Weak stability boundary (WSB), including low-energy transfer, is a concept introduced by Edward Belbruno in 1987. The concept explained how a spacecraft could change orbits using very little fuel. Weak stability boundary is defined for the three-body problem. This problem considers the motion of a particle P of negligible mass moving with respect to two larger bodies, P1, P2, modeled as point masses, where these bodies move in circular or elliptical orbits with respect to each other, and P2 is smaller than P1. The force between the three bodies is the classical Newtonian gravitational force. For example, P1 is the Earth, P2 is the Moon and P is a spacecraft; or P1 is the Sun, P2 is Jupiter and P is a comet, etc. This model is called the restricted three-body problem. The weak stability boundary defines a region about P2 where P is temporarily captured. This region is in position-velocity space. Capture means that the Kepler energy between P and P2 is negative. This is also called weak capture. == Background == This boundary was defined for the first time by Edward Belbruno of Princeton University in 1987. He described a Low-energy transfer which would allow a spacecraft to change orbits using very little fuel. It was for motion about Moon (P2) with P1 = Earth. It is defined algorithmically by monitoring cycling motion of P about the Moon and finding the region where cycling motion transitions between stable and unstable after one cycle. Stable motion means P can completely cycle about the Moon for one cycle relative to a reference section, starting in weak capture. P needs to return to the reference section with negative Kepler energy. Otherwise, the motion is called unstable, where P does not return to the reference section within one cycle or if it returns, it has non-negative Kepler energy. The set of all transition points about the Moon comprises the weak stability boundary, W. The motion of P is sensitive or chaotic as it moves about the Moon within W. A mathematical proof that the motion within W is chaotic was given in 2004. This is accomplished by showing that the set W about an arbitrary body P2 in the restricted three-body problem contains a hyperbolic invariant set of fractional dimension consisting of the infinitely many intersections Hyperbolic manifolds. The weak stability boundary was originally referred to as the fuzzy boundary. This term was used since the transition between capture and escape defined in the algorithm is not well defined and limited by the numerical accuracy. This defines a "fuzzy" location for the transition points. It is also due the inherent chaos in the motion of P near the transition points. It can be thought of as a fuzzy chaos region. As is described in an article in Discover magazine, the WSB can be roughly viewed as the fuzzy edge of a region, referred to as a gravity well, about a body (the Moon), where its force of gravity becomes small enough to be dominated by force of gravity of another body (the Earth) and the motion there is chaotic. A much more general algorithm defining W was given in 2007. It defines W relative to n-cycles, where n = 1,2,3,..., yielding boundaries of order n. This gives a much more complex region consisting of the union of all the weak stability boundaries of order n. This definition was explored further in 2010. The results suggested that W consists, in part, of the hyperbolic network of invariant manifolds associated to the Lyapunov orbits about the L1, L2 Lagrange points near P2. The explicit determination of the set W about P2 = Jupiter, where P1 is the Sun, is described in "Computation of Weak Stability Boundaries: Sun-Jupiter Case". It turns out that a weak stability region can also be defined relative to the larger mass point, P1. A proof of the existence of the weak stability boundary about P1 was given in 2012, but a different definition is used. The chaos of the motion is analytically proven in "Geometry of Weak Stability Boundaries". The boundary is studied in "Applicability and Dynamical Characterization of the Associated Sets of the Algorithmic Weak Stability Boundary in the Lunar Sphere of Influence". == Applications == There are a number of important applications for the weak stability boundary (WSB). Since the WSB defines a region of temporary capture, it can be used, for example, to find transfer trajectories from the Earth to the Moon that arrive at the Moon within the WSB region in weak capture, which is called ballistic capture for a spacecraft. No fuel is required for capture in this case. This was numerically demonstrated in 1987. This is the first reference for ballistic capture for spacecraft and definition of the weak stability boundary. The boundary was operationally demonstrated to exist in 1991 when it was used to find a ballistic capture transfer to the Moon for Japan's Hiten spacecraft. Other missions have used the same transfer type as Hiten, including Grail, Capstone, Danuri, Hakuto-R Mission 1 and SLIM. The WSB for Mars is studied in "Earth-Mars Transfers with Ballistic Capture" and ballistic capture transfers to Mars are computed. The BepiColombo mission of ESA should achieve ballistic capture at the WSB of Mercury in November 2026. The WSB region can be used in the field of Astrophysics. It can be defined for stars within open star clusters. This is done in "Chaotic Exchange of Solid Material Between Planetary Systems: Implications for the Lithopanspermia Hypothesis" to analyze the capture of solid material that may have arrived on the Earth early in the age of the Solar System to study the validity of the lithopanspermia hypothesis. Numerical explorations of trajectories for P starting in the WSB region about P2 show that after the particle P escapes P2 at the end of weak capture, it moves about the primary body, P1, in a near resonant orbit, in resonance with P2 about P1. This property was used to study comets that move in orbits about the Sun in orbital resonance with Jupiter, which change resonance orbits by becoming weakly captured by Jupiter. An example of such a comet is 39P/Oterma. This property of change of resonance of orbits about P1 when P is weakly captured by the WSB of P2 has an interesting application to the field of quantum mechanics to the motion of an electron about the proton in a hydrogen atom. The transition motion of an electron about the proton between different energy states described by the Schrödinger equation is shown to be equivalent to the change of resonance of P about P1 via weak capture by P2 for a family of transitioning resonance orbits. This gives a classical model using chaotic dynamics with Newtonian gravity for the motion of an electron.
