Vivid knowledge refers to a specific kind of knowledge representation. The idea of a vivid knowledge base is to get an interpretation mostly straightforward out of it – it implies the interpretation. Thus, any query to such a knowledge base can be reduced to a database-like query. == Propositional knowledge base == A propositional knowledge base KB is vivid iff KB is a complete and consistent set of literals (over some vocabulary). Such a knowledge base has the property that it as exactly one interpretation, i.e. the interpretation is unique. A check for entailment of a sentence can simply be broken down into its literals and those can be answered by a simple database-like check of KB. == First-order knowledge base == A first-order knowledge base KB is vivid iff for some finite set of positive function-free ground literals KB+, KB = KB+ ∪ Negations ∪ DomainClosure ∪ UniqueNames, whereby Negations ≔ { ¬p | p is atomic and KB ⊭ p }, DomainClosure ≔ { (ci ≠ cj) | ci, cj are distinct constants }, UniqueNames ≔ { ∀x: (x = c1) ∨ (x = c2) ∨ ..., where the ci are all the constants in KB+ }. All interpretations of a vivid first-order knowledge base are isomorphic.
Truth discovery
Truth discovery (also known as truth finding) is the process of choosing the actual true value for a data item when different data sources provide conflicting information on it. Several algorithms have been proposed to tackle this problem, ranging from simple methods like majority voting to more complex ones able to estimate the trustworthiness of data sources. Truth discovery problems can be divided into two sub-classes: single-truth and multi-truth. In the first case only one true value is allowed for a data item (e.g birthday of a person, capital city of a country). While in the second case multiple true values are allowed (e.g. cast of a movie, authors of a book). Typically, truth discovery is the last step of a data integration pipeline, when the schemas of different data sources have been unified and the records referring to the same data item have been detected. == General principles == The abundance of data available on the web makes more and more probable to find that different sources provide (partially or completely) different values for the same data item. This, together with the fact that we are increasing our reliance on data to derive important decisions, motivates the need of developing good truth discovery algorithms. Many currently available methods rely on a voting strategy to define the true value of a data item. Nevertheless, recent studies, have shown that, if we rely only on majority voting, we could get wrong results even in 30% of the data items. The solution to this problem is to assess the trustworthiness of the sources and give more importance to votes coming from trusted sources. Ideally, supervised learning techniques could be exploited to assign a reliability score to sources after hand-crafted labeling of the provided values; unfortunately, this is not feasible since the number of needed labeled examples should be proportional to the number of sources, and in many applications the number of sources can be prohibitive. == Single-truth vs multi-truth discovery == Single-truth and multi-truth discovery are two very different problems. Single-truth discovery is characterized by the following properties: only one true value is allowed for each data item; different values provided for a given data item oppose to each other; values and sources can either be correct or erroneous. While in the multi-truth case the following properties hold: the truth is composed by a set of values; different values could provide a partial truth; claiming one value for a given data item does not imply opposing to all the other values; the number of true values for each data item is not known a priori. Multi-truth discovery has unique features that make the problem more complex and should be taken into consideration when developing truth-discovery solutions. The examples below point out the main differences of the two methods. Knowing that in both examples the truth is provided by source 1, in the single truth case (first table) we can say that sources 2 and 3 oppose to the truth and as a result provide wrong values. On the other hand, in the second case (second table), sources 2 and 3 are neither correct nor erroneous, they instead provide a subset of the true values and at the same time they do not oppose the truth. == Source trustworthiness == The vast majority of truth discovery methods are based on a voting approach: each source votes for a value of a certain data item and, at the end, the value with the highest vote is select as the true one. In the more sophisticated methods, votes do not have the same weight for all the data sources, more importance is indeed given to votes coming from trusted sources. Source trustworthiness usually is not known a priori but estimated with an iterative approach. At each step of the truth discovery algorithm the trustworthiness score of each data source is refined, improving the assessment of the true values that in turn leads to a better estimation of the trustworthiness of the sources. This process usually ends when all the values reach a convergence state. Source trustworthiness can be based on different metrics, such as accuracy of provided values, copying values from other sources and domain coverage. Detecting copying behaviors is very important, in fact, copy allows to spread false values easily making truth discovery very hard, since many sources would vote for the wrong values. Usually systems decrease the weight of votes associated to copied values or even don’t count them at all. == Single-truth methods == Most of the currently available truth discovery methods have been designed to work well only in the single-truth case. Below are reported some of the characteristics of the most relevant typologies of single-truth methods and how different systems model source trustworthiness. === Majority voting === Majority voting is the simplest method, the most popular value is selected as the true one. Majority voting is commonly used as