Step Function Model Research Articles

An exact solution for the magnetic diffusion problem with a step-function resistivity model

An exact solution for the magnetic diffusion problem with a step-function resistivity model

Page curves and entanglement islands for the step-function Vaidya model of evaporating black holes

It was proposed recently that the fine-grained entropy of the Hawking radiation can be expressed by the semiclassical island formula, which reproduces the unitary Page curve. In this paper, we choose the “in” vacuum state and apply the quantum extremal surface construction to study the Page curve for the step-function Vaidya model of evaporating black holes in four dimensions, which is produced by the spherical null shells. Metrics of the three regions of this spacetimes are obtained. In addition, the entanglement islands for the step-function Vaidya model of evaporating black holes at very late times are studied. When cutoff surface A is located in Minkowski region III with uA< uH at very late times, we find that the location of the boundary of island ∂I depends on the value of 8M − vA + vI. Specifically, ∂I is inside, at or outside the horizon when 8M − vA + vI is less than, equal to or larger than zero respectively. Moreover, when cutoff surface A is located in Minkowski region III with uA> uH after the black hole evaporates completely, we find that entanglement island still exists and ∂I is located on an equal-time Cauchy surface of the observer A when {r}_{(A)}^2 ≥ 64GNκc.

Time to onset of cardiovascular and cerebrovascular outcomes after hypertensive disorders of pregnancy: a nationwide, population-based retrospective cohort study

The increased maternal cardiocerebrovascular risk after a pregnancy complicated by hypertensive disorders of pregnancy, is well documented in the literature. Recent evidence has suggested a shorter timeframe for the development of these postnatal outcomes, which could have major clinical implications. This study aimed to determine the risk of and time to onset of maternal cardiovascular and cerebrovascular outcomes after a pregnancy complicated by hypertensive disorders of pregnancy. This study included 2,227,711 women, without preexisting chronic hypertension, who delivered during the period 2008 to 2010: 37,043 (1.66%) were diagnosed with preeclampsia, 34,220 (1.54%) were diagnosed with gestational hypertension, and 2,156,448 had normotensive pregnancies. Hospitalizations for chronic hypertension, heart failure, coronary heart disease, cerebrovascular disease, and peripheral arterial disease were studied. A classical Cox regression was performed to estimate the average effect of hypertensive disorders of pregnancy over 10 years compared with normotensive pregnancy; moreover, an extended Cox regression was performed with a step function model to estimate the effect of the exposure variable in different time intervals: <1, 1 to 3, 3 to 5, and 5 to 10 years of follow-up. The risk of chronic hypertension after a pregnancy complicated by preeclampsia was 18 times higher in the first year (adjusted hazard ratio, 18.531; 95% confidence interval, 16.520-20.787) to only 5 times higher at 5 to 10 years after birth (adjusted hazard ratio, 4.921; 95% confidence interval, 4.640-5.218). The corresponding risks of women with gestational hypertension were 12 times higher (adjusted hazard ratio, 11.727; 95% confidence interval, 10.257-13.409]) and 6 times higher (adjusted hazard ratio, 5.854; 95% confidence interval, 5.550-6.176), respectively. For other cardiovascular and cerebrovascular outcomes, there was also a significant effect with preeclampsia (heart failure: adjusted hazard ratio, 6.662 [95% confidence interval, 4.547-9.762]; coronary heart disease: adjusted hazard ratio, 3.083 [95% confidence interval, 1.626-5.844]; cerebrovascular disease: adjusted hazard ratio, 3.567 [95% confidence interval, 2.600-4.893]; peripheral arterial disease: adjusted hazard ratio, 4.802 [95% confidence interval, 2.072-11.132]) compared with gestational hypertension in the first year of follow-up. A dose-response effect was evident for the severity of preeclampsia with the averaged 10-year adjusted hazard ratios for developing chronic hypertension after early, preterm, and late preeclampsia being 10, 7, and 6 times higher, respectively. The risks of cardiovascular and cerebrovascular outcomes were the highest in the first year after a birth complicated by hypertensive disorders of pregnancy. We found a significant relationship with both the severity of hypertensive disorders of pregnancy and the gestational age of onset suggesting a possible dose-response relationship for the development of cardiovascular and cerebrovascular outcomes. These findings call for an urgent focus on research into effective postnatal screening and cardiocerebrovascular risk prevention for women with hypertensive disorders of pregnancy.

