Combinatorial communications - The target lemma
Target lemma in combinatorial communications - proof of geometric property of multivariate Gaussian distribution
TELECOMMUNICATION↗
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Isotopic gamma lines for identification of shielding materials
Identifying the constituting materials of concealed objects is crucial in a wide range of sectors, such as medical imaging, geophysics, nonproliferation, national security investigations, and so on. Existing methods face limitations, particularly when multiple materials are involved or when there are challenges posed by scattered radiation and large areal mass. Here we introduce a novel brute-force statistical approach for material identification using high spectral resolution detectors, such as HPGe. The method relies upon updated semianalytic formulae for computing uncollided flux from source of gamma radiation, shielded by a sequence of nested spherical or cylindrical materials. These semianalytical formulae make possible rapid flux estimation for material characterization via combinatorial search through all possible combinations of materials, using a high-resolution HPGe counting detector. An important prerequisite for the method is that the geometry of the objects is known (for example, from X-ray radiography). We demonstrate the viability of this material characterization technique in several use cases with both simulated and experimental data in spherical geometry.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Material Identification From Radiographs Without Energy Resolution
We propose a method for performing material identification from radiographs without energy-resolved measurements. Material identification has a wide variety of applications, including in biomedical imaging, nondestructive testing, and security. While existing techniques for radiographic material identification make use of dual energy sources, energy-resolving detectors, or additional (e.g., neutron) measurements, such setups are not always practical— requiring additional hardware and complicating imaging. We tackle material identification without energy resolution, allowing standard X-ray systems to provide material identification information without requiring additional hardware. Assuming a setting where the geometry of each object in the scene is known and the materials come from a known set of possible materials, we pose the problem as a combinatorial optimization with a loss function that accounts for the presence of scatter and an unknown gain and propose a branch and bound algorithm to efficiently solve it. We present experiments on both synthetic data and real, experimental data with relevance to security applications— thick, dense objects imaged with MeV X-rays. We show that material identification can be efficient and accurate, for example, in a scene with three shells (two copper, one aluminum), our algorithm ran in six minutes on a consumer-level laptop and identified the correct materials as being among the top 10 best matches out of 8,000 possibilities.
36 MATERIALS SCIENCE↗
ACES M and S: Unmitigated Factorial Encounter Study on DAA/TCAS Interoperability
Realization of the expected proliferation of Unmanned Aircraft System (UAS) operations in the National Airspace System (NAS) depends on the development and validation of standards for UAS Detect and Avoid (DAA) Systems. The RTCA Special Committee 228 is charged with leading the development of draft Minimum Operational Performance Standards (MOPS) for UAS DAA Systems. NASA, as a participating member of RTCA SC-228 is committed to supporting the development and validation of draft requirements for DAA alerting and guidance systems. This presentation contains the results of two combinatorial encounter analysis studies using NASA's SAA Control fast-time simulation capability for this purpose. In these studies, encounters between two aircraft were simulated one at a time for the full factorial combination of encounter geometries (e.g., encounter angle, CPA offset) and aircraft performance (e.g., ownership and intruder ground speeds and vertical rates). The first study analyzes the relationships (e.g., timeline) between the different alerting-safety regions in the SC-228 MOPS (in order of increasing severity): 1) DAA warning alert, 2) well clear recovery (WCR) guidance, 3) DAA-Collision Avoidance (CA), and 4) TCAS RA. This study will focus primarily on encounter situations in which TCAS RA occurs prior to any of the other alerting-safety boundaries. In particular, this study will investigate whether using vertical distance or vertical distance at closest point of approach (i.e., vertical miss distance or VMD) is more appropriate for the definition of the DAA-CA region. In addition, cases where transitions between different regions skip an intermediate region will be analyzed. The second study in this presentation explores a proposal to use an altitude rate error threshold to determine if vertical maneuvers are acceptable for DAA WCR guidance against non-cooperative intruders. This study incorporates the radar from the Honeywell sensor model and examines a series of pairwise encounters between a non-cooperative intruder and a UAS ownship, with different combinations of intruder states and ownship performance levels. The study uses SAA Control as a simulation platform and pilot model, and Omnibands to provide DWC recovery guidance. Two simulation sets, one that allows vertical DWC recovery guidance and one that does not, are compared to determine if encounters with altitude rate errors above 250 feet-per-minute are more likely to have more severe losses of well clear, as determined by the Loss of Well-Clear Severity metric.
