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Path tracing

Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects and participating media to generate realistic (physically plausible) images. It is based on earlier, more limited, ray tracing algorithms. Path tracing is used to create photorealistic images for artistic purposes, and for applications such as architectural rendering and product design. It is also used to render frames for animated films, and visual effects for film and television. Because it can be very accurate and unbiased, it is commonly used to generate reference images when testing the quality of other rendering algorithms. The technique uses the Monte Carlo method to compute estimates of global illumination and simulate the ways different materials reflect (or scatter), transmit, absorb, and emit light. It can incorporate simple modeling of the effects of aperture and lens (depth of field, and bokeh) and shutter speed (motion blur), or more realistic simulation of the optical components in a camera. The algorithm works by describing illumination in a scene using the rendering equation, or light transport equation, and finding an approximate solution using Monte Carlo integration. An inefficient (but accurate) version of the algorithm can be very simple, and involves tracing a ray from the camera, allowing this ray to bounce in random directions as it hits different objects in the scene, and computing the amount of light transmitted along the path to the camera whenever the path encounters a light source. This process is repeated many times for each pixel (each repetition, with generated path and transmitted light, is called a sample), and the results are averaged. One main difference between this algorithm and standard ray tracing is that a single unbranching path is traced each time, while "Whitted-style" or "Cook-style" ray tracing recursively samples branching paths (e.g. when light is both reflected and refracted by a glass object). More practical versions incorporate improvements such as quasi-Monte Carlo methods (techniques that distribute samples more evenly), importance sampling (take more samples of paths that are likely to transport more light), and next event estimation (allow a very limited form of branching, and sample additional paths that connect to the lights more directly). Because path tracing uses random samples there is noise in the final image, which decreases as more samples are taken. Images commonly require many thousands of samples per pixel (spp) to reduce noise to an acceptable level, and denoising techniques (e.g. based on neural networks) are often used. Denoising is usually necessary when path tracing is used for real-time rendering in video games, because relatively few samples can be taken. Many alternative algorithms for path tracing have been developed, although they do not always outperform more straightforward implementations. These include bidirectional path tracing (which traces paths forwards from the light source as well as backwards from the camera), Metropolis light transport, and ways of combining path tracing with photon mapping. Video games often use biased versions of path tracing to improve performance (e.g. limiting the number of bounces in each path). A family of techniques called ReSTIR has been developed that can help real-time path tracing by sharing data between nearby pixels and consecutive frames. == History == Like all ray tracing methods, path tracing is based on ray casting, which Arthur Appel used for computer graphics rendering in the late 1960s. In 1980, John Turner Whitted published a recursive ray tracing algorithm that allows rendering images of scenes containing mirrored surfaces and refractive transparent objects. In 1984, Cook et al. described a form of ray tracing called distributed ray tracing, which uses Monte Carlo integration to render effects such as depth of field, motion blur, reflection from rough surfaces, and area lights. The same year, the radiosity method (not a ray tracing method) was published, which was the first physically based method for rendering diffuse global illumination. In 1986, Jim Kajiya published a paper exploring how to use distributed ray tracing to render physically-based global illumination, and this paper also introduced and named the method called "path tracing". Path tracing and other distributed ray tracing techniques were further refined in the late 1980s and early 1990s by researchers such as James Arvo and Peter Shirley, and by Greg Ward in the open source Radiance software. Despite being theoretically able to render any lighting, the original form of path tracing can sometimes be very inefficient (or noisy) for rendering light that is reflected or refracted before illuminating a visible surface, including diffuse global illumination where light enters an area through narrow gaps, because it traces paths only from the camera. To address this, variations of path tracing that trace paths from both the camera and from light sources, called bidirectional path tracing, were published in 1993 by Eric Lafortune and Yves Willems, and in 1997 by Eric Veach and Leonidas Guibas. In 1997 Veach and Guibas also published an alternative method called Metropolis light transport, which combines bidirectional path tracing with the Metropolis method. Veach's lengthy Ph.D. dissertation described both techniques, along with the theoretical background of path tracing; later, the book Physically Based Rendering (which won an Academy Award for Technical Achievement in 2014) helped to make information about path tracing more widely available. Path tracing requires tracing a large number of paths of light in order to produce an image with a visually acceptable amount of noise. This made path tracing very slow on computers available in the 1980s and 1990s, and noise remained a problem when trying to reproduce the style of earlier computer graphics animated films. Most animated films produced until around 2010, by studios such as Pixar, used rasterization-based rendering, with ray tracing used selectively for reflections (and later for precomputed or cached global illumination). However the speed of computers rapidly increased during the 1990s. Blue Sky Studios pioneered using Monte Carlo ray tracing for global illumination in animation, including in the 1998 short film "Bunny", but they did not disclose the precise techniques used. Path tracing gradually become more