AI Detector Yang Dipakai Dosen

AI Detector Yang Dipakai Dosen — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Micro stuttering

Micro stuttering is a visual artifact in real-time computer graphics in which the time intervals between consecutively displayed frames are uneven, even though the average frame rate reported by benchmarking software appears adequate. Tools such as 3DMark typically compute frame rates over intervals of one second or more, which can conceal momentary drops in the instantaneous frame rate that the viewer perceives as hitching or jerking of on-screen motion. At low frame rates the effect is visible as a stutter in moving images, degrading the experience in interactive applications such as video games. In severe cases a lower but more consistent frame rate can appear smoother than a higher but more erratic one. The term gained prominence in the late 2000s in discussions of multi-GPU rendering (see History), but micro stuttering also affects single-GPU systems. Common causes on modern hardware include real-time shader compilation, asset streaming from storage, VRAM exhaustion, and driver bugs. == Causes == === Shader compilation === A common cause of micro stuttering on modern PCs is real-time shader compilation. Shaders are small programs that instruct the GPU on how to render visual effects such as lighting, shadows, and reflections. On consoles, developers can pre-compile all shaders for the known, fixed hardware. On PCs, the variety of GPU architectures means shaders must often be compiled at run time, either when the game launches or during gameplay itself. When the rendering engine encounters a shader that has not yet been compiled, the CPU must finish the compilation before the GPU can draw the affected object. This causes a spike in frame time that the player perceives as a hitch. The problem has been particularly associated with games built on Unreal Engine 4 running under DirectX 12, because DX12 shifts more shader management responsibility to the application. Several techniques exist to reduce shader compilation stutter. Pipeline State Object (PSO) pre-caching records the shader permutations used at runtime so that they can be compiled in advance on subsequent launches. Asynchronous shader compilation moves the work to background CPU threads to avoid blocking the main rendering thread. Platform-level services such as Steam's shader pre-caching distribute previously compiled shaders to users with matching GPU hardware. The Steam Deck, which contains a single fixed GPU, benefits from pre-compiled shader caches because all units share the same hardware configuration. === Other causes === Micro stuttering on single-GPU systems can have several additional causes. CPU bottlenecks or scheduling interruptions from background tasks can prevent the processor from preparing frames at regular intervals. Asset streaming during gameplay (loading textures, geometry, or audio from storage) can produce hitches sometimes called traversal stutter; the use of solid-state drives and technologies such as DirectStorage has reduced but not eliminated this. VRAM exhaustion forces data to be swapped between video memory and system memory over the PCI Express bus, which is slower. Graphics driver bugs can also introduce stutter; Nvidia released hotfix driver 551.46 in February 2024 to correct intermittent micro stuttering when V-Sync was enabled. == Measurement == Micro stuttering drew attention to the limitations of average frame rate as a performance metric. In 2013, Scott Wasson at The Tech Report published a series of articles advocating frame time analysis, in which the delivery time of every individual frame is recorded and plotted rather than collapsed into a single frames-per-second figure. This approach was adopted by other hardware review publications in the following years. GPU reviews now routinely report 1% low and 0.1% low frame rates alongside the average. The 1% low is the average frame rate of the slowest 1% of frames in a sample; it serves as an indicator of worst-case smoothness. A large gap between the average and the 1% low suggests poor frame pacing. Tools for capturing per-frame timing data include FRAPS, PresentMon, OCAT, CapFrameX, and MSI Afterburner with RivaTuner Statistics Server. == Mitigation == === Frame pacing === Frame pacing is a software technique that regulates the timing of frame delivery to produce even intervals between displayed frames. Game engines, GPU drivers, and platform libraries all implement frame pacing strategies to varying degrees. On mobile platforms, Google provides the Android Frame Pacing library (Swappy) as part of the Android Game Development Kit. In December 2025, the Khronos Group published the VK_EXT_present_timing Vulkan extension, giving developers explicit control over presentation timing in a cross-platform graphics API for the first time. === Variable refresh rate === Variable refresh rate (VRR) display technologies allow a monitor's refresh rate to change to match the GPU's frame output. Implementations include Nvidia G-Sync (2013), AMD FreeSync (2015), and the VESA Adaptive-Sync standard built into DisplayPort 1.2a and later. VRR eliminates the screen tearing that results from a mismatch between frame rate and refresh rate, and avoids the frame-holding behaviour of V-Sync that can itself cause stutter. It is effective at smoothing moderate frame rate fluctuations but cannot compensate for large sudden spikes in frame time such as those caused by shader compilation or heavy asset streaming. VRR support has become standard in gaming monitors, televisions (via HDMI 2.1), and the Xbox Series X/S and PlayStation 5 consoles. === Frame generation === Beginning with DLSS 3 on the GeForce RTX 40 series in 2022, Nvidia introduced AI-based frame generation, which uses dedicated optical flow hardware and a neural network to create new frames between traditionally rendered ones. AMD followed with FSR 3 in 2023, using an algorithmic approach, and the AI-based FSR 4 for the Radeon RX 9000 series in 2025. DLSS 4, released in January 2025 for the GeForce RTX 50 series, can generate up to three frames per rendered frame using a technique called Multi Frame Generation. Frame generation increases the displayed frame rate but introduces its own frame pacing concerns. If the underlying rendered frames are unevenly timed, the interpolated frames can make the unevenness more apparent rather than less. DLSS 4 addresses this with hardware-level flip metering on the GPU's display engine, which controls the timing of frame presentation more precisely than the CPU-based pacing used in DLSS 3. Both vendors pair frame generation with latency-reduction features (Nvidia Reflex and AMD Anti-Lag+) to offset the additional input latency that results from inserting synthetic frames into the pipeline. === Frame rate limiters === Capping the frame rate below the display's maximum refresh rate, using tools such as RivaTuner Statistics Server, in-game limiters, or driver-level settings, is a common way to improve frame pacing. Preventing the GPU from running ahead of the display reduces variability in frame delivery times and can produce a smoother result than an uncapped but more irregular frame rate. == History == === Multi-GPU configurations === Micro stuttering was first widely documented in the late 2000s as a side effect of multi-GPU configurations using Alternate Frame Rendering (AFR), in which consecutive frames are assigned to alternating GPUs. Because each GPU may take a different amount of time to complete its assigned frame — due to varying scene complexity, driver scheduling, or inter-GPU communication overhead — the resulting frame delivery is irregular even when the average frame rate is high. Both Nvidia SLI and AMD CrossFireX were affected, with dual-GPU setups exhibiting the worst frame pacing irregularities. In 2012 benchmarks using Battlefield 3, dual Radeon HD 7970 cards in CrossFire showed 85% variation in frame delivery times compared with 7% for a single card, while dual GeForce GTX 680 cards in SLI showed only 7% variation compared with 5% for a single card. Multi-GPU micro stuttering became a significant factor in the eventual decline and discontinuation of consumer multi-GPU gaming. Nvidia restricted SLI to a handful of enthusiast-class cards from the GeForce 10 series onward, then replaced it with NVLink on the GeForce RTX 20 series, which saw limited gaming adoption. AMD ceased active CrossFire development around 2017. By the mid-2020s, neither vendor's current consumer GPUs support multi-GPU rendering for games. Other factors that contributed to the decline include DirectX 12 placing multi-GPU support in the hands of game developers rather than driver authors, the incompatibility of temporal anti-aliasing and other temporal rendering techniques with AFR, and the increasing size, power draw, and cost of individual GPUs. The third-party utility RadeonPro could reduce CrossFire micro stuttering through dynamic V-Sync and frame pacing adjustments, and AMD later introduced a driver-level frame paci
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Is an AI Writing Assistant Worth It in 2026?

