title: RedTube

text: The BBC reports that the IP addresses were provided to the law firm by the court in Cologne, which began a retrospective review of its decision after receiving complaints. While sending out cease-and-desist letters to Internet users for copyright offenses related to filesharing had been common practice in Germany before, this marks the first time that legal measures are taken against people for merely watching streamed content from a website.


title: Avogadro constant

text: The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining constant with an exact value of . It is named after the Italian scientist Amedeo Avogadro by Stanislao Cannizzaro, who explained this number four years after Avogadro's death while at the Karlsruhe Congress in 1860.


title: Avogadro constant

text: The numeric value of the Avogadro constant expressed in reciprocal moles, a dimensionless number, is called the Avogadro number. In older literature, the Avogadro number is denoted or , which is the number of particles that are contained in one mole, exactly .


title: Avogadro constant

text: The Avogadro number is the approximate number of nucleons (protons or neutrons) in one gram of ordinary matter. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is approximately the number of nucleons in one constituent particle of the substance. It is numerically equal (for all practical purposes) to the average mass of one molecule (or atom) the compound in daltons (unified atomic mass units); one dalton being of the mass of one carbon-12 atom. For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water ( molecules) is about 18.0153 grams. Thus, the Avogadro constant is the proportionality factor that relates the molar mass of a substance to the average mass of one molecule.


title: Avogadro constant

text: The Avogadro constant also relates the molar volume of a substance to the average volume nominally occupied by one of its particles, when both are expressed in the same units of volume. For example, since the molar volume of water in ordinary conditions is about 18 mL/mol, the volume occupied by one molecule of water is about , or about (cubic angstroms). For a crystalline substance, it similarly relates its molar volume (in mol/mL), the volume of the repeating unit cell of the crystals (in mL), to the number of molecules in that cell.


title: Avogadro constant

text: The Avogadro number (or constant) has been defined in many different ways through its long history. Its approximate value was first determined, indirectly, by Josef Loschmidt in 1865. (Avogadro's number is closely related to the Loschmidt constant, and the two concepts are sometimes confused.) It was initially defined by Jean Perrin as the number of atoms in 16 grams of oxygen. It was later redefined in the 14th conference of the International Bureau of Weights and Measures (BIPM) as the number of atoms in 12 grams of the isotope carbon-12 (C). In each case, the mole was defined as the quantity of a substance that contained the same number of atoms as those reference samples. In particular, when carbon-12 was the reference, one mole of carbon-12 was exactly 12 grams of the element.


title: Avogadro constant

text: These definitions meant that the value of the Avogadro number depended on the experimentally determined value of the mass (in grams) of one atom of those elements, and therefore it was known only to a limited number of decimal digits. However, in its 26th Conference, the BIPM adopted a different approach: effective 20 May 2019, it defined the Avogadro number as the exact value , and redefined the mole as the amount of a substance under consideration that contains constituent particles of the substance. Under the new definition, the mass of one mole of any substance (including hydrogen, carbon-12, and oxygen-16) is times the average mass of one of its constituent particles – a physical quantity whose precise value has to be determined experimentally for each substance.


title: Avogadro constant

text: The Avogadro constant is named after the Italian scientist Amedeo Avogadro (1776–1856), who, in 1811, first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas.


title: Avogadro constant

text: The name "Avogadro's number" was coined in 1909 by the physicist Jean Perrin, who defined it as the number of molecules in exactly 16 grams of oxygen. The goal of this definition was to make the mass of a mole of a substance, in grams, be numerically equal to the mass of one molecule relative to the mass of the hydrogen atom; which, because of the law of definite proportions, was the natural unit of atomic mass, and was assumed to be 1/16 of the atomic mass of oxygen.


