Simulations Of Hundreds Research Articles

Neutral hydrogen lensing simulations in the hubble frontier fields

ABSTRACT Cold gas evolution ties the formation of dark matter haloes to the star formation history of the universe. A primary component of cold gas, neutral atomic hydrogen (HI), can be traced by its 21-cm emission line. However, the faintness of this emission typically limits individual detections to low redshifts ($z\lesssim 0.2$). To address this limitation, we investigate the potential of targeting gravitationally lensed systems. Building on our prior galaxy–galaxy simulations, we have developed a ray-tracing code to simulate lensed HI images for known galaxies situated behind the massive hubble frontier field galaxy clusters. Our findings reveal the existence of high HI mass, high HI magnification systems in these cluster-lensing scenarios. Through simulations of hundreds of sources, we have identified compelling targets within the redshift range $z\approx 0.7 - 1.5$. The most promising candidate from our simulations is the Great Arc at z = 0.725 in Abell 370, which should be detectable by MeerKAT in approximately 50 h. Importantly, the derived HI mass is predicted to be relatively insensitive to systematic uncertainties in the lensing model, and should be constrained within a factor of ${\sim }2.5$ for a 95 per cent confidence interval.

Molecular Simulation of Argon Adsorption and Diffusion in a Microporous Carbon with Poroelastic Couplings.

Neglected for a long time in molecular simulations of fluid adsorption and transport in microporous carbons, adsorption-induced deformations of the matrix have recently been shown to have important effects on both sorption isotherms and diffusion coefficients. Here we investigate in detail the behavior of a recently proposed 3D-connected mature kerogen model, as a generic model of aromatic microporous carbon with atomic H/C ∼ 0.5, in both chemical and mechanical equilibrium with argon at 243 K over an extended pressure range. We show that under these conditions the material exhibits some viscoelasticity, and simulations of hundreds of nanoseconds are required to accurately determine the equilibrium volumes and sorption loadings. We also show that neglecting matrix internal deformations and swelling can lead to underestimations of the loading by up to 19% (swelling only) and 28% (swelling and internal deformations). The volume of the matrix is shown to increase up to about 8% at the largest pressure considered (210 MPa), which induces an increase of about 33% of both pore volume and specific surface area via the creation of additional pores, yet does not significantly change the normalized pore size distribution. Volume swelling is also rationalized by using a well-known linearized microporomechanical model. Finally, we show that self-diffusivity decreases with applied pressure, following an almost perfectly linear evolution with the free volume. Quantitatively, neglecting swelling and internal deformations tends to reduce the computed self-diffusivities.

Modeling Environmental Fate, Transport, and Transformation of Pesticides: First-Order Kinetic Models for Regional and Global Applications

Predicting pesticide residue masses in environments requires time- and cost-efficient fate models, particularly for high-throughput simulations of hundreds of active ingredients registered for use in agriculture. Due to the adaptability of first-order kinetics-based models for simulating the fate of pesticides in environments of varying scales, we conduct a review of these models in the present investigation. We discuss the application of first-order kinetics-based fate models in different types of compartments, such as environmental media, plant tissues, and animal bodies, and at different levels, such as the product-oriented life cycle impact assessment and the chemical-oriented health risk assessment. In addition, the first-order kinetics-based rate constants of pesticides provide process- and scenario-specific information on the fate, transport, and transformation of pesticides, which is essential for predicting pesticide residue masses in different environmental compartments. By varying the level of model complexity and site-specific rate constants of pesticides, the first-order kinetics-based fate models can be used as either comparable or absolute tools for conducting the life cycle impact assessment or the health risk assessment of pesticides, respectively. Bioconcentration, bioaccumulation, and biomagnification of pesticides may be evaluated with the aid of an inventory database of rate constants based on first-order kinetics in future research. We suggest incorporating non-first-order kinetic processes into the first-order kinetics-based model to advance risk assessment, as well as approximating non-first-order kinetic processes using first-order kinetics to facilitate life cycle impact or screening-level risk assessments.