a baseline when assessing the performances of more complex methods. === Web-link based === These methods estimate source trustworthiness exploiting a similar technique to the one used to measure authority of web pages based on web links. The vote assigned to a value is computed as the sum of the trustworthiness of the sources that provide that particular value, while the trustworthiness of a source is computed as the sum of the votes assigned to the values that the source provides. === Information-retrieval based === These methods estimate source trustworthiness using similarity measures typically used in information retrieval. Source trustworthiness is computed as the cosine similarity (or other similarity measures) between the set of values provided by the source and the set of values considered true (either selected in a probabilistic way or obtained from a ground truth). === Bayesian based === These methods use Bayesian inference to define the probability of a value being true conditioned on the values provided by all the sources. P ( v ∣ ψ ( o ) ) = P ( ψ ( o ) ∣ v ) ⋅ P ( v ) P ( ψ ( o ) ) {\displaystyle P(v\mid \psi (o))={\frac {P(\psi (o)\mid v)\cdot P(v)}{P(\psi (o))}}} where v {\displaystyle \textstyle v} is a value provided for a data item o {\displaystyle \textstyle o} and ψ ( o ) {\displaystyle \textstyle \psi (o)} is the set of the observed values provided by all the sources for that specific data item. The trustworthiness of a source is then computed based on the accuracy of the values that provides. Other more complex methods exploit Bayesian inference to detect copying behaviors and use these insights to better assess source trustworthiness. == Multi-truth methods == Due to its complexity, less attention has been devoted to the study of the multi-truth discovery Below are reported two typologies of multi-truth methods and their characteristics. === Bayesian based === These methods use Bayesian inference to define the probability of a group of values being true conditioned on the values provided by all the data sources. In this case, since there could be multiple true values for each data item, and sources can provide multiple values for a single data item, it is not possible to consider values individually. An alternative is to consider mappings and relations between set of provided values and sources providing them. The trustworthiness of a source is then computed based on the accuracy of the values that provides. More sophisticated methods also consider domain coverage and copying behaviors to better estimate source trustworthiness. === Probabilistic Graphical Models based === These methods use probabilistic graphical models to automatically define the set of true values of given data item and also to assess source quality without need of any supervision. == Applications == Many real-world applications can benefit from the use of truth discovery algorithms. Typical domains of application include: healthcare, crowd/social sensing, crowdsourcing aggregation, information extraction and knowledge base construction. Truth discovery algorithms could be also used to revolutionize the way in which web pages are ranked in search engines, going from current methods based on link analysis like PageRank, to procedures that rank web pages based on the accuracy of the information they provide.
Alice AI (AI model family)
Alice AI is a neural network family developed by the Russian company Yandex LLC. Alice AI can create and revise texts, generate new ideas and capture the context of the conversation with the user. Alice AI is trained using a dataset which includes information from books, magazines, newspapers and other open sources available on the internet. The neural network may get facts wrong and hallucinate, but as it learns, it will produce increasingly accurate answers. == Usage == YandexGPT is integrated into virtual assistant Alice (an analog of Siri and Alexa) and is available in Yandex services and applications. The company gives businesses access to the neural network’s API through the public cloud platform Yandex Cloud and develops its own B2B solutions on its basis. Since July 2023, 800 companies have participated in the closed testing of YandexGPT. IT developers, banks, retail businesses, and companies from other industries can use the technology in two modes — API and Playground (an interface in the Yandex Cloud console for testing models and hypotheses). Two model versions are available to businesses: one works in asynchronous mode and is better able to handle complex tasks, while the other is suitable for creating quick responses in real time. As a result, YandexGPT has been tested in dozens of scenarios such as content tasks, tech support, creating chatbots, virtual assistants, etc. == History == In February 2023, Yandex announced that it was working on its own version of the ChatGPT generative neural network while developing a language model from the YaLM (Yet another Language Model) family. The project was tentatively named YaLM 2.0, which was later changed to YandexGPT. On May 17, the company unveiled a neural network called YandexGPT (YaGPT) and enabled its virtual assistant Alice to interact with the new language model. On June 15, 2023, Yandex added the YandexGPT language model to the image generation application Shedevrum. This enabled its users to create fully-fledged posts complete with a title, text, and relevant illustration. In July 2023, YandexGPT launched new features enabling businesses to create virtual assistants and chatbots, as well as generate and structure texts. On September 7, 2023, Yandex presented a new version of the language model, YandexGPT 2, at the Practical ML Conf. Compared to the previous one, the new version is able to perform more types of tasks, and the quality of answers has improved. The developers claimed that YandexGPT 2 answered user questions better than the first version in 67% of cases. From October 6, 2023, YandexGPT can create short retellings of online Russian-language videos on the Internet. It can summarize videos that are from two minutes to four hours long and contain speech.