title: Avogadro constant

text: The value of Avogadro's number (not yet known by that name) was first obtained indirectly by Josef Loschmidt in 1865, by estimating the number of particles in a given volume of gas. This value, the number density of particles in an ideal gas, is now called the Loschmidt constant in his honor, and is related to the Avogadro constant, , by


title: Avogadro constant

text: where is the pressure, is the gas constant, and is the absolute temperature. Because of this work, the symbol is sometimes used for the Avogadro constant, and, in German literature, that name may be used for both constants, distinguished only by the units of measurement. (However, should not be confused with the entirely different Loschmidt constant in English-language literature.)


title: Avogadro constant

text: Perrin himself determined Avogadro's number by several different experimental methods. He was awarded the 1926 Nobel Prize in Physics, largely for this work.


title: Avogadro constant

text: The electric charge per mole of electrons is a constant called the Faraday constant and has been known since 1834, when Michael Faraday published his works on electrolysis. In 1910, Robert Millikan obtained the first measurement of the charge on an electron. Dividing the charge on a mole of electrons by the charge on a single electron provided a more accurate estimate of the Avogadro number.


title: Avogadro constant

text: In 1971, the International Bureau of Weights and Measures (BIPM) decided to regard the amount of substance as an independent dimension of measurement, with the mole as its base unit in the International System of Units (SI). Specifically, the mole was defined as an amount of a substance that contains as many elementary entities as there are atoms in .


title: Avogadro constant

text: By this definition, the common rule of thumb that "one gram of matter contains nucleons" was exact for carbon-12, but slightly inexact for other elements and isotopes. On the other hand, one mole of any substance contained exactly as many molecules as one mole of any other substance.


title: Avogadro constant

text: As a consequence of this definition, in the SI system the Avogadro constant had the dimensionality of reciprocal of amount of substance rather than of a pure number, and had the approximate value with units of mol. By this definition, the value of inherently had to be determined experimentally.


title: Avogadro constant

text: The BIPM also named the "Avogadro "constant"", but the term "Avogadro number" continued to be used especially in introductory works.


title: Avogadro constant

text: In 2017, the BIPM decided to change the definitions of mole and amount of substance. The mole was redefined as being the amount of substance containing exactly elementary entities. One consequence of this change is that the mass of a mole of C atoms is no longer exactly 0.012 kg. On the other hand, the dalton ( universal atomic mass unit) remains unchanged as of the mass of C. Thus, the molar mass constant is no longer exactly 1 g/mol, although the difference ( in relative terms, as of March 2019) is insignificant for practical purposes.


title: Kodak

text: The Eastman Kodak Company (referred to simply as Kodak ) is an American public company that produces various products related to its historic basis in analogue photography. The company is headquartered in Rochester, New York, and is incorporated in New Jersey. Kodak provides packaging, functional printing, graphic communications, and professional services for businesses around the world. Its main business segments are Print Systems, Enterprise Inkjet Systems, Micro 3D Printing and Packaging, Software and Solutions, and Consumer and Film. It is best known for photographic film products.


title: Kodak

text: Kodak was founded by George Eastman and Henry A. Strong on May 23, 1892. During most of the 20th century, Kodak held a dominant position in photographic film. The company's ubiquity was such that its "Kodak moment" tagline entered the common lexicon to describe a personal event that deserved to be recorded for posterity. Kodak began to struggle financially in the late 1990s, as a result of the decline in sales of photographic film and its slowness in moving to digital photography, despite developing the first self-contained digital camera. As a part of a turnaround strategy, Kodak began to focus on digital photography and digital printing, and attempted to generate revenues through aggressive patent litigation.


title: Kodak

text: In January 2012, Kodak filed for Chapter 11 bankruptcy protection in the United States Bankruptcy Court for the Southern District of New York. Shortly thereafter Kodak announced that it would stop making digital cameras, pocket video cameras and digital picture frames and focus on the corporate digital imaging market. Digital cameras are still sold under the Kodak brand by JK Imaging Ltd under an agreement with Kodak. In August 2012, Kodak announced its intention to sell its photographic film, commercial scanners and kiosk operations, as a measure to emerge from bankruptcy, but not its motion picture film operations. In January 2013, the Court approved financing for Kodak to emerge from bankruptcy by mid 2013. Kodak sold many of its patents for approximately $525,000,000 to a group of companies (including Apple, Google, Facebook, Amazon, Microsoft, Samsung, Adobe Systems, and HTC) under the names Intellectual Ventures and RPX Corporation. On September 3, 2013, the company emerged from bankruptcy having shed its large legacy liabilities and exited several businesses. Personalized Imaging and Document Imaging are now part of Kodak Alaris, a separate company owned by the UK-based Kodak Pension Plan.


