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At least 451 records · Page 25

Vicarious Calibration of GOCI for the SeaDAS Ocean Color Retrieval

A key on-orbit calibration step for satellite remote sensing of ocean color is the vicarious calibration. This establishes the final gains for each spectral band on the sensor that minimize bias in the retrieved ocean color signal. The vicarious calibration is specific to the instrument and the atmospheric correction algorithm. The vicarious calibration gains for the Geostationary Ocean Color Imager (GOCI) are presented here, which were derived to optimize the performance ofNASA's standard atmospheric correction algorithm as implemented in the l2gen code and distributed through the SeaDAS open-source software package. Following NASA's protocols, the near-infrared(NIR) bands were calibrated first, and the visible bands were then calibrated relative to this fixed NIR calibration. The gain for the 745-nm NIR band was derived using a fixed aerosol model, which waschosen based on the Angstrom Coefficients derived from MODIS onAqua (MODISA). For the vicarious gains of the visible bands, twosources for the target water-leaving radiances were tested: matchupsfrom MODISA and climatological data from SeaWiFS. A validation analysis using AERONET-OC data shows an improvement in sensor performance when compared with results using the current vicarious gains and results using no vicarious calibration. Good agreement was found in vicarious gains derived using both concurrent MODISA and climatological SeaWiFS as vicarious calibration data sources. These results support the use of a concurrent sensor for the vicarious calibration when in situ data are not available and demonstrate that using climatology from a well-calibrated sensor like SeaWiFSfor the vicarious calibration is a valid alternative when it is not possible to use a concurrent sensor or in situ data. We recommend using the gains derived from concurrent GOCI matchups with MODISA for GOCI processing in SeaDAS/l2gen.

Concha, Javier↗

Comparison of Dead-Time Effects in a WPT System Inverter for Different Fixed-Frequency Modulation Techniques

In this paper, a comparative study of the dead-time effects in a wireless power transfer (WPT) system inverter is performed for different fixed-frequency control techniques. The dead-time is provided between the complementary switching instances of the inverter phase-legs to ensure safe operation of the input power source. Under certain operating conditions, the dead-time results in waveform distortions or voltage-polarity reversal (VPR) at the inverter output. The VPR affects the switching characteristics, harmonic spectrum, switching losses, and output voltage/power of the system. A detailed analysis of the dead-time effect on the WPT system parameters such as output voltage and output power is conducted for the different fixed-frequency control strategies (i.e., traditional phase-shift control, asymmetrical clamped-mode, and asymmetrical duty-cycle control). Furthermore, the impact of dead-time on the inverter switching losses is compared for the different control strategies.

Kavimandan, Utkarsh↗

Tracking Energy Flow Using a Volumetric Acoustic Intensity Imager (VAIM)

A new measurement device has been invented at the Naval Research Laboratory which images instantaneously the intensity vector throughout a three-dimensional volume nearly a meter on a side. The measurement device consists of a nearly transparent spherical array of 50 inexpensive microphones optimally positioned on an imaginary spherical surface of radius 0.2m. Front-end signal processing uses coherence analysis to produce multiple, phase-coherent holograms in the frequency domain each related to references located on suspect sound sources in an aircraft cabin. The analysis uses either SVD or Cholesky decomposition methods using ensemble averages of the cross-spectral density with the fixed references. The holograms are mathematically processed using spherical NAH (nearfield acoustical holography) to convert the measured pressure field into a vector intensity field in the volume of maximum radius 0.4 m centered on the sphere origin. The utility of this probe is evaluated in a detailed analysis of a recent in-flight experiment in cooperation with Boeing and NASA on NASA s Aries 757 aircraft. In this experiment the trim panels and insulation were removed over a section of the aircraft and the bare panels and windows were instrumented with accelerometers to use as references for the VAIM. Results show excellent success at locating and identifying the sources of interior noise in-flight in the frequency range of 0 to 1400 Hz. This work was supported by NASA and the Office of Naval Research.

