In geometry, space partitioning is the process of dividing an entire space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space into non-overlapping regions. Any point in the space can then be identified to lie in exactly one of the regions. == Overview == Space-partitioning systems are often hierarchical, meaning that a space (or a region of space) is divided into several regions, and then the same space-partitioning system is recursively applied to each of the regions thus created. The regions can be organized into a tree, called a space-partitioning tree. Most space-partitioning systems use planes (or, in higher dimensions, hyperplanes) to divide space: points on one side of the plane form one region, and points on the other side form another. Points exactly on the plane are usually arbitrarily assigned to one or the other side. Recursively partitioning space using planes in this way produces a BSP tree, one of the most common forms of space partitioning. == Uses == === In computer graphics === Space partitioning is particularly important in computer graphics, especially heavily used in ray tracing, where it is frequently used to organize the objects in a virtual scene. A typical scene may contain millions of polygons. Performing a ray/polygon intersection test with each would be a very computationally expensive task. Storing objects in a space-partitioning data structure (k-d tree or BSP tree for example) makes it easy and fast to perform certain kinds of geometry queries—for example in determining whether a ray intersects an object, space partitioning can reduce the number of intersection test to just a few per primary ray, yielding a logarithmic time complexity with respect to the number of polygons. Space partitioning is also often used in scanline algorithms to eliminate the polygons out of the camera's viewing frustum, limiting the number of polygons processed by the pipeline. There is also a usage in collision detection: determining whether two objects are close to each other can be much faster using space partitioning. === In integrated circuit design === In integrated circuit design, an important step is design rule check. This step ensures that the completed design is manufacturable. The check involves rules that specify widths and spacings and other geometry patterns. A modern design can have billions of polygons that represent wires and transistors. Efficient checking relies heavily on geometry query. For example, a rule may specify that any polygon must be at least n nanometers from any other polygon. This is converted into a geometry query by enlarging a polygon by n/2 at all sides and query to find all intersecting polygons. === In probability and statistical learning theory === The number of components in a space partition plays a central role in some results in probability theory. See Growth function for more details. === In geography and GIS === There are many studies and applications where Geographical Spatial Reality is partitioned by hydrological criteria, administrative criteria, mathematical criteria or many others. In the context of cartography and GIS - Geographic Information System, is common to identify cells of the partition by standard codes. For example the for HUC code identifying hydrographical basins and sub-basins, ISO 3166-2 codes identifying countries and its subdivisions, or arbitrary DGGs - discrete global grids identifying quadrants or locations. == Data structures == Common space-partitioning systems include: BSP trees Quadtrees Octrees k-d trees Bins == Number of components == Suppose the n-dimensional Euclidean space is partitioned by r {\displaystyle r} hyperplanes that are ( n − 1 ) {\displaystyle (n-1)} -dimensional. What is the number of components in the partition? The largest number of components is attained when the hyperplanes are in general position, i.e, no two are parallel and no three have the same intersection. Denote this maximum number of components by C o m p ( n , r ) {\displaystyle Comp(n,r)} . Then, the following recurrence relation holds: C o m p ( n , r ) = C o m p ( n , r − 1 ) + C o m p ( n − 1 , r − 1 ) {\displaystyle Comp(n,r)=Comp(n,r-1)+Comp(n-1,r-1)} C o m p ( 0 , r ) = 1 {\displaystyle Comp(0,r)=1} - when there are no dimensions, there is a single point. C o m p ( n , 0 ) = 1 {\displaystyle Comp(n,0)=1} - when there are no hyperplanes, all the space is a single component. And its solution is: C o m p ( n , r ) = ∑ k = 0 n ( r k ) {\displaystyle Comp(n,r)=\sum _{k=0}^{n}{r \choose k}} if r ≥ n {\displaystyle r\geq n} C o m p ( n , r ) = 2 r {\displaystyle Comp(n,r)=2^{r}} if r ≤ n {\displaystyle r\leq n} (consider e.g. r {\displaystyle r} perpendicular hyperplanes; each additional hyperplane divides each existing component to 2). which is upper-bounded as: C o m p ( n , r ) ≤ r n + 1 {\displaystyle Comp(n,r)\leq r^{n}+1}
Conversational user interface
A conversational user interface (CUI) is a user interface for computers that emulates a conversation with a human. Historically, computers have relied on text-based user interfaces and graphical user interfaces (GUIs) (such as the user pressing a "back" button) to translate the user's desired action into commands the computer understands. While an effective mechanism of completing computing actions, there is a learning curve for the user associated with GUI. Instead, CUIs provide opportunity for the user to communicate with the computer in their natural language rather than in a syntax specific commands.