SaaControl↗
Kinematic flow from the flow of cuts
The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic flow, expressed using a set of differential forms referred to as the cut basis, from a geometric perspective, relying solely on the cosmological hyperplane arrangement and without invoking bulk physics. Each element of the cut basis corresponds to the positive geometry associated to an independent cut of the physical FRW-form and can be labeled by decorating (minors of) the truncated Feynman graph with an acyclic orientation. We provide a straightforward prescription to associate a logarithmic differential form to each element of the cut basis by considering its corresponding decorated graph. Moreover, we show that the residues of the physical FRW-form are canonical forms of certain graphical zonotopes labeled by the same set of decorated graphs. These zonotopes control the cut combinatorics -- flow of cuts -- of the physical FRW-form and the cut basis (by construction). Using the theory of relative twisted cohomology and intersection theory, we derive a closed form formula for the differential equations of the cut basis. We also introduce combinatorial rules that compute the kinematic differential of any basis element without explicit calculation. The combinatorics of our differential equations is a natural consequence of the flow of cuts and is equivalent (up to rescaling) to the kinematic flow for the recently studied time integral basis. In particular, our differential equations decouple into exponentially many sectors, one for each way of cutting a subset of edges of the graph.
General Relativity and Quantum Cosmology↗
Algebraic Structures in the Coupling of Gravity to Gauge Theories
Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Cosmohedra
It has been a long-standing challenge to find a geometric object underlying the cosmological wavefunction for Tr(ϕ 3 ) theory, generalizing associahedra and surfacehedra for scattering amplitudes. In this note, we describe a new class of polytopes — “cosmohedra” — that provide a natural solution to this problem. The faces of associahedra capture the combinatorics of non-overlapping chords of the momentum polygon, reflecting all partial factorizations of amplitudes. Cosmohedra are far richer — instead of non-overlapping chords, their faces capture the “russian doll” structure of non-overlapping subpolygons that determine the wavefunction. We show that cosmohedra are intimately related to associahedra, obtained by “blowing up” faces of the associahedron in a simple way. We give a full combinatorial description of cosmohedron faces and their factorization properties, and provide an explicit realization in terms of facet inequalities that further “shave” the facet inequalities of the associahedron. We also discuss a novel way for computing the wavefunction from cosmohedron geometry that extends the usual connection with polytope canonical forms. We illustrate cosmohedra with examples at tree-level and one loop; the close connection to surfacehedra suggests the generalization to all loop orders. Moving beyond the wavefunction, we briefly describe “cosmological correlahedra” for full correlators, which are one higher-dimensional polytopes, interpolating between associahedra and cosmohedra on opposite facets in an extra direction associated with the total energy. We speculate on how the existence of cosmohedra might suggest a “stringy” formulation for the cosmological wavefunction/correlators, generalizing the way in which the Minkowski sum decomposition of associahedra naturally extend particle to string amplitudes.
Scattering Amplitudes↗
Initial Results of Heuristic Guided Orbit Selection for a Low Frequency Radio Interferometric Spacecraft Constellation
A constellation of radio telescope spacecraft can leverage interferometry to accurately image distant objects throughout the universe, but mission design must balance among many interrelated constraints. In particular, the number of craft and the selection of time-varying orbital parameters play a pivotal role in determining what interferometric baselines are feasible with respect to different targets, and thus drives the breadth and quality of data available to the constellation. The large combinatorial orbit configuration space and competing concerns present a challenging problem that is not well addressed by traditional mission design processes. This paper describes application of automated optimization methods to help direct mission design effort to the most promising dynamic constellation geometries: those that achieve broad interferometric coverage but remain cost-effective and resilient to failures. Several automatic heuristic-driven optimization algorithms representing complementary search strategies were created to explore among concrete constellation configuration plans. Evaluation of each candidate constellation plan was accelerated by efficiently combining precomputed caches of orbital and interferometric data. Results indicate that leveraging automated optimization for constellation mission design is both practical and illuminating: generated solutions provided both evidence for existing design intuitions as well as fresh insights into novel configurations.
