Digital Commons Network^™

A Unified System For Tree- And Stand-Level Predictions, Quang V. Cao

Faculty Publications

The unified system developed in this study comprises two components, one to predict survival and the other to predict diameter, both at tree and stand levels. The tree survival model defaults to the stand survival model when tree diameter reaches a certain value. Similarly, the tree diameter growth model defaults to the quadratic mean diameter model when tree diameter is equal to quadratic mean diameter. The annual growth approach was used to accommodate growth intervals of different lengths. Parameters of the unified system can be estimated together (Simultaneous Estimation) or separately in two phases (Sequential Estimation). Also investigated was the …

Digital Anthropometry For Body Circumference Measurements: Toward The Development Of Universal Three-Dimensional Optical System Analysis Software, Sima Sobhiyeh, Samantha Kennedy, Alexander Dunkel, Marcelline E. Dechenaud, Jerome A. Weston, John Shepherd, Peter Wolenski, Steven B. Heymsfield

Faculty Publications

Background/Objective: Digital anthropometric (DA) assessments are increasingly being administered with three-dimensional (3D) optical devices in clinical settings that manage patients with obesity and related metabolic disorders. However, anatomic measurement sites are not standardized across manufacturers, precluding use of published reference values and pooling of data across research centers. Subjects/Methods: This study aimed to develop universal 3D analysis software by applying novel programming strategies capable of producing device-independent DA estimates that agree with conventional anthropometric (CA) measurements made at well-defined anatomic sites. A series of technical issues related to proprietary methods of 3D geometrical reconstruction and image analysis were addressed in …

Zynq System-On-Chip Dma Messaging For Processor Monitoring, Daniel F. Koranek, Douglas D. Hodson, Scott R. Graham

Faculty Publications

Xilinx Zynq-7000 System-on-Chip architectures combine an ARM Cortex-A9 core with an FPGA fabric. One benefit of this hybrid architecture is that it allows fast prototyping of designs where the security of either the processing system (PS) is monitored by the programmable logic (PL) or vice versa. The choice of implementing a design in the PS or PL is driven by cost-to-benefit analysis across many factors. This effort examines the design process required to construct security monitoring designs that use both the PS and PL. For background, this effort reviews similar security monitoring projects. For the effort, a PL peripheral was …

Shared Developmental Trajectories For Fractional Reasoning And Fine Motor Ability In 4 And 5 Year Olds, Lindsey Clark, John Shelley-Tremblay, Julie Cwikla

Faculty Publications

We investigated preschool-aged children’s understanding of early fractional tasks and how that performance correlates with fine motor skills and use of gestures while counting. Participants were 33 preschoolers aged 4 to 5 in two Southeastern public elementary schools. Children were tested individually in an interview-like setting. Mathematics tasks were presented in a paper and pencil format and the Grooved Pegboard test assessed fine motor skills. Finally, utilization of gestures was evaluated by taking a behavioral rating of the child’s hand morphology, accuracy of gestures, and synchrony of gestures and spoken word while performing a counting task. Results indicate that performance …

A Synthesis Of Deepwater Horizon Impacts On Coastal And Nearshore Living Marine Resources, Steven A. Murawski, Joshua P. Kilborn, Adriana C. Bejarano, David Chagaris, David Donaldson, Frank J. Hernandez, Timothy C. Macdonald, Craig Newton, Ernst Peebles, Kelly L. Robinson

Faculty Publications

The 2010 Deepwater Horizon (DWH) oil blowout in the Gulf of Mexico began on April 20, originating in the deep sea 66 km off the Louisiana coast. By early June, DWH oil had spread to coastal Louisiana, Mississippi, Alabama and western Florida. An estimated 2,113 km of shoreline were oiled, making DWH the largest marine oil spill in global history by length of affected shoreline. Additionally, a series of oil spill response measures were deployed, including diversions of Mississippi River discharge to forestall oil coming ashore, and the establishment of large-scale fishery closures, with both affecting coastal resources to varying …

