Sample complexity

Sample complexity

The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g., only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. == Definition == Let X {\displaystyle X} be a space which we call the input space, and Y {\displaystyle Y} be a space which we call the output space, and let Z {\displaystyle Z} denote the product X × Y {\displaystyle X\times Y} . For example, in the setting of binary classification, X {\displaystyle X} is typically a finite-dimensional vector space and Y {\displaystyle Y} is the set { − 1 , 1 } {\displaystyle \{-1,1\}} . Fix a hypothesis space H {\displaystyle {\mathcal {H}}} of functions h : X → Y {\displaystyle h\colon X\to Y} . A learning algorithm over H {\displaystyle {\mathcal {H}}} is a computable map from Z {\displaystyle Z} to H {\displaystyle {\mathcal {H}}} . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} . Typical learning algorithms include empirical risk minimization, without or with Tikhonov regularization. Fix a loss function L : Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X × Y {\displaystyle X\times Y} , the expected risk of a hypothesis (a function) h ∈ H {\displaystyle h\in {\mathcal {H}}} is E ( h ) := E ρ [ L ( h ( x ) , y ) ] = ∫ X × Y L ( h ( x ) , y ) d ρ ( x , y ) {\displaystyle {\mathcal {E}}(h):=\mathbb {E} _{\rho }[{\mathcal {L}}(h(x),y)]=\int _{X\times Y}{\mathcal {L}}(h(x),y)\,d\rho (x,y)} In our setting, we have h = A ( S n ) {\displaystyle h={\mathcal {A}}(S_{n})} , where A {\displaystyle {\mathcal {A}}} is a learning algorithm and S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} is a sequence of vectors which are all drawn independently from ρ {\displaystyle \rho } . Define the optimal risk E H ∗ = inf h ∈ H E ( h ) . {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}={\underset {h\in {\mathcal {H}}}{\inf }}{\mathcal {E}}(h).} Set h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , for each sample size n {\displaystyle n} . h n {\displaystyle h_{n}} is a random variable and depends on the random variable S n {\displaystyle S_{n}} , which is drawn from the distribution ρ n {\displaystyle \rho ^{n}} . The algorithm A {\displaystyle {\mathcal {A}}} is called consistent if E ( h n ) {\displaystyle {\mathcal {E}}(h_{n})} probabilistically converges to E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} . In other words, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} , such that, for all sample sizes n ≥ N {\displaystyle n\geq N} , we have Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] < δ . {\displaystyle \Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]<\delta .} The sample complexity of A {\displaystyle {\mathcal {A}}} is then the minimum N {\displaystyle N} for which this holds, as a function of ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . We write the sample complexity as N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} to emphasize that this value of N {\displaystyle N} depends on ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . If A {\displaystyle {\mathcal {A}}} is not consistent, then we set N ( ρ , ϵ , δ ) = ∞ {\displaystyle N(\rho ,\epsilon ,\delta )=\infty } . If there exists an algorithm for which N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is finite, then we say that the hypothesis space H {\displaystyle {\mathcal {H}}} is learnable. In others words, the sample complexity N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} defines the rate of consistency of the algorithm: given a desired accuracy ϵ {\displaystyle \epsilon } and confidence δ {\displaystyle \delta } , one needs to sample N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} data points to guarantee that the risk of the output function is within ϵ {\displaystyle \epsilon } of the best possible, with probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity is polynomial, that is, whether N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is bounded by a polynomial in 1 / ϵ {\displaystyle 1/\epsilon } and 1 / δ {\displaystyle 1/\delta } . If N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is polynomial for some learning algorithm, then one says that the hypothesis space H {\displaystyle {\mathcal {H}}} is PAC-learnable. This is a stronger notion than being learnable. == Unrestricted hypothesis space: infinite sample complexity == One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) < δ , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right)<\delta ,} where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large. Thus, in order to make statements about the rate of convergence of the quantity sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right),} one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. == Restricted hypothesis space: finite sample-complexity == The latter approach leads to concepts such as VC dimension and Rademacher complexity which control the complexity of the space H {\displaystyle {\mathcal {H}}} . A smaller hypothesis space introduces more bias into the inference process, meaning that E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} may be greater than the best possible risk in a larger space. However, by restricting the complexity of the hypothesis space it becomes possible for an algorithm to produce more uniformly consistent functions. This trade-off leads to the concept of regularization. It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}} : H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class. This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. === An example of a PAC-learnable hypothesis space === X = R d , Y = { − 1 , 1 } {\displaystyle X=\mathbb {R} ^{d},Y=\{-1,1\}} , and let H {\displaystyle {\mathcal {H}}} be the space of affine functions on X {\displaystyle X} , that is, functions of the form x ↦ ⟨ w , x ⟩ + b {\displaystyle x\mapsto \langl