Hernandez, Sonia↗
Mapping the Binary Covalent Alloy Space to Pursue Superior Nitrogen Reduction Reaction Catalysts
The electrochemical nitrogen reduction reaction (NRR) has the potential to decarbonize industrial ammonia production. However, NRR has poor activity and selectivity versus the competing hydrogen evolution reaction for catalysts that adhere to scaling relations. Overcoming the limitations imposed by scaling relations requires more complex catalyst materials, however, evaluating materials beyond simple metal systems is a large combinatorial problem that requires an improved understanding of the electrocatalyst surface to rationally guide the discovery of superior catalysts. The study uses grand canonical density functional theory to uncover NRR trends on a large and disparate set of binary covalent alloys (BCA) with variable compositions and active-site geometries. The studied BCAs generally follow scaling relations, albeit with larger variance and several systems that significantly break scaling. BCAs with early- to mid-transition metals tend to lie near the volcano peak and activate the N 2 triple bond via a side-on binding configuration. Trends in the BCA space cannot be readily predicted using simple electronic descriptors, which is ascribed to the large geometric variability of the BCA surfaces. Furthermore, it is anticipated that these findings will provide a foundation for the rational design of superior NRR electrocatalysts with increasing material complexity.
36 MATERIALS SCIENCE↗
Scalar-scaffolded gluons and the combinatorial origins of Yang-Mills theory
We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order description of Tr Φ 3 theory. We propose that in a precise sense the amplitudes for a suitably “stringy” form of these two theories are identical, up to a simple shift of kinematic variables. This connection is made possible by describing the amplitudes for n gluons via a “scalar scaffolding”, arising from the scattering of 2n colored scalars coming in n distinct pairs of flavors fusing to produce the gluons. Fundamental properties of the “u-variables”, describing the “binary geometry” for surfaces appearing in the topological expansion, magically guarantee that the kinematically shifted Tr Φ 3 amplitudes satisfy the physical properties needed to be interpreted as scaffolded gluons. These include multilinearity, gauge invariance, and factorization on tree- and loop-level gluon cuts. Our “stringy” scaffolded gluon amplitudes coincide with amplitudes in the bosonic string for extra-dimensional gluon polarizations at tree-level, but differ (and are simpler) at loop-level. We provide many checks on our proposal, including matching non-trivial leading singularities through two loops. The simple counting problem underlying the u variables autonomously “knows” about everything needed to convert colored scalar to gluon amplitudes, exposing a striking “discovery” of Yang-Mills amplitudes from elementary combinatorial ideas in kinematic space.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
High‐throughput combinatorial approach expedites the synthesis of a lead‐free relaxor ferroelectric system
Abstract Developing novel lead‐free ferroelectric materials is crucial for next‐generation microelectronic technologies that are energy efficient and environment friendly. However, materials discovery and property optimization are typically time‐consuming due to the limited throughput of traditional synthesis methods. In this work, we use a high‐throughput combinatorial synthesis approach to fabricate lead‐free ferroelectric superlattices and solid solutions of (Ba 0.7 Ca 0.3 )TiO 3 (BCT) and Ba(Zr 0.2 Ti 0.8 )O 3 (BZT) phases with continuous variation of composition and layer thickness. High‐resolution x‐ray diffraction (XRD) and analytical scanning transmission electron microscopy (STEM) demonstrate high film quality and well‐controlled compositional gradients. Ferroelectric and dielectric property measurements identify the “optimal property point” achieved at the composition of 48BZT–52BCT. Displacement vector maps reveal that ferroelectric domain sizes are tunable by varying {BCT–BZT} N superlattice geometry. This high‐throughput synthesis approach can be applied to many other material systems to expedite new materials discovery and properties optimization, allowing for the exploration of a large area of phase space within a single growth. image
36 MATERIALS SCIENCE↗
High-throughput combinatorial approach expedites the synthesis of a lead-free relaxor ferroelectric system
Developing novel lead-free ferroelectric materials is crucial for next-generation microelectronic technologies that are energy efficient and environment friendly. However, materials discovery and property optimization are typically time-consuming due to the limited throughput of traditional synthesis methods. In this work, we use a high-throughput combinatorial synthesis approach to fabricate lead-free ferroelectric superlattices and solid solutions of (Ba 0.7 Ca 0.3 )TiO 3 (BCT) and Ba(Zr 0.2 Ti 0.8 )O 3 (BZT) phases with continuous variation of composition and layer thickness. High-resolution x-ray diffraction (XRD) and analytical scanning transmission electron microscopy (STEM) demonstrate high film quality and well-controlled compositional gradients. Ferroelectric and dielectric property measurements identify the “optimal property point” achieved at the composition of 48BZT–52BCT. Displacement vector maps reveal that ferroelectric domain sizes are tunable by varying {BCT–BZT} N superlattice geometry. This high-throughput synthesis approach can be applied to many other material systems to expedite new materials discovery and properties optimization, allowing for the exploration of a large area of phase space within a single growth.
