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Equation-based and data-driven modeling: Open-source software current state and future directions

Here, a review of current trends in scientific computing reveals a broad shift to open-source and higher-level programming languages such as Python and growing career opportunities over the next decade. Open-source modeling tools accelerate innovation in equation-based and data-driven applications. Significant resources have been deployed to develop data-driven tools (PyTorch, TensorFlow, Scikit-learn) from tech companies that rely on machine learning services to meet business needs while keeping the foundational tools open. Open-source equation-based tools such as Pyomo, CasADi, Gekko, and JuMP are also gaining momentum according to user community and development pace metrics. Integration of data-driven and principles-based tools is emerging. New compute hardware, productivity software, and training resources have the potential to radically accelerate progress. However, long-term support mechanisms are still necessary to sustain the momentum and maintenance of critical foundational packages.

97 MATHEMATICS AND COMPUTING↗

Analysis of Oil and Gas Ethane and Methane Emissions in the Southcentral and Eastern United States Using Four Seasons of Continuous Aircraft Ethane Measurements

In the last decade, much work has been done to better understand methane (CH 4 ) emissions from the oil and gas (O&G) industry in the United States. Ethane (C 2 H 6 ), a gas that is co-emitted with thermogenic sources of CH 4 , is emitted in the US predominantly by the O&G sector. Here, in this study, we perform an inverse analysis on 200 h of atmospheric boundary layer C 2 H 6 measurements to estimate C 2 H 6 emissions from the US O&G sector. Measurements were collected from 2017 to 2019 as part of the Atmospheric Carbon and Transport (ACT) America aircraft campaign and encompass much of the central and eastern United States. We find that for the fall, winter, and spring campaigns, C 2 H 6 data consistently exceeds values that would be expected based on EPA O&G leak rate estimates by more than 50%. C 2 H 6 observations from the summer 2019 data set show significantly lower C 2 H 6 enhancements in the southcentral region that cannot be reconciled with data from the other three seasons, either due to complex meteorological conditions or a temporal shift in the emissions. Combining the fall, winter, and spring C 2 H 6 posterior emissions estimate to an inventory of O&G CH 4 emissions, we estimate that O&G CH 4 emissions are larger than EPA inventory values by 48%–76%. Uncertainties in the gas composition data limit the accuracy of using C 2 H 6 as a proxy for O&G CH 4 emissions. These limits could be resolved retroactively by increasing the availability of industry-collected gas composition data.

54 ENVIRONMENTAL SCIENCES↗

On the performance of Trellis coded modulation with octal phase shift keying over the TDRSS channel

As the National Aeronautics and Space Administration moves into the 21st century with programs like Space Station Freedom, a manned mission to Mars, and the new Landsat mission, transmission demands on the Tracking and Data Relay Satellite System (TDRSS) will very likely exceed the available bandwidth. The Manual Lujan, Jr. Center for Space Telemetering and Telecommunications Systems (CSTTS) at New Mexico State University (NMSU) is studying techniques for increasing the data rate capabilities of TDRSS. These techniques include the use of advanced bandwidth efficient modulation formats to increase the data rate that can be sustained in a TDRSS transponder and the use of lossless bandwidth compression of the data to be transmitted to lower the data rate required from the user spacecraft. Based upon current technology the most promising bandwidth efficient modulation technique is Trellis Coded Modulation (TCM) operating with Octal Phase shift Keying (8PSK). Trellis Coded Modulation coding with 8PSK carrier modulation has the capability to increase the data rate which can be transmitted through the TDRSS spacecraft by a factor of 2 to 2.5 times that available with todays coded QPSK systems with only a small penalty in link performance relative to the existing systems. However, before NASA can safely employ TCM coding it is necessary to prove that this complex format can perform on the real TDRSS link as it does in labs and simulation studies. This proof-of-concept test over a live satellite channel was the objective of the construction and testing performed under this task of the NMSU NASA grant referenced above. In conjunction with NASA, NMSU's CSTTS has constructed a system to test a new candidate TDRSS modulation scheme, TCM 8PSK, that can enhance the information throughput of the TDRSS spacecraft. The test system for this project which was constructed over a period of 18 months by NMSU consisted of two racks of commercial and univeristy-designed and -built equipment. This project has included modifications of an existing White Sands Ground Terminal (WSGT) High Rate QPSK Demodulator to demodulate 8PSK as well as the construction of other support hardware. Also, two TCM codecs (coder/decoders) have been constructed to implement two levels of bandwidth efficiency. One was designed and built by the research team at NMSU while the other was created by the University of Notre Dame with the University of South Australia. The NMSU codec achieves a 2-to-1 increase in data rate per unit bandwidth with a coding gain relative to QPSK of about 3dB. The Notre Dame/South Australia codec achieves a 2.5-to-1 increase in data rate per unit of occupied bandwidth and a coding gain of about 2dB.