Jarosław Królewski
Jarosław Królewski ([jaˈrɔswaf kruˈlɛfskʲi]; born September 26, 1986) is a Polish entrepreneur, programmer, sociologist, investor, and philanthropist from Hańczowa, Poland. He is a researcher and lecturer at the AGH University of Krakow. He was selected as a Young Global Leader by the World Economic Forum in 2025. Królewski is a cofounder and chief executive of the software development company Synerise that develops its namesake business intelligence software based on artificial intelligence and big data. He is also the president and a majority stakeholder of the Polish soccer club Wisła Kraków. == Biography == === Scientific activities === Królewski graduated from the AGH University of Kraków and the University of Banking and Management in Kraków. He completed two fields of study: a master's degree in sociology, and an engineer's degree in computer science. He co-created innovative study programs, including social informatics and electronic business, recognized as the most innovative field of study in Poland in 2012 by the Ministry of Science and Higher Education, which led to the AGH receiving a PLN 1 million award for the development of the program. Królewski is a research and teaching employee at AGH, where since 2010 he has been conducting classes and lectures on the Internet, mobile technologies, and UX/UI. He has been preparing a PhD thesis. He is the brand ambassador of the Academy. He is also a mentor of the Polish Development Fund network. In 2019, on the occasion of the AGH University's 100th anniversary, Królewski was honored the title of "AGH Graduate Junior 2018." Królewski is the co-originator of the "Data Science in Business and Administration" doctoral studies organized by the Faculty of Computer Science and Electronic Economy of the Poznań University of Economics. He is a co-author of a textbook E-marketing. Contemporary trends. Starter package (2013), and an Book on algorithmic governance Algocracy. How and why artificial intelligence changes everything (with Krzysztof Rybiński, 2023). === Business career === Throughout the 2000s, Królewski was responsible for issues of usability and user experience at the advertising agency Eskadra in Kraków. In 2012, along with programmer Miłosz Baluś and graphic designer Krzysztof Kochmański, he founded the software house Humanoit Group. The company created a project management software using machine learning and artificial intelligence. In 2013, HG Intelligence was established to create a platform for analytics and automation of business processes called "Synerise" that combined big data with artificial intelligence mechanisms. Królewski became the president of the company's management board. In 2016, the company rebranded itself after its own platform. It is one of the fastest growing enterprises in Poland – in 2019 it was valued at USD 85 million (PLN 323.5 million), and its value is still growing, in 2022 it announced an investment of USD 23 million. Królewski is a supporter of releasing some software in open-source form, an example of which is the open library Cleora.ai. Królewski has been described "one of the most promising young Polish businessmen in the technology industry." According to Forbes, he is a "visionary computer scientist who in many respects resembles the young Bill Gates." Królewski considers himself a “technological determinist and optimist.” He never wants to be a millionaire or billionaire, he spends 80 percent of his private income on education, sports and charities. === Sports === In his youth (2002–2006) he was a football player of the (then 4th-league) club Glinik Gorlice, and represented it at the then-highest level of junior competitions in Poland. He played there with Rafał Wisłocki, later president of Wisła Kraków and vice-president of Bruk-Bet Termalica Nieciecza. In early 2019, Królewski was the initiator of a rescue operation that saved Wisła Kraków from bankruptcy, as well as the originator of the crowdfunding issue of shares of Wisła Kraków, pioneering in Polish sports, during restructuring and searching for a strategic investor. The offered shares constituted 5.1 percent. all the company's shares, which meant that the club was valued at PLN 74.4 million. 