Model-independent Characterization Research Articles

Generalized model-independent characterization of strong gravitational lenses VIII. Automated multiband feature detection to constrain local lens properties

ABSTRACT As established in previous papers of this series, observables in highly distorted and magnified multiple images caused by the strong gravitational lensing effect can be used to constrain the distorting properties of the gravitational lens at the image positions. If the background source is extended and contains substructure, like star forming regions, which is resolved in multiple images, all substructure that can be matched across a minimum of three multiple images can be used to infer the local distorting properties of the lens. In this work, we replace the manual feature selection by an automated feature extraction based on SExtractor for Python and show its superior performance. Despite its aimed development to improve our lens reconstruction, it can be employed in any other approach, as well. Valuable insights on the definition of an ‘image position’ in the presence of noise are gained from our calibration tests. Applying it to observations of a five-image configuration in galaxy cluster CL0024 and the triple-image configuration containing Hamilton’s object, we determine local lens properties for multiple wavebands separately. Within current confidence bounds, all of them are consistent with each other, corroborating the wavelength-independence of strong lensing and offering a tool to detect deviations caused by micro-lensing and dust in further examples.

Raman spectroscopy of thermally perturbed carbon fibers: Discriminating spectral responses of modulus classes and defect types

The mechanical strength properties of carbon fibers are generally thought to be correlated with the presence of underlying atomic-level defects. These defects serve to break the underlying translational symmetry of the graphitic or graphene subunits of the fiber construction, resulting in the emergence of new Raman-active spectral features. However, historical attempts to classify the precise origin of defect contributions to the Raman spectra have been challenging because of indistinct and overlapping features in the carbon fiber Raman spectra. Further, while substantial research exists on high-temperature exposure in inert atmospheres for carbon fiber composites, comparatively less addresses microscale behaviors and Raman spectral alterations to monofilament carbon fibers exposed to high-temperature atmospheric environments. Here, we report Raman spectral responses of nine commercially available high-performance, polyacrylonitrile-based carbon fibers exposed to various atmospheric heat treatments. We introduce a model-independent characterization method, the integrated absolute difference, to quantify the spectral responses to heat treatment of different fiber modulus classes. We combine this new method with a newly reported strategy to standardize spectral fitting for carbon fibers. With this approach, we show that atomic-scale defects in the underlying fiber microstructure manifest in measurably distinct manners and have distinct responses to thermal perturbation. These combined approaches may lay the foundation for disentangling contributions from specific defects in the Raman spectra of carbon fibers.

Entropic characterization of the coil-stretch transition of polymers in random flows.

Polymer molecules in a flow undergo a coil-stretch phase transition on an increase of the velocity gradients. Model-independent identification and characterization of the transition in a random flow has been lacking so far. Here we suggest to use the entropy of the extension statistics as a proper measure due to strong fluctuations around the transition. We measure experimentally the entropy as a function of the local Weisenberg number and show that it has a maximum, which identifies and quantifies the transition. We compare the new approach with the traditional one based on the theory using either linear Oldroyd-B or nonlinear finite extensible nonlinear elastic polymer models.

Effective field theories as a novel probe of fine-tuning of cosmic inflation

The leading account of several salient observable features of our universe today is provided by the theory of cosmic inflation. But an important and thus far intractable question is whether inflation is generic, or whether it is finely tuned—requiring very precisely specified initial conditions. In this paper I argue that a recent, model-independent characterization of inflation—that treats inflation as an effective field theory (EFT)—promises to address this question in a thoroughly modern and significantly more comprehensive way than in the existing literature.To motivate and provide context for this claim, I distill three core problems with the theory of inflation, which I dub the permissiveness problem, the initial conditions problem, and the multiverse problem. I argue that the initial conditions problem lies within the scope of EFTs of inflation as they are currently conceived, whereas the other two problems remain largely intractable: their solution must await a more complete description of the very early universe. I highlight recent work that addresses the initial conditions problem within the context of a dynamical systems analysis of a specific (state-of-the-art) EFT of inflation, and conclude with a roadmap for how such work might be extended to realize the promise claimed above.

