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At least 667 records · Page 37

Analysis of multiloop, multirate sampled-data systems

Based upon new identities between z-transforms at a basis rate, z-transforms at faster rates, and modified z-transforms, the equivalence between the frequency decomposition method and the switch decomposition method is precisely presented so that results of one method are easily obtained from results of the other. Next, a method is developed for determining the closed loop transfer function of multiloop, multirate sampled-data systems with noninteger ratio sampling rates. Previously, this process involved solving a complex system of equations with rational polynomial coefficients. Herein, this is avoided by introducing a systematic decomposition of matrix operators which naturally arise from the switch decomposition method. The matrix operators are simplified by introducing the shifted transforms of signals sampled at one of the faster rates.

Boykin, W. H.↗

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Elrod, Chris↗

Compositional analysis of organosolv poplar lignin by using high-performance liquid chromatography/high-resolution multi-stage tandem mass spectrometry

Organosolv treatment is an efficient and environmentally friendly process to degrade lignin into small compounds. The capability of characterizing the individual compounds in the complex mixtures formed upon organosolv treatment is essential for the optimization of the further lignin conversion processes and for the rational genetic engineering of plants used to produce lignin in order to improve lignin properties. In this study, an organosolv poplar lignin sample was initially analyzed by high-resolution mass spectrometry coupled with negative-ion mode electrospray ionization ((-)ESI HRMS). Lignin monomers and dimers were found to constitute the majority of the compounds in the organosolv lignin sample. Larger lignin oligomers, such as trimers and tetramers, and some not lignin-related compounds, were also detected. A high-performance liquid chromatograph/linear quadrupole ion trap/orbitrap mass spectrometer capable of multi-stage high-resolution tandem mass spectrometry experiments (HRMS n ), equipped with an (-)ESI source (HPLC/(-)ESI HRMS n ), was employed to separate the unknown compounds in the organosolv mixture and to obtain structural information for the deprotonated compounds via collision-activated dissociation (CAD) HRMS n experiments. To improve the understanding of the CAD behavior of deprotonated lignin-related compounds, 16 deprotonated model compounds with different functionalities and linkage types were examined. This approach enabled the assignment of likely structures for several lignin monomers, dimers, trimers, and tetramers, and some not lignin-related compounds, most likely fatty acids. Based on the proposed structures, compounds in the organosolv lignin sample contain β-O-4, 5–5, β-5, and possibly also 4-O-5 linkages. Most compounds contain G- and S-monomeric units although a small amount of H-units were also detected.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface analysis insight note: X‐ray photoelectron spectroscopy analysis of battery electrodes—Challenges with nickel–manganese–cobalt and Li examples using an Al Kα x‐ray source

X‐ray photoelectron spectroscopy (XPS) has become a highly important tool for the analysis of battery materials and components. However, both anecdotal and detailed analysis of selected parts of the literature indicate that many reports of XPS on battery electrodes have significant analysis or data flaws. In this paper, we highlight several of the common challenges that analysts face when using XPS for battery materials, pointing to recent literature that addresses many of the critical issues associated with sample preparation as well as data collection and analysis. A common error for battery materials (and other materials) involves ignoring peak overlaps and interferences. Specifically, when a “minor” peak associated with a component in relatively high concentration overlaps or contributes to the primary peak (or one recommended for quantitative analysis) from a different element in the material. Overlap issues apply to many battery electrodes composed of many elements with complex photoelectron peak structures, as well as those involving peaks with seemingly simpler spectral envelopes such as Li and F. Examples of issues associated with battery systems are highlighted by a discussion of challenges associated with XPS analysis of Li and nickel–manganese–cobalt (NMC) electrodes in battery systems. Lithium analysis has challenges associated with the preparation and an often‐unrecognized peak overlap with F. In our laboratory and in the literature, NMC electrodes are often examined and new XPS users do not always recognize interference of the Auger signal from F KLL (in or on the electrode) with Ni 2p photoelectron spectrum when generated with Al Kα X‐rays. The use of simulated spectra involving both F and NiO demonstrates the extent of F Auger contributions to the Ni 2p signal strength as a function of the F/Ni atom ratio in the material and suggests spectra information that can be used to identify how significant effects will be on the resultant spectra. Our analysis demonstrates that in many cases overlap issues are significant for real electrode materials.

