Fuzzy differential inclusion is the extension of differential inclusion to fuzzy sets introduced by Lotfi A. Zadeh. x ′ ( t ) ∈ [ f ( t , x ( t ) ) ] α {\displaystyle x'(t)\in [f(t,x(t))]^{\alpha }} with x ( 0 ) ∈ [ x 0 ] α {\displaystyle x(0)\in [x_{0}]^{\alpha }} Suppose f ( t , x ( t ) ) {\displaystyle f(t,x(t))} is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal, upper semi-continuous, convex, compactly supported fuzzy subsets of R n {\displaystyle \mathbb {R} ^{n}} . == Second order differential == The second order differential is x ″ ( t ) ∈ [ k x ] α {\displaystyle x''(t)\in [kx]^{\alpha }} where k ∈ [ K ] α {\displaystyle k\in [K]^{\alpha }} , K {\displaystyle K} is trapezoidal fuzzy number ( − 1 , − 1 / 2 , 0 , 1 / 2 ) {\displaystyle (-1,-1/2,0,1/2)} , and x 0 {\displaystyle x_{0}} is a trianglular fuzzy number (-1,0,1). == Applications == Fuzzy differential inclusion (FDI) has applications in Cybernetics Artificial intelligence, Neural network, Medical imaging Robotics Atmospheric dispersion modeling Weather forecasting Cyclone Pattern recognition Population biology
Photoanalysis
Photoanalysis (or photo analysis) refers to the study of pictures to compile various types of data, for example, to measure the size distribution of virtually anything that can be captured by photo. Photoanalysis technology has changed the way mines and mills quantify fragmented material. Images are an effective way to document conditions before, after, and even during blasting activities. The technology is advancing at a high rate, and lenses, storage media memory, light sensitivity and resolution have been improving steadily. Today's digital cameras and camcorders include high-resolution optics, compact size, automatic time and date stamps, good battery life, shutters to freeze motion, and computers to autofocus and eliminate jitter using image stabilization. == Mining == Photoanalysis in mining operations can provide an automated system that forewarns a company of potential problems with materials, leading to economies and reduced damage caused from over-sized materials. It can also help determine the effectiveness of blasts. A company can use this technology to monitor materials moving on a conveyor belt in an underground environment, to measure piles left over from a blast, and even measure the amount of material being carried by dump trucks or vessels to a destination. Photoanalysis is being used on SAG mills worldwide to control the size of rock being crushed. Companies are using this technology to determine the size of particles being processed in the SAG Mill.[1] Archived 2009-05-23 at the Wayback Machine Having oversize material entering the SAG mill makes an operation less efficient, costing companies money in electrical and maintenance costs. Photoanalysis technology can eliminate unwanted material before it enters the mill, keeping rock crushing costs low. == Forestry == Wood chip size can affect the overall quality of a product. With automated photoanalysis systems, companies can remove any unwanted wrong-size particles without stopping their mill process. Photoanalysis can affect how efficiently forestry companies operate. In mills worldwide, photoanalysis technology is improving the use of lumber products, cutting back on the amount of trees being used to operate, and saving companies money through quality control optimization.[2] With the current downturn in the North American forestry industry, operators are looking at making their mills more efficient and effective when processing materials. Photoanalysis technology helps identify any weaknesses in the process by continuously monitoring different sections of an operation. == Agriculture == Agricultural companies can, using photoanalysis, monitor conveyor belts of food without contaminating the product by touching it. Other benefits of photoanalysis systems include: Automated removal of any unwanted material on food conveyor Improved quality control for the most important parts of the agricultural process Pinpoint accuracy that helps the efficiency and effectiveness of product handling techniques The importance of photoanalysis technology is being noticed by the agricultural industry as it identifies any unwanted materials going through the process. In an example, if a mouse is on a conveyor of corn, photoanalysis technology would be able to identify the unwanted object and remove it before it contaminates the whole process. == Origins of photoanalysis technology == Photoanalysis technology was created by using the Waterloo Image Enhancement Process in the 1980s. After further development of the imaging process with explosives producer DuPont, engineers Tom Palangio and Takis Katsabanis began selling photoanalysis software commercially. They later renamed the process WipFrag, standing for Waterloo Image Process Fragmentation Today, photoanalysis technology has evolved into stabilized and portable systems that can automatically capture and analyze results instantly. Thousands of these products are currently being used around the world to measure fragmented material. == Photoanalysis equipment photos == == Fragmentation analysis == Fragmentation analysis is becoming a popular term in mining, agricultural and forestry industries. With the majority of money in these industries directed towards the proper sizing of materials, companies are using fragmentation analysis to determine various factors within an operation.