Fyre, formerly de Jong Explorer, is a cross-platform tool for producing artwork based on histograms of iterated chaotic functions. It implements the Peter de Jong map in a fixed function pipeline through either a GTK GUI frontend, or a command line facility for easier rendering of high-resolution, high quality images. The program was renamed from de Jong Explorer to Fyre simply because 'It wasn't taken yet' and so that in the future, it could support more functions than just the standard Peter de Jong map. Fyre features a sidebar on the left to which the user can input the required variables and on the right is displayed the result of the equation. == Extra features == Additional image manipulation tools such as Gaussian blurs and Gamma controls are included in the program. The advantage to using them directly within Fyre is that the image accuracy and quality do not decline. Fyre features animation capabilities so that a user can link together several maps and create uncompressed AVIs from them. However, the uncompressed animation files are very large and so should be compressed with a separate tool, such as mencoder. == Peter de Jong Map == For most values of a,b,c and d the point (x,y) moves chaotically. The resulting image is a map of the probability that the point lies within the area represented by each pixel. Therefore, the longer that the user lets Fyre render for, the larger the probability map becomes and the more accurate the resulting image.
DataScene
DataScene is a scientific graphing, animation, data analysis, and real-time data monitoring software package. It was developed with the Common Language Infrastructure technology and the GDI+ graphics library. With the two Common Language Runtime engines - the .Net and Mono frameworks - DataScene runs on all major operating systems. With DataScene, the user can plot 39 types 2D & 3D graphs (e.g., Area graph, Bar graph, Boxplot graph, Pie graph, Line graph, Histogram graph, Surface graph, Polar graph, Water Fall graph, etc.), manipulate, print, and export graphs to various formats (e.g., Bitmap, WMF/EMF, JPEG, PNG, GIF, TIFF, PostScript, and PDF), analyze data with different mathematical methods (fitting curves, calculating statics, FFT, etc.), create chart animations for presentations (e.g. with PowerPoint), classes, and web pages, and monitor and chart real-time data. == History == DataScene was first released (version 1.0) in March 2009 for the Windows platform and the .Net 2.0 framework. Since version 2.0, DataScene has been ported to the Mono framework 2.6 and all Linux and Unix/X11 operating systems. Cyberwit offers free licensing for the Express edition of DataScene.
Baum–Welch algorithm
In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch algorithm, the primary method for inference in hidden Markov models, is numerically unstable due to its recursive calculation of joint probabilities. As the number of variables grows, these joint probabilities become increasingly small, leading to the forward recursions rapidly approaching values below machine precision. == History == The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch. The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. One of the first major applications of HMMs was to the field of speech processing. In the 1980s, HMMs were emerging as a useful tool in the analysis of biological systems and information, and in particular genetic information. They have since become an important tool in the probabilistic modeling of genomic sequences. == Description == A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables. It relies on the assumption that the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variables depend only on the current hidden state. The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let X t {\displaystyle X_{t}} be a discrete hidden random variable with N {\displaystyle N} possible values (i.e. We assume there are N {\displaystyle N} states in total). We assume the P ( X t ∣ X t − 1 ) {\displaystyle P(X_{t}\mid X_{t-1})} is independent of time t {\displaystyle t} , which leads to the definition of the time-independent stochastic transition matrix A = { a i j } = P ( X t = j ∣ X t − 1 = i ) . {\displaystyle A=\{a_{ij}\}=P(X_{t}=j\mid X_{t-1}=i).} The initial state distribution (i.e. when t = 1 {\displaystyle t=1} ) is given by π i = P ( X 1 = i ) . {\displaystyle \pi _{i}=P(X_{1}=i).} The observation variables Y t {\displaystyle Y_{t}} can take one of K {\displaystyle K} possible values. We also assume the observation given the "hidden" state is time independent. The probability of a certain observation y i {\displaystyle y_{i}} at time t {\displaystyle t} for state X t = j {\displaystyle X_{t}=j} is given by b j ( y i ) = P ( Y t = y i ∣ X t = j ) . {\displaystyle b_{j}(y_{i})=P(Y_{t}=y_{i}\mid X_{t}=j).