Eden: It's an Endless World!, also known simply as Eden (stylized in all caps), is a Japanese science fiction manga series written and illustrated by Hiroki Endo. It was serialized in Kodansha's seinen manga magazine Monthly Afternoon from September 1997 to June 2008, with its chapters collected in 18 tankōbon volumes. == Premise == The story is set in the near future, following the "closure virus" pandemic has killed 15 percent of the world's population, crippled or disfigured many more, with catastrophic effect on global politics. Its themes and many character names are taken from Gnostic mythology. == Plot == The series begins with a long introduction, with the characters Ennoia and Hannah living a peaceful life on a remote and isolated island called Eden, with researcher Lane Morris, who is their guardian and a victim of the pandemic. The events that led to this situation are revealed in flashbacks, leading up to the return of Ennoia's father, along with the forces of the Propater Federation. Following this, the story moves forwards twenty years, and focuses on Ennoia's son, Elijah, the main character, and his own conflict with the powerful and monopolistic Propater federation to save his sister, Mana Ballard, kidnapped by Propater when he was very young. She is being held to threaten Ennoia Ballard, father of the two characters, who has become a powerful drug lord in South America, feared and despised by many, including, to an extent, his own family. During a terrorist attack, Elijah, aged 15, is separated from his mother and his sister is kidnapped, along with his mother Hannah and now has to handle things on his own. Eden is about his coming-of-age as a man and trying to survive both bodily and morally in world that is too complex for mere "black and white". He encounters many other characters, both allies and enemies, all sharing the same struggle to survive in a post-apocalyptic dystopian world. Many stories are included of the people Elijah meets, telling their past or following life, sometimes volumes later, furthering understanding of the characters and giving increased depth to the world of the book as a whole. Later in the series, the story once again moves forwards in time, jumping four more years ahead. The Closure Virus, the cause of the original pandemic, mutates, this time assimilating non-organic matter as well as organic, known as "colloid" (or "Disclosure Virus"). The story rejoins Elijah, now 19 years old, as well as many other old characters, and some new, as the world begins to deal with this new threat that is swallowing many cities in the world, leaving lakes and craters, and many people. It is later discovered that the several colloids in the world, are linked with a net of underground auto-built "cables," and that the colloid itself, stores all the memories of the people it swallows. == Characters == Elijah Ballard (エリヤ・バラード, Eriya Barādo) Elijah is introduced while on the run from Propater. He becomes involved in his father's criminal activities, and undergoes a coming of age into adulthood. Ennoia Ballard (エンノイア・バラード, Ennoia Barādo) Elijah's father. Hannah Mayall (ハナ・メイオール, Hana Meiōru) Elijah's mother. Mana Ballard (マナ・バラード, Mana Barādo) Elijah's sister, who remains in Propater hands whilst her mother is rescued. Elijah's fight to free her is a focus of the later parts of the story. Nazarbaiev Khan (ナザルバイエフ・カーン, Nazarubaiefu Kān) Colonel Khan is an old soldier from Azerbaijan. He leads the Nomad group (including Kenji and Sophia) fleeing Propater at the start of the series. Khan became Kenji's mentor after killing his brother, and the two share a slightly strained, but at the same time, trusting, relationship. Sophia Theódores (ソフィア・テオドレス, Sofia Teodoresu) A powerful Greek computer hacker, and full-body cyborg. Maya (マーヤ, Māya) A nearly godlike AI, which seems to roughly correspond to the savior of Gnostic mythology. Kenji Asai (ケンジ・アサイ) The brother of a low-level yakuza boss. Helena Montoya (ヘレナ・モントーヤ, Herena Montōya) A prostitute now working in a brothel. Has a complex relationship with Elijah and acts as a surrogate big sister. == Media == === Manga === Eden: It's an Endless World! was written and illustrated by Hiroki Endo. The series ran in Kodansha's Monthly Afternoon magazine from September 25, 1997, to June 25, 2008. Kodansha collected its chapters into 18 tankōbon volumes, released from April 21, 1998, to July 23, 2008. In July 2005, Dark Horse Comics announced in San Diego Comic-Con that it has licensed Eden for North American distribution, with publication to begin in November of that year. As of March 2014, 14 volumes were released in total. ==== Volumes ==== == Reception == Eden was named Wizard magazine's best manga of 2007. In his review of another work by Hiroki Endo titled Hiroki Endo's Tanpenshu, David F. Smith of Newtype USA has called Eden one of the best manga American money can buy.
