In packed pixel or chunky framebuffer organization, the bits defining each pixel are clustered and stored consecutively. For example, if there are 16 bits per pixel, each pixel is represented in two consecutive (contiguous) 8-bit bytes in the framebuffer. If there are 4 bits per pixel, each framebuffer byte defines two pixels, one in each nibble. The latter example is as opposed to storing a single 4-bit pixel in a byte, leaving 4 bits of the byte unused. If a pixel has more than one channel, the channels are interleaved when using packed pixel organization. Packed pixel displays were common on early microcomputer system that shared a single main memory for both the central processing unit (CPU) and display driver. In such systems, memory was normally accessed a byte at a time, so by packing the pixels, the display system could read out several pixels worth of data in a single read operation. Packed pixel is one of two major ways to organize graphics data in memory, the other being planar organization, where each pixel is made of individual bits stored in their own plane. For a 4-bit color value, memory would be organized as four screen-sized planes of one bit each and a single pixel's value built up by selecting the appropriate bit from each plane. Planar organization has the advantage that the data can be accessed in parallel, and is used when memory bandwidth is an issue.
Jeremy Renner Official
Jeremy Renner Official (or Jeremy Renner on the Google Play Store) was a mobile app created by American actor Jeremy Renner. He created the app in March 2017 to hear the input and comments of his fans. The app was shut down in September 2019 in part due to the frequent bullying and trolling that the platform had experienced. The app featured optional microtransactions, with some ranging up to roughly US$400 despite the app itself being free. Upon shutting down the app, Renner issued a mass-refund for the collectible "stars" in the app for purchases made within the last ninety days, from the day the announcement was posted. He then posted an apology to the app itself, and the app was deleted from both the Google Play Store and the App Store shortly after. == Usage == Upon downloading the app, the user was faced with a video of Renner speaking about his fans and superfans, regular giveaways, and real-life updates. While the app was active, Renner posted regular questions and comments for fans. Renner occasionally livestreamed about his work and day-to-day life. The community developed to include memes, selfies, and a "Happy Rennsday" event on Wednesdays. == History == === 2017–2019 === The app launched in March 2017 with a promotional contest. Renner's fans were encouraged to download the app and create comments about being Renner's biggest fan; Renner would then choose a winner and transport the winner and a guest to have lunch with him at the Calgary Expo. In the first few months Renner teased behind-the-scenes of projects he was working on, which he now sporadically does on Instagram. The app was similarly designed to Instagram as well, with a near identically styled layout. Around midway through 2019, a hoax account of Renner was made to mock the celebrity, joking about masturbating to porn and defending another hoax account of Casey Anthony. FastCompany wrote extensively about Renner's app in April 2019, calling it "a surprising new kind of social media". The Ringer stated "Jeremy Renner's Jeremy Renner app is the Jeremy Renner of apps." === After deletion (2019–2020) === After the shutdown of the app, a comedy-based pseudo-app with modular endings was released, called "The Jeremy Renner App Experience", in which the player plays as Jeremy Renner on the day of the Jeremy Renner Official app's shutdown. The app details several different choices on how Renner handles the situation. A six-part podcast was also created to mock the app's deletion, called The Renner Files, featuring Carolyn Goldfarb and Sarah Ramos. == Controversies == === Marketing === One of the main controversies of Renner's app was its marketing. The app's developers, Escapex, specialized in and grew famous for making similar monetized apps for celebrities. The marketing campaign was based on direct contact with Renner, whose chances were increased with regular payments for "stars", although very few encounters seemed to happen with Renner himself. The multiple problems with the app led the CEO of Escapex, Sephi Shapira, to call the app a "freak situation", and added "Am I concerned about this? Not more than I'm concerned about 50 other things I'm dealing with as a startup company." Along with the marketing failures, the app was seen as misrepresenting itself as seemingly erotic with some advertisements featuring Renner suggestively staring at the camera, despite the actual app being initially considered safe for children. === Harassment === After its release in 2017, the app was met with waves of harassment and bullying by many users on the app, most frequently by using impersonation — referenced in Renner's apology/deletion notice. Some death threats were made across the app by fraud accounts pretending to be several controversial celebrities, including O. J. Simpson and Casey Anthony. As early as October 2017, there were claims of censorship, bullying, and "contest-rigging". In September 2019, comedian Stefan Heck publicized his discovery of the fact that replies through the app appeared as if they were sent by Renner himself in push notifications. After several users abused this feature, Renner asked Escapex to shut down the app.