25 ENERGY STORAGE↗

Illustrating galaxy–halo connection in the DESI era with illustrisTNG

ABSTRACT We employ the hydrodynamical simulation illustrisTNG to inform the galaxy–halo connection of the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG) samples of the Dark Energy Spectroscopic Instrument (DESI) survey at redshift z ∼ 0.8. Specifically, we model the galaxy colours of illustrisTNG and apply sliding DESI colour–magnitude cuts, matching the DESI target densities. We study the halo occupation distribution (HOD) model of the selected samples by matching them to their corresponding dark matter haloes in the illustrisTNG dark matter run. We find the HOD of both the LRG and ELG samples to be consistent with their respective baseline models, but also we find important deviations from common assumptions about the satellite distribution, velocity bias, and galaxy secondary biases. We identify strong evidence for concentration-based and environment-based occupational variance in both samples, an effect known as ‘galaxy assembly bias’. The central and satellite galaxies have distinct dependencies on secondary halo properties, showing that centrals and satellites have distinct evolutionary trajectories and should be modelled separately. These results serve to inform the necessary complexities in modelling galaxy–halo connection for DESI analyses and also prepare for building high-fidelity mock galaxies. Finally, we present a shuffling-based clustering analysis that reveals a 10–15 ${{\ \rm per\ cent}}$ excess in the LRG clustering of modest statistical significance due to secondary galaxy biases. We also find a similar excess signature for the ELGs, but with much lower statistical significance. When a larger hydrodynamical simulation volume becomes available, we expect our analysis pipeline to pinpoint the exact sources of such excess clustering signatures.

79 ASTRONOMY AND ASTROPHYSICS↗

Input-output oriented computation algorithms for the control of large flexible structures

An overview is given of work in progress aimed at developing computational algorithms addressing two important aspects in the control of large flexible space structures; namely, the selection and placement of sensors and actuators, and the resulting multivariable control law design problem. The issue of sensor/actuator set selection is particularly crucial to obtaining a satisfactory control design, as clearly a poor choice will inherently limit the degree to which good control can be achieved. With regard to control law design, the researchers are driven by concerns stemming from the practical issues associated with eventual implementation of multivariable control laws, such as reliability, limit protection, multimode operation, sampling rate selection, processor throughput, etc. Naturally, the burden imposed by dealing with these aspects of the problem can be reduced by ensuring that the complexity of the compensator is minimized. Our approach to these problems is based on extensions to input/output oriented techniques that have proven useful in the design of multivariable control systems for aircraft engines. In particular, researchers are exploring the use of relative gain analysis and the condition number as a means of quantifying the process of sensor/actuator selection and placement for shape control of a large space platform.

Minto, K. D.↗

Chemical Cartography with APOGEE: Mapping Disk Populations with a 2-process Model and Residual Abundances

