Energy-resolving photon-counting detectors (PCDs) separate photons from a polychromatic X-ray source into a number of separate energy bins. This spectral information from PCDs would allow advancements in X-ray imaging, such as improving image contrast, quantitative imaging, and material identification and characterization. However, aspects like detector spectral distortions and scattered photons from the object can impede these advantages if left unaccounted for. Scattered X-ray photons act as noise in an image and reduce image contrast, thereby significantly hindering PCD utility. In this paper, we explore and outline several important characteristics of spectral X-ray scatter with examples of soft-material imaging (such as cancer imaging in mammography or explosives detection in airport security). Our results showed critical spectral signatures of scattered photons that depend on a few adjustable experimental factors. Additionally, energy bins over a large portion of the spectrum exhibit lower scatter-to-primary ratio in comparison to what would be expected when using a conventional energy-integrating detector. These important findings allow flexible choice of scatter-correction methods and energy-bin utilization when using PCDs. Our findings also propel the development of efficient spectral X-ray scatter correction methods for a wide range of PCD-based applications.
more »
« less
An accurate treatment of scattering and diffusion in piecewise power-law models for cosmic ray and radiation/neutrino transport
ABSTRACT A popular numerical method to model the dynamics of a ‘full spectrum’ of cosmic rays (CRs), also applicable to radiation/neutrino hydrodynamics, is to discretize the spectrum at each location/cell as a piecewise power law in ‘bins’ of momentum (or frequency) space. This gives rise to a pair of conserved quantities (e.g. CR number and energy) that are exchanged between cells or bins, which in turn give the update to the normalization and slope of the spectrum in each bin. While these methods can be evolved exactly in momentum-space (e.g. considering injection, absorption, continuous losses/gains), numerical challenges arise dealing with spatial fluxes, if the scattering rates depend on momentum. This has often been treated either by neglecting variation of those rates ‘within the bin,’ or sacrificing conservation – introducing significant errors. Here, we derive a rigorous treatment of these terms, and show that the variation within the bin can be accounted for accurately with a simple set of scalar correction coefficients that can be written entirely in terms of other, explicitly evolved ‘bin-integrated’ quantities. This eliminates the relevant errors without added computational cost, has no effect on the numerical stability of the method, and retains manifest conservation. We derive correction terms both for methods that explicitly integrate flux variables (e.g. two-moment or M1-like) methods, as well as single-moment (advection-diffusion, FLD-like) methods, and approximate corrections valid in various limits.
more »
« less
- PAR ID:
- 10443251
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 518
- Issue:
- 4
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 5882 to 5892
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Unfolding is an ill-posed inverse problem in particle physics aiming to infer a true particle-level spectrum from smeared detector-level data. For computational and practical reasons, these spaces are typically discretized using histograms, and the smearing is modeled through a response matrix corresponding to a discretized smearing kernel of the particle detector. This response matrix depends on the unknown shape of the true spectrum, leading to a fundamental systematic uncertainty in the unfolding problem. To handle the ill-posed nature of the problem, common approaches regularize the problem either directly via methods such as Tikhonov regularization, or implicitly by using wide-bins in the true space that match the resolution of the detector. Unfortunately, both of these methods lead to a non-trivial bias in the unfolded estimator, thereby hampering frequentist coverage guarantees for confidence intervals constructed from these methods. We propose two new approaches to addressing the bias in the wide-bin setting through methods called One-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSB intervals are a bin-wise modification of an existing guaranteed-coverage procedure, while the PO intervals are based on a decision-theoretic view of the problem. Importantly, both approaches provide well-calibrated frequentist confidence intervals even in constrained and rank-deficient settings. These methods are built upon a more general answer to the wide-bin bias problem, involving unfolding with fine bins first, followed by constructing confidence intervals for linear functionals of the fine-bin counts. We test and compare these methods to other available methodologies in a wide-bin deconvolution example and a realistic particle physics simulation of unfolding a steeply falling particle spectrum.more » « less
-