Büchi automaton
In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input. A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata recognize the ω-regular languages, the infinite word version of regular languages. They are named after the Swiss mathematician Julius Richard Büchi, who invented them in 1962. Büchi automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic. == Formal definition == Formally, a deterministic Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},\mathbf {F} )} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \to Q} is a function, called the transition function of A {\textstyle A} . q 0 {\textstyle q_{0}} is an element of Q {\textstyle Q} , called the initial state of A {\textstyle A} . F ⊆ Q {\textstyle \mathbf {F} \subseteq Q} is the acceptance condition. A run i _ = i 0 i 1 i 2 ⋯ ∈ Σ ω {\displaystyle {\underline {i}}=i_{0}i_{1}i_{2}\cdots \in \Sigma ^{\omega }} is an infinite string of inputs of A {\displaystyle A} . By calling δ {\displaystyle \delta } recursively, we can extend it to a function δ ω : Σ ω → Q ω {\displaystyle \delta ^{\omega }:\Sigma ^{\omega }\to Q^{\omega }} . A state q ∈ Q {\displaystyle q\in Q} is said to occur infinitely often for a run i _ {\displaystyle {\underline {i}}} when the set { n ∈ N ∣ δ ω ( i _ ) n = q } {\displaystyle \{n\in \mathbb {N} \mid \delta ^{\omega }({\underline {i}})_{n}=q\}} is infinite. Let I n f ( i _ ) {\displaystyle \mathrm {Inf} ({\underline {i}})} be the set of states occurring infinitely often for i _ {\displaystyle {\underline {i}}} . The language of A {\displaystyle A} is then the set of runs of A {\displaystyle A} in which at least one of the infinitely-often occurring states is in F {\textstyle \mathbf {F} } ; in symbols: L ( A ) = { i _ ∈ Σ ω ∣ I n f ( i _ ) ∩ F ≠ ∅ } . {\displaystyle L(A)=\{{\underline {i}}\in \Sigma ^{\omega }\mid \mathrm {Inf} ({\underline {i}})\cap \mathbf {F} \neq \varnothing \}.} In a (non-deterministic) Büchi automaton, the transition function δ {\textstyle \delta } is replaced with a transition relation Δ {\textstyle \Delta } that returns a set of states, and the single initial state q 0 {\textstyle q_{0}} is replaced by a set I {\textstyle I} of initial states. Generally, the term Büchi automaton without qualifier refers to non-deterministic Büchi automata. For more comprehensive formalism see also ω-automaton. == Closure properties == The set of Büchi automata is closed under the following operations. Let A = ( Q A , Σ , Δ A , I A , F A ) {\displaystyle A=(Q_{A},\Sigma ,\Delta _{A},I_{A},{F}_{A})} and B = ( Q B , Σ , Δ B , I B , F B ) {\displaystyle B=(Q_{B},\Sigma ,\Delta _{B},I_{B},{F}_{B})} be Büchi automata and C = ( Q C , Σ , Δ C , I C , F C ) {\displaystyle C=(Q_{C},\Sigma ,\Delta _{C},I_{C},{F}_{C})} be a finite automaton. Union: There is a Büchi automaton that recognizes the language L ( A ) ∪ L ( B ) . {\displaystyle L(A)\cup L(B).} Proof: If we assume, w.l.o.g., Q A ∩ Q B {\displaystyle Q_{A}\cap Q_{B}} is empty then L ( A ) ∪ L ( B ) {\displaystyle L(A)\cup L(B)} is recognized by the Büchi automaton ( Q A ∪ Q B , Σ ∪ Σ , Δ A ∪ Δ B , I A ∪ I B , F A ∪ F B ) . {\displaystyle (Q_{A}\cup Q_{B},\Sigma \cup \Sigma ,\Delta _{A}\cup \Delta _{B},I_{A}\cup I_{B},{F}_{A}\cup {F}_{B}).} Intersection: There is a Büchi automaton that recognizes the language L ( A ) ∩ L ( B ) . {\displaystyle L(A)\cap L(B).} Proof: The Büchi automaton A ′ = ( Q ′ , Σ , Δ ′ , I ′ , F ′ ) {\displaystyle A'=(Q',\Sigma ,\Delta ',I',F')} recognizes L ( A ) ∩ L ( B ) , {\displaystyle L(A)\cap L(B),} where Q ′ = Q A × Q B × { 1 , 2 } {\displaystyle Q'=Q_{A}\times Q_{B}\times \{1,2\}} Δ ′ = Δ 1 ∪ Δ 2 {\displaystyle \Delta '=\Delta _{1}\cup \Delta _{2}} Δ 1 = { ( ( q A , q B , 1 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q A ∈ F A then i = 2 else i = 1 } {\displaystyle \Delta _{1}=\{((q_{A},q_{B},1),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{A}\in F_{A}{\text{ then }}i=2{\text{ else }}i=1\}} Δ 2 = { ( ( q A , q B , 2 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q B ∈ F B then i = 1 else i = 2 } {\displaystyle \Delta _{2}=\{((q_{A},q_{B},2),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{B}\in F_{B}{\text{ then }}i=1{\text{ else }}i=2\}} I ′ = I A × I B × { 1 } {\displaystyle I'=I_{A}\times I_{B}\times \{1\}} F ′ = { ( q A , q B , 2 ) | q B ∈ F B } {\displaystyle F'=\{(q_{A},q_{B},2)|q_{B}\in F_{B}\}} By construction, r ′ = ( q A 0 , q B 0 , i 0 ) , ( q A 1 , q B 1 , i 1 ) , … {\displaystyle