[3] The two main ways a company keeps track of fragmented material are through manual and automated sieving procedures. Manual sieving involves extracting a sample of material to analyze the size distribution. The results can be tabulated within two days. Automated sieving is an advanced way of sieving materials running through a process. Without having to extract the material, photoanalysis can take place, allowing for immediate results with pinpoint accuracy. == Blast Fragmentation Software == Operators are using fragmentation analysis to determine the effectiveness of various blasts. With automated sieving technology, workers can track the success of these blasts and receive instant results. Companies are using these results to determine what blasting method yielded the best results for their specific operation. The common variables associated with blast optimization are the provided Particle Size Distribution (PSD) from a shovel fragmentation system, geology including rock type and fracturing, and energy factor. By using photoanalysis the fragmented materials can be monitored, offering pinpoint accuracy and allowing mine operators to make adjustments to future blasting procedures. See Optical Granulometry to view the automated sieving process. == Pre-crushing analysis == Maintenance costs can be significantly reduced if an operation focuses on the fragmentation of the particles passing through their process. Automated sieving systems can detect and help remove any oversize material before it enters the crusher and causes maintenance problems. It also helps determine the effectiveness of the mining process prior to crushing; the sizing of material is always a critical part of operations in the mining, forestry and agricultural industries. Having an analysis taking place at every major point in an operation allows for the proper tracking of material being processed. Engineers can then determine what part of the process needs improving based solely on the size of material. == Post-crushing analysis == Measuring how effective industrial crushers are, can help save a company millions of dollars in energy costs on an annual basis. There are two components that affect a typical crusher: the size of the material inputted, and the speed at which the crusher is moving. If the user can find a perfect balance between these two components, the materials will be crushed to the right size in the shortest time possible. Meeting the material standards set by governments and large companies can be hard. Having a post-crushing analysis taking place ensures that no oversize material gets shipped; eliminating the chance of getting fined for not meeting industry specifications.
Context-sensitive user interface
A context-sensitive user interface offers the user options based on the state of the active program. Context sensitivity is ubiquitous in current graphical user interfaces, often in context menus. A user-interface may also provide context sensitive feedback, such as changing the appearance of the mouse pointer or cursor, changing the menu color, or with auditory or tactile feedback. == Reasoning and advantages of context sensitivity == The primary reason for introducing context sensitivity is to simplify the user interface. Advantages include: Reduced number of commands required to be known to the user for a given level of productivity. Reduced number of clicks or keystrokes required to carry out a given operation. Allows consistent behaviour to be pre-programmed or altered by the user. Reduces the number of options needed on screen at one time. === Disadvantages === Context sensitive actions may be perceived as dumbing down of the user interface, leaving the operator at a loss as to what to do when the computer decides to perform an unwanted action. Additionally non-automatic procedures may be hidden or obscured by the context sensitive interface causing an increase in user workload for operations the designers did not foresee. A poor implementation can be more annoying than helpful – a classic example of this is Office Assistant. == Implementation == At the simplest level each possible action is reduced to a single most likely action – the action performed is based on a single variable (such as file extension). In more complicated implementations multiple factors can be assessed such as the user's previous actions, the size of the file, the programs in current use, metadata etc. The method is not only limited to the response to imperative button presses and mouse clicks – pop-up menus can be pruned and/or altered, or a web search can focus results based on previous searches. At higher levels of implementation context sensitive actions require either larger amounts of meta-data, extensive