Deep image prior
Deep image prior is a type of convolutional neural network used to enhance a given image with no prior training data other than the image itself. A neural network is randomly initialized and used as prior to solve inverse problems such as noise reduction, super-resolution, and inpainting. Image statistics are captured by the structure of a convolutional image generator rather than by any previously learned capabilities. == Method == === Background === Inverse problems such as noise reduction, super-resolution, and inpainting can be formulated as the optimization task x ∗ = m i n x E ( x ; x 0 ) + R ( x ) {\displaystyle x^{}=min_{x}E(x;x_{0})+R(x)} , where x {\displaystyle x} is an image, x 0 {\displaystyle x_{0}} a corrupted representation of that image, E ( x ; x 0 ) {\displaystyle E(x;x_{0})} is a task-dependent data term, and R(x) is the regularizer. Deep neural networks learn a generator/decoder x = f θ ( z ) {\displaystyle x=f_{\theta }(z)} which maps a random code vector z {\displaystyle z} to an image x {\displaystyle x} . The image corruption method used to generate x 0 {\displaystyle x_{0}} is selected for the specific application. === Specifics === In this approach, the R ( x ) {\displaystyle R(x)} prior is replaced with the implicit prior captured by the neural network (where R ( x ) = 0 {\displaystyle R(x)=0} for images that can be produced by a deep neural networks and R ( x ) = + ∞ {\displaystyle R(x)=+\infty } otherwise). This yields the equation for the minimizer θ ∗ = a r g m i n θ E ( f θ ( z ) ; x 0 ) {\displaystyle \theta ^{}=argmin_{\theta }E(f_{\theta }(z);x_{0})} and the result of the optimization process x ∗ = f θ ∗ ( z ) {\displaystyle x^{}=f_{\theta ^{}}(z)} . The minimizer θ ∗ {\displaystyle \theta ^{}} (typically a gradient descent) starts from a randomly initialized parameters and descends into a local best result to yield the x ∗ {\displaystyle x^{}} restoration function. ==== Overfitting ==== A parameter θ may be used to recover any image, including its noise. However, the network is reluctant to pick up noise because it contains high impedance while useful signal offers low impedance. This results in the θ parameter approaching a good-looking local optimum so long as the number of iterations in the optimization process remains low enough not to overfit data. === Deep Neural Network Model === Typically, the deep neural network model for deep image prior uses a U-Net like model without the skip connections that connect the encoder blocks with the decoder blocks. The authors in their paper mention that "Our findings here (and in other similar comparisons) seem to suggest that having deeper architecture is beneficial, and that having skip-connections that work so well for recognition tasks (such as semantic segmentation) is highly detrimental." == Applications == === Denoising === The principle of denoising is to recover an image x {\displaystyle x} from a noisy observation x 0 {\displaystyle x_{0}} , where x 0 = x + ϵ {\displaystyle x_{0}=x+\epsilon } . The distribution ϵ {\displaystyle \epsilon } is sometimes known (e.g.: profiling sensor and photon noise) and may optionally be incorporated into the model, though this process works well in blind denoising. The quadratic energy function E ( x , x 0 ) = | | x − x 0 | | 2 {\displaystyle E(x,x_{0})=||x-x_{0}||^{2}} is used as the data term, plugging it into the equation for θ ∗ {\displaystyle \theta ^{}} yields the optimization problem m i n θ | | f θ ( z ) − x 0 | | 2 {\displaystyle min_{\theta }||f_{\theta }(z)-x_{0}||^{2}} . === Super-resolution === Super-resolution is used to generate a higher resolution version of image x. The data term is set to E ( x ; x 0 ) = | | d ( x ) − x 0 | | 2 {\displaystyle E(x;x_{0})=||d(x)-x_{0}||^{2}} where d(·) is a downsampling operator such as Lanczos that decimates the image by a factor t. === Inpainting === Inpainting is used to reconstruct a missing area in an image x 0 {\displaystyle x_{0}} . These missing pixels are defined as the