title: Kodak

text: In response to the COVID-19 pandemic in 2020, Kodak announced in late July that year it would begin production of pharmaceutical materials.


title: Kodak

text: The letter "k" was a favorite of Eastman's; he is quoted as saying, "it seems a strong, incisive sort of letter."


title: Kodak

text: He and his mother, Maria, devised the name "Kodak" using an Anagrams set. Eastman said that there were three principal concepts he used in creating the name: it should be short, easy to pronounce, and not resemble any other name or be associated with anything else. According to a 1920 ad, the name "was simply inventedmade up from letters of the alphabet to meet our trade-mark requirements. It was short and euphonious and likely to stick in the public mind."


title: Kodak

text: From the company's founding by George Eastman in 1888, Kodak followed the razor and blades business model of selling inexpensive cameras and making large margins from consumables – film, chemicals, and paper. As late as 1976, Kodak commanded 90% of film sales and 85% of camera sales in the U.S. Kodak developed and patented the first handheld digital camera in 1975.


title: Kodak

text: Kodak began selling its original camera, created by George Eastman, in 1888 in the US for $25. It was a leather-covered box camera that came pre-loaded with 100-exposure roll film. When used up, the entire camera could be sent to the Kodak factory, after which it would be returned loaded with fresh film along with the negatives and mounted prints, for a cost of $10. It was advertised with the slogan "You Press the Button, We Do the Rest". Replacement film was sold for $2 for customers who had access to photographic processing. The ease of use and relatively low cost made photography widely accessible to the general public rather than only professional photographers, beginning the modern era of consumer photography.


title: Kodak

text: The Kodak was a camera box built in the shape of a parallelepiped, with a fixed-focus lens on the front and no viewfinder; two V shape silhouettes at the top aided in aiming in the direction of the subject. At the top it had a rotating key to advance the film, a pull-string to set the shutter, and a button on the side to release it, exposing the celluloid film. Inside, it had a rotating bar (this bar was soon replaced by a simpler mechanism due to its manufacturing price) to operate the shutter: when the user pressed the button to take a photograph, an inner rope was tightened and the photographic exposure began. Once the photograph had been taken, the user had to rotate the upper key to change the selected frame within the celluloid tape.


title: Kodak

text: Japanese competitor Fujifilm entered the U.S. market (via Fuji Photo Film U.S.A.) with lower-priced film and supplies, but Kodak did not believe that American consumers would ever desert its brand. Kodak declined an opportunity to become the official film of the 1984 Los Angeles Olympics; Fuji won these sponsorship rights, which gave it a permanent foothold in the market. Fuji opened a film plant in the U.S., and its aggressive marketing and price cutting began taking market share from Kodak. Fuji went from a 10% share in the early 1990s to 17% in 1997. Fuji also made headway into the professional market with specialty transparency films such as Velvia and Provia, which competed successfully with Kodak's signature professional product, Kodachrome, but used the more economical and common E-6 processing machines which were standard in most processing labs, rather than the dedicated machines required by Kodachrome. Fuji's films soon also found a competitive edge in higher-speed negative films, with a tighter grain structure.


title: Kodak

text: In May 1995, Kodak filed a petition with the US Commerce Department under section 301 of the Commerce Act arguing that its poor performance in the Japanese market was a direct result of unfair practices adopted by Fuji. The complaint was lodged by the United States with the World Trade Organization. On January 30, 1998, the WTO announced a "sweeping rejection of Kodak's complaints" about the film market in Japan. Kodak's financial results for the year ending December 1997 showed that the company's revenues dropped from $15.97 billion in 1996 to $14.36 billion in 1997, a fall of more than 10%; its net earnings went from $1.29 billion to just $5 million for the same period. Kodak's market share declined from 80.1% to 74.7% in the United States, a one-year drop of five percentage points that had observers suggesting that Kodak was slow to react to changes and underestimated its rivals.


