Engineering topics

Tegmark, Max

Publications and source records attributed to Tegmark, Max.

8 records

DOE OSTI2021

Symbolic pregression: Discovering physical laws from distorted video

In this work, we present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled synthetic video (or, more generally, for discovering and modeling predictable features in time-series data). We first train an autoencoder that maps each video frame into a low-dimensional latent space where the laws of motion are as simple as possible, by minimizing a combination of nonlinearity, acceleration, and prediction error. Differential equations describing the motion are then discovered using Pareto-optimal symbolic regression. We find that our pre-regression (“pregression”) step is able to rediscover Cartesian coordinates of unlabeled moving objects even when the video is distorted by a generalized lens. Using intuition from multidimensional knot theory, we find that the pregression step is facilitated by first adding extra latent space dimensions to avoid topological problems during training and then removing these extra dimensions via principal component analysis. An inertial frame is autodiscovered by minimizing the combined equation complexity for multiple experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

What next-generation 21 cm power spectrum measurements can teach us about the epoch of reionization

A number of experiments are currently working toward a measurement of the 21 cm signal from the epoch of reionization (EoR). Whether or not these experiments deliver a detection of cosmological emission, their limited sensitivity will prevent them from providing detailed information about the astrophysics of reionization. In this work, we consider what types of measurements will be enabled by the next generation of larger 21 cm EoR telescopes. To calculate the type of constraints that will be possible with such arrays, we use simple models for the instrument, foreground emission, and the reionization history. We focus primarily on an instrument modeled after the ∼0.1 km{sup 2} collecting area Hydrogen Epoch of Reionization Array concept design and parameterize the uncertainties with regard to foreground emission by considering different limits to the recently described 'wedge' footprint in k space. Uncertainties in the reionization history are accounted for using a series of simulations that vary the ionizing efficiency and minimum virial temperature of the galaxies responsible for reionization, as well as the mean free path of ionizing photons through the intergalactic medium. Given various combinations of models, we consider the significance of the possible power spectrum detections, the ability to trace the power spectrum evolution versus redshift, the detectability of salient power spectrum features, and the achievable level of quantitative constraints on astrophysical parameters. Ultimately, we find that 0.1 km{sup 2} of collecting area is enough to ensure a very high significance (≳ 30σ) detection of the reionization power spectrum in even the most pessimistic scenarios. This sensitivity should allow for meaningful constraints on the reionization history and astrophysical parameters, especially if foreground subtraction techniques can be improved and successfully implemented.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

GALAXY CLUSTERING IN THE COMPLETED SDSS REDSHIFT SURVEY: THE DEPENDENCE ON COLOR AND LUMINOSITY

We measure the luminosity and color dependence of galaxy clustering in the largest-ever galaxy redshift survey, the main galaxy sample of the Sloan Digital Sky Survey Seventh Data Release. We focus on the projected correlation function w{sub p} (r{sub p}) of volume-limited samples, extracted from the parent sample of {approx}700,000 galaxies over 8000 deg{sup 2}, extending up to redshift of 0.25. We interpret our measurements using halo occupation distribution (HOD) modeling assuming a {Lambda}CDM cosmology (inflationary cold dark matter with a cosmological constant). The amplitude of w{sub p} (r{sub p}) grows slowly with luminosity for L < L{sub *} and increases sharply at higher luminosities, with a large-scale bias factor b(> L) x ({sigma}{sub 8}/0.8) = 1.06 + 0.21(L/L{sub *}){sup 1.12}, where L is the sample luminosity threshold. At fixed luminosity, redder galaxies exhibit a higher amplitude and steeper correlation function, a steady trend that runs through the 'blue cloud' and 'green valley' and continues across the 'red sequence'. The cross-correlation of red and blue galaxies is close to the geometric mean of their autocorrelations, dropping slightly below at r{sub p} < 1 h{sup -1} Mpc. The luminosity trends for the red and blue galaxy populations separately are strikingly different. Blue galaxies show a slow but steady increase of clustering strength with luminosity, with nearly constant shape of w{sub p} (r{sub p}). The large-scale clustering of red galaxies shows little luminosity dependence until a sharp increase at L > 4 L{sub *}, but the lowest luminosity red galaxies (0.04-0.25 L{sub *}) show very strong clustering on small scales (r{sub p} < 2 h{sup -1} Mpc). Most of the observed trends can be naturally understood within the {Lambda}CDM+HOD framework. The growth of w{sub p} (r{sub p}) for higher luminosity galaxies reflects an overall shift in the mass scale of their host dark matter halos, in particular an increase in the minimum host halo mass M{sub min}. The mass at which a halo has, on average, one satellite galaxy brighter than L is M{sub 1} {approx} 17 M{sub min}(L) over most of the luminosity range, with a smaller ratio above L{sub *}. The growth and steepening of w{sub p} (r{sub p}) for redder galaxies reflects the increasing fraction of galaxies that are satellite systems in high-mass halos instead of central systems in low-mass halos, a trend that is especially marked at low luminosities. Our extensive measurements, provided in tabular form, will allow detailed tests of theoretical models of galaxy formation, a firm grounding of semiempirical models of the galaxy population, and new constraints on cosmological parameters from combining real-space galaxy clustering with mass-sensitive statistics such as redshift-space distortions, cluster mass-to-light ratios, and galaxy-galaxy lensing.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