Biophysical Characteristics Of Lipid-Induced Aβ Oligomers Correlate To Distinctive Phenotypes In Transgenic Mice, Jhinuk Saha, Dexter N. Dean, Shailendra Dhakal, Kelli A. Stockmal, Sarah E. Morgan, Kristy D. Dillon, Munir F. Adamo, Yona Levites, Vijayaraghavan Rangachari

Faculty Publications

Alzheimer's disease (AD) is a progressive neurodegenerative disorder that affects cognition and memory. Recent advances have helped identify many clinical sub-types in AD. Mounting evidence point toward structural polymorphism among fibrillar aggregates of amyloid-β (Aβ) to being responsible for the phenotypes and clinical manifestations. In the emerging paradigm of polymorphism and prion-like propagation of aggregates in AD, the role of low molecular weight soluble oligomers, which are long known to be the primary toxic agents, in effecting phenotypes remains inconspicuous. In this study, we present the characterization of three soluble oligomers of Aβ42, namely 14LPOs, 16LPOs, and GM1Os with discreet …

Streamline-Based Simulation Of Nanoparticle Transport In Field-Scale Heterogeneous Subsurface Systems, Bin Wang, Yin Feng, John Blears, Karsten Thompson, Richard Hughes

Faculty Publications

Nanoparticle (NP) transport is increasingly relevant to subsurface engineering applications such as aquifer characterization and enhanced oil recovery. An efficient field-scale simulation framework is critical for predicting NP performance and designing subsurface applications. In this work, for the first time, a streamline-based model is presented to simulate NP transport in field-scale subsurface systems with heterogeneous permeability. It considers a series of smart behaviors exhibited by engineered nanoparticles (NPs), including time-triggered encapsulation, retention, formation damage effects and variable nanofluid viscosity. The key methods employed by the algorithm are streamline-based simulation (SLS) and an operator-splitting (OS) technique for modeling NP transport. The …

Sparc: Statistical Performance Analysis With Relevance Conclusions, Justin C. Tullos, Scott R. Graham, Jeremy D. Jordan, Pranav R. Patel

Faculty Publications

The performance of one computer relative to another is traditionally characterized through benchmarking, a practice occasionally deficient in statistical rigor. The performance is often trivialized through simplified measures, such as the approach of central tendency, but doing so risks a loss of perspective of the variability and non-determinism of modern computer systems. Authentic performance evaluations are derived from statistical methods that accurately interpret and assess data. Methods that currently exist within performance comparison frameworks are limited in efficacy, statistical inference is either overtly simplified or altogether avoided. A prevalent criticism from computer performance literature suggests that the results from difference …

Photoinduced Trapping Of Charge At Sulfur Vacancies And Copper Ions In Photorefractive Sn2P2S6 Crystals, Timothy D. Gustafson, Eric M. Golden, Elizabeth M. Scherrer, Nancy C. Giles, A. A. Grabar, Sergey A. Basun, Jonathan E. Slagle [*], Larry E. Halliburton

Faculty Publications

Electron paramagnetic resonance (EPR) is used to monitor photoinduced changes in the charge states of sulfur vacancies and Cu ions in tin hypothiodiphosphate. A Sn₂P₂S₆ crystal containing Cu+ (3d10) ions at Sn²⁺ sites was grown by the chemical vapor transport method. Doubly ionized sulfur vacancies (V²⁺S) are also present in the as-grown crystal (where they serve as charge compensators for the Cu+ ions). For temperatures below 70 K, exposure to 532 or 633 nm laser light produces stable Cu²⁺ (3d⁹) ions, as electrons move from Cu⁺ ions to …

Effect Of Membrane Properties On The Carbonation Of Anion Exchange Membrane Fuel Cells, Yiwei Zheng, Lyzmarie Nicole Irizarry, Noor Ui Hassan, Eric R. Williams, Morgan Stefik, Jacob M. Lamanna, Daniel S. Hussey, Mustain E William