We apply a novel statistical analysis to measurements of 16 elemental abundances in 34,410 Milky Way disk stars from the final data release (DR17) of APOGEE-2. Building on recent work, we fit median abundance ratio trends [X/Mg] versus [Mg/H] with a 2-process model, which decomposes abundance patterns into a "prompt" component tracing core-collapse supernovae and a "delayed" component tracing Type Ia supernovae. For each sample star, we fit the amplitudes of these two components, then compute the residuals Δ[X/H] from this two-parameter fit. The rms residuals range from ~0.01–0.03 dex for the most precisely measured APOGEE abundances to ~0.1 dex for Na, V, and Ce. The correlations of residuals reveal a complex underlying structure, including a correlated element group comprised of Ca, Na, Al, K, Cr, and Ce and a separate group comprised of Ni, V, Mn, and Co. Selecting stars poorly fit by the 2-process model reveals a rich variety of physical outliers and sometimes subtle measurement errors. Residual abundances allow for the comparison of populations controlled for differences in metallicity and [α/Fe]. Relative to the main disk (R = 3–13 kpc), we find nearly identical abundance patterns in the outer disk (R = 15–17 kpc), 0.05–0.2 dex depressions of multiple elements in LMC and Gaia Sausage/Enceladus stars, and wild deviations (0.4–1 dex) of multiple elements in ω Cen. The residual abundance analysis opens new opportunities for discovering chemically distinctive stars and stellar populations, for empirically constraining nucleosynthetic yields, and for testing chemical evolution models that include stochasticity in the production and redistribution of elements.

79 ASTRONOMY AND ASTROPHYSICS↗

A colorimetric method to measure in vitro nitrogenase functionality for engineering nitrogen fixation

Biological nitrogen fixation (BNF) is the reduction of N 2 into NH 3 in a group of prokaryotes by an extremely O 2 -sensitive protein complex called nitrogenase. Transfer of the BNF pathway directly into plants, rather than by association with microorganisms, could generate crops that are less dependent on synthetic nitrogen fertilizers and increase agricultural productivity and sustainability. In the laboratory, nitrogenase activity is commonly determined by measuring ethylene produced from the nitrogenase-dependent reduction of acetylene (ARA) using a gas chromatograph. The ARA is not well suited for analysis of large sample sets nor easily adapted to automated robotic determination of nitrogenase activities. Here, we show that a reduced sulfonated viologen derivative (S 2 V red ) assay can replace the ARA for simultaneous analysis of isolated nitrogenase proteins using a microplate reader. We used the S 2 V red to screen a library of NifH nitrogenase components targeted to mitochondria in yeast. Two NifH proteins presented properties of great interest for engineering of nitrogen fixation in plants, namely NifM independency, to reduce the number of genes to be transferred to the eukaryotic host; and O 2 resistance, to expand the half-life of NifH iron-sulfur cluster in a eukaryotic cell. This study established that NifH from Dehalococcoides ethenogenes did not require NifM for solubility, [Fe-S] cluster occupancy or functionality, and that NifH from Geobacter sulfurreducens was more resistant to O 2 exposure than the other NifH proteins tested. It demonstrates that nitrogenase components with specific biochemical properties such as a wider range of O 2 tolerance exist in Nature, and that their identification should be an area of focus for the engineering of nitrogen-fixing crops.

59 BASIC BIOLOGICAL SCIENCES↗

A review on recent machine learning applications for imaging mass spectrometry studies

Imaging mass spectrometry (IMS) is a powerful analytical technique widely used in biology, chemistry, and materials science fields that continue to expand. IMS provides a qualitative compositional analysis and spatial mapping with high chemical specificity. The spatial mapping information can be 2D or 3D depending on the analysis technique employed. Due to the combination of complex mass spectra coupled with spatial information, large high-dimensional datasets (hyperspectral) are often produced. Therefore, the use of automated computational methods for an exploratory analysis is highly beneficial. The fast-paced development of artificial intelligence (AI) and machine learning (ML) tools has received significant attention in recent years. These tools, in principle, can enable the unification of data collection and analysis into a single pipeline to make sampling and analysis decisions on the go. There are various ML approaches that have been applied to IMS data over the last decade. Here, in this review, we discuss recent examples of the common unsupervised (principal component analysis, non-negative matrix factorization, k-means clustering, uniform manifold approximation and projection), supervised (random forest, logistic regression, XGboost, support vector machine), and other methods applied to various IMS datasets in the past five years. The information from this review will be useful for specialists from both IMS and ML fields since it summarizes current and representative studies of computational ML-based exploratory methods for IMS.

