Serge Belamant (born 1953) is a French-born South African entrepreneur best known for designing the Universal Electronic Payment System (UEPS) and the Chip Offline Pre-authorised Card (COPAC). He founded the cash-payments company Net1 UEPS Technologies in 1989, led it through dual listings on the NASDAQ and the Johannesburg Stock Exchange, and oversaw the contentious welfare-payments contract with the South African Social Security Agency (SASSA) until his retirement in 2017. Since 2018 he has been non-executive chair of London-based buy-now-pay-later fintech Zilch. == Early life and education == Belamant moved from France to South Africa with his family in 1967 and matriculated from Highlands North Boys' High School, Johannesburg. In 1972 he entered the University of the Witwatersrand to study civil engineering but switched to computer science and applied mathematics in his second year. He left the university without a degree and later took short courses in information systems at the University of South Africa (UNISA). == Early career and SASWITCH (1981–1989) == Belamant worked for Control Data Corporation as a systems analyst for a decade before joining SASWITCH Ltd in 1985. Economic sanctions had left the consortium's national ATM network dependent on unsupported Christian Rovsing computers. Belamant led a rebuild on fault-tolerant Stratus hardware and wrote protocol-translation software that allowed fourteen banks to connect without altering their host systems. By 1988 SASWITCH was handling about three million ATM transactions a month, according to the Competition Commission. The switch—now run by BankservAfrica—remains the backbone of South Africa's shared ATM network. == Net1 UEPS Technologies (1989–2017) == === Founding and UEPS === In 1989, Serge Belamant developed the Universal Electronic Payment System (UEPS), enabling secure, real-time transactions even in areas with limited connectivity. In the same year, he founded NET1 UEPS Technologies Inc., serving as its CEO and Director. === COPAC for VISA === In 1995, VISA tasked Belamant with designing the Chip Offline Pre-authorized Card (COPAC), a technology still widely used in chip-enabled credit and debit cards. A year later, he listed his company APLITEC (Applied Technology Holdings Limited) on the Johannesburg Stock Exchange. === Listings and acquisitions === In 1999, Belamant acquired Cash Payment Services (CPS) from First National Bank of South Africa, modernizing its welfare payment system to serve millions in rural areas. In 2005, he led NET1 Technologies to an IPO, listing it as NET1 UEPS Technologies Inc. on the Nasdaq. A secondary listing on the Johannesburg Stock Exchange (JSE) followed in 2008. === SASSA contract === Under Belamant's leadership, NET1 managed welfare payments for the South African Social Security Agency (SASSA), handling payments for over 10 million beneficiaries monthly. Despite criticism over handling the SASSA contract, investigations by the U.S. Department of Justice and the South African Constitutional Court found no wrongdoing. == Zilch (2018–present) == Belamant co-founded London-based "buy-now-pay-later" firm Zilch Technology in 2018 and serves as non-executive chair. Zilch reported £145 million in annual-recurring revenue and 4.5 million customers in January 2025. == Patents == Belamant is listed as inventor on more than a dozen payment-security patents, including: "Funds transfer system" (US RE36,788, 2000) – the basis for UEPS. "Financial transactions with a varying PIN" (WO 2014/037869, 2014).
Weak artificial intelligence
Weak artificial intelligence (weak AI) is artificial intelligence that implements a limited part of the mind, or, as narrow AI, artificial narrow intelligence (ANI), is focused on one narrow task. Weak AI is contrasted with strong AI, which can be interpreted in various ways: Artificial general intelligence (AGI): a machine with the ability to apply intelligence to any problem, rather than just one specific problem. Artificial superintelligence (ASI): a machine with a vastly superior intelligence to the average human being. Artificial consciousness: a machine that has consciousness, sentience and mind (John Searle uses "strong AI" in this sense). Narrow AI can be classified as being "limited to a single, narrowly defined task. Most modern AI systems would be classified in this category." Artificial general intelligence is conversely the opposite. == Applications and risks == Some examples of narrow AI are AlphaGo, self-driving cars, robot systems used in the medical field, and diagnostic doctors. Narrow AI systems are sometimes dangerous if unreliable. And the behavior that it follows can become inconsistent. It could be difficult for the AI to grasp complex patterns and get to a solution that works reliably in various environments. This "brittleness" can cause it to fail in unpredictable ways. Narrow AI failures can sometimes have significant consequences. It could for example cause disruptions in the electric grid, damage nuclear power plants, cause global economic problems, and misdirect autonomous vehicles. Medicines could be incorrectly sorted and distributed. Also, medical diagnoses can ultimately have serious and sometimes deadly consequences if the AI is faulty or biased. Simple AI programs have already worked their way into society, oftentimes unnoticed by the public. Autocorrection for typing, speech recognition for speech-to-text programs, and vast expansions in the data science fields are examples. Narrow AI has also been the subject of some controversy, including resulting in unfair prison sentences, discrimination against women in the workplace for hiring, resulting in death via autonomous driving, among other cases. Despite being "narrow" AI, recommender systems are efficient at predicting user reactions based on their posts, patterns, or trends. For instance, TikTok's "For You" algorithm can determine a user's interests or preferences in less than an hour. Some other social media AI systems are used to detect bots that may be involved in propaganda or other potentially malicious activities. == Weak AI versus strong AI == John Searle contests the possibility of strong AI (by which he means conscious AI). He further believes that the Turing test (created by Alan Turing and originally called the "imitation game", used to assess whether a machine can converse indistinguishably from a human) is not accurate or appropriate for testing whether an AI is "strong". Scholars such as Antonio Lieto have argued that the current research on both AI and cognitive modelling are perfectly aligned with the weak-AI hypothesis (that should not be confused with the "general" vs "narrow" AI distinction) and that the popular assumption that cognitively inspired AI systems espouse the strong AI hypothesis is ill-posed and problematic since "artificial models of brain and mind can be used to understand mental phenomena without pretending that that they are the real phenomena that they are modelling" (as, on the other hand, implied by the strong AI assumption).