Digital sculpting

Digital sculpting, also known as sculpt modeling or 3D sculpting, is the use of software that offers tools to push, pull, smooth, grab, pinch or otherwise manipulate a digital object as if it were made of a real-life substance such as clay. == Sculpting technology == The geometry used in digital sculpting programs to represent the model can vary; each offers different benefits and limitations. The majority of digital sculpting tools on the market use mesh-based geometry, in which an object is represented by an interconnected surface mesh of polygons that can be pushed and pulled around. This is somewhat similar to the physical process of beating copper plates to sculpt a scene in relief. Other digital sculpting tools use voxel-based geometry, in which the volume of the object is the basic element. Material can be added and removed, much like sculpting in clay. Still other tools make use of more than one basic geometry representation. A benefit of mesh-based programs is that they support sculpting at multiple resolutions on a single model. Areas of the model that are finely detailed can have very small polygons while other areas can have larger polygons. In many mesh-based programs, the mesh can be edited at different levels of detail, and the changes at one level will propagate to higher and lower levels of model detail. A limitation of mesh-based sculpting is the fixed topology of the mesh; the specific arrangement of the polygons can limit the ways in which detail can be added or manipulated. A benefit of voxel-based sculpting is that voxels allow complete freedom over form. The topology of a model can be altered continually during the sculpting process as material is added and subtracted, which frees the sculptor from considering the layout of polygons on the model's surface. After sculpting, it may be necessary to retopologize the model to obtain a clean mesh for use in animation or real-time rendering. Voxels, however, are more limited in handling multiple levels of detail. Unlike mesh-based modeling, broad changes made to voxels at a low level of detail may completely destroy finer details. == Uses == Sculpting can often introduce details to meshes that would otherwise have been difficult or impossible to create using traditional 3D modeling techniques. This makes it preferable for achieving photorealistic and hyperrealistic results, though, many stylized results are achieved as well. Sculpting is primarily used in high poly organic modeling (the creation of 3D models which consist mainly of curves or irregular surfaces, as opposed to hard surface modeling). It is also used by auto manufacturers in their design of new cars. It can create the source meshes for low poly game models used in video games. In conjunction with other 3D modeling and texturing techniques and Displacement and Normal mapping, it can greatly enhance the appearance of game meshes often to the point of photorealism. Some sculpting programs like 3D-Coat, Zbrush, and Mudbox offer ways to integrate their workflows with traditional 3D modeling and rendering programs. Conversely, 3D modeling applications like 3ds Max, Maya and MODO are now incorporating sculpting capability as well, though these are usually less advanced than tools found in sculpting-specific applications. High poly sculpts are also extensively used in CG artwork for movies, industrial design, art, photorealistic illustrations, and for prototyping in 3D printing. == 3D print == Sculptors and digital artists use digital sculpting to create a model (or Digital Twin) to be materialized through CNC technologies including 3D printing. The final sculptures are often called Digital Sculpture or 3D printed art. While digital technologies have emerged in many art disciplines (painting, photography), this is less the case for digital sculpture due to the higher complexity and technology limitations to produce the final sculpture. == Sculpting Process == The best way to learn sculpture is by understanding primary, secondary and tertiary forms. First, break down the object you want to make down its basic shapes, such as a sphere or cube. Focus on making the large, overall shape of the object. After that, work on the bigger shapes on top of or inside the object. These can be protrusions or cut outs. Then, do a final detail pass, such as pores or lines to break up the shape. == Sculpting programs == There are a number of digital sculpting tools available. Some popular tools for creating are: Traditional 3D modeling suites are also beginning to include sculpting capability. 3D modeling programs which currently feature some form of sculpting include the following:

Social media mining

Social media mining is the process of obtaining data from user-generated content on social media in order to extract actionable patterns, form conclusions about users, and act upon the information. Mining supports targeting advertising to users or academic research. The term is an analogy to the process of mining for minerals. Mining companies sift through raw ore to find the valuable minerals; likewise, social media mining sifts through social media data in order to discern patterns and trends about matters such as social media usage, online behaviour, content sharing, connections between individuals, buying behaviour. These patterns and trends are of interest to companies, governments and not-for-profit organizations, as such organizations can use the analyses for tasks such as design strategies, introduce programs, products, processes or services. Social media mining uses concepts from computer science, data mining, machine learning, and statistics. Mining is based on social network analysis, network science, sociology, ethnography, optimization and mathematics. It attempts to formally represent, measure and model patterns from social media data. In the 2010s, major corporations, governments and not-for-profit organizations began mining to learn about customers, clients and others. Platforms such as Google, Facebook (partnered with Datalogix and BlueKai) conduct mining to target users with advertising. Scientists and machine learning researchers extract insights and design product features. Users may not understand how platforms use their data. Users tend to click through Terms of Use agreements without reading them, leading to ethical questions about whether platforms adequately protect users' privacy. During the 2016 United States presidential election, Facebook allowed Cambridge Analytica, a political consulting firm linked to the Trump campaign, to analyze the data of an estimated 87 million Facebook users to profile voters, creating controversy when this was revealed. == Background == As defined by Kaplan and Haenlein, social media is the "group of internet-based applications that build on the ideological and technological foundations of Web 2.0, and that allow the creation and exchange of user-generated content." There are many categories of social media including, but not limited to, social networking (Facebook or LinkedIn), microblogging (Twitter), photo sharing (Flickr, Instagram, Photobucket, or Picasa), news aggregation (Google Reader, StumbleUpon, or Feedburner), video sharing (YouTube, MetaCafe), livecasting (Ustream or Twitch), virtual worlds (Kaneva), social gaming (World of Warcraft), social search (Google, Bing, or Ask.com), and instant messaging (Google Talk, Skype, or Yahoo! messenger). The first social media website was introduced by GeoCities in 1994. It enabled users to create their own homepages without having a sophisticated knowledge of HTML coding. The first social networking site, SixDegrees.com, was introduced in 1997. Since then, many other social media sites have been introduced, each providing service to millions of people. These individuals form a virtual world in which individuals (social atoms), entities (content, sites, etc.) and interactions (between individuals, between entities, between individuals and entities) coexist. Social norms and human behavior govern this virtual world. By understanding these social norms and models of human behavior and combining them with the observations and measurements of this virtual world, one can systematically analyze and mine social media. Social media mining is the process of representing, analyzing, and extracting meaningful patterns from data in social media, resulting from social interactions. It is an interdisciplinary field encompassing techniques from computer science, data mining, machine learning, social network analysis, network science, sociology, ethnography, statistics, optimization, and mathematics. Social media mining faces grand challenges such as the big data paradox, obtaining sufficient samples, the noise removal fallacy, and evaluation dilemma. Social media mining represents the virtual world of social media in a computable way, measures it, and designs models that can help us understand its interactions. In addition, social media mining provides necessary tools to mine this world for interesting patterns, analyze information diffusion, study influence and homophily, provide effective recommendations, and analyze novel social behavior in social media. == Uses == Social media mining is used across several industries including business development, social science research, health services, and educational purposes. Once the data received goes through social media analytics, it can then be applied to these various fields. Often, companies use the patterns of connectivity that pervade social networks, such as assortativity—the social similarity between users that are induced by influence, homophily, and reciprocity and transitivity. These forces are then measured via statistical analysis of the nodes and connections between these nodes. Social analytics also uses sentiment analysis, because social media users often relay positive or negative sentiment in their posts. This provides important social information about users' emotions on specific topics. These three patterns have several uses beyond pure analysis. For example, influence can be used to determine the most influential user in a particular network. Companies would be interested in this information in order to decide who they may hire for influencer marketing. These influencers are determined by recognition, activity generation, and novelty—three requirements that can be measured through the data mined from these sites. Analysts also value measures of homophily: the tendency of two similar individuals to become friends. Users have begun to rely on information of other users' opinions in order to understand diverse subject matter. These analyses can also help create recommendations for individuals in a tailored capacity. By measuring influence and homophily, online and offline companies are able to suggest specific products for individuals consumers, and groups of consumers. Social media networks can use this information themselves to suggest to their users possible friends to add, pages to follow, and accounts to interact with. == Perception == Modern social media mining is a controversial practice that has led to exponential gains in user growth for tech giants such as Facebook, Inc., Twitter, and Google. Companies such as these, considered "Big Tech" are companies that build algorithms that take advantage of user input to understand their preferences, and keep them on the platform as much as possible. These inputs, that can be as simple as time spent on a given screen, provide the data being mined, and lead to companies profiting heavily from using that data to capitalize on extremely accurate predictions about user behavior. The growth of platforms accelerated rapidly once these strategies were put in place; Most of the largest platforms now average over 1 billion active users per month as of 2021. It has been claimed by a multitude of anti-algorithm personalities, like Tristan Harris or Chamath Palihapitiya, that certain companies (specifically Facebook) valued growth above all else, and ignored potential negative impacts from these growth engineering tactics. At the same time, users have now created their own data arbitrages with the help of their own data, through content monetization and becoming influencers. Users typically have access to a varied set of analytics specific to people that interact with them on social media, and can use these as building blocks for their own targeting and growth strategies through ads and posts that cater to their audiences. Influencers also commonly promote products and services for established brands, creating one of the largest digital industries: Influencer marketing. Instagram, Facebook, Twitter, YouTube, Google, and others have long given access to platform analytics, and allowed third parties to access that information as well, at times unbeknownst to even the user whose data is being viewed/bought. == Research == === Research areas === Social media event detection – Social networks enable users to freely communicate with each other and share their recent news, ongoing activities or views about different topics. As a result, they can be seen as a potentially viable source of information to understand the current emerging topics/events. Public health monitoring and surveillance - Using large-scale analysis of social media to study large cohorts of patients and the general public, e.g. to obtain early warning signals of drug-drug interactions and adverse drug reactions, or understand human reproduction and sexual interest. Community structure (Community Detection/Evolution/Evaluation) – Identifying communities on social networks, how t