40,000 shares were put up for sale, each worth PLN 100. Within 24 hours, they were purchased by 9,124 investors through an equity crowdfunding platform Beesfund, earning the club PLN 4 million. In March 2019, Królewski became vice-chairman of Wisła's supervisory board, a position he held until 2021. In April 2020, he became Wisła's co-owner, along with the footballer Jakub Błaszczykowski, and Tomasz Jażdżyński, president of Gremi Media (publisher of the news outlets Rzeczpospolita and Parkiet). The three granted a bridging loan to the club of PLN 4 million, each supporting PLN 1.33 million. The funds were used to repay the club's debts to players. In November 2022, the supervisory board of Wisła Kraków appointed Królewski as the president of the club's management board. In December 2022, Królewski took over a majority stake in the club. In January 2024, based on match statistics, he used AI tools to select Wisła's new coach, Albert Rudé. === Social activities === Królewski is the creator and originator of the nationwide educational project "AI Schools & Academy", the first artificial intelligence teaching program in Polish kindergartens, primary and secondary schools in Polish history. Launched in 2018, the project was financed by Synerise business partners: Carrefour, CCC, Ernst & Young, IDC, Media Expert, Microsoft, Orange Foundation, Oriflame, Bank Pekao, Photon, PZU, and Żabka. Physicists, mathematicians, and computer scientists conduct special classes in 1,500 kindergartens, primary and secondary schools. Outstanding students and teachers are awarded scholarships. The project was appreciated by experts. In the years 2018–2020, Królewski was the main sponsor of Glinik Gorlice. He also supported the women's football team Staszkówka Jelna (of Staszkówka). After taking over the shares of Wisła Kraków in 2020, he launched socially conscience initiatives along with other shareholders, including a women's football team, the amp football section, and the blind football section. He has privately sponsored social charities. == Accolades and awards == In 2017, Królewski along with the Synerise co-founders Baluś and Kochmański was included in the “New Europe 100” list of eastern Europe's brightest and best citizens changing the region's societies, politics, or business environments, according to Res Publica, along with the International Visegrad Fund, Google and the Financial Times. Królewski was included on Ernst & Young's list of the 30 most promising technology entrepreneurs in the world. In 2018, he was honored with the Special Jury Award in the Polish edition of the Ernst & Young Entrepreneur of the Year Award competition, for combining scientific activities with entrepreneurship. The same year, Królewski won an award in the competition Digital Shapers, distinguishing outstanding tech personalities by the Digital Poland Foundation. He was also selected to Ernst & Young startup program EY Accelerating Entrepreneurs for businesses that focus on disruptive fields. In 2019, as part of the AI Awards competition, Królewski received the title of AI Person of the Year. == Private life == Królewski comes from a Lemko family from Hańczowa in the Low Beskids. He is married to Aleksandra Królewska.