Problematic social media use
Excessive use of social media can lead to problems including impaired functioning and a reduction in overall wellbeing, for both users and those around them. Such usage is associated with a risk of mental health problems, sleep problems, academic struggles, and daytime fatigue. Psychological or behavioural dependence on social media platforms can result in significant negative functions in peoples daily lives. The risk of problems is also related to the type of platform of social media or online community being used. People of different ages and genders may be affected in different ways by problematic social media use. == Signs and symptoms == Signs of social media addiction or excessive use of social media include many behaviours similar to substance use disorders, including mood modification, salience, tolerance, stress withdrawal symptoms, psychological distress, anxiety and depression, conflict, and relapse, and low self esteem. People with problematic social media habits are at risk of being addicted and may require more time on social media as time passes. Frequent social media use may also be associated with self-reported symptoms of attention deficit hyperactivity disorder. Social anxiety (or fear of missing out) is another potential symptom. Social anxiety is defined as having intense anxiety or fear of being judged, negatively evaluated, or rejected in a social or performance situation. The fear of missing out can contribute to excessive usage due to frequent checking the media constantly throughout the day to check in and see what others are doing instead of doing other activities. Common signs include displacement, or replacing meaningful other activities with social media, and loneliness. == Causes and mechanisms == There are many theories for the mechanism or cause behind a person having problematic social media use. The transition from normal to problematic social media use occurs when a person relies on it to relieve stress, loneliness, depression, or provide continuous rewards. Cognitive-behavioral model – People increase their use of social media when they are in unfamiliar environments or awkward situations; Social skill model – People pull out their phones and use social media when they prefer virtual communication as opposed to face-to-face interactions because they lack self-presentation skills; Socio-cognitive model – This person uses social media because they love the feeling of people liking and commenting on their photos and tagging them in pictures. They are attracted to the positive outcomes they receive on social media. There are parallels to the gambling industry inherent to the design of various social media sites, with "'ludic loops' or repeated cycles of uncertainty, anticipation and feedback" potentially contributing to problematic social media use. Another factor directly facilitating the development of addiction to social media is the implicit attitude toward the IT artifact. Social media use may also stimulate the reward pathway in the brain. There is also a theory that social media addiction fulfills a basic evolutionary drives in the wake of mass urbanization worldwide. The basic psychological needs of "secure, predictable community life that evolved over millions of years" remain unchanged, leading some to find online communities to cope with the new individualized way of life in some modern societies. The "Evolutionary Mismatch" hypothesis holds that modern digital platforms amplify social competition and comparison in ways our ancestors never faced, possibly triggering maladaptive patterns such as anxiety, depression, or compulsive use. Similarly, some scholars compare social media to "junk food": The approach taken to develop social media platforms may contribute to problematic social media use. The ability to scroll and stream content endlessly and how app developers distort time by affecting the 'flow' of content when scrolling, potentially resulting in the Zeigarnik effect (the human brain will continue to pursue an unfinished task until a satisfying closure. Autoplay modes, the personalized nature of the content results in emotional attachment (the user values this above its actual value, which is referred to as the endowment effect), and the exposure effect (repeated exposure to a distinct stimulus by the user can condition the user into an enhanced or improved attitude toward it). The interactive nature of the platforms, including the ability to "like" content has also been linked. Even though social media can satisfy personal communication needs, those who use it at higher rates are shown to have higher levels of psychological distress. == Diagnosis == While there is no official diagnostic term or measurement, problematic social media use is conceptualized as a non-substance-related disorder, resulting in preoccupation and compulsion to engage excessively in social media platforms despite negative consequences. No diagnosis exists for problematic social media use in either the ICD-11 or DSM-5. Excessive use of an activity, like social media, does not directly equate with addiction. There are other factors that could lead to someone's social media addiction including personality traits and pre-existing tendencies. While the extent of social media use and addiction are positively correlated, it is erroneous to employ use (the degree to which one makes use of the site's features, the effort exerted during use sessions, access frequency, etc.) as a proxy for addiction. Indicators of a potential dependence on social media include: Mood swings: a person uses social media to regulate his or her mood, or as a means of escaping real world conflicts. Relevance: social media starts to dominate a person's thoughts at the expense of other activities. Salience: social media becomes the most important part of someone's life. Tolerance: a person increases their time spent on social media to experience previously associated feelings they had while using social media. Withdrawal: when a person can not access social media their sleeping or eating habits change or signs of depression or anxiety can become present. Conflicts in real life: when social media is used excessively, it can affect real-life relationships with family and friends. Relapse: the tendency for previously