Super-resolution optical fluctuation imaging
Super-resolution optical fluctuation imaging (SOFI) is a post-processing method for the calculation of super-resolved images from recorded image time series that is based on the temporal correlations of independently fluctuating fluorescent emitters. SOFI has been developed for super-resolution of biological specimen that are labelled with independently fluctuating fluorescent emitters (organic dyes, fluorescent proteins). In comparison to other super-resolution microscopy techniques such as STORM or PALM that rely on single-molecule localization and hence only allow one active molecule per diffraction-limited area (DLA) and timepoint, SOFI does not necessitate a controlled photoswitching and/ or photoactivation as well as long imaging times. Nevertheless, it still requires fluorophores that are cycling through two distinguishable states, either real on-/off-states or states with different fluorescence intensities. In mathematical terms SOFI-imaging relies on the calculation of cumulants, for what two distinguishable ways exist. For one thing an image can be calculated via auto-cumulants that by definition only rely on the information of each pixel itself, and for another thing an improved method utilizes the information of different pixels via the calculation of cross-cumulants. Both methods can increase the final image resolution significantly although the cumulant calculation has its limitations. Actually SOFI is able to increase the resolution in all three dimensions. == Principle == Likewise to other super-resolution methods SOFI is based on recording an image time series on a CCD- or CMOS camera. In contrary to other methods the recorded time series can be substantially shorter, since a precise localization of emitters is not required and therefore a larger quantity of activated fluorophores per diffraction-limited area is allowed. The pixel values of a SOFI-image of the n-th order are calculated from the values of the pixel time series in the form of a n-th order cumulant, whereas the final value assigned to a pixel can be imagined as the integral over a correlation function. The finally assigned pixel value intensities are a measure of the brightness and correlation of the fluorescence signal. Mathematically, the n-th order cumulant is related to the n-th order correlation function, but exhibits some advantages concerning the resulting resolution of the image. Since in SOFI several emitters per DLA are allowed, the photon count at each pixel results from the superposition of the signals of all activated nearby emitters. The cumulant calculation now filters the signal and leaves only highly correlated fluctuations. This provides a contrast enhancement and therefore a background reduction for good measure. As it is implied in the figure on the left the fluorescence source distribution: ∑ k = 1 N δ ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) {\displaystyle \sum _{k=1}^{N}\delta ({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t)} is convolved with the system's point spread function (PSF) U(r). Hence the fluorescence signal at time t and position r → {\displaystyle {\vec {r}}} is given by F ( r → , t ) = ∑ k = 1 N U ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) . {\displaystyle F({\vec {r}},t)=\sum _{k=1}^{N}U({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t).} Within the above equations N is the amount of emitters, located at the positions r → k {\displaystyle {\vec {r}}_{k}} with a time-dependent molecular brightness ε k ⋅ s k {\displaystyle \varepsilon _{k}\cdot s_{k}} where ε k {\displaystyle \varepsilon _{k}} is a variable for the constant molecular brightness and s k ( t ) {\displaystyle s_{k}(t)} is a time-dependent fluctuation function. The molecular brightness is just the average fluorescence count-rate divided by the number of molecules within a specific region. For simplification it has to be assumed that the sample is in a stationary equilibrium and therefore the fluorescence signal can be expressed as a zero-mean fluctuation: δ F ( r → , t ) = F ( r → , t ) − ⟨ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=F({\vec {r}},t)-\langle F({\vec {r}},t)\rangle _{t}} where ⟨ ⋯ ⟩ t {\displaystyle \langle \cdots \rangle _{t}} denotes time-averaging. The auto-correlation here e.g. the second-order can then be described deductively as follows for a certain time-lag τ {\displaystyle \tau } : δ F ( r → , t ) = ⟨ δ F ( r → , t + τ ) ⋅ δ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=\langle \delta F({\vec {r}},t+\tau )\cdot \delta F({\vec {r}},t)\rangle _{t}} From these equations it follows that the PSF of the optical system has to be taken to the power of the order of the correlation. Thus in a second-order correlation the PSF would be reduced along all dimensions by a factor of 2 {\displaystyle {\sqrt {2}}} . As a result, the resolution of the SOFI-images increases according to this factor. === Cumulants versus correlations === Using only the simple correlation function for a reassignment of pixel values, would ascribe to the independency of fluctuations of the emitters in time in a way that no cross-correlation terms would contribute to the new pixel value. Calculations of higher-order correlation functions would suffer from lower-order correlations for what reason it is superior to calculate cumulants, since all lower-order correlation terms vanish. == Cumulant-calculation == === Auto-cumulants === For computational reasons it is convenient to set all time-lags in higher-order cumulants to zero so that a general expression for the n-th order auto-cumulant can be found: A C n ( r → , τ 1 … n − 1 = 0 ) = ∑ k = 1 N U n ( r → − r → k ) ε k n w k ( 0 ) {\displaystyle AC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\sum _{k=1}^{N}U^{n}({\vec {r}}-{\vec {r}}_{k})\varepsilon _{k}^{n}w_{k}(0)} w k {\displaystyle w_{k}} is a specific correlation based weighting function influenced by the order of the cumulant and mainly depending on the fluctuation properties of the emitters. Albeit there is no fundamental limitation in calculating very high orders of cumulants and thereby shrinking the FWHM of the PSF there are practical limitations according to the weighting of the values assigned to the final image. Emitters with a higher molecular brightness will show a strong increase in terms of the pixel cumulant value assigned at higher-orders as well as this performance can be expected from a diverse appearance of fluctuations of different emitters. A wide intensity range of the resulting image can therefore be expected and as a result dim emitters can get masked by bright emitters in higher-order images:. The calculation of auto-cumulants can be realized in a very attractive way in a mathematical sense. The n-th order cumulant can be calculated with a basic recursion from moments K n ( r → ) = μ n ( r → ) − ∑ i = 1 n − 1 ( n − 1 i ) K n − i ( r → ) μ i ( r → ) {\displaystyle K_{n}({\vec {r}})=\mu _{n}({\vec {r}})-\sum _{i=1}^{n-1}{\begin{pmatrix}n-1\\i\end{pmatrix}}K_{n-i}({\vec {r}})\mu _{i}({\vec {r}})} where K is a cumulant of the index's order, likewise μ {\displaystyle \mu } represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating cumulants with standard formulas. It allows for the calculation of cumulants with only little time of computing and is, as it is well implemented, even suitable for the calculation of high-order cumulants on large images. === Cross-cumulants === In a more advanced approach cross-cumulants are calculated by taking the information of several pixels into account. Cross-cumulants can be described as follows: C C n ( r → , τ 1 … n − 1 = 0 ) = ∏ j < l n U ( r → j − r → l n ) ⋅ ∑ i = 1 N U n ( r → i − ∑ k n r → k n ) ε i n w i ( 0 ) {\displaystyle CC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\prod _{j The Online Safety Amendment (Social Media Minimum Age) Act 2024 is an Australian act of parliament that prohibits minors under the age of 16 from holding an account on certain social media platforms. It is an amendment to the Online Safety Act 2021 and was passed by the Parliament of Australia on 29 November 2024. It imposes monetary penalties on social media companies that fail to take reasonable steps to prevent minors under 16 that are located in Australia from having accounts on their services. The legislation allows the government to determine which social media platforms must ban age‑restricted users and proclaim a date for the commencement of the ban, with those provisions taking effect on 10 December 2025. Facebook, Instagram, Reddit, Snapchat, TikTok, Twitter, Threads, Twitch, Kick, and YouTube were age‑restricted on 10 December 2025, with the possibility that more platforms may be added. The act is being challenged in the High Court by the Digital Freedom Project. == Background == The ban on access to social media by young people by the federal government originated in November 2023, when shadow communications minister David Coleman introduced a private member's bill requiring the government to conduct a trial for age-verification technology on pornography and social media platforms. While the bill did not succeed, the Albanese government funded the trial in the 2024 Australian federal budget. In June 2024, opposition leader Peter Dutton