r'=(q_{A}^{0},q_{B}^{0},i^{0}),(q_{A}^{1},q_{B}^{1},i^{1}),\dots } is a run of automaton A' on input word w {\textstyle w} if r A = q A 0 , q A 1 , … {\displaystyle r_{A}=q_{A}^{0},q_{A}^{1},\dots } is run of A {\textstyle A} on w {\textstyle w} and r B = q B 0 , q B 1 , … {\displaystyle r_{B}=q_{B}^{0},q_{B}^{1},\dots } is run of B {\textstyle B} on w {\textstyle w} . r A {\textstyle r_{A}} is accepting and r B {\textstyle r_{B}} is accepting if r ′ {\textstyle r'} is concatenation of an infinite series of finite segments of 1-states (states with third component 1) and 2-states (states with third component 2) alternatively. There is such a series of segments of r ′ {\textstyle r'} if r ′ {\textstyle r'} is accepted by A ′ {\textstyle A'} . Concatenation: There is a Büchi automaton that recognizes the language L ( C ) ⋅ L ( A ) . {\displaystyle L(C)\cdot L(A).} Proof: If we assume, w.l.o.g., Q C ∩ Q A {\displaystyle Q_{C}\cap Q_{A}} is empty then the Büchi automaton A ′ = ( Q C ∪ Q A , Σ , Δ ′ , I ′ , F A ) {\displaystyle A'=(Q_{C}\cup Q_{A},\Sigma ,\Delta ',I',F_{A})} recognizes L ( C ) ⋅ L ( A ) {\displaystyle L(C)\cdot L(A)} , where Δ ′ = Δ A ∪ Δ C ∪ { ( q , a , q ′ ) | q ′ ∈ I A and ∃ f ∈ F C . ( q , a , f ) ∈ Δ C } {\displaystyle \Delta '=\Delta _{A}\cup \Delta _{C}\cup \{(q,a,q')|q'\in I_{A}{\text{ and }}\exists f\in F_{C}.(q,a,f)\in \Delta _{C}\}} if I C ∩ F C is empty then I ′ = I C otherwise I ′ = I C ∪ I A {\displaystyle {\text{ if }}I_{C}\cap F_{C}{\text{ is empty then }}I'=I_{C}{\text{ otherwise }}I'=I_{C}\cup I_{A}} ω-closure: If L ( C ) {\displaystyle L(C)} does not contain the empty word then there is a Büchi automaton that recognizes the language L ( C ) ω . {\displaystyle L(C)^{\omega }.} Proof: The Büchi automaton that recognizes L ( C ) ω {\displaystyle L(C)^{\omega }} is constructed in two stages. First, we construct a finite automaton A ′ {\textstyle A'} such that A ′ {\textstyle A'} also recognizes L ( C ) {\displaystyle L(C)} but there are no incoming transitions to initial states of A ′ {\textstyle A'} . So, A ′ = ( Q C ∪ { q new } , Σ , Δ ′ , { q new } , F C ) , {\displaystyle A'=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta ',\{q_{\text{new}}\},F_{C}),} where Δ ′ = Δ C ∪ { ( q new , a , q ′ ) | ∃ q ∈ I C . ( q , a , q ′ ) ∈ Δ C } . {\displaystyle \Delta '=\Delta _{C}\cup \{(q_{\text{new}},a,q')|\exists q\in I_{C}.(q,a,q')\in \Delta _{C}\}.} Note that L ( C ) = L ( A ′ ) {\displaystyle L(C)=L(A')} because L ( C ) {\displaystyle L(C)} does not contain the empty string. Second, we will construct the Büchi automaton A ″ {\textstyle A''} that recognize L ( C ) ω {\displaystyle L(C)^{\omega }} by adding a loop back to the initial state of A ′ {\textstyle A'} . So, A ″ = ( Q C ∪ { q new } , Σ , Δ ″ , { q new } , { q new } ) {\displaystyle A''=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta '',\{q_{\text{new}}\},\{q_{\text{new}}\})} , where Δ ″ = Δ ′ ∪ { ( q , a , q new ) | ∃ q ′ ∈ F C . ( q , a , q ′ ) ∈ Δ ′ } . {\displaystyle \Delta ''=\Delta '\cup \{(q,a,q_{\text{new}})|\exists q'\in F_{C}.(q,a,q')\in \Delta '\}.} Complementation:
Magnetic ink character recognition
Magnetic ink character recognition code, known in short as MICR code, is a character recognition technology used mainly by the banking industry to streamline the processing and clearance of cheques and other documents. MICR encoding, called the MICR line, is at the bottom of cheques and other vouchers and typically includes the document-type indicator, bank code, bank account number, cheque number, cheque amount (usually added after a cheque is presented for payment), and a control indicator. The format for the bank code and bank account number is country-specific. The technology allows MICR readers to scan and read the information directly into a data-collection device. Unlike barcode and similar technologies, MICR characters can be read easily by humans. MICR encoded documents can be processed much faster and more accurately than conventional OCR encoded documents. == Pre-Unicode standard representation == The ISO standard ISO 2033:1983, and the corresponding Japanese Industrial Standard JIS X 9010:1984 (originally JIS C 6229–1984), define character encodings for OCR-A, OCR-B and E-13B. == International spread == There are two major MICR fonts in use: E-13B and CMC-7. There is no particular international agreement on which countries use which font. In practice, this does not create particular problems as cheques and