affected individuals to revert to previous patterns of excessive social media use. There have been several scales developed and validated that help to understand the issues regarding problematic social media use. There is not one single scale that is being used by all researchers. == Treatment == Screen time recommendations for children and families have been developed by the American Academy of Pediatrics. Possible therapeutic interventions published include: Self-help interventions, including application-specific timers; Cognitive behavioural therapy; and Organisational and schooling support. Medications have not been shown to be effective in randomized, controlled trials for the related conditions of Internet addiction disorder or gaming disorder. == Prevention == Prevention approaches include screen time monitoring apps and other tech-based approaches to improve efficiency and decrease screen time and tools to help with addiction to online platform products. Parents' methods for monitoring, regulating, and understanding their children's social media use are referred to as parental mediation. Parental mediation strategies include active, restrictive, and co-using methods. Active mediation involves direct parent-child conversations that are intended to educate children on social media norms and safety, as well as the variety and purposes of online content. Restrictive mediation entails the implementation of rules, expectations, and limitations regarding children's social media use and interactions. Co-use is when parents jointly use social media alongside their children, and is most effective when parents are actively participating (like asking questions, making inquisitive/supportive comments) versus being passive about it. Active mediation is the most common strategy used by parents, though the key to success for any mediation strategy is consistency/reliability. When parents reinforce rules inconsistently, have no mediation strategy, or use highly restrictive strategies for monitoring their children's social media use, there is an observable increase in children's aggressive behaviours. When parents openly express that they are supportive of their child's autonomy and provide clear, consistent rules for media use, problematic usage and aggression decreases. Knowing that consistent, autonomy-supportive mediation has more positive outcomes than inconsistent, controlling mediation, parents can consciously foster more direct, involved, and genuine dialogue with their children. This can help prevent or reduce problematic social media use in children and teenagers. == Outcomes == === Adolescents and teens === Increased social medi
Quality of experience
Quality of experience (QoE) is a measure of the delight or annoyance of a customer's experiences with a service (e.g., web browsing, phone call, TV broadcast). QoE focuses on the entire service experience; it is a holistic concept, similar to the field of user experience, but with its roots in telecommunication. QoE is an emerging multidisciplinary field based on social psychology, cognitive science, economics, and engineering science, focused on understanding overall human quality requirements. == Definition and concepts == In 2013, within the context of the COST Action QUALINET, QoE has been defined as:The degree of delight or annoyance of the user of an application or service. It results from the fulfillment of his or her expectations with respect to the utility and / or enjoyment of the application or service in the light of the user’s personality and current state.This definition has been adopted in 2016 by the International Telecommunication Union in Recommendation ITU-T P.10/G.100. Before, various definitions of QoE had existed in the domain, with the above-mentioned definition now finding wide acceptance in the community. QoE has historically emerged from Quality of Service (QoS), which attempts to objectively measure service parameters (such as packet loss rates or average throughput). QoS measurement is most of the time not related to a customer, but to the media or network itself. QoE however is a purely subjective measure from the user's perspective of the overall quality of the service provided, by capturing people's aesthetic and hedonic needs. QoE looks at a vendor's or purveyor's offering from the standpoint of the customer or end user, and asks, "What mix of goods, services, and support, do you think will provide you with the perception that the total product is providing you with the experience you desired and/or expected?" It then asks, "Is this what the vendor/purveyor has actually provided?" If not, "What changes need to be made to enhance your total experience?" In short, QoE provides an assessment of human expectations, feelings, perceptions, cognition and satisfaction with respect to a particular product, service or application. QoE is a blueprint of all human subjective and objective quality needs and experiences arising from the interaction of a person with technology and with business entities in a particular context. Although QoE is perceived as subjective, it is an important measure that counts for customers of a service. Being able to measure it in a controlled manner helps operators understand what may be wrong with their services and how to improve them. == QoE factors == QoE aims at taking into consideration every factor that contributes to a user's perceived quality of a system or service. This includes system, human and contextual factors. The following so-called "influence factors" have been identified and classified by Reiter et al.: Human Influence Factors Low-level processing (visual and auditory acuity, gender, age, mood, …) Higher-level processing (cognitive processes, socio-cultural and economic background, expectations, needs and goals, other personality traits…) System Influence Factors Content-related Media-related (encoding, resolution, sample rate, …) Network-related (bandwidth, delay, jitter, …) Device-related (screen resolution, display size, …) Context Influence Factors Physical context (location and space) Temporal context (time of day, frequency of use, …) Social context (inter-personal relations during experience) Economic context Task context (multitasking, interruptions, task type) Technical and information context (relationship between