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All sources NASA NTRS DOE OSTI

DOE OSTI2022

Autonomous System Subversion Tactics: Prototypes and Recommended Countermeasures

One of the fielding requirements for Advanced and Small Modular Reactors (AR/SMR) is the ability to support remote and autonomous operations. Autonomous Control Systems (ACS) are found on platforms such as Autonomous Space Vehicles, Cruise Missiles, and advanced driver-assistance systems. Each of these ACS implementations depends upon a set of decision support subsystems responsible for supporting Autonomous Mission Managers (names vary based upon field and author preferences). These Autonomous Mission Managers receive inputs from system sensors (e.g., LIDAR collection from an automobile travelling down a street; transients from a nuclear reactor), and perform a set of classifications (e.g., Red Traffic Light; Small Pedestrian at 10m; Load Rejection; Single Coolant Pump Trip), and then use these classifications in combination with recommendation algorithms to achieve platform goals (e.g., Stop the Vehicle at the Traffic Light, Avoid the Small Pedestrian; Trip the Reactor to prevent a Safety Event). The design, implementation, and fielding of an ACS capability will alter the cyber-attack surface such that existing risk management plans will need to be updated to include how to protect and defend against data-science and decision-support-system attack classes. These attack classes would include protection of the design and training environments where algorithm selection and testing and training data would be obvious attack vectors. These attack classes would also require an informed set of detection and response procedures to identify anomalous behaviors and document best practices for anomaly assessment and vulnerability mitigation and remediation. Last year we published a Cyber Threat Assessment Methodology for Autonomous and Remote Operations for AR/SMRs along with a companion publication on Cyber Attack and Defense Use Cases. The focus of the methodology was on describing and enumerating ACS processes, components, and functions such that security engineers could: evaluate subversion options against the target; identify threat actor attributes and capabilities derived from each subversion option; and identify security controls and response countermeasures. The Use Cases document offered detailed methodology examples including an assessment of a Military Base SMR, an Autonomous System Decision Loop, and implementation of AR/SMR Machine Learning algorithms. Our proposal at the end of last year was to focus on implementation of subversion prototypes related to the last Use Case area: AR/SMR Machine Learning (ML) Algorithms. We included six attack scenarios in our Use Cases paper: a Poisoning Attack against ML functions implemented using an FPGA; a Trojaning Attack against ML classifiers exploiting the excitability of Nuclear Engineers; a Backdooring Attack against ML Training environments to ensure persistence of an attack vector; a False Positive Evasion Attack against multi-factor Access Control Systems using clever inputs; an Inference Attack against ML models by an Insider with access to the Operational environment; and an Adversarial Reprogramming Attack against a Material Access Control Video Surveillance System. At the beginning of this year these six attack scenarios were provided to our research teams at Georgia Tech and Idaho State University and each team successfully implemented a subversion attack against a ML implementation to include transient misclassifications. While this is a notable outcome from this type of research, this paper offers the reader insight into not only how to structure and execute these types of attacks, but into the thought process behind how the researcher investigated the problem space, performed initial algorithm implementation, and the trial-and-error behind arriving at the successful subversion prototypes. We include in this paper a set of associated Scenarios on how these subversion prototypes could be implemented and an initial set of guidance for AR/SMR architects, Nuclear Regulators, and Cyber Defenders to implement awareness and defense capabilities into their current operational portfolios.

42 ENGINEERING↗

DOE OSTI2023

Chaconne: A Statistical Approach to Nonlocal Compression for Supervised Learning, Semi-Supervised Learning, and Anomaly Detection

This project developed a novel statistical understanding of compression analytics (CA), which has challenged and clarified some core assumptions about CA, and enabled the development of novel techniques that address vital challenges of national security. Specifically, this project has yielded the development of novel capabilities including 1. Principled metrics for model selection in CA, 2. Techniques for deriving/applying optimal classification rules and decision theory to supervised CA, including how to properly handle class imbalance and differing costs of misclassification, 3. Two techniques for handling nonlocal information in CA, 4. A novel technique for unsupervised CA that is agnostic with regard to the underlying compression algorithm, 5. A framework for semisupervised CA when a small number of labels are known in an otherwise large unlabeled dataset. 6. The academic alliance component of this project has focused on the development of a novel exemplar-based Bayesian technique for estimating variable length Markov models (closely related to PPM [prediction by partial matching] compression techniques). We have developed examples illustrating the application of our work to text, video, genetic sequences, and unstructured cybersecurity log files.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2025

