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All sources NASA NTRS DOE OSTI

NASA NTRS1998

Preliminary Work for Examining the Scalability of Reinforcement Learning

Researchers began studying automated agents that learn to perform multiple-step tasks early in the history of artificial intelligence (Samuel, 1963; Samuel, 1967; Waterman, 1970; Fikes, Hart & Nilsonn, 1972). Multiple-step tasks are tasks that can only be solved via a sequence of decisions, such as control problems, robotics problems, classic problem-solving, and game-playing. The objective of agents attempting to learn such tasks is to use the resources they have available in order to become more proficient at the tasks. In particular, each agent attempts to develop a good policy, a mapping from states to actions, that allows it to select actions that optimize a measure of its performance on the task; for example, reducing the number of steps necessary to complete the task successfully. Our study focuses on reinforcement learning, a set of learning techniques where the learner performs trial-and-error experiments in the task and adapts its policy based on the outcome of those experiments. Much of the work in reinforcement learning has focused on a particular, simple representation, where every problem state is represented explicitly in a table, and associated with each state are the actions that can be chosen in that state. A major advantage of this table lookup representation is that one can prove that certain reinforcement learning techniques will develop an optimal policy for the current task. The drawback is that the representation limits the application of reinforcement learning to multiple-step tasks with relatively small state-spaces. There has been a little theoretical work that proves that convergence to optimal solutions can be obtained when using generalization structures, but the structures are quite simple. The theory says little about complex structures, such as multi-layer, feedforward artificial neural networks (Rumelhart & McClelland, 1986), but empirical results indicate that the use of reinforcement learning with such structures is promising. These empirical results make no theoretical claims, nor compare the policies produced to optimal policies. A goal of our work is to be able to make the comparison between an optimal policy and one stored in an artificial neural network. A difficulty of performing such a study is finding a multiple-step task that is small enough that one can find an optimal policy using table lookup, yet large enough that, for practical purposes, an artificial neural network is really required. We have identified a limited form of the game OTHELLO as satisfying these requirements. The work we report here is in the very preliminary stages of research, but this paper provides background for the problem being studied and a description of our initial approach to examining the problem. In the remainder of this paper, we first describe reinforcement learning in more detail. Next, we present the game OTHELLO. Finally we argue that a restricted form of the game meets the requirements of our study, and describe our preliminary approach to finding an optimal solution to the problem.

Clouse, Jeff↗

NASA NTRS1997

Real-Time Simulation

Coryphaeus Software, founded in 1989 by former NASA electronic engineer Steve Lakowske, creates real-time 3D software. Designer's Workbench, the company flagship product, is a modeling and simulation tool for the development of both static and dynamic 3D databases. Other products soon followed. Activation, specifically designed for game developers, allows developers to play and test the 3D games before they commit to a target platform. Game publishers can shorten development time and prove the "playability" of the title, maximizing their chances of introducing a smash hit. Another product, EasyT, lets users create massive, realistic representation of Earth terrains that can be viewed and traversed in real time. Finally, EasyScene software control the actions among interactive objects within a virtual world. Coryphaeus products are used on Silican Graphics workstation and supercomputers to simulate real-world performance in synthetic environments. Customers include aerospace, aviation, architectural and engineering firms, game developers, and the entertainment industry.

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NASA NTRS1997

Stress Management by Biofeedback

In the 1980's, Dr. Patrick Doyle served on a project to train U.S. astronauts at Johnson Space Center in biofeedback techniques to control anxiety and hypertension. Traditional biofeedback concepts were found to be too mundane, repetitive and boring, so Doyle developed Bio-Games with more interesting and involved formats. The first product, Bio-Ball, is an interactive, multimedia baseball video game that is played by relaxing in order to hit the ball. Gradually the player is able to relax at will, and with practice is able to apply the skills to real-life situations. Doyle has since gone on to create a number of biofeedback games marketed by Creative MultiMedia Inc. including Bio-Golf, Clutch City, and Pachyderm. Stress-busting screen savers are also being marketed under the Buddies series. In addition to being used in the corporate world, Bio-Games have been recognized by the Starbright Foundation which focuses on improving the total hospital environments of critically injured and chronically-ill children.