systems) Studies in the field of QoE have typically focused on system factors, primarily due to its origin in the QoS and network engineering domains. Through the use of dedicated test laboratories, the context is often sought to be kept constant. == QoE versus User Experience == QoE is strongly related to but different from the field of User Experience (UX), which also focuses on users' experiences with services. Historically, QoE has emerged from telecommunication research, while UX has its roots in Human–Computer Interaction. Both fields can be considered multi-disciplinary. In contrast to UX, the goal of improving QoE for users was more strongly motivated by economic needs. Wechsung and De Moor identify the following key differences between the fields: == QoE measurement == As a measure of the end-to-end performance at the service level from the user's perspective, QoE is an important metric for the design of systems and engineering processes. This is particularly relevant for video services because – due to their high traffic demands –, bad network performance may highly affect the user's experience. So, when designing systems, the expected output, i.e. the expected QoE, is often taken into account – also as a system output metric and optimization goal. To measure this level of QoE, human ratings can be used. The mean opinion score (MOS) is a widely used measure for assessing the quality of media signals. It is a limited form of QoE measurement, relating to a specific media type, in a controlled environment and without explicitly taking into account user expectations. The MOS as an indicator of experienced quality has been used for audio and speech communication, as well as for the assessment of quality of Internet video, television and other multimedia signals, and web browsing. Due to inherent limitations in measuring QoE in a single scalar value, the usefulness of the MOS is often debated. Subjective quality evaluation requires a lot of human resources, establishing it as a time-consuming process. Objective evaluation methods can provide quality results faster, but require dedicated computing resources. Since such instrumental video quality algorithms are often developed based on a limited set of subjective data, their QoE prediction accuracy may be low when compared to human ratings. QoE metrics are often measured at the end devices and can conceptually be seen as the remaining quality after the distortion introduced during the preparation of the content and the delivery through the network, until it reaches the decoder at the end device. There are several elements in the media preparation and delivery chain, and some of them may introduce distortion. This causes degradation of the content, and several elements in this chain can be considered as "QoE-relevant" for the offered services. The causes of degradation are applicable for any multimedia service, that is, not exclusive to video or speech. Typical degradations occur at the encoding system (compression degradation), transport network, access network (e.g., packet loss or packet delay), home network (e.g. WiFi performance) and end device (e.g. decoding performance). == QoE management == Several QoE-centric network management and bandwidth management solutions have been proposed, which aim to improve the QoE delivered to the end-users. When managing a network, QoE fairness may be taken into account in order to keep the users sufficiently satisfied (i.e., high QoE) in a fair manner. From a QoE perspective, network resources and multimedia services should be managed in order to guarantee specific QoE levels instead of classical QoS parameters, which are unable to reflect the actual delivered QoE. A pure QoE-centric management is challenged by the nature of the Internet itself, as the Internet protocols and architecture were not originally designed to support today's complex and high demanding multimedia services. As an example for an implementation of QoE management, network nodes can become QoE-aware by estimating the status of the multimedia service as perceived by the end-users. This information can then be used to improve the delivery of the multimedia service over the network and proactively improve the users' QoE. This can be achieved, for example, via traffic shaping. QoE management gives the service provider and network operator the capability to minimize storage and network resources by allocating only the resources that are sufficient to maintain a specific level of user satisfaction. As it may involve limiting resources for some users or services in order to increase the overall network performance and QoE, the practice of QoE management requires that net neutrality regulations are considered.
Algorithmic radicalization
Algorithmic radicalization is the concept that recommender algorithms on popular social media sites, such as YouTube and Facebook, drive users toward progressively more extreme content over time, leading to the development of radicalized extremist political views. Algorithms meticulously record user interactions, encompassing likes, dislikes and the duration of time watching content, with the objective of generating an endless stream of media designed to sustain user engagement. The phenomenon of echo chamber channels has been demonstrated to exacerbate the polarization of consumers, primarily through the reinforcement of media preferences and the validation of one's existing beliefs. Algorithmic radicalization remains a controversial phenomenon as it is often not in the best interest of social media companies to remove echo chamber channels. To what extent recommender algorithms are actually responsible for radicalization remains disputed. Studies have found contradictory results regarding the promotion of extremist content by algorithms. == Social media echo chambers and filter bubbles == Social media platforms learn the interests and likes of the user to modify their experiences in their feed to keep them engaged and scrolling, known as a filter bubble. An echo chamber is formed when users come across beliefs that magnify or reinforce their thoughts and form a group of like-minded users in a closed system. Echo chambers spread information without any opposing beliefs and can possibly lead to confirmation bias. According to group polarization