Normalized Nonlinear Semiempirical MOST Model Used in Monolithic RF Class A-to-C PAs

This paper presents a simple but accurate normalized nonlinear large-signal semiempirical MOS transistor model to be used in monolithic RF Class A-to-C PAs. MOS transistor characteristics, saved in lookup tables, are extracted for different PVT corners, allowing the study of the PA performance spread. Model accuracy is ratified by the excellent matching obtained when comparing data algebraically calculated with electrical simulations of hundreds of PAs, and with the measurement data of a fabricated 2.4 GHz PA.

Analysis of two partially-saturated-cell methods for lattice Boltzmann simulation of granular suspension rheology

The lattice Boltzmann method (LBM) has been widely used to simulate fluid–solid flows with various approaches to couple the two phases. We study the partially-saturated-cell (PSC) approach proposed by Nobel and Torcyznski [27], which modifies the LB equation by an additional solid collision term weighted by the lattice solid fraction. We analyse two different PSC schemes with regard to its capability of accurately computing the hydrodynamic stresslet, which is essential to computing the stress, hence the rheology of suspensions of granular particles. Through simulations of single and pair particles in a simple shear flow field, we show that a commonly used solid collision term based on non-equilibrium bounce-back fails to correctly capture the stresslet, although can result in a numerically accurate hydrodynamic torque, when compared to the analytical solutions. In contrast, a model using superposition, which has neither hitherto been analysed nor extensively applied, is demonstrated to be able to accurately calculate both the stresslet and the torque. We finally highlight the importance of using the correct model when simulating suspension rheology, showing the viscosity obtained in simulations of hundreds of mono-disperse particles at various solid fractions sheared homogeneously using the Lees-Edwards boundary condition.

The volumetric rate of normal type Ia supernovae in the local Universe discovered by the Palomar Transient Factory

Abstract We present the volumetric rate of normal type Ia supernovae (SNe Ia) discovered by the Palomar Transient Factory (PTF). Using strict data-quality cuts, and considering only periods when the PTF maintained a regular cadence, PTF discovered 90 SNe Ia at z ≤ 0.09 in a well-controlled sample over three years of operation (2010–2012). We use this to calculate the volumetric rate of SN Ia events by comparing this sample to simulations of hundreds of millions of SN Ia light curves produced in statistically representative realizations of the PTF survey. This quantifies the recovery efficiency of each PTF SN Ia event, and thus the relative weighting of each event. From this, the volumetric SN Ia rate was found to be $r_\mathrm{ v}=2.43\pm 0.29\, \text{(stat)}_{-0.19}^{+0.33}\text{(sys)}\times 10^{-5}\, \rm{SNe\,yr}^{-1}\, \text{Mpc}^{-3}\, h_{70}^{3}$. This represents the most precise local measurement of the SN Ia rate. We fit a simple SN Ia delay-time distribution model, ∝ t−β, to our PTF rate measurement combined with a literature sample of rate measurements from surveys at higher redshifts. We find β ∼ 1, consistent with a progenitor channel governed by the gravitational inspiral of binary white dwarfs.

Conformation Dependence of Diphenylalanine Self-Assembly Structures and Dynamics: Insights from Hybrid-Resolution Simulations.

The molecular design of peptide-assembled nanostructures relies on extensive knowledge pertaining to the relationship between conformational features of peptide constituents and their behavior regarding self-assembly, and characterizing the conformational details of peptides during their self-assembly is experimentally challenging. Here, we demonstrate that a hybrid-resolution modeling method can be employed to investigate the role that conformation plays during the assembly of terminally capped diphenylalanines (FF) through microsecond simulations of hundreds or thousands of peptides. Our simulations discovered tubular or vesicular nanostructures that were consistent with experimental observation while reproducing critical self-assembly concentration and secondary structure contents in the assemblies that were measured in our experiments. The atomic details provided by our method allowed us to uncover diverse FF conformations and conformation dependence of assembled nanostructures. We found that the assembled morphologies and the molecular packing of FFs in the observed assemblies are linked closely with side-chain angle and peptide bond orientation, respectively. Of various conformations accessible to soluble FFs, only a select few are compatible with the assembled morphologies in water. A conformation resembling a FF crystal, in particular, became predominant due to its ability to permit highly ordered and energetically favorable FF packing in aqueous assemblies. Strikingly, several conformations incompatible with the assemblies arose transiently as intermediates, facilitating key steps of the assembly process. The molecular rationale behind the role of these intermediate conformations were further explained. Collectively, the structural details reported here advance the understanding of the FF self-assembly mechanism, and our method shows promise for studying peptide-assembled nanostructures and their rational design.