In search of the best AI writing assistant? An AI writing assistant is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI writing assistant slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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How to Choose an AI Voice Assistant

Curious about the best AI voice assistant? An AI voice assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI voice assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Krzysztof Wołk

Krzysztof Wołk (born 16 August 1986) is a Polish IT researcher who specializes in artificial intelligence, machine learning, mobile applications, linguistic engineering, multimedia, NLP and graphic applications. His research works have been cited in more than 70 international research journals, books and research papers. He is member of scientific committee at the Health and Social Care Information Systems and Technologies (HCist), an international conference which brings in new ideas, new technologies, academic scientists, healthcare IT professionals, managers and solution providers from all over the world. His research in statistical machine learning has been recognized as one of the most cited researches in the world. He is the member of Scientific Committee-Reviewers at Research Conference in Technical Disciplines (RCITD), based in Slovakia, which brings together the academic scientists and researchers from all around the world. == Biography == He obtained the doctorate degree in 2016 from the Polish-Japanese Academy of Information and Technology in Warsaw, Poland. He is currently working as researcher and assistant professor at the Polish-Japanese Computer Science Academy (PJATK) in Warsaw, Poland. == Achievements == He has published three books: Biblia Windows Server 2012, Administrator's Guide, Mac OS X Server 10.8, and MAC OS X Server 10.6 and 10.7 Practical Guide has been cited by many researchers in the scholarly books, research journals and articles. His research work on the Polish-English statistical machine translation has been featured in the book New Research in Multimedia and Internet System. Similarly, his works regarding the machine translation system have been featured in the books New Perspective in Information System and Technologies Volume 1, Multimedia and Network Information System, and Recent Advances in Information Systems and Technologies, Volume 1.
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Spell checker

