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At least 163 records · Page 9

Towards optimal sensor placement for inverse problems in spaces of measures

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in the sensor configuration and robust with respect to the source, yet relatively easy to compute in practice, compared to a direct evaluation of the error by a large number of samples. In particular, we consider the identification of a measure consisting of an unknown linear combination of point sources from a finite number of measurements contaminated by Gaussian noise. The statistical framework for recovery relies on two main ingredients: first, a convex but non-smooth variational Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger–Kantorovich distance to the ground truth. To quantify the error, we employ a non-degenerate source condition as well as careful linearization arguments to derive a computable upper bound. This leads to asymptotically sharp error estimates in expectation that are explicit in the sensor configuration. Thus they can be used to estimate the expected reconstruction error for a given sensor configuration and guide the placement of sensors in sparse inverse problems.

97 MATHEMATICS AND COMPUTING↗

Advancing Enhanced Raman Spectroscopy to Detect and Measure NOW Pheromones (CPRB 2022 proposal)

Insect sex pheromones are chemical compounds that insects release to attract their partners over distances of hundreds of meters or even kilometers, in complete darkness and without any audible signals. Use of synthetic forms of key compounds have in some cases become an essential component of monitoring and/or managing key pests of agricultural crops, including navel orangeworm (Amyelois transitella) (NOW) in California tree nuts. These pheromone-based strategies can include monitoring, mating disruption, mass trapping, attract-and-kill and push-pull. There are currently multiple commercially available mating disruption products available for NOW and recent studies have demonstrated that they can be effectively used to reduce crop damage by this pest. Just how mating disruption works is not fully established and likely varies across products and target species. For instance, the extent to which synthetic pheromones compete with natural pheromone is not well understood, or in the case of monitoring, how efficaciously the insect follows the diffusing plumes, especially across large blocks and at plot borders. Furthermore, there may be specific conditions under which poor or impeded diffusion of synthetic pheromone diminishes the disruption effect, which could result in some males effectively locating females for reproduction. At the same time, many commercially available synthetic lures are also available, and growers have been effectively using them to track population development – although the attractive range of these lures remains unclear. That is, while pheromone lures can attract many moths, the relationship between trap capture and local populations, much less crop damage, remains unclear. Regardless of the emission source (aerosol puffers, meso emitters, lures etc.), we currently lack the ability to fully understand how these synthetic pheromone compounds diffuse away from their point-source of emission – and subsequently how this might affect the efficacy of mating disruption and/or the accuracy of monitoring efforts. Raman spectroscopy (RS) may offer a means to detect synthetic pheromone because of its analytical properties and recent technological advancements. In combination with nanostructured probes, RS has a demonstrated capability to detect volatiles at extremely low concentrations. While other methods for detecting pheromones have proven to be successful, such analytical methods like mass spectrometry (MS) gas chromatography (GC) require sampling in the fields and are not real-time. Other methods such as EAG/ EAD are also invasive (use antennas) but are of course valuable. Opto-electronic, micro and nano sensors just recently enticed interest. We fall in this latter category, proposing the use of optical spectroscopy (Raman) in a fiber aided by nanostructures to provide a chemical fingerprint without transductions and in real-time (i.e. no sampling). To date, we have been able to generate Raman signatures for the main chemicals in synthetic pheromones (a first for science, to the best of our knowledge), observe their trends at different concentrations, and also provide a clear distinction of such signatures in mixed samples via Principal Component Analysis (PCA) – all of which strengthens our conclusions on the ability of RS to detect emissions in more realistic conditions. We also established processes to enhance the detection sensitivity via preconcentration with Solid Phase Micro Extraction (SPME) fibers and Surface Enhanced Raman Spectroscopy (SERS) to increase the overall optical signals. Furthermore, we explored limitations and requirements for detecting from dispensers, lures, or live moths, including Dept. of Energy and CA State regulatory approvals. Finally, we setup some of our first “orchard in a box” experiments to measure pheromone diffusion along with developing appropriate models.