Hallin's spheres
Hallin's spheres is a theory of news reporting and its rhetorical framing posited by journalism historian Daniel C. Hallin in his 1986 book The Uncensored War to explain the news coverage of the Vietnam War. Hallin divides the world of political discourse into three concentric spheres: consensus, legitimate controversy, and deviance. In the sphere of consensus, journalists assume everyone agrees. The sphere of legitimate controversy includes the standard political debates, and journalists are expected to remain neutral. The sphere of deviance falls outside the bounds of legitimate debate, and journalists can ignore it. These boundaries shift, as public opinion shifts. Hallin's spheres, which deals with the media, are similar to the Overton window, which deals with public opinion generally, and posits a sliding scale of public opinion on any given issue ranging from conventional wisdom to unacceptable. Hallin used the concept of framing to describe the presentation and reception of issues in public. For example, framing the use of drugs as criminal activity can encourage the public to consider that behavior anti-social. Hallin's work was later referred to in the controversial formulation of the concept of an opinion corridor, in which the range of acceptable public opinion narrows, and opinion outside that corridor moves from legitimate controversy into deviance. == Description == === Sphere of consensus === This sphere contains those topics on which there is widespread agreement, or at least the perception thereof. Within the sphere of consensus, "journalists feel free to invoke a generalized 'we' and to take for granted shared values and shared assumptions". Examples include such things as motherhood and apple pie. For topics in this sphere, journalists feel free to be advocating cheerleaders without having to be neutral or present any opposing view point and be disinterested observers." === Sphere of legitimate controversy === For topics in this sphere rational and informed people hold differing views within limited range. These topics are therefore the most important to cover, and also ones upon which journalists are seemingly obliged to remain disinterested reporters, rather than advocating for or against a particular view. Schudson notes that Hallin, in his influential study of the US media during the Vietnam War, argues that journalism's commitment to objectivity has always been compartmentalized. That is, within a certain sphere—the sphere of legitimate controversy—journalists seek conscientiously to be balanced and objective. The work of Walter Williams professor at the University of Missouri, Rod Petersen, advanced the idea that priming—controlling the narratives that media covers—can be the tool that media use to get deviant news subjects into the legitimate controversial circles of new coverage. === Sphere of deviance === Topics in this sphere are rejected by journalists as being unworthy of general consideration. Such views are perceived as being out of hand, unfounded, taboo, or of such minor consequence that they are not newsworthy. Hallin argues that in the sphere of deviance, "journalists also depart from standard norms of objective reporting and feel authorized to treat as marginal, laughable, dangerous". They either avoid mentioning or ridicule the controversial subject as outside the bounds of acceptable controversy; and they censor the individuals and groups who are associated with it. A simple example: a person claiming that aliens are manipulating college basketball scores might have difficulty finding sports media coverage for such a claim. A more political example: the US media regulator FCC's "Fairness Doctrine" aimed at radio stations, advocated balance between right and left political news and opinions, yet specified that broadcasters did not have to reserve any space or time for Communist viewpoints. == Uses of the terms == Craig Watkins (2001, pp. 92–94) makes use of the Hallin's spheres in a paper examining ABC, CBS, and NBC television network television news coverage of the Million Man March, a demonstration that took place in Washington, D.C., on October 16, 1995. Watkins analyzes the dominant framing practices—problem definition, rhetorical devices, use of sources, and images—employed by journalists to make sense of this particular expression of political protest. He argues that Hallin's three spheres are a way for media framing practices to develop specific reportorial contexts, and each sphere develops its own distinct style of news reporting resources by different rhetorical tropes and discourses. Piers Robinson (2001, p. 536) uses the concept in relation to debates that have emerged over the extent to which the mass media serves elite interests or, alternatively, plays a powerful role in shaping political outcomes. His article reviews Hallin's spheres as an example of media-state relations, that highlights theoretical and empirical shortcomings in the 'manufacturing consent' thesis (Chomsky, McChesney). Robinson argues that a more nuanced and bi-directional understanding is needed of the direction of influence between media and the state that builds upon, rather than rejecting, existing theoretical accounts. Hallin's theory assumed a relatively homogenized media environment, where most producers were trying to reach most consumers. A more fractured media landscape can challenge this assumption because different audiences may place topics in different spheres, a concept related to the filter bubble, which posits that many members of the public choose to limit their media consumption to the areas of consensus and deviance that they personally prefer.