Klos, Jacob↗

Thomas Leps Internship Abstract

An optical navigation system is being flown as the backup system to the primary Deep Space Network telemetry for navigation and guidance purposes on Orion. This is required to ensure Orion can recover from a loss of communication, which would simultaneously cause a loss of DSN telemetry. Images taken of the Moon and Earth are used to give range and position information to the navigation computer for trajectory calculations and maneuver execution. To get telemetry data from these images, the size and location of the moon need to be calculated with high accuracy and precision. The reentry envelope for the Orion EM-1 mission requires the centroid and radius of the moon images to be determined within 1/3 of a pixel 3 sigma. In order to ensure this accuracy and precision can be attained, I was tasked with building precise dot grid images for camera calibration as well as building a hardware in the loop test stand for flight software and hardware proofing. To calibrate the Op-Nav camera a dot grid is imaged with the camera, the error between the image dot location and the actual dot location can be used to build a distortion map of the camera and lens system so that images can be fixed to display truth locations. To build the dot grid images I used the Electro Optics Lab optical bench Bright Object Simulator System, and gimbal. The gimbal was slewed to a series of elevations and azimuths. An image of the collimated single point light source was then taken at each position. After a series of 99 images were taken at different locations the single light spots were extracted from each image and added to a composite image containing all 99 points. During the development of these grids it was noticed that an intermittent error in the artificial "star" locations occurred. Prior to the summer this error was attributed to the gimbal having glitches in it's pointing direction and was going to be replaced, however after further examining the issue I determined it to be a software issue. I have since narrowed the likely source of the error down to a Software Development Kit released by the camera supplier PixeLink. I have since developed a workaround in order to build star grids for calibration until the software bug can be isolated and fixed. I was also tasked with building a Hardware in the Loop test stand in order to test the full Op-Nav system. A 4k screen displays simulated Lunar and Terrestrial images from a possible Orion trajectory. These images are then projected through a collimator and then captured with an Op-Nav camera controlled by an Intel NUC computer running flight software. The flight software then analyzes the images to determine attitude and position, this data is then reconstructed into a trajectory and matched to the simulated trajectory in order to determine the accuracy of the attitude and position estimates. In order for the system to work it needs to be precisely and accurately aligned. I developed an alignment procedure that allows the screen, collimator and camera to be squared, centered and collinear with each other within a micron spatially and 5 arcseconds in rotation. I also designed a rigid mount for the screen that was machined on site in Building 10 by another intern. While I was working in the EOL we received a $500k Orion startracker for alignment procedure testing. Due to my prior experience in electronics development, as an ancillary duty, I was tasked with building the cables required to operate and power the startracker. If any errors are made building these cables the startracker would be destroyed, I was honored that the director of the lab entrusted such a critical component with me. This internship has cemented my view on public space exploration. I always preferred public sector to privatization because, as a scientist, the most interesting aspects of space for me are not necessarily the most profitable. I was concerned that the public sector was faltering however, and that in order to improve human space exploration I would be forced into private sector. I now know that, at least at JSC, human spaceflight is still progressing, and exciting work is still being done. I am now actively seeking employment at JSC after I complete my Ph.D and have met with my branch chiefs and mentor to discuss transitioning to a grad Co-op position.

Leps, Thomas↗

Space charge effects in the SπRIT time projection chamber

Time projection chambers (TPCs) are widely used in nuclear and particle physics. They are particularly useful when measuring reaction products from heavy ion collisions. Most nuclear experiments at low energy are performed in a fixed target configuration, in which the unreacted beam will pass through the detection volume. As the beam intensity increases, the buildup of positive ions created from the ionization of the detector gas by the beam creates the main source of space charge, distorting the nominal electric field of the TPC. This has a profound effect on the accuracy of the measured momenta of the emitted particles. In this paper we will discuss the magnitude of the effects and construct an observable appropriate for fixed target experiments to study the effects. Finally, we will present an algorithm for correcting the space charge and discuss some of the implications it has on the momentum determination.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Open Source Platform for Live Processing of High Data Rate Electron Microscopy (SBIR Phase I Award Topic 15, Subtopic B, Final Scientific / Technical Report)