47 OTHER INSTRUMENTATION↗

A Bootstrap Approach to Quantifying Reliabilities and Uncertainties of Complex Systems

While much work has been done in analyzing margins and uncertainties at the component level, a gap exists in NNSA methodology relating component level reliabilities and uncertainties to system level reliability and uncertainty. This paper shows how component level reliability data can be combined via a bootstrap analysis to estimate system level reliabilities and uncertainties. The performance of the bootstrap for this problem is validated through simulation studies. This paper extends the original work of Crowder by including sensitivity analyses related to changes in samples sizes and component failure probabilities. The use of the bootstrap as a decision-making tool is thus developed by quantifying the effect of such changes on system reliability.

97 MATHEMATICS AND COMPUTING↗

Experimental Data Curation at Large Instrument Facilities with Open Source Software

The National Synchrotron Light Source II operating at Brookhaven National Laboratory since 2014 for the US Department of Energy is one of the newest and brightest storage-ring synchrotron facility in the world. NSLS-II, like other facilities, provides pre-processing of the raw data and some analysis capabilities to its users. We describe the research collaborations and open source infrastructure developed at large instrument facilities such as NSLS-II for the purpose of curating high value scientific data along the early stages of the data lifecycle. Data acquisition and curation tasks include storing experiment configuration, detector metadata, raw data acquisition with infrastructure that converts proprietary instrument formats to industry standards. In addition, we describe a specific effort for discovering sample information at NSLS-II and tracing the provenance of analysis performed on acquired images. We show that curation tasks must be embedded into software along the data life cycle for effectiveness and ease of use, and that loosely defined collaborations evolve around shared open source tools. Finally we discuss best practices for experimental metadata capture in such facilities, data access and the new challenges of scale and complexity posed by AI-based discovery for the synthesis of new materials.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Laser Doppler velocimeter measurements of boundary layer velocity and turbulent intensities in Mach 2.5 flow

In recent years, the interest in developing a high-speed civil transport has increased. This has led to an increase in research activity on compressible supersonic flows, in particular the boundary layer. The structure of subsonic boundary layers has been extensively documented using conditional sampling techniques which exploit the knowledge of both u and v velocities. Researchers using these techniques have been able to explore some of the complex three-dimensional motions which are responsible for Reynolds stress production and transport in the boundary layer. As interest in turbulent structure has grown to include supersonic flows, a need for simultaneous multicomponent velocity measurements in these flows has developed. The success of conditional analysis in determining the characteristics of coherent motions and structures in the boundary layer relies on accurate, simultaneous measurement of two instantaneous velocity components.

Sewell, Jesse↗

Examination of the Atomic Pair Distribution Function (PDF) of SiC Nanocrystals by In-situ High Pressure Diffraction

Key properties of nanocrystals are determined by their real atomic structure, therefore a reasonable understanding and meaningful interpretation of their properties requires a realistic model of the structure. In this paper we present an evidence of a complex response of the lattice distances to external pressure indicating a presence of a complex structure of Sic nanopowders. The experiments were performed on nanocrystalline Sic subjected to hydrostatic or isostatic pressure using synchrotron and neutron powder diffraction. Elastic properties of the samples were examined based on X-ray diffraction data using a Diamond Anvil Cell (DAC) in HASYLAB at DESY. The dependence'of the lattice parameters and of the Bragg reflections width with pressure exhibits a ha1 nature of the properties (compressibilities) of the powders and indicates a complex structure of the grains. We interpreted tws behaviour as originating from different elastic properties of the grain interior and surface. Analysis of the dependence of individual interatomic distances on pressure was based on in-situ neutron diffraction measurements done with HbD diffractometer at LANSCE in Los Alamos National Laboratory with the Paris-Edinburgh cell under pressures up to 8 GPa (Qmax = 26/A). Interatomic distances were obtained by PDF analysis using the PDFgetN program. We have found that the interatomic distances undergo a complex, non-monotonic changes. Even under substantial pressures a considerable relaxation of the lattice may take place: some interatomic distances increase with an increase in pressure. We relate this phenomenon to: (1), changes of the microstructure of the densified material, in particular breaking of its fractal chain structure and, (2), its complex structure resembling that of a material composed of two phases, each with its distinct elastic properties.