Social media and suicide

Since the rise of social media, there have been numerous cases of individuals being influenced towards committing suicide or self-harm through their use of social media, and even of individuals arranging to broadcast suicide attempts, some successful, on social media. Researchers have studied social media and suicide to determine what, if any, risks social media poses in terms of suicide, and to identify methods of mitigating such risks, if they exist. The search for a correlation has not yet uncovered a clear answer. == Background == Suicide is one of the leading causes of death worldwide, and as of 2020, the second leading cause of death in the United States for those aged 15–34. According to the Center for Disease Control and Prevention, suicide was the third leading cause of death among adolescents in the US, from 1999 to 2006. In 2020, people in the US had a suicide rate of 13.5 per 100,000. Suicide was a leading cause of death in the United States accounting for 48,183 deaths in 2021. Suicide rates increased by 30 per cent from 2000 to 2018 and declined in 2019 and 2020. Suicide remains a significant public health issue worldwide, despite prevention efforts and treatments. Suicide has been identified not only as an individual phenomenon but also as being influenced by social and environmental factors. There is growing evidence that online activity has influenced suicide-related behavior. The use of social media throughout the 21st century has grown exponentially. For this reason, there are a variety of sources that are accessible to the public in various forms, especially social media sites such as Facebook, Instagram, Twitter, YouTube, Snapchat, TikTok and many more. Although these platforms were intended to allow people to connect virtually, these platforms can lead to cyber-bullying, insecurity, and emotional distress, and sometimes may influence a person to attempt suicide. Bullying, whether on social media or elsewhere, physical or not, significantly increases victims' risk of suicidal behavior. Since social media was introduced some people have taken their lives as a result of cyberbullying. Furthermore, suicide rates among teenagers have increased from 2010 to 2022 as social media has become something that people interact with more throughout their day-to-day lives. Media algorithms tend to popularize videos and posts to inform the country of the rising trouble, which may create a popular appeal to the young and immature minds of teenagers. This is why, social media could provide higher risks with the promotion of different kinds of pro-suicidal sites, message boards, chat rooms, and forums. Moreover, the Internet not only reports suicide incidents but documents suicide methods (for example, suicide pacts, an agreement between two or more people to kill themselves at a particular time and often by the same lethal means). Therefore, the role the Internet plays, particularly social media, in suicide-related behavior is a topic of growing interest. == Cyberbullying == There is substantial evidence that the Internet and social media can influence suicide-related behavior. Such evidence includes an increase in exposure to graphic content. A research study conducted by Sameer Hinduja and Justin Patchin found a correlation between cyberbullying and suicide. According to their findings, cyber-bullying increases suicidal thoughts by 14.5 percent and suicide attempts by 8.7 percent. Particularly alarming is the fact that children and young people under 25 who are victims of cyberbullying are more than twice as likely to self-harm and engage in suicidal behavior. Overall, teen suicide rates have increased within the past decade.This presents a significant public health concern, with over 40,000 suicides in the United States and nearly one million worldwide annually. Adolescents involved in cyberbullying often downplay its seriousness by calling it a joke or blaming the victim. These moral disengagement strategies can normalize harmful behavior and reduce feelings of guilt. This normalization may increase emotional distress and contribute to risks like depression and suicidal thoughts. Recent data from the Centers for Disease Control and Prevention reveals that 14.9 per cent of teenagers have experienced online bullying, while 13.6 per cent of teenagers have seriously attempted suicide. Both of these incidents are in increasing numbers in the United States. Furthermore, in numerous recent incidents, cyber-bullying