practical for film production in the early 2000s. The Arnold renderer, developed by Marcos Fajardo, was used by Sony Pictures Imageworks to produce the feature-length film Monster House, released in 2006. Pixar rewrote their RenderMan software to use path tracing, and released their first feature-length path-traced film Finding Dory in 2016. Although path tracing still had a large computational cost, animation studios discovered that less human labor was required when using it, for example because global illumination no longer needed to be faked by manually placing lights. The amount of noise present in path traced images still caused difficulties, particularly when rendering motion blur (which was used extensively by earlier animated films) but denoising techniques were developed to address this. New techniques were also needed for rendering hair and fur, and to handle the extremely large scenes sometimes required by films. Renderers such as Arnold, and Disney's Hyperion, originally only used CPUs for rendering, but as GPUs became more capable (and APIs such as CUDA, OpenCL, and OptiX were released) researchers and developers began adapting algorithms and implementations to use GPUs. GPUs can dramatically reduce rendering time: for example using a high-end GPU to accelerate portions of the rendering code can make it over 30 times faster than using only a high-end CPU. == Description == Kajiya's 1986 paper defined a recursive integral equation called the rendering equation, which describes a simplified form of light transport. Using Monte Carlo integration for the integral on the right side of the equation leads fairly directly to the path tracing algorithm: I ( x , x ′ ) = g ( x , x ′ ) [ ϵ ( x , x ′ ) + ∫ S ρ ( x , x ′ , x ″ ) I ( x ′ , x ″ ) d x ″ ] {\displaystyle I(x,x')=g(x,x')\left[\epsilon (x,x')+\int _{S}\rho (x,x',x'')I(x',x'')dx''\right]} This expresses I(x,x'), the light arriving at point x from point x', as the product of a geometry term, g(x,x'), which is 0 if there is something blocking the light between the two points and 1 otherwise, and the amount of light leaving point x' and traveling towards x. The light leaving point x' is the sum of the light emitted by the surface at x', and the integral of the light arriving at x' from all other points in the scene (the integration domain S) and being reflected towards x. The factor ρ(x,x',x''), which calculates how much light is reflected, must take into account the angles at which the light is arriving and leaving, and
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Eurotra

Eurotra was a machine translation project established and funded by the European Commission from 1978 until 1992. == History == In 1976, the European Commission started using the commercially developed machine translation system SYSTRAN with a plan to make it work for further languages than originally developed for (Russian-English and English-French), which however turned out to be difficult. This and the potential in existing systems within European research center, led to the decision in 1978 to start the project Eurotra, first through a preparatory Eurotra Coordination Group. Four years later, the European Commission and coordination group gained the approval of the European Parliament. The goal of the project as to create machine translation system for the official languages of the European Community, which at the time were Danish, Dutch, German, English, French, Italian, later including Greek, Spanish and Portuguese. However, as time passed, expectations became tempered; "Fully Automatic High Quality Translation" was not a reasonably attainable goal. The true character of Eurotra was eventually acknowledged to be in fact pre-competitive research rather than prototype development. The project was motivated by one of the founding principles of the EU: that all citizens had the right to read any and all proceedings of the Commission in their own language. As more countries joined, this produced a combinatorial explosion in the number of language pairs involved, and the need to translate every paper, speech and even set of meeting minutes produced by the EU into the other eight languages meant that translation rapidly became the overwhelming component in the administrative budget. To solve this problem Eurotra was devised. The project was unusual in that rather than consisting of a single research team, it had member groups distributed around the member countries, organised along language rather than national lines (for example, groups in Leuven and Utrecht worked closely together), and the secretariat was based at the European Commission in Luxembourg. The actual design of the project was unusual as MT projects go. Older systems, such as SYSTRAN, were heavily dictionary-based, with minor support for rearranging word order. More recent systems have often worked on a probabilistic approach, based on parallel corpora. Eurotra addressed the constituent structure of the text to be translated, going through first a syntactic parse followed by a second parse to produce a dependency structure followed by a final parse with a third grammar to produce what was referred to internally as Intermediate Representation (IR). Since all three modules were implemented as Prolog programs, it would then in principle be possible to put this structure backwards through the corresponding modules for another language to produce a translated text in any of the other languages. However, in practice this was not in fact how language pairs were implemented. The first "live" translation occupied a 4Mb Microvax running Ultrix and C-Prolog for a complete weekend some time in early 1987. The sentence, translated from English into Danish, was "Japan makes computers". The main problem faced by the system was the generation of so-called "Parse Forests" - often a large number of different grammar rules could be applied to any particular phrase, producing hundreds, even thousands of (often identical) parse trees. This used up huge quantities of computer store, slowing the whole process down unnecessarily. While Eurotra never delivered a "working" MT system, the project made a far-reaching long-term impact on the nascent language industries in European member states, in particular among the southern countries of Greece, Italy, Spain, and Portugal. There is at least one commercial MT system (developed by an academic/commercial consortium in Denmark) derived from Eurotra technology.