binary mask m ∈ { 0 , 1 } H × V {\displaystyle m\in \{0,1\}^{H\times V}} . The data term is defined as E ( x ; x 0 ) = | | ( x − x 0 ) ⊙ m | | 2 {\displaystyle E(x;x_{0})=||(x-x_{0})\odot m||^{2}} (where ⊙ {\displaystyle \odot } is the Hadamard product). The intuition behind this is that the loss is computed only on the known pixels in the image, and the network is going to learn enough about the image to fill in unknown parts of the image even though the computed loss doesn't include those pixels. This strategy is used to remove image watermarks by treating the watermark as missing pixels in the image. === Flash–no-flash reconstruction === This approach may be extended to multiple images. A straightforward example mentioned by the author is the reconstruction of an image to obtain natural light and clarity from a flash–no-flash pair. Video reconstruction is possible but it requires optimizations to take into account the spatial differences. == Implementations == A reference implementation rewritten in Python 3.6 with the PyTorch 0.4.0 library was released by the author under the Apache 2.0 license: deep-image-prior A TensorFlow-based implementation written in Python 2 and released under the CC-SA 3.0 license: deep-image-prior-tensorflow A Keras-based implementation written in Python 2 and released under the GPLv3: machine_learning_denoising == Example == See Astronomy Picture of the Day (APOD) of 2024-02-18
Synthesia (company)
Synthesia Limited is a British multinational artificial intelligence company based in London, United Kingdom. It is a synthetic media-generation software developer and creator of AI-generated video content, including audio-visual agents and cloned avatars. Britain's largest generative-AI firm, it is used by 70% of FTSE 100 and over 90% of Fortune 100 companies. == Overview == Synthesia is most often used by corporations for localized communication, orientation, employee training videos, advertising campaigns, reporting, product demonstrations, customer service, and to create chatbots. Its software algorithm mimics speech and facial movements based on video recordings of an individual’s speech and facial expressions. From this, a text-to-speech video is created to look and sound like the individual. Swiss bank UBS incorporated Synthesia AI-powered avatars of their human financial experts, for instance, in 2025. Users create content via the platform's pre-generated AI presenters or by creating digital representations of themselves, or personal avatars, using the platform's AI video editing tool. These avatars can be used to narrate videos generated from text. As of August 2021, Synthesia's voice database included multiple gender options in over 60 languages. Its free voice library doubled by 2025, to 140 languages and accents, and its Express-Voice technology can clone a user's own voice, or generate a synthetic one. === Deepfakes === The platform prohibits use of its software to create non-consensual clones, including of celebrities or political figures for satirical purposes. Explicit consent must be provided in addition to a strict pre-screening regimen for use of an individual's likeness to avoid “deepfaking”. While the company prohibits use of its technology for misinformation or "news-like content", an October 2023 Freedom House report stated that Synthesia tools had been used by governments in Venezuela, China, Burkina Faso, and Russia to create videos of fake TV news outlets with AI-generated avatars in order to spread propaganda. Actor Dan Dewhirst signed a contract with the company in 2021, becoming one of the first actors whose likeness would be made into an AI avatar, finding his likeness used in the Venezuelan generated-videos. The company stated, in February 2024, that it had improved its misuse detection systems, and, in April 2024, that new users of its technology are screened by the company, and content employing it is further vetted by Synthesia moderators. == History == Synthesia's software utilizes deep learning architecture