Variance Of Fluctuations Research Articles

Dose-dependent effects of transcranial photobiomodulation on brain temperature in patients with major depressive disorder: a spectroscopy study.

This study aimed to evaluate the dose-dependent brain temperature effects of transcranial photobiomodulation (t-PBM). Thirty adult subjects with major depressive disorder were randomized to three t-PBM sessions with different doses (low: 50 mW/cm2, medium: 300 mW/cm2, high: 850 mW/cm2) and a sham treatment. The low and medium doses were administered in continuous wave mode, while the high dose was administered in pulsed wave mode. A 3T MRI scanner was used to perform proton magnetic resonance spectroscopy (1H-MRS). A voxel with a volume of 30 × 30 × 15 mm3 was placed on the left prefrontal region. Brain temperature (°C) was derived by analyzing 1H-MRS spectrum chemical shift differences between the water (~ 4.7 ppm) and N-acetyl aspartate (NAA) (~ 2.01 ppm) peaks. After quality control of the data, the following group numbers were available for both pre- and post-temperature estimations: sham (n = 10), low (n = 11), medium (n = 10), and high (n = 8). We did not detect significant temperature differences for any t-PBM-active or sham groups post-irradiation (p-value range = 0.105 and 0.781). We also tested for potential differences in the pre-post variability of brain temperature in each group. As for t-PBM active groups, the lowest fluctuation (variance) was observed for the medium dose (σ2 = 0.29), followed by the low dose (σ2 = 0.47), and the highest fluctuation was for the high dose (σ2 = 0.67). t-PBM sham condition showed the overall lowest fluctuation (σ2 = 0.11). Our 1H-MRS thermometry results showed no significant brain temperature elevations during t-PBM administration.

On a Correlation Model for Laser Scanners: A Large Eddy Simulation Experiment

Large Eddy Simulations (LES) allow the generation of spatio-temporal fields of the refractivity index for various meteorological conditions and provide a unique way to simulate turbulence-distorted phase measurements as those from geodetic sensors. This approach enables a statistical quantification of the von Kármán model’s adequacy in describing the phase spectrum and the assessment of the validity of common assumptions such as isotropy or the Taylor frozen hypothesis. This contribution shows that the outer scale length, defined using the Taylor frozen hypothesis as the saturation frequency of the phase spectrum, can be statistically estimated, along with an error fit factor between the model and its estimation. It is found that this parameter strongly varies with height and meteorological conditions (convective or wind-driven boundary layer). The simulations further highlight the linear dependency with the variance of the turbulent phase fluctuations but no dependency on the local outer scale length as defined by Tatarskii. An application of these results within a geodetic context is proposed, where an understanding and solid estimation of the outer scale length is mandatory in avoiding biased decisions during statistical deformation analysis. The LES presented in this contribution support derivations for an improved stochastic model of terrestrial laser scanners.

Quantum-limited transmission distance of optically repeating systems using a hybrid EDFA/Raman-amplifier.

The transmission distance of optically repeating systems is ultimately bounded by quantum noises arising from attenuation and amplification. It is known that fiber Raman amplifiers (FRAs) can achieve longer quantum-limited distances than other amplification schemes owing to their distributed amplification characteristics. However, all-FRA systems are difficult to implement in practice. Therefore, a hybrid erbium-doped fiber amplifier (EDFA)/FRA system may be a reasonable solution for long-haul transmission. In this study, the quantum-limited transmission distance of hybrid EDFA/FRA systems is investigated. A formula for the quantum fluctuation variance during transmission was derived based on quantum mechanical treatment. Calculation results obtained with the derived formula quantitatively indicate that the quantum-limited transmission distance increases as the EDFA/FRA hybrid ratio varies from EDFAs alone to FRAs alone.