case analysis based programming, or other artificial intelligence algorithms. === In computer and video games === Context sensitivity is important in video games, especially those controlled by a gamepad, joystick or computer mouse in which the number of buttons available is limited. It is primarily applied when the player is in a certain place and is used to interact with a person or object. For example, if the player is standing next to a non-player character, an option may come up allowing the player to talk with them. Implementations range from the embryonic 'Quick Time Event' to context sensitive sword combat in which the attack used depends on the position and orientation of both the player and opponent, as well as the virtual surroundings. A similar range of use is found in the 'action button' which, depending upon the in-game position of the player's character, may cause it to pick something up, open a door, grab a rope, punch a monster or opponent, or smash an object. The response does not have to be player activated – an on-screen device may only be shown in certain circumstances, e.g. 'targeting' cross hairs in a flight combat game may indicate the player should fire. An alternative implementation is to monitor the input from the player (e.g. level of button pressing activity) and use that to control the pace of the game in an attempt to maximize enjoyment or to control the excitement or ambience. The method has become increasingly important as more complex games are designed for machines with few buttons (keyboard-less consoles). Bennet Ring commented (in 2006) that "Context-sensitive is the new lens flare". === Context-sensitive help === Context sensitive help is a common implementation of context sensitivity, a single help button is actioned and the help page or menu will open a specific page or related topic.
AI-generated content in American politics
In American politics since the 2020s, political figures have deployed AI-generated images, videos, and audio to attack opponents, create misleading narratives, or inflame emotions. The use of generative AI by American political figures has been subject to criticism from many sides of the political spectrum. Republican president Donald Trump has notably used generative AI in several posts to Truth Social during his second term, many of which have made headlines due to their inflammatory nature. == Background == Generative artificial intelligence is a subfield of artificial intelligence that uses generative models to generate text, images, videos, audio, software code or other forms of data. In the mid 2020s with the release of 15.ai, ChatGPT, DALL-E and other generative artificial intelligence applications there was an AI boom. There has been an increase of usage of generative-AI within the United States political field during this boon, with both Republican and Democratic party members using it. The Trump administration during his second term, have embraced the use of AI-generated images, causing some misinformation experts to raise concerns about the continued usage would cause the erosion of public perception of the truth. In response to some criticisms White House deputy communications director Kaelan Dorr posted on X that the "memes will continue" with White House deputy press secretary Abigail Jackson also mocking concerns. == History of usage == === 2023 === In April 2023, the Republican National Committee released an attack ad made entirely with AI-generated images depicting a dystopian future under Joe Biden's re-election. === 2024 === Generative AI has increased the efficiency with which political candidates were able to raise money by analyzing donor data and identifying possible donors and target audiences. In March 2024 Democratic consultant working for Dean Phillips has admitted to using AI to generate a robocall which used Joe Biden's voice to discourage voter participation. In August 2024, The Atlantic noted that AI slop was becoming associated with the political right in the United States, who were using it for shitposting and engagement farming on social media, with the technology offering "cheap, fast, on-demand fodder for content". AI slop is frequently used in political campaigns in an attempt at gaining attention through content farming. === 2025 === The initial version of the Make Our Children Healthy Again Assessment of children's health issues, released by a commission of cabinet members and officials of the Trump administration, and led by US Department of Health and Human Services Secretary Robert F. Kennedy Jr., reportedly cited nonexistent and garbled references generated using artificial intelligence. Democratic governor Gavin Newsom has used AI-generated images to criticize Trump. In the midst of disruptions to food stamp distribution during the 2025 US government shutdown, anonymous social media users began using OpenAI's Sora to post slop videos of welfare queens complaining, stealing, and rioting in supermarkets; many comments to the videos appeared unaware that they were AI-generated, or acknowledged that they were AI-generated