Asymptotic posterior normality of the generalized extreme value distribution

The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analysing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed theoretical investigation, which has thus far been underdeveloped. Even the most basic asymptotic results are difficult to obtain because the GEV fails to satisfy standard regularity conditions. Here, we prove that the posterior distribution of the GEV parameter vector, given an independent and identically distributed sequence of observations, converges to a normal distribution centred at the true parameter. The proof necessitates analysing integrals of the GEV likelihood function over the entire parameter space, which requires considerable care because the support of the GEV density depends on the parameters in complicated ways

The Redox Couple of the Cytochrome \u3cem\u3ec\u3c/em\u3e Cyanide Complex: The Contribution of Heme Iron Ligation to the Structural Stability, Chemical Reactivity, and Physiological Behavior of Horse Cytochrome \u3cem\u3ec\u3c/em\u3e

Contrary to most heme proteins, ferrous cytochrome c does not bind ligands such as cyanide and CO. In order to quantify this observation, the redox potential of the ferric/ferrous cytochrome c–cyanide redox couple was determined for the first time by cyclic voltammetry. Its E0′ was −240 mV versus SHE, equivalent to −23.2 kJ/mol. The entropy of reaction for the reduction of the cyanide complex was also determined. From a thermodynamic cycle that included this new value for the cyt c cyanide complex E0′, the binding constant of cyanide to the reduced protein was estimated to be 4.7 × 10−3 LM−1 or 13.4 kJ/mol (3.2 kcal/mol), which is 48.1 kJ/mol (11.5 kcal/mol) less favorable than the binding of cyanide to ferricytochrome c. For coordination of cyanide to ferrocytochrome c, the entropy change was earlier experimentally evaluated as 92.4 Jmol−1K−1 (22.1 e.u.) at 25 K, and the enthalpy change for the same net reaction was calculated to be 41.0 kJ/mol (9.8 kcal/mol). By taking these results into account, it was discovered that the major obstacle to cyanide coordination to ferrocytochrome c is enthalpic, due to the greater compactness of the reduced molecule or, alternatively, to a lower rate of conformational fluctuation caused by solvation, electrostatic, and structural factors. The biophysical consequences of the large difference in the stabilities of the closed crevice structures are discussed

A mean-field games laboratory for generative modeling

In this paper, we demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. There is a pervasive sense in the generative modeling community that the various flow and diffusion-based generative models have some common foundational structure and interrelationships. We establish connections between MFGs and major classes of flow and diffusion-based generative models including continuous-time normalizing flows, score-based models, and Wasserstein gradient flows. We derive these three classes of generative models through different choices of particle dynamics and cost functions. Furthermore, we study the mathematical structure and properties of each generative model by studying their associated MFG's optimality condition, which is a set of coupled forward-backward nonlinear partial differential equations (PDEs). The theory of MFGs, therefore, enables the study of generative models through the theory of nonlinear PDEs. Through this perspective, we investigate the well-posedness and structure of normalizing flows, unravel the mathematical structure of score-based generative modeling, and derive a mean-field game formulation of the Wasserstein gradient flow. From an algorithmic perspective, the optimality conditions of MFGs also allow us to introduce HJB regularizers for enhanced training of a broad class of generative models. In particular, we propose and demonstrate an Hamilton-Jacobi-Bellman regularized SGM with improved performance over standard SGMs. We present this framework as an MFG laboratory which serves as a platform for revealing new avenues of experimentation and invention of generative models. This laboratory will give rise to a multitude of well-posed generative modeling formulations and will provide a consistent theoretical framework upon which numerical and algorithmic tools may be developed.Comment: 38 pages, 10 figures. Version 4 includes derivation of the score probability flo

Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase

Ultrafast two-dimensional spectroscopy utilizes correlated multiple light-matter interactions for retrieving dynamic features that may otherwise be hidden under the linear spectrum. Its extension to the terahertz regime of the electromagnetic spectrum, where a rich variety of material degrees of freedom reside, remains an experimental challenge. Here we report ultrafast two-dimensional terahertz spectroscopy of gas-phase molecular rotors at room temperature. Using time-delayed terahertz pulse pairs, we observe photon echoes and other nonlinear signals resulting from molecular dipole orientation induced by three terahertz field-dipole interactions. The nonlinear time-domain orientation signals are mapped into the frequency domain in two-dimensional rotational spectra which reveal J-state-resolved nonlinear rotational dynamics. The approach enables direct observation of correlated rotational transitions and may reveal rotational coupling and relaxation pathways in the ground electronic and vibrational state.Comment: 31 pages, 14 figure

Development of a dynamic external CFD and BES coupling framework for application of urban neighbourhoods energy modelling

© 2018 Elsevier Ltd Current building energy models are weak at representing the interactions between neighbourhoods of buildings in cities. The effect of a neighbourhood on the local microclimate is complex, varying from one building to another, meaning that neighbourhood effects on the airflow around a particular building. A failure to account for this may lead to the miss-calculation of heat transfer and energy demand. Current building energy simulation (BES) tools apply convective heat transfer coefficient (CHTC) correlations, which were developed by using a simplified model of wind flow that neglects neighbourhood effects. Computational Fluid Dynamics (CFD) techniques are able to model these neighbourhood effects and can be used to improve CHTC correlations. This work aims to develop a framework that couples CFD and BES tools to enhance the modelling of outdoor convective heat transfer in different urban neighbourhoods. A dynamic external coupling method was used to combine the benefits from both domains. Firstly, a microclimate CFD model was validated before the coupling stage using wind tunnel data. Secondly, the framework was tested using a benchmark model of a building block. Fully converged values of the surface temperature and CHTC were achieved at each time-step by the BES and CFD domains. The results highlight the importance of neighbourhood effect while the prediction of the hourly averaged external convection using coupling method can amend the simulation by up to 64% comparing to the standalone conventional BES models with DOE-2 CHTC approach

Do Outcomes of Arthroscopic Subscapularis Tendon Repairs Depend on Rotator Cuff Fatty Infiltration?

