Physical Sciences and Mathematics Commons^™

Spectral Broadening Effects On Pulsed-Source Digital Holography, Steven A. Owens, Mark F. Spencer, Glen P. Perram

Faculty Publications

Using a pulsed configuration, a digital-holographic system is setup in the off-axis image plane recording geometry, and spectral broadening via pseudo-random bit sequence is used to degrade the temporal coherence of the master-oscillator laser. The associated effects on the signal-to-noise ratio are then measured in terms of the ambiguity and coherence efficiencies. It is found that the ambiguity efficiency, which is a function of signal-reference pulse overlap, is not affected by the effects of spectral broadening. The coherence efficiency, on the other hand, is affected. As a result, the coherence efficiency, which is a function of effective fringe visibility, is …

Complexity Heliophysics: A [New] System Science That Transcends The Previous Boundaries Of Our Field, Ryan M. Mcgranaghan, Seebany Datta-Barua, Jeffrey Thayer, Joe Borovsky, Jay R. Johnson, Simon Wing, Dan Baker, Massimo Materassi

Faculty Publications

Synopsis

1. The 21st century is the time of complexity. We delineate it and its importance as necessary to solve ‘wicked problems.’

2. Inherently transdisciplinary, trans-scale, and interconnected to living systems, the solution to Heliophysics’ identity crisis and to unlock the next generation of scientific discovery may be to embrace complexity.

3. With the right foresight, direction, and incentive over the next ten years, Heliophysics can become a beacon for how all of society thinks about and does complexity science.

Propagation Of Spatiotemporal Optical Vortex Beams In Linear, Second-Order Dispersive Media, Milo W. Hyde Iv, Miguel A. Porras

Faculty Publications

In this paper, we study the behaviors of spatiotemporal optical vortex (STOV) beams propagating in linear dispersive media. Starting with the Fresnel diffraction integral, we derive a closed-form expression for the STOV field at any propagation distance z in a general second-order dispersive medium. We compare our general result to special cases published in the literature and examine the characteristics of higher-order STOV beams propagating in dispersive materials by varying parameters of the medium and source-plane STOV field. We validate our analysis by comparing theoretical predictions to numerical computations of a higher-order STOV beam propagating through fused silica, where we …

The Emergence Of Convergence, Shana M. Sundstrom, David G. Angeler, Jessica G. Ernakovich, Jorge H. Garcia, Joseph A. Hamm, Orville Huntington, Craig R. Allen

Faculty Publications

Science is increasingly a collaborative pursuit. Although the modern scientific enterprise owes much to individuals working at the core of their field, humanity is increasingly confronted by highly complex problems that require the integration of a variety of disciplinary and methodological expertise. In 2016, the U.S. National Science Foundation launched an initiative prioritizing support for convergence research as a means of “solving vexing research problems, in particular, complex problems focusing on societal needs.” We discuss our understanding of the objectives of convergence research and describe in detail the conditions and processes likely to generate successful convergence research. We use our …

Wave Optics Approach To Solar Cell Brdf Modeling With Experimental Results, Madilynn Compean, Todd V. Small, Milo W. Hyde Iv, Michael Marciniak

Faculty Publications

Light curve analysis is often used to discern information about satellites in geosynchronous orbits. Solar panels, comprising a large part of the satellite’s body, contribute significantly to these light curves. Historically, theoretical bidirectional reflectance distribution functions (BRDFs) have failed to capture key features in the scattered light from solar panels. In recently published work, a new solar cell BRDF was developed by combining specular microfacet and “two-slit” diffraction terms to capture specular and periodic/array scattering, respectively. This BRDF was experimentally motivated and predicted many features of the solar cell scattered irradiance. However, the experiments that informed the BRDF were limited …

A Hybrid Metaheuristic And Computer Vision Approach To Closed-Loop Calibration Of Fused Deposition Modeling 3d Printers, Graig S. Ganitano, Shay V. Wallace, Benji Maruyama, Gilbert L. Peterson