title: Kodak

text: Although from the 1970s both Fuji and Kodak recognized the upcoming threat of digital photography, and although both sought diversification as a mitigation strategy, Fuji was more successful at diversification.


title: Kodak

text: Although Kodak developed the first handheld digital camera in 1975, the product was dropped for fear it would threaten Kodak's main income, its photographic film business. In the 1990s, Kodak planned a decade-long journey to move to digital technology. CEO George M. C. Fisher reached out to Microsoft and other new consumer merchandisers. Apple's pioneering QuickTake consumer digital cameras, introduced in 1994, had the Apple label but were produced by Kodak. The DC-20 and DC-25 launched in 1996. Overall, though, there was little implementation of the new digital strategy. Kodak's core business faced no pressure from competing technologies, and as Kodak executives could not imagine a world without traditional film there was little incentive to deviate from that course. Consumers gradually switched to the digital offerings from companies such as Sony. In 2001 film sales dropped, which was attributed by Kodak to the financial shocks caused by the September 11 attacks. Executives hoped that Kodak might be able to slow the shift to digital through aggressive marketing.


title: Kodak

text: Under Daniel Carp, Fisher's successor as CEO, Kodak made its move in the digital camera market, with its EasyShare family of digital cameras. Kodak spent tremendous resources studying customer behavior, finding out that women in particular loved taking digital photos but were frustrated in moving them to their computers. This key unmet consumer need became a major opportunity. Once Kodak got its product development machine started, it released a wide range of products which made it easy to share photos via PCs. One of their key innovations was a printer dock, where consumers could insert their cameras into this compact device, press a button, and watch their photos roll out. By 2005, Kodak ranked No. 1 in the U.S. in digital camera sales that surged 40% to $5.7 billion.


title: Kodak

text: Despite the high growth, Kodak failed to anticipate how fast digital cameras became commodities, with low profit margins, as more companies entered the market in the mid-2000s. In 2001, Kodak held the No. 2 spot in U.S. digital camera sales (behind Sony) but it lost $60 on every camera sold, while there was also a dispute between employees from its digital and film divisions. The film business, where Kodak enjoyed high profit margins, fell 18% in 2005. The combination of these two factors resulted in disappointing profits overall. Its digital cameras soon became undercut by Asian competitors that could produce their offerings more cheaply. Kodak had a 27% market-leading share in 1999 that dropped to 15% by 2003. In 2007, Kodak was No. 4 in U.S. digital camera sales with a 9.6% share, and by 2010, it held 7% in seventh place behind Canon, Sony, Nikon, and others, according to research firm IDC. Also, an ever-smaller percentage of digital pictures were being taken on dedicated digital cameras, being gradually displaced in the late 2000s by cameras on cellphones, smartphones, and tablets.


title: Kodak

text: Kodak then began a strategy shift: while Kodak had previously done everything in-house, CEO Antonio Pérez shut down film factories and eliminated 27,000 jobs as it outsourced its manufacturing. Pérez invested heavily in digital technologies and new services that capitalized on its technology innovation to boost profit margins. He also spent hundreds of millions of dollars to build up a high-margin printer ink business to replace falling film sales. Kodak's ink strategy rejected the razor and blades business model used by dominant market leader Hewlett-Packard in that Kodak's printers were expensive but the ink was cheaper. As of 2011, these new lines of inkjet printers were said to be on verge of turning a profit, although some analysts were skeptical as printouts had been replaced gradually by electronic copies on computers, tablets, and smartphones. Home photograph printers, high-speed commercial inkjet presses, workflow software, and packaging were viewed as the company's new core businesses, with sales from those four businesses projected to double to nearly $2 billion in revenue in 2013 and account for 25% of all sales. However, while Kodak named home printers as a core business as late as August 2012, at the end of September declining sales forced Kodak to announce an exit from the consumer inkjet market.