Osborne, William P.↗

Data-driven results for light-quark connected and strange-plus-disconnected hadronic g − 2 short- and long-distance windows

A key issue affecting the attempt to reduce the uncertainty on the Standard Model prediction for the muon anomalous magnetic moment is the current discrepancy between lattice-QCD and data-driven results for the hadronic vacuum polarization. Progress on this issue benefits from precise data-driven determinations of the isospin-limit light-quark-connected (lqc) and strange-plus-light-quark-disconnected ( s + lqd ) components of the related RBC/UKQCD windows. In this paper, using a strategy employed previously for the intermediate window, we provide data-driven results for the lqc and s + lqd components of the short- and long-distance RBC/UKQCD windows. Comparing these results with those from the lattice, we find significant discrepancies in the lqc parts but good agreement for the s + lqd components. We also explore the impact of recent CMD- 3 e + e − → π + π − cross section results, demonstrating that an upward shift in the ρ -peak region of the type seen in the CMD-3 data serves to eliminate the discrepancies for the lqc components without compromising the good agreement between lattice and data-driven s + lqd results. Published by the American Physical Society 2025

Benton, Genessa (ORCID:0009000515763654)↗

Is Linear Displacement Information Or Angular Displacement Information Used During The Adaptation of Pointing Responses To An Optically Shifted Image?

Twenty-four observers looked through a pair of 20 diopter wedge prisms and pointed to an image of a target which was displaced vertically from eye level by 6 cm at a distance of 30 cm. Observers pointed 40 times, using only their right hand, and received error-corrective feedback upon termination of each pointing response (terminal visual feedback). At three testing distances, 20, 30, and 40 cm, ten pre-exposure and ten post-exposure pointing responses were recorded for each hand as observers reached to a mirror-viewed target located at eye level. The difference between pre- and post-exposure pointing response (adaptive shift) was compared for both Exposed and Unexposed hands across all three testing distances. The data were assessed according to the results predicted by two alternative models for processing spatial-information: one using angular displacement information and another using linear displacement information. The angular model of spatial mapping best predicted the observer's pointing response for the Exposed hand. Although the angular adaptive shift did not change significantly as a function of distance (F(2,44) = 1.12, n.s.), the linear adaptive shift increased significantly over the three testing distances 02 44) = 4.90 p less than 0.01).

Bautista, Abigail B.↗

Phase-Imaging with a Sharpened Multi-Walled Carbon Nanotube AFM Tip: Investigation of Low-k Dielectric Polymer Hybrids

Phase shift tapping mode scanning force microscopy (TMSFM) has evolved into a very powerful technique for the nanoscale surface characterization of compositional variations in heterogeneous samples. Phase shift signal measures the difference between the phase angle of the excitation signal and the phase angle of the cantilever response. The signal correlates to the tip-sample inelastic interactions, identifying the different chemical and/or physical property of surfaces. In general, the resolution and quality of scanning probe microscopic images are highly dependent on the size of the scanning probe tip. In improving AFM tip technology, we recently developed a technique for sharpening the tip of a multi-walled carbon nanotube (CNT) AFM tip, reducing the radius of curvature of the CNT tip to less than 5 nm while still maintaining the inherent stability of multi-walled CNT tips. Herein we report the use of sharpened (CNT) AFM tips for phase-imaging of polymer hybrids, a precursor for generating nanoporous low-k dielectrics for on-chip interconnect applications. Using sharpened CNT tips, we obtained phase-contrast images having domains less than 10 nm. In contrast, conventional Si tips and unsharpened CNT tips (radius greater than 15 nm) were not able to resolve the nanoscale domains in the polymer hybrid films. C1early, the size of the CNT tip contributes significantly to the resolution of phase-contrast imaging. In addition, a study on the nonlinear tapping dynamics of the multi-walled CNT tip indicates that the multi-walled CNT tip is immune to conventional imaging instabilities related to the coexistence of attractive and repulsive tapping regimes. This factor may also contribute to the phase-contrast image quality of multi-walled CNT AFM tips. This presentation will also offer data in support of the stability of the CNT tip for phase shift TMSFM.