Faculty Publications

Fused deposition modeling (FDM) is one of the most popular additive manufacturing (AM) technologies for reasons including its low cost and versatility. However, like many AM technologies, the FDM process is sensitive to changes in the feedstock material. Utilizing a new feedstock requires a time-consuming trial-and-error process to identify optimal settings for a large number of process parameters. The experience required to efficiently calibrate a printer to a new feedstock acts as a barrier to entry. To enable greater accessibility to non-expert users, this paper presents the first system for autonomous calibration of low-cost FDM 3D printers that demonstrates optimizing …

Hyperspectral Point Cloud Projection For The Semantic Segmentation Of Multimodal Hyperspectral And Lidar Data With Point Convolution-Based Deep Fusion Neural Networks, Kevin T. Decker, Brett J. Borghetti

Faculty Publications

The fusion of dissimilar data modalities in neural networks presents a significant challenge, particularly in the case of multimodal hyperspectral and lidar data. Hyperspectral data, typically represented as images with potentially hundreds of bands, provide a wealth of spectral information, while lidar data, commonly represented as point clouds with millions of unordered points in 3D space, offer structural information. The complementary nature of these data types presents a unique challenge due to their fundamentally different representations requiring distinct processing methods. In this work, we introduce an alternative hyperspectral data representation in the form of a hyperspectral point cloud (HSPC), which …

The Characteristics Of Successful Military It Projects: A Cross-Country Empirical Study, Helene Berg, Jonathan D. Ritschel

Faculty Publications

No abstract provided.

Short-Term Responses Of Soil Carbon, Nitrogen, And Microbial Biomass To Cover Crop Mixtures And Monocultures, Igor Alexandre De Souza, Amanda B. Daly, Jorg Schnecker, Nicholas D. Warren, Adalfredo Rocha Lobo Jr., Richard G. Smith, Andre Fonseca Brito, A. Stuart Grandy

Faculty Publications

Increasingly, cover crops are being adopted for the purpose of improving soil health, yet the timescale and magnitude by which living annual cover crops might modify soil chemical and biological aspects of soil health is not well understood. At the same time, there is growing interest among farmers in cover crop mixtures due to perceptions that species-rich cover crop communities will enhance soil health relative to monocultures. In a field experiment in southeast New Hampshire, we investigated how groups of cover crops grown as monocultures and mixtures for specific seasonal niches (winter/spring, summer, and fall) influenced levels of soil nitrogen …

Accurate Covariance Estimation For Pose Data From Iterative Closest Point Algorithm, Rick H. Yuan, Clark N. Taylor, Scott L. Nykl

Faculty Publications

One of the fundamental problems of robotics and navigation is the estimation of the relative pose of an external object with respect to the observer. A common method for computing the relative pose is the iterative closest point (ICP) algorithm, where a reference point cloud of a known object is registered against a sensed point cloud to determine relative pose. To use this computed pose information in downstream processing algorithms, it is necessary to estimate the uncertainty of the ICP output, typically represented as a covariance matrix. In this paper, a novel method for estimating uncertainty from sensed data is …

Scalable Preparation Of The Masked Acyl Cyanide Tbs-Mac, Haley Hinton, Jack Patterson, Jared Hume, Krunal Patel, Julie Pigza

Faculty Publications

This paper describes the three-step synthesis of TBS-MAC, a masked acyl cyanide (MAC) and a versatile one-carbon oxidation state three synthon. We have developed a scalable and detailed synthesis that involves: (1) acetylation of malononitrile to form the sodium enolate, (2) protonation of the enolate to form acetylmalononitrile, and (3) epoxidation of the enol, rearrangement to an unstable alcohol, and TBS-protection to form the title compound. Both the sodium enolate and acetylmalononitrile are bench-stable precursors to the intermediate hydroxymalononitrile, which can be converted to other MAC reagents beyond TBS by varying the protecting group (Ac, MOM, EE, etc.).

