Uniform convergence in probability

Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family uniformly converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory. Specifically, the Glivenko-Cantelli theorem and the homonymous classes of functions are fundamentally related to uniform convergence. The law of large numbers says that, for each single event A {\displaystyle A} , its empirical frequency in a sequence of independent trials converges (with high probability) to its theoretical probability. In many application however, the need arises to judge simultaneously the probabilities of events of an entire class S {\displaystyle S} from one and the same sample. Moreover, it, is required that the relative frequency of the events converge to the probability uniformly over the entire class of events S {\displaystyle S} . The Uniform Convergence Theorem gives a sufficient condition for this convergence to hold. Roughly, if the event-family is sufficiently simple (its VC dimension is sufficiently small) then uniform convergence holds. == Definitions == For a class of predicates H {\displaystyle H} defined on a set X {\displaystyle X} and a set of samples x = ( x 1 , x 2 , … , x m ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{m})} , where x i ∈ X {\displaystyle x_{i}\in X} , the empirical frequency of h ∈ H {\displaystyle h\in H} on x {\displaystyle x} is Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | . {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|.} The theoretical probability of h ∈ H {\displaystyle h\in H} is defined as Q P ( h ) = P { y ∈ X : h ( y ) = 1 } . {\displaystyle Q_{P}(h)=P\{y\in X:h(y)=1\}.} The Uniform Convergence Theorem states, roughly, that if H {\displaystyle H} is "simple" and we draw samples independently (with replacement) from X {\displaystyle X} according to any distribution P {\displaystyle P} , then with high probability, the empirical frequency will be close to its expected value, which is the theoretical probability. Here "simple" means that the Vapnik–Chervonenkis dimension of the class H {\displaystyle H} is small relative to the size of the sample. In other words, a sufficiently simple collection of functions behaves roughly the same on a small random sample as it does on the distribution as a whole. The Uniform Convergence Theorem was first proved by Vapnik and Chervonenkis using the concept of growth function. == Uniform Convergence Theorem == The statement of the Uniform Convergence Theorem is as follows: If H {\displaystyle H} is a set of { 0 , 1 } {\displaystyle \{0,1\}} -valued functions defined on a set X {\displaystyle X} and P {\displaystyle P} is a probability distribution on X {\displaystyle X} then for ε > 0 {\displaystyle \varepsilon >0} and m {\displaystyle m} a positive integer, we have: P m { | Q P ( h ) − Q x ^ ( h ) | ≥ ε for some h ∈ H } ≤ 4 Π H ( 2 m ) e − ε 2 m / 8 . {\displaystyle P^{m}\{|Q_{P}(h)-{\widehat {Q_{x}}}(h)|\geq \varepsilon {\text{ for some }}h\in H\}\leq 4\Pi _{H}(2m)e^{-\varepsilon ^{2}m/8}.} In the above, for any x ∈ X m , {\displaystyle x\in X^{m},} Q P ( h ) = P { ( y ∈ X : h ( y ) = 1 } , {\displaystyle Q_{P}(h)=P\{(y\in X:h(y)=1\},} Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|} and | x | = m . {\displaystyle |x|=m.} P m {\displaystyle P^{m}} indicates that the probability is taken over x {\displaystyle x} consisting of m {\displaystyle m} i.i.d. draws from the distribution P . {\displaystyle P.} Finally, the growth function Π H {\displaystyle \Pi _{H}} is defined in the following way, for any { 0 , 1 } {\displaystyle \{0,1\}} -valued functions H {\displaystyle H} over X {\displaystyle X} and for any natural number m {\displaystyle m} : Π H ( m ) = max | { h ∩ D : D ⊆ X , | D | = m , h ∈ H } | . {\displaystyle \Pi _{H}(m)=\max |\{h\cap D:D\subseteq X,|D|=m,h\in H\}|.