Nguyen, Cattien V.↗

The effects of temperature and NaCl concentration on tetragonal lysozyme face growth rates

Measurements were made of the (110) and (101) face growth rates of the tetragonal form of hen egg white lysozyme at 0.1M sodium acetate buffer, pH 4.0, from 4 to 22 C and with 3.0%, 5.0%, and 7.0% NaCl used as the precipitating salt. The data were collected at supersaturation ratios ranging from approximately 4 to approximately 63. Both decreasing temperature and increasing salt concentrations shifted plots of the growth rate versus C/C(sat) to the right, i.e. higher supersaturations were required for comparable growth rates. The observed trends in the growth data are counter to those expected from the solubility data. If tetragonal lysozyme crystal growth is by addition of ordered aggregates from the solution, then the observed growth data could be explained as a result of the effects of lowered temperature and increased salt concentration on the kinetics and equilibrium processes governing protein-protein interactions in solution. The data indicate that temperature would be a more tractable means of controlling the growth rate for tetragonal lysozyme crystals contrary to the usual practice in, e.g., vapor diffusion protein crystal growth, where both the precipitant and protein concentrations are simultaneously increased. However, the available range for control is dependent upon the protein concentration, with the greatest growth rate control being at the lower concentration.

Forsythe, Elizabeth↗

Grassmannian Shape Representations for Aerodynamic Applications: Preprint

Airfoil shape design is a classical problem in engineering, science, and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, shifting). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.

blade representation↗

Grassmannian Shape Representations for Aerodynamic Applications

Airfoil shape design is a classical problem in engineering, science, and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, shifting). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.

blade representation↗

Ionosphere total electron measurements as extracted from satellite tracking data

The Goddard Range and Range Rate System (GRARR) determines the range of a spacecraft by measuring the group delay of a modulated wave and the range rate by measuring the Doppler phase shift of the carrier. An analytical technique is presented for obtaining corrections and equivalent total electron content along the vertical, using VHF GRARR data and a radial model of the ionosphere. The results of computation for a representative pass are given, and estimated accuracy is discussed from a statistical view point. Using VHF GRARR data and a radial model of the ionosphere. The results of computation for a representative pass are given, and estimated accuracy is discussed from a statistical view point. Using GRARR range, range rate, and angle tracking data from Explorer 41, values of total electron content on the order of 10 to the 17th to 10 to the 18th power (electrons/sq m) were obtained. These values agree with estimates of the total electron content from ionospheric profiles using f sub o F sub 2 predict data.

Murray, C. W., Jr.↗

Evidence for dispersing 1D Majorana channels in an iron-based superconductor

The possible realization of Majorana fermions as quasiparticle excitations in condensed-matter physics has created much excitement. Most studies have focused on Majorana bound states; however, propagating Majorana states with linear dispersion have also been predicted. Here, we report scanning tunneling spectroscopic measurements of crystalline domain walls (DWs) in FeSe 0.45 Te 0.55 . We located DWs across which the lattice structure shifts by half a unit cell. These DWs have a finite, flat density of states inside the superconducting gap, which is a hallmark of linearly dispersing modes in one dimension. This signature is absent in DWs in the related superconductor, FeSe, which is not in the topological phase. Our joint data are consistent with the observation of dispersing Majorana states at a π-phase shift DW in a proximitized topological material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A novel cosmic filament catalogue from SDSS data

Here, in this work, we present a new catalogue of cosmic filaments obtained from the latest Sloan Digital Sky Survey (SDSS) public data. In order to detect filaments, we implement a version of the Subspace-Constrained Mean-Shift algorithm that is boosted by machine learning techniques. This allows us to detect cosmic filaments as one-dimensional maxima in the galaxy density distribution. Our filament catalogue uses the cosmological sample of SDSS, including Data Release 16, and therefore inherits its sky footprint (aside from small border effects) and redshift coverage. In particular, this means that, taking advantage of the quasar sample, our filament reconstruction covers redshifts up to z = 2.2, making it one of the deepest filament reconstructions to our knowledge. We follow a tomographic approach and slice the galaxy data in 269 shells at different redshift. The reconstruction algorithm is applied to 2D spherical maps. The catalogue provides the position and uncertainty of each detection for each redshift slice. The quality of our detections, which we assess with several metrics, show improvement with respect to previous public catalogues obtained with similar methods. We also detect a highly significant correlation between our filament catalogue and galaxy cluster catalogues built from microwave observations of the Planck Satellite and the Atacama Cosmology Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

Temperature-Dependent Communication between Pt/Al 2 O 3 Catalysts and Anatase TiO 2 Dilutant: the Effects of Metal Migration and Carbon Transfer on the Reverse Water–Gas Shift Reaction