Faculty Publications

Anion exchange membrane fuel cells (AEMFC) are potentially very low-cost replacements for proton exchange membrane fuel cells. However, AEMFCs suffer from one very serious drawback: significant performance loss when CO2 is present in the reacting oxidant gas (e.g., air) due to carbonation. Although the chemical mechanisms for how carbonation leads to voltage loss in operating AEMFCs are known, the way those mechanisms are affected by the properties of the anion exchange membrane (AEM) has not been elucidated. Therefore, this work studies AEMFC carbonation using numerous high-functioning AEMs from the literature and it was found that the ionic conductivity of the …

T2k Measurements Of Muon Neutrino And Antineutrino Disappearance Using 3.13×1021 Protons On Target, K. Abe, N. Akhlaq, R. Akutsu, A. Ali, C. Alt, C. Andreopoulos, M. Antonova, S. Aoki, T. Arihara, Y. Asada, Y. Ashida, E. T. Atkin, Y. Awataguchi, G. J. Barker, G. Barr, D. Barrow, M. Batkiewicz-Kwasniak, A. Beloshapkin, F. Bench, V. Berardi, L. Berns, S. Bhadra, A. Blondel, S. Bolognesi, T. Bonus, B. Bourguille, S. B. Boyd, A. Bravar

Faculty Publications

We report measurements by the T2K experiment of the parameters θ23 and Δm322, which govern the disappearance of muon neutrinos and antineutrinos in the three-flavor PMNS neutrino oscillation model at T2K's neutrino energy and propagation distance. Utilizing the ability of the experiment to run with either a mainly neutrino or a mainly antineutrino beam, muon-like events from each beam mode are used to measure these parameters separately for neutrino and antineutrino oscillations. Data taken from 1.49×1021 protons on target (POT) in neutrino mode and 1.64×1021 POT in antineutrino mode are used. The best-fit values obtained by T2K were sin2(θ23)=0.51-0.07+0.06(0.43-0.05+0.21) and …

Linking Genes To Traits In Fungi, A. L. Romero-Olivares, Eric W. Morrison, A. Pringle, Serita D. Frey

Faculty Publications

Fungi are mediators of the nitrogen and carbon cycles in terrestrial ecosystems. Examining how nitrogen uptake and organic matter decomposition potential differs in fungi can provide insight into the underlying mechanisms driving fungal ecological processes and ecosystem functioning. In this study, we assessed the frequency of genes encoding for specific enzymes that facilitate nitrogen uptake and organic matter decomposition in 879 fungal genomes with fungal taxa grouped into trait-based categories. Our linked gene-trait data approach revealed that gene frequencies vary across and within trait-based groups and that trait-based categories differ in trait space. We present two examples of how this …

Covariance Of The Extended Holonomy, Rodolfo Gambini, Jorge Pullin, Aureliano Skirzewski

Faculty Publications

It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops must satisfy in order to yield covariant holonomies. This makes a quantum representation for Yang-Mills theories and gravity based on extended loops viable.

Development Of A Modular Mixed-Radiation Directional Rotating Scatter Mask Detection System, Bryan V. Egner, Darren E. Holland, Larry W. Burggraf, James E. Bevins

Faculty Publications

The ability to simultaneously identify the direction of both fast neutrons, above 1 MeV, and gamma rays using a light-weight system consisting of a single 1” EJ-309 organic liquid scintillator and a plastic Spartan rotating scatter mask (RSM) is demonstrated computationally through Monte Carlo simulations and validated with experimental measurements. Two sets of directional measurements were performed with an americium–beryllium source, emitting both neutrons and gamma rays. The RSM identified the direction of the source within one 10° rotational increment in the azimuthal and polar directions based on both the neutron and gamma-ray induced signals discriminated by charge integration pulse-shape …

Neighborhood Characteristics And The Mental Health Of Caregivers Cohabiting With Care Recipients Diagnosed With Alzheimer’S Disease, Dana M. Alhasan, Jana A. Hirsch, Chandra L. Jackson, Margaret Chandlee Miller, Bo Cai Ph.D., Matthew C. Lohman Ph.D.