led the victim to commit suicide; this phenomenon is now known as cyberbullicide. Many parents and children are unaware of the dangers and potential legal consequences of cyberbullying. As a response, anti-bullying regulations implemented by schools aim to prevent any form of bullying, including through technology, and protect students from online harassment. While some states have enacted laws against cyberbullying, there are currently no federal regulations addressing this issue. == Social media's influence on suicide == The media may portray suicidal behavior or language which can potentially influence people to act on these suicidal ideation. This may include news reports of actual suicides that have occurred or television shows and films that reenact suicides. Some organizations have proposed guidelines about how the media should report suicide. There is evidence that compliance with the guidelines varies. Some research showed that it is unclear whether the guidelines have successfully reduced the number of suicides. On the contrary, other research studies stated that the guidelines have worked in some cases. == Impact of pro-suicidal sites, message boards, chat rooms and forums == Social media platforms have transformed traditional methods of communication by allowing instantaneous and interactive sharing of information created and controlled by individuals, groups, organizations, and governments. As of the third quarter of 2022, Facebook had 266 million monthly active users, between Canada and the US. An immense quantity of information on the topic of suicide is available on the Internet and via social media. The information available on social media on the topic of suicide can influence suicidal behavior, both negatively and positively. The social cognitive theory plays a vital role in suicide attempts influenced through social media. This theory is demonstrated when one is influenced by what they see through various processes that form into modeled behaviors. This can be shown when people post their suicide attempts online or promote suicidal behavior in general. Contributors to these social media platforms may also exert peer pressure and encourage others to take their own lives, idolize those who have killed themselves, and facilitate suicide pacts. These pro-suicidal sites reported the following. For example, on a Japanese message board in 2008, it was shared that people can kill themselves using hydrogen sulfide gas. Shortly afterwards, 220 people attempted suicide in this way, and 208 were successful. Biddle et al. conducted a systematic Web search of 12 suicide-associated terms (e.g., suicide, suicide methods, how to kill yourself, and best suicide methods) to analyze the search results, and found that pro-suicide sites and chat rooms that discussed general issues associated with suicide most often occurred within the first few hits of a search. In another study, 373 suicide-related websites were found using Internet search engines and examined. Among them, 31% were suicide-neutral, 29% were anti-suicide, and 11% were pro-suicide. Together, these studies have shown that obtaining pro-suicide information on the Internet, including detailed information on suicide methods, is very easy. While social media has been prevalent in young adult suicide, some young adults find comfort and solace through these platforms. Young adults are making connections with people in like situations that are helping them feel less lonely. Although the public opinion is that message boards are harmful, the following studies show how they point to suicide prevention and have positive influences. A study using content analysis analyzed all of the postings on the AOL Suicide Bulletin Board over 11 months and concluded that most contributions contained positive, empathetic, and supportive postings. Then, a multi-method study was able to demonstrate that the users of such forums experience a great deal of social support and only a small amount of social strain. Lastly, in the survey participants were asked to assess the extent of their suicidal thoughts on a 7-level scale (0, absolutely no suicidal thoughts, to 7, very strong suicidal thoughts) for the time directly before their first forum visit and at the time of the survey. The study found a significant reduction after using the forum. The study however cannot conclude the forum is the only reason for the decrease. Together, these studies show how forums can reduce the number of