but nonetheless useful in pushing a narrative of widespread welfare fraud. On September 6, 2025, Trump posted an image on Truth Social making a reference to "Chipocalypse Now". Trump's post consisted of an AI-generated image showing Trump frowning and wearing a U.S. Cavalry hat and sunglasses, in front of Lake Michigan with the city of Chicago behind him with a smoke and fire spread across the background with five U.S. Army helicopters in the sky. The words "Chipocalypse Now" are rendered in a font resembling that in which the title of the 1979 film Apocalypse Now was styled. === 2026 === On February 5, 2026, Donald Trump shared a video of Barack and Michelle Obama depicted as apes in a Truth Social post. The two-second AI-generated clip of the Obamas portrayed as apes set to "The Lion Sleeps Tonight" appeared at the end of a one-minute two second long video, the rest of which was about false claims of voter fraud during the 2020 presidential election. The post received at least 4,650 likes, 409 comments, and 1,470 reTruths before it was deleted the next morning. The short clip was part of a longer AI-generated video posted in October 2025. The post received widespread backlash and bipartisan condemnation of the video as racist. In April 2026, Trump posted a picture of himself depicted as Jesus, drawing widespread criticism from Evangelicals and Catholics, resulting in Trump deleting the post hours later and claiming he believed he was depicted as a doctor. == Examples of use == === Election campaigns === In 2023, while he was still running for re-election, the presidential campaign of Joe Biden prepared a task force to respond to AI images and videos. The campaign for the 2024 Republican nominee, Donald Trump, has used deepfake videos of political opponents in campaign ads and fake images showing Trump with black supporters. During the first five months of his second term in 2025, Trump posted several AI-generated images of himself on official government social media accounts, including him as the Pope, him as a Jedi, and him as a muscular man. In August 2024, Trump posted a series of AI-generated images on his social media platform, Truth Social, that portrayed fans of the singer Taylor Swift in "Swifties for Trump" T-shirts, as well as a photo of the singer herself appearing to endorse Trump's 2024 presidential campaign. The images originated from the conservative Twitter account @amuse, which posted numerous AI slop images leading up to the 2024 United States elections that were shared by other high-profile figures within the US Republican Party, such as Elon Musk, who has publicly endorsed the utilization of generative AI, furthering this association. In 2024, Michigan GOP candidate Anthony Hudson posted an AI-generated video showing Martin Luther King Jr. endorsing his campaign, later claiming it was uploaded by a volunteer. In his 2025 bid to be the Democratic nominee for governor of New Jersey, Rep. Josh Gottheimer drew attention and criticism when he released a TV ad that used AI to portray him as a shirtless boxer sparring with Donald Trump in a boxing ring. In November 2025, the campaign of Mike Collins, a GOP candidate in the 2026 United States Senate election in Georgia released a fake video, generated by artificial intelligence, that depicted Democrat Jon Ossoff defending his vote on the 2025 United States federal government shutdown by declaring he could never say no to Chuck Schumer and that SNAP recipients did not attend his out-of-state fundraisers. The Collins campaign also shared an AI-generated video featuring Collins as a shirtless blue jeans model, referencing an American Eagle Outfitters advertisement featuring Sydney Sweeney. During the 2026 Los Angeles mayoral election, candidate Spencer Pratt reposted an AI-generated video portraying Pratt as Batman and prominent California politicians such as Karen Bass, Gavin Newsom, and Kamala Harris, as unruly aristocrats. Former governor of Florida Jeb Bush described the ad as “maybe the best political ad of the year.” In response, a spokesperson for Bass's campaign said, he was "doing his best Trump impression." Bass further responded that the AI ads are "taking on a violent trend." === Protests === In response to the nation-wide No Kings protests in October 2025, Donald Trump posted a video depicting himself flying a fighter jet and releasing feces on crowds of demonstrators, including Democratic influencer Harry Sisson. === Foreign interference === Officials from the ODNI and FBI have stated that Russia, Iran, and China used generative artificial intelligence tools to create fake and divisive text, photos, video, and audio content to foster anti-Americanism and engage in covert influence campaigns. The use of artificial intelligence was described as an accelerant rather than a revolutionary change to influence efforts. Regulation of AI with regard to elections was unlikely to see a resolution for most of the 2024 United States general election season. === Disasters and wars === In the aftermath of Hurricane Helene in the United States, members of the Republican Party circulated an AI-generated image of a young girl holding a puppy in a flood, and used it as evidence of the failure of President Joe Biden to respond to the disaster. Some, like Trump supporter Amy Kremer, shared the image on social media but acknowledged that it was not genuine. In February 2025, Donald Trump shared an AI-generated video on Truth Social depicting a hypothetical Gaza after a Trump takeover. The video's creator claimed it was made as political satire. == Reception == Ramesh Srinivasan, a professor at UCLA raised concerns about the use of AI-generative images stating that many people are questioning where they can find trustab