} Taking into account all the possible values of Y t {\displaystyle Y_{t}} and X t {\displaystyle X_{t}} , we obtain the N × K {\displaystyle N\times K} matrix B = { b j ( y i ) } {\displaystyle B=\{b_{j}(y_{i})\}} where b j {\displaystyle b_{j}} belongs to all the possible states and y i {\displaystyle y_{i}} belongs to all the observations. An observation sequence is given by Y = ( Y 1 = y 1 , Y 2 = y 2 , … , Y T = y T ) {\displaystyle Y=(Y_{1}=y_{1},Y_{2}=y_{2},\ldots ,Y_{T}=y_{T})} . Thus we can describe a hidden Markov chain by θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} . The Baum–Welch algorithm finds a local maximum for θ ∗ = a r g m a x θ P ( Y ∣ θ ) {\displaystyle \theta ^{}=\operatorname {arg\,max} _{\theta }P(Y\mid \theta )} (i.e. the HMM parameters θ {\displaystyle \theta } that maximize the probability of the observation). === Algorithm === Set θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} with random initial conditions. They can also be set using prior information about the parameters if it is available; this can speed up the algorithm and also steer it toward the desired local maximum. ==== Forward procedure ==== Let α i ( t ) = P ( Y 1 = y 1 , … , Y t = y t , X t = i ∣ θ ) {\displaystyle \alpha _{i}(t)=P(Y_{1}=y_{1},\ldots ,Y_{t}=y_{t},X_{t}=i\mid \theta )} , the probability of seeing the observations y 1 , y 2 , … , y t {\displaystyle y_{1},y_{2},\ldots ,y_{t}} and being in state i {\displaystyle i} at time t {\displaystyle t} . This is found recursively: α i ( 1 ) = π i b i ( y 1 ) , {\displaystyle \alpha _{i}(1)=\pi _{i}b_{i}(y_{1}),} α i ( t + 1 ) = b i ( y t + 1 ) ∑ j = 1 N α j ( t ) a j i . {\displaystyle \alpha _{i}(t+1)=b_{i}(y_{t+1})\sum _{j=1}^{N}\alpha _{j}(t)a_{ji}.} Since this series converges exponentially to zero, the algorithm will numerically underflow for longer sequences. However, this can be avoided in a slightly modified algorithm by scaling α {\displaystyle \alpha } in the forward and β {\displaystyle \beta } in the backward procedure below. ==== Backward procedure ==== Let β i ( t ) = P ( Y t + 1 = y t + 1 , … , Y T = y T ∣ X t = i , θ ) {\displaystyle \beta _{i}(t)=P(Y_{t+1}=y_{t+1},\ldots ,Y_{T}=y_{T}\mid X_{t}=i,\theta )} that is the probability of the ending partial sequence y t + 1 , … , y T {\displaystyle y_{t+1},\ldots ,y_{T}} given starting state i {\displaystyle i} at time t {\displaystyle t} . We calculate β i ( t ) {\displaystyle \beta _{i}(t)} as, β i ( T ) = 1 , {\displaystyle \beta _{i}(T)=1,} β i ( t ) = ∑ j = 1 N β j ( t + 1 ) a i j b j ( y t + 1 ) . {\displaystyle \beta _{i}(t)=\sum _{j=1}^{N}\beta _{j}(t+1)a_{ij}b_{j}(y_{t+1}).} ==== Update ==== We can now calculate the temporary variables, according to Bayes' theorem: γ i ( t ) = P ( X t = i ∣ Y , θ ) = P ( X t = i , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) β i ( t ) ∑ j = 1 N α j ( t ) β j ( t ) , {\displaystyle \gamma _{i}(t)=P(X_{t}=i\mid Y,\theta )={\frac {P(X_{t}=i,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)\beta _{i}(t)}{\sum _{j=1}^{N}\alpha _{j}(t)\beta _{j}(t)}},} which is the probability of being in state i {\displaystyle i} at time t {\displaystyle t} given the observed sequence Y {\displaystyle Y} and the parameters θ {\displaystyle \theta } ξ i j ( t ) = P ( X t = i , X t + 1 = j ∣ Y , θ ) = P ( X t = i , X t + 1 = j , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) a i j β j ( t + 1 ) b j ( y t + 1 ) ∑ k = 1 N ∑ w = 1 N α k ( t ) a k w β w ( t + 1 ) b w ( y t + 1 ) , {\displaystyle \xi _{ij}(t)=P(X_{t}=i,X_{t+1}=j\mid Y,\theta )={\frac {P(X_{t}=i,X_{t+1}=j,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)a_{ij}\beta _{j}(t+1)b_{j}(y_{t+1})}{\sum _{k=1}^{N}\sum _{w=1}^{N}\alpha _{k}(t)a_{kw}\beta _{w}(t+1)b_{w}(y_{t+1})}},} which is the probability of being in state i {\displaystyle i} and j {\displaystyle j} at times t {\displaystyle t} and t + 1 {\displaystyle t+1} respectively given the observed sequence Y {\displaystyle Y} and parameters θ {\displaystyle \theta } . The denominators of γ i ( t ) {\displaystyle \gamma _{i}(t)} and ξ i j ( t ) {\displaystyle \xi _{ij}(t)} are the same ; they represent the probability of making the observation Y {\displaystyle Y} given the parameters θ {\displaystyle \theta } . The parameters of the hidden Markov model θ {\displaystyle \theta } can now be updated: π i ∗ = γ i ( 1 ) , {\displaystyle \pi _{i}^{}=\gamma _{i}(1),} which is the expected