Relaxation and fluctuations of a mass- and dipole-conserving stochastic lattice gas

Han [] have recently introduced a classical stochastic lattice gas model which, in addition to particle conservation, also conserves the particles' dipole moment. Because of its intrinsic nonlinearity this model exhibits unusual macroscopic scaling behaviors, different from those of lattice gases that conserve only the number of particles. Here we investigate some basic relaxation and fluctuation properties of this model at large scales and at long times. These properties crucially depend on whether the total number of particles is infinite or finite. We find similarity solutions, describing relaxation of the dipole-conserving gas (DCG) in several standard settings. A major part of our effort is an extension to this model of the macroscopic fluctuation theory (MFT), previously developed for lattice gases where only the number of particles is conserved. We apply the MFT to the calculation of the variance of nonequilibrium fluctuations of the excess number of particles on the positive semi-axis when starting from an (either deterministic, or random) constant density at t=0. Using the MFT, we also identify the equilibrium Boltzmann-Gibbs distribution for the DCG. Finally, based on these results, we determine the probability distribution of, and the most probable density history leading to, a large deviation in the form of a macroscopic void of a given size in an initially uniform DCG at equilibrium. Published by the American Physical Society 2024

Discussion of sound propagation through the turbulent Martian atmosphere and implications for inference of turbulence spectra.

Chide et al. [J. Acoust. Soc. Am. 155, 420-435 (2024)] provide a first attempt to infer the spectrum of temperature fluctuations on Mars from experimental data on the variances of travel-time and log-amplitude fluctuations recorded by the microphone on board the Perseverance rover. However, the theoretical formulations that were used to interpret the travel-time data have limitations. In addition to explaining those issues, this article also outlines approaches for predicting statistical characteristics of acoustic signals in the Martian atmosphere. In particular, the experimentally observed dependence of the travel-time variance on the propagation range can be attributed to ground-blocking of buoyantly produced turbulent velocity fluctuations and the non-Markov character of phase fluctuations.

Weight fluctuations in deep linear neural networks and a derivation of the inverse-variance flatness relation

We investigate the stationary (late-time) training regime of single- and two-layer underparameterized linear neural networks within the continuum limit of stochastic gradient descent (SGD) for synthetic Gaussian data. In the case of a single-layer network in the weakly underparameterized regime, the spectrum of the noise covariance matrix deviates notably from the Hessian, which can be attributed to the broken detailed balance of SGD dynamics. The weight fluctuations, are in this case, generally anisotropic but effectively experience an isotropic loss. For an underparameterized two-layer network, we describe the stochastic dynamics of the weights in each layer and analyze the associated stationary covariances. We identify the interlayer coupling as a distinct source of anisotropy for the weight fluctuations. In contrast to the single-layer case, the weight fluctuations are effectively subject to an anisotropic loss, the flatness of which is inversely related to the fluctuation variance. We thereby provide an analytical derivation of the recently observed inverse-variance flatness relation in a model of a deep linear neural network. Published by the American Physical Society 2024

Two-Stage Robust Optimization for Large Logistics Parks to Participate in Grid Peak Shaving

As new energy integration increases, power grid load curves become steeper. Large logistics parks, with their substantial cooling load, show great peak shaving potential. Leveraging this load while maintaining staff comfort, product quality, and operational costs is a major challenge. This paper proposes a two-stage robust optimization method for large logistics parks to participate in grid peak shaving. First, a Cooling Load’s Economic Contribution (CLEC) index is introduced, integrating the Predicted Mean Vote (PMV) and Sales Pressure Index (SPI). Then, an optimization model is established, accounting for renewable energy uncertainties and maximizing large logistics parks’ participation in peak shaving. Results illustrate that the proposed method leads to a reduction in the peak shaving pressure on the distribution network. Specifically, under the scenario tolerating the maximum potential uncertainty in renewable energy output, the absolute peak-to-valley difference and fluctuation variance of the park’s net load are decreased by 45.82% and 54.59%, respectively. Furthermore, the PMV and the SPI indexes are reduced by 39.12% and 26.36%, respectively. In comparison with the determined optimization method, despite a slight cost increase of 20.06%, the proposed method significantly reduces EDR load shedding by 98.1%.