other vouchers do not usually flow out of a particular jurisdiction. The E-13B font has been adopted as an international standard in ISO 1004-1:2013, and is the standard in Australia, Canada, the United Kingdom, the United States, as well as Central America and much of Asia, besides other countries. The CMC-7 font has been adopted as an international standard in ISO 1004-2:2013, and is widely used in Europe, including France and Italy, Mexico, and South America, including Argentina, Brazil, Chile, besides other countries. Israel is the only country that can use both fonts simultaneously, though the practice makes the system significantly less efficient. This situation is the product of the Israelis adopting CMC-7, while the Palestinians opted for E-13B. == Fonts == === E-13B === E-13B is a 14-character set, comprising the 10 decimal digits, and the following symbols: ⑆ (transit: used to delimit a bank code); ⑈ (on-us: used to delimit a customer account number); ⑇ (amount: used to delimit a transaction amount); ⑉ (dash: used to delimit parts of numbers—e.g., routing numbers or account numbers). In the check printing and banking industries the E-13B MICR line is also commonly referred to as the TOAD line. This reference comes from the 4 characters: Transit, On-us, Amount, and Dash. Compared to CMC-7, some pairs of E-13B characters (notably 2 and 5) can produce relatively similar results when magnetically scanned; however, as a fallback if magnetic reading fails, E-13B also performs well under optical character recognition. The E-13B repertoire can be represented in Unicode (see below). The official Unicode names contain misnomers. For example, the ⑈ on-us symbol is official titled "OCR Dash". Prior to Unicode, it could be encoded according to ISO 2033:1983, which encodes digits in their usual ASCII locations, transit as 0x3A, on-us as 0x3C, amount as 0x3B, and dash as 0x3D. For EBCDIC, IBM code page 1001 encodes digits in their usual EBCDIC locations, transit as 0xDB, on-us as 0xEB, amount as 0xCB, and dash as 0xFB. IBM code page 1032 extends code page 1001 by adding alternative encodings for transit at 0x5C, 0x7A and 0xC1, on-us at 0x4C, 0x61 and 0xC3, amount at 0x5B, 0x5E and 0xC2 and dash at 0x60, 0x7E and 0xC4, in addition to a zero-width space at 0x5A. These alternative representations were added for interoperability with Siemens and Océ printers. === CMC-7 === CMC-7 includes 10 numeric digits, 26 capital letters, and 5 control characters: S I (internal), S II (terminator), S III (amount), S IV (an unused character), and S V (routing). CMC-7 has a barcode format, with every character having two distinct large gaps in different places, as well as distinct patterns in between, to minimize any chance for character confusion while reading magnetically; however, these bars are too close and narrow to be reliably recognised at a typical scan resolution if falling back to optical scanning. CMC-7 can also produce superficially successful, but incorrect, scans of upside-down MICR lines. Unicode does not include support for the CMC-7 control symbols. IBM code page 1033 encodes: Digits and capitals in their usual EBCDIC locations S I (internal) as 0x5E, 0x61 or 0xCB; S II (terminator) as 0x4C, 0x5B or 0xEB; S III (amount) as 0x60, 0x7E or 0xFB; S IV as 0x50, 0x7A or 0xDB; S V (routing) as 0x5C, 0x6E or 0xBB. == MICR reader == MICR characters are printed on documents in one of the two MICR fonts, using magnetizable (commonly known as magnetic) ink or toner, usually containing iron oxide. In scanning, the document is passed through a MICR reader, which performs two functions: magnetization of the ink, and detection of the characters. The characters are read by a MICR reader head, a device similar to the playback head of a tape recorder. As each character passes over the head, it produces a unique waveform that can be easily identified by the system. MICR readers are the primary tool for cheque sorting and are used across the cheque distribution network at multiple stages. For example, a merchant will use a MICR reader to sort cheques by bank and send the sorted cheques to a clearing house for redistribution to those banks. Upon receipt, the banks perform another MICR sort to determine which customer's account is charged and to which branch the cheque should be sent on its way back to the customer. However, many banks no longer offer this last step of returning the cheque to the customer. Instead, cheques are scanned and stored