Combined Lattice–Boltzmann and rigid-body method for simulations of shear-thickening dense suspensions of hard particles

We present a high-fidelity simulation model for dense suspensions of spherical and non-spherical particles suspended in a Lattice–Boltzmann Method (LBM) based fluid. The non-spherical particles are composed of an arbitrary number of overlapping spheres of different sizes and arbitrary relative positions in the particle reference frame which stay fixed during the simulation. This approach allows to approximate a wide range of rigid particle shapes. Fluid Structure Interactions (FSI) are realized using a hybrid of immersed-boundary methods and bounce-back schemes, that employs coupling coefficients dependent upon particle overlap with the fluid lattice, resulting in smooth hydrodynamic interactions when particles move over the lattice. Numerical lubrication breakdown is overcome by applying appropriate corrections for small inter-particle gaps and hydrodynamic interactions are resolved down to scales much smaller than the LBM lattice spacing. For improved numerical stability in the limit of stiff particle-particle interactions, a generalized-α method together with a dynamically refined time-step is used for rigid body dynamics. An unbounded shear flow with large shear rates is realized by splitting the computational domain into multiple co-moving reference frames coupled through Galilean transformations of both fluid and particle phase. For fast simulations of hundreds of particles over physical times-spans of seconds, the LBM sub-model and FSI computations are accelerated on GPUs and MPI/OpenMP are used to parallelize the computation over networked/shared-memory resources. All these innovations together lead to a very powerful simulation environment for sheared dense suspensions, facilitating study of rheology close to the jamming limit. In this paper we present benchmark results and simulations of continuous and discontinuous shear-thickening of dense polydisperse frictional suspensions, demonstrating the accuracy and predictive power of the model over a large range of volume fractions of suspended particles and a large range of shear rates.

Thermodynamics, morphology, and kinetics of early-stage self-assembly of π-conjugated oligopeptides

Synthetic oligopeptides containing -conjugated cores self-assemble novel materials with attractive electronic and photophysical properties. All-atom, explicit solvent molecular dynamics simulations of Asp-Phe-Ala-Gly-OPV3-Gly-Ala-Phe-Asp peptides were used to parameterise an implicit solvent model to simulate early-stage self-assembly. Under low-pH conditions, peptides assemble into -sheet-like stacks with strongly favorable monomer association free energies of . Aggregation at high-pH produces disordered aggregates destabilised by Coulombic repulsion between negatively charged Asp termini (). In simulations of hundreds of monomers over 70 ns we observe the spontaneous formation of up to undecameric aggregates under low-pH conditions. Modeling assembly as a continuous-time Markov process, we infer transition rates between different aggregate sizes and microsecond relaxation times for early-stage assembly. Our data suggests a hierarchical model of assembly in which peptides coalesce into small clusters over tens of nanoseconds followed by structural ripening and diffusion limited aggregation on longer time scales. This work provides new molecular-level understanding of early-stage assembly, and a means to study the impact of peptide sequence and aromatic core chemistry upon the thermodynamics, assembly kinetics, and morphology of the supramolecular aggregates.

Many-body microhydrodynamics of colloidal particles with active boundary layers

Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.

Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis

The simplest way to describe the influence of the relative diffusion of the reactants on the time course of bimolecular reactions is to modify or renormalize the phenomenological rate constants that enter into the rate equations of conventional chemical kinetics. However, for macromolecules with multiple inequivalent reactive sites, this is no longer sufficient, even in the low concentration limit. The physical reason is that an enzyme (or a ligand) that has just modified (or dissociated from) one site can bind to a neighboring site rather than diffuse away. This process is not described by the conventional chemical kinetics, which is only valid in the limit that diffusion is fast compared with reaction. Using an exactly solvable many-particle reaction-diffusion model, we show that the influence of diffusion on the kinetics of multisite binding and catalysis can be accounted for by not only scaling the rates, but also by introducing new connections into the kinetic scheme. The rate constants that describe these new transitions or reaction channels turn out to have a transparent physical interpretation: The chemical rates are scaled by the appropriate probabilities that a pair of reactants, which are initially in contact, bind rather than diffuse apart. The theory is illustrated by application to phosphorylation of a multisite substrate.

Performance Optimal Online DVFS and Task Migration Techniques for Thermally Constrained Multi-Core Processors

Extracting high performance from multi-core processors requires increased use of thermal management techniques. In contrast to offline thermal management techniques, online techniques are capable of sensing changes in the workload distribution and setting the processor controls accordingly. Hence, online solutions are more accurate and are able to extract higher performance than the offline techniques. This paper presents performance optimal online thermal management techniques for multicore processors. The techniques include dynamic voltage and frequency scaling and task-to-core allocation or task migration. The problem formulation includes accurate power and thermal models, as well as leakage dependence on temperature. This paper provides a theoretical basis for deriving the optimal policies and computationally efficient implementations. The effectiveness of our DVFS and task-to-core allocation techniques are demonstrated by numerical simulations. The proposed task-to-core allocation method showed a 20.2% improvement in performance over a power-based thread migration approach. The techniques have been incorporated in a thermal-aware architectural-level simulator called MAGMA that allows for design space exploration, offline, and online dynamic thermal management. The simulator is capable of handling simulations of hundreds of cores within reasonable time.

Simulated extreme value fatigue sensitivity to inclusions and pores in martensitic gear steels

The objective of this work is to model the sensitivity of high cycle fatigue resistance of secondary hardening martensitic gear steels to variability in extrinsic inhomogeneities such as primary inclusions, and pores, coupled with intrinsic microstructure variability. A simplified approach is presented to quantify the variability in the driving force for fatigue crack formation in the matrix at non-metallic inclusions and pores in lath martensitic gear steels using a three-dimensional crystal plasticity constitutive model. The utility of a simulation-based strategy for exploring sensitivity of minimum fatigue lifetime (low probability of failure) to microstructure lies in its inherent capability to consider parametric simulations of hundreds of inclusions and microstructures in contrast to limited numbers of physical experiments. Experiments are used to calibrate the polycrystalline cyclic stress–strain response and mean (50% probability) fatigue crack formation life. Several remote loading conditions are considered in the high cycle fatigue (HCF) regime relevant to typical gear applications. Idealized inhomogenieties (spherical) in the form of hard (Al 2O 3), soft inclusions (La 2O 2S), and pores are systematically investigated in this parametric computational study. Relations between remote loading conditions and local plasticity are discussed as a function of stress amplitude and microstructure. The maximum plastic shear strain range is used in the modified form of Fatemi–Socie parameter evaluated at the grain scale as a measure of the driving force for fatigue crack formation (nucleation and early growth to lengths on the order of several times the average grain size). Multiple realizations of the polycrystal microstructure are considered to obtain a statistical distribution of this fatigue indicator parameter (FIP). The results are used to construct an extreme value Gumbel distribution of the FIPs for the selected microstructures. Subsequently, a computational micromechanics based minimum life estimate that corresponds to 1% fatigue crack formation probability is calculated.