title: Kodak

text: Kodak has also turned to litigation to generate revenue. In 2010, it received $838 million from patent licensing that included a settlement with LG.


title: Kodak

text: In 2010, Apple filed a patent-infringement claim against Kodak. On May 12, 2011, Judge Robert Rogers rejected Apple's claims that two of its digital photography patents were being violated by Kodak.


title: Kodak

text: On July 1, 2011, the U.S. International Trade Commission partially reversed a January decision by an administrative law judge stating that neither Apple nor Research in Motion had infringed upon Kodak's patents. The ITC remanded the matter for further proceedings before the ALJ.


title: Kodak

text: In 2011, despite the turnaround progress, Kodak rapidly used up its cash reserves, stoking fears of bankruptcy; it had $957 million in cash in June 2011, down from $1.6 billion in January 2001. In 2011, Kodak reportedly explored selling off or licensing its vast portfolio of patents to stave off bankruptcy. By January 2012, analysts suggested that the company could enter bankruptcy followed by an auction of its patents, as it was reported to be in talks with Citigroup to provide debtor-in-possession financing. This was confirmed on January 19, 2012, when the company filed for Chapter 11 bankruptcy protection and obtained a $950 million, 18-month credit facility from Citigroup to enable it to continue operations. Under the terms of its bankruptcy protection, Kodak had a deadline of February 15, 2013, to produce a reorganization plan.


title: Kodak

text: On September 3, 2013, Kodak announced that it emerged from bankruptcy as a technology company focused on imaging for business. Its main business segments are Digital Printing & Enterprise and Graphics, Entertainment & Commercial Films.


title: Kodak

text: On March 12, 2014, Kodak announced that Jeffrey J. Clarke had been named as chief executive officer and a member of its board of directors.


title: Kodak

text: On January 1, 2015, Kodak announced a new five business division structure; Print Systems, Enterprise Inkjet Systems, Micro 3D Printing and Packaging, Software and Solutions, and Consumer and Film.


title: Kodak

text: Kodak provides packaging, functional printing, graphic communications, and professional services for businesses around the world. Its main business segments are Print Systems, Enterprise Inkjet Systems, Micro 3D Printing and Packaging, Software and Solutions, and Consumer and Film.


title: Kodak

text: Kodak currently produces a wide range of photographic film in both 35mm and 120 film formats. The current film resurgence caused film shortages worldwide, increasing the price of current film stocks. Kodak has been actively hiring new employees since 2020, especially in film production, to meet the current market demand for films.


title: Kodak

text: In 2018, Kodak launched a newly formulated version of the iconic Kodak Ektachrome 100 color reversal film in 35mm film format. The following year, the company announced the film stock in 120mm and 4x5 film format. Due to its specific look, HBO shot the second season of the hit TV series Euphoria on Kodak Ektachrome with cinematographer Marcell Rév.


title: Kodak

text: Kodak provides high-speed, high-volume commercial inkjet, and color and black-and-white electrophotographic printing equipment and related consumables and services. It has an installed base of more than 5,000 units.


title: Kodak

text: Its Prosper platform uses Stream inkjet technology, which delivers a continuous flow of ink that enables constant and consistent operation, with uniform size and accurate placement, even at very high print speeds. Applications for Prosper include publishing, commercial print, direct mail, and packaging. The business also includes the customer base of Kodak VersaMark products.


title: Kodak

text: The NexPress platform is used for printing short-run, personalized print applications for purposes such as direct mail, books, marketing collateral and photo products. The Digimaster platform uses monochrome electrophotographic printing technology to create high-quality printing of statements, short-run books, corporate documentation, manuals and direct mail.


title: Kodak

text: Kodak designs and manufactures products for flexography printing. Its Flexcel line of flexo printing systems allow label printers to produce their own digital plates for customized flexo printing and flexible printed packaging.