Google Research
Google Research (also known as Research at Google) is the research division of Google, a subsidiary of Alphabet Inc.. According to its official website, Google Research publishes findings, releases open-source software, and applies research results within Google products and services as well as within the wider scientific community. == Notable contributions == The 2017 landmark paper Attention Is All You Need, which introduced the Transformer architecture, which has subsequently been used to build modern large language models. Advances in neural machine translation powering Google Translate. Time series forecasting. Development of scalable learning systems and infrastructure for large-model training. Flood forecasting. Research into computational discovery via Google Accelerated Science including demonstrating the first below-threshold quantum calculations.
MetaMask
MetaMask is a software cryptocurrency wallet developed by ConsenSys for interacting with the Ethereum blockchain and other EVM-compatible networks. It enables users to manage Ethereum accounts and connect to decentralized applications (dApps) via a browser extension or mobile app. As of early 2026, MetaMask reports over 100 million users worldwide. == Overview == MetaMask allows users to store and manage private keys, send and receive Ethereum-based cryptocurrencies and tokens (including ERC-20 and ERC-721 standards), broadcast transactions, and interact with dApps. dApps connect to the wallet via JavaScript interfaces, prompting users to approve signatures or transactions. The wallet features MetaMask Swaps, an in-app token swap aggregator sourcing liquidity from multiple decentralized exchanges (DEXs), with a service fee of 0.875%. In 2025, MetaMask introduced the MetaMask Rewards program (initially mobile-only), where users earn points for activities such as swaps, bridging, and referrals. Season 1 (October 2025 – January 2026) distributed over $30 million in Linea tokens and other perks to participants. == History == MetaMask launched in 2016 as open-source software under the MIT license. It initially supported browser extensions for Chrome and Firefox. Mobile versions were in closed beta from 2019 and publicly released for iOS and Android in September 2020. In August 2020, the license changed to a custom proprietary one. MetaMask Swaps launched on desktop in October 2020 and on mobile in March 2021. The Rewards program launched in late 2025 with Linea integration. == Criticism == MetaMask has faced criticism over privacy, including default analytics settings that share some user data (which can be disabled). Its reliance on Infura (acquired by ConsenSys in 2019) has raised concerns about centralization in Ethereum infrastructure. The wallet regularly issues warnings about phishing scams and fake airdrops impersonating MetaMask.