In software, a spell checker (or spelling checker or spell check) is a software feature that checks for misspellings in a text. Spell-checking features are often embedded in software or services, such as a word processor, email client, electronic dictionary, or search engine. == Design == A basic spell checker carries out the following processes: It scans the text and extracts the words contained in it. It then compares each word with a known list of correctly spelled words (i.e. a dictionary). This might contain just a list of words, or it might also contain additional information, such as hyphenation points or lexical and grammatical attributes. An additional step is a language-dependent algorithm for handling morphology. Even for a lightly inflected language like English, the spell checker will need to consider different forms of the same word, such as plurals, verbal forms, contractions, and possessives. For many other languages, such as those featuring agglutination and more complex declension and conjugation, this part of the process is more complicated. It is unclear whether morphological analysis—allowing for many forms of a word depending on its grammatical role—provides a significant benefit for English, though its benefits for highly synthetic languages such as German, Hungarian, or Turkish are clear. As an adjunct to these components, the program's user interface allows users to approve or reject replacements and modify the program's operation. Spell checkers can use approximate string matching algorithms such as Levenshtein distance to find correct spellings of misspelled words. An alternative type of spell checker uses solely statistical information, such as n-grams, to recognize errors instead of correctly-spelled words. This approach usually requires a lot of effort to obtain sufficient statistical information. Key advantages include needing less runtime storage and the ability to correct errors in words that are not included in a dictionary. In some cases, spell checkers use a fixed list of misspellings and suggestions for those misspellings; this less flexible approach is often used in paper-based correction methods, such as the see also entries of encyclopedias. Clustering algorithms have also been used for spell checking combined with phonetic information. == History == === Pre-PC === In 1961, Les Earnest, who headed the research on this budding technology, saw it necessary to include the first spell checker that accessed a list of 10,000 acceptable words. Ralph Gorin, a graduate student under Earnest at the time, created the first true spelling checker program written as an applications program (rather than research) for general English text: SPELL for the DEC PDP-10 at Stanford University's Artificial Intelligence Laboratory, in February 1971. Gorin wrote SPELL in assembly language, for faster action; he made the first spelling corrector by searching the word list for plausible correct spellings that differ by a single letter or adjacent letter transpositions and presenting them to the user. Gorin made SPELL publicly accessible, as was done with most SAIL (Stanford Artificial Intelligence Laboratory) programs, and it soon spread around the world via the new ARPAnet, about ten years before personal computers came into general use. SPELL, its algorithms and data structures inspired the Unix ispell program. The first spell checkers were widely available on mainframe computers in the late 1970s. A group of six linguists from Georgetown University developed the first spell-check system for the IBM corporation. Henry Kučera invented one for the VAX machines of Digital Equipment Corp in 1981. === Unix === The International Ispell program commonly used in Unix is based on R. E. Gorin's SPELL. It was converted to C by Pace Willisson at MIT. The GNU project has its spell checker GNU Aspell. Aspell's main improvement is that it can more accurately suggest correct alternatives for misspelled English words. Due to the inability of traditional spell checkers to check words in complex inflected languages, Hungarian László Németh developed Hunspell, a spell checker that supports agglutinative languages and complex compound words. Hunspell also uses Unicode in its dictionaries. Hunspell replaced the previous MySpell in OpenOffice.org in version 2.0.2. Enchant is another general spell checker, derived from AbiWord. Its goal is to combine programs supporting different languages such as Aspell, Hunspell, Nuspell, Hspell (Hebrew), Voikko (Finnish), Zemberek (Turkish) and AppleSpell under one interface. === PCs === The first spell checkers for personal computers appeared in 1980, such as "WordCheck" for Commodore systems which was released in late 1980 in time for advertisements to go to print in January 1981. Developers such as Maria Mariani and Random House rushed OEM packages or end-user products into the rapidly expanding software market. On the pre-Windows PCs, these spell checkers were standalone programs, many of which could be run in terminate-and-stay-resident mode from within word-processing packages on PCs with sufficient memory. However, the market for standalone packages was short-lived, as by the mid-1980s developers of popular word-processing packages like WordStar and WordPerfect had incorporated spell checkers in their packages, mostly licensed from the above companies, who quickly expanded support from just English to many European and eventually even Asian languages. However, this required increasing sophistication in the morphology routines of the software, particularly with regard to heavily-agglutinative languages like Hungarian and Finnish. Although the size of the word-processing market in a country like Iceland might not have justified the investment of implementing a spell checker, companies like WordPerfect nonetheless strove to localize their software for as many national markets as possible as part of their global marketing strategy. When Apple developed "a system-wide spelling checker" for Mac OS X so that "the operating system took over spelling fixes," it was a first: one "didn't have to maintain a separate spelling checker for each" program. Mac OS X's spellcheck coverage includes virtually all bundled and third party applications. Visual Tools' VT Speller, introduced in 1994, was "designed for developers of applications that support Windows." It came with a dictionary but had the ability to build and incorporate use of secondary dictionaries. === Browsers === Web browsers such as Firefox and Google Chrome offer spell checking support, using Hunspell. Prior to using Hunspell, Firefox and Chrome used MySpell and GNU Aspell, respectively. === Specialties === Some spell checkers have separate support for medical dictionaries to help prevent medical errors. == Functionality == The first spell checkers were "verifiers" instead of "correctors." They offered no suggestions for incorrectly spelled words. This was helpful for typos but it was not so helpful for logical or phonetic errors. The challenge the developers faced was the difficulty in offering useful suggestions for misspelled words. This requires reducing words to a skeletal form and applying pattern-matching algorithms. It might seem logical that where spell-checking dictionaries are concerned, "the bigger, the better," so that correct words are not marked as incorrect. In practice, however, an optimal size for English appears to be around 90,000 entries. If there are more than this, incorrectly spelled words may be skipped because they are mistaken for others. For example, a linguist might determine on the basis of corpus linguistics that the word baht is more frequently a misspelling of bath or bat than a reference to the Thai currency. Hence, it would typically be more useful if a few people who write about Thai currency were slightly inconvenienced than if the spelling errors of the many more people who discuss baths were overlooked. The first MS-DOS spell checkers were mostly used in proofing mode from within word processing packages. After preparing a document, a user scanned the text looking for misspellings. Later, however, batch processing was offered in such packages as Oracle's short-lived CoAuthor and allowed a user to view the results after a document was processed and correct only the words that were known to be wrong. When memory and processing power became abundant, spell checking was performed in the background in an interactive way, such as has been the case with the Sector Software produced Spellbound program released in 1987 and Microsoft Word since Word 95. Spell checkers became increasingly sophisticated; now capable of recognizing grammatical errors. However, even at their best, they rarely catch all the errors in a text (such as homophone errors) and will flag neologisms and foreign words as misspellings. Nonetheless, spell checkers can be considered as a type of foreign language writing aid that non-native language lea
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Is an AI Code-review Tool Worth It in 2026?