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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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Moore machine

In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in contrast to a Mealy machine, whose output values are determined both by its current state and by the values of its inputs. Like other finite state machines, in Moore machines, the input typically influences the next state. Thus the input may indirectly influence subsequent outputs, but not the current or immediate output. The Moore machine is named after Edward F. Moore, who presented the concept in a 1956 paper, “Gedanken-experiments on Sequential Machines.” == Formal definition == A Moore machine can be defined as a 6-tuple ( S , s 0 , Σ , Λ , δ , G ) {\displaystyle (S,s_{0},\Sigma ,\Lambda ,\delta ,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 δ : S × Σ → S {\displaystyle \delta :S\times \Sigma \rightarrow S} mapping a state and the input alphabet to the next state An output function G : S → Λ {\displaystyle G:S\rightarrow \Lambda } mapping each state to the output alphabet "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. A Moore machine can be regarded as a restricted type of finite-state transducer. == Visual representation == === Table === A state transition table is a table listing all the triples in the transition relation δ : S × Σ → S {\displaystyle \delta :S\times \Sigma \rightarrow S} . === Diagram === The state diagram for a Moore machine, or Moore diagram, is a state diagram that associates an output value with each state. == Relationship with Mealy machines == As Moore and Mealy machines are both types of finite-state machines, they are equally expressive: either type can be used to parse a regular language. The difference between Moore machines and Mealy machines is that in the latter, the output of a transition is determined by the combination of current state and current input ( S × Σ {\displaystyle S\times \Sigma } as the domain of G {\displaystyle G} ), as opposed to just the current state ( S {\displaystyle S} as the domain of G {\displaystyle G} ). When represented as a state diagram, for a Moore machine, each node (state) is labeled with an output value; for a Mealy machine, each arc (transition) is labeled with an output value. Every Moore machine M {\displaystyle M} is equivalent to the Mealy machine with the same states and transitions and the output function G ( s , σ ) = G M ( δ M ( s , σ ) ) {\displaystyle G(s,\sigma )=G_{M}(\delta _{M}(s,\sigma ))} , which takes each state-input pair ( s , σ ) {\displaystyle (s,\sigma )} and yields G M ( δ M ( s , σ ) ) {\displaystyle G_{M}(\delta _{M}(s,\sigma ))} , where G M {\displaystyle G_{M}} is M {\displaystyle M} 's output function and δ M {\displaystyle \delta _{M}} is M {\displaystyle M} 's transition function. However, not every Mealy machine can be converted to an equivalent Moore machine. Some can be converted only to an almost equivalent Moore machine, with outputs shifted in time. This is due to the way that state labels are paired with transition labels to form the input/output pairs. Consider a transition s i → s j {\displaystyle s_{i}\rightarrow s_{j}} from state s i {\displaystyle s_{i}} to state s j {\displaystyle s_{j}} . The input causing the transition s i → s j {\displaystyle s_{i}\rightarrow s_{j}} labels the edge ( s i , s j ) {\displaystyle (s_{i},s_{j})} . The output corresponding to that input, is the label of state s i {\displaystyle s_{i}} . Notice that this is the source state of the transition. So for each input, the output is already fixed before the input is received, and depends solely on the present state. This is the original definition by E. Moore. It is a common mistake to use the label of state s j {\displaystyle s_{j}} as output for the transition s i → s j {\displaystyle s_{i}\rightarrow s_{j}} . == Examples == Types according to number of inputs/outputs. === Simple === Simple Moore machines have one input and one output: edge detector using XOR binary adding machine clocked sequential systems (a restricted form of Moore machine where the state changes only when the global clock signal changes) Most digital electronic systems are designed as clocked sequential systems. Clocked sequential systems are a restricted form of Moore machine where the state changes only when the global clock signal changes. Typically the current state is stored in flip-flops, and a global clock signal is connected to the "clock" input of the flip-flops. Clocked sequential systems are one way to solve metastability problems. A typical electronic Moore machine includes a combinational logic chain to decode the current state into the outputs (lambda). The instant the current state changes, those changes ripple through that chain, and almost instantaneously the output gets updated. There are design techniques to ensure that no glitches occur on the outputs during that brief period while those changes are rippling through the chain, but most systems are designed so that glitches during that brief transition time are ignored or are irrelevant. The outputs then stay the same indefinitely (LEDs stay bright, power stays connected to the motors, solenoids stay energized, etc.), until the Moore machine changes state again. ==== Worked example ==== A sequential network has one input and one output. The output becomes 1 and remains 1 thereafter when at least two 0's and two 1's have occurred as inputs. A Moore machine with nine states for the above description is shown on the right. The initial state is state A, and the final state is state I. The state table for this example is as follows: === Complex === More complex Moore machines can have multiple inputs as well as multiple outputs. == Gedanken-experiments == In Moore's 1956 paper "Gedanken-experiments on Sequential Machines", the ( n ; m ; p ) {\displaystyle (n;m;p)} automata (or machines) S {\displaystyle S} are defined as having n {\displaystyle n} states, m {\displaystyle m} input symbols and p {\displaystyle p} output symbols. Nine theorems are proved about the structure of S {\displaystyle S} , and experiments with S {\displaystyle S} . Later, " S {\displaystyle S} machines" became known as "Moore machines". At the end of the paper, in Section "Further problems", the following task is stated: Another directly following problem is the improvement of the bounds given at the theorems 8 and 9. Moore's Theorem 8 is formulated as: Given an arbitrary ( n ; m ; p ) {\displaystyle (n;m;p)} machine S {\displaystyle S} , such that every two of its states are distinguishable from one another, then there exists an experiment of length n ( n − 1 ) 2 {\displaystyle {\tfrac {n(n-1)}{2}}} which determines the state of S {\displaystyle S} at the end of the experiment. In 1957, A. A. Karatsuba proved the following two theorems, which completely solved Moore's problem on the improvement of the bounds of the experiment length of his "Theorem 8". Theorem A. If S {\displaystyle S} is an ( n ; m ; p ) {\displaystyle (n;m;p)} machine, such that every two of its states are distinguishable from one another, then there exists a branched experiment of length at most ( n − 1 ) ( n − 2 ) 2 + 1 {\displaystyle {\tfrac {(n-1)(n-2)}{2}}+1} through which one may determine the state of S {\displaystyle S} at the end of the experiment. Theorem B. There exists an ( n ; m ; p ) {\displaystyle (n;m;p)} machine, every two states of which are distinguishable from one another, such that the length of the shortest experiments establishing the state of the machine at the end of the experiment is equal to ( n − 1 ) ( n − 2 ) 2 + 1 {\displaystyle {\tfrac {(n-1)(n-2)}{2}}+1} . Theorems A and B were used for the basis of the course work of a student of the fourth year, A. A. Karatsuba, "On a problem from the automata theory", which was distinguished by testimonial reference at the competition of student works of the faculty of mechanics and mathematics of Moscow State University in 1958. The paper by Karatsuba was given to the journal Uspekhi Mat. Nauk on 17 December 1958 and was published there in June 1960. Until the present day (2011), Karatsuba's result on the length of experiments is the only exact nonlinear result, both in automata theory, and in similar problems of computational complexity theory.