title: Kodak

text: The company currently has strategic relationships with worldwide touch-panel sensor leaders, such as the partnerships with UniPixel announced on April 16, 2013, and Kingsbury Corp. launched on June 27, 2013.


title: Kodak

text: Enterprise professional services offers print and managed media services, brand protection solutions and services, and document management services to enterprise customers, including government, pharmaceuticals, and health, consumer and luxury good products, retail and finance.


title: Kodak

text: In 1997, Heidelberg Printing Machines AG and Eastman Kodak Co. created Nexpress Solutions LLC, a joint venture to develop a digital color printing press for the high-end market segment. Heidelberg acquired Eastman Kodak Co.'s Office Imaging black and white digital printing activities in 1999. In 2000, they launched the Digimaster 9110 black and white production printer and the NexPress 2100 digital color press.


title: Kodak

text: In March 2004, Heidelberg transferred its Digital Print division to Eastman Kodak Co. under mutual agreement.


title: Kodak

text: At present, Kodak has commercial web-fed presses, commercial imprinting systems – Prosper, VersaMark and commercial sheet-fed presses – NexPress digital production color press and DIGIMASTER HD digital black and white production printer.


title: Kodak

text: Kodak entered into consumer inkjet photo printers in a joint venture with manufacturer Lexmark in 1999 with the Kodak Personal Picture Maker.


title: Kodak

text: In February 2007, Kodak re-entered the market with a new product line of All-in-One (AiO) inkjet printers that employ several technologies marketed as Kodacolor Technology. Advertising emphasizes low price for ink cartridges rather than for the printers themselves.


title: Kodak

text: Kodak announced plans to stop selling inkjet printers in 2013 as it focuses on commercial printing but will still sell ink.


title: Kodak

text: Kodak's graphics business consists of computer to plate (CTP) devices, which Kodak first launched in 1995 when the company introduced the first thermal CTP to market. Kodak's Graphics portfolio includes front-end controllers, production workflow software, CTP output devices, and digital plates.


title: Kodak

text: Kodak's Global Technical Services ("GTS") for Commercial Imaging is focused on selling service contracts for Kodak products, including the following service categories: field services, customer support services, educational services, and professional services.


title: Kodak

text: Kodak's Entertainment Imaging and Commercial Film group ("E&CF") encompasses its motion picture film business, providing motion imaging products (camera negative, intermediate, print and archival film), services and technology for the professional motion picture and exhibition industries.


title: Kodak

text: E&CF also offers Aerial and Industrial Films including KODAK Printed Circuit Board film and delivers external sales for the company's component businesses: Polyester Film, Specialty Chemicals, Inks and Dispersions and Solvent Recovery.


title: Kodak

text: The Kodak company played a role in the invention and development of the motion picture industry. Many cinema and TV productions are shot on Kodak film stocks.


title: Kodak

text: The home market-oriented 8mm and Super 8 formats were also developed by Kodak. Kodak also entered the professional television production video tape market, briefly in the mid-1980s, under the product portfolio name of Eastman Professional Video Tape Products. In 1990, Kodak launched a Worldwide Student Program working with university faculty throughout the world to help nurture the future generation of film-makers. Kodak formed Educational Advisory Councils in the US, Europe and Asia made up of deans and chairs of some of the most prestigious film schools throughout the world to help guide the development of their program.


title: Kodak

text: Kodak previously owned the visual effects film post-production facilities Cinesite in Los Angeles and London and also LaserPacific in Los Angeles. Kodak sold Cinesite to Endless LLP, an independent British private equity house.


title: Kodak

text: In April 2010, Kodak sold LaserPacific and its subsidiaries Laser-Edit, Inc, and Pacific Video, Inc., in April 2010 for an undisclosed sum to TeleCorps Holdings, Inc.


title: Kodak

text: Kodak also sold Pro-Tek Media Preservation Services, a film storage company in Burbank, California, to LAC Group in October 2013.