frequency spent in state i {\displaystyle i} at time 1 {\displaystyle 1} . a i j ∗ = ∑ t = 1 T − 1 ξ i j ( t ) ∑ t = 1 T − 1 γ i ( t ) , {\displaystyle a_{ij}^{}={\frac {\sum _{t=1}^{T-1}\xi _{ij}(t)}{\sum _{t=1}^{T-1}\gamma _{i}(t)}},} which is the expected number of transitions from state i to state j compared to the expected total number of transitions starting in state i, including from state i to itself. The number of transitions starting in state i is equivalent to the number of times state i is observed in the sequence from t = 1 to t = T − 1. b i ∗ ( v k ) = ∑ t = 1 T 1 y t = v k γ i ( t ) ∑ t = 1 T γ i ( t ) , {\displaystyle b_{i}^{}(v_{k})={\frac {\sum _{t=1}^{T}1_{y_{t}=v_{k}}\gamma _{i}(t)}{\sum _{t=1}^{T}\gamma _{i}(t)}},} where 1 y t = v k = { 1 if y t = v k , 0 otherwise {\displaystyle 1_{y_{t}=v_{k}}={\begin{cases}1&{\text{if }}y_{t}=v_{k},\\0&{\text{otherwise}}\end{cases}}} is an indicator function, and b i ∗ ( v k ) {\displaystyle b_{i}^{}(v_{k})} is the expected number of times the output observations have been equal to v k {\displaystyle v_{k}} while in state i {\displaystyle i} over the expected total number of times in state i {\displaystyle i} . These steps are now repeated iteratively until a desired level of convergence. Note: It is possible to over-fit a particular data set. That is, P ( Y ∣ θ final ) > P ( Y ∣ θ true ) {\displaystyle P(Y\mid \theta _{\text{final}})>P(Y\mid \theta _{\text{true}})} . The algorithm also does not guarantee a global maximum. ==== Multiple sequences ==== The algorithm described thus far assumes a single observed sequence Y = y 1 , … , y T {\displaystyle Y=y_{1},\ldots ,y_{T}} . However, in many situations, there are several sequences observed: Y 1 ,
Top 10 AI Bug Finders Compared (2026)
Trying to pick the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
StarDict
StarDict, developed by Hu Zheng (胡正), is a free GUI released under the GPL-3.0-or-later license for accessing StarDict dictionary files (a dictionary shell). It is the successor of StarDic, developed by Ma Su'an (馬蘇安), continuing its version numbers. According to StarDict's earlier homepage on SourceForge, the project has been removed from SourceForge due to copyright infringement reports. It moved to Google Code and then back to SourceForge, while development is now seemingly continued on GitHub. == Supported platforms == StarDict runs under Linux, Windows, FreeBSD, Maemo and Solaris. Dictionaries of the user's choice are installed separately. Dictionary files can be created by converting dict files. Several programs compatible with the StarDict dictionary format are available for different platforms. For the iPhone, iPod Touch and iPad, applications available in the App Store include GuruDic, TouchDict, weDict, Dictionary Universal, Alpus and others, as well as the free iStarDict, which is available for the Cydia Store. == Dictionaries available == One can find here the partial list of FreeDict dictionaries which can be converted to the StarDict format. These include, in particular, some older versions of Webster's dictionary and many dictionaries for various languages. == Features == While StarDict is in scan mode, results are displayed in a tooltip, allowing easy dictionary lookup. When combined with Freedict, StarDict will quickly provide rough translations of foreign language websites. On September 25, 2006, an online version of Stardict began operation. This online version includes access to all the major dictionaries of StarDict, as well as Wikipedia in Chinese. Previous versions of StarDict were very similar to the PowerWord dictionary program, which is developed by a Chinese company, KingSoft. Since version 2.4.2, however, StarDict has diverged from the design of PowerWord by increasing its search capabilities and adding lexicons in a variety of languages. This was assisted by the collaboration of many developers with the author. == sdcv == Evgeniy A. Dushistov produced a command line version of StarDict called sdcv. It employed all the dictionary files that belong to StarDict. It is written in C++ and licensed under the terms of the GNU General Public License. sdcv runs under Linux, FreeBSD, and Solaris. As in StarDict, dictionaries of the user's choice have to be installed separately. At the end of 2006, software developer Hu Zheng cited personal financial problems as an excuse to charge users for downloading dictionary files from his website, which temporarily aroused strong doubts and dissatisfaction in the Linux community. In the end, under the pressure of public opinion, the charging plan was forced to be canceled and ended hastily.