Faculty Publications

While studies have documented the influence of caregiver and care recipient factors on caregiver health, it is important to address the potential impact of neighborhood contexts. This study estimated the cross-sectional associations between neighborhood characteristics and mental health among caregivers cohabiting with Alzheimer’s disease care recipients that were experiencing severe or non-severe neuropsychiatric symptoms (NPSs) (e.g., aggression/anxiety). We obtained data collected in 2010 on caregivers and care recipients (n

While studies have documented the influence of caregiver and care recipient factors on caregiver health, it is important to address the potential impact of neighborhood contexts. This study estimated the cross-sectional …

Trends In Growth Modeling In Fisheries Science, Shane A. Flinn, Stephen R. Midway

Faculty Publications

No abstract provided.

Accuracy Assessment Of Global Internal-Tide Models Using Satellite Altimetry, Loren Carrere, Brian K. Arbic, Brian Dushaw, Gary Egbert, Svetlana Erofeeva, Florent Lyard, Richard D. Ray, Clement Ubelmann, Edward Zaron, Zhongxiang Zhao, Jay F. Shriver, Maarten Cornelis Buijsman, Nicolas Picot

Faculty Publications

Altimeter measurements are corrected for several geophysical parameters in order to access ocean signals of interest, like mesoscale or sub-mesoscale variability. The ocean tide is one of the most critical corrections due to the amplitude of the tidal elevations and to the aliasing phenomena of high-frequency signals into the lower-frequency band, but the internal-tide signatures at the ocean surface are not yet corrected globally.

Internal tides can have a signature of several centimeters at the surface with wavelengths of about 50–250 km for the first mode and even smaller scales for higher-order modes. The goals of the upcoming Surface Water …

Asymptotic Security Of Discrete-Modulation Protocols For Continuous-Variable Quantum Key Distribution, Eneet Kaur, Saikat Guha, Mark M. Wilde

Faculty Publications

We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation …

Identify Rna-Associated Subcellular Localizations Based On Multi-Label Learning Using Chou’S 5-Steps Rule, Hao Wang, Yijie Ding, Jijun Tang Ph.D., Quan Zou, Fei Guo

Faculty Publications

Background: Biological functions of biomolecules rely on the cellular compartments where they are located in cells. Importantly, RNAs are assigned in specific locations of a cell, enabling the cell to implement diverse biochemical processes in the way of concurrency. However, lots of existing RNA subcellular localization classifiers only solve the problem of single-label classification. It is of great practical significance to expand RNA subcellular localization into multi-label classification problem.

Results: In this study, we extract multi-label classification datasets about RNA-associated subcellular localizations on various types of RNAs, and then construct subcellular localization datasets on four RNA categories. In order to …

Fracture Diodes: Directional Asymmetry Of Fracture Toughness, N. R. Brodnik, S. Brach, C. M. Long, G. Ravichandran, B. Bourdin, K. T. Faber, K. Bhattacharya

Faculty Publications

Toughness describes the ability of a material to resist fracture or crack propagation. It is demonstrated here that fracture toughness of a material can be asymmetric, i.e., the resistance of amedium to a crack propagating from right to left can be significantly different from that to a crack propagating from left to right. Such asymmetry is unknown in natural materials, but we show that it can be built into artificial materials through the proper control of microstructure. This paves the way for control of crack paths and direction, where fracture - when unavoidable - can be guidedthrough predesigned paths to …

On-Chip Silicon Photonic Controllable 2 × 2 Four-Mode Waveguide Switch, Cao Dung Truong, Duy Nguyen Thi Hang, Hengky Chandrahalim, Minh Tuan Trinh

Faculty Publications

Multimode optical switch is a key component of mode division multiplexing in modern high-speed optical signal processing. In this paper, we introduce for the first time a novel 2 × 2 multimode switch design and demonstrate in the proof-of-concept. The device composes of four Y-multijunctions and 2 × 2 multimode interference coupler using silicon-on-insulator material with four controllable phase shifters. The shifters operate using thermo-optic effects utilizing Ti heaters enabling simultaneous switching of the optical signal between the output ports on four quasi-transverse electric modes with the electric power consumption is in order of 22.5 mW and the switching time …

Beam Spin Asymmetry In Semi-Inclusive Electroproduction Of Hadron Pairs, M. Mirazita, H. Avakian, A. Courtoy, S. Pisano, S. Pisano, S. Adhikari, M. J. Amaryan, Giovanni Angelini, H. Atac, N. A. Baltzell, L. Barion, M. Battaglieri, I. Bedlinskiy, Fatiha Benmokhtar, A. Bianconi, A. S. Biselli, F. Bossù, S. Boiarinov, W. J. Briscoe, W. K. Brooks, Steffen Strauch, Et. Al.