Play Integrity API
Play Integrity API (formerly known as SafetyNet) consists of several application programming interfaces (APIs) offered by the Google Play Services to support security sensitive applications and enforce DRM. Currently, these APIs include device integrity verification, app verification, recaptcha and web address verification. It uses an environment called DroidGuard to perform the attestation. == Attestation == The SafetyNet Attestation API, one of the APIs under the SafetyNet umbrella, provides verification that the integrity of the device is not compromised. In practice, non-official ROMs such as LineageOS fail the hardware attestation and thus prevent the user from using a non-compliant ROM with third-party apps (mainly banking) that require the API. Due to this, some consider this a monopolistic practice deterring the entrance of competing mobile operating systems in the market. It requires a network connection to Google servers and validates the hardware signatures. Amongst the checks, the API looks for bootloader unlock status, ROM signatures, kernel strings, it also uses AVB2.0 and dm-verity attestations. Upon successful checks, Google Play will mark the device as Certified. The attestation runs in an environment called DroidGuard (com.google.android.gms.unstable). The SafetyNet Attestation API (one of the four APIs under the SafetyNet umbrella) has been deprecated. As of 6 October 2023, Google planned to replace it with the Play Integrity API by the end of January 2025. The transition ended on 20 May 2025, breaking applications which hadn't been updated. These attestations are offered by Google Play Services and thus are not available on free Android environments, like AOSP. Therefore, developers can require the API to be available and may refuse to execute on AOSP builds. == Google Play Protect == Under the same umbrella, Play Protect is a mechanism to find and remove "vulnerable" apps from one's Android device as well as store apps. Although it's meant to scan for malware-containing apps, it also looks for non-DRM compliant apps. == Criticism == Multiple groups have criticised SafetyNet and the Play Integrity API. Criticisms include that it offers weaker protection compared to alternatives such as Android's hardware attestation API, which provides a stronger form of verification while having the ability to remain compatible with more secure Android operating systems like GrapheneOS. Critics argued it undermines competition by effectively requiring developers to rely on Google's proprietary services, strengthening its monopoly over the Android ecosystem and disadvantaging alternative, privacy-focused operating systems. Users have also developed tools, such as the Play Integrity Fix module for Magisk/KernelSU/APatch, which tricks the attestation using leaked fingerprints of vulnerable devices. Furthermore, some have questioned the effectiveness of the attestation, claiming it does not deliver the level of security promised by Google and instead serves more as a form of vendor lock-in than a meaningful security measure. Activists have also raised concerns that it may violate antitrust and competition laws, like the Digital Markets Act.
Hit-testing
In computer graphics programming, hit-testing (hit detection, picking, or pick correlation) is the process of determining whether a user-controlled cursor (such as a mouse cursor or touch-point on a touch-screen interface) intersects a given graphical object (such as a shape, line, or curve) drawn on the screen. Hit-testing may be performed on the movement or activation of a mouse or other pointing device. Hit-testing is used by GUI environments to respond to user actions, such as selecting a menu item or a target in a game based on its visual location. In web programming languages such as HTML, SVG, and CSS, this is associated with the concept of pointer-events (e.g. user-initiated cursor movement or object selection). Collision detection is a related concept for detecting intersections of two or more different graphical objects, rather than intersection of a cursor with one or more graphical objects. == Algorithm == There are many different algorithms that may be used to perform hit-testing, with different performance or accuracy outcomes. One common hit-test algorithm for axis aligned bounding boxes. A key idea is that the box being tested must be either entirely above, entirely below, entirely to the right or left of the current box. If this is not possible, they are colliding. Example logic is presented in the pseudo-code below: In Python:
Microsoft Support Diagnostic Tool
The Microsoft Support Diagnostic Tool (MSDT) is a legacy service in Microsoft Windows that allows Microsoft technical support agents to analyze diagnostic data remotely for troubleshooting purposes. In April 2022 it was observed to have a security vulnerability that allowed remote code execution which was being exploited to attack computers in Russia and Belarus, and later against the Tibetan government in exile. Microsoft advised a temporary workaround of disabling the MSDT by editing the Windows registry. == Use == When contacting support the user is told to run MSDT and given a unique "passkey" which they enter. They are also given an "incident number" to uniquely identify their case. The MSDT can also be run offline which will generate a .CAB file which can be uploaded from a computer with an internet connection. == Security vulnerabilities == === Follina === Follina is the name given to a remote code execution (RCE) vulnerability, a type of arbitrary code execution (ACE) exploit, in the Microsoft Support Diagnostic Tool (MSDT) which was first widely publicized on May 27, 2022, by a security research group called Nao Sec. This exploit allows a remote attacker to use a Microsoft Office document template to execute code via MSDT. This works