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NASA NTRS2004

Product Distribution Theory for Control of Multi-Agent Systems

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Lee, Chia Fan↗

NASA NTRS2010

Route Generation for a Synthetic Character (BOT) Using a Partial or Incomplete Knowledge Route Generation Algorithm in UT2004 Virtual Environment

This paper presents a new Route Generation Algorithm that accurately and realistically represents human route planning and navigation for Military Operations in Urban Terrain (MOUT). The accuracy of this algorithm in representing human behavior is measured using the Unreal Tournament(Trademark) 2004 (UT2004) Game Engine to provide the simulation environment in which the differences between the routes taken by the human player and those of a Synthetic Agent (BOT) executing the A-star algorithm and the new Route Generation Algorithm can be compared. The new Route Generation Algorithm computes the BOT route based on partial or incomplete knowledge received from the UT2004 game engine during game play. To allow BOT navigation to occur continuously throughout the game play with incomplete knowledge of the terrain, a spatial network model of the UT2004 MOUT terrain is captured and stored in an Oracle 11 9 Spatial Data Object (SOO). The SOO allows a partial data query to be executed to generate continuous route updates based on the terrain knowledge, and stored dynamic BOT, Player and environmental parameters returned by the query. The partial data query permits the dynamic adjustment of the planned routes by the Route Generation Algorithm based on the current state of the environment during a simulation. The dynamic nature of this algorithm more accurately allows the BOT to mimic the routes taken by the human executing under the same conditions thereby improving the realism of the BOT in a MOUT simulation environment.

Hanold, Gregg T.↗

NASA NTRS2011

Microsoft Kinect Sensor Evaluation

My summer project evaluates the Kinect game sensor input/output and its suitability to perform as part of a human interface for a spacecraft application. The primary objective is to evaluate, understand, and communicate the Kinect system's ability to sense and track fine (human) position and motion. The project will analyze the performance characteristics and capabilities of this game system hardware and its applicability for gross and fine motion tracking. The software development kit for the Kinect was also investigated and some experimentation has begun to understand its development environment. To better understand the software development of the Kinect game sensor, research in hacking communities has brought a better understanding of the potential for a wide range of personal computer (PC) application development. The project also entails the disassembly of the Kinect game sensor. This analysis would involve disassembling a sensor, photographing it, and identifying components and describing its operation.

Billie, Glennoah↗

NASA NTRS2017

Space Science Investigation: NASA ISS Stowage Simulator

During this internship the opportunity was granted to work with the Integrated, Graphics, Operations and Analysis Laboratory (IGOAL) team. The main assignment was to create 12 achievement patches for the Space Station training simulator called the "NASA ISS Stowage Training Game." This project was built using previous IGOAL developed software. To accomplish this task, Adobe Photoshop and Adobe Illustrator were used to craft the badges and other elements required. Blender, a 3D modeling software, was used to make the required 3D elements. Blender was a useful tool to make things such as a CTB bag for the "No More Bob" patch which shows a gentleman kicking a CTB bag into the distance. It was also used to pose characters to the positions that was optimal for their patches as in the "Station Sanitation" patch which portrays and astronaut waving on a U.S module on a truck. Adobe Illustrator was the main piece of software for this task. It was used to craft the badges and upload them when they were completed. The style of the badges were flat, meaning that they shouldn't look three dimensional in any way, shape or form. Adobe Photoshop was used when any pictures need brightening and was where the texture for the CTB bag was made. In order for the patches to be ready for the game's next major release, they have to go under some critical reviewing, revising and re-editing to make sure the other artists and the rest of the staff are satisfied with the final products. Many patches were created and revamped to meet the flat setting and incorporate suggestions from the IGOAL team. After the three processes were completed, the badges were implemented into the game (reference fig1 for badges). After a month of designing badges, the finished products were placed into the final game build via the programmers. The art was the final piece in showcasing the latest build to the public for testing. Comments from the testers were often exceptional and the feedback on the badges were outstanding. The latest build will also be tested by astronauts to determine if the product could potentially be incorporated into the astronaut training program. This experience has provided the opportunity to experience the feeling of working with research and development organization. The art skills and programming skills received at the internship will provide and maintain and strong foundation for a career in computer programming and digital media.