NeuroSymbolic Approaches as a Vector for Assured Artificial Intelligence

The deployment of artificial intelligence systems in critical applications requires higher levels of assurance for safety, security, and interpretability. While neurosymbolic (NESY) approaches combining neural networks with symbolic reasoning offer potential advantages for assured AI, existing differentiable neurosymbolic frameworks face significant limitations including computational overhead and performance constraints. This report investigates the ISED (InferSampleEstimateDescend) framework as an alternative approach that enables neurosymbolic learning without requiring endtoend differentiability. We evaluate ISED’s utility for geointelligence applications by comparing neurosymbolic models against standard neural networks on aircraft classification tasks using the RarePlanes and MTARSI imagery datasets. Our results demonstrate that while ISEDbased models achieve slightly lower accuracy (89.7% vs 92.1% on RarePlanes; 91.1% vs 92.5% on MTARSI), they provide critical explainability capabilities that enable tracing incorrect predictions back to specific attribute misclassifications. We also present an automated pipeline that generates both attributeclass mappings and neurosymbolic model architectures from natural language descriptions, significantly reducing the manual effort required for NESY model deployment. These findings suggest that ISED offers a promising direction for developing assured AI systems where interpretability and reasoning transparency are prioritized alongside performance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

The Double-edged Sword of Data-driven Super-Resolution: Adversarial Super-resolution Models

Data-driven super-resolution (SR) methods are often integrated into imaging pipelines as preprocessing steps to improve downstream tasks such as classification and detection. However, these SR models introduce a previously unexplored attack surface into imaging pipelines. In this paper, we present AdvSR, a framework demonstrating that adversarial behavior can be embedded directly into SR model weights during training, requiring no access to inputs at inference time. Unlike prior attacks that perturb inputs or rely on backdoor triggers, AdvSR operates entirely at the model level. By jointly optimizing for reconstruction quality and targeted adversarial outcomes, AdvSR produces models that appear benign under standard image quality metrics while inducing downstream misclassification. We evaluate AdvSR on three SR architectures (SRCNN, EDSR, SwinIR) paired with a YOLOv11 classifier and demonstrate that AdvSR models can achieve high attack success rates with minimal quality degradation. These findings highlight a new model-level threat for imaging pipelines, with implications for how practitioners source and validate models in safety-critical applications.

Sullivan, Haley [ORNL] (ORCID:0000000274069217)↗

DOE OSTI2023

A computational modeling framework for pre-clinical evaluation of cardiac mapping systems

There are a variety of difficulties in evaluating clinical cardiac mapping systems, most notably the inability to record the transmembrane potential throughout the entire heart during patient procedures which prevents the comparison to a relevant “gold standard”. Cardiac mapping systems are comprised of hardware and software elements including sophisticated mathematical algorithms, both of which continue to undergo rapid innovation. The purpose of this study is to develop a computational modeling framework to evaluate the performance of cardiac mapping systems. The framework enables rigorous evaluation of a mapping system’s ability to localize and characterize (i.e., focal or reentrant) arrhythmogenic sources in the heart. The main component of our tool is a library of computer simulations of various dynamic patterns throughout the entire heart in which the type and location of the arrhythmogenic sources are known. Our framework allows for performance evaluation for various electrode configurations, heart geometries, arrhythmias, and electrogram noise levels and involves blind comparison of mapping systems against a “silver standard” comprised of computer simulations in which the precise transmembrane potential patterns throughout the heart are known. A feasibility study was performed using simulations of patterns in the human left atria and three hypothetical virtual catheter electrode arrays. Activation times (AcT) and patterns (AcP) were computed for three virtual electrode arrays: two basket arrays with good and poor contact and one high-resolution grid with uniform spacing. The average root mean squared difference of AcTs of electrograms and those of the nearest endocardial action potential was less than 1 ms and therefore appears to be a poor performance metric. In an effort to standardize performance evaluation of mapping systems a novel performance metric is introduced based on the number of AcPs identified correctly and those considered spurious as well as misclassifications of arrhythmia type; spatial and temporal localization accuracy of correctly identified patterns was also quantified. This approach provides a rigorous quantitative analysis of cardiac mapping system performance. Proof of concept of this computational evaluation framework suggests that it could help safeguard that mapping systems perform as expected as well as provide estimates of system accuracy.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