42 ENGINEERING↗

Radiological Source Term Estimation and Isotopic Identification with Parallel Log Domain Particle Filters

This paper presents a parallel log-domain particle filtering algorithm combined with gamma spectrum unfolding to perform localization, identification, and evaluation of multiple point sources of various isotopes in an environment with attenuating obstacles. The method uses sets of precomputed attenuation kernels that map the attenuation characteristics of the environment. These kernels are specific to the energy level of a photopeak of interest. The spectral measurements are deconvolved into count measurements of each photopeak. These count measurements are fed into a set of parallel particle filters using attenuation kernels computed for that photopeak’s energy level. The individual regularized particle filters perform all likelihood calculations in the logarithmic domain to mitigate the effects of particle degeneracy. The output of each particle filter is combined to estimate which isotopes are present as well as their positions and strengths. The performance of the algorithm is characterized in a lab-scale environment using a mobile robot equipped with a gamma ray spectrometer in the presence of up to three different radioactive isotopes simultaneously. The sources were localized to within 10 cm, and their strengths were estimated within 10% of their true values. Furthermore, the isotopes were all correctly identified, and no spurious sources were reported.

42 ENGINEERING↗

Enhanced Pu emission with solution-loaded laser ablation modified sources (SLLAMS) for thermal ionization mass spectrometry

This study presents a new approach to filament modification by laser ablation for analysis of femtograms of plutonium (Pu) by thermal ionization mass spectrometry (TIMS). This method simplifies the often rigorous and labor-intensive sample loading necessary for low-level analyses by TIMS with solution-loaded laser ablation modified sources (SLLAMS). By applying a para-film coating to the surface of the filament and then ablating through the film to reveal metal beneath, a point source is created. A solution containing ppt-levels of Pu can then be applied over the ablated region, dried slowly into the crater, and then carburized. All analyses were made by multiple ion counting system of a Nu Instruments TIMS. Furthermore, we report errors of 10% 2σ for 240 Pu/ 239 Pu of CRM-137 samples totaling 5 – 7 femtograms (fg; 1E-15 g) with an average sample utilization efficiency of 1.3%. Results from SLLAMS demonstrate an improvement in precision, accuracy and ease of use over resin bead loads.

47 OTHER INSTRUMENTATION↗

Techno-economic analysis of carbon dioxide capture from low concentration sources using membranes

Rising carbon dioxide (CO 2 ) levels in the atmosphere lead to global warming, causing climate change. As such, carbon capture has become necessary to slow the increase and reduce CO 2 levels in the atmosphere. Point source emissions have a wide range of CO 2 concentrations, but emissions below 3% CO 2 have mostly been ignored because Carbon capture from these sources has been viewed as costly and economically unsustainable. Membrane technologies are considered the most viable solution by virtue of more energy-efficient operation. Our group at Idaho National Laboratory (INL) has developed poly[bis((2-methoxyethoxy)ethoxy)phosphazene] (MEEP)-based carbon dioxide selective membranes with CO 2 /N 2 selectivity greater than 40 and CO 2 permeability greater than 450 Barrer. To understand the economics of carbon capture, a spreadsheet-based techno-economic analysis (TEA) model was developed to consider multiple parameters, including selectivity and permeability of the membranes, performance conditions such as the number of stages, module material, electricity price, membrane price, and capital financing. The cost of carbon capture in US $\$$/metric ton was calculated at various purities and compared with other membrane processes, cryogenic capture, solvent-based capture, and pressure swing adsorption-based capture. It was determined that a MEEP-based three-stage process had a capture cost of US $\$$ 50.1/metric ton for 99.8% purity CO 2 from a 1% CO 2 feed source in nitrogen (N 2 ). In conclusion, the capture cost using the best performing Pebax-based membrane was 464% higher, cryogenic capture was 60%–140% higher, pressure swing adsorption was 55%–165% higher, and chemical absorption was -10%–110% higher than MEEP-based membrane capture, respectively.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Inverting infrasound data for the seismoacoustic source time functions and surface spall at the Source Physics Experiments Phase II: Dry Alluvium Geology

