A deadbot, deathbot, or griefbot is a digital avatar, created with artificial intelligence, which resembles a person who is dead. Griefbots employ natural language processing and machine-learning techniques to approximate the style and personality of a deceased person. They may appear as chatbots, voice assistants, or animated avatars, and are often trained on an individual's digital remains. == History == Among the earliest researchers, Muhammad Aurangzeb Ahmad of the University of Washington, developed the Grandpa Bot project, a conversational simulation of his late father designed for his children to interact with. Other efforts include journalist James Vlahos's Dadbot, which evolved into the commercial platform HereAfter AI. Hossein Rahnama's Augmented Eternity research at MIT Media Lab and Toronto Metropolitan University, and game designer Jason Rohrer's "Project December", have enabled users to converse with language-model representations of loved ones. Early commercial projects such as Eternime, founded by Marius Ursache, also popularized the notion of interactive digital immortality. == Cultural and societal impact == Scholars have proposed frameworks and critiques addressing the ethics of these technologies. Tomasz Hollanek and Katarzyna Nowaczyk-Basińska developed a design-ethics taxonomy distinguishing the data donor, data recipient, and interactant. Edina Harbinja and Lilian Edwards formalized the concept of post-mortem privacy, and Carl J. Öhman at the Oxford Internet Institute studied the management of large-scale digital remains. Cultural acceptance varies: while some view them as expressions of remembrance, others regard them as unsettling or ethically problematic. Concerns have been raised about deadbots' potential for creating psychological harm. Griefbots are considered part of the phenomenon of artificial intimacy.
Intelligent decision support system
An intelligent decision support system (IDSS) is a decision support system that makes extensive use of artificial intelligence (AI) techniques. Use of AI techniques in management information systems has a long history – indeed terms such as "Knowledge-based systems" (KBS) and "intelligent systems" have been used since the early 1980s to describe components of management systems, but the term "Intelligent decision support system" is thought to originate with Clyde Holsapple and Andrew Whinston in the late 1970s. Examples of specialized intelligent decision support systems include Flexible manufacturing systems (FMS), intelligent marketing decision support systems and medical diagnosis systems. Ideally, an intelligent decision support system should behave like a human consultant: supporting decision makers by gathering and analysing evidence, identifying and diagnosing problems, proposing possible courses of action and evaluating such proposed actions. The aim of the AI techniques embedded in an intelligent decision support system is to enable these tasks to be performed by a computer, while emulating human capabilities as closely as possible. Many IDSS implementations are based on expert systems, a well established type of KBS that encode knowledge and emulate the cognitive behaviours of human experts using predicate logic rules, and have been shown to perform better than the original human experts in some circumstances. Expert systems emerged as practical applications in the 1980s based on research in artificial intelligence performed during the late 1960s and early 1970s. They typically combine knowledge of a particular application domain with an inference capability to enable the system to propose decisions or diagnoses. Accuracy and consistency can be comparable to (or even exceed) that of human experts when the decision parameters are well known (e.g. if a common disease is being diagnosed), but performance can be poor when novel or uncertain circumstances arise. Research in AI focused on enabling systems to respond to novelty and uncertainty in more flexible ways is starting to be used in IDSS. For example, intelligent agents that perform complex cognitive tasks without any need for human intervention have been used in a range of decision support applications. Capabilities of these intelligent agents include knowledge sharing, machine learning, data mining, and automated inference. A range of AI techniques such as case based reasoning, rough sets and fuzzy logic have also been used to enable decision support systems to perform better in uncertain conditions. A 2009 research about a multi-artificial system intelligence system named IILS is proposed to automate problem-solving processes within the logistics industry. The system involves integrating intelligence modules based on case-based reasoning, multi-agent systems, fuzzy logic, and artificial neural networks aiming to offer advanced logistics solutions and support in making well-informed, high-quality decisions to address a wide range of customer needs and challenges.