} From the point of view of Learning Theory one can consider H {\displaystyle H} to be the Concept/Hypothesis class defined over the instance set X {\displaystyle X} . Crucially, the Sauer–Shelah lemma implies that Π H ( m ) ≤ m d {\displaystyle \Pi _{H}(m)\leq m^{d}} , where d {\displaystyle d} is the VC dimension of H {\displaystyle H} . == Proof of the Uniform Convergence Theorem == and are the sources of the proof below. Before we get into the details of the proof of the Uniform Convergence Theorem we will present a high level overview of the proof. Symmetrization: We transform the problem of analyzing | Q P ( h ) − Q ^ x ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon } into the problem of analyzing | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} , where r {\displaystyle r} and s {\displaystyle s} are i.i.d samples of size m {\displaystyle m} drawn according to the distribution P {\displaystyle P} . One can view r {\displaystyle r} as the original randomly drawn sample of length m {\displaystyle m} , while s {\displaystyle s} may be thought as the testing sample which is used to estimate Q P ( h ) {\displaystyle Q_{P}(h)} . Permutation: Since r {\displaystyle r} and s {\displaystyle s} are picked identically and independently, so swapping elements between them will not change the probability distribution on r {\displaystyle r} and s {\displaystyle s} . So, we will try to bound the probability of | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} for some h ∈ H {\displaystyle h\in H} by considering the effect of a specific collection of permutations of the joint sample x = r | | s {\displaystyle x=r||s} . Specifically, we consider permutations σ ( x ) {\displaystyle \sigma (x)} which swap x i {\displaystyle x_{i}} and x m + i {\displaystyle x_{m+i}} in some subset of 1 , 2 , . . . , m {\displaystyle {1,2,...,m}} . The symbol r | | s {\displaystyle r||s} means the concatenation of r {\displaystyle r} and s {\displaystyle s} . Reduction to a finite class: We can now restrict the function class H {\displaystyle H} to a fixed joint sample and hence, if H {\displaystyle H} has finite VC Dimension, it reduces to the problem to one involving a finite function class. We present the technical details of the proof. It should be stressed that this proof glosses over details like the measurability of the events V {\displaystyle V} and R {\displaystyle R} ; measurability is granted in the case of H {\displaystyle H} being finite or countable, but this is not normally the case in standard applications of the theorem (e.g. for statistical learning theory or to prove the Glivenko-Cantelli theorem). To get measurability, one needs to use a notion of separability of the underlying space, possibly related to H {\displaystyle H} . === Symmetrization === Lemma: Let V = { x ∈ X m : | Q P ( h ) − Q ^ x ( h ) | ≥ ε for some h ∈ H } {\displaystyle V=\{x\in X^{m}:|Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon {\text{ for some }}h\in H\}} and R = { ( r , s ) ∈ X m × X m : | Q r ^ ( h ) − Q ^ s ( h ) | ≥ ε / 2 for some h ∈ H } . {\displaystyle R=\{(r,s)\in X^{m}\times X^{m}:|{\widehat {Q_{r}}}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2{\text{ for some }}h\in H\}.} Then for m ≥ 2 ε 2 {\displaystyle m\geq {\frac {2}{\varepsilon ^{2}}}} , P m ( V ) ≤ 2 P 2 m ( R ) {\displaystyle P^{m}(V)\leq 2P^{2m}(R)} . Proof: By the triangle inequality, if | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2} then | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} . Therefore, P 2 m ( R ) ≥ P 2 m { ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } = ∫ V P m { s : ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } d P m ( r ) = A {\displaystyle {\begin{aligned}&P^{2m}(R)\\[5pt]\geq {}&P^{2m}\{\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\\[5pt]={}&\int _{V}P^{m}\{s:\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\,dP^{m}(r)\\[5pt]={}&A\end{aligned}}} since r {\displaystyle r} and s {\displaystyle s} are independent. Now for r ∈ V {\displaystyle r\in V} fix an h ∈ H {\displaystyle h\in H} such that | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } . For this h {\displaystyle h} , we shall