developed by Lourdes Agapito and Matthias Niessner. The company was co-founded in 2017 by Agapito, Niessner, Victor Riparbelli, and Steffen Tjerrild. In 2018, the company first demonstrated the software's capabilities on the BBC programme Click when it presented a digitization of Matthew Amroliwala speaking Spanish, Mandarin, and Hindi. Through Synthesia's first two years of existence, it employed 10 people and struggled to make sales, leading to an expansion of the company's focus. It moved on from just targeting entertainment studios to a variety of businesses. In 2020, Synthesia users were reported to include Amazon, Tiffany & Co. and IHG Hotels & Resorts. In January 2024, the company introduced its AI video assistant, which turns text-to-video. That April, with a reported 55,000 customers, including half of the Fortune 100, Synthesia launched "expressive avatars". That September, an enhanced dubbing feature was launched, to translate video in 30 languages with naturalized lip-syncing. Peter Hill joined Synthesia as CTO in January 2025, following 25 years at Amazon, and two years as CEO and CPO of Wildfire Studios. That March, a million dollar base of shares was formed to furnish human actors, employed to generate digital avatars, with company stock, which all of its employees hold. By June of that year, 150,000 individuals from among Synthesia's 65,000 customers had created AI-generated avatars of themselves. In July 2025, the company's new global headquarters at Regent’s Place was opened by London mayor Sadiq Khan, who described Britain's largest generative-AI company, then valued at over $2 billion, as a "London success story". By that October, its technology was employed by 90% of the Fortune 100, and Synthesia 3.0 was launched, with hyper-realistic digital avatars equipped with AI-powered dubbing and translation, and a built-in video assistant. In January 2026, it reached a $4 billion valuation, with 70% of FTSE 100 companies noted among its customers. === Funding === The company raised $3.1 million in seed funding in 2019. In April 2021, the company raised $12.5 million in Series A funding. In December 2021, it raised $50 million in a Series B funding round led by Kleiner Perkins and GV (then Google Ventures). Synthesia gained a total valuation of $1 billion, and achieved unicorn status, when it raised $90 million from Accel and Nvidia partnership NVentures, in June 2023, during its Series C funding round. Counting 60,000 customers by January 2025, including over 60% of Fortune 100 companies; the company raised $180 million in a Series D round led by NEA, with new investors World Innovation Lab (WiL), Atlassian Ventures and PSP Growth, as well as existing investors GV, MMC Ventures and FirstMark, doubling Synthesia's valuation to $2.1 billion. Capital raised by 2025 had reached $330 million, with investments slated to further product innovation, talent growth, and company expansion in North America, Europe, Japan and Australia. In April 2025, Adobe Inc. invested £10 million in the company for a strategic partnership. Synthesia subsequently rejected a $3 billion acquisition offer from Adobe, choosing to remain independent. With a revenue stream then exceeding $100 million annually; GV led a Series E funding round in October 2025, resulting in Synthesia's $4 billion valuation, raising $200 million from GV, Nvidia and Accel to develop, in 2026, interactive audio-visual avatar "agents" that converse on topic, for automated sales training and corporate communications, such as recruiting. == Recognition == In 2021, Synthesia partnered with Lay's to create the Messi Messages campaign featuring Argentine footballer Lionel Messi. Users created personalized messages with Synthesia's software and sent custom artificial reality video messages from Messi based on their text input. The campaign received a Cannes Lion Award under the Bronze category. In February 2025, UK Science and Technology Minister Peter Kyle commended Synthesia's "pioneering generative AI innovations."