digitally. Sorting of cheques is done as per the geographical coverage of banks in a nation. == Unicode == OCR and MICR characters have been included in the Unicode Standard since at least version 1.1 (June 1993). Since the Unicode Character Database only tracks characters starting with version 1.1, they may also have been present in Unicode 1.0 or 1.0.1. The Unicode block that includes OCR and MICR characters is called Optical Character Recognition and covers U+2440–U+245F. Of the characters in this block, four are from the MICR E-13B font: U+2446 ⑆ OCR BRANCH BANK IDENTIFICATION U+2447 ⑇ OCR AMOUNT OF CHECK U+2448 ⑈ OCR DASH (corrected alias MICR ON US SYMBOL) U+2449 ⑉ OCR CUSTOMER ACCOUNT NUMBER (corrected alias MICR DASH SYMBOL) The names of the latter two characters were inadvertently switched when they were named in ISO/IEC 10646:1993, and they have been assigned accurate names as formal aliases. Per the Unicode Stability Policy, the existing names remain, allowing their use as stable identifiers. Additionally, all four characters have informative (non-formal) aliases in the Unicode charts: "transit", "amount", "on-us", and "dash" respectively. Prior to Unicode, these symbols had been encoded by the ISO-IR-98 encoding defined by ISO 2033:1983, in which they were simply named SYMBOL ONE through SYMBOL FOUR. They were encoded immediately following the digits, which were encoded at their ASCII locations. Although ISO 2033 also specifies encoding for OCR-A and OCR-B, its encoding for E-13B is known simply as ISO_2033-1983 by the IANA. == History == Before the mid-1940s, cheques were processed manually using the Sort-A-Matic or Top Tab Key method. The processing and cheque clearing was very time-consuming and was a significant cost in cheque clearance and bank operations. As the number of cheques increased, ways were sought for automating the process. Standards were developed to ensure uniformity in financial institutions. By the mid-1950s, the Stanford Research Institute and General Electric Computer Laboratory had developed the first automated system to process cheques using MICR. The same team also developed the E-13B MICR font. "E" refers to the font being the fifth considered, and "B" to the fact that it was the second version. The "13" refers to the 0.013-inch character grid. The trial of MICR E-13B font was shown to the American Bankers Association (ABA) in July 1956, which adopted it in 1958 as the MICR standard for negotiable documents in the United States. ABA adopted MICR as its standard because machines could read MICR accurately, and MICR could be printed using existing technology. In addition, MICR remained machine readable, even through overstamping, marking, mutilation and more. The first cheques using MICR were printed by the end of 1959. Although compliance with MICR standards was voluntary in the United States, it had been almost universally adopted in the United States by 1963. In 1963, ANSI adopted the ABA's E-13B font as the American standard for MICR printing, and E-13B was also standardized as ISO 1004:1995. Other countries set their own standards, though the MICR readers and m
Danqi Chen
Danqi Chen (Chinese: 陈丹琦; pinyin: Chén Dānqí, IPA: [ʈ͡ʂʰə̌n tan t͡ɕʰǐ]; born in Changsha, China) is a Chinese computer scientist and assistant professor at Princeton University specializing in the AI field of natural language processing (NLP). In 2019, she joined the Princeton NLP group, alongside Sanjeev Arora, Christiane Fellbaum, and Karthik Narasimhan. She was previously a visiting scientist at Facebook AI Research (FAIR). She earned her Ph.D. at Stanford University and her BS from Tsinghua University. Chen is the author of Neural Reading Comprehension and Beyond, a dissertation on using artificial intelligence to access knowledge in ordinary and structured documents. She is the author or co-author of a number of journal articles, including Reading Wikipedia to Answer Open-Domain Questions. Google's SyntaxNet is based on algorithms developed by Danqi Chen and Christopher Manning at Stanford. Her primary research interests are in text understanding and knowledge representation and reasoning. She won a gold medal at the 2008 International Informatics Olympiad. She is known among friends as CDQ. A well known algorithm in competitive programming, CDQ Divide and Conquer, is named after this acronym. She is married to Huacheng Yu, an assistant professor in theoretical computer science at Princeton University.