theory, an echo chamber can potentially lead users and groups towards more extreme radicalized positions. According to the National Library of Medicine, "Users online tend to prefer information adhering to their worldviews, ignore dissenting information, and form polarized groups around shared narratives. Furthermore, when polarization is high, misinformation quickly proliferates." == By site == === Facebook === Facebook's algorithm focuses on recommending content that makes the user want to interact. They rank content by prioritizing popular posts by friends, viral content, and sometimes divisive content. Each feed is personalized to the user's specific interests which can sometimes lead users towards an echo chamber of troublesome content. Users can find their list of interests the algorithm uses by going to the "Your ad Preferences" page. According to a Pew Research study, 74% of Facebook users did not know that list existed until they were directed towards that page in the study. It is also relatively common for Facebook to assign political labels to their users. In recent years, Facebook has started using artificial intelligence to change the content users see in their feed and what is recommended to them. A document known as The Facebook Files has revealed that their AI system prioritizes user engagement over everything else. The Facebook Files has also demonstrated that controlling the AI systems has proven difficult to handle. In an August 2019 internal memo leaked in 2021, Facebook has admitted that "the mechanics of our platforms are not neutral", concluding that in order to reach maximum profits, optimization for engagement is necessary. In order to increase engagement, algorithms have found that hate, misinformation, and politics are instrumental for app activity. As referenced in the memo, "The more incendiary the material, the more it keeps users engaged, the more it is boosted by the algorithm." According to a 2018 study, "false rumors spread faster and wider than true information... They found falsehoods are 70% more likely to be retweeted on Twitter than the truth, and reach their first 1,500 people six times faster. This effect is more pronounced with political news than other categories." === YouTube === YouTube has been around since 2005 and has more than 2.5 billion monthly users. YouTube discovery content systems focus on the user's personal activity (watched, favorites, likes) to direct them to recommended content. YouTube's algorithm is accountable for roughly 70% of users' recommended videos and what drives people to watch certain content. According to a 2022 study by the Mozilla Foundation, users have little power to keep unsolicited videos out of their suggested recommended content. This includes videos about hate speech, livestreams, etc. YouTube has been identified as an influential platform for spreading radicalized content. Al-Qaeda and similar extremist groups have been linked to using YouTube for recruitment videos and engaging with international media outlets. In a research study published by the American Behavioral Scientist Journal, they researched "whether it is possible to identify a set of attributes that may help explain part of the YouTube algorithm's decision-making process". The results of the study showed that YouTube's algorithm recommendations for extremism content factor into the presence of radical keywords in a video's title. In February 2023, in the case of Gonzalez v. Google, the question at hand is whether or not Google, the parent company of YouTube, is protected from lawsuits claiming that the site's algorithms aided terrorists in recommending ISIS videos to users. Section 230 is known to generally protect online platforms from civil liability for the content posted by its users. Multiple studies have found little to no evidence to suggest that YouTube's algorithms direct attention towards far-right content to those not already engaged with it. === TikTok === TikTok is a platform that recommends videos to a user's 'For You Page' (FYP), making every users' page different. With the nature of the algorithm behind the app, TikTok's FYP has been linked to showing more explicit and radical videos over time based on users' previous interactions on the app. Since TikTok's inception, the app has been scrutinized for misinformation and hate speech as those forms of media usually generate more interactions to the algorithm. Various extremist groups, including jihadist organizations, have utilized TikTok to disseminate propaganda, recruit followers, and incite violence. The platform's algorithm, which recommends content based on user engagement, can expose users to extremist content that aligns with their interests or interactions. As of 2022, TikTok's head of US Security has put out a statement that "81,518,334 videos were removed globally between April – June for violating our Community Guidelines or Terms of Service" to cut back on hate speech, harassment, and misinformation. Studies have noted instances where individuals were radicalized through content encountered on TikTok. For example, in early 2023, Austrian authorities thwarted a plot against an LGBTQ+ pride parade that involved two teenagers and a 20-year-old who were inspired by jihadist content on TikTok. The youngest suspect, 14 years old, had been exposed to videos created by Islamist influencers glorifying jihad. These videos led him to further engagement with similar content, eventually resulting in his involvement in planning an attack. Another case involved the arrest of several teenagers in Vienna, Austria, in 2024, who were planning to carry out a terrorist attack at a Taylor Swift concert. The investigation revealed that some of the suspects had been radicalized online, with TikTok being one of the platforms used to disseminate extremist content that influenced their beliefs and actions. == Self-radicalization == The U.S. Department of Justice defines 'Lone-wolf' (self) terrorism as "someone who acts alone in a terrorist attack without the help or encouragement of a government or a terrorist organization". Through social media outlets on the internet, 'Lone-wolf' terrorism has been on the rise, being linked to algorithmic radicalization. Through echo-chambers on the internet, viewpoints typically seen as radical were accepted