High order resolution of the Maxwell–Fokker–Planck–Landau model intended for ICF applications

A high order, deterministic direct numerical method is proposed for the non-relativistic 2Dx×3Dv Vlasov–Maxwell system, coupled with Fokker–Planck–Landau collision operators. The magnetic field is perpendicular to the 2Dx plane surface of computation, whereas the electric fields occur in this plane. Such a system is devoted to modelling of electron transport and energy deposition in the general frame of Inertial Confinement Fusion applications. It is able to describe the kinetics of the plasma electrons in the nonlocal equilibrium regime, and permits to consider a large anisotropy degree of the distribution function. We develop specific methods and approaches for validation, that might be used in other fields where couplings between equations, multiscale physics, and high dimensionality are involved. Fast algorithms are employed, which makes this direct approach computationally affordable for simulations of hundreds of collisional times.

Analyzing brain oscillations with EEG/fMRI fusion

Event Abstract Back to Event Analyzing brain oscillations with EEG/fMRI fusion P. Valdés-Sosa1* 1 Cuban Neuroscience Center, Cuba This presentation reviews progress and challenges in analyzing brain oscillations with EEG/fMRI fusion, the principled combination of information from both recording modalities to achieve images with simultaneously high spatial and temporal resolution. Fusion methods may be either data driven or model driven. At a data driven level, mapping the covariation between EEG alpha power and BOLD, or between primary current density and net metabolic demand, show positive relations between frontal cortices and thalamus and negative ones for the occipital region. A simple heuristic model argues that these findings may be due to changes in synchronization of EEG generators. Model driven approaches to fusion repeatedly generate EEG/fMRI simulations and maximize their likelihood given the data by adjusting the parameters of neural mass oscillators coupled at each voxel to the balloon model (modeled by Random Differential equations RDE). However, the estimation procedure is critical in order to preserves the dynamical properties of the continuous time models. An approach with optimal properties is 1) Integration of RDE by local linearization (assuming the Jacobian of the system locally constant in time; 2) Using innovations obtained by Kalman filtering to evaluate the likelihood. This LL-innovation method has been already applied to models with a modest number of voxels. More realistically sized models involve integrating large sets of RDE and therefore depend critically on algorithmic advances. Simulations of hundreds of voxels can be based on Krylov subspace approximations to the required matrix exponential of the Jacobian. Even larger models of tens of thousands of voxels may be addressed by decoupling connectivity/delay parameters to form a RDE-delay algebraic system which my may be solved semi-analytically. Both types of methods produce simulations in good concordance with observations and the heuristic model. A remaining obstacle is the filtering step in these large models which we discuss may be tackled either by ensemble or variational approach which may be extended to Bayesian estimation. Conference: 10th International Conference on Cognitive Neuroscience, Bodrum, Türkiye, 1 Sep - 5 Sep, 2008. Presentation Type: Oral Presentation Topic: Symposium 14: Multimodal Studies of Oscillations Citation: Valdés-Sosa P (2008). Analyzing brain oscillations with EEG/fMRI fusion. Conference Abstract: 10th International Conference on Cognitive Neuroscience. doi: 10.3389/conf.neuro.09.2009.01.070 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 01 Dec 2008; Published Online: 01 Dec 2008. * Correspondence: P. Valdés-Sosa, Cuban Neuroscience Center, Havana, Cuba, pedro.valdes.sosa@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers P. Valdés-Sosa Google P. Valdés-Sosa Google Scholar P. Valdés-Sosa PubMed P. Valdés-Sosa Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

On the Orientation of a Designed Transmembrane Peptide: Toward the Right Tilt Angle?