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Light scanning photomacrography

Light Scanning Photomacrography (LSP), also known as Scanning Light Photomacrography (SLP) or Deep-Field Photomacrography, is a photographic film technique that allows for high magnification light imaging with exceptional depth of field (DOF). This method overcomes the limitations of conventional macro photography, which typically only keeps a portion of the subject in acceptable focus at high magnifications. == Historical background == The principles of LSP were first documented in the early 1960s by Dan McLachlan Jr., who highlighted its capability for extreme focal depth in microscopy and in 1968 patented the process. The technique was revived and further developed in the 1980s by photographers such as Darwin Dale and Nile Root, a faculty member at the Rochester Institute of Technology. In the early 1990s, William Sharp and Charles Kazilek, both researchers at Arizona State University, also published articles describing their technique and system setup for capturing SLP images. == Predecessor to stack image photography == Light Scanning Photomacrography offered a powerful analog tool for high-detail imaging in the age of film photography. It provided a comprehensive depth of field, making it invaluable in scientific and biomedical photography. As technology and techniques continue to evolve, LSP has been replaced by digital image focus stacking. This technique uses a collection of images captured in series at different focal depths, which are then processed using computer software to create a single image with a greater focus depth than any single image. == LSP technique and results == LSP involves the use of a thin plane of light that scans across the subject, which is mounted on a stage moving perpendicular to the film plane. The technique utilizes traditional optics and is governed by the physical laws of depth of field. By moving the subject through a narrow band of illumination, the entire subject can be recorded in sharp focus from the nearest details to the farthest ones. This analog process produces sharp and detailed images by slowly recording the image on film as the specimen passes through the sheet of light that is thinner than the effective DOF. Because the image is captured at the same relative distance from the camera lens, the resulting images are axonometric rather than perspective projection, which is what the human eye sees and is typically captured by a film camera. Because all parts of an LSP image are captured at the same distance from the lens, relative measurements can be taken from an LSP photograph and can be used for comparison. == Equipment and setup == A typical LSP setup includes: A stage that can move the subject perpendicular to the film plane. Light sources, in some cases modified projectors, are used to project a thin plane of light. A camera mounted on a stable stand such as a tabletop copy stand. In 1991, Sharp and Kazilek described their SLP system that used three Kodak Ektagraphic slide projectors with zoom lenses to create a thin plane of light. The projectors each had a slide mount with two razor blades placed edge-to-edge to create a thin slit for the light to pass through. The image was captured using a Nikon FE-2 SLR camera mounted above the specimen. Kodachrome 25 slide film was used to record the image and to minimize film grain size and maximize image sharpness == Commercial systems == A commercial SLP instrument was produced by the Irvine Optical Corp. Their DYNAPHOT system was based on a photomacroscope and could capture images on 4x5 film. The instrument came with two or three illumination sources and a motorized specimen stage. The system advertised a 2X – 40X magnification range and the ability to capture images in black and white and color. Other systems have been developed by Nile Root and Theodore Clarke and reported higher magnification (up to 100X). == LSP process == Alignment and Focusing: The light sources are aligned and focused to project a thin, consistent plane of light across the subject. Stage Movement: The subject stage moves at a controlled speed, scanning through the plane of light. Image Capture: The camera shutter is set to a long exposure or can be opened and closed manually. As the subject moves through the illuminated plane, it is recorded on the film. This process is very much like painting an image onto the film using photons instead of paint. == Applications == LSP was particularly useful in biomedical photography, where it was used to document magnified subjects with increased depth of field over traditional macro and micro photography. It has been employed to capture detailed images of biological specimens, such as imaging small insects and their parts. SLP has been used to document shell collections for scientific documentation and research. Other applications include forensic science, mineralogy, and the imaging of fractured surfaces and parts == Advantages and challenges of LSP imaging == === Advantages === Exceptional depth of field: Subjects are rendered in sharp focus throughout. High magnification: Detailed images at significant magnification without sacrificing DOF. Analog precision: Provides a non-digital solution with accurate image representation. Versatility: Can be used for a range of subject sizes, from macro to non-macro scales. === Challenges === Technical complexity: Requires precise setup and alignment. Exposure time: Typically requires long exposure times due to the scanning process. Contrast control: The highly directional lighting can create harsh shadows and high contrast, which may need to be managed. Digital competition: Focus stacking has largely replaced LSP in the digital era due to convenience and flexibility. == DIY contributions == Enthusiasts and researchers have contributed to the development and accessibility of LSP by creating and sharing DIY guides. These contributions have enabled others to build their own LSP systems using readily available materials and components. Nile Root's publications provide detailed instructions and recommendations for constructing an LSP setup. These DIY systems have allowed a wider audience to explore and utilize the benefits of LSP imaging in various fields.