4D scanning transmission electron microscopy (STEM) is experiencing a revolution both in terms of data size, and data veracity, as are many other areas of experimental data acquisition. This presents enormous opportunities to make new scientific discoveries, but is also hamstrung by aging software that is no longer fit for purpose. Experimental data acquisition platforms must make the same investments in software infrastructure that the simulation community made decades ago to take advantage of high-performance computing (HPC) if they hope to realize the full potential of the latest advances made in detector technology. This requires rethinking the design and deployment of hardware, moving away from small, fixed commodity computing capabilities with closed interfaces to open, modular, scalable systems designed for parallelism and throughput. The technical approach will leverage best-in-class open source technologies, and develop new approaches strategically to build an open source platform for experimental data acquisition targeting high data rate electron microscopy. The project will develop a software platform that uses the power and performance of modern HPC resources to ingest the large volume of data produced by electron microscopes using direct electron detectors. A set of configurable pipelines will be used to enable the processing to be tailored to the problem being investigated with builtin visualization of data at interactive rates. This project will leverage investments made by the DOE and other agencies to provide a powerful software platform for the experimental data community working with most powerful electron microscopes, such as 4D STEM detectors. It will create a platform that serves as a reference for the community. Permissive open source licensing will make the platform available to all, with a simple deployment strategy offering the ability to keep data close to where it is generated. This advanced software platform will require customization for each deployment, creating opportunities for software services that are typically offered to extend open source software platforms.

97 MATHEMATICS AND COMPUTING↗

n-Butanol production by Rhodopseudomonas palustris TIE-1

Anthropogenic carbon dioxide (CO 2 ) release in the atmosphere from fossil fuel combustion has inspired scientists to study CO 2 to biofuel conversion. Oxygenic phototrophs such as cyanobacteria have been used to produce biofuels using CO 2 . However, oxygen generation during oxygenic photosynthesis adversely affects biofuel production efficiency. To produce n-butanol (biofuel) from CO 2 , here we introduce an n-butanol biosynthesis pathway into an anoxygenic (non-oxygen evolving) photoautotroph, Rhodopseudomonas palustris TIE-1 (TIE-1). Using different carbon, nitrogen, and electron sources, we achieve n-butanol production in wild-type TIE-1 and mutants lacking electron-consuming (nitrogen-fixing) or acetyl-CoA-consuming (polyhydroxybutyrate and glycogen synthesis) pathways. The mutant lacking the nitrogen-fixing pathway produce the highest n-butanol. Coupled with novel hybrid bioelectrochemical platforms, this mutant produces n-butanol using CO 2 , solar panel-generated electricity, and light with high electrical energy conversion efficiency. Overall, this approach showcases TIE-1 as an attractive microbial chassis for carbon-neutral n-butanol bioproduction using sustainable, renewable, and abundant resources.

60 APPLIED LIFE SCIENCES↗

Respiratory energy demands and scope for demand expansion and destruction

Photosynthesis is the primary energy input to plants, but most plant metabolic processes are powered much or all of the time by ATP and NAD(P)H that come from respiratory oxidation of photosynthetically produced carbohydrates, that is, “dark respiration” (Amthor, 1994). The processes of growth, nutrient uptake and assimilation, active transport, and maintenance are thus all clients of respiration and compete for their share of a respiratory energy budget that is capped by photosynthate income. The economic principle of opportunity cost applies to these clients’ competing demands: spending respiratory energy on process A means missing the benefit of investing that energy in process B (Mahmoudabadi et al., 2019). This principle is key to assessing prospects for crop improvement by metabolic engineering. As de Lorenzo (2015) put it: “metabolism…frames and ultimately resolves whether a given genetic program (existing…or engineered) can be deployed or not.” Foreign or reconfigured native processes bolted on to a crop-plant’s metabolic chassis must compete for respiratory energy with native ones without crashing the energy economy. A proviso on plant carbon budgets is that photosynthetic carbon fixation (“source activity”) can in certain cases increase to meet increased carbon demand (“sink activity”), that is, budget envelopes are not always fixed (Smith et al., 2018). However, as there is some consensus that productivity is most often limited or co-limited by carbon supply (Ainsworth and Long, 2005; Körner, 2015; Sonnewald and Fernie, 2018), we make this our basal assumption in the analyses below.