Background: When phenotypic characters are described in the literature, they may be constrained or clarified with additional information such as the location or degree of expression, these terms are called “modifiers”. With effort underway to convert narrative character descriptions to computable data, ontologies for such modifiers are needed. Such ontologies can also be used to guide term usage in future publications. Spatial and method modifiers are the subjects of ontologies that already have been developed or are under development. In this work, frequency (e.g., rarely, usually), certainty (e.g., probably, definitely), degree (e.g., slightly, extremely), and coverage modifiers (e.g., sparsely, entirely) are collected, reviewed, and used to create two modifier ontologies with different design considerations. The basic goal is to express the sequential relationships within a type of modifiers, for example, usually is more frequent than rarely, in order to allow data annotated with ontology terms to be classified accordingly. Method: Two designs are proposed for the ontology, both using the list pattern: a closed ordered list (i.e., five-bin design) and an open ordered list design. The five-bin design puts the modifier terms into a set of 5 fixed bins with interval object properties, for example, one_level_more/less_frequently_than, where new terms can only be added as synonyms to existing classes. The open list approach starts with 5 bins, but supports the extensibility of the list via ordinal properties, for example, more/less_frequently_than, allowing new terms to be inserted as a new class anywhere in the list. The consequences of the different design decisions are discussed in the paper. CharaParser was used to extract modifiers from plant, ant, and other taxonomic descriptions. After a manual screening, 130 modifier words were selected as the candidate terms for the modifier ontologies. Four curators/experts (three biologists and one information scientist specialized in biosemantics) reviewed and categorized the terms into 20 bins using the Ontology Term Organizer (OTO) (http://biosemantics.arizona.edu/OTO). Inter-curator variations were reviewed and expressed in the final ontologies. Results: Frequency, certainty, degree, and coverage terms with complete agreement among all curators were used as class labels or exact synonyms. Terms with different interpretations were either excluded or included using “broader synonym” or “not recommended” annotation properties. These annotations explicitly allow for the user to be aware of the semantic ambiguity associated with the terms and whether they should be used with caution or avoided. Expert categorization results showed that 16 out of 20 bins contained terms with full agreements, suggesting differentiating the modifiers into 5 levels/bins balances the need to differentiate modifiers and the need for the ontology to reflect user consensus. Two ontologies, developed using the Protege ontology editor, are made available as OWL files and can be downloaded from https://github.com/biosemantics/ontologies. Contribution: We built the first two modifier ontologies following a consensus-based approach with terms commonly used in taxonomic literature. The five-bin ontology has been used in the Explorer of Taxon Concepts web toolkit to compute the similarity between characters extracted from literature to facilitate taxon concepts alignments. The two ontologies will also be used in an ontology-informed authoring tool for taxonomists to facilitate consistency in modifier term usage.more » « less
-
The Berry connection encodes the momentum-space geometry of occupied Bloch states in gapped insulators and plays a central role in topological materials. While gauge-invariant quantities can be evaluated from overlap matrices between neighboring points, accessing the Berry connection itself as a smooth field requires specifying a continuous gauge over the Brillouin zone. Wannier-based workflows achieve this through projection onto localized orbitals, enabling stable evaluation of geometric quantities and response functions. In this setting, the Berry connection enters directly in Wannier-interpolated calculations of polarization, Berry curvature, and related response functions. In practical implementations, however, the projection-gauge Berry connection is typically constructed from finite-difference overlaps between neighboring points, discretizing momentum derivatives and introducing errors tied to -mesh spacing and gauge alignment. These effects can become numerically delicate in systems with small band gaps or when evaluating higher-order responses such as the Chern-Simons axion angle. Here, we derive an exact expression for the non-Abelian Berry connection in the projection gauge that is local in crystal momentum. Starting from projected and orthonormalized Bloch-like states, we obtain a closed-form equation expressed entirely in terms of local quantities. We validate the formulation in one and three dimensions by computing the Berry phase and Chern-Simons axion angle in tight-binding models. The resulting framework provides a stable route to evaluating geometric properties within Wannier-interpolation schemes and future first-principles implementations.more » « less
-
Abstract Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.more » « less
An official website of the United States government