The Stories of Ibis
The Stories of Ibis (アイの物語, Ai no Monogatari) is a Japanese science-fiction light novel by Hiroshi Yamamoto (山本 弘) and translated by Takami Nieda. Yamamoto considered this to be an easier read than his earlier science fiction novel 'God Never Keeps Silent' because of its "light novel touch". The light novel was published in Japanese by Kadokawa Shoten and in English by Viz Media under their 'Haikasoru' imprint. The Stories of Ibis is told through a collection of short stories. All but two had been previously published. The two that Yamamoto wrote for the novel were 'The Day Shion Came' and 'AI's Story'. This is similar to The Illustrated Man by Ray Bradbury. Yamamoto drew from Bradbury's idea of short stories that were loosely connected. He represented this influence in the novel by giving Ibis a facial tattoo. == Plot == The Stories of Ibis begins with a wandering storyteller who encounters Ibis. He has the mindset that all robots are a threat to humanity and must be fought against for survival. He attacks the robot Ibis, not aware of who she is, as a result of his mindset. Ibis tells the storyteller that she is far more proficient in battle. During the battle the storyteller becomes injured and Ibis takes him to an android hospital to care for him. While he is recovering Ibis offers to tell him stories. While originally skeptical he agrees after Ibis makes it clear that the stories are not taboo. The space after each story is referred to as intermission and is a time for Ibis to comment on the story she just told. === The Universe on my Hands === The story is about a group of friends who are writing a science fiction story over the internet. One of the group members kills someone in real life. The rest of the short story is about how the group fights to convince this man to not commit suicide, but to turn himself in. He resolves to turn himself in, being hopeful to the future because he knows he has friends who care about him. The ending words of the story are a commentary. While the story they were writing was not real, the emotions they were feeling were real. === A Romance in Virtual Space === This is another story about human interactions over the internet. The device that allows people to enter virtual reality (VR) is MUGEN Net. Such devices are extremely expensive and most people need to go to a public server to use one. However the girl's parents in this story are wealthy enough to own one. This girl is shopping in VR when a boy meets her and asks her out for ice cream. All goes well and they plan for another. After some time of VR dating and awesome adventures with a female heroine, they agree to meet up in real life. He discovers that in reality, she is blind, yet he thinks she is brave and they continue dating. It's a wonderful short story of a secret utopia inside a dystopian culture of technology. === Mirror Girl === A short story about an artificial intelligence that grows over time with human interaction. The inspiration for this story was Ray Bradbury's I Sing the Body Electric. The mirror girl Shalice starts off with basic knowledge and by interacting with her owner develops. The owner grows up and marries a technician who incubates Shalice by teaching her in the virtual world at many thousand times faster than average life. When he is done, Strong Eye is created. Strong Eye is the fully developed and completely intelligent AI. === Black Hole Diver === A futuristic story about an artificial space station and people who go diving into a black hole. The space station cannot stop people but is sorry that they go to their deaths because none of them get past the event horizon. Then one girl comes who has the space ship, the training, and the research necessary to attempt to dive into the black hole. As she goes into the black hole the space station can no longer observe. She may have made it, she could have been destroyed. === A World Where Justice is Just === An anime flavored story about the intelligence of people being scanned onto a computer network. The AIs in the network fight crime and live repeating lives. At the end of each year they start anew, but different story lines. Thousands of 'extras' populate the network and are the ones subject to harm and deletion. The protagonist has a pen pal in real life who explains to her that the real world is under attack and that there are no respawns and no extras. The AI finds this so cruel