A method for 21 cm power spectrum estimation in the presence of foregrounds

The technique of 21 cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizing this promise will require the extraction of a cosmological power spectrum from beneath overwhelmingly large sources of foreground contamination. In this paper, we develop a unified matrix-based framework for foreground subtraction and power spectrum estimation, which allows us to quantify the errors and biases that arise in the power spectrum as a result of foreground subtraction. We find that existing line-of-sight foreground subtraction proposals can lead to substantial mode mixing as well as residual noise and foreground biases, whereas our proposed inverse-variance foreground subtraction eliminates noise and foreground biases, gives smaller error bars, and produces less correlated measurements of the power spectrum. We also numerically confirm the intuitive belief in the literature that 21 cm foreground subtraction is best done using frequency rather than angular information.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2011

Testing two-field inflation

We derive accurate semianalytic formulas for the power spectra from two-field inflation assuming an arbitrary potential and arbitrary noncanonical kinetic terms, and we use them both to build phenomenological intuition and to constrain classes of two-field models using WMAP data. Using covariant formalism, we first develop a framework for understanding the background field kinematics and introduce a ''slow-turn'' approximation. Next, we find covariant expressions for the evolution of the adiabatic/curvature and entropy/isocurvature modes, and we discuss how the evolution of modes can be inferred mostly from the background kinematics and the geometry of the field manifold. From these expressions, we derive semianalytic formulas for the curvature, isocurvature, and cross spectra, and the standard spectral observables, all to second order in the slow-roll and slow-turn approximations. In tandem, we show how our covariant formalism provides useful intuition into how the general features of the inflationary Lagrangian translate into distinct features in the observable power spectra. In particular, we find that key features of the power spectra can be directly read off from the nature of the roll path, the curve the field vector rolls along with respect to the two-dimensional field manifold. For example, models whose roll path makes a sharp turn around 60 e-foldings before the end of inflation tend to be ruled out because they produce stronger departures from scale invariance than are allowed by the latest CMB observations. Finally, we apply our formalism to confront four classes of two-field models with WMAP data, including doubly quadratic and quartic potentials and nonstandard kinetic terms, showing how whether a model is ruled out or not depends not only on certain features of the inflationary Lagrangian, but also on the initial conditions. Ultimately, for a two-field model to be consistent with observations, we show that it must possess the right balance of certain kinematical and dynamical behaviors, which we reduce to a set of functions that represent the main characteristics of any two-field model of inflation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1996

The Angular Power Spectrum of BATSE 3B Gamma-Ray Bursts

We compute the angular power spectrum C(sub l) from the BATSE 3B catalog of 1122 gamma-ray bursts and find no evidence for clustering on any scale. These constraints bridge the entire range from small scales (which probe source clustering and burst repetition) to the largest scales (which constrain possible anisotropics from the Galactic halo or from nearby cosmological large-scale structures). We develop an analysis technique that takes the angular position errors into account. For specific clustering or repetition models, strong upper limits can be obtained down to scales l approx. equal to 30, corresponding to a couple of degrees on the sky. The minimum-variance burst weighting that we employ is visualized graphically as an all-sky map in which each burst is smeared out by an amount corresponding to its position uncertainty. We also present separate bandpass-filtered sky maps for the quadrupole term and for the multipole ranges l = 3-10 and l = 11-30, so that the fluctuations on different angular scales can be inspected separately for visual features such as localized 'hot spots' or structures aligned with the Galactic plane. These filtered maps reveal no apparent deviations from isotropy.

Tegmark, Max↗

NASA NTRS1996

Improved Limits on Gamma-Ray Burst Repetition from BATSE

We tighten previous upper limits on gamma-ray burst repetition by analyzing the angular power spectrum of the BATSE 3B catalog of 1122 bursts. At 95% confidence, we find that no more than 2% of all observed bursts can be labeled as repeaters, even if no sources are observed to repeat more than once. If a fraction f of all observed bursts can be labeled as repeaters that are observed to burst upsilon times each, then all models with (upsilon - 1)f greater than or equal to 0.05 are ruled out at 99% confidence, as compared to the best previous 99% limit (upsilon - 1)f greater than or equal to 0.27. At 95% confidence, our new limit is (upsilon - 1)f greater than or equal to 0.02. Thus, even a cluster of six events from a single source would have caused excess power above that present in the 3B catalog. We conclude that the current BATSE data are consistent with no repetition of classical gamma-ray bursts and that any repeater model is severely constrained by the near-perfect isotropy of their angular distribution.

Tegmark, Max↗

NASA NTRS1996

Improved Limits on Gamma-Ray Burst Repetition from BATSE

We tighten previous upper limits on gamma-ray burst repetition by analyzing the angular power spectrum of the BATSE 3B catalog of 1122 bursts. At 95% confidence, we find that no more than 2% of all observed bursts can be labeled as repeaters, even if no sources are observed to repeat more than once. If a fraction f of all observed bursts can be labeled as repeaters that are observed to burst nu times each, then all models with (nu - 1)f greater than or equal to 0.05 are ruled out at 99% confidence, as compared to the best previous 99% limit (nu - 1)f greater than or equal to 0.27. At 95% confidence, our new limit is (nu - 1)f greater than or equal to 0.02. Thus, even a cluster of six events from a single source would have caused excess power above that present in the 3B catalog. We conclude that the current BATSE data are consistent with no repetition of classical gamma-ray bursts and that any repeater model is severely constrained by the near-perfect isotropy of their angular dis- tribution.

Tegmark, Max↗