On model-based time trend adjustments in platform trials with non-concurrent controls

BackgroundPlatform trials can evaluate the efficacy of several experimental treatments compared to a control. The number of experimental treatments is not fixed, as arms may be added or removed as the trial progresses. Platform trials are more efficient than independent parallel group trials because of using shared control groups. However, for a treatment entering the trial at a later time point, the control group is divided into concurrent controls, consisting of patients randomised to control when that treatment arm is in the platform, and non-concurrent controls, patients randomised before. Using non-concurrent controls in addition to concurrent controls can improve the trial’s efficiency by increasing power and reducing the required sample size, but can introduce bias due to time trends.MethodsWe focus on a platform trial with two treatment arms and a common control arm. Assuming that the second treatment arm is added at a later time, we assess the robustness of recently proposed model-based approaches to adjust for time trends when utilizing non-concurrent controls. In particular, we consider approaches where time trends are modeled either as linear in time or as a step function, with steps at time points where treatments enter or leave the platform trial. For trials with continuous or binary outcomes, we investigate the type 1 error rate and power of testing the efficacy of the newly added arm, as well as the bias and root mean squared error of treatment effect estimates under a range of scenarios. In addition to scenarios where time trends are equal across arms, we investigate settings with different time trends or time trends that are not additive in the scale of the model.ResultsA step function model, fitted on data from all treatment arms, gives increased power while controlling the type 1 error, as long as the time trends are equal for the different arms and additive on the model scale. This holds even if the shape of the time trend deviates from a step function when patients are allocated to arms by block randomisation. However, if time trends differ between arms or are not additive to treatment effects in the scale of the model, the type 1 error rate may be inflated.ConclusionsThe efficiency gained by using step function models to incorporate non-concurrent controls can outweigh potential risks of biases, especially in settings with small sample sizes. Such biases may arise if the model assumptions of equality and additivity of time trends are not satisfied. However, the specifics of the trial, scientific plausibility of different time trends, and robustness of results should be carefully considered.

Characteristics of atmospheric air pollution by fine particles based on regional monitoring data

Introduction. Air pollution with particulate matter (PM) is a serious global problem. In the Russian Federation, regular field measurements of PMs in the ambient air are carried out only in a few cities, and the data, as a rule, are not systematized. Aim of the study: long-term analysis of the data set on concentrations of fine particles in the ambient air of the city of Kazan. Material and methods. Long-term analysis of ambient air pollution by fine particles in the city of Kazan for the period from 2016 to 2020 has been carried out. To study the effect of separate factors (year, measurement time during the day, climatic conditions, the presence of other pollutants) on the levels of PM10 and PM2.5, regression analysis was applied based on the method of mixed models. To characterize the elemental composition of the PM2.5 fraction, sampling of atmospheric air on PVC filters was carried out by use of 100 NR impactor (TSI, USA). The step function and MPPD model were applied to calculate the number of particles and the mass of the deposited fraction of fine particulate matter in different regions of the human respiratory tract. Results. The PM10 concentrations remained stable over a 5-year period, while the PM2.5 concentrations decreased. At the same time, an increase in the maximum annual concentrations of both fractions was observed. The concentrations of PM10 and PM2.5 significantly depended on climatic conditions. The presence of nitrogen oxides and organic carbon in the ambient air was significantly associated with higher concentrations of PM10 and PM2.5. The elemental composition of PM2.5 fraction was represented mainly by carbon (C) (from 86.16% to 93.45%). Mathematical modeling has shown that PM10 is mainly deposited in the upper respiratory tract, and their presence in the tracheobronchial and alveolar zones is insignificant. PM2.5 particles reach the lower respiratory tract and alveolar area. Conclusion. A statistically significant upward long-term trend in the maximum annual ambient concentrations for both fractions of fine particles can increase health risks. Secondary pollutants (nitrogen oxides, organic carbon) are important factors for the formation of secondary particles in the ambient air. The results obtained indicate that when assessing the risks to public health, it is necessary not only to use the concentrations of fine particles in ambient air, but also to consider the degree of deposition of separate fractions in different parts of the human respiratory tract, considering the alleged pathogenesis and priority target cells characteristic of individual diseases.