Looking for the best AI code-review tool? An AI code-review tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI code-review tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Best AI Coding Assistants in 2026

Curious about the best AI coding assistant? An AI coding assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI coding assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Tf–idf

In information retrieval, tf–idf (term frequency–inverse document frequency, TFIDF, TFIDF, TF–IDF, or Tf–idf) is a measure of importance of a word to a document in a collection or corpus, adjusted for the fact that some words appear more frequently in general. Like the bag-of-words model, it models a document as a multiset of words, without word order. It is a refinement over the simple bag-of-words model, by allowing the weight of words to depend on the rest of the corpus. It was often used as a weighting factor in searches of information retrieval, text mining, and user modeling. A survey conducted in 2015 showed that 83% of text-based recommender systems in digital libraries used tf–idf. Variations of the tf–idf weighting scheme were often used by search engines as a central tool in scoring and ranking a document's relevance given a user query. One of the simplest ranking functions is computed by summing the tf–idf for each query term; many more sophisticated ranking functions are variants of this simple model. == Motivations == Karen Spärck Jones (1972) conceived a statistical interpretation of term-specificity called Inverse Document Frequency (idf), which became a cornerstone of term weighting: The specificity of a term can be quantified as an inverse function of the number of documents in which it occurs.For example, the df (document frequency) and idf for some words in Shakespeare's 37 plays might be represented as follows: We see that "Romeo", "Falstaff", and "salad" appears in very few plays, so seeing these words, one could get a good idea as to which play it might be. In contrast, "good" and "sweet" appears in every play and are completely uninformative as to which play it is. == Definition == The tf–idf is the product of two statistics, term frequency and inverse document frequency. There are various ways for determining the exact values of both statistics. A formula that aims to define the importance of a keyword or phrase within a document or a web page. === Term frequency === Term frequency, tf(t,d), is the relative frequency of term t within document d, t f ( t , d ) = f t , d ∑ t ′ ∈ d f t ′ , d {\displaystyle \mathrm {tf} (t,d)={\frac {f_{t,d}}{\sum _{t'\in d}{f_{t',d}}}}} , where ft,d is the raw count of a term in a document, i.e., the number of times that term t occurs in document d. Note the denominator is simply the total number of terms in document d (counting each occurrence of the same term separately). There are various other ways to define term frequency: the raw count itself: tf(t,d) = ft,d Boolean "frequencies": tf(t,d) = 1 if t occurs in d and 0 otherwise; logarithmically scaled frequency: tf(t,d) = log (1 + ft,d); augmented frequency, to prevent a bias towards longer documents, e.g. raw frequency divided by the raw frequency of the most frequently occurring term in the document: t f ( t , d ) = 0.5 + 0.5 ⋅ f t , d max { f t ′ , d : t ′ ∈ d } {\displaystyle \mathrm {tf} (t,d)=0.5+0.5\cdot {\frac {f_{t,d}}{\max\{f_{t',d}:t'\in d\}}}} === Inverse document frequency === The inverse document frequency is a measure of how much information the word provides, i.e., how common or rare it is across all documents. It is the logarithmically scaled inverse fraction of the documents that contain the word (obtained by dividing the total number of documents by the number of documents containing the term, and then taking the logarithm of that quotient): i d f ( t , D ) = log ⁡ N n t {\displaystyle \mathrm {idf} (t,D)=\log {\frac {N}{n_{t}}}} with D {\displaystyle D} : is the set of all documents in the corpus N = | D | {\displaystyle N={|D|}} : total number of documents in the corpus n t = | { d ∈ D : t ∈ d } | {\displaystyle n_{t}=|\{d\in D:t\in d\}|} : number of documents where the term t {\displaystyle t} appears (i.e., t f ( t , d ) ≠ 0 {\displaystyle \mathrm {tf} (t,d)\neq 0} ). If the term is not in the corpus, this will lead to a division-by-zero. It is therefore common to adjust the numerator to 1 + N {\displaystyle 1+N} and the denominator to 1 + | { d ∈ D : t ∈ d } | {\displaystyle 1+|\{d\in D:t\in d\}|} . === Term frequency–inverse document frequency === Then tf–idf is calculated as t f i d f ( t , d , D ) = t f ( t , d ) ⋅ i d f ( t , D ) {\displaystyle \mathrm {tfidf} (t,d,D)=\mathrm {tf} (t,d)\cdot \mathrm {idf} (t,D)} A