Grzanka, E.↗

Nuclear Microprobe using Elastic Recoil Detection (ERD) for Hydrogen Profiling in High Temperature Protonic Conductors

The interaction between hydrogen and various high temperature protonic conductors (HTPC) has not been clearly understood due to poor densification and unreacted secondary phases. the melt-processing technique is used in producing fully dense simple SrCe(0.9)Y (0.10) O(3-delta) and complex Sr3Ca(1+x)Nb(2+x)O(9-delta) perovskites that can not be achieved by solid-state sintering. the possibilities of ion beam analysis have been investigated to quantify hydrogen distribution in HTPC perovskites subjected to water heat treatment. Nuclear microprobe technique is based on the interactions of a focused ion beam of MeV light ions (H-1, H-2, He-3, He-4,.) with the sample to be analyzed to determine local elemental concentrations at the cubic micrometer scale, the elastic recoil detection analysis technique (ERDA) has been carried out using He-4(+) microbeams and detecting the resulting recoil protons. Mappings of longitudinal sections of water treated SrCeO3 and Sr(Ca(1/3)Nb(2/3))O3 perovskites have been achieved, the water treatment strongly alters the surface of simple SrCe(0.9)Y(0.10)O(3-delta) perovskite. From Rutherford Back Scattering measurements (RBS), both Ce depletion and surface re-deposition is evidenced. the ERDA investigations on water treated Sr3Ca(1+x)Nb(2+x)O(9-delta) perovskite did not exhibit any spatial difference for the hydrogen incorporation from the surface to the centre. the amount of hydrogen incorporation for Sr3Ca(1+x)Nb(2+x)O(9-delta) was low and required further development of two less conventional techniques, ERDA in forward geometry and forward elastic diffusion H-1(p,p) H-1 with coincidence detection.