Zoho Office Suite

Zoho Office Suite is an online office suite developed by Zoho Corporation. == History == Zoho Office Suite was launched in 2005 with a web-based word processor. Additional products, such as those for spreadsheets and presentations, were incorporated later into the suite. The applications are distributed as software as a service (SaaS). == Products == Zoho uses an open API for its Writer, Sheet, Show, Creator, Meeting, and Planner products. It also has plugins into Microsoft Word and Excel, an OpenOffice.org plugin, and a plugin for Firefox. Zoho Office Suite is free for individuals but offers a plan for teams, which includes Zoho WorkDrive, Zoho Workplace and other Zoho apps. In October 2009, Zoho integrated some of their applications with the Google Apps online suite.

CrySyS Lab

CrySyS Lab (Hungarian pronunciation: [ˈkriːsis]) is part of the Department of Telecommunications at the Budapest University of Technology and Economics. The name is derived from "Laboratory of Cryptography and System Security", the full Hungarian name is CrySys Adat- és Rendszerbiztonság Laboratórium. == History == CrySyS Lab. was founded in 2003 by a group of security researchers at the Budapest University of Technology and Economics. Currently, it is located in the Infopark Budapest. The heads of the lab were Dr. István Vajda (2003–2010) and Dr. Levente Buttyán (2010-now). Since its establishment, the lab participated in several research and industry projects, including successful EU FP6 and FP7 projects (SeVeCom, a UbiSecSens and WSAN4CIP). == Research results == CrySyS Lab is recognized in research for its contribution to the area of security in wireless embedded systems. In this area, the members of the lab produced 5 books 4 book chapters 21 journal papers 47 conference papers 3 patents 2 Internet Draft The above publications had an impact factor of 30+ and obtained more than 7500 references. Several of these publications appeared in highly cited journals (e.g., IEEE Transactions on Dependable and Secure Systems, IEEE Transactions on Mobile Computing). == Forensics analysis of malware incidents == The laboratory was involved in the forensic analysis of several high-profile targeted attacks. In October 2011, CrySyS Lab discovered the Duqu malware; pursued the analysis of the Duqu malware and as a result of the investigation, identified a dropper file with an MS 0-day kernel exploit inside; and finally released a new open-source Duqu Detector Toolkit to detect Duqu traces and running Duqu instances. In May 2012, the malware analysis team at CrySyS Lab participated in an international collaboration aiming at the analysis of an as yet unknown malware, which they call sKyWIper. At the same time Kaspersky Lab analyzed the malware Flame and Iran National CERT (MAHER) the malware Flamer. Later, they turned out to be the same. Other analysis published by CrySyS Lab include the password analysis of the Hungarian ISP, Elender, and a thorough Hungarian security survey of servers after the publications of the Kaminsky DNS attack.

Correlation immunity

In mathematics, the correlation immunity of a Boolean function is a measure of the degree to which its outputs are uncorrelated with some subset of its inputs. Specifically, a Boolean function is said to be correlation-immune of order m if every subset of m or fewer variables in x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} is statistically independent of the value of f ( x 1 , x 2 , … , x n ) {\displaystyle f(x_{1},x_{2},\ldots ,x_{n})} . == Definition == A function f : F 2 n → F 2 {\displaystyle f:\mathbb {F} _{2}^{n}\rightarrow \mathbb {F} _{2}} is k {\displaystyle k} -th order correlation immune if for any independent n {\displaystyle n} binary random variables X 0 … X n − 1 {\displaystyle X_{0}\ldots X_{n-1}} , the random variable Z = f ( X 0 , … , X n − 1 ) {\displaystyle Z=f(X_{0},\ldots ,X_{n-1})} is independent from any random vector ( X i 1 … X i k ) {\displaystyle (X_{i_{1}}\ldots X_{i_{k}})} with 0 ≤ i 1 < … < i k < n {\displaystyle 0\leq i_{1}<\ldots