Background:Rotator cuff fatty infiltration has been correlated with poorer radiographic and clinical outcomes in supraspinatus and infraspinatus tendon repairs, but this has not been well-studied in subscapularis tendon repairs. Purpose:To evaluate the influence of preoperative rotator cuff fatty infiltration on postoperative outcomes for patients undergoing arthroscopic subscapularis tendon repair. Study Design:Cohort study; Level of evidence, 3. Methods:Patients who underwent arthroscopic subscapularis repair between 2010 and 2016 were retrospectively identified, and demographic data and surgical findings were recorded. The extent of fatty infiltration was determined on preoperative magnetic resonance imaging by the Fuchs modification of the Goutallier classification. At the most recent follow-up, patients completed the Patient-Reported Outcomes Measurement Information System for Upper Extremity (PROMIS-UE) computer adaptive test and a postoperative visual analog scale for pain. The distribution of fatty infiltration was compared between patients undergoing subscapularis tendon repair versus subscapularis tendon repair combined with a posterior cuff repair. Outcomes were compared for patients using Goutallier grade 0-1 versus grade ≥2 changes in each rotator cuff muscle. Multivariate linear regression analysis was performed to evaluate the influence of muscle quality, as well as demographic factors, on PROMIS-UE scores. Significance was defined as P < .05. Results:There were 140 shoulders included (mean age, 61.8 years; 42.1% female; mean follow-up, 51.7 months). The prevalence of Goutallier grade 2 changes or higher was significantly greater in patients with multitendon repair relative to isolated subscapularis tendon repair. For the overall group of all patients undergoing subscapularis tendon repair, whether in isolation or as part of a multitendon repair, PROMIS-UE scores were significantly lower for patients with infraspinatus muscle grade 2 or higher Goutallier changes relative to grade 0 or 1. After adjustment for age, body mass index, patient sex, and fatty infiltration in other rotator cuff muscles, poor infraspinatus muscle quality remained the only significant predictor for lower PROMIS-UE scores. Conclusion:Patients undergoing arthroscopic subscapularis tendon repair with poor infraspinatus muscle quality had worse patient-reported outcomes. This was true whether subscapularis tendon repair was isolated or was performed in conjunction with supraspinatus and infraspinatus tendon repairs

Shear thickening in densely packed suspensions of spheres and rods confined to few layers

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.Comment: 21 pages, 14 figures. submitted to the Journal of Rheolog

Structure and dynamics of the E. coli chemotaxis core signaling complex by cryo-electron tomography and molecular simulations

To enable the processing of chemical gradients, chemotactic bacteria possess large arrays of transmembrane chemoreceptors, the histidine kinase CheA, and the adaptor protein CheW, organized as coupled core-signaling units (CSU). Despite decades of study, important questions surrounding the molecular mechanisms of sensory signal transduction remain unresolved, owing especially to the lack of a high-resolution CSU structure. Here, we use cryo-electron tomography and sub-tomogram averaging to determine a structure of the Escherichia coli CSU at sub-nanometer resolution. Based on our experimental data, we use molecular simulations to construct an atomistic model of the CSU, enabling a detailed characterization of CheA conformational dynamics in its native structural context. We identify multiple, distinct conformations of the critical P4 domain as well as asymmetries in the localization of the P3 bundle, offering several novel insights into the CheA signaling mechanism

Impacts of large-scale Sahara solar farms on global climate and vegetation cover

Large‐scale photovoltaic solar farms envisioned over the Sahara Desert can meet the world's energy demand while increasing regional rainfall and vegetation cover. However, adverse remote effects resulting from atmospheric teleconnections could offset such regional benefits. We use state‐of‐the‐art Earth system model simulations to evaluate the global impacts of Sahara solar farms. Our results indicate a redistribution of precipitation causing Amazon droughts and forest degradation, and global surface temperature rise and sea‐ice loss, particularly over the Arctic due to increased polarward heat transport, and northward expansion of deciduous forests in the Northern Hemisphere. We also identify reduced El Niño‐Southern Oscillation and Atlantic Niño variability and enhanced tropical cyclone activity. Comparison to proxy inferences for a wetter and greener Sahara ∼6,000 years ago appear to substantiate these results. Understanding these responses within the Earth system provides insights into the site selection concerning any massive deployment of solar energy in the world's deserts

Altered brain energetics induces mitochondrial fission arrest in Alzheimer's Disease.

Altered brain metabolism is associated with progression of Alzheimer's Disease (AD). Mitochondria respond to bioenergetic changes by continuous fission and fusion. To account for three dimensional architecture of the brain tissue and organelles, we applied 3-dimensional electron microscopy (3D EM) reconstruction to visualize mitochondrial structure in the brain tissue from patients and mouse models of AD. We identified a previously unknown mitochondrial fission arrest phenotype that results in elongated interconnected organelles, "mitochondria-on-a-string" (MOAS). Our data suggest that MOAS formation may occur at the final stages of fission process and was not associated with altered translocation of activated dynamin related protein 1 (Drp1) to mitochondria but with reduced GTPase activity. Since MOAS formation was also observed in the brain tissue of wild-type mice in response to hypoxia or during chronological aging, fission arrest may represent fundamental compensatory adaptation to bioenergetic stress providing protection against mitophagy that may preserve residual mitochondrial function. The discovery of novel mitochondrial phenotype that occurs in the brain tissue in response to energetic stress accurately detected only using 3D EM reconstruction argues for a major role of mitochondrial dynamics in regulating neuronal survival