pledged that a Coalition government would implement a ban on social media for under-16s within 100 days of taking office. The following month, prime minister Anthony Albanese announced the government would introduce legislation banning under-16s from social media. The Online Safety Amendment (Social Media Minimum Age) Bill 2024 was introduced into parliament by minister for communications Michelle Rowland on 21 November 2024, passing both houses on 28 November 2024. The ban on access to social media by young people by the federal government also gained momentum following an entreaty by the wife of the premier of South Australia, Peter Malinauskas, to her husband. She requested that he read The Anxious Generation by Jonathan Haidt and take action to address the impact of social media on the mental health of children. The couple have four young children, and, thinking of them, the premier thought that government should play a part in helping parents to regulate use of social media by their children at home. Malinauskas contacted former High Court chief justice Robert French, who agreed to look at the issue, and in September 2024 handed the premier a 267 page proposal, which he dubbed a "Swiss Army knife" rather than a machete, to adjust to social media's "changing landscape and its complexity". The leaders of other states and territories gave their support to Malinauskas's idea, and he took the French report to National Cabinet to collaborate with chief ministers, premiers, and the prime minister. Community support swelled after stories of parents who had lost their children to suicide after being bullied on social media were published. Albanese himself was moved by a personal letter received from Kelly O'Brien, whose 12-year-old daughter Charlotte had taken her own life due to bullying at school. An event took place at the sidelines of the United Nations General Assembly session in September 2025 at which a mother spoke of her daughter's suicide as "death by bullying ... enabled by social media". The speech won support from world leaders in Greece, Fiji, Tonga and the president of the European Commission Ursula von der Leyen. In early September 2024, South Australia proposed legislation similar to the federal law now in place. The state-based version was intended to ban users under the age of 14, unlike the federal law, which bans those under 16. The state-based law also proposed to require parental consent for 14 and 15‑year‑olds. Later in September, prime minister Anthony Albanese announced that his government intended to introduce legislation to set a minimum age requirement for social media. In November 2024, the federal government indicated their intention to engage the Age Check Certification Scheme following a tender process for an age assurance technology trial. The Albanese government's proposed ban was supported by the governments of every state and territory. Albanese described social media as a "scourge", and said "I want people to spend more time on the footy field or the netball court than they're spending on their phones", that family members are "worried sick about the safety of our kids online", and that social media "is having a negative impact on young people's mental health and on anxiety". Albanese's statements followed an earlier pledge by Liberal opposition leader Peter Dutton who was pushed by the early advocacy of shadow communications minister David Coleman to implement a ban on social media for under 16s within 100 days of being elected. The opposition organised an open letter signed by 140 experts who specialise in child welfare and technology. The opposition was concerned about the invasion of privacy that will occur with the introduction of identification-based age checks. An advocacy group for digital companies in Australia called the plans a "20th Century response to 21st Century challenges". A director of a mental health service voiced concerns, stating that "73% of young people across Australia who accessed mental health support did so through social media". == Implementation == Social media companies will receive a transition period of one year after the legislation is enacted to introduce reasonable controls preventing minors under the age of 16 from holding accounts on their services while physically located in Australia. Enforcement will involve fines of up to A$49.5 million for companies failing to take such steps, with no consequences for parents and children who violate the restrictions. There are no parental consent exceptions to the ban, and while the use of virtual private networks (VPNs) to access these services remains legal in Australia, the services are expected to try to stop under 16s from using VPNs to pretend to be