The orientation of the transmembrane peptide WALP23 under small hydrophobic mismatch has been assessed through long-time-scale molecular dynamics simulations of hundreds of nanoseconds. Each simulation gives systematically large tilt angles (>30 degrees). In addition, the peptide visits various azimuthal rotations that mostly depend on the initial conditions and converge very slowly. In contrast, small tilt angles as well as a well-defined azimuthal rotation were suggested by recent solid-state 2H NMR studies on the same system. To optimally compare our simulations with NMR data, we concatenated the different trajectories in order to increase the sampling. The agreement with 2H NMR quadrupolar splittings is spectacularly better when these latter are back-calculated from the concatenated trajectory than from any individual simulation. From these ensembled-average quadrupolar splittings, we then applied the GALA method as described by Strandberg et al. (Biophys J. 2004, 86, 3709-3721), which basically derives the peptide orientation (tilt and azimuth) from the splittings. We find small tilt angles (6.5 degrees), whereas the real observed tilt in the concatenated trajectory presents a higher value (33.5 degrees). We thus propose that the small tilt angles estimated by the GALA method are the result of averaging effects, provided that the peptide visits many states of different azimuthal rotations. We discuss how to improve the method and suggest some other experiments to confirm this hypothesis. This work also highlights the need to run several and rather long trajectories in order to predict the peptide orientation from computer simulations.

Autonomous boids

AbstractThe classical work of bird‐like objects of Reynolds simulates polarized motion of groups of oriented particles, bird‐like objects, or simply boids. To do this, three steering vectors are introduced. Cohesion is the tendency of boids to stay in the center of the flock, alignment smoothes their velocities to similar values, and separation helps them to avoid mutual collisions. If no impetus is introduced the boids wander somewhat randomly so an external leading force is necessary for the correct flock behavior. As can be observed during the bird flocking in the fall, birds sometimes move in a way that is not captured by the above described framework. Some of the birds, typically the ones on the edge of the flock, suddenly shoot‐off. The flock then pursues this leader. In the original work by Reynolds the cohesion and separation are two complementary steers. We introduce a complementary force to the alignment that we call the change of leadership. This steer defines the chance of the boid to become a leader and try to escape. The leadership is derived from the boid position and the flock eccentricity. If a boid is on the front edge of the flock it has a higher chance to escape. Escaping from the flock is simulated as a sequence of velocity increases that are added to the current velocity of the boid. The entire system is easy to implement, is efficient, and runs simulations of hundreds of boids on a standard computer at 30 frames per second. Our system is aimed to real‐time simulations and has the potential to be used in games, crowd simulations, etc. Copyright © 2006 John Wiley & Sons, Ltd.

A Model for Representing the Dynamics of a System of Synfire Chains

Competitive synchronization among synfire chains may model the dynamics of binding and compositionality. Typically, such models require simulations of hundreds of thousands of neurons. Here we show that the behavior of such large systems can be numerically analyzed by representing the neuronal activity in a synfire chain as a wave. The position and velocity of waves are the only parameters needed to represent the neural activity within a synfire chain. With this wave model we describe how waves are generated, decay, interact within a single chain and among chains. The behavior of the wave model is compared to the behavior of detailed simulations of synfire chains with no qualitative difference. We show that interacting waves tend to become locked to each other (wave synchronization). Finally we prove that: (1) Within a system of many synfire chains with symmetric interchain connections, as long as waves do not fade away or become fully synchronized, the total synchrony among waves can only increase (or stay constant), but never decrease. (2) A wave that increases its speed during the synchronization process becomes more stable.

The Factor Analytic Approach to Simultaneous Inference in the General Linear Model

Abstract Consider the general linear model (GLM) Y = Xβ + e. Suppose Θ1,…, Θk, a subset of the β's, are of interest; Θ1,…, Θk may be treatment contrasts in an ANOVA setting or regression coefficients in a response surface setting. Existing simultaneous confidence intervals for Θ1,…, Θk are relatively conservative or, in the case of the MEANS option in PROC GLM of SAS, possibly misleading. The difficulty is with the multidimensionality of the integration required to compute exact coverage probability when X does not follow a nice textbook design. Noting that such exact coverage probabilities can be computed if the correlation matrix R of the estimators of Θ1, …, Θk has a one-factor structure in the factor analytic sense, it is proposed that approximate simultaneous confidence intervals be computed by approximating R with the closest one-factor structure correlation matrix. Computer simulations of hundreds of randomly generated designs in the settings of regression, analysis of covariance, and unbalanced bl...