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The Best Free AI Presentation Maker for Beginners

Shopping for the best AI presentation maker? An AI presentation maker 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 presentation maker 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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Pushpak Bhattacharyya

Pushpak Bhattacharyya (3 July 1962 – 5 October 2025) was an Indian computer scientist and professor in the Department of Computer Science and Engineering at the IIT Bombay. He served as the Director of the IIT Patna from 2015 to 2021. He was a past President of the Association for Computational Linguistics (2016–17), and held the Vijay and Sita Vashee Chair Professorship at IIT Bombay. Bhattacharyya led the Natural Language Processing (NLP) research group at the Centre for Indian Language Technology (CFILT) at IIT Bombay until his death. At the inauguration of the Nilekani Centre at AI4Bharat, IIT Madras, Nandan Nilekani, Co-founder and Non-Executive Chairman of Infosys, referred to Bhattacharyya as the "Godfather of Indian NLP". == Early life and education == Bhattacharyya was born in Shillong in 1962. He completed his schooling at Jail Road Boys' High School, Shillong. He obtained a B.Tech. in Computer Science from the IIT Kharagpur, followed by an M.Tech. from the IIT Kanpur, and a Ph.D. in Computer Science from IIT Bombay in 1994. == Research == Bhattacharyya’s research areas includes Natural language processing, Artificial intelligence, Machine learning, Psycholinguistics, Eye tracking, and Information retrieval. He made contributions to the development of multilingual lexical databases such as IndoWordNet and other projects related to machine translation and computational linguistics. He authored and co-authored multiple academic works, including Investigations in Computational Sarcasm (with Aditya Joshi), Cognitively Inspired Natural Language Processing: An Investigation Based on Eye Tracking (with Abhijit Mishra), and Machine Translation and Transliteration of Low Resource Related Languages (with Anoop Kunchukuttan). Over his career, Bhattacharyya published more than 350 research papers in journals and conference proceedings and supervised over 300 undergraduate, master’s, and doctoral students. His projects often addressed computational challenges for Indian languages, such as developing wordnets, building translation systems for low-resource languages, and studying cognitive aspects of language processing. He also led government- and industry-funded research initiatives supported by organizations including IBM, Microsoft, Yahoo, and the United Nations. == Death == Bhattacharyya died on 5 October 2025, at the age of 63. == Awards == Patwardhan Award, IIT Bombay, for Technology Development VNMM Award, IIT Roorkee, for Technology Development Fellow, Indian National Academy of Engineering Eminent Engineer Award, Institution of Engineers (India)
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Myhill–Nerode theorem

In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 (Nerode & Sauer 1957, p. ii). == Statement == Given a language L {\displaystyle L} , and a pair of strings x {\displaystyle x} and y {\displaystyle y} , define a distinguishing extension to be a string z {\displaystyle z} such that exactly one of the two strings x z {\displaystyle xz} and y z {\displaystyle yz} belongs to L {\displaystyle L} . Define a relation ∼ L {\displaystyle \sim _{L}} on strings as x ∼ L y {\displaystyle x\;\sim _{L}\ y} if there is no distinguishing extension for x {\displaystyle x} and y {\displaystyle y} . It is easy to show that ∼ L {\displaystyle \sim _{L}} is an equivalence relation on strings, and thus it divides the set of all strings into equivalence classes. The Myhill–Nerode theorem states that a language L {\displaystyle L} is regular if and only if ∼ L {\displaystyle \sim _{L}} has a finite number of equivalence classes, and moreover, that this number is equal to the number of states in the minimal deterministic finite automaton (DFA) accepting L {\displaystyle L} . Furthermore, every minimal DFA for the language is isomorphic to the canonical one (Hopcroft & Ullman 1979). Generally, for any language, the constructed automaton is a state automaton acceptor. However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language regularity. Some authors refer to the ∼ L {\displaystyle \sim _{L}} relation as Nerode congruence, in honor of Anil Nerode. == Use and consequences == The Myhill–Nerode theorem may be used to show that a language L {\displaystyle L} is regular by proving that the number of equivalence classes of ∼ L {\displaystyle \sim _{L}} is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equivalence classes until no more can be found. For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. Given two binary strings x , y {\displaystyle x,y} , extending them by one digit gives 2 x + b , 2 y + b {\displaystyle 2x+b,2y+b} , so 2 x + b ≡ 2 y + b mod 3 {\displaystyle 2x+b\equiv 2y+b\mod 3} iff x ≡ y mod 3 {\displaystyle x\equiv y\mod 3} . Thus, 00 {\displaystyle 00} (or 11 {\displaystyle 11} ), 01 {\displaystyle 01} , and 10 {\displaystyle 10} are the only distinguishing extensions, resulting in the 3 classes. The minimal automaton accepting our language would have three states corresponding to these three equivalence classes. Another immediate corollary of the theorem is that if for a language L {\displaystyle L} the relation ∼ L {\displaystyle \sim _{L}} has infinitely many equivalence classes, it is not regular. It is this corollary that is frequently used to prove that a language is not regular. == Generalizations == The Myhill–Nerode theorem can be generalized to tree automata.
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Zesta

Zesta is an online food ordering and delivery platform operating across the African region. Formerly known as Square Eats, the company rebranded to Zesta in 2025. Zesta connects customers with restaurants and stores, offering delivery services for food, groceries, parcel delivery and other essentials. == History == Zesta was originally founded as Square Eats in 2020 by twin brothers Henry Newman and Randall Newman when they were 21 years old. It was launched in Gaborone, Botswana, and quickly gained traction as a leading food delivery service in the country. The company halted operations and took a strategic decision to reinvent the business in 2022. In 2025, the company announced its rebranding to Zesta, highlighting its commitment to evolving beyond food delivery to become a super app. === COVID-19 initiative === During the COVID-19 pandemic, Zesta (then Square Eats) implemented measures to ensure safety and hygiene, including providing free gloves and hand sanitizer to drivers and introducing contactless delivery options. These efforts positioned the platform as a trusted service during the pandemic. == Service == Zesta facilitates delivery from a wide range of merchant partners via a smartphone app, available on iOS and Android platforms, or through its website. Customers can browse their favorite restaurants, place orders, and have meals delivered to their doorstep efficiently.