Faculty Publications

A first measurement of the longitudinal beam spin asymmetry 𝐴_𝐿⁢𝑈 in the semi-inclusive electroproduction of pairs of charged pions is reported. 𝐴_𝐿⁢𝑈 is a higher-twist observable and offers the cleanest access to the nucleon twist-3 parton distribution function 𝑒⁡(𝑥). Data have been collected in the Hall-B at Jefferson Lab by impinging a 5.498-GeV electron beam on a liquid-hydrogen target, and reconstructing the scattered electron and the pion pair with the CLAS detector. One-dimensional projections of the 𝐴^{sin⁡𝜙𝑅} _LU moments are extracted for the kinematic variables of interest in the valence quark region. The understanding of dihadron production …

Journal Of Water Sanitation And Hygiene For Development Use Of Single Particle Icp-Ms To Estimate Silver Nanoparticle Penetration Through Baby Porcine Mucosa, Ilaria Zanoni, Matteo Crosera, Elena Pavoni, Gianpiero Adami, Marcella Mauro, Anna Luisa Costa, Jamie Lead, Francesca Larese

Faculty Publications

Children are potentially exposed to products that contain nanoparticles (NPs). In particular, silver NPs are commonly present both in products used by and around children, primarily due to their antibacterial properties. However, very few data are available regarding the ability of silver NPs to penetrate through the oral mucosa in children. In the present work, we used baby porcine buccal mucosa mounted on vertical Franz diffusion cells, as an in vitro model to investigate penetration of silver NPs (19 ± 5 nm). Permeability experiments were performed using pristine physiologically-relevant saline solution in the receiver chamber and known concentrations of NPs …

Use Of Single Particle Icp-Ms To Estimate Silver Nanoparticle Penetration Through Baby Porcine Mucosa, Ilaria Zanoni, Matteo Crosera, Elena Pavoni, Gianpiero Adami, Marcella Mauro, Anna Luisa Costa, Jamie Lead, Francesca Larese Filon

Faculty Publications

Children are potentially exposed to products that contain nanoparticles (NPs). In particular, silver NPs are commonly present both in products used by and around children, primarily due to their antibacterial properties. However, very few data are available regarding the ability of silver NPs to penetrate through the oral mucosa in children. In the present work, we used baby porcine buccal mucosa mounted on vertical Franz diffusion cells, as an in vitro model to investigate penetration of silver NPs (19 ± 5 nm). Permeability experiments were performed using pristine physiologically-relevant saline solution in the receiver chamber and known concentrations of NPs …

Integrated Profiling Identifies Itgb3bp As Prognostic Biomarker For Hepatocellular Carcinoma, Qiuli Liang, Chao Tan, Feifei Xiao, Fuqiang Yin, Meiliang Liu, Lei Lei, Liuyu Wu, Yu Yang, Jennifer Hui Juan Tan, Shun Liu, Xiaoyun Zeng

Faculty Publications

Hepatocellular carcinoma (HCC) is a highly malignant tumor. In this study, we sought to identify a novel biomarker for HCC by analyzing transcriptome and clinical data. The R software was used to analyze the differentially expressed genes (DEGs) in the datasets GSE74656 and GSE84598 downloaded from the Gene Expression Omnibus database, followed by a functional annotation. A total of 138 shared DEGs were screened from two datasets. They were mainly enriched in the “Metabolic pathways” pathway (Padj = 8.21E-08) and involved in the carboxylic acid metabolic process (Padj = 0.0004). The top 10 hub genes were found by protein-protein interaction …

Search For Slow Magnetic Monopoles With The Nova Detector On The Surface, M. A. Acero, P. Adamson, L. Aliaga, T. Alion, V. Allakhverdian, N. Anfimov, A. Antoshkin, E. Arrieta-Diaz, L. Asquith, A. Aurisano, A. Back, C. Backhouse, M. Biard, N. Balashov, P. Baldi, B. A. Bambah, S. Bashar, K. Bays, S. Bending, R. Bernstein, Roberto Petti, Sanjib R. Mishra Ph.D., Et. Al.