Crawford, Gary↗

NASA NTRS2018

Internship in Augmented and Virtual Reality - Rapid Model Import Tool

The integration of virtual and augmented reality, sometimes called mixed reality, is an emerging technology which will likely skyrocket overnight much in the way smartphones did a decade ago. Kennedy Space Center's Augmented and Virtual Reality (AVR) Lab is developing a Rapid Model Import Tool (RMIT) to create a quick and efficient way to bring NASA's complex engineering 3D models into virtual and augmented environments. The long-term objective is to create a tool that will ultimately benefit KSC engineers. Its various uses within NASA can potentially span from astronaut training, to marketing, to public outreach, to name a few. Unity is a prolific cross-platform game engine that allows users to build high quality 2D and 3D games for desktop, mobile, web, and game console platforms. It is perhaps also the most widely used software for virtual reality game development. At the AVR lab, we are looking at alternative uses of Unity to build tools for NASA engineers to perform design, development, testing, and training on spacecraft, rocket delivery systems, ground support equipment, and facilities at KSC. As an intern for the RMIT project, I am charged with the task of performing research on Unity-compatible file types to develop an efficient, affordable, preservative process to bring models from CATIA 3D engineering software into the Unity environment. With a tool called the NASA Enterprise Visualization Application (NEVA), developed by the Boeing Design Visualization group at KSC, we are able to easily convert CATIA's design models to. DAE (also known as COLLADA) and .OBJ file formats. I first reduce the polygon count of the model within CATIA itself, make any necessary tweaks to reduce the model further, and then export using NEVA. The .OBJ or. DAE files that I am left with are then converted by another intern to a Unity-compatible file format using a custom Python script. I have generated extensive documentation of this process in a NEVA User Guide. By the end of this semester, we will have built a solid framework for RMIT based on a thorough understanding of virtual reality specifications and file requirements, allowing future software development teams to go forward with development on the custom tool.

Leap Motion↗

DOE OSTI2016

Value of Information in Fuel Cycle Decision-making

Transitions between nuclear fuel cycles with uncertain key parameters (e.g., SNF and HLW disposal costs, fast reactor capital costs) have been examined using a decision-making under uncertainty methodology. The methodology explicitly incorporates uncertainties in key parameters into the decision-making process by constructing a stochastic model and embedding uncertainties as bifurcations in the decision-tree. The framework of this methodology allows for interpretation using a real options valuation or game theoretic approach, reviewed in. The work presented here extends the decision-making under uncertainty framework to calculate the value of information, which may be used to inform a game against nature. These games against nature have been applied to resource allocation problems, where scarce resources are allocated to maximize expected payoffs. More broadly, the value of developing alternative technologies may be considered under the same framework, where an investment portfolio for technology deployment may be developed. Here, the value of information is taken as the value of reducing uncertainty in key parameters, and these values may be substituted for the traditional payoff matrix when considering allocating scarce resources. Games against nature may provide a unique perspective on R and D funding decisions when considering transitions between nuclear fuel cycles. By determining the value of reducing uncertainties (of gaining information on probability distributions) scarce resources may be allocated in such a way to maximize their utility. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

Development of Real-Time Quantitative Safety Evaluation Method for Nuclear Power Plants