outside Australia. The expectation is to make best-efforts to implement the ban on platforms including Facebook, Instagram, Reddit, Snapchat, TikTok, Twitter, Threads, Twitch, Kick and YouTube. Some social media companies are now obligated to become good enough at profiling Australian children under 16 to satisfy the Australian government they tried to implement the ban to avoid being fined. Consequently, social media companies said they will try to identify restricted users using various methods including behavioural inferencing. On 5 November 2025, it was announced that online gaming platform Roblox will not be banned, but Reddit and live-streaming platform Kick will be added to the list of platforms to be banned. A report by Age Check Certification Scheme, a UK company recruited by the government to consult on the technology used to implement the restrictions, was issued in June 2025, ahead of the December deadline to implement the ban. In June 2025, the preliminary report was released, which stated that "there are no significant technological barriers" to implementing the ban. In late July 2025, Google warned that it would sue the Australian government if YouTube was included in the ban. On 30 July, the government announced that it would extend its social media age limit to include YouTube, following advice from Grant. On 30 July 2025, the minister for communications, Anika Wells, published the Online Safety (Age-Restricted Social Media Platforms) Rules 2025, which specify exactly which types of social media platforms will be banned for certain users. On 31 August 2025, the full report was released, which stated that it would technically be possible to implement the ban; however, coordination among different services is required to successfully implement it. It also highlighted the benefits and flaws of different methods of age verification. On 16 September 2025, it was announced that the eSafety Commissioner will be able to take legal action against social media companies that have not pursued reasonable steps to bar users under the age of 16, and that fines can range up to A$49.5 million against these companies in court. On 19 November 2025, Meta announced that from 4 December their platforms (Instagram, Facebook, and Threads) would be removing users under the age of 16 ahead of the 10 December deadline. Users will be able to scan a face or provide an identity document to prove their age. On 21 November 2025, the eSafety Commissioner announced that the live-streaming platform Twitch will be included in the ban, but that Pinterest would not be. In December 2025, eSafety Commissioner Julie Inman Grant suggested efforts to block users include use by social media companies of various "signals" to identify children that are SPKAC (Signed Public Key and Challenge, also known as Netscape SPKI) is a format for sending a certificate signing request (CSR): it encodes a public key, that can be manipulated using OpenSSL. It is created using the little documented HTML keygen element inside a number of Netscape compatible browsers. == Standardisation == There exists an ongoing effort to standardise SPKAC through an Internet Draft in the Internet Engineering Task Force (IETF). The purpose of this work has been to formally define what has existed prior as a de facto standard, and to address security deficiencies, particular with respect to historic insecure use of MD5 that has since been declared unsafe for use with digital signatures. == Implementations == HTML5 originally specified the Cryptovirology refers to the study of cryptography use in malware, such as ransomware and asymmetric backdoors. Traditionally, cryptography and its applications are defensive in nature, and provide privacy, authentication, and security to users. Cryptovirology employs a twist on cryptography, showing that it can also be used offensively. It can be used to mount extortion based attacks that cause loss of access to information, loss of confidentiality, and information leakage, tasks which cryptography typically prevents. The field was born with the observation that public-key cryptography can be used to break the symmetry between what an antivirus analyst sees regarding malware and what the attacker sees. The antivirus analyst sees a public key contained in the malware, whereas the attacker sees the public key contained in the malware as well as the corresponding private key (outside the malware) since the attacker created the key pair for the attack. The public key allows the malware to perform trapdoor one-way operations on the victim's computer that only the attacker can undo. == Overview == The field encompasses covert malware attacks in which the attacker securely steals private information such