59 BASIC BIOLOGICAL SCIENCES↗

A study of poultry processing plant noise characteristics and potential noise control techniques

The noise environment in a typical poultry processing plant was characterized by developing noise contours for two representative plants: Central Soya of Athens, Inc., Athens, Georgia, and Tip Top Poultry, Inc., Marietta, Georgia. Contour information was restricted to the evisceration are of both plants because nearly 60 percent of all process employees are stationed in this area during a normal work shift. Both plant evisceration areas were composed of tile walls, sheet metal ceilings, and concrete floors. Processing was performed in an assembly-line fashion in which the birds travel through the area on overhead shackles while personnel remain at fixed stations. Processing machinery was present throughout the area. In general, the poultry processing noise problem is the result of loud sources and reflective surfaces. Within the evisceration area, it can be concluded that only a few major sources (lung guns, a chiller component, and hock cutters) are responsible for essentially all direct and reverberant sound pressure levels currently observed during normal operations. Consequently, any effort to reduce the noise problem must first address the sound power output of these sources and/or the absorptive qualitities of the room.

Wyvill, J. C.↗

CORRELATED ERRORS IN EARTH POINTING MISSIONS

Two different Earth-pointing missions dealing with attitude control and dynamics changes illustrate concerns with correlated error sources and coupled effects that can occur. On the OrbView-2 (OV-2) spacecraft, the assumption of a nearly-inertially-fixed momentum axis was called into question when a residual dipole bias apparently changed magnitude. The possibility that alignment adjustments and/or sensor calibration errors may compensate for actual motions of the spacecraft is discussed, and uncertainties in the dynamics are considered. Particular consideration is given to basic orbit frequency and twice orbit frequency effects and their high correlation over the short science observation data span. On the Tropical Rainfall Measuring Mission (TRMM) spacecraft, the switch to a contingency Kalman filter control mode created changes in the pointing error patterns. Results from independent checks on the TRMM attitude using science instrument data are reported, and bias shifts and error correlations are discussed. Various orbit frequency effects are common with the flight geometry for Earth pointing instruments. In both dual-spin momentum stabilized spacecraft (like OV-2) and three axis stabilized spacecraft with gyros (like TRMM under Kalman filter control), changes in the initial attitude state propagate into orbit frequency variations in attitude and some sensor measurements. At the same time, orbit frequency measurement effects can arise from dynamics assumptions, environment variations, attitude sensor calibrations, or ephemeris errors. Also, constant environment torques for dual spin spacecraft have similar effects to gyro biases on three axis stabilized spacecraft, effectively shifting the one-revolution-per-orbit (1-RPO) body rotation axis. Highly correlated effects can create a risk for estimation errors particularly when a mission switches an operating mode or changes its normal flight environment. Some error effects will not be obvious from attitude sensor measurement residuals, so some independent checks using imaging sensors are essential and derived science instrument attitude measurements can prove quite valuable in assessing the attitude accuracy.

Steve Bilanow↗

Positive-Buoyancy Rover for Under Ice Mobility

A buoyant rover has been developed to traverse the underside of ice-covered lakes and seas. The rover operates at the ice/water interface and permits direct observation and measurement of processes affecting freeze- over and thaw events in lake and marine environments. Operating along the 2- D ice-water interface simplifies many aspects of underwater exploration, especially when compared to submersibles, which have difficulty in station-keeping and precision mobility. The buoyant rover consists of an all aluminum body with two aluminum sawtooth wheels. The two independent body segments are sandwiched between four actuators that permit isolation of wheel movement from movement of the central tether spool. For normal operations, the wheels move while the tether spool feeds out line and the cameras on each segment maintain a user-controlled fixed position. Typically one camera targets the ice/water interface and one camera looks down to the lake floor to identify seep sources. Each wheel can be operated independently for precision turning and adjustments. The rover is controlled by a touch- tablet interface and wireless goggles enable real-time viewing of video streamed from the rover cameras. The buoyant rover was successfully deployed and tested during an October 2012 field campaign to investigate methane trapped in ice in lakes along the North Slope of Alaska.