Intrinsic Point Defects (Vacancies And Antisites) In Cdgep2 Crystals, Timothy D. Gustafson, Nancy C. Giles, Peter G. Schunemann, Kevin T. Zawilski, Kent L. Averett, Jonathan E. Slagle, Larry E. Halliburton

Faculty Publications

Cadmium germanium diphosphide (CdGeP₂) crystals, with versatile terahertz-generating properties, belong to the chalcopyrite family of nonlinear optical materials. Other widely investigated members of this family are ZnGeP₂ and CdSiP₂. The room-temperature absorption edge of CdGeP₂ is near 1.72 eV (720 nm). Cadmium vacancies, phosphorous vacancies, and germanium-on-cadmium antisites are present in as-grown CdGeP₂ crystals. These unintentional intrinsic point defects are best studied below room temperature with electron paramagnetic resonance (EPR) and optical absorption. Prior to exposure to light, the defects are in charge states that have no unpaired spins. Illuminating a CdGeP_{2 …}

Optimal Estimation Inversion Of Ionospheric Electron Density From Gnss-Pod Limb Measurements: Part I-Algorithm And Morphology, Dong L. Wu, Nimalan Swarnalingam, Cornelius Csar Jude H. Salina, Daniel J. Emmons, Tyler C. Summers, Robert Gardiner-Garden

Faculty Publications

GNSS-LEO radio links from Precise Orbital Determination (POD) and Radio Occultation (RO) antennas have been used increasingly in characterizing the global 3D distribution and variability of ionospheric electron density (Ne). In this study, we developed an optimal estimation (OE) method to retrieve Ne profiles from the slant total electron content (hTEC) measurements acquired by the GNSS-POD links at negative elevation angles (ε < 0°). Although both OE and onion-peeling (OP) methods use the Abel weighting function in the Ne inversion, they are significantly different in terms of performance in the lower ionosphere. The new OE results can overcome the large Ne oscillations, sometimes negative values, seen in the OP retrievals in the E-region ionosphere. In the companion paper in this Special Issue, the HmF2 and NmF2 from the OE retrieval are validated against ground-based ionosondes and radar observations, showing generally good agreements in NmF2 from all sites. Nighttime hmF2 measurements tend to agree better than the daytime when the ionosonde heights tend to be slightly lower. The OE algorithm has been applied to all GNSS-POD data acquired from the COSMIC-1 (2006–2019), COSMIC-2 (2019–present), and Spire (2019–present) constellations, showing a consistent ionospheric Ne morphology. The unprecedented spatiotemporal sampling of the ionosphere from these constellations now allows a detailed analysis of the frequency–wavenumber spectra for the Ne variability at different heights. In the lower ionosphere (~150 km), we found significant spectral power in DE1, DW6, DW4, SW5, and SE4 wave components, in addition to well-known DW1, SW2, and DE3 waves. In the upper ionosphere (~450 km), additional wave components are still present, including DE4, DW4, DW6, SE4, and SW4. The co-existence of eastward- and westward-propagating wave4 components implies the presence of a stationary wave4 (SPW4), as suggested by other earlier studies. Further improvements to the OE method are proposed, including a tomographic inversion technique that leverages the asymmetric sampling about the tangent point associated with GNSS-LEO links.

Numerical Simulation Of The Korteweg–De Vries Equation With Machine Learning, Kristina O. F. Williams *, Benjamin F. Akers

Faculty Publications

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse …

Marine Anoxia Initiates Giant Sulfur-Bacteria Mat Proliferation And Associated Changes In Benthic Nitrogen, Sulfur, And Iron Cycling In The Santa Barbara Basin, California Borderland, David J. Yousavich, De'marcus Robinson, Xuefeng Peng, Sebastian J.E. Krause, Frank Wenzhoefer, Felix Janßen, Na Liu, Jonathan Tarn, Frank Kinnaman, David L. Valentine, Tina Treude

Faculty Publications

The Santa Barbara Basin naturally experiences transient deoxygenation due to its unique geological setting in the southern California Borderland and seasonal changes in ocean currents. Long-term measurements of the basin showed that anoxic events and subsequent nitrate exhaustion in the bottom waters have been occurring more frequently and lasting longer over the past decade. One characteristic of the Santa Barbara Basin is the seasonal development of extensive mats of benthic nitrate-reducing sulfur-oxidizing bacteria, which are found at the sediment–water interface when the basin's bottom waters reach anoxia but still provide some nitrate. To assess the mat's impact on the benthic …