Study of consecutive eclipses of pulsar J0024-7204O

ABSTRACT The eclipses seen in the radio emission of some pulsars can be invaluable to study the properties of the material from the companion stripped away by the pulsar. We present a study of six consecutive eclipses of PSR J0024–7204O in the globular cluster 47 Tucanae as seen by the MeerKAT radio telescope in the UHF (544–1088 MHz) band. A high scintillation state boosted the signal during one of the orbits and allowed a detailed study of the eclipse properties. We measure significant dispersion measure (DM) variations and detect strong scattering that seems to be the dominating mechanism of the eclipses at these frequencies. A complete drop in the linear polarization together with a small increase in the rotation measure suggests the presence of a magnetic field of $\sim 2$ mG. The study of multiple eclipses allowed us to measure difference in the lengths of the eclipses and DM differences of $\sim 0.01$ pc cm$^{-3}$ in consecutive orbits. One orbit, in particular, shows a delay in recovery of the linear polarization and a visible delay in the arrival of the pulses caused by a stronger scattering event. We suggest that these are caused by a higher variance of density fluctuations during the event.

Towards optimal customized electricity pricing via iterative two-layer optimization for consumers and prosumers

Designing an electricity price mechanism that efficiently enables users to manage their self-production and consumption behavior to accommodate renewable energy and regulate peak load is a hard task with the emergence of prosumer with photovoltaic and energy storage. To address this issue, we propose an iterative two-layer optimization to investigate customized price of electricity for different types of users in the presence of photovoltaic uncertainty. By taking into account power flow restrictions, the model is used to explore the optimal time-of-use, demand, and on-grid prices for both electricity consumers and prosumers. The consumer and prosumer peak-flat-valley periods are initially divided in the upper layer. Then, a model for distribution system operator profit maximization is proposed to minimize operation cost, power loss, and peak–valley difference. A stochastic optimization model is presented in the lower layer for consumer and prosumer to hedge against the risk of uncertain photovoltaic with the aim of minimizing electricity tariff, demand tariff, and life cycle cost of energy storage. Numerical experiments conducted on modified 15-bus and 69-bus distribution systems with different types of users show the effectiveness of the iterative two-layer optimization for customized price of electricity in peak-shaving and valley-filling while ensuring the interests of distribution system operator and users. Results show that the total profit increases by more than 4% and the net load fluctuation variance reduces higher than 20% compared with the traditional pricing method.

Temporal variability can promote migration between habitats

Understanding the conditions that promote the evolution of migration is important in ecology and evolution. When environments are fixed and there is one most favorable site, migration to other sites lowers overall growth rate and is not favored. Here we ask, can environmental variability favor migration when there is one best site on average? Previous work suggests that the answer is yes, but a general and precise answer remained elusive. Here we establish new, rigorous inequalities to show (and use simulations to illustrate) how stochastic growth rate can increase with migration when fitness (dis)advantages fluctuate over time across sites. The effect of migration between sites on the overall stochastic growth rate depends on the difference in expected growth rates and the variance of the fluctuating difference in growth rates. When fluctuations (variance) are large, a population can benefit from bursts of higher growth in sites that are worse on average. Such bursts become more probable as the between-site variance increases. Our results apply to many (≥ 2) sites, and reveal an interplay between the length of paths between sites, the average differences in site-specific growth rates, and the size of fluctuations. Our findings have implications for evolutionary biology as they provide conditions for departure from the reduction principle, and for ecological dynamics: even when there are superior sites in a sea of poor habitats, variability and habitat quality across space determine the importance of migration.

Generalized scaling laws for the irrotational motions bordering a turbulent region.