Leichty, John M.↗

Beyond Price Taker: Conceptual Design and Optimization of Integrated Energy Systems Using Machine Learning Market Surrogates

Future electricity generation systems must be optimized to provide flexibility that counteracts the variability of non-dispatchable renewable energy sources and ensures the reliability and safety of critical infrastructure, including the electric grid. The current state-of-the-art is to co-optimize the design and operation of integrated energy systems (IES) treating historical or predicted time-series electricity prices as fixed parameters. Recent literature has shown the limitations of this price taker assumption, which neglects how IES optimization decisions influence market outcomes. As such, this paper proposes a new optimization formulation that uses machine learning surrogate models, trained from a library of annual market operation simulations, to embed IES market interactions into the co-optimization problem directly. Using a thermal generator example built in the open-source IDAES computational environment, we show that the price taker approach routinely over-predicts annual revenues by 8% or more compared to a validation simulation, where the proposed approach has a typical relative error of 1% or less.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

X-Ray Detection and Processing Models for Spacecraft Navigation and Timing

The current primary method of deepspace navigation is the NASA Deep Space Network (DSN). High-performance navigation is achieved using Delta Differential One-Way Range techniques that utilize simultaneous observations from multiple DSN sites, and incorporate observations of quasars near the line-of-sight to a spacecraft in order to improve the range and angle measurement accuracies. Over the past four decades, x-ray astronomers have identified a number of xray pulsars with pulsed emissions having stabilities comparable to atomic clocks. The x-ray pulsar-based navigation and time determination (XNAV) system uses phase measurements from these sources to establish autonomously the position of the detector, and thus the spacecraft, relative to a known reference frame, much as the Global Positioning System (GPS) uses phase measurements from radio signals from several satellites to establish the position of the user relative to an Earth-centered fixed frame of reference. While a GPS receiver uses an antenna to detect the radio signals, XNAV uses a detector array to capture the individual xray photons from the x-ray pulsars. The navigation solution relies on detailed xray source models, signal processing, navigation and timing algorithms, and analytical tools that form the basis of an autonomous XNAV system. Through previous XNAV development efforts, some techniques have been established to utilize a pulsar pulse time-of-arrival (TOA) measurement to correct a position estimate. One well-studied approach, based upon Kalman filter methods, optimally adjusts a dynamic orbit propagation solution based upon the offset in measured and predicted pulse TOA. In this delta position estimator scheme, previously estimated values of spacecraft position and velocity are utilized from an onboard orbit propagator. Using these estimated values, the detected arrival times at the spacecraft of pulses from a pulsar are compared to the predicted arrival times defined by the pulsar s pulse timing model. A discrepancy provides an estimate of the spacecraft position offset, since an error in position will relate to the measured time offset of a pulse along the line of sight to the pulsar. XNAV researchers have been developing additional enhanced approaches to process the photon TOAs to arrive at an estimate of spacecraft position, including those using maximum-likelihood estimation, digital phase locked loops, and "single photon processing" schemes that utilize all available time data associated with each photon. Using pulsars from separate, non-coplanar locations provides range and range-rate measurements in each pulsar s direction. Combining these different pulsar measurements solves for offsets in position and velocity in three dimensions, and provides accurate overall navigation for deep space vehicles.