A Bit-Parallel Tabu Search Algorithm For Finding Es2 -Optimal And Minimax-Optimal Supersaturated Designs, Luis B. Morales, Dursun A. Bulotuglu

Faculty Publications

We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, s_max=4t+i, where i ∈ {0,2}, t ∈ Z^≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most (N+4t+i)/4 points. Using this equivalence, we formulate the search for two-symbol E(s²)-optimal and minimax-optimal SSDs with s_max ∈ {2,4,6} as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E(s²)-optimal and minimax-optimal SSDs achieving the sharpest known E(s²) lower bound with …

A Comparison Of Quaternion Neural Network Backpropagation Algorithms, Jeremiah Bill, Bruce A. Cox, Lance Champaign

Faculty Publications

This research paper focuses on quaternion neural networks (QNNs) - a type of neural network wherein the weights, biases, and input values are all represented as quaternion numbers. Previous studies have shown that QNNs outperform real-valued neural networks in basic tasks and have potential in high-dimensional problem spaces. However, research on QNNs has been fragmented, with contributions from different mathematical and engineering domains leading to unintentional overlap in QNN literature. This work aims to unify existing research by evaluating four distinct QNN backpropagation algorithms, including the novel GHR-calculus backpropagation algorithm, and providing concise, scalable implementations of each algorithm using a …

Fate And Transport Of Per- And Polyfluoroalkyl Substances (Pfas) At Aqueous Film Forming Foam (Afff) Discharge Sites: A Review, Jeffery T. Mcgarr, Eric G. Mbonimpa, Drew C. Mcavoy, Mohamad R. Soltanian

Faculty Publications

Per- and polyfluorinated alkyl substances (PFAS) are an environmentally persistent group of chemicals that can pose an imminent threat to human health through groundwater and surface water contamination. In this review, we evaluate the subsurface behavior of a variety of PFAS chemicals with a focus on aqueous film forming foam (AFFF) discharge sites. AFFF is the primary PFAS contamination risk at sites such as airports and military bases due to use as a fire extinguisher. Understanding the fate and transport of PFAS in the subsurface environment is a multifaceted issue. This review focuses on the role of adsorbent, adsorbate, and …

Microbial Carbon Use Efficiency Promotes Global Soil Carbon Storage, Feng Tao, Yuanyuan Huang, Bruce A. Hungate, Stefano Manzoni, Serita D. Frey, Michael W. I. Schmidt, Markus Reichstein, Nuno Carvalhais, Philippe Ciais, Lifen Jiang, Johannes Lehmann, Ying-Ping Wang, Benjamin Z. Houlton, Bernhard Ahrens, Umakant Mishra, Gustaf Hugelius, Toby D. Hocking, Xingjie Lu, Zheng Shi, Kostiantyn Viatkin, Ronald Vargas, Yusuf Yigini, Christian Omuto, Ashish A. Malik, Guillermo Peralta, Rosa Cuevas-Corona, Luciano E. Di Paolo, Isabel Luotto, Cuijuan Liao, Yi-Shuang Liang, Vinisa S. Saynes, Xiaomeng Huang, Yiqi Luo

Faculty Publications

Soils store more carbon than other terrestrial ecosystems1,2. How soil organic carbon (SOC) forms and persists remains uncertain1,3, which makes it challenging to understand how it will respond to climatic change3,4. It has been suggested that soil microorganisms play an important role in SOC formation, preservation and loss5,6,7. Although microorganisms affect the accumulation and loss of soil organic matter through many pathways4,6,8,9,10,11, microbial carbon use efficiency (CUE) is an integrative metric that can capture the balance of these processes12,13. Although CUE has the potential to act as a predictor of variation in SOC storage, the role of CUE in SOC …

Seasonal And Diurnal Variations Of Kelvin-Helmholtz Instability At Terrestrial Magnetopause, S. Kavosi, J. Raeder, Jay R. Johnson, K. Nykyri, C. J. Farrugia