Generalized model-independent characterization of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe

ABSTRACT We determine the cosmic expansion rate from supernovae of type Ia to set up a data-based distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrization of a Friedmann cosmological model. The scale, determined by the Hubble constant H0, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio D is determined from the Pantheon sample. Inserting D and its uncertainty into the lensing equations for given H0, especially the time-delay equation between a pair of multiple images, allows to determine lens properties, especially differences in the lensing potential (Δϕ), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximum-likelihood weights for the basis functions by a globally optimal χ2-parameter estimation, and derive confidence bounds by Monte Carlo simulations. For typical strong lensing configurations between z = 0.5 and 1.0, Δϕ can be determined with a relative imprecision of 1.7 per cent, assuming imprecisions of the time delay and the redshift of the lens on the order of 1 per cent. With only a small, tolerable loss in precision, the model-independent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine D in favour of a data-based distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for z ≤ 2.3 that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.

Generalised model-independent characterisation of strong gravitational lenses – VI. The origin of the formalism intrinsic degeneracies and their influence on H0

We give a physical interpretation of the formalism intrinsic degeneracies of the gravitational lensing formalism that we derived on a mathematical basis in part IV of this series. We find that all degeneracies occur due to the partition of the mass density along the line of sight. Usually, it is partitioned into a background (cosmic) density and a foreground deflecting object. The latter can be further partitioned into a main deflecting object and perturbers. Weak deflecting objects along the line of sight are also added, either to the deflecting object or as a correction of the angular diameter distances, perturbing the cosmological background density. A priori, this is an arbitrary choice of reference frame and partition. They can be redefined without changing the lensing observables which are sensitive to the integrated deflecting mass density along the entire line of sight. Reformulating the time delay equation such that this interpretation of the degeneracies becomes easily visible, we note that the source can be eliminated from this formulation, which simplifies reconstructions of the deflecting mass distribution or the inference of the Hubble constant, $H_0$. Subsequently, we list necessary conditions to break the formalism intrinsic degeneracies and discuss ways to break them by model choices or including non-lensing observables like velocity dispersions along the line of sight with their advantages and disadvantages. We conclude with a systematic summary of all formalism intrinsic degeneracies and possibilities to break them.

Wavelet-based techniques for the gamma-ray sky

We demonstrate how the image analysis technique of wavelet decomposition can be applied to the gamma-ray sky to separate emission on different angular scales. New structures on scales that differ from the scales of the conventional astrophysical foreground and background uncertainties can be robustly extracted, allowing a model-independent characterization with no presumption of exact signal morphology. As a test case, we generate mock gamma-ray data to demonstrate our ability to extract extended signals without assuming a fixed spatial template. For some point source luminosity functions, our technique also allows us to differentiate a diffuse signal in gamma-rays from dark matter annihilation and extended gamma-ray point source populations in a data-driven way.

FROM COMPUTING TO INTERACTION: ON THE EXPRESSIVENESS OF ASYNCHRONOUS PI-CALCULUS

In line with the framework of Theory of Interaction proposed by Yuxi Fu, we formalize the asynchronous theory in model independent way. Borrowing the idea from Church-Turing Thesis, we introduce ℂ-calculus as a minimal interaction model. We give model independent characterization for asynchronous bisimulation equivalence which is generalized to subbisimilarity used as the criteria for Interaction Completeness of interaction models. We present an encoding from ℂ-calculus to asynchronous π-calculus and prove that it satisfies the subbisimilarity statements.

Model-independent Characterization of Charge Diffusion in Thick Fully Depleted CCDs

ABSTRACTWe present a new method to measure charge diffusion in charge-coupled devices (CCDs). The method is based on a statistical characterization of the shapes of charge clouds produced by low-energy X-rays using known properties of the two-dimensional Gaussian point-spread function (PSF). The algorithm produces reliable upper and lower bounds on the size of the PSF for photons converting near the entrance window of a device. It is optimally suited to the case of thick back-illuminated CCDs where the X-ray absorption length is smaller than the silicon thickness and the diffusion scale is of the same order as the pixel size. The only assumptions are that the charge cloud width is a monotonically increasing function of distance from the conversion point to the buried channel, and that the conversion probability is peaked at the surface. Otherwise, no physical models of carrier transport or knowledge of the electric field profile in the CCD are needed. In suboptimal conditions, the upper bound increases and the lower bound is unaffected, so confidence in the correctness of results is retained. The new method has been benchmarked against Monte Carlo simulations and tested on X-ray images measured on thick high-resistivity prototype CCDs for the Large Synoptic Survey Telescope. In Monte Carlo simulations of noiseless images having the optimal diffusion scale, the upper bound approximated the true PSF within 5%, increasing to 10% in simulations with added noise. Even with severely undersampled or truncated PSFs, the method brackets the true value to within 25%. Our method is accurate and computationally efficient and offers a fast and simple experimental setup.