Sheikh, Suneel↗

InP MMIC Chip Set for Power Sources Covering 80-170 GHz

We will present a Monolithic Millimeter-wave Integrated Circuit (MMIC) chip set which provides high output-power sources for driving diode frequency multipliers into the terahertz range. The chip set was fabricated at HRL Laboratories using a 0.1-micrometer gate-length InAlAs/InGaAs/InP high electron mobility transistor (HEMT) process, and features transistors with an f(sub max) above 600 GHz. The HRL InP HEMT process has already demonstrated amplifiers in the 60-200 GHz range. In this paper, these high frequency HEMTs form the basis for power sources up to 170 GHz. A number of state-of-the-art InP HEMT MMICs will be presented. These include voltage-controlled and fixed-tuned oscillators, power amplifiers, and an active doubler. We will first discuss an 80 GHz voltage-controlled oscillator with 5 GHz of tunability and at least 17 mW of output power, as well as a 120 GHz oscillator providing 7 mW of output power. In addition, we will present results of a power amplifier which covers the full WRIO waveguide band (75-110 GHz), and provides 40-50 mW of output power. Furthermore, we will present an active doubler at 164 GHz providing 8% bandwidth, 3 mW of output power, and an unprecedented 2 dB of conversion loss for an InP HEMT MMIC at this frequency. Finally, we will demonstrate a power amplifier to cover 140-170 GHz with 15-25 mW of output power and 8 dB gain. These components can form a power source in the 155-165 GHz range by cascading the 80 GHz oscillator, W-band power amplifier, 164 GHz active doubler and final 140-170 GHz power amplifier for a stable, compact local oscillator subsystem, which could be used for atmospheric science or astrophysics radiometers.

Ngo, Catherine↗

Mutual Diffusion Coefficients and Refractive Index Increments of K 2 SO 4 (aq) at 298.15 K from Rayleigh Interferometry

Here, isothermal mutual diffusion coefficients (interdiffusion coefficients) were measured for K 2 SO 4 (aq) at 298.15 ± 0.005 K, at numerous concentrations ranging from dilute solutions to near saturation (0.59648 mol∙dm -3 ; 0.61349 mol∙kg -1 ) under free diffusion boundary conditions, using high precision Rayleigh interferometry. Under the experimental conditions these diffusion coefficients are on the volume-fixed reference frame D v . Two series of experiments were performed, the first using the traditional experimental approach with a mercury lamp source and with the interference patterns being recorded on glass photographic plates, and the second with a He-Ne laser light source and computerized data acquisition using a photodiode array. The results from both series of experiments are in excellent agreement, and generally yield diffusion coefficients precise to at least 0.002 x 10 -9 m 2 ∙s 1 (0.15% to 0.19%) and in most cases to 0.001 x 10 -9 m 2 ∙s -1 (0.07% to 0.1%). These experiments also yield accurate values of the refractive index differences for the solution pairs used in the diffusion experiments. The new diffusion coefficients are compared to two sets of published values of diffusion coefficients for K 2 SO 4 (aq) which are somewhat discrepant from each other. This study extends and complements our earlier work on the diffusion coefficients of the most common brine salts: NaCl(aq), KCl(aq), MgCl 2 (aq), CaCl 2 (aq), Na 2 SO 4 (aq), ] MgSO 4 (aq), NaHCO 3 (aq), and KHCO 3 (aq) at 298.15 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurements with silicon photomultipliers of dose-rate effects in the radiation damage of plastic scintillator tiles in the CMS hadron endcap calorimeter

Measurements are presented of the reduction of signal output due to radiation damage for two types of plastic scintillator tiles used in the hadron endcap (HE) calorimeter of the CMS detector. The tiles were exposed to particles produced in proton-proton (pp) collisions at the CERN LHC with a center-of-mass energy of 13 TeV, corresponding to a delivered luminosity of 50 fb−1. The measurements are based on readout channels of the HE that were instrumented with silicon photomultipliers, and are derived using data from several sources: a laser calibration system, a movable radioactive source, as well as hadrons and muons produced in pp collisions. Results from several irradiation campaigns using 60Co sources are also discussed. The damage is presented as a function of dose rate. Within the range of these measurements, for a fixed dose the damage increases with decreasing dose rate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states like the entanglement entropy can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resource for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive auxiliary field quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear—and unique—signatures of the underlying electronic behavior even when those features are less pronounced in conventional correlation functions. Altogether, this work provides a systematic means of characterizing the entanglement within quantum systems that can grant a deeper understanding of the complicated electronic behavior that underlies quantum phase transitions and crossovers in many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