Faculty Publications

Kelvin-Helmholtz Instability is ubiquitous at Earth’s magnetopause and plays an important role in plasma entry into the magnetosphere during northward interplanetary magnetic fields. Here, using one solar cycle of data from NASA THEMIS (Time History of Events and Macro scale Interactions during Substorms) and MMS (Magnetospheric Multiscale) missions, we found that KHI occurrence rates show seasonal and diurnal variations with the rate being high near the equinoxes and low near the solstices. The instability depends directly on the Earth’s dipole tilt angle. The tilt toward or away from the Sun explains most of the seasonal and diurnal variations, while the …

Search For B Mesogenesis At Babar, J. P. Lees, V. Poireau, E. Grauges, A. Palano, G. Eigen, D. N. Brown, Yu. G. Kolomensky, M. Fritsch, H. Koch, R. Cheaib, C. Hearty, T. S. Mattison, J. A. Mckenna, R. Y. So, V. E. Blinov, A. R. Buzykaev, V. P. Druzhinin, E. A. Kozyrev, Milind Purohit, Et. Al.

Faculty Publications

A new mechanism has been proposed to simultaneously explain the presence of dark matter and the matter-antimatter asymmetry in the Universe. This scenario predicts exotic B-meson decays into a baryon and a dark-sector antibaryon (ψD) with branching fractions accessible at B factories. We present a search for B→Λψ_D decays using data collected by the BABAR experiment at SLAC. This reaction is identified by fully reconstructing the accompanying B meson and requiring the presence of a single Λ baryon in the remaining particles. No significant signal is observed, and bounds on the B→Λψ …

A Predator-Prey Biological Model With Combined Birth Rates, Self-Limitation And Competition Terms, Joon Hyuk Kang, Lucinda Ford

Faculty Publications

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rⁿ. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive …

Information Horizon Of Solar Active Regions, Jay R. Johnson, Simon Wing, Carson O'Ffill, Bishwa Neupane

Faculty Publications

Information theory is used to characterize the solar active region periodicities and memories from the Carrington map images 1974–2021. The active regions typically evolve and move from one map to the next. In order to track these active region structures in sequences of images, an innovative method based on information theory is developed. Image entropy provides a measure of the organization of structures in the images. The entropy can also be used as a filter to identify structures and partition the active regions, which are then registered for each image. The partitions are used to compute the mutual information and …

Measuring Radiation Protection: Partners From Across The Nuclear Enterprise Evaluate The Radiation Protection Of Us Army Vehicles, Andrew W. Decker, Robert Prins

Faculty Publications

Recent mounting nuclear threats and postures from adversary nation-states, such as Russia, China, North Korea, and Iran, represent a clear danger to the interests and security of the United States of America and its Allies. To meet these threats, the 2022 Nuclear Posture Review requires the Department of Defense (DoD) to design, develop, and manage a combat-credible U.S. military which, among other prioritizations, is survivable. A survivable force can generate combat power despite adversary attacks. As such, the US Army must prepare today to set the conditions for successful conventional warfare on the nuclear battlefields of tomorrow. Our Army cannot …

Traffic Lights For Catalysis: Stimuli-Responsive Molecular And Extended Catalytic Systems, Grace C. Thaggard, Johanna Haimeri, Roland A. Fischer Prof. Dr., Kyoung Chul Park, Natalia B. Shustova Prof. Dr.

Faculty Publications

The advances made in the field of stimuli-responsive catalysis during the last five years with a focus on the novel recently-emerged directions and applications have been surveyed. Metal-free catalysts and organometallic complexes, as well as biomimetic systems and extended structures, which display switchable catalytic activity for a variety of organic transformations, are discussed. Light-activated systems comprised of photochromic molecules capable of modulating reaction rate, yield, or enantioselectivity based on geometric and electronic changes associated with photoisomerization are the focus of the detailed discussion. Alternative stimuli, including pH and temperature, which could be applied either alone or in combination with light, …

Trait-Based Assembly Of Arbuscular Mycorrhizal Fungal Communities Determines Soil Carbon Formation And Retention, Caitlyn C. A. Horsch, Pedro M. Antunes, Catherine Fahey, A. Stuart Grandy, Cynthia M. Kallenbach

Faculty Publications

Fungi are crucial for soil organic carbon (SOC) formation, especially for the more persistent mineral-associated organic C (MAOC) pool. Yet, evidence for this often overlooks arbuscular mycorrhizal fungi (AMF) communities and how their composition and traits impact SOC accumulation.