Sex differences in social media use

Men and women use social media in different ways and with different frequencies. In general, several researchers have found that women tend to use social network services (SNSs) more than men and primiarly to socialize. == Differences == === Predilection for usage === Many studies have found that women are more likely to use either specific SNSs such as Facebook or MySpace or SNSs in general. In 2015, 73% of online men and 80% of online women used social networking sites. The gap in gender differences has become less apparent in LinkedIn. In 2015 about 26 percent of online men and 25% of online women used the business-and employee-oriented networking site. Researchers who have examined the gender of users of multiple SNSs have found contradictory results. Hargittai's groundbreaking 2007 study examining race, gender, and other differences between undergraduate college student users of SNSs found that women were not only more likely to have used SNSes than men but that they were also more likely to have used many different services, including Facebook, MySpace, and Friendster; these differences persisted in several models and analyses. Although she only surveyed students at one institution – the University of Illinois at Chicago – Hargittai selected that institution intentionally as "an ideal location for studies of how different kinds of people use online sites and services." In contrast, data collected by the Pew Internet & American Life Project found that men were more likely to have multiple SNS profiles. Although the sample sizes of the two surveys are comparable – 1,650 Internet users in the Pew survey compared with 1,060 in Hargittai's survey – the data from the Pew survey are newer and arguably more representative of the entire adult United States population. Pinterest, Facebook, and Instagram attract more females. Picture sharing sites overall are very popular among women. Pinterest alone attracts three times as many female users than male. However, use of Pinterest by men has increased from 5% in 2012. Facebook attracts about 77% of women online. Instagram is also more likely to attract women. Men are more likely to participate in online forums like Reddit, Digg or Slashdot. One in five men claim to be a part of an online forum. === Uses === In general, women seem to use SNSs more to explicitly foster social connections. A study conducted by Pew research centers found that women were more avid users of social media. In November 2010, the gap between men and women was as high as 15%. Female participants in a multi-stage study conducted in 2007 to discover the motivations of Facebook users scored higher on scales for social connection and posting of photographs. Studies have also been conducted on the differences between females and males with regards to blogging. The Pew Research Center found that younger females are more likely to blog than males their own age, even males that are older than them. Similarly, in a study of blogs maintained in MySpace, women were found to be more likely to not only write blogs but also write about family, romantic relationships, friendships, and health in those blogs. A study of Swedish SNS users found that women were more likely to have expressions of friendship, specifically in the areas of (a) publishing photos of their friends, (b) specifically naming their best friends, and (c) writing poems to and about their friends. Women were also more likely to have expressions related to family relationships and romantic relationships. One of the key findings of this research is that those men who do have expressions of romantic relationships in their profile had expressions just as strong as the women. However, the researcher speculated that this may be in part due to a desire to publicly express heterosexual behaviors and mannerisms instead of merely expressing romantic feelings. A large-scale study of gender differences in MySpace found that both men and women tended to have a majority of female Friends, and both men and women tended to have a majority of female "Top" Friends in the site. A later study found women to author disproportionately many (public) comments in MySpace, but an investigation into the role of emotion in public MySpace comments found that women both give and receive stronger positive emotion. It was hypothesised that women are simply more effective at using social networking sites because they are better able to harness positive emotion. A study focused on the influence of gender and personality on individuals' use of online social networking websites such as Facebook, reported that men use social networking sites with the intention of forming new relationships, whereas, women use them more for relationship maintenance. In addition to this, women are more likely to use Facebook or MySpace to compare themselves to others and also to search for information. Men, however, are more likely to look at other people's profiles with in the intention to find friends. Women were less successful at actually finding new friends, but more successful at "maintaining existing relationships, making new relationships, using for academic purposes and following specific agenda". Similarly, men also self-reported this motivation "while women reported using them more for relationship maintenance". === Personality === OCEAN personality traits are known to systematically vary between human males and females. In one study, the same women were more extraverted and agreeable, such as less neurotic while on social media than offline. Other studies associated neuroticism with female use of social media. === Privacy === Privacy has been the primary topic of many studies of SNS users, and many of these studies have found differences between male and female SNS users, although some studies have found results contradictory to those found in other studies. Some researchers have found that women are more protective of their personal information and more likely to have private profiles. Other researchers have found that women are less likely to post some types of information. Acquisti and Gross found that women in their sample were less likely to reveal their sexual orientation, personal address, or cell phone number. This is similar to Pew Internet & American Life research of children users of SNSs that found that boys and girls presented different views of privacy and behaviors, with girls being more concerned about and restrictive of information such as city, town, last name, and cell phone number that could be used to locate them. At least one group of researchers has found that women are less likely to share information that "identifies them directly – last name, cell phone number, and address or home phone number," linking that resistance to women's greater concerns about "cyberstalking", "cyberbullying", and security problems. Despite these concerns about privacy, researchers have found that women are more likely to maintain up-to-date photos of themselves. Further, Kolek and Saunders found in their sample of college student Facebook users that women were more likely to not only post a photograph of themselves in their profile but that they were more likely to have a publicly viewable Facebook account (a contradictory finding compared to many other studies), post photos, and post photo albums. Women were more likely to have: (a) a publicly viewable Facebook account, (b) more photo albums, (c) more photos, (d) a photo of themselves as their profile picture, (e) positive references to alcohol, partying, or drugs, and (f) more positive references to or about the institution or institution-related activities. In general, women were more likely to disclose information about themselves in their Facebook profile, with the primary exception of sharing their telephone number. Similarly, female respondents to Strano's study were more likely to keep their profile photo recent and choose a photo that made them appear attractive, happy, and fun-loving. Citing several examples, Strano opined that there may also be a difference in how men and women Facebook users display and interpret profile photos depicting relationships. Privacy has also been a concern for the SnapChat app, which allows you to send messages either text or photo or video which then disappear. One study has shown that security is not a major concern for the majority of users and that most do not use Snapchat to send sensitive content (although up to 25% may do so experimentally). As part of their research almost no statistically significant gender differences were found. === Cyberbullying === Past research carried out to investigate if there are any gender differences in cyber-bullying has found that boys commit more cyber verbal bullying, cyber forgery and more violence based on hidden identity or presenting themselves as other person. === Mansplaining === A 2021 article found that mansplaining could be seen more prominent online rather than offl