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Trie

In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's position within the trie determines its associated key, with the connections between nodes defined by individual characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A notable optimization is the radix tree, which provides more efficient prefix-based storage. While tries store character strings, they can be adapted to work with any ordered sequence of elements, such as permutations of digits or shapes. A notable variant is the bitwise trie, which uses individual bits from fixed-length binary data (such as integers or memory addresses) as keys. == History, etymology, and pronunciation == The idea of a trie for representing a set of strings was first abstractly described by Axel Thue in 1912. Tries were first described in a computer context by René de la Briandais in 1959. The idea was independently described in 1960 by Edward Fredkin, who coined the term trie, pronouncing it (as "tree"), after the middle syllable of retrieval. However, other authors pronounce it (as "try"), in an attempt to distinguish it verbally from "tree". == Overview == Tries are a form of string-indexed look-up data structure, which is used to store a dictionary list of words that can be searched on in a manner that allows for efficient generation of completion lists. A prefix trie is an ordered tree data structure used in the representation of a set of strings over a finite alphabet set, which allows efficient storage of words with common prefixes. Tries can be efficacious on string-searching algorithms such as predictive text, approximate string matching, and spell checking in comparison to binary search trees. A trie can be seen as a tree-shaped deterministic finite automaton. == Operations == Tries support various operations: insertion, deletion, and lookup of a string key. Tries are composed of nodes that contain links, which either point to other suffix child nodes or null. As for every tree, each node except the root is pointed to by only one other node, called its parent. Each node contains as many links as the number of characters in the applicable alphabet (although tries tend to have a substantial number of null links). In some cases, the alphabet used is simply that of the character encoding—resulting in, for example, a size of 128 in the case of ASCII. The null links within the children of a node emphasize the following characteristics: Characters and string keys are implicitly stored in the trie, and include a character sentinel value indicating string termination. Each node contains one possible link to a prefix of strong keys of the set. A basic structure type of nodes in the trie is as follows: Node {\displaystyle {\text{Node}}} may contain an optional Value {\displaystyle {\text{Value}}} , which is associated with the key that corresponds to the node. === Searching === Searching for a value in a trie is guided by the characters in the search string key, as each node in the trie contains a corresponding link to each possible character in the given string. Thus, following the string within the trie yields the associated value for the given string key. A null link during the search indicates the inexistence of the key. The following pseudocode implements the search procedure for a given string key in a rooted trie x. In the above pseudocode, x and key correspond to the pointer of the trie's root node and the string key, respectively. The search operation takes O ( m ) {\displaystyle O(m)} time, where m {\displaystyle m} is the size of the string parameter key. In a balanced binary search tree, on the other hand, it takes O ( m log ⁡ n ) {\displaystyle O(m\log n)} time, in the worst case, since key needs to be compared with O ( log ⁡ n ) {\displaystyle O(\log n)} other keys and each comparison takes O ( m ) {\displaystyle O(m)} time, in the worst case. The trie occupies less space, in comparison with a binary search tree, in the case of a large number of short strings, since nodes share common initial string subsequences and store the keys implicitly. === Insertion === Insertion into a trie is guided by using the character sets as indexes to the children array until the last character of the string key is reached. Each node in the trie corresponds to one call of the radix sorting routine, as the trie structure reflects the execution pattern of the top-down radix sort. If null links are encountered before reaching the last character of the string key, new nodes are created. The input value is assigned to the value of the last node traversed, which is the node that corresponds to the key. === Deletion === Deletion of a key–value pair from a trie involves finding the node corresponding to the key, setting its value to null, and recursively removing nodes that have no children. The procedure begins by examining key; an empty string indicates arrival at the node corresponding to the (original) key, in which case its value is set to null. If the node, then, has null value and no children, it is removed from the trie by returning null; otherwise, the node is kept by returning the node itself. == Replacing other data structures == === Replacement for hash tables === A trie can be used to replace a hash table, over which it has the following advantages: Searching for a node with an associated key of size m {\displaystyle m} has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may have numerous colliding keys, and the worst-case lookup speed of such a table would be O ( N ) {\displaystyle O(N)} , where N {\displaystyle N} denotes the total number of nodes within the table. Tries do not need a hash function for the operation, unlike a hash table; there are also no collisions of different keys in a trie. Within a trie, keys can be efficiently sorted lexicographically. However, tries are less efficient than a hash table when the data is directly accessed on a secondary storage device such as a hard disk drive that has higher random access time than the main memory. == Implementation strategies == Tries can be represented in several ways, corresponding to different trade-offs between memory use and speed of the operations. Using a vector of pointers for representing a trie consumes enormous space; however, memory space can be reduced at the expense of running time if a singly linked list is used for each node vector, as most