A Bode Plot Characterization of All Stabilizing Controllers

In this technical note, we consider continuous-time control systems and present a new characterization of the Nyquist criterion in terms of Bode plots of the plant and the controller. This gives a nonparametric, and model independent characterization of arbitrary order stabilizing controllers. The result shows that the frequency response of any stabilizing controller must satisfy constraints on its magnitude, phase, and rate of change of phase at certain frequencies that are imposed by the frequency response of the inverse plant.

Elongation dynamics shape bursty transcription and translation

Cells in isogenic populations may differ substantially in their molecular make up because of the stochastic nature of molecular processes. Stochastic bursts in process activity have a great potential for generating molecular noise. They are characterized by (short) periods of high process activity followed by (long) periods of process silence causing different cells to experience activity periods varying in size, duration, and timing. We present an analytically solvable model of bursts in molecular networks, originally developed for the analysis of telecommunication networks. We define general measures for model-independent characterization of bursts (burst size, significance, and duration) from stochastic time series. Inspired by the discovery of bursts in mRNA and protein production by others, we use those indices to investigate the role of stochastic motion of motor proteins along biopolymer chains in determining burst properties. Collisions between neighboring motor proteins can attenuate bursts introduced at the initiation site on the chain. Pausing of motor proteins can give rise to bursts. We investigate how these effects are modulated by the length of the biopolymer chain and the kinetic properties of motion. We discuss the consequences of those results for transcription and translation.

A Nearly Model-Independent Characterization of Dark Energy Properties as a Function of Redshift

Understanding the acceleration of the universe and its cause is one of the key problems in physics and cosmology today, and is best studied using a variety of mutually complementary approaches. Daly and Djorgovski (2003, 2004) proposed a model independent approach to determine the expansion and acceleration history of the universe and a number of important physical parameters of the dark energy as functions of redshift directly from the data. Here, we apply the method to explicitly determine the first and second derivatives of the coordinate distance with respect to redshift, y ′ and y ″ , and combine them to solve for the kinetic and potential energy density of the dark energy as functions of redshift, K ( z ) and V ( z ) . A data set of 228 supernova and 20 radio galaxy measurements with redshifts from zero to 1.79 is used for this study. Values of y ′ and y ″ are combined to study the dimensionless acceleration rate of the universe as a function of redshift, q ( z ) . The only assumptions underlying our determination of q ( z ) are that the universe is described by a Robertson-Walker (RW) metric and is spatially flat. We find that the universe is accelerating today, and was decelerating in the recent past. The transition from acceleration to deceleration occurs at a redshift of about z T = 0.42 ± 0.06 0.08 . Values of y ′ and y ″ are combined to determine K ( z ) and V ( z ) . These are shown to be consistent with the values expected in a standard Lambda Cold Dark Matter (LCDM) model.

1.65 $\mathsf{\mu m}$ (H-band) surface photometry of galaxies

As a result of a systematic NIR H-band (m) imaging survey of normal galaxies in the local universe that includes objects both in the Virgo cluster and in the “Great Wall” (including A1367, A1656 as well as the “isolated” population in the bridge between the two clusters), we are able to measure in a highly homogeneous way photometric and structural properties for a sample of 1143 galaxies. We base our analysis on a quantitative structural parameter, the concentration index C31 (defined as the ratio between the radii that enclose 75% and 25% of the total luminosity), instead of relying on the galaxies' morphological classification. The C31 parameter provides a model independent, quantitative and continuous characterization of the light distribution within galaxies, and it is thus to be preferred to either the Hubble type or a parameter like the bulge-to-disk or bulge-to-total light ratio. Low C31 objects are typically found among disk galaxies, while high C31 describes bulge-dominated systems. We confirm our previous claim that C31 correlates strongly and non-linearly with the galaxy total luminosity. values are found only at (giant ellipticals mixed with early-type spirals), while at galaxies have (dwarf Irregulars mixed with ellipticals). At high luminosity, low C31 are allowed (bulge-less giant Scs). Thus C31 and the total luminosity are not sufficient to fully characterize the family of galaxies. However we find that galaxies can be completely described by three parameters, namely: a scale parameter (the H-band luminosity), a shape parameter (the concentration index C31) and a colour parameter (e.g. the colour). At low luminosity dEs and dIs, having similar C31, are colour-discriminated, while at very high luminosity different C31 discriminate S0s from Scs, otherwise undistinguishable on the basis of their colour. A single, monotonic relation exists between luminosity and in the H-band, as opposed to the two separate regimes that are generally observed in the B-band. As NIR luminosity traces quite accurately the galaxy mass distribution, this relation re-enforces the indication in favour of a scale-dependent mass collapse mechanism which produces higher surface-brightness and more centrally peaked galaxies with increasing mass. However, the presence of high-luminosity low-C31 galaxies hints at other machanisms and physical properties (such as angular momentum) playing an important role in galaxy formation.