as symmetric keys, private keys, PRNG state, and the victim's data. Examples of such covert attacks are asymmetric backdoors. An asymmetric backdoor is a backdoor (e.g., in a cryptosystem) that can be used only by the attacker, even after it is found. This contrasts with the traditional backdoor that is symmetric, i.e., anyone that finds it can use it. Kleptography, a subfield of cryptovirology, is the study of asymmetric backdoors in key generation algorithms, digital signature algorithms, key exchanges, pseudorandom number generators, encryption algorithms, and other cryptographic algorithms. The NIST Dual EC DRBG random bit generator has an asymmetric backdoor in it. The EC-DRBG algorithm utilizes the discrete-log kleptogram from kleptography, which by definition makes the EC-DRBG a cryptotrojan. Like ransomware, the EC-DRBG cryptotrojan contains and uses the attacker's public key to attack the host system. The cryptographer Ari Juels indicated that NSA effectively orchestrated a kleptographic attack on users of the Dual EC DRBG pseudorandom number generation algorithm and that, although security professionals and developers have been testing and implementing kleptographic attacks since 1996, "you would be hard-pressed to find one in actual use until now." Due to public outcry about this cryptovirology attack, NIST rescinded the EC-DRBG algorithm from the NIST SP 800-90 standard. Covert information leakage attacks carried out by cryptoviruses, cryptotrojans, and cryptoworms that, by definition, contain and use the public key of the attacker is a major theme in cryptovirology. In "deniable password snatching," a cryptovirus installs a cryptotrojan that asymmetrically encrypts host data and covertly broadcasts it. This makes it available to everyone, noticeable by no one (except the attacker), and only decipherable by the attacker. An attacker caught installing the cryptotrojan claims to be a virus victim. An attacker observed receiving the covert asymmetric broadcast is one of the thousands, if not millions of receivers, and exhibits no identifying information whatsoever. The cryptovirology attack achieves "end-to-end deniability." It is a covert asymmetric broadcast of the victim's data. Cryptovirology also encompasses the use of private information retrieval (PIR) to allow cryptoviruses to search for and steal host data without revealing the data searched for even when the cryptotrojan is under constant surveillance. By definition, such a cryptovirus carries within its own coding sequence the query of the attacker and the necessary PIR logic to apply the query to host systems. == History == The first cryptovirology attack and discussion of the concept was by Adam L. Young and Moti Yung, at the time called "cryptoviral extortion" and it was presented at the 1996 IEEE Security & Privacy conference. In this attack, a cryptovirus, cryptoworm, or cryptotrojan contains the public key of the attacker and hybrid encrypts the victim's files. The malware prompts the user to send the asymmetric ciphertext to the attacker who will decipher it and return the symmetric decryption key it contains for a fee. The victim needs the symmetric key to decrypt the encrypted files if there is no way to recover the original files (e.g., from backups). The 1996 IEEE paper predicted that cryptoviral extortion attackers would one day demand e-money, long before Bitcoin even existed. Many years later, the media relabeled cryptoviral extortion as ransomware. In 2016, cryptovirology attacks on healthcare providers reached epidemic levels, prompting the U.S. Department of Health and Human Services to issue a Fact Sheet on Ransomware and HIPAA. The fact sheet states that when electronic protected health information is encrypted by ransomware, a breach has occurred, and the attack therefore constitutes a disclosure that is not permitted under HIPAA, the rationale being that an adversary has taken control of the information. Sensitive data might never leave the victim organization, but the break-in may have allowed data to be sent out undetected. California enacted a law that defines the introduction of ransomware into a computer system with the intent of extortion as being against the law. == Examples == === Tremor virus === While viruses in the wild have used cryptography in the past, the only purpose of such usage of cryptography was to avoid detection by antivirus software. For example, the tremor virus used polymorphism as a defensive technique in an attempt to avoid detection by anti-virus software. Though cryptography does assist in such cases to enhance the longevity of a virus, the capabilities of cryptography are not used in the payload. The One-half virus was amongst the first viruses