Pixel-art scaling algorithms
Pixel art scaling algorithms are graphical filters that attempt to enhance the appearance of hand-drawn 2D pixel art graphics. These algorithms are a form of automatic image enhancement. Pixel art scaling algorithms employ methods significantly different than the common methods of image rescaling, which have the goal of preserving the appearance of images. As pixel art graphics are commonly used at very low resolutions, they employ careful coloring of individual pixels. This results in graphics that rely on a high amount of stylized visual cues to define complex shapes. Several specialized algorithms have been developed to handle re-scaling of such graphics. These specialized algorithms can improve the appearance of pixel-art graphics, but in doing so they introduce changes. Such changes may be undesirable, especially if the goal is to faithfully reproduce the original appearance. Since a typical application of this technology is improving the appearance of fourth-generation and earlier video games on arcade and console emulators, many pixel art scaling algorithms are designed to run in real-time for sufficiently small input images at 60-frames per second. This places constraints on the type of programming techniques that can be used for this sort of real-time processing. Many work only on specific scale factors. 2× is the most common scale factor, while 3×, 4×, 5×, and 6× exist but are less used. == Algorithms == === SAA5050 'Diagonal Smoothing' === The Mullard SAA5050 Teletext character generator chip (1980) used a primitive pixel scaling algorithm to generate higher-resolution characters on the screen from a lower-resolution representation from its internal ROM. Internally, each character shape was defined on a 5 × 9 pixel grid, which was then interpolated by smoothing diagonals to give a 10 × 18 pixel character, with a characteristically angular shape, surrounded to the top and the left by two pixels of blank space. The algorithm only works on monochrome source data, and assumes the source pixels will be logically true or false depending on whether they are 'on' or 'off'. Pixels 'outside the grid pattern' are assumed to be off. The algorithm works as follows: A B C --\ 1 2 D E F --/ 3 4 1 = B | (A & E & !B & !D) 2 = B | (C & E & !B & !F) 3 = E | (!A & !E & B & D) 4 = E | (!C & !E & B & F) Note that this algorithm, like the Eagle algorithm below, has a flaw: If a pattern of 4 pixels in a hollow diamond shape appears, the hollow will be obliterated by the expansion. The SAA5050's internal character ROM carefully avoids ever using this pattern. The degenerate case: becomes: === EPX/Scale2×/AdvMAME2× === Eric's Pixel Expansion (EPX) is an algorithm developed by Eric Johnston at LucasArts around 1992, when porting the SCUMM engine games from the IBM PC (which ran at 320 × 200 × 256 colors) to the early color Macintosh computers, which ran at more or less double that resolution. The algorithm works as follows, expanding P into 4 new pixels based on P's surroundings: 1=P; 2=P; 3=P; 4=P; IF C==A => 1=A IF A==B => 2=B IF D==C => 3=C IF B==D => 4=D IF of A, B, C, D, three or more are identical: 1=2=3=4=P Later implementations of this same algorithm (as AdvMAME2× and Scale2×, developed around 2001) are slightly more efficient but functionally identical: 1=P; 2=P; 3=P; 4=P; IF C==A AND C!=D AND A!=B => 1=A IF A==B AND A!=C AND B!=D => 2=B IF D==C AND D!=B AND C!=A => 3=C IF B==D AND B!=A AND D!=C => 4=D AdvMAME2× is available in DOSBox via the scaler=advmame2x dosbox.conf option. The AdvMAME4×/Scale4× algorithm is just EPX applied twice to get 4× resolution. ==== Scale3×/AdvMAME3× and ScaleFX ==== The AdvMAME3×/Scale3× algorithm (available in DOSBox via the scaler=advmame3x dosbox.conf option) can be thought of as a generalization of EPX to the 3× case. The corner pixels are calculated identically to EPX. 1=E; 2=E; 3=E; 4=E; 5=E; 6=E; 7=E; 8=E; 9=E; IF D==B AND D!=H AND B!=F => 1=D IF (D==B AND D!=H AND B!=F AND E!=C) OR (B==F AND B!=D AND F!=H AND E!=A) => 2=B IF B==F AND B!=D AND F!=H => 3=F IF (H==D AND H!=F AND D!=B AND E!=A) OR (D==B AND D!=H AND B!=F AND E!=G) => 4=D 5=E IF (B==F AND B!=D AND F!=H AND E!=I) OR (F==H AND F!=B AND H!=D AND E!=C) => 6=F IF H==D AND H!=F AND D!=B => 7=D IF (F==H AND F!=B AND H!=D AND E!=G) OR (H==D AND H!=F AND D!=B AND E!=I) => 8=H IF F==H AND F!=B AND H!