This report presents the infrasound data recorded as part of the Source Physics Experiment - Phase 2, Dry Alluvium Geology. This experiment, also known colloquially as DAG, consisted of four underground chemical explosions at the Nevada National Security Site. We focus our analysis on only the fourth explosion (DAG-4) as we determined that this was the only event that produced clear source-generated infrasound energy as recorded by the DAG sensors. We analyze the data using two inversion methods. The first method is designed to estimate the point-source seismoacoustic source time functions, and the second inversion method is designed to estimate the first-order characteristics (e.g. horizontal dimensions and maximum amplitude) of the actual spall surface. For both analysis methods, we are able to fit the data reasonably well, with various assumptions of the source model. The estimated seismoacoustic source appears to be a combination of a buried, isotropic explosion with a maximum amplitude of ~2 x 10 9 Nm and a vertically oriented force, applied to the Earth's surface with a maximum amplitude of 4 x 10 7 N. We use the vertically oriented force to simulate surface spall. The estimated spall surface has an approximate radius of ~40 m with a maximum acceleration magnitude in the range of 0.8 to 1.5 m/s/s. These estimates are approximately similar to the measured surface acceleration at the site.

58 GEOSCIENCES↗

ANTARES and IceCube Combined Search for Neutrino Point-like and Extended Sources in the Southern Sky

A search for point-like and extended sources of cosmic neutrinos using data collected by the ANTARES and IceCube neutrino telescopes is presented. The data set consists of all the track-like and shower-like events pointing in the direction of the Southern Sky included in the nine-year ANTARES point-source analysis, combined with the throughgoing track-like events used in the seven-year IceCube point-source search. The advantageous field of view of ANTARES and the large size of IceCube are exploited to improve the sensitivity in the Southern Sky by a factor of ~2 compared to both individual analyses. In this work, the Southern Sky is scanned for possible excesses of spatial clustering, and the positions of preselected candidate sources are investigated. In addition, special focus is given to the region around the Galactic Center, whereby a dedicated search at the location of SgrA* is performed, and to the location of the supernova remnant RXJ 1713.7-3946. Furthermore, no significant evidence for cosmic neutrino sources is found, and upper limits on the flux from the various searches are presented.

79 ASTRONOMY AND ASTROPHYSICS↗

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗

Biphasic solvents for post-combustion CO 2 capture from natural gas flue Gas

Fossil fuel fired power plants are generally expected to remain one of the most significant global sources of electricity for decades to come. Consequently, carbon management technologies are needed to reduce or eliminate ongoing emissions from these sources. Amongst the many techniques for carbon capture, aqueous amine-based absorbents (monoethanolamine, MEA, in particular) are, presently, considered the leading technology for post-combustion CO 2 point-source capture. These technologies are nevertheless limited by their high capital and regeneration energy costs. Biphasic solvents have been identified as an attractive alternative to traditional MEA based absorbents due to their potential energy savings. Thus far, however, the research on biphasic solvents has largely focused on their performance in coal flue gas while more dilute natural gas flue gas applications have received relatively little attention. Here, this work examines the performances of two novel biphasic solvent blends, diethylenetriamine (DETA) and triethylenetetramine (TETA), in CO 2 capture from a natural gas flue gas simulant. Across several regeneration tests, both solvents achieved considerable energy savings over the benchmark MEA solution. Specifically, the energy consumption per mol CO 2 recovered for the DETA-based and TETA-based solvents was 46 % and 35 % less than that of the benchmark MEA solution, respectively. Molecular dynamics simulations were also performed to gain a deeper understanding of the phase separation phenomena that occur as a consequence of CO 2 absorption. These simulations indicated that phase change was driven by the strong interaction between the absorption products and water, while the degree of separation depended on the CO 2 loading.