Narrow-line X-ray-selected galaxies in the Chandra-COSMOS field. Ii. Optically elusive X-ray AGNs

In the Chandra-COSMOS (C-COSMOS) survey, we have looked for X-ray-selected active galactic nuclei (AGNs), which are not detected as such in the optical, the so-called elusive AGNs. A previous study based on XMM-Newton and Sloan Digital Sky Survey observations has found a sample of 31 X-ray AGNs optically misclassified as star-forming (SF) galaxies at z<0.4, including 17 elusive Sy2s. Using Chandra observations provides a sample of fainter X-ray sources and so, for a given X-ray luminosity, extends to higher redshifts. To study the elusive Sy2s in the C-COSMOS field, we have removed the NLS1s that contaminate the narrow-line sample. Surprisingly, the contribution of NLS1s is much lower in the C-COSMOS sample (less than 10% of the optically misclassified X-ray AGNs) than in Pons and Watson. The optical misclassification of the X-ray AGNs (L{sub X}>10{sup 42} erg s{sup −1}) can be explained by the intrinsic weakness of these AGNs, in addition to, in some cases, optical dilution by the host galaxies. Interestingly, we found the fraction of elusive Sy2s (narrow emission-line objects) optically misclassified as SF galaxies up to z∼1.4 to be 10% ± 3% to 17% ± 4%, compared to the 6% ± 1.5% of the Pons and Watson work (up to z∼0.4). This result seems to indicate an evolution with redshift of the number of elusive Sy2s.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

WIRED for EC: New White Dwarfs with WISE Infrared Excesses and New Classification Schemes from the Edinburgh–Cape Blue Object Survey

We present a simple method for identifying candidate white dwarf systems with dusty exoplanetary debris based on a single temperature blackbody model fit to the infrared excess. We apply this technique to a sample of Southern Hemisphere white dwarfs from the recently completed Edinburgh–Cape Blue Object Survey and identify four new promising dusty debris disk candidates. We demonstrate the efficacy of our selection method by recovering three of the four Spitzer confirmed dusty debris disk systems in our sample. Further investigation using archival high-resolution imaging shows that Spitzer data of the unrecovered fourth object is likely contaminated by a line-of-sight object that either led to a misclassification as a dusty disk in the literature or is confounding our method. Finally, in our diagnostic plot, we show that dusty white dwarfs, which also host gaseous debris, lie along a boundary of our dusty debris disk region, providing clues to the origin and evolution of these especially interesting systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Angular Correlation Function Estimators Accounting for Contamination from Probabilistic Distance Measurements

With the advent of surveys containing millions to billions of galaxies, it is imperative to develop analysis techniques that utilize the available statistical power. In galaxy clustering, even small sample contamination arising from distance uncertainties can lead to large artifacts, which the standard estimator for two-point correlation functions does not account for. We first introduce a formalism, termed decontamination, that corrects for sample contamination by utilizing the observed cross-correlations in the contaminated samples; this corrects any correlation function estimator for contamination. Using this formalism, we present a new estimator that uses the standard estimator to measure correlation functions in the contaminated samples but then corrects for contamination. We also introduce a weighted estimator that assigns each galaxy a weight in each redshift bin based on its probability of being in that bin. We demonstrate that these estimators effectively recover the true correlation functions and their covariance matrices. Our estimators can correct for sample contamination caused by misclassification between object types as well as photometric redshifts; they should be particularly helpful for studies of galaxy evolution and baryonic acoustic oscillations, where forward modeling the clustering signal using the contaminated redshift distribution is undesirable.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Recognizing Blazars Using Radio Morphology from the VLA Sky Survey