AlphaEvolve
AlphaEvolve is an evolutionary coding agent for designing advanced algorithms based on large language models such as Gemini. It was developed by Google DeepMind and unveiled in May 2025. == Design == AlphaEvolve aims to autonomously discover and refine algorithms through a combination of large language models (LLMs) and evolutionary computation. AlphaEvolve needs an evaluation function with metrics to optimize, and an initial algorithm. At each step, AlphaEvolve uses the LLM to produce variants of the existing algorithms, and then selects the most effective ones. Unlike domain-specific predecessors like AlphaFold or AlphaTensor, AlphaEvolve is designed as a general-purpose system. It can operate across a wide array of scientific and engineering tasks by automatically modifying code and optimizing for multiple objectives. Its architecture allows it to evaluate code programmatically, reducing reliance on human input and mitigating risks such as hallucinations common in standard LLM outputs. == Achievements == According to Google, across a selection of 50 open mathematical problems, the model was able to rediscover state-of-the-art solutions 75% of the time and discovered improved solutions 20% of the time, for example advancing the kissing number problem. AlphaEvolve was also used to optimize Google's computing ecosystem. Improved data center scheduling heuristics, enabled the recovery of 0.7% of stranded resources. It was also used to optimize TPU circuit design and Gemini's training matrix multiplication kernel. == Open source implementations == Following the publication of AlphaEvolve, several open source implementations have been developed by the research community. One such implementation is OpenEvolve, which implements distributed evolutionary algorithms, multi-language support, integration with various large language model providers, and automated discovery of high-performance GPU kernels that outperform expert-engineered baselines.
Computer audition
Computer audition (CA) or machine listening is the general field of study of algorithms and systems for audio interpretation by machines. Since the notion of what it means for a machine to "hear" is very broad and somewhat vague, computer audition attempts to bring together several disciplines that originally dealt with specific problems or had a concrete application in mind. The engineer Paris Smaragdis, interviewed in Technology Review, talks about these systems — "software that uses sound to locate people moving through rooms, monitor machinery for impending breakdowns, or activate traffic cameras to record accidents." Inspired by models of human audition, CA deals with questions of representation, transduction, grouping, use of musical knowledge and general sound semantics for the purpose of performing intelligent operations on audio and music signals by the computer. Technically this requires a combination of methods from the fields of signal processing, auditory modelling, music perception and cognition, pattern recognition, and machine learning, as well as more traditional methods of artificial intelligence for musical knowledge representation. == Applications == Like computer vision versus image processing, computer audition versus audio engineering deals with understanding of audio rather than processing. It also differs from problems of speech understanding by machine since it deals with general audio signals, such as natural sounds and musical recordings. Applications of computer audition are widely varying, and include search for sounds, genre recognition, acoustic monitoring, music transcription, score following, audio texture, music improvisation, emotion in audio and so on. == Related disciplines == Computer Audition overlaps with the following disciplines: Music information retrieval: methods for search and analysis of similarity between music signals. Auditory scene analysis: understanding and description of audio sources and events. Computational musicology and mathematical music theory: use of algorithms that employ musical knowledge for analysis of music data. Computer music: use of computers in creative musical applications. Machine musicianship: audition driven interactive music systems. == Areas of study == Since audio signals are interpreted by the human ear–brain system, that complex perceptual mechanism should be simulated somehow in software for "machine listening". In other words, to perform on par with humans, the computer should hear and understand audio content much as humans do. Analyzing audio accurately involves several fields: electrical engineering (spectrum analysis, filtering, and audio transforms); artificial intelligence (machine learning and sound classification); psychoacoustics (sound perception); cognitive sciences (neuroscience and artificial intelligence); acoustics (physics of sound production); and music (harmony, rhythm, and timbre). Furthermore, audio transformations such as pitch shifting, time stretching, and sound object filtering, should be perceptually and musically meaningful. For best results, these transformations require perceptual understanding of spectral models, high-level feature extraction, and sound analysis/synthesis. Finally, structuring and coding the content of an audio file (sound and metadata) could benefit from efficient compression schemes, which discard inaudible information in the sound. Computational models of music and sound perception and cognition can lead to a more meaningful representation, a more intuitive digital manipulation and generation of sound and music in musical human-machine interfaces. The study of CA could be roughly divided into the following sub-problems: Representation: signal and symbolic. This aspect deals with time-frequency representations, both in terms of notes and spectral models, including pattern playback and audio texture. Feature extraction: sound descriptors, segmentation, onset, pitch