In heterogeneous catalysis, unexpected effects from the supposedly inert reactor dilutant are not rare, but related understanding is lacking and inconsistent. Here we report investigations of the impacts of the anatase TiO 2 dilutant on the reverse water-gas shift (rWGS) reaction over Pt/Al 2 O 3 catalysts. Combining detailed kinetic data with microscopic and spectroscopic results, we demonstrate that the catalyst-dilutant communication depends on temperature. At high temperature (400 °C), Pt migrate from Al 2 O 3 to TiO 2 , resulting in higher dispersion and activity, without changing reaction mechanisms. The Pt migration is general to catalysts of different Pt nuclearity and various oxide dilutants. In contrast, at low temperature (250 °C), carboxylic acids (in particular acetic acid) present in the ambient air and adsorbed on TiO 2 are transferred onto Al 2 O 3 in close contact, effectively blocking the formate rWGS pathway. As a result, the rWGS can only proceed through the carboxyl pathway, and hence is significantly slower. The acetate transfer affects catalysts of different Pt nuclearity and support, but is unique to anatase TiO 2 dilutant. As the acetate layer is slowly removed under H 2 or the rWGS stream, the activity recovers. This work elucidates the complicated communication between catalysts and dilutants, which has general implications in heterogeneous catalysis, and resolves inconsistency in related reports in the literature. Finally, the impacts that anatase TiO 2 dilution has on the rWGS also unveil mechanistic understanding that further confirms the two co-existing rWGS pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Far Ultraviolet Imaging from the Image Spacecraft: System Design - 1

Direct imaging of the magnetosphere by the IMAGE spacecraft A,ill be supplemented by observation of the global aurora, the footprint of magnetospheric regions. To assure the simultaneity of these observations and tile measurement of the magnetospheric back-round neutral gas density, the IMAGE satellite instrument complement includes three Far Ultraviolet (FUV) instruments. In tile wavelength region 120-1 90 nm. a downward-viewing aurora imager is only minimally contaminated sunlight, scattered from clouds and ground, and radiance of the aurora observed in a nadir viewing geometry can be observed in the presence of the high-latitude day-low. Tile Wideband Imaging Camera (WIC) will provide broadband ultraviolet images of the aurora for maximum spatial and temporal resolution by imaging the LBH N2 bands of the aurora. The Spectrographic Imager (SI), a monochromatic imager, will image different types of aurora, filtered by wavelength. By measuring the Doppler-shifted Lyman-alpha, the proton-induced component of the aurora will be imaged separately. Finally, the GEO instrument will observe the distribution of the geocoronal emission, which is a measure of the neutral background density source of the charge exchange in the magnetosphere. The FUV instrument complement looks radially outward from the rotating IMAGE satellite and, therefore, it spends only a short time observing tile aurora and the Earth during, each spin. Detailed descriptions of the WIC, Si, GEO, and their individual performance validations are discussed in companion papers. This paper summarizes the system requirements and system design approach taken to satisfy the science requirements. One primary requirement is to maximize photon collection efficiency and use efficiently tile short time available foe exposures. The FUV auroral imagers WIC and SI both have wide fields of view and take data continuously as the auroral region proceeds through the field of view. To minimize data volume, multiple images are taken and electronically co-added by suitably shifting each image to compensate for the spacecraft rotation. In order to minimize resolution loss, the images have to be distortion-corrected in real time foe both WIC and Si prior to co-adding. The distortion correction is accomplished using high-speed look Lip tables that are pre-generated by least square fitting to polynomial functions by the on-orbit processor. The instruments were calibrated individually while on stationary platforms, mostly in vacuum chambers as described in the companion papers. Extensive -round-based testing was performed with visible and near UV simulators mounted oil a rotating platform to estimate their on-orbit performance. The predicted instrument system performance is summarized and some of the preliminary data formats are shown.

Mende, S. B.↗

Equation of state for He bubbles in W and model of He bubble growth and bursting near W{100} surfaces derived from molecular dynamics simulations