Abstract Blazars are radio-loud active galactic nuclei whose jets have a very small angle to our line of sight. Observationally, the radio emissions are mostly compact or compact-core with a one-sided jet. With 2.″5 resolution at 3 GHz, the Very Large Array Sky Survey (VLASS) enables us to resolve the structure of some blazar candidates in the sky north of decl. −40°. We introduce an algorithm to classify radio sources as either blazar-like or non-blazar-like based on their morphology in the VLASS images. We apply our algorithm to three existing catalogs, including one of the known blazars (Roma-BzCAT) and two blazar candidates identified by Wide-field Infrared Survey Explorer colors and radio emission (WIBRaLS, KDEBLLACS). We show that in all three catalogs, there are objects with morphologies inconsistent with being blazars. Considering all the catalogs, more than 12% of the candidates are unlikely to be blazars, based on this analysis. Notably, we show that 3% of the Roma-BzCATconfirmedblazars could be a misclassification based on their VLASS morphology. The resulting table with all sources and their radio morphological classification is available online.

Astronomy & Astrophysics↗

DOE OSTI2024

The Impact of Void-finding Algorithms on Galaxy Classification

We explore how the definition of a void influences the conclusions drawn about the impact of the void environment on galactic properties using two void-finding algorithms in the Void Analysis Software Toolkit: Voronoi Voids (V 2 ), a Python implementation of ZOnes Bordering On Voidness (ZOBOV); and VoidFinder, an algorithm that grows and merges spherical void regions. Using the Sloan Digital Sky Survey Data Release 7, we find that galaxies found in VoidFinder voids tend to be bluer and fainter and to have higher (specific) star formation rates than galaxies in denser regions. Conversely, galaxies found in V 2 voids show less significant differences when compared to galaxies in denser regions, less consistent with the large-scale environmental effects on galaxy properties expected from both simulations and previous observations. These results align with previous simulation results that show V 2 -identified voids “leak” into the dense walls between voids because their boundaries extend up to the density maxima in the walls. As a result, when using ZOBOV-based void-finders, galaxies likely to be part of wall regions are instead classified as void galaxies, a misclassification that can be critical to our understanding of galaxy evolution.

cosmic web↗

DOE OSTI2026

Robust Measurement of Stellar Streams around the Milky Way: Correcting Spatially Variable Observational Selection Effects in Optical Imaging Surveys

Observations of density variations in stellar streams are a promising probe of low-mass dark matter substructure in the Milky Way. However, survey systematics such as variations in seeing and sky brightness can also induce artificial fluctuations in the observed densities of known stellar streams. These variations arise because survey conditions affect both object detection and star–galaxy misclassification rates. To mitigate these effects, we use Balrog synthetic source injections in the Dark Energy Survey (DES) Y3 data to calculate detection rate variations and classification rates as functions of survey properties. We show that these rates are nearly separable with respect to survey properties and can be estimated with sufficient statistics from the synthetic catalogs. Applying these corrections reduces the standard deviation of relative detection rates across the DES footprint by a factor of 5, and our corrections significantly change the inferred linear density of the Phoenix stream when including faint objects. Additionally, for artificial streams with DES-like survey properties we are able to recover density power spectra with reduced bias. We also find that uncorrected power-spectrum results for Legacy Survey of Space and Time (LSST)-like data can be around 5 times more biased, highlighting the need for such corrections in future ground-based surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Three Statistically Validated K2 Transiting Warm Jupiter Exoplanets Confirmed as Low-mass Stars