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI x_{2} much bigger than the integral scale L in the nearby turbulent region (x_{2}≫L), the variance of the velocity fluctuations 〈u_{i}^{2}〉 (i=1,2,3) depends on the shape of the kinetic energy spectrum in the infrared region E(k)∼k^{n} [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of n. While the cases n=4 (Batchelor turbulence) and n=2 (Saffman turbulence) have been previously derived, with 〈u_{i}^{2}〉∼x_{2}^{-4} and 〈u_{i}^{2}〉∼x_{2}^{-3}, for n=4 and n=2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296.], we extend these results by including any other value of n. In particular, we obtain 〈u_{i}^{2}〉∼x_{2}^{-2} and 〈u_{i}^{2}〉∼x_{2}^{-4}, for n=1 and n≥5, respectively, while n=3 yields 〈u_{i}^{2}〉∼x_{2}^{-4}ln(x_{2}). These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

Experimental investigation of the structure of plane turbulent wall jets. Part 1. Spectral analysis

Plane turbulent wall jets are traditionally considered to be composed of a turbulent boundary layer (TBL) topped by a half-free jet. However, certain peculiar features, such as counter-gradient momentum flux occurring below velocity maximum in experiments and numerical simulations, suggest a different structure of turbulence therein. Here, we hypothesize that turbulence in wall jets has two distinct structural modes, wall mode scaling on wall variables and free-jet mode scaling on jet variables. To investigate this hypothesis, experimental data from our wall jet facility are acquired using single hot-wire anemometry and two-dimensional particle image velocimetry at three nozzle Reynolds numbers 10 244, 15 742 and 21 228. Particle image velocimetry measurements with four side-by-side cameras capture the longest field of view studied so far in wall jets. Direct spatial spectra of these fields reveal modal spectral contributions to variances of velocity fluctuations, Reynolds shear stress, shear force, turbulence production, velocity fluctuation triple products and turbulent transport. The free-jet mode has wavelengths scaling on the jet length scale ${z_{T}}$ , and contains two dominant submodes with wavelengths $5{z_{T}}$ and $2.5{z_{T}}$ . The region of flow above the velocity maximum shows the presence of the outer jet mode whereas the region below it shows robust bimodal behaviour attributed to both wall and inner jet modes. Counter-gradient momentum flux is effected by the outer jet mode intruding into the region below velocity maximum. These findings support the hypothesis of wall and free-jet structural modes, and indicate that the region below velocity maximum could be much complex than a conventional TBL.

Polarization and coherence properties of a partially coherent elegant Laguerre–Gaussian vortex beam in turbulent plasma

The analytical expressions for the cross-spectral density matrix elements of the partially coherent elegant Laguerre–Gaussian (eLG) vortex beam propagating through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel principle and used to study the changes in the polarization degree and the coherence degree of the partially coherent eLG vortex beam in the turbulent plasma. The numerical results show that the polarization degree of a partially coherent eLG vortex beam reaches a specific value (which is equal to the degree of polarization in the source plane) after a long propagation distance in the turbulent plasma. Moreover, this value is independent of the beam order, topological charge, correlation coefficient, wavelength of the source plane, anisotropy parameter, refractive index fluctuation variance, and outer and inner scales of the turbulent plasma. The results also show that with increasing distance, the coherence degree first decreases from unity and then oscillates around zero. However, this oscillation gradually disappears after traveling a long distance. Our results intuitively present the beam polarization and coherence properties through anisotropic hypersonic turbulence, which can be useful for optical communication in hypersonic turbulent environments.

Multiple scattering, radiative transfer, and parameter regimes

We have established the radiative transfer regime in a four-parameter space spanned by amplitude and scale of fluctuations, convergence rate, and spatial range. The derivation of radiative transfer equations from wave equations offers a better understanding of the underlying physics in radiative transfer theory. One approach is based on tools borrowed from quantum field theory (QFT) and employs the Dyson and Bethe–Salpeter equations as the foundation. This has allowed us to investigate the small scale fluctuation regime, kl = O ( ε ) . We also investigated this regime using the scale-separated asymptotics approach and found that the conditions on the parameters are the same as in the QFT approach if the convergence rate of the Dyson series is O ( ε 2 ) . Furthermore, we found that there is a multitude of regimes where radiative transfer manifests. We hence infer that for a fixed spatial range, increase in the scale size of fluctuations leads to decrease in the upper bound of variance of permittivity fluctuations along with diminished convergence rate of the Wigner series. Also, for a fixed scale size and convergence rate, the spatial range where radiative transport manifests decreases with increase in strength of fluctuations.