Abstract Molecular dynamics (MD) simulations are performed to derive an equation of state (EOS) for helium (He) bubbles in tungsten (W) and to study the growth of He bubbles under a W(100) surface until they burst. We study the growth as a function of the initial nucleation depth of the bubbles. During growth, successive loop-punching events are observed, accompanied by shifts in the depth of the bubble towards the surface. Subsequently, the MD data are used to derive models that describe the conditions that cause the loop punching and bursting events. Simulations have been performed at 500, 933, 1500, 2000, and 2500 K to fit the parameters in the models. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an EOS for He bubbles in tungsten with an accompanying volume model to compute the bubble volume for a given number of vacancies ( $$N_\text {V}$$ N V ), He atoms ( $$N_\text {He}$$ N He ), and temperature ( T ). To derive the bubble EOS, we firstly derive the EOS for a free He gas. The derived free-gas EOS can accurately predict all MD data included in the analysis (which span up to 54 GPa at 2500 K). Subsequently, the bubble EOS is derived based on the free-gas EOS by correcting the gas density to account for the interaction between He and W atoms. The EOS for the bubbles is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and sizes up to about 3 nm in diameter. The pressure of subsurface bubbles at the loop punching events as calculated using the bubble-EOS and the volume model agrees well with the pressure obtained directly from the MD simulations. In the loop punching model, for bubbles consisting of $$N_\text {V}$$ N V vacancies and $$N_\text {He}$$ N He helium atoms, the $$N_\text {He}/N_\text {V}$$ N He / N V ratio that causes the event, the resulting increase in $$N_\text {V}$$ N V , and the associated shift of the bubble depth are formulated as a function of $$N_\text {V}$$ N V and T . In the bursting model, a bubble must simultaneously reach a certain depth and $$N_\text {He}/N_\text {V}$$ N He / N V ratio in order to burst. The burst depth and $$N_\text {He}/N_\text {V}$$ N He / N V are also modeled as a function of $$N_\text {V}$$ N V and T . The majority of the loop punching events occur at bubble pressures between 20 and 60 GPa, depending on the bubble size and temperature. The larger the bubble and the higher the temperature, the lower the bubble pressure. Furthermore, our results indicate that at a higher temperature, a bubble can burst from a deeper region.

36 MATERIALS SCIENCE↗

Theory of Periodic-Binary-Sequence Generators

Algorithms yield feedback shift registers with maximum regularity. Report provides extensive mathematical treatment of new and previous results related to generation of pseudo-noise binary sequences by feedback shift registers. Generator architectures amenable to efficient implementation in very-large-scale integrated (VLSI) circuits. Report includes literature references to applications of such sequences in random-number generation, radar, VLSI testing, data encryption and decryption, algebraic error-detection and error-correction encoding and decoding, and feedback-shift-register synthesis of sequential machines.

Perlman, M.↗

Phase Shift Interferometer and Growth Set Up to Step Pattern Formation During Growth From Solutions. Influence of the Oscillatory solution Flow on Stability

We have assembled an experimental setup based on Michelson interferometry with the growing crystal surface as one of the reflective surfaces. The crystallization part of the device allows optical monitoring of a face of a crystal growing at temperature stable within 0.05 C in a flow of solution of controlled direction and speed. The reference arm of the interferometer contains a liquid crystal element that allows controlled shifts of the phase of the interferograms. We employ an image-processing algorithm, which combines five images with a pi/2 phase difference between each pair of images. The images are transferred to a computer by a camera capable of capturing 60 frames per second. The device allows data collection on surface morphology and kinetics during the face layers growth over a relatively large area (approximately 4 sq. mm) in situ and in real time during growth. The estimated depth resolution of the phase shifting interferometry is approximately 50 Angstroms. The data will be analyzed in order to reveal and monitor step bunching during the growth process. The crystal chosen as a model for study in this work is KH2PO4 (KDP). This optically non-linear material is widely used in frequency doubling applications. There have been a number of studies of the kinetics of KDP crystallization that can serve as a benchmark for our investigations. However, so far, systematic quantitative characteristics of step interaction and bunching are missing. We intend to present our first quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, flow rate, and flow direction. Behavior of a vicinal face growing from solution flowing normal to the steps and periodically changing its direction in time was considered theoretically. It was found that this oscillating flow reduces both stabilization and destabilization effects resulted from the unidirectional solution flow directed up the step stream and down the step stream. This reduction of stabilization and destabilization comes from effective mixing which entangles the phase shifts between the spatially periodic interface perturbation and the concentration wave induced by this perturbation. Numerical results and simplified mixing criterion will be discussed.

Chernov, Alex A.↗

Constraining the phase shift of relativistic species in DESI BAOs

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $\beta _{\phi }$ and apply it to the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $\beta _{\phi }$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $\beta _{\phi }$ for the different tracers, and additionally a combined fit to $\beta _{\phi }$ resulting in $\beta _{\phi } = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using Planck we find $\beta _{\phi } = 2.7^{+0.60}_{-0.67}$ suggesting $\beta _{\phi } > 0$ at 4.3$\sigma$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm {eff}}$ or could be a upwards statistical fluctuation in the measured $\beta _{\phi }$; this result relaxes in models with additional freedom beyond Lambda-cold dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