Biphasic solvents↗

Using extended MHD to explore lasers as a trigger for x-pinches

X-pinches have been shown to be a source of extremely intense x-ray emissions useful for diagnosing plasma dynamics and imaging biological objects. The most striking feature of an x-pinch is the hotspot, the point source from where all the x rays come from. Unfortunately, the exact timing and location of the hotspot are still unpredictable. Since an x-pinch hotspot forms from instabilities (like an m = 0 mode), we will computationally explore whether we can use a high-power laser to control the timing and location of these instabilities. Our goal is to reduce the temporal and spatial jitter associated with the x-ray burst. Using an extended MHD (XMHD) code, we explore the non-relativistic instability generation using a current profile of a 250 kA linear transformer driver system and laser characteristics of SLAC's Matter in Extreme Conditions laboratory. Our results include both laser-penetration results using a boundary-defined electromagnetic (EM) wave and instability results from a power-deposition method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Looking in the axion mirror: An all-sky analysis of stimulated decay

Axion dark matter (DM) produces echo images of bright radio sources via stimulated decay. These images appear as a faint radio line centered at half the axion mass, with the line width set by the DM velocity dispersion. Due to the kinematics of the decay, the echo can be emitted in the direction nearly opposite to the incoming source of stimulating radiation, meaning that axions effectively behave as imperfect monochromatic mirrors. We present an all-sky analysis of axion DM-induced echo images using extragalactic radio point sources, Galactic supernova remnants (SNRs), and Galactic synchrotron radiation (GSR) as sources of stimulating radiation. The aggregate signal strength is not significantly affected by unknown properties of individual sources of stimulating radiation, which we sample from an empirical distribution to generate an ensemble of realizations for the all-sky signal template. We perform forecasts for CHIME, HERA, CHORD, HIRAX, and BURSTT, finding that they can run as competitive axion experiments simultaneously with other objectives, requiring no new hardware.

79 ASTRONOMY AND ASTROPHYSICS↗

Space-dependent calculation of the multiplicity moments for shells

In earlier work, we extended the methodology of multiplicity counting in nuclear safeguards, by elaborating the one-speed stochastic transport theory of the calculation of the so-called multiplicity moments, i.e. the factorial moments of the number of neutrons emitted from a fissile item, following a source event from an internal neutron source (spontaneous fission and (α, n) reactions). Calculations were made for spheres and cylinders of various shapes. In all our work so far, the material of the items was homogeneous, and the distribution of the internal source was assumed to be uniformly distributed within the item, with the neutron emission assumed to be isotropic. In the present work the calculations are extended to the case of a point source inside either a solid sphere or in a spherical shell. This necessitates the extension of the theory to non-homogeneous items and non-uniform and non-isotropic sources. This work describes the extension of the theory and provides some quantitative results. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Search for Multi-flare Neutrino Emissions in 10 yr of IceCube Data from a Catalog of Sources

A recent time-integrated analysis of a catalog of 110 candidate neutrino sources revealed a cumulative neutrino excess in the data collected by IceCube between 2008 April 6 and 2018 July 10. This excess, inconsistent with the background hypothesis in the Northern Hemisphere at the 3.3σ level, is associated with four sources: NGC 1068, TXS 0506+056, PKS 1424+240, and GB6 J1542+6129. Here, this Letter presents two time-dependent neutrino emission searches on the same data sample and catalog: a point-source search that looks for the most significant time-dependent source of the catalog by combining space, energy, and time information of the events, and a population test based on binomial statistics that looks for a cumulative time-dependent neutrino excess from a subset of sources. Compared to previous time-dependent searches, these analyses enable a feature to possibly find multiple flares from a single direction with an unbinned maximum-likelihood method. M87 is found to be the most significant time-dependent source of this catalog at the level of 1.7σ post-trial, and TXS 0506+056 is the only source for which two flares are reconstructed. The binomial test reports a cumulative time-dependent neutrino excess in the Northern Hemisphere at the level of 3.0σ associated with four sources: M87, TXS 0506+056, GB6 J1542+6129, and NGC 1068.