title: Kodak

text: Kodak markets Picture CDs and other photo products such as calendars, photo books and photo enlargements through retail partners such as CVS, Walmart and Target and through its Kodak Gallery online service, formerly known as Ofoto.


title: Kodak

text: On January 13, 2004, Kodak announced it would stop marketing traditional still film cameras (excluding disposable cameras) in the United States, Canada and Western Europe, but would continue to sell film cameras in India, Latin America, Eastern Europe and China. By the end of 2005, Kodak had ceased manufacturing cameras that used the Advanced Photo System. Kodak licensed the manufacture of Kodak branded cameras to Vivitar in 2005 and 2006. After 2007 Kodak did not license the manufacture of any film camera with the Kodak name.


title: Kodak

text: After losing a patent battle with Polaroid Corporation, Kodak left the instant camera business on January 9, 1986. The Kodak instant camera included models known as the Kodamatic and the Colorburst.


title: Kodak

text: Polaroid was awarded damages in the patent trial in the amount of $909,457,567, a record at the time. (Polaroid Corp. v. Eastman Kodak Co., U.S. District Court District of Massachusetts, decided October 12, 1990, case no. 76-1634-MA. Published in the U.S. Patent Quarterly as 16 USPQ2d 1481). See also the following cases: Polaroid Corp. v. Eastman Kodak Co., 641 F.Supp. 828 [228 USPQ 305] (D. Mass. 1985), stay denied, 833 F.2d 930 [5 USPQ2d 1080] (Fed. Cir.), aff'd, 789 F.2d 1556 [229 USPQ 561] (Fed. Cir.), cert. denied, 479 U.S. 850 (1986).


title: Kodak

text: Kodak was the exclusive supplier of negatives for Polaroid cameras from 1963 until 1969, when Polaroid chose to manufacture its own instant film.


title: Kodak

text: As part of its move toward higher end products, Kodak announced on September 15, 2006, that the new Leica M8 camera incorporates Kodak's KAF-10500 image sensor. This was the second recent partnership between Kodak and the German optical manufacturer. In 2011, Kodak sold its Image Sensor Solutions business to Platinum Equity, which subsequently renamed it Truesense Imaging, Inc.


title: Kodak

text: In 1983, Kodak introduced a non-standard 3.3 million byte diskette; it was manufactured by an outside company, DriveTec. Another was announced in 1984. Kodak's 1985 purchase of Verbatim, "a leading manufacturer of floppy disks" with over 2,000 employees, expanded their presence; part of this acquisition was Verbatim's "Data Encore" unit, which "copies software onto floppy disks in a way that makes it difficult for software 'pirates' to re-copy the material."


title: Kodak

text: In 1982, prior to this purchase, Verbatim had partnered with a Japanese firm; in 1990 Kodak exited the diskette business and sold Verbatim to this firm, the forerunner of Mitsubishi Chemical Corporation. Kodak held onto Verbatim's optical disk unit.


title: Kodak

text: Many of Kodak's early compact digital cameras were designed and built by Chinon Industries, a Japanese camera manufacturer. In 2004, Kodak Japan acquired Chinon and many of its engineers and designers joined Kodak Japan.


title: Kodak

text: The Kodak DCS series of digital single-lens reflex cameras and digital camera backs were released by Kodak in the 1990s and 2000s, and discontinued in 2005. They were based on existing 35mm film SLRs from Nikon and Canon and the range included the original Kodak DCS, the first commercially available digital SLR.


title: Kodak

text: In July 2006, Kodak announced that Flextronics would manufacture and help design its digital cameras.


title: Kodak

text: Kodak first entered the digital picture frame market with the Kodak Smart Picture Frame in the fourth quarter of 2000. It was designed by Weave Innovations and licensed to Kodak with an exclusive relationship with Weave's StoryBox online photo network. Smart Frame owners connected to the network via an analog telephone connection built into the frame. The frame could hold 36 images internally and came with a six-month free subscription to the StoryBox network.