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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
Mark Heimann
Mark A. Heimann is an American chess grandmaster and machine learning researcher. == Chess career == Heimann began playing chess at the age of 5 after his father bought him and his twin brother Alexander a chess set. He then won several national grade-level championships as well as the Pennsylvania and Ohio state championships in middle school and high school. In October 2007, he was ranked as the national #2 under-14 player, only behind future grandmaster Marc Tyler Arnold. In the February 2008 national rankings, he moved up to being the top-ranked under-14 player. In December 2012, he played for Washington University St. Louis' "A" team in the Pan-American Intercollegiate Chess Championships, where he was the second-most successful player, recording 4 wins, 1 draw, and 1 loss. The university's team also won the Division II championship title. In three tournaments between September and December 2022, Heimann earned three international master title norms, earning the international master title at the age of 29. In November 2024, he scored a GM norm at the U.S. Masters Chess Championship. He finished the event in joint-6th place. The following week, at the Saint Louis Masters tournament, he earned his final grandmaster norm and crossed 2500 in live rating, achieving the Grandmaster title. It was formally awarded to him in April 2025. == Research career == He obtained a bachelor's degree from Washington University in St. Louis in the School of Arts and Sciences and got his PhD from the University of Michigan. He is a machine learning researcher at Lawrence Livermore National Laboratory. == Personal life == Outside of chess and research, he also plays several instruments and is a competitive powerlifter.
Deconvolution
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of weather forecasting and economics. == Description == In general, the objective of deconvolution is to find the solution f of a convolution equation of the form: f ∗ g = h {\displaystyle fg=h\,} Usually, h is some recorded signal, and f is some signal that we wish to recover, but has been convolved with a filter or distortion function g, before we recorded it. Usually, h is a distorted version of f and the shape of f can't be easily recognized by the eye or simpler time-domain operations. The function g represents the impulse response of an instrument or a driving force that was applied to a physical system. If we know g, or at least know the form of g, then we can perform deterministic deconvolution. However, if we do not know g in advance, then we need to estimate it. This can be done using methods of statistical estimation or building the physical principles of the underlying system, such as the electrical circuit equations or diffusion equations. There are several deconvolution techniques, depending on the choice of the measurement error and deconvolution parameters: === Raw deconvolution === When the measurement error is very low (ideal case), deconvolution collapses into a filter reversing. This kind of deconvolution can be performed in the Laplace domain. By computing the Fourier transform of the recorded signal h and the system response function g, you get H and G, with G as the transfer function. Using the convolution theorem, F = H / G {\displaystyle F=H/G\,} where F is the estimated Fourier transform of f. Finally, the inverse Fourier transform of the function F is taken to find the estimated deconvolved signal f. Note that G is at the denominator and could amplify elements of the error model if present. === Deconvolution with noise === In physical measurements, the situation is usually closer to ( f ∗ g ) + ε = h {\displaystyle (fg)+\varepsilon =h\,} In this case ε is noise that has entered our recorded signal. If a noisy signal or image is assumed to be noiseless, the statistical estimate of g will be incorrect. In turn, the estimate of ƒ will also be incorrect. The lower the signal-to-noise ratio, the worse the estimate of the deconvolved signal will be. That is the reason why inverse filtering the signal (as in the "raw deconvolution" above) is usually not a good solution. However, if at least some knowledge exists of the type of noise in the data (for example, white noise), the estimate of ƒ can be improved through techniques such as Wiener deconvolution. == Applications == === Seismology === The concept of deconvolution had an early application in reflection seismology. In 1950, Enders Robinson was a graduate student at MIT. He worked with others at MIT, such as Norbert Wiener, Norman Levinson, and economist Paul Samuelson, to develop the "convolutional model" of a reflection seismogram. This model assumes that the recorded seismogram s(t) is the convolution of an Earth-reflectivity function e(t) and a seismic wavelet w(t) from a point source, where t represents recording time. Thus, our convolution equation is s ( t ) = ( e ∗ w ) ( t ) . {\displaystyle s(t)=(ew)(t).