Social media reach

Social media reach is a media analytics metric that refers to the number of users who have come across a particular content on a particular social media platform. Social media platforms have their own individual ways of tracking, analyzing and reporting the traffic on each of the individual platforms. As these platforms are a main source of communication between companies and their target audiences, by conducting research, companies are able to utilize analytical information, such as the reach of their posts, to better understand the interactions between the users and their content. There are multiple underlying factors that will determine what shows up on a newsfeed or timeline. Algorithms, for example, are a type of factor that can alter the reach of a post due to the way the algorithm is coded, which can affect who sees a post and when. Other examples of factors that can impede the reach can include the time at which posts are made, as well as how frequent the posts are between one another. In comparison, an impression is the total number of circumstances where content has been shown on a social timeline, meanwhile, engagement looks at how people interact with the content that they see on a social platform such as like, share or retweet. == Reach on Facebook == Facebook has their own analytic platform which allows the user to see how other users are interacting with their posts, with the use of multiple metrics. This is not something the average user uses, but rather a tool that is used by pages or public figures. For example, Facebook pages that represent a business often look at the activity their posts have generated. There are three types of reach that can be looked at on the Facebook analytic platform. === Types of reach === ==== Organic Reach ==== This type of reach regards the number of distinct users that have seen a specific post on their feed. Organic reach, in other words is the number of people who have seen the post being analyzed on their Facebook newsfeed. Data gathered from this type of reach can give intel to those doing the analysis, such as the demographics of those who have seen the post. ==== Paid Reach ==== This type of reach regards the number of times that distinct users have come across sponsored posts, ads or content. In other words, paid reach is the number of times Facebook users have seen a post that has been paid for by a company. Data collected can give insight, to advertisers or marketers for example, on the activity based around the reach of their post. ==== Viral Reach ==== This type of reach regards the number of views by distinct users on posts that have been commented on or shared by their friends on Facebook. In other words, viral reach looks at the number of people who have seen a post after a friend of theirs commented or shared the original post, therefore it showed on their timeline. Viral reach can be looked at in terms of a collective number of times that the post has been on individual user's timelines. Data collected from viral reach can be used in multiple ways, for example, it can be used to analyze the type of content that gets shared or commented on and can be further used to compare to other posts. === Engaged users === This refers to the number of individual users who have clicked and interacted with a post on Facebook. == Reach on Twitter == Twitter gives access to any of their users to analytics of their tweets as well as their followers. Their dashboard is user friendly, which allows anyone to take a look at the analytics behind their Twitter account. This open access is useful for both the average user and companies as it can provide a quick glance or general outlook of who has seen their tweets. The way that Twitter works is slightly different than the way of Facebook in terms of the reach. On Twitter, especially for users with a higher profile, they are not only engaging with the people who follow them, but also with the followers of their own followers. The reach metric on Twitter looks at the quantity of Twitter users who have been engaged, but also the number of users that follow them as well. This metric is useful to see the if the tweets/content being shared on Twitter are contributing to the growth of audience on this platform. == Reach on Instagram == Instagram gives their users access to their reach, in the Instagram Insights section. Instagram insights can be used to learn more about an account's followers and performance. Reach indicates the total number of unique Instagram accounts that have seen your Instagram post or story. You can find this data by looking at each individual post insights. == Uses of reach == The reach can be a useful metric to analyze for marketers and advertisers. Social media is a platform that is used by marketers to directly target their intended audience with ease. These platforms not only allow marketers to get a better understanding of their audience, but also allow advertisers to insert their ads onto the timelines of specific users to later be able to conduct research to see the reach of their posts/content. The basic goal of marketers is to increase their reach as much as possible to impact bigger audiences of their dream customers and, in the end, make more sales. When doing organic social media marketing, using paid methods like ads or doing influencer marketing whether it is paid or free, it allows marketers to track the performance of their strategy and tweak it based on what works and what does not. == Analytics and reach == Social analytics looks at the data collected based on the interactions of users on social media platforms. A lot of information can be gathered which can provide intel based on user activities on social media. When looking into analytics in regard to social media, each company or group has a different goal in mind to engage their audience. At a glance, the three might seem as if they are very similar, however the differences between them are significant. There are many aspects that can be analyzed from the data gathered from social media platforms, depending on what is being observed, the correct metric would then be selected to further analyze. One example of the many metrics that can be used through social analytics is the reach. == Reach formula == To calculate social media reach one can use the following formula: R = I f ¯ {\displaystyle R={\frac {I}{\bar {f}}}} where R {\displaystyle R} — is social media reach, I {\displaystyle I} stands for the number of impressions, f ¯ {\displaystyle {\bar {f}}} is the average frequency of impressions per user. f ¯ {\displaystyle {\bar {f}}} represents the number of events when the ad is shown to a particular user. The average value should be calculated over the time period with stable settings of advertisement campaign. == Commenting For Better Reach == Commenting For Better Reach also known as "CFBR" is a widely used strategy for organically boosting post reach on social media platforms. Algorithms tend to favor posts with substantial likes and comments, granting them broader exposure compared to less engaging content. Primarily seen on LinkedIn, a platform geared toward professional networking and business connections, the use of CFBR signals active engagement aimed at enhancing post visibility. It is important to note that genuine and meaningful comments are key to effective engagement. Spammy or irrelevant comments not only detract from the conversation but may also limit a post's potential reach and impact.