known to have encrypted affected files. === Tro_Ransom.A virus === An example of a virus that informs the owner of the infected machine to pay a ransom is the virus nicknamed Tro_Ransom.A. This virus asks the owner of the infected machine to send $10.99 to a given account through Western Union. Virus.Win32.Gpcode.ag is a classic cryptovirus. This virus partially uses a version of 660-bit RSA and encrypts files with many different extensions. It instructs the owner of the machine to email a given mail ID if the owner desires the decryptor. If contacted by email, the user will be asked to pay a certain amount as ransom in return for the decryptor. === CAPI === It has been demonstrated that using just 8 different calls to Microsoft's Cryptographic API (CAPI), a cryptovirus can satisfy all its encryption needs. == Other uses of cryptography-enabled malware == Apart from cryptoviral extortion, there are other potential uses of cryptoviruses, such as deniable password snatching, cryptocounters, private information retrieval, and in secure communication between different instances of a distributed cryptovirus. Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from two-dimensional cross-sections or projections, as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example. The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron. Shape factors are often normalized, that is, the value ranges from zero to one. A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube. == Aspect ratio == The most common shape factor is the aspect ratio, a function of the largest diameter and the smallest diameter orthogonal to it: A R = d min d max {\displaystyle A_{R}={\frac {d_{\min }}{d_{\max }}}} The normalized aspect ratio varies from approaching zero for a very elongated particle, such as a grain in a cold-worked metal, to near unity for an equiaxed grain. The reciprocal of the right side of the above equation is also used, such that the AR varies from one to approaching infinity. == Circularity == Another very common shape factor is the circularity (or isoperimetric quotient), a function of the perimeter P and the area A: f circ = 4 π A P 2 {\displaystyle f_{\text{circ}}={\frac {4\pi A}{P^{2}}}} The circularity of a circle is 1, and much less than one for a starfish footprint. The reciprocal of the circularity equation is also used, such that fcirc varies from one for a circle to infinity. == Elongation shape factor == The less-common elongation shape factor is defined as the square root of the ratio of the two second moments in of the particle around its principal axes. f elong = i 2 i 1 {\displaystyle f_{\text{elong}}={\sqrt {\frac {i_{2}}{i_{1}}}}} == Compactness shape factor == The compactness shape factor is a function of the polar second moment in of a particle and a circle of equal area A. f comp = A 2 2 π i 1 2 + i 2 2 {\displaystyle f_{\text{comp}}={\frac {A^{2}}{2\pi {\sqrt {{i_{1}}^{2}+{i_{2}}^{2}}}}}} The fcomp of a circle is one, and much less than one for the cross-section of an I-beam. == Waviness shape factor == The waviness shape factor of the perimeter is a function of the convex portion Pcvx of the perimeter to the total. f wav = P cvx P {\displaystyle f_{\text{wav}}={\frac {P_{\text{cvx}}}{P}}} Some properties of metals and ceramics, such as fracture toughness, have been linked to grain shapes. == An application of shape factors == Greenland, the largest island in the world, has an area of 2,166,086 km2; a coastline (perimeter) of 39,330 km; a north–south length of 2670 km; and an east–west length of 1290 km. The aspect ratio of Greenland is A R = 1290 2670 = 0.483 {\displaystyle A_{R}={\frac {1290}{2670}}=0.483} The circularity of Greenland is f circ = 4 π ( 2166086 ) 39330 2 = 0.0176. {\displaystyle f_{\text{circ}}={\frac {4\pi (2166086)}{39330^{2}}}=0.0176.} The aspect ratio is agreeable with an eyeball-estimate on a globe. Such an estimate on a typical flat map, using the Mercator projection, would be less accurate due to the distorted scale at high latitudes. The circularity is deceptively low, due to the fjords that give Greenland a very jagged coastline (see the coastline paradox). A low value of circularity does not necessarily indicate a lack of symmetry, and shape factors are not limited to microscopic objects. A virtual influencer, sometimes described as a virtual persona or virtual model, is a computer-generated fictional character that can be used for a variety of marketing-related purposes, but most frequently for social media marketing, in lieu of online human "influencers". Most virtual influencers are designed using computer graphics and motion capture technology to resemble real people in realistic situations. Common derivatives of virtual influencers