Human operators involved with large process control systems such as nuclear power plants (NPPs) perform significant roles in the operation of systems. In this reason, deficiencies in human factors such as poor HSI (Human System Interface) design, procedure, and training, are significant contributing factors to NPPs incidents and accidents. In this regard, many kinds of studies including human reliability analysis (HRA), operation support system, automation, have been conducted in order to reduce human errors. Among these fields of studies, automation has its own specialty since it mainly focuses on eliminating the human error-inducing tasks to reduce human error, while other topics are primarily focusing on reducing human error by aiding human operators during operation. It is commonly believed that replacing human operators to the automated system would guarantee greater efficiency, lower workloads, and fewer human errors. However, these beliefs are not always true in large and complex systems such as NPP, since excessive automation can generate new roles for human operators, change human operators' activities in unexpected ways, and inducing 'out-of-the-loop' (OOTL) problem. Especially, although human error probability drastically increases during abnormal situations in NPP due to overload of information, high workload, and short time available for diagnosis, automation is not actively adopted since conventional machine learning techniques are neither capable nor reliable to handle overwhelmingly complex abnormal situations in NPP. Recently, newly developed 'deep learning' techniques have been actively applied to many fields, and some of these studies proved that the artificial intelligences (AI) based on deep learning techniques show better performance than that of human being. In 2015, deep Q-network (DQN) which is one of the deep learning techniques was developed and applied to train AI that automatically plays various Atari 2800 games, and this AI surpassed the human-level playing in many kind of games. Also in 2016, 'AlphaGo', which was developed by 'Google Deepmind' based on deep learning technique to play the game of Go, was defeated Se-dol Lee who is the World Go champion with score of 4:1. In the point of view that the game of Go is considered as one of the challenging area in machine learning field, it is verified that these new machine learning techniques can perform well, even better than the human being in high-complexity tasks. Previously, most of AI applications in nuclear field were focusing on supporting human operators' tasks such as diagnosis and decision making by rapid classification and prediction, based on fixed training data sets. However, it is expected that AI can be applied to solve more complicated problems (i.e. automation during abnormal states in NPP) by adopting advanced machine learning methodologies. In order to apply the automation system in NPP, firstly it is needed to evaluate the status of the plant quantitatively in real-time, since the information about which state is better (i.e. safe) or worse (i.e. unsafe) is essential for training properly working automation AI. Currently, there are several methodologies for NPP safety evaluation such as probabilistic safety assessment (PSA), safety performance indicator (SPI). However, existing methodologies are not feasible for development of automated system since they are not capable for the cases which are not included in the underlying model, not able to consider delicate changes in the NPP, and hard to evaluate in real-time. Therefore, development of new NPP safety evaluation methodology which can cover previously mentioned requirements is needed to conduct the study on NPP automation further. In this study, the concept of early warning score (EWS) in medical field was adopted to develop the methodology which can evaluate the safety level of the NPP quantitatively and in real-time. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2012

Exploring Earth and the Solar System: Educational Outreach Through NASA's Space Place, SciJinks, and Climate Kids Websites

NASA's Space Place team publishes engaging content and creates an effective environment to inspire a young audience to dare mighty things. NASA uses the Space Place, Climate Kids, and SciJinks websites to cultivate interest among elementary-school-aged children in both science and technology. During my summer internship at Jet Propulsion Laboratory I used Adobe Flash and ActionScript 3 to develop content for the Space Place, Climate Kids, and SciJinks sites. In addition, I was involved in the development process for ongoing and new projects during my internship. My involvement allowed me to follow a project from concept to design, implementation, and release. I personally worked on three projects this summer, two of which are currently in deployment. The first is a scrambled letter-tile guessing game titled Solar System Scramble. The second, Butterfrog Mix-Up, is a rotating-tile puzzle game. The third project is a unfinished prototype for a maze game.

video games↗

DOE OSTI2021

Quantum Computational Advantage with String Order Parameters of One-Dimensional Symmetry-Protected Topological Order

Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between limited computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and -1. Finally, our construction demonstrates that sufficiently large string order parameters of such SPTOs are indicative of globally constrained correlations useful for the unconditional computational separation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Decoupling Coupled Constraints Through Utility Design

Several multiagent systems exemplify the need for establishing distributed control laws that ensure the resulting agents' collective behavior satisfies a given coupled constraint. This technical note focuses on the design of such control laws through a game-theoretic framework. In particular, this technical note provides two systematic methodologies for the design of local agent objective functions that guarantee all resulting Nash equilibria optimize the system level objective while also satisfying a given coupled constraint. Furthermore, the designed local agent objective functions fit into the framework of state based potential games. Consequently, one can appeal to existing results in game-theoretic learning to derive a distributed process that guarantees the agents will reach such an equilibrium.

Li, N↗

DOE OSTI2024

Timeseries Unlabeled and Labeled Photos, Modeled Stream Elevation, and (Meta)Data of Variably Inundated Streams Across The Yakima River Basin, Washington, United States (v2)

This dataset is associated with the “River Monitoring Photos” (RMP) study and subsequent manuscript (Bao et al. 2025. Monitoring river flow status using low-cost wildlife camera and image segmentation artificial intelligence doi: 10.1016/j.envsoft.2025.106715). Game camera timeseries photos were collected to evaluate stream variable inundation via changes in width. A subset of photos was labeled for training the YOLOv8 and Mask2Former models and used to segment water surface fractions from all the game camera photos.This data package was originally published in March 2024. It was updated in October 2025 (v2) to add additional photos and files associated with the manuscript (i.e., processed data, labeled photos, and trained models). For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About.In addition to a readme, this data package also includes two file-level metadata (FLMD) files that describes each file and two data dictionaries (DD) that describe all column/row headers and variable definitions. This dataset is comprised of (1) file-level metadata; (2) data dictionary; (3) readme; (4) field metadata; and (5) folders containing game camera photos and manuscript-associated files. Each Yakima River Basin site has a folder that contains subfolders for each month photos were collected. There is also a folder for files associated with the manuscript which has subfolders for labeled data, trained models, Yakima River Basin site water surface fractions, and USGS site water surface fractions. All files are .csv, .json, .txt, .yaml, .pth, .pt, or .pdf. We thank the Confederated Tribes and Bands of the Yakama Nation Tribal Council and Yakama Nation Fisheries for working with us to facilitate sample collection and optimization of data usage according to their values and worldview.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Post-fire time series photos from five sites across the Oak Creek watershed, Washington

This dataset supports a broader study examining wildfire impacts on hydrologic connectivity across 5 sites within the Oak Creek watershed and the resulting biogeochemical impacts. Sites were selected using the Advanced Terrestrial Simulator (ATS) hydrologic model to identify locations with varying groundwater contributions and hydrologic responses across different burn severity scenarios. The Retreat Fire burned from July 23 to August 2, 2024, affecting all five sites. This dataset provides time series game camera photos, while the broader study includes continuous water quality monitoring, biogeochemical sampling of water and soils, precipitation data, and organic matter analysis. The other data types and additional metadata (include site environmental information) can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3018020. Because this study is ongoing, this data package will be updated regularly to include newly collected photos. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) file-level metadata; (2) data dictionary; (3) field metadata; (4) readme; (5) field protocol; and (6) folders of game camera photos. The game camera photos are organized by site with subfolders by month of collection. The field metadata contains a subset of the information collected that is most relevant to photo-processing. The full set of field metadata can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3018020. All files are .csv, .pdf, or .jpg.

Burn severity↗

DOE OSTI2014

Validating agent based models through virtual worlds.