Google Vids

Google Vids (not to be confused with Google Video) is an online timeline-based video editing application included as part of the Google Workspace suite. It is designed to help users create informational videos for work-related purposes. The app uses Google's Gemini technology to enable users to create video storyboards manually or with AI assistance using simple prompts. Features include uploading media, choosing stock videos, images, background music, and a voiceover feature with script generation using AI. The app is currently in testing with select Google Workspace Labs users. Like Kapwing and Capcut, Google Vids is primarily for creating work-related content like sales training, onboarding videos, vendor outreach, and project updates. It offers various styles and templates, collaborative features, and is not limited to videos without the short integration at the moment. Google Vids was announced on April 9, 2024. In September 2025, Google began to roll out a basic version of the application to Google Workspace users.

Bitcoin Satoshi Vision

Bitcoin Satoshi Vision (BSV) is a cryptocurrency that is a hard fork of Bitcoin Cash. Bitcoin Satoshi Vision was created in November 2018 by a group of individuals led by Craig Steven Wright, who has claimed since 2015 to be Satoshi Nakamoto, the creator of the original bitcoin. == History == === 2018 split from Bitcoin Cash === On 15 November 2018, a hard fork chain split of Bitcoin Cash occurred between two rival factions called Bitcoin Cash and Bitcoin SV. On 15 November 2018 Bitcoin Cash traded at about $289, and Bitcoin SV traded at about $96.50, down from $425.01 on 14 November for the un-split Bitcoin Cash. The split originated from what was described as a "civil war" in two competing Bitcoin Cash camps. The first camp, supported by entrepreneur Roger Ver and Jihan Wu of Bitmain, promoted the software entitled Bitcoin ABC (short for Adjustable Blocksize Cap), which would maintain the block size at 32 MB. The second camp led by Craig Steven Wright and billionaire Calvin Ayre put forth a competing software version Bitcoin SV, short for "Bitcoin Satoshi Vision", which would increase the block size limit to 128 MB. === 2019 de-listing from Binance === In April 2019, an online feud broke out between those who supported the claims of Bitcoin SV supporter Craig Wright that he was Satoshi Nakamoto, and those who did not. The feud resulted in cryptocurrency exchange Binance de-listing Bitcoin SV from their platform, stating that: At Binance, we periodically review each digital asset we list to ensure that it continues to meet the high level of standard we expect. When a coin or token no longer meets this standard, or the industry changes, we conduct a more in-depth review and potentially delist it. We believe this best protects all of our users. When we conduct these reviews, we consider a variety of factors. Here are some that drive whether we decide to delist a digital asset: Commitment of team to project Level and quality of development activity Network / smart contract stability Level of public communication Responsiveness to our periodic due diligence requests Evidence of unethical / fraudulent conduct Contribution to a healthy and sustainable crypto ecosystem === 2021 network attack === In August 2021, Bitcoin SV suffered a 51% attack, after previously suffering attacks in June and July of the same year. Such an attack involves cryptocurrency miners gaining control of more than half of a network's computing power; these kinds of network attacks have the goal of preventing new transactions from gaining confirmations, allowing the attackers to double-spend coins. Adam James, senior editor at OKEx Insights claimed that "In the intermediate term, the attack has seemingly somewhat-negligible impact on its current price action," however "Faith in [Bitcoin SV] will likely be reduced following the incident." === 2024 high court ruling === In March 2024, Mr Justice James Mellor in the British High Court ruled that Wright is not Satoshi Nakamoto.