Berger, Pascal↗

40 Years of Processing Pieces of Space

This year marks the 40th year anniversary for the Antarctic Search for Meteorite (ANSMET) program. In 1976, the ANSMET program led the first expedition to Antarctica. The ANSMET program is a US-led field-based science project that recovers meteorite samples from Antarctica. Once a year from late November to late January, a field team consisting of 8 to 12 people, spends 6-8 weeks camping on the ice and collecting meteorites. Since 1976, more than 22,000 meteorite samples have been recovered. These meteorites come from asteroids, planets and other bodies of the solar system. Once collected, the Antarctic meteorites are shipped to NASA/Johnson Space Center (JSC) Houston, TX. in a refrigerated truck and are kept frozen to minimize oxidation until they are ready for initial processing. In Antarctica each meteorite is given a field tag which consists of numbers, once in the lab, this is replaced by an official tag, consisting of the Antarctic field location and year collected. The types and numbers of meteorites that have been classified include 849 carbonaceous chondrites, 135 enstatites, 512 achondrites, 64 stony, 115 irons, 48 others (27 R chondrites, 7 ungrouped), 6,161 H chondrites, 7,668 L chondrites, and 4,589 LL chondrites. Although 80-85 percent of the collected meteorites fall in the ordinary chondrite group, the other approximately 15 percent represent rare types of achondrites and carbonaceous chondrites. These rare meteorites include 25 lunar meteorites, 15 Martian meteorites, scores of various types of carbonaceous chondrites, and unique achondrites. The Antarctic meteorites that have been collected are processed in the Meteorite Processing Lab at JSC in Houston, TX. Initial processing of the meteorites begins with thawing/drying the meteorites in a nitrogen glove box for 24 to 48 hours. The meteorites are then photographed, measured, weighed and a description of the interior and exterior of each meteorite is written. The meteorite is broken and a representative sample, either a 1-3 gram chip or thin section is sent to the Smithsonian Institution for classification. After Antarctic meteorites have been classified and approved by the Nomenclature Committee of the Meteoritical Society, they are announced in the Antarctic Meteorite Newsletter, which is published twice per year (fall and spring) so that scientists may review which meteorites are available to study. Requests for Antarctic Meteorite samples are welcomed from research scientists, regardless of their current state of funding for meteorite studies. Since its inception over 3,300 requests have been made for pieces of these meteorites and over 400 investigators worldwide are active in the study of meteorites.. Research on these samples has been published in more than1500 peer reviewed articles; a listing of papers for any meteorite sample can be generated by accessing http://curator.jsc.nasa.gov/antmet/referencesearch.cfm. Antarctic meteorite samples requested by scientists are prepared several different ways. Most samples are prepared as chips, either using a rock splitter or using a chisel and chipping bowl. In special situations, a researcher may request a meteorite slab in which case the samples are cut using a diamond-bladed bandsaw inside of a dry nitrogen glove box. The meteorites are always cut in a 100 percent liquid-free environment. Additionally, thin/thick sections of Antarctic meteorites are also prepared at JSC. The meteorite thin section lab at JSC can prepare standard 30-micron thin sections, thick sections of variable thickness (100 to 200 microns), or demountable sections using superglue, all section are prepared without using water. Although many of the techniques used back in the '70's are still used today, advances in computers, software, databases, available tools and instrumentation have helped to streamline and shorten the duration of the classification process. In conjunction with present day missions to asteroids and other planets, meteorite studies have not only led to a better understanding of the complex histories of these bodies but have also tied certain meteorite groups to particular asteroid bodies. New meteorite discoveries by the ANSMET program provide a cost effective method for obtaining samples of previously unsampled bodies, allowing scientists to learn more about the origin, composition, and evolution of the solar system. Preservation in our cleanrooms at NASA allows material to be archived for future generations and advances in instrumentation and analysis.

Satterwhite, C. E.↗

Enhanced Quantification of 3D Woven Composites Via Fourier Analysis and Structure Tensors Applied to CT Scans

NASA's development of advanced 3D woven carbon composites, such as HEEET and 3MDCP, represents a significant leap in materials designed to endure extreme atmospheric entry conditions. However, the internal complexity of these materials introduces a variety of structures and novel defect types. Traditional characterization methods rely on labor-intensive, manual examination of X-ray CT scans, demanding considerable time and expertise. This process, while thorough, is not sustainable for large-scale analysis and defect tracking. Addressing this critical challenge, this presentation introduces an innovative suite of automated tools and analytical techniques, pioneered by the Mars Sample Return (MSR) Earth Entry System (EES) Thermal Protection System (TPS) project. These advancements offer a more efficient and accurate approach for quantifying CT data and characterizing the defects of 3D woven composites.

Magnus Haw↗

Quantitative Characterization of 3D Woven Composites Via Fourier Analysis and Structure Tensors Applied to CT Scans

NASA's development of advanced 3D woven carbon composites, such as HEEET and 3MDCP, represents a significant leap in materials designed to endure extreme atmospheric entry conditions. However, the internal complexity of these materials introduces a variety of structures and novel defect types. Traditional characterization methods rely on labor-intensive, manual examination of X-ray CT scans, demanding considerable time and expertise. This process, while thorough, is not sustainable for large-scale analysis and defect tracking. Addressing this critical challenge, this presentation introduces an innovative suite of automated tools and analytical techniques, pioneered by the Mars Sample Return (MSR) Earth Entry System (EES) Thermal Protection System (TPS) project. These advancements offer a more efficient and accurate approach for quantifying CT data and characterizing the defects of 3D woven composites.

3D Woven↗

Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.

This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.

97 MATHEMATICS AND COMPUTING↗