and quickly adopted by other extremists. These viewpoints are encouraged by forums, group chats, and social media to reinforce their beliefs. == References in media == === The Social Dilemma === The Social Dilemma is a 2020 docudrama about how algorithms behind social media enables addiction, while possessing abilities to manipulate people's views, emotions, and behavior to spread conspiracy theories and disinformation. The film repeatedly uses buzz words such as 'echo chambers' and 'fake news' to prove psychological manipulation on social media, therefore leading to political manipulation. In the film, Ben falls deeper into a social media addiction as the algorithm found that his social media page has a 62.3% chance of long-term engagement. This leads into more videos on the recommended feed for Ben and he eventually becomes more immersed into propaganda and conspiracy theories, becoming more polarized with each video. == Proposed solutions == === United States: Weakening Section 230 protections === In the Communications Decency Act, Section 230 states t
Rademacher complexity
In computational learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with respect to a probability distribution. The concept can also be extended to real valued functions. == Definitions == === Rademacher complexity of a set === Given a set A ⊆ R m {\displaystyle A\subseteq \mathbb {R} ^{m}} , the Rademacher complexity of A is defined as follows: Rad ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] {\displaystyle \operatorname {Rad} (A):={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{a\in A}\sum _{i=1}^{m}\sigma _{i}a_{i}\right]} where σ 1 , σ 2 , … , σ m {\displaystyle \sigma _{1},\sigma _{2},\dots ,\sigma _{m}} are independent random variables drawn from the Rademacher distribution i.e. Pr ( σ i = + 1 ) = Pr ( σ i = − 1 ) = 1 / 2 {\displaystyle \Pr(\sigma _{i}=+1)=\Pr(\sigma _{i}=-1)=1/2} for i ∈ { 1 , 2 , … , m } {\displaystyle i\in \{1,2,\dots ,m\}} , and a = ( a 1 , … , a m ) ∈ A {\displaystyle a=(a_{1},\ldots ,a_{m})\in A} . Some authors take the absolute value of the sum before taking the supremum, but if A {\displaystyle A} is symmetric this makes no difference. === Rademacher complexity of a function class === Let S = { z 1 , z 2 , … , z m } ⊆ Z {\displaystyle S=\{z_{1},z_{2},\dots ,z_{m}\}\subseteq Z} be a sample of points and consider a function class F {\displaystyle {\mathcal {F}}} of real-valued functions over Z {\displaystyle Z} . Then, the empirical Rademacher complexity of F {\displaystyle {\mathcal {F}}} given S {\displaystyle S} is defined as: Rad S ( F ) = 1 m E σ [ sup f ∈ F | ∑ i = 1 m σ i f ( z i ) | ] {\displaystyle \operatorname {Rad} _{S}({\mathcal {F}})={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{f\in {\mathcal {F}}}\left|\sum _{i=1}^{m}\sigma _{i}f(z_{i})\right|\right]} This can also be written using the previous definition: Rad S ( F ) = Rad ( F ∘ S ) {\displaystyle \operatorname {Rad} _{S}({\mathcal {F}})=\operatorname {Rad} ({\mathcal {F}}\circ S)} where F ∘ S {\displaystyle {\mathcal {F}}\circ S} denotes function composition, i.e.: F ∘ S := { ( f ( z 1 ) , … , f ( z m ) ) ∣ f ∈ F } {\displaystyle {\mathcal {F}}\circ S:=\{(f(z_{1}),\ldots ,f(z_{m}))\mid f\in {\mathcal {F}}\}} The worst case empirical Rademacher complexity is Rad ¯ m ( F ) = sup S = { z 1 , … , z m } Rad S ( F ) {\displaystyle {\overline {\operatorname {Rad} }}_{m}({\mathcal {F}})=\sup _{S=\{z_{1},\dots ,z_{m}\}}\operatorname {Rad} _{S}({\mathcal {F}})} Let P {\displaystyle P} be a probability distribution over Z {\displaystyle Z} . The Rademacher complexity of the function class F {\displaystyle {\mathcal {F}}} with respect to P {\displaystyle P} for sample size m {\displaystyle m} is: Rad P , m ( F ) := E S ∼ P m [ Rad S ( F ) ] {\displaystyle \operatorname {Rad} _{P,m}({\mathcal {F}}):=\mathbb {E} _{S\sim P^{m}}\left[\operatorname {Rad} _{S}({\mathcal {F}})\right]} where the above expectation is taken over an identically independently distributed (i.i.d.) sample S = ( z 1 , z 2 , … , z m ) {\displaystyle S=(z_{1},z_{2},\dots ,z_{m})} generated according to P {\displaystyle P} . == Intuition == The Rademacher complexity is typically applied on a function class of models that are used for classification, with the goal of measuring their ability to classify points drawn from a probability space under arbitrary labellings. When the function class is rich enough, it contains functions that can appropriately adapt for each arrangement of labels, simulated by the random draw of σ i {\displaystyle \sigma _{i}} under the expectation, so that this quantity in the sum is maximized. The Rademacher complexity of a set A {\displaystyle A} can be rewritten as Rad ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] = 1 m 2 m ∑ σ ∈ { − 1 / m , + 1 / m } m [ sup a ∈ A ⟨ σ , a ⟩ ] . {\displaystyle \operatorname {Rad} (A):={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{a\in A}\sum _{i=1}^{m}\sigma _{i}a_{i}\right]={\frac {1}{{\sqrt {m}}2^{m}}}\sum _{\sigma \in \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}}\left[\sup _{a\in A}\langle \sigma ,a\rangle \right].} Each term in the summation is the farthest distance of the set A {\displaystyle A} from the origin, along a unit-length direction σ {\displaystyle \sigma } . The directions are along the vertices of a hypercube. Thus, we can also write it as Rad ( A ) = 1 2 m 1 2 m − 1 ∑ σ ∈ { − 1 / m , + 1 / m } m / { − 1 , + 1 } [ sup a ∈ A ⟨ σ , a ⟩ − inf a ∈ A ⟨ σ , a ⟩ ] {\displaystyle \operatorname {Rad} (A)={\frac {1}{2{\sqrt {m}}}}{\frac {1}{2^{m-1}}}\sum _{\sigma \in \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}/\{-1,+1\}}\left[\sup _{a\in A}\langle \sigma ,a\rangle -\inf _{a\in A}\langle \sigma ,a\rangle \right]} Here, the set { − 1 / m , + 1 / m } m / { − 1 , + 1 } {\displaystyle \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}/\{-1,+1\}} denotes half of the vertices of a hypercube, selected so that each diagonal has exactly one vertex selected. In words, this states that 2 m Rad ( A ) {\displaystyle 2{\sqrt {m}}\operatorname {Rad} (A)} is precisely the average width of the set A {\displaystyle A} along all diagonal directions of a hypercube. == Examples == A singleton set has 0 width in any direction, so it has Rademacher complexity 0. The set A = { ( 1 , 1 ) , ( 1 , 