Thinkfree Office

Thinkfree Office is a web-based commercial office productivity suite developed by South Korea-based Thinkfree Inc. It includes Word (a word processor), Spreadsheet (a spreadsheet) and Presentation (a presentation program). They are compatible with Microsoft Office's Word, PowerPoint, and Excel. It also features collaborative editing. The product is hosted on the client's server. == Supported file formats == Thinkfree Office supports ISO/IEC international standard ISO/IEC 26300 Open Document Format for Office Applications (odf, odt, odp, ods, odg). It also supports Microsoft's XML formats (docx, pptx, xlsx) and Microsoft's legacy binary formats (doc, ppt, xls). == Naming == The software was previously marketed under different names, such as Thinkfree Server, Thinkfree Online, Hancom Office Online, and Hancom Office Web. Eventually, the brand was consolidated under the name Thinkfree Office. == History == In June 2000, Thinkfree Inc. released Thinkfree Office, based in Silicon Valley, California. It is recognized as the world's first online office editor (predating Google Docs and Microsoft 365) and attracted significant media coverage, including reports on CNN. In 2001, Microsoft CEO Steve Ballmer highlighted Thinkfree as a significant competitor in a magazine interview, considering it a potential threat to his company, second only to Linux. In November 2003, Hancom, a South Korean office software company, signed a memorandum of understanding and subsequently acquired Thinkfree. In January 2004, Thinkfree expanded into other foreign markets. Subsidiary Haansoft USA, Inc. was created in San Jose, California to begin formal commercial operations in the US market. At the same time, a partnership was established with Riverdeep with the purpose of improving marketshare. In February 2004, expansion into the Japanese market began. A commercial agency agreement was signed with PSI in Shinjuku, Japan, which allowed for localized distribution. In addition, a global agreement was entered into with Yamada Denki, one of the three main computer distributors in Japan, for a total of 180,000 units. In May 2006, Thinkfree Office received the "Product of the Year" award at the Well-Connected Awards, USA. In January 2009, Thinkfree Mobile was launched at CES 2009 in Las Vegas. In April 2009, Thinkfree Live, Korea's first web office service, was launched. In June 2018, a partnership was formed with Amazon Web Services to integrate Thinkfree Office into WorkDocs, an in-house office suite. In October 2023, Hancom split its online office business unit as "Thinkfree Inc.".

Media engagement framework

The media engagement framework is a planning framework used by marketing professionals to understand the behavior of social media marketing-based audiences. The construct was introduced in the book, ROI of Social Media. Powell’s background in marketing ROI and Groves' experience and understanding of the applications of social media in business led to a collaboration. Dimos joined as a brand strategist for Litmus Group, a global management consulting firm. The media engagement framework consists of the definitions of personas (Individuals, Consumers and Influencers), referenced by the competitive set or constraint that applies to that persona and the measurement framework that might be applied to those personas. It is referenced at the center of the marketing process diagram, surrounded by the marketing functions of strategy, tactics, metrics and ROI. The marketing process diagram describes how the media engagement framework can apply to any strategic marketing activity but was developed to establish a completely integrated framework describing how both traditional and social media marketing activities can be planned, executed, measured and improved. == Application == The media engagement framework provides a strategic planning construct in which measurements and metrics play a crucial role. Applying the media engagement framework aids in the development and management of an effective online marketing presence leveraging social media to engage a market or audience. By first personifying the audience, the marketer is able to identify the limiting aspect of the engagements possible with that audience segment and then, understand the type of engagement metrics to apply. Each persona makes decisions differently about how he/she acts in the social media universe. A framework metric can be applied for each of these personas: Endorsement funnel for influencers Community engagement funnel for individuals Purchase funnel for consumers Individuals, influencers and consumers make decisions based on alternatives available to them and constraints put on them. To engage with an individual brands must realize they are competing against the time an individual spends on line. If they find something else more engaging, they will engage with that activity. Brands compete against other brands for the purchases of consumers acting in the category. Lastly, influencers have only so many endorsements they can make and therefore brands compete with other endorsers for the endorsement of an influencer. Creating engaging content by keeping target audience in mind like create content that audience find it funny, interesting, and relatable will encourage audience to share it on social networks. Which will be beneficial for you brand, getting more people to know about your business and brand. Contact Digilord to create engaging content for your brand. Use of listening tools (Google Alerts, Twitter Search, SocialMention.com, Veooz.com, Alterian SM2, Radian6, Sysomos, Buzzient etc.) can be employed within the model to help identify the members of the audience segment and to support the formation of other social engagement planning and management tools.