How much of physics isjustcomputation?

We explore an emergent interpretation of the action integral and the lagrangian in physics, and discuss its connection with the concept of ‘amount of computation’. We give an abstract definition of action, and argue (1) that it provides a general, model-independent characterization of ‘amount of computation’; and that (2) the action of physics is a special case of this general action. Much as entropy quantifies the lack of information one has about thestateof a system, action quantifies the lack of information about the system'slaw—or, equivalently, itsbehavior. In this approach, action is to dynamics what entropy is to statics.

Root Mean Square Anisotropy in theCOBEDMR Four‐Year Sky Maps

The sky rms is the simplest model-independent characterization of a cosmological anisotropy signal. We show that the rms temperature fluctuations determined from the COBE Differential Microwave Radiometer (DMR) 4 yr sky maps are frequency independent, consistent with the Planckian spectrum expected for the cosmic microwave background signal and therefore with the hypothesis that they are cosmological in origin. The typical rms amplitude is ~35 ± 2 μK at 7° and ~29 ± 1 μK at 10°. An analysis of the rms anisotropy determined from the data in both Galactic and ecliptic coordinates is used to determine the rms quadrupole normalization, Qrms-PS, for a scale-invariant Harrison-Zeldovich power-law model. Corrections are applied for small biases observed in the likelihood analysis. While there are variations depending on the data selection, all results are consistent with a Qrms-PS normalization of ~18 ± 2 μK. This is also shown to be true for a standard cold dark matter model of cosmological anisotropy. The difference in the normalization amplitudes derived when the quadrupole is either included or excluded from the analysis is attributable to contamination of the observed sky quadrupole by foreground Galactic emission.

Phenomenological analysis of the clotting curve

A model-independent (phenomenological) characterization of the clotting curve is proposed. Three parameters are used to encapsulate the main features of the increase in absorbance observed at 350 nm due to the reaction of thrombin with fibrinogen that leads to clot formation: (1) the maximum increase in absorbance per unit time, delta Am, at the inflection point of the clotting curve; (2) the time needed to reach the maximum increase in absorbance, tm; and (3) the clotting time, tc, obtained from extrapolation of the slope at tm to the zero absorbance baseline. Clotting curves at low fibrinogen concentrations (0.125 divided by 0.250 microM), well below the Km, where thrombin amidase activity is rate-limiting with respect to the subsequent aggregation process, have been measured under a wide variety of experimental conditions, (i.e., as a function of thrombin concentration, pH and temperature) in order to explore the basic response of each parameter to changes in solution conditions. Under all conditions examined in this study we have observed that tm and tc are linked through a linear relationship that appears to be an important invariant property of the clotting curve, regardless of experimental conditions. No such clear relationship exists between delta Am and tc, with tc being associated with several possible values of delta Am and vice versa, depending upon solution conditions. It is proposed that tc is strictly dependent on thrombin amidase activity, while delta Am reflects properties of the aggregation process leading to clot formation. The clotting time shows a pH and temperature dependence that closely resembles that of Km/Vm for synthetic amide substrates. Furthermore, tc changes linearly with either the inverse thrombin concentration and the concentration of competitive inhibitors of fibrinogen binding to thrombin, as expected for the ratio Km/Vm. We show how the analysis of clotting curves obtained at different thrombin and inhibitor concentrations yields a quantitative measure of KI that is in excellent agreement with the value determined independently from steady-state measurements of thrombin amidase activity.