=D => 9=F There is also a variant improved over Scale3× called ScaleFX, developed by Sp00kyFox, and a version combined with Reverse-AA called ScaleFX-Hybrid. === Eagle === Eagle works as follows: for every in pixel, we will generate 4 out pixels. First, set all 4 to the color of the pixel we are currently scaling (as nearest-neighbor). Next look at the three pixels above, to the left, and diagonally above left: if all three are the same color as each other, set the top left pixel of our output square to that color in preference to the nearest-neighbor color. Work similarly for all four pixels, and then move to the next one. Assume an input matrix of 3 × 3 pixels where the centermost pixel is the pixel to be scaled, and an output matrix of 2 × 2 pixels (i.e., the scaled pixel) first: |Then . . . --\ CC |S T U --\ 1 2 . C . --/ CC |V C W --/ 3 4 . . . |X Y Z | IF V==S==T => 1=S | IF T==U==W => 2=U | IF V==X==Y => 3=X | IF W==Z==Y => 4=Z Thus if we have a single black pixel on a white background it will vanish. This is a bug in the Eagle algorithm but is solved by other algorithms such as EPX, 2xSaI, and HQ2x. === 2×SaI === 2×SaI, short for 2× Scale and Interpolation engine, was inspired by Eagle. It was designed by Derek Liauw Kie Fa, also known as Kreed, primarily for use in console and computer emulators, and it has remained fairly popular in this niche. Many of the most popular emulators, including ZSNES and VisualBoyAdvance, offer this scaling algorithm as a feature. Several slightly different versions of the scaling algorithm are available, and these are often referred to as Super 2×SaI and Super Eagle. The 2xSaI family works on a 4 × 4 matrix of pixels where the pixel marked A below is scaled: I E F J G A B K --\ W X H C D L --/ Y Z M N O P For 16-bit pixels, they use pixel masks which change based on whether the 16-bit pixel format is 565 or 555. The constants colorMask, lowPixelMask, qColorMask, qLowPixelMask, redBlueMask, and greenMask are 16-bit masks. The lower 8 bits are identical in either pixel format. Two interpolation functions are described: INTERPOLATE(uint32 A, UINT32 B). -- linear midpoint of A and B if (A == B) return A; return ( ((A & colorMask) >> 1) + ((B & colorMask) >> 1) + (A & B & lowPixelMask) ); Q_INTERPOLATE(uint32 A, uint32 B, uint32 C, uint32 D) -- bilinear interpolation; A, B, C, and D's average x = ((A & qColorMask) >> 2) + ((B & qColorMask) >> 2) + ((C & qColorMask) >> 2) + ((D & qColorMask) >> 2); y = (A & qLowPixelMask) + (B & qLowPixelMask) + (C & qLowPixelMask) + (D & qLowPixelMask); y = (y >> 2) & qLowPixelMask; return x + y; The algorithm checks A, B, C, and D for a diagonal match such that A==D and B!=C, or the other way around, or if they are both diagonals or if there is no diagonal match. Within these, it checks for three or four identical pixels. Based on these conditions, the algorithm decides whether to use one of A, B, C, or D, or an interpolation among only these four, for each output pixel. The 2xSaI arbitrary scaler can enlarge any image to any resolution and uses bilinear filtering to interpolate pixels. Since Kreed released the source code under the GNU General Public License, it is freely available to anyone wishing to utilize it in a project released under that license. Developers wishing to use it in a non-GPL project would be required to rewrite the algorithm without using any of Kreed's existing code. It is available in DOSBox via scaler=2xsai option. === hqnx family === Maxim Stepin's hq2x, hq3x, and hq4x are for scale factors of 2:1, 3:1, and 4:1 respectively. Each work by comparing the color value of each pixel to those of its eight immediate neighbors, marking the neighbors as close or distant, and using a pre-generated lookup table to find the proper proportion of input pixels' values for each of the 4, 9 or 16 corresponding output pixels. The hq3x family will perfectly smooth any diagonal line whose slope is ±0.5, ±1, or ±2 and which is not anti-aliased in the input; one with any other slope will alternate between two slopes in the output. It will also smooth very tight curves. Unlike 2xSaI, it anti-aliases the output. hqnx was initially created for the Super NES emulator ZSNES. The author of bsnes has released a space-efficient implementation of hq2x to the public domain. A port to shaders, which has comparable quality to the early versions of xBR, is available. Before the port, a shader called "scalehq" has often been confused for hqx. === xBR family === There are 6 filters in this family: xBR , xBRZ, xBR-Hybrid, Super xBR, xBR+3D and Super xBR+3D. xBR ("scale by rules"), cre
Eric Xing