36 MATERIALS SCIENCE↗
Development of a versatile, high-temperature, high-throughput ion irradiation system
We report ion irradiation has long been used as a surrogate for neutron irradiation experiments which are comparatively slower, more expensive, and often can leave materials activated and difficult to handle post-irradiation. However, with the growing use of combinatorial synthesis methods and high-throughput, automated characterization techniques, ion irradiation facilities will need to upgrade their capabilities to be able to accommodate these new material platforms. To address this challenge, a high-throughput ion irradiation system has been developed at the University of Wisconsin-Madison Ion Beam Laboratory (IBL). The system is capable of accommodating large sample arrays of arbitrary geometries and heat samples individually using an infrared laser to enable high-temperature, high-throughput ion irradiation while mitigating the risk of annealing the irradiation damage in nearby samples. To control stage motion, laser power, and beam current measurement, among other tasks, the program Chronos was developed which enables automated high-throughput irradiation experiments.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Improved Statistics for F-theory Standard Models
Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where the computation is combinatorial and straightforward. The question remains to relate the (a priori possibly smaller) value on the original curve to the singular one. In this work, we introduce some elementary techniques (pruning trees and removing interior edges) for simplifying the resulting nodal curves to a small collection of terminal ones that can be handled directly. When applied to the QSMs, these techniques yield optimal results in the sense that obtaining more precise answers would require currently unavailable information about the QSM geometries. This provides us with an opportunity to enhance the statistical bounds established in earlier research regarding the absence of vector-like exotics on the quark-doublet curve.
Bies, Martin↗
Deciphering the Cofilin Oligomers via Intermolecular Disulfide Bond Formation: A Coarse-Grained Molecular Dynamics Approach to Understanding Cofilin’s Regulation on Actin Filaments
Cofilin, a key actin-binding protein, orchestrates the dynamics of the actomyosin network through its actin-severing activity and by promoting the recycling of actin monomers. Recent experimental work suggests that cofilin also forms functionally distinct oligomers through thiol post-translational modification (PTM) that encourages actin nucleation and assembly. Despite these advances, the structural conformations of cofilin oligomers that modulate actin activity remain elusive because there are combinatorial ways to oxidize thiols in cysteines to form disulfide bonds rapidly. This study employs molecular dynamics simulations to investigate human cofilin 1 as a case study for exploring cofilin dimers via disulfide bond formation. Using the free energy profiling, our simulations unveil a range of probable cofilin dimer structures not represented in current Protein Data Bank entries. These candidate dimers are characterized by their distinct population distributions and relative free energies. Of particular note is a dimer featuring an interface between cysteines 139 and 147 residues, which demonstrates stable free energy characteristics and intriguingly symmetrical geometry. In contrast, the experimentally proposed dimer structure exhibits a less stable free energy profile. Here, we also evaluate frustration quantification based on the energy landscape theory in the protein-protein interactions at the dimer interfaces. Notably, the 39-39 dimer configuration emerges as a promising candidate for forming cofilin tetramers, as substantiated by frustration analysis. Additionally, docking simulations with actin filaments further evaluate the stability of these cofilin dimer-actin complexes. Our findings thus offer a computational framework for understanding the role of thiol post-translational modification cofilin proteins in regulating oligomerization, and the subsequent cofilin-mediated actin dynamics in the actomyosin network.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A Method for Aircraft Concept Selection Using Multicriteria Interactive Genetic Algorithms
The problem of aircraft concept selection has become increasingly difficult in recent years as a result of a change from performance as the primary evaluation criteria of aircraft concepts to the current situation in which environmental effects, economics, and aesthetics must also be evaluated and considered in the earliest stages of the decision-making process. This has prompted a shift from design using historical data regression techniques for metric prediction to the use of physics-based analysis tools that are capable of analyzing designs outside of the historical database. The use of optimization methods with these physics-based tools, however, has proven difficult because of the tendency of optimizers to exploit assumptions present in the models and drive the design towards a solution which, while promising to the computer, may be infeasible due to factors not considered by the computer codes. In addition to this difficulty, the number of discrete options available at this stage may be unmanageable due to the combinatorial nature of the concept selection problem, leading the analyst to arbitrarily choose a sub-optimum baseline vehicle. These concept decisions such as the type of control surface scheme to use, though extremely important, are frequently made without sufficient understanding of their impact on the important system metrics because of a lack of computational resources or analysis tools. This paper describes a hybrid subjective/quantitative optimization method and its application to the concept selection of a Small Supersonic Transport. The method uses Genetic Algorithms to operate on a population of designs and promote improvement by varying more than sixty parameters governing the vehicle geometry, mission, and requirements. In addition to using computer codes for evaluation of quantitative criteria such as gross weight, expert input is also considered to account for criteria such as aeroelasticity or manufacturability which may be impossible or too computationally expensive to consider explicitly in the analysis. Results indicate that concepts resulting from the use of this method represent designs which are promising to both the computer and the analyst, and that a mapping between concepts and requirements that would not otherwise be apparent is revealed.