Heterogeneous irradiated-pristine polyethylene nanofiber junction as a high-performance solid-state thermal diode

In this work, we demonstrate two types of heterogeneous irradiated-pristine polyethylene nanofiber junctions, ‘heavily-irradiated-pristine’ (HI-P) and ‘lightly-irradiated-pristine’ (LI-P) junctions, as high-performance solid-state thermal diodes. The HI-P junction rectifies heat flux in a single direction, while the LI-P junction shows dual-directional rectification under different working temperatures. We accurately model the phase transition of polyethylene nanofibers with a finite temperature range rather than a step function. The finite-temperature-range model suggests that the rectification factor increases with temperature bias and there is a minimum threshold of temperature bias for notable rectification. Besides, the finite-temperature-range model shows better prediction for the heat flow data from experiments, while the step function model tends to overestimate the rectification performance around the optimal length fraction of irradiation. Although both the models show that an optimal rectification occurs when the interface temperatures in the forward and the reverse biases are equal, the optimized rectification factor is determined by the temperature bias and the temperature range of phase transition. This work elucidates the influence of both the temperature bias and the temperature range of phase transition on thermal rectification performance, which could incredibly benefit the evaluation and design of thermal diodes.

EFFICIENCY OF OPERATIONAL DATA PROCESSING FOR RADIO ELECTRONIC EQUIPMENT

The paper deals with the statistical data processing algorithms in operation system of radio electronic equipment. The main purpose is analysis of data processing algorithm efficiency according to the analytical calculations and simulation results. During radio electronic equipment operation failures are possible. These failures affect on the equipment’s technical condition that can deteriorate. In case of condition-based maintenance, it is necessary to detect the time moment of deterioration beginning. Therefore, in this paper the deterioration detection algorithm was developed according to Neyman-Pearson criterion with a fixed sample size. The initial data are times between failures of radio electronic equipment, and these data can be identified by the exponential probability density function. The step-function model was chosen for failure rate change description. To estimate efficiency the operating characteristic was calculated. The simulation based on Monte-Carlo method confirmed the correctness of theoretical calculations.

Using Weibull Distribution for Modeling Bimodal Diffusion Curves: A Naive Framework to Study Product Life Cycle

With the purpose of understanding differing shapes of sales curve (unimodal and bimodal) this paper discusses a naive way for viewing the diffusion process for consumer durables. In this paper, a step functional model involving two-step Weibull distribution with four unknown parameters is characterized wherein the shape of the density function of the models depends upon the shape and scale parameter of Weibull distribution. Empirical analysis on real life sales datasets indicates that the Weibull step function model is more flexible and fits better than the other models.

Operational and Experimental Tasks, Performance, and Voice in Space.

BACKGROUND: Voice analysis offers an unobtrusive approach for psychological monitoring. We demonstrate the relationship between voice parameters and cognitive performance in: 1) a task with psychological test character, and 2) performance in an operational, mission-relevant task. The central methodological aim was to verify the usefulness of voice commands and counting in providing anchor values for the step-function model of voice pitch.METHODS: During a 22-yr period, 42 cosmonauts participated in the Russian space experiment "Pilot", which was a hand-controlled docking maneuver. As reference the experiment included the cognitive task "Manometer." This task was controlled through voice commands. These voice commands were stored and are the basis for the present analysis.RESULTS: Cosmonauts differed in their working style and respective performance during the Manometer task. Clustered groups can be assumed to represent different effort. Importantly, these groups differed in the changes of voice pitch among mission phases and among task repetitions. However, there were no differences between these motivation groups and performance in the professional task.DISCUSSION: The differing effort is the effect of different motivation of cosmonauts for experimental test tasks vs. mission-relevant professional tasks. Latter ones provide a more reliable chance to assess the real actual state and skills of a cosmonaut. Voice pitch measurement seems to be reliable and useful under space conditions for monitoring this volitional effort.Johannes B, Bronnikov SV, Bubeev JA, Kotrovskaya TI, Shastlivtseva DV, Piechowski S, Hoermann H-J, Rittweger J, Jordan J. Operational and experimental tasks, performance, and voice in space. Aerosp Med Hum Perform. 2019; 90(7):624-631.

A Prospective Cohort Study Examining the Associations of Maternal Arsenic Exposure With Fetal Loss and Neonatal Mortality.