include VTubers, which broadly refer to online entertainers and YouTubers who represent themselves using virtual avatars instead of their physical selves. == History == Virtual influencers are fundamentally synonymous with virtual idols, which originate from Japan's anime and Japanese idol culture that dates back to the 1980s. The first virtual idol created was Lynn Minmay, a fictional singer and main character of the anime television series Super Dimension Fortress Macross (1982) and the animated film adaptation Macross: Do You Remember Love? (1984). Minmay's success led to the production of more Japanese virtual idols, such as EVE from the Japanese cyberpunk anime Megazone 23 (1985), and Sharon Apple in Macross Plus (1994). Virtual idols were not always well received – in 1995, Japanese talent agency Horipro created Kyoko Date, which was inspired by the Macross franchise and dating sim games such as Tokimeki Memorial (1994). Date failed to gain commercial success despite drawing headlines for her debut as a CGI idol, largely due to technical limitations leading to issues such as unnatural movements, an issue also known as the uncanny valley. Since their inception, many virtual idols created have achieved continual success, with notable names including the Vocaloid singer Hatsune Miku, and the VTuber Kizuna AI. Technological advancements have also enabled production teams to use artificial intelligence and advanced techniques to customize the personalities and behavior of virtual idols. Due to modern-day advancements in technology, many virtual idols have held real-life tours and events. Notable ones include Hatsune Miku's titular tour Miku Expo and Hololive's concerts with many of their idols from their English, Japanese and Indonesian branches. Some notable events including virtual singers and influencers have included: Hatsune Miku opening for Lady Gaga in 2014 and Hoshimachi Suisei's concerts at the famous Budokan venue in Japan and her addition to the Forbes Japan list of '30 Under 30' individuals who are changing the world in their respective fields. == Benefits and criticism == From a branding perspective, virtual influencers are perceived to be much less likely to be mired in scandals. In China, celebrities caught in bad publicity such as singer Wang Leehom and entertainer Kris Wu have heightened the appeal of virtual influencers, since their existence relies entirely on computer-generated imagery and they are therefore unlikely to cause any damage to a brand's image by association. Some studies have also suggested that Generation Z consumers have a unique appetite for virtual idols and influencers, since they grew up in the age of the internet. Studies also show that human-like appearance of virtual influencers show higher message credibility than anime-like virtual influencers. Scholars and commentators have also questioned the ethics and cultural impact of virtual influencers, arguing that computer-generated personas can entrench unrealistic beauty standards while diffusing accountability for labor, identity, and consent. Business and marketing analysts have also warned that disclosure and governance remain inconsistent, recommending clearer guardrails and transparency when brands deploy synthetic spokespeople. In 2025, reporting highlighted concerns that AI-driven "virtual humans" could displace human creators and sales workers, intensifying debates over the future of creative labor and authenticity online. == Notable examples == === Virtual bands === Eternity - A South Korean virtual idol group formed by Pulse9. Gorillaz - A virtual band formed in 1998. K/DA - A virtual K-pop girl group created as part of the League of Legends video game franchise. MAVE: - A South Korean virtual girl group formed in 2023 by Metaverse Entertainment. Pentakill - A virtual heavy metal band created as part of the League of Legends video game franchise. Plave (band) - A South Korean virtual boy band formed by VLast. Squid Sisters and Off the Hook - Two virtual pop idol duos as part of the Splatoon series. Studio Killers - A Finnish-Danish-British virtual band formed in 2011. === Vocaloids === Hatsune Miku (modeled after Saki Fujita) Kagamine Rin/Len (modeled after Asami Shimoda) Megurine Luka (modeled after Yū Asakawa) Meiko (modeled after Meiko Haigō) Kaito (modeled after Naoto Fūga) === VTubers === Kano Kizuna AI Neuro-sama VShojo Ironmouse Projekt Melody Nijisanji Hololive Akai Haato Gawr Gura Hoshimachi Suisei Natsuiro Matsuri === Other examples === Ami Yamato Crazy Frog FN Meka IA Kuki AI Kyoko Date Kyra Miquela Naevis Shudu GramOnline Safety Amendment (Social Media Minimum Age) Act 2024
SPKAC
Cryptovirology
Shape factor (image analysis and microscopy)
Virtual influencer