high weight in tf–idf is reached by a high term frequency (in the given document) and a low document frequency of the term in the whole collection of documents; the weights hence tend to filter out common terms. Since the ratio inside the idf's log function is always greater than or equal to 1, the value of idf (and tf–idf) is greater than or equal to 0. As a term appears in more documents, the ratio inside the logarithm approaches 1, bringing the idf and tf–idf closer to 0. == Justification of idf == Idf was introduced as "term specificity" by Karen Spärck Jones in a 1972 paper. Although it has worked well as a heuristic, its theoretical foundations have been troublesome for at least three decades afterward, with many researchers trying to find information theoretic justifications for it. Spärck Jones's own explanation did not propose much theory, aside from a connection to Zipf's law. Attempts have been made to put idf on a probabilistic footing, by estimating the probability that a given document d contains a term t as the relative document frequency, P ( t | D ) = | { d ∈ D : t ∈ d } | N , {\displaystyle P(t|D)={\frac {|\{d\in D:t\in d\}|}{N}},} so that we can define idf as i d f = − log ⁡ P ( t | D ) = log ⁡ 1 P ( t | D ) = log ⁡ N | { d ∈ D : t ∈ d } | {\displaystyle {\begin{aligned}\mathrm {idf} &=-\log P(t|D)\\&=\log {\frac {1}{P(t|D)}}\\&=\log {\frac {N}{|\{d\in D:t\in d\}|}}\end{aligned}}} Namely, the inverse document frequency is the logarithm of "inverse" relative document frequency. This probabilistic interpretation in turn takes the same form as that of self-information. However, applying such information-theoretic notions to problems in information retrieval leads to problems when trying to define the appropriate event spaces for the required probability distributions: not only documents need to be taken into account, but also queries and terms. == Link with information theory == Both term frequency and inverse document frequency can be formulated in terms of information theory; it helps to understand why their product has a meaning in terms of joint informational content of a document. A characteristic assumption about the distribution p ( d , t ) {\displaystyle p(d,t)} is that: p ( d | t ) = 1 | { d ∈ D : t ∈ d } | {\displaystyle p(d|t)={\frac {1}{|\{d\in D:t\in d\}|}}} This assumption and its implications, according to Aizawa: "represent the heuristic that tf–idf employs." The conditional entropy of a "randomly chosen" document in the corpus D {\displaystyle D} , conditional to the fact it contains a specific term t {\displaystyle t} (and assuming that all documents have equal probability to be chosen) is: H ( D | T = t ) = − ∑ d p d | t log ⁡ p d | t = − log ⁡ 1 | { d ∈ D : t ∈ d } | = log ⁡ | { d ∈ D : t ∈ d } | | D | + log ⁡ | D | = − i d f ( t ) + log ⁡ | D | {\displaystyle H({\cal {D}}|{\cal {T}}=t)=-\sum _{d}p_{d|t}\log p_{d|t}=-\log {\frac {1}{|\{d\in D:t\in d\}|}}=\log {\frac {|\{d\in D:t\in d\}|}{|D|}}+\log |D|=-\mathrm {idf} (t)+\log |D|} In terms of notation, D {\displaystyle {\cal {D}}} and T {\displaystyle {\cal {T}}} are "random variables" corresponding to respectively draw a document or a term. The mutual information can be expressed as M ( T ; D ) = H ( D ) − H ( D | T ) = ∑ t p t ⋅ ( H ( D ) − H ( D | W = t ) ) = ∑ t p t ⋅ i d f ( t ) {\displaystyle M({\cal {T}};{\cal {D}})=H({\cal {D}})-H({\cal {D}}|{\cal {T}})=\sum _{t}p_{t}\cdot (H({\cal {D}})-H({\cal {D}}|W=t))=\sum _{t}p_{t}\cdot \mathrm {idf} (t)} The last step is to expand p t {\displaystyle p_{t}} , the unconditional probability to draw a term, with respect to the (random) choice of a document, to obtain: M ( T ; D ) = ∑ t , d p t | d ⋅ p d ⋅ i d f ( t ) = ∑ t , d t f ( t , d ) ⋅ 1 | D | ⋅ i d f ( t ) = 1 | D | ∑ t , d t f ( t , d ) ⋅ i d f ( t ) . {\displaystyle M({\cal {T}};{\cal {D}})=\sum _{t,d}p_{t|d}\cdot p_{d}\cdot \mathrm {idf} (t)=\sum _{t,d}\mathrm {tf} (t,d)\cdot {\frac {1}{|D|}}\cdot \mathrm {idf} (t)={\frac {1}{|D|}}\sum _{t,d}\mathrm {tf} (t,d)\cdot \mathrm {idf} (t).} This expression shows that summing the Tf–idf of all possible terms and documents recovers the mutual information between documents and term taking into account all the specificities of their joint distribution. Each Tf–idf hence carries the "bit of information" attached to a term x document pair. == Link with statistical theory == Tf–idf is closely related to the negative logarithmically transformed p-value from a one-tailed formulation of Fisher's exact test when the underlying corpus documents satisfy certain idealized assumptions. More recently, tf–idf variants were shown to arise as components in the test st
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Colors!