Arsenic crosses the placenta, possibly increasing the risk of adverse reproductive outcomes. We aimed to examine the association between maternal arsenic exposure and fetal/neonatal survival using data from a prospective cohort study of 1,616 maternal-infant pairs recruited at a gestational age of ≤16 weeks in Bangladesh (2008-2011). Arsenic concentration in maternal drinking water was measured at enrollment. Extended Cox regression (both time-dependent coefficients and step functions) was used to estimate the time-varying association between maternal arsenic exposure and fetal/neonatal death (all mortality between enrollment and 1 month after birth). In a sensitivity analysis, we assessed gestational arsenic exposure using maternal urine samples taken at enrollment. We observed 203 fetal losses and 20 neonatal deaths. Higher arsenic exposure was associated with a slightly decreased mortality rate up to the middle of the second trimester, and then the mortality rate switched directions around 20 weeks' gestation. In the step function model, the hazard ratios for combined mortality (fetal loss and neonatal death) per unit increase in the natural log of drinking water arsenic concentration (μg/L) ranged from 1.35 (95% CI: 1.08, 1.69) in weeks 25-28 to 0.81 (95% CI: 0.65, 1.02) in weeks 9-12. This nonlinear association suggests that arsenic may exert survival pressure on developing fetuses, potentially contributing to survival bias, and may also indicate that arsenic toxicity differs by fetal developmental stage.

Distributed parameter unsteady flow model for the Han River

An unsteady flow model that allows a variable roughness coefficient for each computational point according to its spatial position (x) and the value of discharge (Q) was developed. A step function and a power function were considered for functional relationships between discharge and Manning’s roughness coefficient (n). The model was applied to the main reach of the Han River and model parameters were estimated by optimization. From the model calibration, spatial variation and discharge dependence of Manning’s n were identified by testing different n(x, Q) functions. First, the value of the roughness coefficient is higher for the upstream reach of the Wangsook Stream junction than it is for the downstream reach. Second, estimated parameters of both the step function model and the power function model show that Manning’s n decreases as discharge increases. This tendency is more noticeable for the upstream reach of the Wangsook Stream junction compared to the downstream reach. Further, the stages calculated by the variable roughness coefficient model are more consistent with the observed ones than those from the conventional constant parameter model. Regarding the variation of Manning’s n relative to discharge, adopting a power function as the Manning’s n-discharge relationship seems to be more appropriate than adopting a step function because it is easy to apply and the performance is as good as that of the step function model.

A statistical study of the inferred transverse density profile of coronal loop threads observed with SDO/AIA

Aims. We carry out a statistical study of the inferred coronal loop cross-sectional density profiles using extreme ultraviolet (EUV) imaging data from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Methods. We analysed 233 coronal loops observed during 2015/2016. We consider three models for the density profile; the step function (model S ), the linear transition region profile (model L), and a Gaussian profile (model G). Bayesian inference is used to compare the three corresponding forward modelled intensity profiles for each loop. These are constructed by integrating the square of the density from a cylindrical loop cross section along the line of sight, assuming an isothermal cross section, and applying the instrumental point spread function. Results. Calculating the Bayes factors for comparisons between the models, it was found that in 47 % of cases there is very strong evidence for model L over model S and in 45 % of cases very strong evidence for model G over S . Using multiple permutations of the Bayes factor the favoured density profile for each loop was determined for multiple evidence thresholds. There were a similar number of cases where model L or G are favoured, showing evidence for inhomogeneous layers and constantly varying density cross sections, subject to our assumptions and simplifications. Conclusions. For sufficiently well resolved loop threads with no visible substructure it has been shown that using Bayesian inference and the observed intensity profile we can distinguish between the proposed density profiles at a given AIA wavelength and spatial resolution. We have found very strong evidence for inhomogeneous layers, with model L being the most general, and a tendency towards thicker or even continuous layers.

A three-dimensional anisotropic point process characterization for pharmaceutical coatings

Spatial characterization and modeling of the structure of a material may provide valuable knowledge on its properties and function. Especially, for a drug formulation coated with a polymer film, understanding the relationship between pore structure and drug release properties is important to optimize the coating film design. Here, we use methods from image analysis and spatial statistics to characterize and model the pore structure in pharmaceutical coatings. More precisely, we use and develop point process theory to characterize the branching structure of a polymer blended film with data from confocal laser scanning microscopy. Point patterns, extracted by identifying branching points of pore channels, are both inhomogeneous and anisotropic. Therefore, we introduce a directional version of the inhomogeneous K-function to study the anisotropy and then suggest two alternative ways to model the anisotropic three-dimensional structure. First, we apply a linear transformation to the data such that it appears isotropic and subsequently fit isotropic inhomogeneous Strauss or Lennard-Jones models to the transformed pattern. Second, we include the anisotropy directly in a Lennard-Jones and a more flexible step-function model with anisotropic pair-potential functions. The methods presented will be useful for anisotropic inhomogeneous point patterns in general and for characterizing porous material in particular.