that people would willingly kill each other when they can't come back. === The Day Shion Came === The stories leading up to this were all relatively short. This and the next took up over 100 pages each. This is a story about an android named Shion who works in a Japanese nursing facility. Shion comes with only extensive nursing training but lacks the knowledge of how to communicate with the residents. After months of training she informs her adviser that she believes all humans have dementia, which explains their irrational behavior. Near the end of the story one of the residents threatens suicide but Shion convinces him to step down and be rational. === AI's Story === The culminating story of the entire novel. It is about Ibis herself. She starts off as a virtual reality fighting program and over time develops intelligence. Her master gains enough funds to create her a body in the real world or level 0. There is significant hate against TAIs (True Artificial Intelligence) in the real world. Ibis and her friend Raven rebel against their masters to make a point. Human hatred was destroying them. After many years robots took prevalence and most humans realized they were not worthy to be the guardians of Earth and died in peace. The remaining population was stubborn and fought against the robots for centuries. The storyteller is a child of this generation, being raised in hatred and ignorance. The robots sought to take him captive, and teach him the truth so that he could go to the villages where people lived and teach them the truth. The whole point was they cared for the humans and wanted them to live in peace, rather than fighting for their survival. == Reception == It was reviewed by the Denver Post to be an "excellent novel". Being a Japanese novel translated to English, it has a small audience. The novel was given a 3.85 of 5 by the reviewers at Librarything.com. The reviewers of Google Books gave it a 4.33 of 5.
Collateral freedom
Collateral freedom is an anti-censorship strategy that attempts to make it economically prohibitive for censors to block content on the Internet. This is achieved by hosting content on cloud services that are considered by censors to be "too important to block", and then using encryption to prevent censors from identifying requests for censored information that is hosted among other content, forcing censors to either allow access to the censored information or take down entire services.
Combs method
The Combs method is a rule base reduction method of writing fuzzy logic rules described by William E. Combs in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules. The Combs method takes advantage of the logical equality ( ( p ∧ q ) ⇒ r ) ⟺ ( ( p ⇒ r ) ∨ ( q ⇒ r ) ) {\displaystyle ((p\land q)\Rightarrow r)\iff ((p\Rightarrow r)\lor (q\Rightarrow r))} . == Equality proof == The simplest proof of given equality involves usage of truth tables: == Combinatorial explosion == Suppose we have a fuzzy system that considers N variables at a time, each of which can fit into at least one of S sets. The number of rules necessary to cover all the cases in a traditional fuzzy system is S N {\displaystyle S^{N}} , whereas the Combs method would need only S × N {\displaystyle S\times N} rules. For example, if we have five sets and five variables to consider to produce one output, covering all the cases would require 3125 rules in a traditional system, while the Combs method would require only 25 rules, taming the combinatorial explosion that occurs when more inputs or more sets are added to the system. This article will focus on the Combs method itself. To learn more about the way rules are traditionally formed, see fuzzy logic and fuzzy associative matrix. == Example == Suppose we were designing an artificial personality system that determined how friendly the personality is supposed to be towards a person in a strategic video game. The personality would consider its own fear, trust, and love in the other person. A set of rules in the Combs system might look like this: The table translates to: [IF Fear IS Unafraid THEN Friendship IS Enemies OR IF Fear IS ModerateFear THEN Friendship IS Neutral OR IF Fear IS Afraid THEN Friendship IS GoodFriends ] OR [IF Trust IS Distrusting THEN Friendship IS Enemies OR IF Trust IS ModerateTrust THEN Friendship IS Neutral OR IF Trust IS Trusting THEN Friendship IS GoodFriends] OR [IF Love IS Unloving THEN Friendship IS Enemies OR IF Love IS ModerateLove THEN Friendship IS Neutral OR IF Love IS Loving THEN Friendship IS GoodFriends] In this case, because the table follows a straightforward pattern in the output, it could be rewritten as: Each column of the table maps to the output provided in the last row. To obtain the output of the system, we just average the outputs of each rule for that output. For example, to calculate how much the computer is Enemies with the player, we take the average of how much the computer is Unafraid, Distrusting, and Unloving of the player. When all three averages are obtained, the result can then be defuzzified by any of the traditional means.