What is the best simulation approach for measuring local density fluctuations near solvo-/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F(r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

A robust internal model control design for low-quality waste heat power generation systems

Recovering low-quality waste heat using industrial waste heat is challenging, and the reuse technology needs to erupt. Moreover, the gas source of low-quality waste heat is relatively volatile, which makes it challenging to keep the actual working condition of the plant stable. Therefore, it is inspiring to research the robustness of root-waste heat power generation processed measurement and control system to improve the stability of the plant operation. Hence, in this paper, we have applied uncertainty theory to analyze it and formulate the uncertainty model based on the Bode diagram. We also proposed a control method based on the uncertainty model, which combines robust control and internal model control to make the roots waste heat power generation system operate stably under the effect of external disturbances and changes of internal structure or parameters in actual operation. Experimental results show that the robust internal model control method has a speed deviation of no more than 7.9 r/min compared with the PID control method. The adjustment time to track the set value does not exceed 73.1 seconds within the allowed fluctuation range. The fluctuation variance is 30.95% of that of the PID controller. The dynamic performance is better, with strong anti-interference capability and significantly improved tracking performance. It ensures the stability of the roots-type waste heat utilization system, which is essential for future intelligent grid-connected power generation.

A modified lognormal approximation of the Lyman-α forest: comparison with full hydrodynamic simulations at 2 ≤ z ≤ 2.7

Observations of the Lyman-α forest in distant quasar spectra with upcoming surveys are expected to provide significantly larger and higher-quality datasets. To interpret these datasets, it is imperative to develop efficient simulations. One such approach is based on the assumption that baryonic densities in the intergalactic medium (IGM) follow a lognormal distribution. We extend our earlier work to assess the robustness of the lognormal model of the Lyman-α forest in recovering the parameters characterizing IGM state, namely, the mean-density IGM temperature (T 0), the slope of the temperature-density relation (γ), and the hydrogen photoionization rate (Γ12), by comparing with high-resolution Sherwood SPH simulations across the redshift range 2 ≤ z ≤ 2.7. These parameters are estimated through a Markov Chain Monte Carlo (MCMC) technique, using the mean and power spectrum of the transmitted flux. We find that the usual lognormal distribution of IGM densities cannot recover the parameters of the SPH simulations. This limitation arises from the fact that the SPH baryonic density distribution cannot be described by a simple lognormal form. To address this, we extend the model by scaling the linear density contrast by a parameter ν. While the resulting baryonic density is still lognormal, the additional parameter gives us extra freedom in setting the variance of density fluctuations. With this extension, values of T 0 and γ implied in the SPH simulations are recovered at ∼ 1 - σ (≲ 10%) of the median (best-fit) values for most redshifts bins. However, this extended lognormal model cannot recover Γ12 reliably, with the best-fit value discrepant by ≳ 3 - σ for z > 2.2. Despite this limitation in the recovery of Γ12, whose origins we explain, we argue that the model remains useful for constraining cosmological parameters.

Environmental and economic dispatching strategy for power system with the complementary combination of wind-solar-hydro-thermal-storage multiple sources