2 ) } ⊆ R 2 {\displaystyle A=\{(1,1),(1,2)\}\subseteq \mathbb {R} ^{2}} has average width 1 / 2 {\displaystyle 1/{\sqrt {2}}} along the two diagonal directions of the square, so it has Rademacher complexity 1 / 4 {\displaystyle 1/4} . The unit cube [ 0 , 1 ] m {\displaystyle [0,1]^{m}} has constant width m {\displaystyle {\sqrt {m}}} along the diagonal directions, so it has Rademacher complexity 1 / 2 {\displaystyle 1/2} . Similarly, the unit cross-polytope { x ∈ R m : ‖ x ‖ 1 ≤ 1 } {\displaystyle \{x\in \mathbb {R} ^{m}:\|x\|_{1}\leq 1\}} has constant width 2 / m {\displaystyle 2/{\sqrt {m}}} along the diagonal directions, so it has Rademacher complexity 1 / m {\displaystyle 1/m} . == Using the Rademacher complexity == The Rademacher complexity can be used to derive data-dependent upper-bounds on the learnability of function classes. Intuitively, a function-class with smaller Rademacher complexity is easier to learn. === Bounding the representativeness === In machine learning, it is desired to have a training set that represents the true distribution of some sample data S {\displaystyle S} . This can be quantified using the notion of representativeness. Denote by P {\displaystyle P} the probability distribution from which the samples are drawn. Denote by H {\displaystyle H} the set of hypotheses (potential classifiers) and denote by F {\displaystyle {\mathcal {F}}} the corresponding set of error functions, i.e., for every hypothesis h ∈ H {\displaystyle h\in H} , there is a function f h ∈ F {\displaystyle f_{h}\in F} , that maps each training sample (features,label) to the error of the classifier h {\displaystyle h} (note in this case hypothesis and classifier are used interchangeably). For example, in the case that h {\displaystyle h} represents a binary classifier, the error function is a 0–1 loss function, i.e. the error function f h {\displaystyle f_{h}} returns 0 if h {\displaystyle h} correctly classifies a sample and 1 else. We omit the index and write f {\displaystyle f} instead of f h {\displaystyle f_{h}} when the underlying hypothesis is irrelevant. Define: L P ( f ) := E z ∼ P [ f ( z ) ] {\displaystyle L_{P}(f):=\mathbb {E} _{z\sim P}[f(z)]} – the expected error of some error function f ∈ F {\displaystyle f\in {\mathcal {F}}} on the real distribution P {\displaystyle P} ; L S ( f ) := 1 m ∑ i = 1 m f ( z i ) {\displaystyle L_{S}(f):={1 \over m}\sum _{i=1}^{m}f(z_{i})} – the estimated error of some error function f ∈ F {\displaystyle f\in {\mathcal {F}}} on the sample S {\displaystyle S} . The representativeness of the sample S {\displaystyle S} , with respect to P {\displaystyle P} and F {\displaystyle {\mathcal {F}}} , is defined as: Rep P ( F , S ) := sup f ∈ F ( L P ( f ) − L S ( f ) ) {\displaystyle \operatorname {Rep} _{P}({\mathcal {F}},S):=\sup _{f\in F}(L_{P}(f)-L_{S}(f))} Smaller representativeness is better, since it provides a way to avoid overfitting: it means that the true error of a classifier is not much higher than its estimated error, and so selecting a classifier that has low estimated error will ensure that the true error is also low. Note however that the concept of representativeness is relative and hence can not be compared across distinct samples. The expected representativeness of a sample can be bounded above by the Rademacher complexity of the function class: If F {\displaystyle {\mathcal {F}}} is a set of functions with range within [ 0 , 1 ] {\displaystyle [0,1]} , then Rad P , m ( F ) − ln 2 2 m ≤ E S ∼ P m [ Rep P ( F , S ) ] ≤ 2 Rad P , m ( F ) {\displaystyle \operatorname {Rad} _{P,m}({\mathcal {F}})-{\sqrt {\frac {\ln 2}{2m}}}\leq \mathbb {E} _{S\sim P^{m}}[\operatorname {Rep} _{P}({\
News ticker
A news ticker (sometimes called a crawler, crawl, slide, zipper, ticker tape, or chyron) is a horizontal or vertical (depending on the language's writing system) text-based display either in the form of a graphic that typically resides in the lower third of the screen space on a television station or network (usually during news programming) or as a long, thin scoreboard-style display seen around the facades of some offices or public buildings dedicated to presenting headlines or minor pieces of news. It is an evolution of the paper strips tapes, a continuous paper print-out of stock quotes from a printing telegraph which was mainly used to transmit companies' share price information over telegraph lines before the advance of technology in the 1960s. News tickers have been used in Europe in countries such as United Kingdom, Germany and Ireland for some years; they are also used in several Asian countries and Australia. In the United States, tickers were long used on a special event basis by broadcast television stations to disseminate weather warnings, school closings, and election results. Sports telecasts occasionally used a ticker to update other contests in progress before the expansion of cable news networks and the internet for news content. In addition, some ticker displays are used to relay continuous business and financial information. Most tickers are traditionally displayed in the form of scrolling text running from right to left across the screen or building display (or in the opposite direction for right-to-left writing systems such as Arabic script and Hebrew), allowing for headlines of varying degrees of detail; some used by television broadcasters, however, display stories in a static manner (allowing for the seamless switching of each story individually programmed for display) or utilize a "flipping" effect (in which each individual headline is shown for a few seconds before transitioning to the next, instead of scrolling across the screen, usually resulting in a relatively quicker run through of all of the information programmed into the ticker). Since the growth in usage of the World Wide Web, some news tickers have syndicated news stories posted largely on websites of broadcasters or by other independent news agencies. == Current uses == === Television === The presentation of headlines or other information in a news ticker has become a common element of many different news networks. The use of the ticker has differed on a number of channels: News networks and local newscasts commonly use a setup in which news headlines are scrolled across an area near the bottom of the screen, though