Powerset (company)
Powerset was an American company based in San Francisco, California, that, in 2006, was developing a natural language search engine for the Internet. On July 1, 2008, Powerset was acquired by Microsoft for an estimated $100 million (~$143 million in 2024). Powerset was working on building a natural language search engine that could find targeted answers to user questions (as opposed to keyword based search). For example, when confronted with a question like "Which U.S. state has the highest income tax?", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the process of "building a natural language search engine that reads and understands every sentence on the Web". The company has licensed natural language technology from PARC, the former Xerox Palo Alto Research Center. On May 11, 2008, the company unveiled a tool for searching a fixed subset of English Wikipedia using conversational phrases rather than keywords. Acquisition by Microsoft: One significant milestone in Powerset's history was its acquisition by Microsoft on July 1, 2008, for an estimated $100 million. This acquisition was part of Microsoft's broader strategy to enhance its search capabilities and compete more effectively with other search engine providers, particularly Google. Natural Language Search Engine: Powerset's primary focus was on developing a natural language search engine capable of understanding and interpreting user queries in a more human-like manner. Instead of simply matching keywords, Powerset aimed to comprehend the meaning behind the words, allowing for more accurate and contextually relevant search results. Technology and Partnerships: Powerset had licensed natural language technology from PARC, the Xerox Palo Alto Research Center. This technology likely played a crucial role in the development of Powerset's NLP capabilities. Wikipedia Search Tool: In May 2008, Powerset unveiled a search tool that allowed users to search a fixed subset of English Wikipedia using conversational phrases rather than traditional keywords. This demonstrated the potential of Powerset's NLP technology in providing more precise and relevant search results. == Powerlabs == In a form of beta testing, Powerset opened an online community called Powerlabs on September 17, 2007. Business Week said: "The company hopes the site will marshal thousands of people to help build and improve its search engine before it goes public next year." Said The New York Times: "[Powerset Labs] goes far beyond the 'alpha' or 'beta' testing involved in most software projects, when users put a new product through rigorous testing to find its flaws. Powerset doesn’t have a product yet, but rather a collection of promising natural language technologies, which are the fruit of years of research at Xerox PARC." Powerlabs' initial search results are taken from Wikipedia. == Notable people == Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge University in 1993, where he was a Marshall Scholar. He has worked at NASA, as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000) and at Whizbang! Labs. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Steve Newcomb was the COO and co-founder of Powerset. Prior to joining Powerset, he was a co-founder of Loudfire, General Manager at Promptu, and was on the board of directors at Jaxtr. He left Powerset in October 2007 to form Virgance, a social startup incubator. Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin. Ronald Kaplan, former manager of research in Natural Language Theory and Technology at PARC, served as the company's CTO and CSO. Ryan Ferrier is a member of the founding team of Powerset. He managed personnel and internal operations. After 2008 he went on to co-found Serious Business, which made Facebook applications and was later bought by Zynga. Another Powerset alumnus, Alex Le, became CTO of Serious Business and went on to become an executive producer at Zynga when it bought the company. Siqi Chen founded a stealth startup in mobile computing after leaving Powerset. Tom Preston-Werner worked at Powerset and left after the acquisition to found GitHub. == Investors == Powerset attracted a wide range of investors, many of whom had considerable experience in the venture capital field. The company received $12.5 million (~$18.2 million in 2024) in Series A funding during November 2007, co-led by the venture capital firms Foundation Capital and The Founders Fund. Among the better-known investors: Esther Dyson, founding chairman of ICANN, founder of the newsletter Release 1.0 and editor at Cnet Peter Thiel, founder and former CEO of PayPal Luke Nosek, founder of PayPal Todd Parker. Managing Partner, Hidden River Ventures Reid Hoffman, executive vice president of PayPal and founder of LinkedIn First Round Capital, seed-stage venture firm
How to Choose an AI Avatar Generator
Trying to pick the best AI avatar generator? An AI avatar generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI avatar generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.