Colors! is a series of digital painting applications for handheld game consoles and mobile devices. Originally created as a homebrew application for Nintendo DS (as Colors!), which was since legitimately distributed on PlayStation Vita, iOS, and Android, the project eventually evolved into an officially licensed application for Nintendo 3DS (as Colors! 3D) and Nintendo Switch (as Colors Live). == History == === Colors! === Colors! was originally released in June 2007 as a simple homebrew painting application for the Nintendo DS. It was developed by Jens Andersson, a programmer and designer on sabbatical from the games industry who wanted to experiment with the potential of the new handheld platform. Shortly after, Rafał Piasek created an online gallery where users could upload paintings made with the program. Colors! quickly became one of the best-known homebrew applications on the Nintendo DS, and in September 2008, it was also released for the iPhone and iPod Touch. As of August 2010, it had been downloaded almost half a million times. It was voted the most popular homebrew application on the Nintendo DS by readers of the R4 for DS blog. Development of Colors! DS homebrew officially ended in December 2010 although the official gallery still accepted submissions from DS users until 2020 when Colors! Gallery was discontinued. === Colors! 3D === Colors! 3D is a successor to the application Colors! for the Nintendo 3DS. It was released as an officially licensed application for the Nintendo eShop in North America on April 5, 2012, and in the PAL region on April 19, 2012. It was later released in Japan on August 21, 2013, published by Arc System Works. Colors! 3D allows users to draw on five layers, each on their own stereoscopic 3D plane. Drawing is done on the bottom screen, while the top screen displays the painting in 3D. While drawing, players can use the various controls on the Nintendo 3DS to change layers, zoom and pan, and alter the pressure of their brush. Pressing the L button allows users to access a menu to change brush type, size, and opacity, modify the layers, use the camera to provide references, and more. When the user finishes their painting, they can export it to the SD card for viewing in the Nintendo 3DS Camera application. Users can also upload their finished creations to an online gallery, viewed on the 3DS or the official website. Gallery features include hashtags and the ability to follow artists and post comments. Each painting also features a replay feature that allows viewers to see how it was drawn. The application also features local multiplayer, allowing several people to work cooperatively on a painting. In April 2024, the developers of Colors! 3D collaborated with the Pretendo Network project to officially add support for the application, meaning Colors! 3D will continue to operate as normal when using Pretendo Network. ==== Reception ==== IGN gave the application a score of 9.0 and an Editor's Choice award, praising its simple interface and tutorials. Destructoid gave the app a 9.0, calling it "a simple and incredibly fun tool with an amazing community of artists proudly displaying their beautiful and funny 3D images." Nintendo Life gave the app a 9/10, stating, "Though lacking in any structured play, Colors! 3D’s robust free drawing system and unique ability to let anyone create their own three-dimensional artwork more than make up for this." === Colors Live === A Nintendo Switch successor called Colors Live (stylised as Colors L!ve) was released in 2020 after being funded via a Kickstarter campaign. This expanded upon the features of previous installments by adding new brushes, increasing the maximum number of layers to ten, and introducing blend modes. A new game mode called Colors Quest was also included. A pressure-sensitive pen called the Colors SonarPen was developed in collaboration with GreenBulb to facilitate drawing on the Nintendo Switch, and comes pre-bundled with physical copies of the game. ==== Colors Quest ==== This new mode acts as a story-driven adventure wherein players are given a daily drawing challenge with a specific theme and certain stipulations that must be fulfilled. Once the drawing is complete, players must anonymously score other players' submissions, these scores are then aggregated to produce a personal ranking that measures the improvement in the player's art skills over time.
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Quotient automaton