entries of the vector contains nil {\displaystyle {\text{nil}}} . Techniques such as alphabet reduction may reduce the large space requirements by reinterpreting the original string as a longer string over a smaller alphabet. For example, a string of n bytes can alternatively be regarded as a string of 2n four-bit units. This can reduce memory usage by a factor of eight; but lookups need to visit twice as many nodes in the worst case. Another technique includes storing a vector of 256 ASCII pointers as a bitmap of 256 bits representing ASCII alphabet, which reduces the size of individual nodes dramatically. === Bitwise tries === Bitwise tries are used to address the enormous space requirement for the trie nodes in a naive simple pointer vector implementations. Each character in the string key set is represented via individual bits, which are used to traverse the trie over a string key. The implementations for these types of trie use vectorized CPU instructions to find the first set bit in a fixed-length key input (e.g. GCC's __builtin_clz() intrinsic function). Accordingly, the set bit is used to index the first item, or child node, in the 32- or 64-entry based bitwise tree. Search then proceeds by testing each subsequent bit in the key. This procedure is also cache-local and highly parallelizable due to register independency, and thus performant on out-of-order execution CPUs. === Compressed tries === Radix tree, also known as a compressed trie, is a space-optimized variant of a trie in which any node with only one child gets merged with its parent; elimination of branches of the nodes with a single child results in better metrics in both space and time. This works best when the trie remains static and set of keys stored are very sparse within their representation space. One more approach for static tries is to "pack" the trie by storing disjoint
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Yi Zeng (AI researcher)

Yi Zeng (Chinese: 曾毅) is a Chinese artificial intelligence researcher and professor at the Chinese Academy of Sciences, who also serves as the founding director of Center for Long-term AI, and as a member of the United Nations Advisory Body on AI. == Career == On May 25, 2019, Zeng led the team that published the Beijing Artificial Intelligence Principles, proposed as an initiative for the long-term research, governance and planning of AI, and the "realization of beneficial AI for mankind and nature". He was named on the Time 100 AI list, a list featuring the hundred most influential figures in artificial intelligence of the year, in 2023. In July 2023, Zeng addressed the United Nations Security Council in a meeting on the risks posed by recent strides in artificial intelligence. He said that AI models “cannot be trusted as responsible agents that can help humans to make decisions,” and warned of the risk of extinction posed by both near-term and long-term AI, arguing that “in the long term, we haven’t given superintelligence any practical reasons why they should protect humans”. Zeng stated that humans should always be responsible for final decision-making on the use of nuclear weapons, and that the United Nations must produce an international framework on AI development and governance, to ensure global peace and security. In October 2023, UN Secretary-General António Guterres announced the creation of an advisory body on issues surrounding the international governance of AI, of which Zeng would be a member. He leads teams of researchers at the Institute of Philosophy and the Institute of Automation of the Chinese Academy of Sciences, including doctoral candidates, postdoctoral fellows, research fellows, assistant professors, and associate professors. Among them is his first international PhD student, Ammar Younas, a lawyer and arbitrator whose research focuses on cross-cultural dimensions of AI ethics and governance.
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Stefano Soatto

Stefano Soatto is professor of computer science at the University of California, Los Angeles (UCLA), in Los Angeles, CA, where he is also professor of electrical engineering and founding director of the UCLA Vision Lab. He is also Vice President of applied science for Amazon Web Services' (AWS) AI division. == Academic biography == Soatto obtained his D. Eng. in electrical engineering, cum laude, from the University of Padua in 1992, was an EAP Fellow at the University of California, Berkeley in 1990–1991, and received his Ph.D. in control and dynamical systems from the California Institute of Technology in 1996 with dissertation "A Geometric Approach to Dynamic Vision". In 1996–97 he was a postdoctoral scholar at Harvard University, and subsequently held positions as assistant and associate professor of electrical engineering and biomedical engineering at Washington University in St. Louis, and of mathematics and computer science at the University of Udine, Italy. He has been at UCLA since 2000. He is also Vice President of applied science for Amazon Web Services' (AWS) AI division. == Research == Soatto's research focuses on computer vision, machine learning and robotics. He co-developed optimal algorithms for structure from motion (SFM, or visual SLAM, simultaneous localization and mapping, in robotics; Best Paper Award at CVPR 1998), characterized its ambiguities (David Marr Prize at ICCV 1999), also characterized the identifiability and observability of visual-inertial sensor fusion (Best Paper Award at ICRA 2015). His research focus is the development of representations, that are functions of the data that capture their informative content and discard irrelevant variability in the data (a generalized form of 'noise' or 'clutter'). Soatto's lab first to demonstrate real-time SFM and augmented reality (AR) on commodity hardware in live demos at CVPR 2000, ICCV 2001, and ECCV 2002. He also co-led the UCLA-Golem Team in the second DARPA Grand Challenge for autonomous vehicles, with Emilio Frazzoli (co-founder of NuTonomy), and Amnon Shashua (co-founder of Mobileye). == Recognition == Soatto was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2013 for contributions to dynamic visual processes. He received the David Marr Prize in Computer Vision in 1999. He was named to the 2022 class of ACM Fellows, "for contributions to the foundations and applications of visual geometry and visual representations learning".