Faculty Publications

We report a search for a magnetic monopole component of the cosmic-ray flux in a 95-day exposure of the NOvA experiment’s Far Detector, a 14 kt segmented liquid scintillator detector designed primarily to observe GeV-scale electron neutrinos. No events consistent with monopoles were observed, setting an upper limit on the flux of 2 × 10⁻¹⁴ cm⁻² s⁻¹ sr⁻¹ at 90% C.L. for monopole speed 6 × 10⁻⁴ < β < 5 × 10⁻³ and mass greater than 5 × 10⁸ GeV. Because of NOvA’s small overburden of 3 meters-water equivalent, this constraint covers a previously unexplored low-mass region.

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Critical Points In Coupled Nonlinear Systems. I: Mathematical Framework, Dan Gabriel Cacuci

Faculty Publications

This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP), which enables the exact and efficient computation of the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) of coupled nonlinear models of physical systems characterized by imprecisely known parameters underlying the models, boundaries, and interfaces between the coupled systems. Responses defined at critical points are important in many applications, including system optimization, safety analyses and licensing. For the design and licensing of nuclear reactors, such essentially important responses include the maximum temperatures of the fuel and cladding in hot channels. The …

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology For Critical Points In Coupled Nonlinear Systems. Ii: Application To A Nuclear Reactor Thermal-Hydraulics Safety Benchmark, Dan Gabriel Cacuci

Faculty Publications

Responses defined at critical points are particularly important for reactor safety analyses and licensing (e.g., the maximum fuel and/or clad temperature). The novel mathematical framework of the first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP) is applied in this work to develop a reactor safety thermal-hydraulics benchmark model which admits exact closed-form expressions for the adjoint functions and for the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) in physical systems characterized by imprecisely known parameters, external and internal boundaries. This benchmark model is designed for verifying the capabilities and accuracies of computational tools …

Self-Assembled Thermoresponsive Nanogel From Grafted Hyaluronic Acid As A Biocompatible Delivery Platform For Curcumin With Enhanced Drug Loading And Biological Activities, Jittima Amie Luckanagul, Pahweenvaj Ratnatilaka Na Bhuket, Chawanphat Muangnoi, Pranee Rojsitthisak, Qian Wang, Pornchai Rojsitthisak

Faculty Publications

A hyaluronic acid-grafted poly(N-isopropylacrylamide) (HA-pNIPAM) was synthesized as a polymeric nanogel platform for encapsulation and delivery of hydrophobic bioactive compounds using curcumin as a model drug. As demonstrated by transmission electron microscopy and dynamic light scattering techniques, the HA-pNIPAM was simply assembled into spherical nano-sized particles with the thermoresponsive behavior. The success of curcumin aqueous solubilization was confirmed by fluorescent spectroscopy. The resulting nanogel formulation enhanced the aqueous solubility and uptake into NIH-3T3 cells of curcumin. This nanogel formulation also demonstrates cytocompatibility against NIH-3T3 cells, which deems it safe as a delivery vehicle. Moreover, the formulation has a slight skin-protection …

Quantum Statistical Learning Via Quantum Wasserstein Natural Gradient, Simon Becker, Wuchen Li

Faculty Publications

In this article, we introduce a new approach towards the statistical learning problem argminρ(θ )∈P_θ W² _Q(_ρ*, ρ(θ )) to approximate a target quantum state ρ_* by a set of parametrized quantum states ρ(θ ) in a quantum L²-Wasserstein metric. We solve this estimation problem by considering Wasserstein natural gradient flows for density operators on finite-dimensional C^∗ algebras. For continuous parametric models of density operators, we pull back the quantum Wasserstein metric such that the parameter space becomes a Riemannian manifold with quantum Wasserstein information matrix. Using a quantum analogue …