79 ASTRONOMY AND ASTROPHYSICS↗

Opportunistic experiments to constrain aerosol effective radiative forcing

Aerosol–cloud interactions (ACIs) are considered to be the most uncertain driver of present-day radiative forcing due to human activities. The nonlinearity of cloud-state changes to aerosol perturbations make it challenging to attribute causality in observed relationships of aerosol radiative forcing. Using correlations to infer causality can be challenging when meteorological variability also drives both aerosol and cloud changes independently. Natural and anthropogenic aerosol perturbations from well-defined sources provide “opportunistic experiments” (also known as natural experiments) to investigate ACI in cases where causality may be more confidently inferred. These perturbations cover a wide range of locations and spatiotemporal scales, including point sources such as volcanic eruptions or industrial sources, plumes from biomass burning or forest fires, and tracks from individual ships or shipping corridors. We review the different experimental conditions and conduct a synthesis of the available satellite datasets and field campaigns to place these opportunistic experiments on a common footing, facilitating new insights and a clearer understanding of key uncertainties in aerosol radiative forcing. Cloud albedo perturbations are strongly sensitive to background meteorological conditions. Strong liquid water path increases due to aerosol perturbations are largely ruled out by averaging across experiments. Opportunistic experiments have significantly improved process-level understanding of ACI, but it remains unclear how reliably the relationships found can be scaled to the global level, thus demonstrating a need for deeper investigation in order to improve assessments of aerosol radiative forcing and climate change.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Morphological Model to Separate Resolved–Unresolved Sources in the DESI Legacy Surveys: Application in the LS4 Alert Stream

Separating resolved and unresolved sources in large imaging surveys is a fundamental step to enable downstream science, such as searching for extragalactic transients in wide-field time-domain surveys. Here we present our method to effectively separate point sources from the resolved, extended sources in the Dark Energy Spectroscopic Instrument (DESI) Legacy Surveys (LS). We develop a supervised machine learning model based on the Gradient Boosting algorithm XGBoost. The features input to the model are purely morphological and are derived from the tabulated LS data products. We train the model using ∼2 × 10 5 LS sources in the COSMOS field with HST morphological labels and evaluate the model performance on LS sources with spectroscopic classification from the DESI Data Release 1 (∼2 × 10 7 objects) and the Sloan Digital Sky Survey Data Release 17 (∼3 × 10 6 objects), as well as on ∼2 × 10 8 Gaia stars. A significant fraction of LS sources are not observed in every LS filter, and we therefore build a “Hybrid” model as a linear combination of two XGBoost models, each containing features combining aperture flux measurements from the “blue” (gr) and “red” (iz) filters. The Hybrid model shows a reasonable balance between sensitivity and robustness, and achieves higher accuracy and flexibility compared to the LS morphological typing. With the Hybrid model, we provide classification scores for ∼3 × 10 9 LS sources, making this the largest ever machine learning catalog separating resolved and unresolved sources. The catalog has been incorporated into the real-time pipeline of the La Silla Schmidt Southern Survey (LS4), enabling the identification of extragalactic transients within the LS4 alert stream.

astrostatistics↗

The brighter-fatter effect in the JWST MIRI Si:As IBC detectors: I. Observations, impact on science, and modeling

Context.The Mid-Infrared Instrument (MIRI) on board theJames WebbSpace Telescope (JWST) uses three Si:As impurity band conduction (IBC) detector arrays. The output voltage level of each MIRI detector pixel is digitally recorded by sampling up the ramp. For uniform or low-contrast illumination, the pixel ramps become nonlinear in a predictable way, but in areas of high contrast, the nonlinearity curve becomes much more complex. The origin of the effect is poorly understood and currently not calibrated out of the data. Aims.We provide observational evidence of the brighter-fatter effect (BFE) in MIRI conventional and high-contrast coronagraphic imaging, low-resolution spectroscopy, and medium-resolution spectroscopy data, and we investigate the physical mechanism that gives rise to the effect on the MIRI detector pixel raw voltage integration ramps. Methods.We used public data from the JWST/MIRI commissioning and Cycle 1 phase. We also developed a numerical electrostatic model of the MIRI detectors using a modified version of the publicPoisson_CCDcode. Results.We find that the physical mechanism behind the BFE manifesting in MIRI data is fundamentally different to that of charge-coupled devices and photodiode arrays such as the Hawaii-XRG near-infrared detectors used by the NIRISS, NIRCam, and NIRSpec instruments on board JWST. Observationally, the BFE makes the JWST MIRI data yield 10–25% larger point sources and spectral line profiles as a function of the relative level of de-biasing of neighboring detector pixels. This broadening impacts the MIRI absolute flux calibration, time-series observations of faint companions, and point spread function modeling and subtraction. We also find that the intra-pixel 2D profile of the shrinking Si:As IBC detector depletion region directly impacts the accuracy of the pixel ramp nonlinearity calibration model.