In computer science, in particular in formal language theory, a quotient automaton can be obtained from a given nondeterministic finite automaton by joining some of its states. The quotient recognizes a superset of the given automaton; in some cases, handled by the Myhill–Nerode theorem, both languages are equal. == Formal definition == A (nondeterministic) finite automaton is a quintuple A = ⟨Σ, S, s0, δ, Sf⟩, where: Σ is the input alphabet (a finite, non-empty set of symbols), S is a finite, non-empty set of states, s0 is the initial state, an element of S, δ is the state-transition relation: δ ⊆ S × Σ × S, and Sf is the set of final states, a (possibly empty) subset of S. A string a1...an ∈ Σ is recognized by A if there exist states s1, ..., sn ∈ S such that ⟨si-1,ai,si⟩ ∈ δ for i=1,...,n, and sn ∈ Sf. The set of all strings recognized by A is called the language recognized by A; it is denoted as L(A). For an equivalence relation ≈ on the set S of A’s states, the quotient automaton A/≈ = ⟨Σ, S/≈, [s0], δ/≈, Sf/≈⟩ is defined by the input alphabet Σ being the same as that of A, the state set S/≈ being the set of all equivalence classes of states from S, the start state [s0] being the equivalence class of A’s start state, the state-transition relation δ/≈ being defined by δ/≈([s],a,[t]) if δ(s,a,t) for some s ∈ [s] and t ∈ [t], and the set of final states Sf/≈ being the set of all equivalence classes of final states from Sf. The process of computing A/≈ is also called factoring A by ≈. == Example == For example, the automaton A shown in the first row of the table is formally defined by ΣA = {0,1}, SA = {a,b,c,d}, sA0 = a, δA = { ⟨a,1,b⟩, ⟨b,0,c⟩, ⟨c,0,d⟩ }, and SAf = { b,c,d }. It recognizes the finite set of strings { 1, 10, 100 }; this set can also be denoted by the regular expression "1+10+100". The relation (≈) = { ⟨a,a⟩, ⟨a,b⟩, ⟨b,a⟩, ⟨b,b⟩, ⟨c,c⟩, ⟨c,d⟩, ⟨d,c⟩, ⟨d,d⟩ }, more briefly denoted as a≈b,c≈d, is an equivalence relation on the set {a,b,c,d} of automaton A’s states. Building the quotient of A by that relation results in automaton C in the third table row; it is formally defined by ΣC = {0,1}, SC = {a,c}, sC0 = a, δC = { ⟨a,1,a⟩, ⟨a,0,c⟩, ⟨c,0,c⟩ }, and SCf = { a,c }. It recognizes the finite set of all strings composed of arbitrarily many 1s, followed by arbitrarily many 0s, i.e. { ε, 1, 10, 100, 1000, ..., 11, 110, 1100, 11000, ..., 111, ... }; this set can also be denoted by the regular expression "10". Informally, C can be thought of resulting from A by glueing state a onto state b, and glueing state c onto state d. The table shows some more quotient relations, such as B = A/a≈b, and D = C/a≈c. == Properties == For every automaton A and every equivalence relation ≈ on its states set, L(A/≈) is a superset of (or equal to) L(A). Given a finite automaton A over some alphabet Σ, an equivalence relation ≈ can be defined on Σ by x ≈ y if ∀ z ∈ Σ: xz ∈ L(A) ↔ yz ∈ L(A). By the Myhill–Nerode theorem, A/≈ is a deterministic automaton that recognizes the same language as A. As a consequence, the quotient of A by every refinement of ≈ also recognizes the same language as A.
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Emma Brunskill

Emma Patricia Brunskill is an American computer scientist. Her research combines machine learning with human–computer interaction by studying the effects of AI systems in human-centered applications including educational software and healthcare, and the theory of reinforcement learning in situations where mistakes impose high risks or costs. She is an associate professor of computer science at Stanford University, where she also holds a courtesy appointment in the Stanford Graduate School of Education and is an affiliate of the King Center on Global Development. == Education and career == Brunskill grew up in Seattle and Edmonds, Washington, and entered the University of Washington at age 15. She graduated magna cum laude in 2000, with a bachelor's degree in computer engineering and physics. A Rhodes Scholarship took her to Magdalen College, Oxford in England, where she received a master's degree in neuroscience in 2002. After a summer working in Rwanda, she became a graduate student of computer science at the Massachusetts Institute of Technology, where she completed her Ph.D. in 2009. Her doctoral dissertation, Compact parametric models for efficient sequential decision making in high-dimensional, uncertain domains, was supervised by Nicholas Roy. After working as an NSF Postdoctoral Research Fellow at the University of California, Berkeley, she joined Carnegie Mellon University (CMU) in 2011 as an assistant professor of computer science. She moved from CMU to Stanford University in 2017. == Recognition == Brunskill was a 2014 recipient of the National Science Foundation CAREER Award and a 2015 recipient of the Office of Naval Research Young Investigator Award. She was one of two alumni of the University of Washington's Paul G. Allen School of Computer Science and Engineering to be honored in 2020 by the school's Alumni Impact Awards. She was elected as a Fellow of the Association for the Advancement of Artificial Intelligence in 2025, "for significant contributions to the field of reinforcement learning, and applications for societal benefit, in particular AI for education".
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The Best Free AI Code Generator for Beginners

In search of the best AI code generator? An AI code generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI code generator slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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Gooch shading