some variations have formed, such as showing one headline at a time with a scrolling or "flipper" effect. Financial news channels use two or more tickers displaying company shares prices and business headlines. Networks with a focus on sports often use a slightly different system, where scores and statuses of ongoing and finished games are displayed one by one, along with minor sports highlights, statistics and sports news headlines. They are typically divided into categories devoted to specific leagues and events (with college basketball and football usually focusing on the top 25 ranked teams on the AP Poll, occasionally supplemented by sections for specific conferences). Some programs, including news-based programs emphasizing viewer interactivity, or special events, may also use tickers to display messages and reactions from viewers and others that relate to the program. These comments are often sourced from social networking services such as Facebook and Twitter, typically curating comments from a specific page or hashtag. Due to their current prevalence, they have been occasionally been made targets of pranks and vandalism. In one such example, News 14 Carolina allowed viewers to submit relevant information such as school closings or traffic delays via telephone or the Internet that would be incorporated into the ticker; the system was exploited in February 2004 to display humorous and crude messages, including the infamous "All your base are belong to us". Occasionally messages intended for training accidentally end up being put on the live ticker as happened on BBC News in 2022 when "Weather rain everywhere" and "Manchester United are rubbish" appeared on the live news ticker. Some businesses and organizations have utilized tickers intended for relaying weather-related closings as a surreptitious source for free guerrilla marketing, proclaiming they were open rather than closed and giving their phone number if possible, allowing them to 'advertise' on a television station all day for free. Since then, many stations have required pre-registration of businesses or organizations with an authorized representative and a signed affidavit on company letterhead affirming their authenticity, along with filtering out unfamiliar businesses and organizations, before being able to display their closing announcements. Stations also confirm all closings involving school districts with authorized officials to prevent situations in which students either show up to canceled classes in dangerous conditions, or do not attend school due to an erroneous, prank-submitted, or false listing. === On personal computers === Various applications have been developed over time to install news tickers on personal computer desktops using RSS feeds from news organizations, which are displayed in a fashion similar to those used by television channels but enable the user to access to underlying news stories, a feature not offered by traditional television channels. The Bloomberg Terminal and other financial information-tracking programs and devices also utilize tickers. A ticker may also be used as an unobtrusive method by businesses in order to deliver important information to their staff. The ticker can be set to reappear, stay on screen, or be put into a retractable mode (where a small tab is left visible on-screen). In the United Kingdom, broadcasters have stopped using this technology as other forms of communications have become available and increased in popularity. BBC News and Sky News discontinued their respective desktop tickers in March 2011 and 2012 to focus on other products, such as smartphone applications, to deliver updated information on breaking news and sport stories. === News tickers on buildings === Since the advent of the telegraph, newspapers commonly used their buildings to share the latest headlines. At first simple chalkboard signs were used for bulletins, but limelight illumination, electric lights, magic lantern projections, and other novel techniques were later employed. The method of using electric lights to spell out moving letters was invented by Frank C. Reilly (August 20, 1888 – April 10, 1947) and patented in 1923. Reilly called his invention the Motograph News Bulletin. In 1928, The New York Times installed a Motograph News Bulletin to display news headlines on the sides of Times Tower. The display was 388 feet (118 m) long, 5 feet (1.5 m) high, and employed over 14,800 light bulbs. Popularly known as the "Zipper", the sign remained in use until the building was sold in 1961. The sign was darkened during World War II to comply with wartime lighting restrictions. The Motograph operated until 1994 and was replaced by an electronic version in 1995, which was in turn removed in 2017 due to the replacement of all individual screens on the front of One Times Square with a 350 foot (110 m)-tall LED billboard in 2018. Ticker displays appear today on the exterior of the News Corp Building, which houses the headquarters for Fox News Channel/News Corp in the west extension of Manhattan's Rockefeller Center, as well as one that displays delayed stock market data that is located in Times Square. NASDAQ itself features a large display screen on the facade of the NASDAQ MarketSite building in Times Square. The Reuters buildings at Canary Wharf and in Toronto have news and stock tickers; the latter type features market data for the New York Stock Exchange, NASDAQ and London Stock Exchange, while the Toronto building's ticker also includes quotes from the Toronto Stock Exchange. A red-LED ticker was added to the perimeter of 10 Rockefeller Center in 1994, as the building was being renovated to accommodate the studios for NBC's Today. Placed at the juncture of the first and second floors, the ticker is visible to spectators in Rockefeller Plaza and passersby on West 49th Street and updates continuously, even at times when Today is not being produced and broadcast. As of 2015, the ticker strip is only a small part of a large two-floor LCD video display that is placed within the window of the studio showing promotional information. The Martin Place Headquarters of Seven News, the news division of Australian television broadcaster Seven Network, also incorporates a ticker that wraps around the building. == In popular culture == The use of new