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DABUS

DABUS (Device for the Autonomous Bootstrapping of Unified Sentience) is an artificial intelligence (AI) system created by Stephen Thaler. It reportedly conceived of two novel products — a food container constructed using fractal geometry, which enables rapid reheating, and a flashing beacon for attracting attention in an emergency. The filing of patent applications designating DABUS as inventor has led to decisions by patent offices and courts on whether a patent can be granted for an invention reportedly made by an AI system. == History in different jurisdictions == === Australia === On 17 September 2019, Thaler filed an application to patent a "Food container and devices and methods for attracting enhanced attention," naming DABUS as the inventor. On 21 September 2020, IP Australia found that section 15(1) of the Patents Act 1990 (Cth) is inconsistent with an artificial intelligence machine being treated as an inventor, and Thaler's application had lapsed. Thaler sought judicial review, and on 30 July 2021, the Federal Court set aside IP Australia's decision and ordered IP Australia to reconsider the application. On 13 April 2022, the Full Court of the Federal Court set aside that decision, holding that only a natural person can be an inventor for the purposes of the Patents Act 1990 (Cth) and the Patents Regulations 1991 (Cth), and that such an inventor must be identified for any person to be entitled to a grant of a patent. On 11 November 2022, Thaler was refused special leave to appeal to the High Court. === European Patent Office === On 17 October 2018 and 7 November 2018, Thaler filed two European patent applications with the European Patent Office. The first claimed invention was a "Food Container" and the second was "Devices and Methods for Attracting Enhanced Attention." On 27 January 2020, the EPO rejected the applications on the grounds that the application listed an AI system named DABUS, and not a human, as the inventor, based on Article 81 and Rule 19(1) of the European Patent Convention (EPC). On 21 December 2021, the Board of Appeal of the EPO dismissed Thaler's appeal from the EPO's primary decision. The Board of Appeal confirmed that "under the EPC the designated inventor has to be a person with legal capacity. This is not merely an assumption on which the EPC was drafted. It is the ordinary meaning of the term inventor." === United Kingdom === Similar applications were filed by Thaler to the United Kingdom Intellectual Property Office on 17 October and 7 November 2018. The Office asked Thaler to file statements of inventorship and of right of grant to a patent (Patent Form 7) in respect of each invention within 16 months of the filing date. Thaler filed those forms naming DABUS as the inventor and explaining in some detail why he believed that machines should be regarded as inventors in the circumstances. His application was rejected on the grounds that: (1) naming a machine as inventor did not meet the requirements of the Patents Act 1977; and (2) the IPO was not satisfied as to the manner in which Thaler had acquired rights that would otherwise vest in the inventor. Thaler was not satisfied with the decision and asked for a hearing before an official known as the "hearing officer". By a decision dated 4 December 2019 the hearing officer rejected Thaler's appeal. Thaler appealed against the hearing officer's decision to the Patents Court (a specialist court within the Chancery Division of the High Court of England and Wales that determines patent disputes). On 21 September 2020, Mr Justice Marcus Smith upheld the decision of the hearing officer. On 21 September 2021, Thaler's further appeal to the Court of Appeal was dismissed by Arnold LJ and Laing LJ (Birss LJ dissenting). On 20 December 2023, the UK Supreme Court dismissed a further appeal by Thaler. In its judgment, the court held that an "inventor" under the Patents Act 1977 must be a natural person. === United States === The patent applications on the inventions were refused by the USPTO, which held that only natural persons can be named as inventors in a patent application. Thaler first fought this result by filing a complaint under the Administrative Procedure Act alleging that the decision was "arbitrary, capricious, an abuse of discretion and not in accordance with the law; unsupported by substantial evidence, and in excess of Defendants’ statutory authority." A month later on August 19, 2019, Thaler filed a petition with the USPTO as allowed in 37 C.F.R. § 1.181 stating that DABUS should be the inventor. The judge and Thaler agreed in this case that Thaler himself is unable to receive the patent on behalf of DABUS. In their August 5, 2022, Thaler decision, the US Court of Appeals for the Federal Circuit affirmed that only a natural person could be an inventor, which means that the AI that invents any other type of invention is not addressed by the "who" mentioned in the legislation. === New Zealand === On January 31, 2022, the Intellectual Property Office of New Zealand (IPONZ) decided that a patent application (776029) filed by Stephen Thaler was void, on the basis that no inventor was identified on the patent application. IPONZ determined that DABUS could not be "an actual devisor of the invention" as required by the Patents Act 2013, and that this must be a natural person as held by the previous patent offices above. The High Court of New Zealand confirmed the decision in 2023. === South Africa === On 24 June 2021, the South African Companies and Intellectual Property Commission (CIPC) accepted Dr Thaler's Patent Cooperation Treaty, for a patent in respect of inventions generated by DABUS. In July 2021, the CIPC released a notice of issuance for the patent. It is the first patent granted for an AI invention. === Switzerland === On June 26, 2025, the Swiss Federal Administrative Court ruled that artificial intelligence systems such as DABUS cannot be listed as inventors in patent applications. The court upheld the existing practice of the Swiss Federal Institute of Intellectual Property (IPI), which requires that only natural persons can be recognized as inventors under Swiss patent law. The case concerned a patent application, which sought to designate DABUS as the sole inventor of a food container designed with a fractal geometry to enhance heat distribution. The IPI had rejected the application, arguing that both the absence of a human inventor and the attribution of inventorship to an AI system were inadmissible. While the court dismissed Thaler's main request, it accepted a subsidiary request: if a human applicant recognizes and files a patent based on an AI-generated invention, that person may be considered the inventor. As a result, the application may proceed with Thaler listed as the inventor. The decision (B-2532/2024) can still be appealed to the Swiss Federal Supreme Court.
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Lin-Shan Lee

Lin-Shan Lee (Chinese: 李琳山; born 23 September 1952) is a Taiwanese computer scientist. == Education and career == Lee earned a bachelor's degree in electrical engineering from National Taiwan University in 1974, and pursued a doctorate in the same subject at Stanford University, graduating in 1977. He subsequently returned to Taiwan and joined the NTU faculty in 1982. Lee is a 1993 fellow of the Institute of Electrical and Electronics Engineers, recognized "[f]or contributions to computer voice input/output techniques for Mandarin Chinese and to engineering education." The International Speech Communication Association elevated him to fellow status in 2010 "[f]or his contributions to Chinese spoken language processing and speech information retrieval, and his service to the speech language community." In 2016, Lee was elected a member of Academia Sinica.
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AI Coding Assistants: Free vs Paid (2026)

In search of the best AI coding assistant? An AI coding 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 coding assistant 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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