Quantum image processing
Quantum image processing (QIMP) is using quantum computing or quantum information processing to create and work with quantum images. Due to some of the properties inherent to quantum computation, notably entanglement and parallelism, it is hoped that QIMP technologies will offer capabilities and performances that surpass their traditional equivalents, in terms of computing speed, security, and minimum storage requirements. == Background == A. Y. Vlasov's work in 1997 focused on using a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images and detect the posture of certain targets. Notably, more optics-based interpretations for quantum imaging were initially experimentally demonstrated in and formalized in after seven years. In 2003, Salvador Venegas-Andraca and S. Bose presented Qubit Lattice, the first published general model for storing, processing and retrieving images using quantum systems. Later on, in 2005, Latorre proposed another kind of representation, called the Real Ket, whose purpose was to encode quantum images as a basis for further applications in QIMP. Furthermore, in 2010 Venegas-Andraca and Ball presented a method for storing and retrieving binary geometrical shapes in quantum mechanical systems in which it is shown that maximally entangled qubits can be used to reconstruct images without using any additional information. Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups: Quantum-assisted digital image processing (QDIP): These applications aim at improving digital or classical image processing tasks and applications. Optics-based quantum imaging (OQI) Classically inspired quantum image processing (QIMP) A survey of quantum image representation has been published in. Furthermore, the recently published book Quantum Image Processing provides a comprehensive introduction to quantum image processing, which focuses on extending conventional image processing tasks to the quantum computing frameworks. It summarizes the available quantum image representations and their operations, reviews the possible quantum image applications and their implementation, and discusses the open questions and future development trends. == Quantum image representations == There are various approaches for quantum image representation, that are usually based on the encoding of color information. A common representation is FRQI (Flexible Representation for Quantum Images), that captures the color and position at every pixel of the image, and defined as: | I ⟩ = 1 2 n ∑ i = 0 2 2 n − 1 | c i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{i=0}^{2^{2n-1}}\vert c_{i}\rangle \otimes \vert i\rangle } where | i ⟩ {\textstyle |i\rangle } is the position and | c i ⟩ = c o s θ i | 0 ⟩ + s i n θ i | 1 ⟩ {\textstyle \vert c_{i}\rangle =cos\theta _{i}\vert 0\rangle +sin\theta _{i}\vert 1\rangle } the color with a vector of angles θ i ∈ [ 0 , π / 2 ] {\textstyle \theta _{i}\in \left[0,\pi /2\right]} . As it can be seen, | c i ⟩ {\textstyle \vert c_{i}\rangle } is a regular qubit state of the form | ψ ⟩ = α | 0 ⟩ + β | 1 ⟩ {\displaystyle \vert \psi \rangle =\alpha \vert 0\rangle +\beta \vert 1\rangle } , with basis states | 0 ⟩ = ( 1 0 ) {\textstyle \vert 0\rangle ={\begin{pmatrix}1\\0\end{pmatrix}}} and | 1 ⟩ = ( 0 1 ) {\textstyle \vert 1\rangle ={\begin{pmatrix}0\\1\end{pmatrix}}} , as well as amplitudes α {\textstyle \alpha } and β {\textstyle \beta } that satisfy | α | 2 + | β | 2 = 1 {\textstyle \left|\alpha \right|^{2}+\left|\beta \right|^{2}=1} . Another common representation is MCQI (Multi-Channel Representation for Quantum Images), that uses the RGB channels with quantum states and following FRQI definition: | I ⟩ = 1 2 n + 1 ∑ i = 0 2 2 n − 1 | C R G B i ⟩ ⊗ | i ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n+1}}}\sum _{i=0}^{2^{2n-1}}\vert C_{RGB}^{i}\rangle \otimes \vert i\rangle } | C R G B i ⟩ = cos θ R i | 000 ⟩ + cos θ G i | 001 ⟩ + cos θ B i | 010 ⟩ + sin θ R i | 100 ⟩ + sin θ G i | 101 ⟩ + sin θ B i | 110 ⟩ + cos θ α | 011 ⟩ + sin θ α | 111 ⟩ {\displaystyle {\begin{aligned}{\begin{aligned}\vert C_{RGB}^{i}\rangle &={\cos \theta _{R}^{i}\vert 000\rangle }+{\cos \theta _{G}^{i}\vert 001\rangle }+{\cos \theta _{B}^{i}\vert 010\rangle }\\&\quad +{\sin \theta _{R}^{i}\vert 100\rangle }+{\sin \theta _{G}^{i}\vert 101\rangle }+{\sin \theta _{B}^{i}\vert 110\rangle }\\&\quad +{\cos {\theta _{\alpha }}\vert 011\rangle }+{\sin \theta _{\alpha }\vert 111\rangle }\end{aligned}}\end{aligned}}} Departing from the angle-based approach of FRQI and