and envelope detection, chroma, and auditory representations. Musical knowledge structures: analysis of tonality, rhythm, and harmonies. Sound similarity: methods for comparison between sounds, sound identification, novelty detection, segmentation, and clustering. Sequence modeling: matching and alignment between signals and note sequences. Source separation: methods of grouping of simultaneous sounds, such as multiple pitch detection and time-frequency clustering methods. Auditory cognition: modeling of emotions, anticipation and familiarity, auditory surprise, and analysis of musical structure. Multi-modal analysis: finding correspondences between textual, visual, and audio signals. === Representation issues === Computer audition deals with audio signals that can be represented in a variety of fashions, from direct encoding of digital audio in two or more channels to symbolically represented synthesis instructions. Audio signals are usually represented in terms of analogue or digital recordings. Digital recordings are samples of acoustic waveform or parameters of audio compression algorithms. One of the unique properties of musical signals is that they often combine different types of representations, such as graphical scores and sequences of performance actions that are encoded as MIDI files. Since audio signals usually comprise multiple sound sources, then unlike speech signals that can be efficiently described in terms of specific models (such as source-filter model), it is hard to devise a parametric representation for general audio. Parametric audio representations usually use filter banks or sinusoidal models to capture multiple sound parameters, sometimes increasing the representation size in order to capture internal structure in the signal. Additional types of data that are relevant for computer audition are textual descriptions of audio contents, such as annotations, reviews, and visual information in the case of audio-visual recordings. === Features === Description of contents of general audio signals usually requires extraction of features that capture specific aspects of the audio signal. Generally speaking, one could divide the features into signal or mathematical descriptors such as energy, description of spectral shape etc., statistical characterization such as change or novelty detection, special representations that are better adapted to the nature of musical signals or the auditory system, such as logarithmic growth of sensitivity (bandwidth) in frequency or octave invariance (chroma). Since parametric models in audio usually require very many parameters, the features are used to summarize properties of multiple parameters in a more compact or salient representation. === Musical knowledge === Finding specific musical structures is possible by using musical knowledge as well as supervised and unsupervised machine learning methods. Examples of this include detection of tonality according to distribution of frequencies that correspond to patterns of occurrence of notes in musical scales, distribution of note onset times for detection of beat structure, distribution of energies in different frequencies to detect musical chords and so on. === Sound similarity and sequence modeling === Comparison of sounds can be done by comparison of features with or without reference to time. In some cases an overall similarity can be assessed by close values of features between two sounds. In other cases when temporal structure is important, methods of dynamic time warping need to be applied to "correct" for different temporal scales of acoustic events. Finding repetitions and similar sub-sequences of sonic events is important for tasks such as texture synthesis and machine improvisation. === Source separation === Since one of the basic characteristics of general audio is that it comprises multiple simultaneously sounding sources, such as multiple musical instruments, people talking, machine noises or animal vocalization, the ability to identify and separate individual sources is very desirable. Unfortunately, there are no methods that can solve this problem in a robust fashion. Existing methods of source separation rely sometimes on correlation between different audio channels in multi-channel recordings. The ability to separate sources from stereo signals requires different techniques than those usually applied in communications where multiple sensors are available. Other source separation methods rely on training or clustering of features in mono recording, such as tracking harmonically related partials for multiple pitch detection. Some methods, before explicit recognition, rely on revealing structures in data without knowing the structures (like recognizing objects in abstract pictures without attributing them meaningful labels) by finding the least complex data representations, for instance describing audio scenes as generated by a few tone patterns and their trajectories (polyphonic voices) and acoustical contours drawn by a tone (c
Catholic Church and artificial intelligence
The Catholic Church views artificial intelligence as a significant technological development that must be governed by strict ethical principles rooted in human dignity and the common good. In January 2025, the Church issued the doctrinal note Antiqua et nova co-issued by the Dicastery for the Doctrine of the Faith and the Dicastery for Culture and Education. It addresses the "relationship between artificial intelligence and human intelligence" and offers reflections on the "anthropological and ethical challenges raised by AI". In August 2025, Time magazine included Pope Leo XIV in its 2025 list of the World’s Most Influential People in Artificial Intelligence. In May 2026, Pope Leo XIV approved the creation of a new Vatican commission on artificial intelligence. He released his first papal encyclical, titled Magnifica humanitas, on the topic later in the month.