by exploiting the ability of Microsoft Office document templates to download additional content from a remote server. If the size of the downloaded content is large enough it causes a buffer overflow allowing a payload of Powershell code to be executed without explicit notification to the user. On May 30 Microsoft issued CVE-2022-30190 with guidance that users should disable MSDT. Malicious actors have been observed exploiting the bug to attack computers in Russia and Belarus since April, and it is believed Chinese state actors had been exploiting it to attack the Tibetan government in exile based in India. Microsoft patched this vulnerability in its June 2022 patches. === DogWalk === The DogWalk vulnerability is a remote code execution (RCE) vulnerability in the Microsoft Support Diagnostic Tool (MSDT). It was first reported in January 2020, but Microsoft initially did not consider it to be a security issue. However, the vulnerability was later exploited in the wild, and Microsoft released a patch for it in August 2022. The vulnerability is caused by a path traversal vulnerability in the sdiageng.dll library. This vulnerability allows an attacker to trick a victim into opening a malicious diagcab file, which is a type of Windows cabinet file that is used to store support files. When the diagcab file is opened, it triggers the MSDT tool, which then executes the malicious code. Originally discovered by Mitja Kolsek, the DogWalk vulnerability is caused by a path traversal vulnerability in the sdiageng.dll library. This vulnerability allows an attacker to trick a victim into opening a malicious diagcab file, which is a type of Windows cabinet file that is used to store support files. When the diagcab file is opened, it triggers the MSDT tool, which then executes the malicious code. The vulnerability is exploited by creating a malicious diagcab file that contains a specially crafted path. This path contains a sequence of characters that is designed to exploit the path traversal vulnerability in the sdiageng.dll library. When the diagcab file is opened, the MSDT tool will attempt to follow the path. However, the path will contain characters that are not valid for a Windows path. This will cause the MSDT tool to crash. When the MSDT tool crashes, it will generate a memory dump. This memory dump will contain the malicious code that was executed by the MSDT tool. The attacker can then use this memory dump to extract the malicious code and execute it on their own computer. == Retirement == Microsoft will no longer be supporting the Windows legacy inbox Troubleshooters. In 2025, Microsoft will remove the MSDT platform entirely. Get Help is the replacement tool. == Windows versions == Windows 7 Windows 8.1 Windows 10 Windows 11 (up to 22H2) Future versions and feature upgrades will deprecate the MSDT after May 23, 2023.
Headway (app)
Headway, also known as the Headway App, is an educational technology (EdTech) product that provides short text and audio summaries of nonfiction books. The product was launched in 2019 by Anton Pavlovsky and is developed by Headway Inc, a global consumer tech company that operates in the lifelong learning space. == History == The Headway app was launched in January 2019, with the first version of the application released the same year. In 2021, Headway ranked first globally in downloads within the book summary application niche. In 2022, the application received the Golden Novum Design Award for product design. In 2023 and 2024, Headway appeared in several App Store editorial selections, including App of the Day in multiple countries, and received an Editors’ Choice label in the United States. In April 2025, the application was listed as a Webby Honoree in the Learning & Education category. The company has also launched the Headway Scholarship for Book Lovers. As of 2025, publicly available reporting notes that the Headway app has surpassed 50 million downloads and is among the Top 10 iOS applications by revenue in the Education category worldwide. == Products and features == The Headway app provides short-form summaries of nonfiction books in both text and audio formats. Content is produced by an in-house team of writers, editors, and voice actors. Features include highlighting and saving key insights, spaced repetition for knowledge retention, and offline access to downloaded summaries. The app is available on iOS, iPadOS, watchOS, Android, CarPlay, and Android Auto, and supports multiple languages. == Pricing == Headway operates on a subscription business model, with optional paid plans alongside free access. The company publicly provides its terms of use, privacy policy, subscription details, and AI usage policy on its official website. == Technology and integrations == Headway reports that its book summaries are written and edited manually, while artificial intelligence tools are used in limited supporting functions, such as experimental conversational features and selected marketing processes. == Adoption == According to figures released by the company, the app has exceeded 50 million downloads worldwide. Sensor Tower data indicates that Headway has been the most downloaded application in its niche since October 2020. In January 2025, the app claimed the #1 position in the Education category in both the United States and United Kingdom App Stores and remained among the Top 10 iOS applications globally by revenue within the Education category. == Awards == The Headway app has received several product-level distinctions. In 2023 and 2024, it appeared in multiple App Store editorial selections, including App of the Day features and an Editors’ Choice label in the United States. In 2025, the app was recognized as a Webby Honoree in the Learning & Education category. The product has also been featured in independent media roundups of notable educational applications.