Buonanno, Michael↗
Automated Fiber Placement Through Thickness Defect Stacking Optimization
In its 2022 commercial market outlook, Boeing forecasted an 80% increase in the global fleet through 2041 compared to 2019 pre-pandemic levels. This sharp rise in demand will drive pressure onto airframe manufacturers to ramp up production and find more efficient ways to design and manufacture airplanes. Complicating this challenge is the industry’s recent transformation from traditional metal-based airframes towards hybrid composite-metal aircraft. While composites have been used in aviation for decades, aircraft manufacturers are still struggling to design and manufacture quality parts at a high rate. Automated Fiber Placement (AFP) is one of the main manufacturing techniques used to produce large-scale composite parts. After a design has been created, a manufacturing strategy has to be developed based on the working material, part geometry, and machine capabilities. This process planning stage is essential to the AFP workflow and currently requires a high level of manual input from an experienced process planner. In an effort to automate and optimize this stage, the Computer Aided Process Planning (CAPP) module was developed. CAPP assists process planners in identifying optimal starting point location and layup strategy for each ply of a laminate. This Ply-Level Optimization (PLO) phase operates on the quantification of ply quality through predictable geometry-based defects such as gaps, overlaps, angle deviation, and steering. As you move from PLO to Laminate-Level Optimization (LLO) the design space grows exponentially, emphasizing the need for automated optimization. The work presented in this thesis expands CAPP’s functionality by comparing the planned fiber paths through the thickness of the laminate to mitigate stacked area defects and achieve an optimal laminate-level manufacturing strategy. Within CAPP, predicted gap and overlap defects are imported from Vericut Composites Programming (VCP) and then discretized to streamline the through-thickness comparison. Two objective functions are used to score different combinations of ply layup strategies based on defect stacking both globally and locally. Four combinatorial optimization algorithms were coupled with these objective functions to investigate the laminate-level manufacturing strategy design space and converge on the optimal plan. These algorithms were evaluated based on accuracy and efficiency through virtual testing on a complex tool surface. A separate LLO approach was developed to achieve near-optimal laminates in significantly less time. The end result is a software package which greatly reduces the required input from process planners, shortening the design-build cycle time and improving part quality.
AFP↗
Evaluation of Nanostructured β-Mn 2 V 2 O 7 Thin Films as Photoanodes for Photoelectrochemical Water Oxidation
β-Mn 2 V 2 O 7 (β-MVO) was recently reported to be a promising candidate for photoelectrochemical (PEC) water splitting, with a suitable band gap and band edge positions and reasonable stability and photoactivity in preliminary tests in alkaline solution. Here, we present an in-depth evaluation of the PEC performance and stability of phase-pure nanostructured β-Mn 2 V 2 O 7 films made by calcination of a spin-cast molecular ink. We show that β-Mn 2 V 2 O 7 dissolves in pure water, corrodes in aqueous electrolytes at pH 7 and 9, and converts to amorphous manganese (hydr)oxides within minutes at pH 13. Our β-Mn 2 V 2 O 7 films yielded only miniscule photocurrents (~uA cm -2 ) for the oxidation of iodide, sulfite, or water and the reduction of iodate or water in borate- and phosphate-buffered electrolytes at pH 7 and 9, the oxidation of [Fe(CN) 6 ] 4- or water at pH 13, and the oxidation of bromide in acetonitrile, regardless of film calcination temperature and time, film thickness, and illumination geometry. Minimal photoactivity was observed even in electrolytes in which film degradation was insignificant over the duration of the PEC tests. Ultrafast transient absorption spectroscopy shows that the poor photoactivity is likely the result of fast hole trapping and recombination at the MVO surface that leaves few free charge carriers beyond the picosecond time scale. Given its poor charge transport/extraction and chemical stability, native nanostructured β-Mn 2 V 2 O 7 is ineffective for solar water splitting and future research on this material should focus on the development of superior syntheses and film morphologies, MVO alloys, heterostructures, and surface coatings to alleviate recombination and boost operational stability. This work underscores the importance of careful follow-up studies of materials identified as "hits" in combinatorial materials discovery campaigns.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