Cognitive Profiling Useful for Unraveling Cross-Disorder Mechanisms

Cognitive subtyping may be essential for understanding shared mechanisms underlying attention-deficit/hyperactivity disorder (ADHD) and autism spectrum disorder (ASD). Participants from a population-based sample ( n = 360) and an ASD/ADHD clinic-based sample ( n = 254), ages 5 to 17 years, were administered a broad cognitive battery. Latent class analyses revealed a similar four-cognitive-class solution in both samples mainly characterized by speed–accuracy tradeoff differences instead of specific strengths and weaknesses. The classes were strongly predictive of both ASD and ADHD (and comorbid) symptoms in the clinical, but not the population, sample. Results support the hypothesis that both disorders are manifestations of the same overarching disorder and illustrate the effectiveness of subtyping based on cognitive profiles. Results also support a step-function endophenotype model, in which cognitive problems mediate the gene–psychopathology associations but only in a clinically relevant way in the subgroup of children with high genetic susceptibility. Pre-onset longitudinal research is needed to corroborate this.

Solids Retention Time Dependent Phototrophic Growth and Population Changes in Chemostat Cultivation Using Wastewater

There has been renewed interest in using algae for wastewater polishing and treatment in recent years. Because solids retention time (SRT) is a key design and operating parameter in bioreactor operation, this research determined the effect of SRT on phototrophic growth and microbial population dynamics in continuous-flow chemostat systems. There was a unique feature of phototrophic growth that differed from chemotrophic growth in chemostat. It was found that the phototrophic biomass concentration increased proportionally as SRT increased from 3 to 9 days. Regardless of the change in SRT, a step function model was successfully applied with the predicted phototrophic production rate of 4.5 ± 0.9 g/m(2)·d at the light intensity of 68.5 μmol/m(2)·s. Even though the continuous-flow systems were initially seeded with a 1:1 mixture of green algae and cyanobacteria, Chlorella vulgaris always dominated (98%) in the continuous-flow chemostat systems under steady-state conditions.

Using Hand Grip Force as a Correlate of Longitudinal Acceleration Comfort for Rapid Transit Trains.

Longitudinal acceleration comfort is one of the essential metrics used to evaluate the ride comfort of train. The aim of this study was to investigate the effectiveness of using hand grip force as a correlate of longitudinal acceleration comfort of rapid transit trains. In the paper, a motion simulation system was set up and a two-stage experiment was designed to investigate the role of the grip force on the longitudinal comfort of rapid transit trains. The results of the experiment show that the incremental grip force was linearly correlated with the longitudinal acceleration value, while the incremental grip force had no correlation with the direction of the longitudinal acceleration vector. The results also show that the effects of incremental grip force and acceleration duration on the longitudinal comfort of rapid transit trains were significant. Based on multiple regression analysis, a step function model was established to predict the longitudinal comfort of rapid transit trains using the incremental grip force and the acceleration duration. The feasibility and practicably of the model was verified by a field test. Furthermore, a comparative analysis shows that the motion simulation system and the grip force based model were valid to support the laboratory studies on the longitudinal comfort of rapid transit trains.

Ecological threshold and environmental management: A note on statistical methods for detecting thresholds

Many statistical models are available for detecting and quantifying ecological thresholds. The proper model can be selected through the comparison of the goodness-of-fit of multiple alternative models to the same data. In the context of selecting the appropriate threshold model, three sources of information should be used: patterns in model residuals, model predicted versus observed, and the posterior change point distributions. Applying alternative models to several ecological metrics measured along a total phosphorus gradient from a mesocosm experiment conducted in the Everglades, I conclude that changes in these metrics along the gradient are more likely to be gradual. The previously found strong threshold response is likely a result of the use of the step function model.