\,} The seismologist is interested in e, which contains information about the Earth's structure. By the convolution theorem, this equation may be Fourier transformed to S ( ω ) = E ( ω ) W ( ω ) {\displaystyle S(\omega )=E(\omega )W(\omega )\,} in the frequency domain, where ω {\displaystyle \omega } is the frequency variable. By assuming that the reflectivity is white, we can assume that the power spectrum of the reflectivity is constant, and that the power spectrum of the seismogram is the spectrum of the wavelet multiplied by that constant. Thus, | S ( ω ) | ≈ k | W ( ω ) | . {\displaystyle |S(\omega )|\approx k|W(\omega )|.\,} If we assume that the wavelet is minimum phase, we can recover it by calculating the minimum phase equivalent of the power spectrum we just found. The reflectivity may be recovered by designing and applying a Wiener filter that shapes the estimated wavelet to a Dirac delta function (i.e., a spike). The result may be seen as a series of scaled, shifted delta functions (although this is not mathematically rigorous): e ( t ) = ∑ i = 1 N r i δ ( t − τ i ) , {\displaystyle e(t)=\sum _{i=1}^{N}r_{i}\delta (t-\tau _{i}),} where N is the number of reflection events, r i {\displaystyle r_{i}} are the reflection coefficients, t − τ i {\displaystyle t-\tau _{i}} are the reflection times of each event, and δ {\displaystyle \delta } is the Dirac delta function. In practice, since we are dealing with noisy, finite bandwidth, finite length, discretely sampled datasets, the above procedure only yields an approximation of the filter required to deconvolve the data. However, by formulating the problem as the solution of a Toeplitz matrix and using Levinson recursion, we can relatively quickly estimate a filter with the smallest mean squared error possible. We can also do deconvolution directly in the frequency domain and get similar results. The technique is closely related to linear prediction. === Optics and other imaging === In optics and imaging, the term "deconvolution" is specifically used to refer to the process of reversing the optical distortion that takes place in an optical microscope, electron microscope, telescope, or other imaging instrument, thus creating clearer images. It is usually done in the digital domain by a software algorithm, as part of a suite of microscope image processing techniques. Deconvolution is also practical to sharpen images that suffer from fast motion or jiggles during capturing. Early Hubble Space Telescope images were distorted by a flawed mirror and were sharpened by deconvolution. The usual method is to assume that the optical path through the instrument is optically perfect, convolved with a point spread function (PSF), that is, a mathematical function that describes the distortion in terms of the pathway a theoretical point source of light (or other waves) takes through the instrument. Usually, such a point source contributes a small area of fuzziness to the final image. If this function can be determined, it is then a matter of computing its inverse or complementary function, and convolving the acquired image with that. The result is the original, undistorted image. In practice, finding the true PSF is impossible, and usually an approximation of it is used, theoretically calculated or based on some experimental estimation by using known probes. Real optics may also have different PSFs at different focal and spatial locations, and the PSF may be non-linear. The accuracy of the approximation of the PSF will dictate the final result. Different algorithms can be employed to give better results, at the price of being more computationally intensive. Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information. Regularization in iterative algorithms (as in expectation-maximization algorithms) can be applied to avoid unrealistic solutions. When the PSF is unknown, it may be possible to deduce it by systematically trying different possible PSFs and assessing whether the image has improved. This procedure is called blind deconvolution. Blind deconvolution is a well-established image restoration technique in astronomy, where the point nature of the objects photographed exposes the PSF thus making it more feasible. It is also used in fluorescence microscopy for image restoration, and in fluorescence spectral imaging for spectral separation of multiple unknown fluorophores. The most common iterative algorithm for the purpose is the Richardson–Lucy deconvolution algorithm; the Wiener deconvolution (and approximations) are the most common non-iterative algorithms. For some specific imaging systems such as laser pulsed terahertz systems, PSF can be modeled mathematically. As a result, as shown in the figure, deconvolution of the modeled PS
Top 10 AI Photo Editors Compared (2026)
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