Astronomy & Astrophysics↗

A new aerial approach for quantifying and attributing methane emissions: implementation and validation

Methane (CH 4 ) is a powerful greenhouse gas that is produced by a diverse set of natural and anthropogenic emission sources. Biogenic methane sources generally involve anaerobic decay processes such as those occurring in wetlands, melting permafrost, or the digestion of organic matter in the guts of ruminant animals. Thermogenic CH 4 sources originate from the breakdown of organic material at high temperatures and pressure within the Earth's crust, a process which also produces more complex trace hydrocarbons such as ethane (C 2 H 6 ). Here, we present the development and deployment of an uncrewed aerial system (UAS) that employs a fast (1 Hz) and sensitive (1–0.5 ppb s -1 ) CH 4 and C 2 H 6 sensor and ultrasonic anemometer. The UAS platform is a vertical-takeoff, hexarotor drone (DJI Matrice 600 Pro, M600P) capable of vertical profiling to 120 m altitude and plume sampling across scales up to 1 km. Simultaneous measurements of CH 4 and C 2 H 6 concentrations, vector winds, and positional data allow for source classification (biogenic versus thermogenic), differentiation, and emission rates without the need for modeling or a priori assumptions about winds, vertical mixing, or other environmental conditions. The system has been used for direct quantification of methane point sources, such as orphan wells, and distributed emitters, such as landfills and wastewater treatment facilities. With detectable source rates as low as 0.04 and up to ~1500 kg h -1 , this UAS offers a direct and repeatable method of horizontal and vertical profiling of emission plumes at scales that are complementary to regional aerial surveys and localized ground-based monitoring.

54 ENVIRONMENTAL SCIENCES↗

Extracting the Galactic Center excess’ source-count distribution with neural nets

The two leading hypotheses for the Galactic Center excess (GCE) in the Fermi data are an unresolved population of faint millisecond pulsars (MSPs) and dark-matter (DM) annihilation. The dichotomy between these explanations is typically reflected by modeling them as two separate emission components. However, point sources (PSs) such as MSPs become statistically degenerate with smooth Poisson emission in the ultrafaint limit (formally where each source is expected to contribute much less than one photon on average), leading to an ambiguity that can render questions such as whether the emission is PS-like or Poissonian in nature ill defined. We present a conceptually new approach that describes the PS and Poisson emission in a unified manner and only afterwards derives constraints on the Poissonian component from the so obtained results. For the implementation of this approach, we leverage deep learning techniques, centered around a neural network-based method for histogram regression that expresses uncertainties in terms of quantiles. We demonstrate that our method is robust against a number of systematics that have plagued previous approaches, in particular DM/PS misattribution. In the Fermi data, we find a faint GCE described by a median source-count distribution (SCD) peaked at a flux of ~ 4 x 10 -11 counts cm -2 s -1 (corresponding to ~ 3-4 expected counts per PS), which would require N ~ $\mathscr{O}$(10 4 ) sources to explain the entire excess (median value N = 29,300 across the sky). Although faint, this SCD allows us to derive the constraint η ρ ≤ 66% for the Poissonian fraction of the GCE flux η ρ at 95% confidence, suggesting that a substantial amount of the GCE flux is due to PSs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