages, affects and capacities, we document what happens when research methods and techniques interact with the events they wish to study. Micropolitically, many of these techniques and methods have unintended effects of specifying and aggregating events, with the consequently that the knowledge produced by social inquiry is invested with these specifications and aggregations. We argue that rather than abandoning these social research tools, we may use the micropolitical analysis to assess precisely how each method affects knowledge production, and engineer the research designs we use accordingly. This forms the justification for mixing methods that are highly aggregative or specifying with those that are less so, effectively rehabilitating methods that have often been rejected by social researchers, including surveys and experiments

Challenges in Quantifying Air‐Water Carbon Dioxide Flux Using Estuarine Water Quality Data: Case Study for Chesapeake Bay

Estuaries play an uncertain but potentially important role in the global carbon cycle via CO2 outgassing. The uncertainty mainly stems from the paucity of studies that document the full spatial and temporal variability of estuarine surface water partial pressure of carbon dioxide ( p CO2). Here, we explore the potential of utilizing the abundance of pH data from historical water quality monitoring programs to fill the data void via a case study of the mainstem Chesapeake Bay (eastern United States). We calculate p CO2 and the air‐water CO2 flux at monthly resolution from 1998 to 2018 from tidal fresh to polyhaline waters, paying special attention to the error estimation. The biggest error is due to the pH measurement error, and errors due to the gas transfer velocity, temporal sampling, the alkalinity mixing model, and the organic alkalinity estimation are 72%, 27%, 15%, and 5%, respectively, of the error due to pH. Seasonal, interannual, and spatial variability in the air‐water flux and surface p CO2 is high, and a correlation analysis with oxygen reveals that this variability is driven largely by biological processes. Averaged over 1998–2018, the mainstem bay is a weak net source of CO2 to the atmosphere of 1.2 (1.1, 1.4) mol m−2 yr−1 (best estimate and 95% confidence interval). Our findings suggest that the abundance of historical pH measurements in estuaries around the globe should be mined in order to constrain the large spatial and temporal variability of the CO2 exchange between estuaries and the atmosphere

Economic Evaluation of Lupus Nephritis in the Systemic Lupus International Collaborating Clinics Inception Cohort Using a Multistate Model Approach.

OBJECTIVE: Little is known about the long-term costs of lupus nephritis (LN). The costs were compared between patients with and without LN using multistate modeling. METHODS: Patients from 32 centers in 11 countries were enrolled in the Systemic Lupus International Collaborating Clinics inception cohort within 15 months of diagnosis and provided annual data on renal function, hospitalizations, medications, dialysis, and selected procedures. LN was diagnosed by renal biopsy or the American College of Rheumatology classification criteria. Renal function was assessed annually using the estimated glomerular filtration rate (GFR) or estimated proteinuria. A multistate model was used to predict 10-year cumulative costs by multiplying annual costs associated with each renal state by the expected state duration. RESULTS: A total of 1,545 patients participated; 89.3% were women, the mean ± age at diagnosis was 35.2 ± 13.4 years, 49% were white, and the mean followup duration was 6.3 ± 3.3 years. LN developed in 39.4% of these patients by the end of followup. Ten-year cumulative costs were greater in those with LN and an estimated glomerular filtration rate (GFR)/minute ($310,579 2015 Canadian dollars versus$19,987 if no LN and estimated GFR \u3e60 ml/minute) or with LN and estimated proteinuria \u3e3 gm/day ($84,040 versus$20,499 if no LN and estimated proteinuria CONCLUSION: Patients with estimated GFR/minute incurred 10-year costs 15-fold higher than those with normal estimated GFR. By estimating the expected duration in each renal state and incorporating associated annual costs, disease severity at presentation can be used to anticipate future health care costs. This is critical knowledge for cost-effectiveness evaluations of novel therapies