Electrical Phenomena of Soft Particles. A Soft Step Function Model

Simple analytic expressions are derived for the electrophoretic mobility of a soft particle consisting of the hard particle core covered with an ion-penetrable surface layer of polyelectrolyte for the case where the electric potential is low. The effect of the distribution of the polymer segments is taken into account by modeling the surface layer as a soft step function with the inhomogeneous distribution width δ. It is shown that the electrophoretic mobility becomes lower than that for the hard step function model and that the maximum deviation of the soft step function model from the hard step function model, which is a function of λδ (where 1/λ is the softness parameter) and κ/λ (where κ is the Debye-Hückel parameter), is 2.7% at λδ = 0.1, 5.1% at λδ = 0.2, and 11% at λδ = 0.5. In the limit of very high electrolyte concentrations, the obtained mobility expression tends to the result derived from the conventional hard step function model. In addition, an analytic expression for the interaction energy between two similar soft plates is derived on the basis of the present soft step function model. The magnitude of the interaction energy is shown to decrease by a factor 1/(1 + κδ)(2). Approximate analytic expressions for the interaction energies between two similar soft spheres and between two similar soft cylinders are also derived with the help of Derjaguin's approximation.

Comparação bayesiana de modelos com uma aplicação para o equilíbrio de Hardy-Weinberg usando o coeficiente de desequilíbrio

O equilíbrio de Hardy-Weinberg é um dos principais assuntos estudados pela Genética de populações. Neste contexto, o presente trabalho aborda a análise e a comparação bayesiana de modelos utilizando o coeficiente de desequilíbrio (D A). Para isso, realizou-se um estudo de simulação no qual as seguintes distribuições a priori foram consideradas: Dirichlet (modelo 1); beta - função degrau uniforme (modelo 2); uniforme - função degrau uniforme (modelo 3); e as prioris independentes uniformes (modelo 4). Exemplos de aplicação a dados reais de grupos raciais também são apresentados e discutidos. As amostras das distribuições marginais a posteriori para os parâmetros de interesse foram obtidas mediante o algoritmo Metropolis-Hastings, o qual foi implementado no software livre R. A convergência das cadeias geradas por este algoritmo foi monitorada pelos critérios de Geweke e Gelman &amp; Rubin, os quais estão implementados no pacote BOA do R. Quanto às comparações entre os modelos, efetuadas por meio do fator de Bayes, observa-se que, para os dados simulados, o modelo 4 é o mais indicado para os casos de D A=0,146, D A=0,02 e D A=-0,02 com n=200; o modelo 2 é o mais indicado para D A=-0,02 e n=50 e o modelo 3 é o mais indicado para D A=-0,02 e n=1000. Para os dados reais, em cada caso analisado, nota-se uma grande diferenciação na escolha de modelos, em que apenas o modelo 1 não é recomendado.

Thermal regime in the central Alpine Fault zone, New Zealand: Constraints from microstructures, biotite chemistry and fluid inclusion data

The thermal state within plate boundary fault zones is likely to influence the dimensions of large co-seismic fault ruptures, and strain localisation in underlying mylonitic shear zones. Vein microstructures, biotite chemistry and fluid inclusion data offer new insights into the thermal structure of the mylonitic shear zone down dip of the Alpine Fault, the main Pacific–Australian plate boundary structure through southern New Zealand. Quartz veins within the fault rocks were formed and deformed at temperatures ranging from > 500 °C to immediately above that of the brittle–viscous transition (∼ 325 °C), illustrating that fluids are present throughout the fault zone. Microthermometric data from primary, mixed CO 2–H 2O fluid inclusions in boudin-neck quartz–carbonate veins indicate that these inclusions were trapped at temperatures of 325 ± 15 °C and pressures of c. 40 MPa. Vein microstructures indicate that fluid temperatures were equal to rock temperatures. Assuming hydrostatic fluid pressure, the veins were trapped at depths of < 8 km for an average density of mixed H 2O–CO 2 fluids in the shallower crust of > 500 kg m − 3 . Biotite grains in the mylonites are a mixture of porphyroclastic grains with high R = Ti/Mg# inherited from the parent Alpine Schist, and smaller, low R grains that recrystallised during mylonitisation, particularly those that are found within syn-mylonitic shear bands. Assuming a simple step-function model approximating diffusive equilibration, the changes in biotite chemistry indicate Δ T during mylonitic deformation of ∼−340 °C according to the Ti-in-biotite thermometer of Henry et al. (2005). A best-fit uplift P– T path to existing data and these new results indicate that the uplift path P– T gradient of fault zone rocks above the brittle–viscous transition is of the order of 40 °C km − 1 . Below the brittle–viscous transition, the uplift path P– T gradient is 10 °C km − 1 . The P– T profile within the fault rocks is comparable to that in the immediate hanging wall Alpine Schist, indicating there is no peak in the crustal isotherms in the fault hanging wall, as was indicated by previous numerical models, and analyses that did not consider data from the fault rocks themselves.