Eric Poe Xing (Chinese: 邢波) is an American computer scientist who has been serving as president of Mohamed bin Zayed University of Artificial Intelligence (MBZUAI) since January 2021. He is also a professor in the Carnegie Mellon University School of Computer Science where he founded the SAILING Lab in 2004, and is the co-founder of the AI companies Petuum and GenBio AI. Xing's research focuses on statistical machine learning, probabilistic graphical models, and systems for distributed machine learning. He was elected a Fellow of the Institute of Electrical and Electronics Engineers in 2019 for "contributions to machine learning algorithms and systems" and a Fellow of the Association for Computing Machinery in 2022 for "contributions to algorithms, architectures, and applications in machine learning." == Education == Xing earned a B.Sc. in physics from Tsinghua University in 1993, and an M.Sc. in computer science from Rutgers University in 1998. He earned a Ph.D. in molecular biology and biochemistry from Rutgers in 1999, supervised by molecular cancer researcher Chung S. Yang. His dissertation examined the inactivation of the Rb and p53 pathways in human esophageal squamous cell carcinoma. He earned a second Ph.D. in computer science from the University of California, Berkeley in 2004, supervised by Richard Karp, Michael I. Jordan, and Stuart J. Russell. His thesis applied probabilistic graphical models to motif identification and haplotype inference in genomic data. == Career == Xing joined Carnegie Mellon University (CMU) as a faculty member in 2004, where he created the Statistical Artificial Intelligence and Integrative Genomics (SAILING) Lab. He held visiting appointments from 2010 to 2011, serving as a visiting research professor at Facebook Inc. and as a visiting associate professor in the Department of Statistics at Stanford University. He served as co-Program Chair of the International Conference on Machine Learning (ICML) in 2014 and General Chair in 2019. Xing served as the founding director of CMU’s Center for Machine Learning and Health, established in 2015 as part of the Pittsburgh Health Data Alliance, a collaboration between CMU, the University of Pittsburgh, and the University of Pittsburgh Medical Center. In 2016, Xing co-founded Petuum Inc., a US-based startup. In 2017, Petuum raised $93 million in a round of venture funding from SoftBank. In 2018 Petuum was named a World Economic Forum Technology Pioneer. In 2019, Xing received the Carnegie Science Award for Startup Entrepreneurs in recognition of his leadership of Petuum. On 29 November 2020, Xing was appointed president of the Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), with the appointment taking effect in January 2021. In 2024, Xing co-founded GenBio AI where he is chief scientist. The US-based startup, which he co-founded with David Baker, Ziv Bar-Joseph, Emma Lundberg, Le Song and Fred Hu, aims to create AI-driven digital organisms (AIDO) for the purposes of modeling medical treatments. Xing has overseen the launch of the MBZUAI Institute of Foundation Models (IFM), which focuses on research and development of large-scale foundation models. In 2025–2026, IFM released the open-source reasoning model K2 Think, which was covered internationally as part of the UAE’s push to develop domestically controlled (“sovereign”) AI capabilities. IFM presented PAN as a “world model” research project and demonstrated related systems publicly. MBZUAI also collaborated with G42 and Cerebras Systems on the Jais language model, an open-source Arabic–English large language model released in 2023, according to Reuters. == Awards and honors == Xing is a recipient of the National Science Foundation (NSF) Career Award and the Alfred P. Sloan Research Fellowship. Xing is an elected Fellow of the following institutes and associations: Association for the Advancement of Artificial Intelligence (AAAI) 2016 Institute of Electrical and Electronics Engineers (IEEE) 2019 for "contributions to machine learning algorithms and systems" American Statistical Association (ASA) 2022 Association for Computing Machinery (ACM) 2022 for "contributions to algorithms, architectures, and applications in machine learning" Institute of Mathematical Statistics (IMS) 2023 International Society for Computational Biology (ISCB) 2026 == Selected publications == Eric P. Xing; Michael I. Jordan; Stuart J. Russell; Andrew Y. Ng (2003). "Distance Metric Learning with Application to Clustering with Side-Information" (PDF). Advances in Neural Information Processing Systems 15. Advances in Neural Information Processing Systems. Wikidata Q77691192. Edoardo M. Airoldi; David M. Blei; Stephen E Fienberg; Eric P Xing (1 September 2008). "Mixed Membership Stochastic Blockmodels". Journal of Machine Learning Research. 9: 1981–2014. ISSN 1533-7928. PMC 3119541. PMID 21701698. Wikidata Q35058357. Eric P. Xing; Michael I. Jordan; Richard M. Karp (28 June 2001), Feature selection for high-dimensional genomic microarray data, vol. 18, pp. 601–608, Wikidata Q138678867 Xing EP; Karp RM (1 January 2001). "CLIFF: clustering of high-dimensional microarray data via iterative feature filtering using normalized cuts". Bioinformatics. 17 Suppl 1: S306-15. doi:10.1093/BIOINFORMATICS/17.SUPPL_1.S306. ISSN 1367-4803. PMID 11473022. Wikidata Q30657299.