We have identified three K2 transiting star–planet systems, K2-51 (EPIC 202900527), K2-67 (EPIC 206155547), and K2-76 (EPIC 206432863), as stellar binaries with low-mass stellar secondaries. The three systems were statistically validated as transiting planets, and through measuring their orbits by radial velocity (RV) monitoring we have derived the companion masses to be 0.1459{sub −0.0032}{sup +0.0029} M{sub ⊙} (EPIC 202900527 B), 0.1612{sub −0.0067}{sup +0.0072} M{sub ⊙} (EPIC 206155547 B), and 0.0942 ± 0.0019 M{sub ⊙} (EPIC 206432863 B). Therefore, they are not planets but small stars, part of the small sample of low-mass stars with measured radius and mass. The three systems are at an orbital period range of 12–24 days, and the secondaries have a radius within 0.9–1.9 R{sub J}, not inconsistent with the properties of warm Jupiter planets. These systems illustrate some of the existing challenges in the statistical validation approach. We point out a few possible origins for the initial misclassification of these objects, including poor characterization of the host star, the difficulty in detecting a secondary eclipse in systems on an eccentric orbit, and the difficulty in distinguishing between the smallest stars and gas giant planets as the two populations have indistinguishable radius distributions. Our work emphasizes the need for obtaining medium-precision RV measurements to distinguish between companions that are small stars, brown dwarfs, and gas giant planets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

AI ensemble for signal detection of higher order gravitational wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

We introduce spatiotemporal-graph models that concurrently process data from the twin advanced LIGO detectors and the advanced Virgo detector. We trained these AI classifiers with 2.4 million IMRPhenomXPHM waveforms that describe quasi-circular, spinning, non-precessing binary black hole mergers with component masses m{1,2}∈[3M⊙,50M⊙], and individual spins sz{1,2}∈[−0.9,0.9]; and which include the (ℓ,|m|)={(2,2),(2,1),(3,3),(3,2),(4,4)} modes, and mode mixing effects in the ℓ=3,|m|=2 harmonics. We trained these AI classifiers within 22 hours using distributed training over 96 NVIDIA V100 GPUs in the Summit supercomputer. We then used transfer learning to create AI predictors that estimate the total mass of potential binary black holes identified by all AI classifiers in the ensemble. We used this ensemble, 3 classifiers for signal detection and 2 total mass predictors, to process a year-long test set in which we injected 300,000 signals. This year-long test set was processed within 5.19 minutes using 1024 NVIDIA A100 GPUs in the Polaris supercomputer (for AI inference) and 128 CPU nodes in the ThetaKNL supercomputer (for post-processing of noise triggers), housed at the Argonne Leadership Computing Facility. These studies indicate that our AI ensemble provides state-of-the-art signal detection accuracy, and reports 2 misclassifications for every year of searched data. This is the first AI ensemble designed to search for and find higher order gravitational wave mode signals.

Tian, Minyang↗

DOE OSTI2013

Relating Aerosol Absorption due to Soot, Organic Carbon, and Dust to Emission Sources Determined from In-situ Chemical Measurements

Estimating the aerosol contribution to the global or regional radiative forcing can take advantage of the relationship between the spectral aerosol optical properties and the size and chemical composition of aerosol. Long term global optical measurements from observational networks or satellites can be used in such studies, and using in-situ chemical mixing state measurements can help us to constrain the limitations of such an estimation. In this study, the Absorption Ångström Exponent (AAE) and the Scattering Ångström Exponent (SAE) are used to develop a new methodology for deducing chemical speciation based on wavelength dependence of the optical properties. In addition, in-situ optical properties and single particle chemical composition measured during three aircraft field campaigns are combined in order to validate the methodology for the estimation of aerosol composition using spectral optical properties. Results indicate a dominance of mixed types in the classification leading to an underestimation of the primary sources, however secondary sources are better classified. The distinction between carbonaceous aerosols from fossil fuel and biomass burning origins is not clear. On the other hand, the knowledge of the aerosol sources in California from chemical studies help to identify other misclassification such as the dust contribution.

absorption↗

DOE OSTI2026

Leveraging machine learning to enhance aerosol classification using Single-Particle Mass Spectrometry