MCQI, and using a qubit sequence, NEQR (Novel Enhanced Representation for Quantum Images) is another representation approach, that uses a function f ( y , x ) = C y x q − 1 C y x q − 2 … C y x 1 C y x 0 {\textstyle f\left(y,x\right)=C_{yx}^{q-1}C_{yx}^{q-2}\ldots C_{yx}^{1}C_{yx}^{0}} to encode color values for a 2 n × 2 n {\displaystyle 2^{n}\times 2^{n}} image: | I ⟩ = 1 2 n ∑ y = 0 2 n − 1 ∑ x = 0 2 n − 1 | f ( y , x ) ⟩ | y x ⟩ {\displaystyle \vert I\rangle ={\frac {1}{2^{n}}}\sum _{y=0}^{2^{n}-1}\sum _{x=0}^{2^{n}-1}\vert f\left(y,x\right)\rangle \vert yx\rangle } == Quantum image manipulations == A lot of the effort in QIMP has been focused on designing algorithms to manipulate the position and color information encoded using flexible representation of quantum images (FRQI) and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations and restricted geometric transformations to constrain these operations to a specified area of an image were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image and quantum image scaling to resize a quantum image were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. Later, Multi-Channel Quantum Image-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels have been fully discussed. To illustrate the feasibility and capability of QIMP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction, quantum image segmentation, quantum image morphology, quantum image comparison, quantum image filtering, quantum image classification, quantum image stabilization, among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of watermarking, encryption, and steganography etc., which form the core security technologies highlighted in this area. In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIMP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols. == Quantum image transform == By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Given an image F = ( F i , j ) M × L {\displaystyle F=(F_{i,j})_{M\times L}} , where F i , j {\displaystyle F_{i,j}} represents the pixel value at position ( i , j ) {\displaystyle (i,j)} with i = 1 , … , M {\displaystyle i=1,\dots ,M} and j = 1 , … , L {\displaystyle j=1,\dots ,L} , a vector f → {\displaystyle {\vec {f}}} with M L {\displaystyle ML} elements can be formed by letting the first M {\displaystyle M} elements of f → {\displaystyle {\vec {f}}} be the first column of F {\displaystyle F} , the next M {\displaystyle M} elements the second column, etc. A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering. In the quantum computing, the linear transformation can be represented as | g ⟩ = U ^ | f ⟩ {\displaystyle |g\rangle ={\hat {U}}|f\rangle } with the input image state | f ⟩ {\displaystyle |f\rangle } and the output image state | g ⟩ {\displaystyle |g\rangle } . A unitary transformation can be implemented as a unitary evolution. Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, an
Immuni
Immuni was an open-source COVID-19 contact tracing app used for digital contact tracing in Italy, dismissed on 31 December 2022, after a long and debated criticism for having been a failure due to the lack of trust placed by citizens. Immuni COVID-19 contact-tracing app had in fact been downloaded only by 12% of Italians between 14 and 75 years old (the government had previously stated that, in order for the app to work properly, it should have been downloaded by at least 60% of Italians). It makes use of the Apple/Google Exposure Notification system. == Development == It was developed by Bending Spoons and released by the Italian Ministry of Health on 1 June 2020. After a testing phase in 4 Italian regions (Abruzzo, Apulia, Liguria, Marche), the app started being active in the whole country on 15 June 2020. The app was initially released on App Store and Google Play, and since 1 February 2021 it is available on the Huawei AppGallery as well. === Source code === The source code was published on GitHub on the 25 May. The app only works in Italy, but compatibility with other European contact tracing apps was a goal. Since 19 October 2020 the app supports key-exchanges with the EU Interoperability Gateway and is therefore able to communicate with contact tracing apps of other EU countries. == Shutdown == As of 16 December 2020, the app was downloaded more than 10 million times, a number which increased to 21.882.502 downloads the day before the app's shutdown. On 27 December 2022 the Italian Ministry of Health announced that the app and its infrastructures will be dismissed on the 31 December of the same year.