Gooch shading is a non-photorealistic rendering technique for shading objects. It is also known as "cool to warm" shading, and is widely used in technical illustration. == History == Gooch shading was developed by Amy Gooch et al. at the University of Utah School of Computing and first presented at the 1998 SIGGRAPH conference. It has since been implemented in shader libraries, software, and games released by Autodesk, Nvidia, and Valve. == Process == Gooch shading defines an additional two colors in conjunction with the original model color: a warm color (such as yellow) and a cool color (such as blue). The warm color indicates surfaces that are facing toward the light source while the cool color indicates surfaces facing away. This allows shading to occur only in mid-tones so that edge lines and highlights remain visually prominent. The Gooch shader is typically implemented in two passes: all objects in the scene are first drawn with the "cool to warm" shading, and in the second pass the object's edges are rendered in black.
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Top 10 AI Chatbots Compared (2026)

Shopping for the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI chatbot slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Mealy machine

In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore machine, whose output values are determined solely by its current state. A Mealy machine is a deterministic finite-state transducer: for each state and input, at most one transition is possible. == History == The Mealy machine is named after George H. Mealy, who presented the concept in a 1955 paper, "A Method for Synthesizing Sequential Circuits". == Formal definition == A Mealy machine is a 6-tuple ( S , S 0 , Σ , Λ , T , G ) {\displaystyle (S,S_{0},\Sigma ,\Lambda ,T,G)} consisting of the following: a finite set of states S {\displaystyle S} a start state (also called initial state) S 0 {\displaystyle S_{0}} which is an element of S {\displaystyle S} a finite set called the input alphabet Σ {\displaystyle \Sigma } a finite set called the output alphabet Λ {\displaystyle \Lambda } a transition function T : S × Σ → S {\displaystyle T:S\times \Sigma \rightarrow S} mapping pairs of a state and an input symbol to the corresponding next state. an output function G : S × Σ → Λ {\displaystyle G:S\times \Sigma \rightarrow \Lambda } mapping pairs of a state and an input symbol to the corresponding output symbol. In some formulations, the transition and output functions are coalesced into a single function T : S × Σ → S × Λ {\displaystyle T:S\times \Sigma \rightarrow S\times \Lambda } . "Evolution across time" is realized in this abstraction by having the state machine consult the time-changing input symbol at discrete "timer ticks" t 0 , t 1 , t 2 , . . . {\displaystyle t_{0},t_{1},t_{2},...} and react according to its internal configuration at those idealized instants, or else having the state machine wait for a next input symbol (as on a FIFO) and react whenever it arrives. == Comparison of Mealy machines and Moore machines == Mealy machines tend to have fewer states: Different outputs on arcs (n2) rather than states (n). When implemented as electronic circuits (rather than as mathematical abstractions or code): Moore machines are safer to use than Mealy machines: Outputs change at the clock edge (always one cycle later). In Mealy machines, input change can cause output change as soon as logic is done — a big problem when two machines are interconnected – asynchronous feedback may occur if one isn't careful. Mealy machines react faster to inputs: React in the same cycle—they don't need to wait for the clock. In Moore machines, more logic may be necessary to decode state into outputs—more gate delays after clock edge. == Diagram == The state diagram for a Mealy machine associates an output value with each transition edge, in contrast to the state diagram for a Moore machine, which associates an output value with each state. When the input and output alphabet are both Σ, one can also associate to a Mealy automata a Helix directed graph (S × Σ, (x, i) → (T(x, i), G(x, i))). This graph has as vertices the couples of state and letters, each node is of out-degree one, and the successor of (x, i) is the next state of the automata and the letter that the automata output when it is instate x and it reads letter i. This graph is a union of disjoint cycles if the automaton is bireversible. == Examples == === Simple === A simple Mealy machine has one input and one output. Each transition edge is labeled with the value of the input (shown in red) and the value of the output (shown in blue). The machine starts in state Si. (In this example, the output is the exclusive-or of the two most-recent input values; thus, the machine implements an edge detector, outputting a 1 every time the input flips and a 0 otherwise.) === Complex === More complex Mealy machines can have multiple inputs as well as multiple outputs. == Applications == Mealy machines provide a rudimentary mathematical model for cipher machines. Considering the input and output alphabet the Latin alphabet, for example, then a Mealy machine can be designed that given a string of letters (a sequence of inputs) can process it into a ciphered string (a sequence of outputs). However, although a Mealy model could be used to describe the Enigma, the state diagram would be too complex to provide feasible means of designing complex ciphering machines. Moore/Mealy machines are DFAs that have also output at any tick of the clock. Modern CPUs, computers, cell phones, digital clocks and basic electronic devices/machines have some kind of finite state machine to control it. Simple software systems, particularly ones that can be represented using regular expressions, can be modeled as finite state machines. There are many such simple systems, such as vending machines or basic electronics. By finding the intersection of two finite state machines, one can design in a very simple manner concurrent systems that exchange messages for instance. For example, a traffic light is a system that consists of multiple subsystems, such as the different traffic lights, that work concurrently.
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