Advancing automated classification of atmospheric aerosols from Single-Particle Mass Spectrometry (SPMS) data remains challenging due to overlapping ion signatures, compositional diversity, and limited labeled data. This study evaluates supervised and semi-supervised learning frameworks to enhance aerosol identification by jointly leveraging labeled and unlabeled spectra. Four models were compared: a supervised Support Vector Machine (SVM), a self-training SVM, a stacked autoencoder classifier, and a stacked autoencoder trained using a temporal-ensembling Mean Teacher approach. All models achieved high and stable accuracies (90.0 %–91.1 %), surpassing previous results on the same dataset (87 %) and matching the performance of state-of-the-art deep learning methods. Despite small global metric differences (≤ 1 %), semi-supervised variants yielded up to 5 %–10 % improvements for compositionally rare particle types – such as soot (0.77 % of spectra, F1-score: 0.93–0.97) and hazelnut pollen (0.98 % of spectra, F1-score: 0.97–1.00) – equating to roughly ∼ 187 additional correctly classified spectra. These gains are scientifically significant, as such rare particles exert disproportionate influence on radiative absorption and ice nucleation processes; their improved detection reduces modeled uncertainties in aerosol absorption optical depth and mixed-phase cloud ice nucleation rates. The models' residual misclassifications (≈ 9 %) largely arise from true spectral overlap among chemically adjacent species (e.g., Na- vs. K-feldspar, coated vs. uncoated feldspars), reflecting physical compositional continuity rather than algorithmic error. Collectively, these findings demonstrate that leveraging unlabeled data to learn robust spectral representations and refine classification enhances both fidelity and interpretability, bridging data-driven analysis with aerosol–climate process understanding.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Ensemble photometric redshifts

Upcoming imaging surveys, such as LSST, will provide an unprecedented view of the Universe, but with limited resolution along the line-of-sight. Common ways to increase resolution in the third dimension, and reduce misclassifications, include observing a wider wavelength range and/or combining the broad-band imaging with higher spectral resolution data. The challenge with these approaches is matching the depth of these ancillary data with the original imaging survey. However, while a full 3D map is required for some science, there are many situations where only the statistical distribution of objects (dN/dz) in the line-of-sight direction is needed. In such situations, there is no need to measure the fluxes of individual objects in all of the surveys. Rather a stacking procedure can be used to perform an `ensemble photo-z'. We show how a shallow, higher spectral resolution survey can be used to measure dN/dz for stacks of galaxies which coincide in a deeper, lower resolution survey. The galaxies in the deeper survey do not even need to appear individually in the shallow survey. We give a toy model example to illustrate tradeoffs and considerations for applying this method. This approach will allow deep imaging surveys to leverage the high resolution of spectroscopic and narrow/medium band surveys underway, even when the latter do not have the same reach to high redshift.

galaxies:distances and redshifts↗

DOE OSTI2020

Integrating Predictions for Improving Defect Classification Accuracy in NDT-based Assessment of Concrete - 20229

There is an increasing need to create predictive models for defect classification in concrete using the output of non-destructive testing (NDT) techniques. Recent advancement of machine-learning algorithms has offered several techniques for developing classification models for different types of data sets. However, the performance of these algorithms is very uncertain, mainly when applied to small and noisy datasets. For example, when human access is limited (e.g., nuclear facility), robot-based NDT is preferred. But compared to manual tests with humans present on site, the data sets are small, and more noise can exist. Therefore, it is imperative to develop new approaches to ensure a consistently high classification accuracy for inadequate data sets. This study explores the classification performance on NDT dataset using classifiers from different machine-learning algorithms, namely k-Nearest Neighbor (kNN), Decision Tree, Naive Bayes, Logistic Regression, and Support Vector Machine (SVM). The authors further integrated the predictions from these classifiers using proposed methods. The integration strategy combines the output of the classifiers based on two different measures, accuracy, and performance (ACC and PERF), using equations such as sum, average, and square-root-of-sums-of-squares (SRSS). Our results reveal varying classification accuracies across individual classifiers with different misclassifications across the test data set. The integration strategy provided significant improvement in the classification accuracy compared to the individual classifiers. Furthermore, the results indicate minimal variation across the integration methods as compared to the variation across the individual classifiers. To conclude, prediction integration offers a unique approach for combining the output of multiple classifiers to create redundancies with the potential of achieving high classification performance and improved reliability in predictive models for defect detection in concrete. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

Open Set Recognition for Unknown Waveform Classification

This presentation applies open set recognition to classify unknown waveforms, enabling systems to not only identify known types but also reliably detect when waveforms fall outside the training distribution. This approach enhances robustness by avoiding forced misclassification of novel or anomalous signals.

99 - GENERAL AND MISCELLANEOUS↗