The linkage, coordination, and complementary cooperation of energy supply can improve the efficiency of transportation and utilization. At present, the level of new energy consumption needs to be improved, the coordination of the source network load storage link is insufficient, and the insufficient complementarity of various types of power sources in the power system. This article fully explores the differences and complementarities of various types of wind-solar-hydro-thermal-storage power sources, a hierarchical environmental and economic dispatch model for the power system has been established. Among them, the upper level model takes the flexible consumption of new energy as the optimization goal, the middle level model uses a combination of hydropower station and energy storage to minimizes the fluctuation variance and peak-to-valley difference of the net load curve, the lower level model aims to achieve optimal environmental and economic benefits of the power system, comprehensively considers the coal consumption cost, startup and shutdown cost, energy storage operation cost, and pollutant emissions of thermal power units, determines the startup and shutdown mode and output power of thermal power units. Finally, an improved IEEE 6-machine 30-node system is used as an example for simulation analysis, the results show that after applying the proposed hierarchical environmental and economic dispatch strategy of the power system, the fluctuation variance and the peak-to-valley difference of the net load curve have been reduced by 46.3% and 31.5%, respectively, and the environmental and economic benefits of the system is improved by 5.1% compared with the traditional economic dispatch strategy. It can meet the requirements of energy system cleaning and decarbonization while improving the operation economy, which verifies the effectiveness of the proposed environmental economic dispatch model.

Stochastic subgrid-scale modeling for particles dispersion and deposition for a filtered DNS channel flow field

The effect of subgrid-scale velocity fluctuations on the deposition and dispersion of solid particles in a filtered DNS turbulent channel flow at Reτ=180, and for particles with Stokes numbers of St = 1, 2, 5, 24 was studied. First, the turbulent flow field was simulated using the DNS on a high-resolution grid. Then, the filtered DNS flow fields were generated using several low-resolution grids. Particle tracking was performed for the DNS and filtered DNS channel flow fields, and the effects of filtering on particle deposition and concentration were studied. It was shown that filtering significantly decreases the particle deposition velocities at lower Stokes numbers (St = 1, 2, 5). However, at higher Stokes numbers (St = 24), the deposition velocity was less affected. Next, the ability of a stochastic model to generate the correct particle deposition velocities and concentration profiles was studied. A Langevin stochastic equation for modeling the subgrid-scale (SGS) fluid velocity fluctuations as seen by particles was developed and tested. The two input parameters of the stochastic model are the variance of SGS fluctuations in the wall-normal direction and the Lagrangian SGS time-scale. It was seen that the model prediction is sensitive to the SGS time scale used in the Langevin equation. The model was capable of predicting the correct deposition velocities and concentration profiles of lower inertia particles when the proper time-scale was used. For higher inertia particles and when a larger amount of energy was removed by filtering, the model was unable to predict the deposition velocities.

Estimands for clinical endpoints in tuberculosis treatment randomized controlled trials: a retrospective application in a completed trial

BackgroundRandomized trials for the treatment of tuberculosis (TB) rely on a composite primary outcome to capture unfavorable treatment responses. However, variability between trials in the outcome definition and estimation methods complicates across-trial comparisons and hinders the advancement of treatment guidelines. The International Council for Harmonization (ICH) provides international regulatory standards for clinical trials. The estimand framework outlined in the recent ICH E9(R1) addendum offers a timely opportunity for randomized trials of TB treatment to adopt broadly standardized outcome definitions and analytic approaches. We previously proposed and defined four estimands for use in this context. Our objective was to evaluate how the use of these estimands and choice of estimation method impacts results and interpretation of a large phase III TB trial.MethodsWe reanalyzed participant-level data from the REMoxTB trial. We applied four estimands and various methods of estimation to assess non-inferiority of both novel 4-month treatment regimens against standard of care.ResultsWith each of the four estimands, we reached the same conclusion as the original trial analysis that the novel regimens were not non-inferior to standard of care. Each estimand and method of estimation gave similar estimates of the treatment effect with fluctuations in variance and differences driven by the methods applied for handling intercurrent events.ConclusionsOur application of estimands defined by the ICH E9 (R1) addendum offers a formalized framework for addressing the primary TB treatment trial objective and can promote uniformity in future trials by limiting heterogeneity in trial outcome definitions. We demonstrated the utility of our proposal using data from the REMoxTB randomized trial. We outlined methods for estimating each estimand and found consistent conclusions across estimands. We recommend future late-phase TB treatment trials to implement some or all of our estimands to promote rigorous outcome definitions and reduce variability between trials.Trial registrationClinicalTrials.gov NCT00864383. Registered on March 2009