As the US continues its vigilance against distributed, embedded threats, understanding the political and social structure of these groups becomes paramount for predicting and dis- rupting their attacks. Agent-based models (ABMs) serve as a powerful tool to study these groups. While the popularity of social network tools (e.g., Facebook, Twitter) has provided extensive communication data, there is a lack of ne-grained behavioral data with which to inform and validate existing ABMs. Virtual worlds, in particular massively multiplayer online games (MMOG), where large numbers of people interact within a complex environ- ment for long periods of time provide an alternative source of data. These environments provide a rich social environment where players engage in a variety of activities observed between real-world groups: collaborating and/or competing with other groups, conducting battles for scarce resources, and trading in a market economy. Strategies employed by player groups surprisingly re ect those seen in present-day con icts, where players use diplomacy or espionage as their means for accomplishing their goals. In this project, we propose to address the need for ne-grained behavioral data by acquiring and analyzing game data a commercial MMOG, referred to within this report as Game X. The goals of this research were: (1) devising toolsets for analyzing virtual world data to better inform the rules that govern a social ABM and (2) exploring how virtual worlds could serve as a source of data to validate ABMs established for analogous real-world phenomena. During this research, we studied certain patterns of group behavior to compliment social modeling e orts where a signi cant lack of detailed examples of observed phenomena exists. This report outlines our work examining group behaviors that underly what we have termed the Expression-To-Action (E2A) problem: determining the changes in social contact that lead individuals/groups to engage in a particular behavior. Results from our work indicate that virtual worlds have the potential for serving as a proxy in allocating and populating behaviors that would be used within further agent-based modeling studies.

Lakkaraju, Kiran↗

DOE OSTI2015

Cyber Security Research Frameworks For Coevolutionary Network Defense

Several architectures have been created for developing and testing systems used in network security, but most are meant to provide a platform for running cyber security experiments as opposed to automating experiment processes. In the first paper, we propose a framework termed Distributed Cyber Security Automation Framework for Experiments (DCAFE) that enables experiment automation and control in a distributed environment. Predictive analysis of adversaries is another thorny issue in cyber security. Game theory can be used to mathematically analyze adversary models, but its scalability limitations restrict its use. Computational game theory allows us to scale classical game theory to larger, more complex systems. In the second paper, we propose a framework termed Coevolutionary Agent-based Network Defense Lightweight Event System (CANDLES) that can coevolve attacker and defender agent strategies and capabilities and evaluate potential solutions with a custom network defense simulation. The third paper is a continuation of the CANDLES project in which we rewrote key parts of the framework. Attackers and defenders have been redesigned to evolve pure strategy, and a new network security simulation is devised which specifies network architecture and adds a temporal aspect. We also add a hill climber algorithm to evaluate the search space and justify the use of a coevolutionary algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Energize: An Interactive Evaluation Tool for Engaging the General Public with Energy Decision Making - Final Report

The public has an ever-increasing interest in the economic, environmental, and social impacts of global energy production. To support informed decision making, the scientific community has a responsibility to communicate reliable and straight-forward information to the general public, in an engaging way, regarding energy systems and how choices made at different stages of an energy technology life cycle can impact the cost, amount of materials used, and waste produced. Our objective is to enhance public engagement via an interactive electrical energy game (Energ!ze) through which players interact with one another in their quest to develop an electrical energy portfolio that optimizes economic (e.g., company profit), environmental (e.g., reduced CO 2 emissions), and social (e.g., public opinion) impacts. The design and development of Energ!ze was an iterative process involving an interdisciplinary team of engineers, discipline-based scientists, computer scientists, and education experts. The development objectives were two-fold: (1) Accurate and quantifiable modeling of electrical energy systems and (2) Engaging and interactive user interface within the construct of the game narrative. The major game mechanics in the current playable Energ!ze version focus on economic metrics, and the database is scaffolded to add environmental and social metrics for future versions. This report details the outcome of the funding period (Section 2 and 3) and describes the development process, along with recommendations for future development (Section 4).

29 ENERGY PLANNING, POLICY, AND ECONOMY↗