We grew sudangrass with AMF communities representing different traits conserved at the family level: competitors, from the Gigasporaceae family; ruderals, from the Glomeraceae family; or both families combined. We labeled sudangrass with 13C-CO2 to assess AMF contributions to SOC, impacts on SOC priming, and fungal biomass persistence in MAOC.

Single-family AMF communities decreased total SOC by 13.8%, likely due to fungal …

Off-Shell Effects In Bound Nucleons And Parton Distributions From 1H, 2H, 3H, And 3He Data, S. I. Alekhin, S. A. Kulagin, Roberto Petti

Faculty Publications

We report the results of a new global QCD analysis including deep-inelastic scattering data off ¹H, ²H, ³H, and ³He targets. Nuclear corrections are treated in terms of a nuclear convolution approach with off-shell bound nucleons. The off-shell (OS) corrections responsible for the modification of the structure functions (SFs) of bound nucleons are constrained in a global fit along with the proton parton distribution functions (PDFs) and the higher-twist (HT) terms. We investigate the proton-neutron difference for the OS correction and discuss our predictions for the SF ratio F ⁿ ₂ / F ^p ₂ and …

Measurement Of The Double-Differential Muon-Neutrino Charged-Current Inclusive Cross Section In The Nova Near Detector, M. A. Acero, P. Adamson, L. Aliaga, N. Anfimov, A. Antoshkin, E. Arrieta-Diaz, L. Asquith, A. Aurisano, A. Back, M. Baird, N. Balashov, P. Baldi, B. A. Bambah, S. Bashar, K. Bays, B. Behera, R. Bernstein, V. Bhatnagar, D. Bhattarai, B. Bhuyan, Roberto Petti, Et. Al.

Faculty Publications

We report cross-section measurements of the final-state muon kinematics for ν_μ charged-current interactions in the NOvA near detector using an accumulated 8.09×10²⁰ protons on target in the NuMI beam. We present the results as a double-differential cross section in the observed outgoing muon energy and angle, as well as single-differential cross sections in the derived neutrino energy, E_ν, and square of the four-momentum transfer, Q². We compare the results to inclusive cross-section predictions from various neutrino event generators via χ² calculations using a covariance matrix that accounts for bin-to-bin correlations of systematic uncertainties. …

Toward A Simulation Model Complexity Measure, J. Scott Thompson, Douglas D. Hodson, Michael R. Grimaila, Nicholas Hanlon, Richard Dill

Faculty Publications

Is it possible to develop a meaningful measure for the complexity of a simulation model? Algorithmic information theory provides concepts that have been applied in other areas of research for the practical measurement of object complexity. This article offers an overview of the complexity from a variety of perspectives and provides a body of knowledge with respect to the complexity of simulation models. The key terms model detail, resolution, and scope are defined. An important concept from algorithmic information theory, Kolmogorov complexity, and an application of this concept, normalized compression distance, are used to indicate the possibility of measuring changes …

Search For Heavy Neutral Leptons Using Tau Lepton Decays At Babar, J. P. Lees, V. Poireau, V. Tisserand, E. Grauges, A. Palano, G. Eigen, D. N. Brown, Yu. G. Kolomensky, M. Fritsch, H. Koch, R. Cheaib, C. Hearty, T. S. Mattison, J. A. Mckenna, R. Y. So, V. E. Blinov, A. R. Buzykaev, V. P. Druzhinin, E. A. Kravchenko, Milind Purohit, Et. Al.

Faculty Publications

This article presents a model-independent search for an additional, mostly sterile, heavy neutral lepton (HNL), that is capable of mixing with the Standard Model τ neutrino with a mixing strength of |U_τ4| 2, corresponding to the absolute square of the extended Pontecorvo-Maki-Nakagawa-Sakata matrix element. Data from the BABAR experiment, with a total integrated luminosity of 424 fb⁻¹, are analyzed using a kinematic approach that makes no assumptions on the model behind the origins of the HNL, its lifetime or decay modes. No significant signal is found. Upper limits on |U_τ4|² at the 95% …