title: Kodak

text: Kodak re-entered the digital photo frame market at CES in 2007 with the introduction of four new EasyShare-branded models that were available in sizes from , included multiple memory card slots, and some of which included Wi-Fi capability to connect with the Kodak Gallerythat gallery functionality has now been compromised due to gallery policy changes (see below).


title: Kodak

text: In June 2001, Kodak purchased the photo-developing website Ofoto, later renamed Kodak Gallery. The website enables users to upload their photos into albums, publish them into prints, and create mousepads, calendars, etc. On March 1, 2012, Kodak announced that it sold Kodak Gallery to Shutterfly for $23.8 million.


title: Kodak

text: Kodak provides scanning technology. Historically this industry began when George Eastman partnered with banks to image checks in the 1920s. Through the development of microfilm technology, Eastman Kodak was able to provide long term document storage. Document imaging was one of the first imaging solutions to move to "digital imaging" technology. Kodak manufactured the first digital document scanners for high speed document imaging. Today Kodak manufactures scanners for banking, finance, insurance, healthcare and other vertical industries. Kodak also provides associated document capture software and business process services. Eastman Kodak acquired the Bowe Bell & Howell scanner division in September 2009.


title: Kodak

text: Kodak entered the plain paper photocopier market in 1975 with the Kodak Ektaprint 100 Copier-Duplicator. In 1986 they announced the Ektaprint 235 copier-duplicator, capable of producing 5,100 copies per hour, and the Ektaprint 300, capable of producing 6,000 copies per hour. In 1988 IBM exited the Photocopier industry, selling its interests to Kodak for an undisclosed sum. On Sept. 10, 1996 Kodak announced it was selling its Copier business to Danka for $684 million in cash, while Danka was later acquired by Konica Minolta in 2008.


title: Kodak

text: Kodak continues to produce specialty films and film for newer and more popular consumer formats, but it has discontinued the manufacture of film in older and less popular formats.


title: Kodak

text: Kodak is a leading producer of silver halide (AgX) paper used for printing from film and digital images. Minilabs located in retail stores and larger central photo lab operations (CLOs) use silver halide paper for photo printing. In 2005, Kodak announced it would stop producing black-and-white photo paper.


title: Kodak

text: Kodak is a manufacturer of self-service photo kiosks that produce "prints in seconds" from multiple sources including digital input, scanned prints, Facebook, the Kodak Gallery and orders placed on-line using thermosublimation printers. The company has placed over 100,000 Picture Kiosks in retail locations worldwide. Employing similar technology, Kodak also offers larger printing systems with additional capabilities including duplex greeting cards, large format poster printers, photobooks and calendars under the brand name "APEX".


title: Kodak

text: After two years in development, Kodak launched its on-demand photography service platform, Kodakit, offering one tap photography service in 92 cities, 37 countries in early 2016. The launch was formally announced in January 2017 at Consumer Electronics Show in Las Vegas. Kodakit initially targeted consumers looking for wedding and portrait photography, but soon shifted towards businesses seeking high volume photography – real estate, food photography, and head shots. Having failed to generate enough traction to justify its existence and facing competition from fast growing startups like Meero and Splento, the Singapore-based subsidiary announced that it will be shutting down the operations.


title: Kodak

text: The Kodak Research Laboratories were founded in 1912 with Kenneth Mees as the first director. Principal components of the Kodak Research Laboratories were the "Photographic Research Laboratories" and then the "Imaging Research Laboratories". Additional organizations included the "Corporate Research Laboratories". Over nearly a century, scientists at these laboratories produced thousands of patents and scientific publications.


title: Kodak

text: In 2005, Kodak Canada donated its entire historic company archives to Ryerson University in Toronto, Ontario, Canada. The Ryerson University Library also acquired an extensive collection of materials on the history of photography from the private collection of Nicholas M. and Marilyn A. Graver of Rochester, New York. The Kodak Archives, begun in 1909, contain the company's Camera Collection, historic photos, files, trade circulars, Kodak magazines, price lists, daily record books, equipment, and other ephemera. It includes the contents of the Kodak Heritage Collection Museum, a museum established in 1999 for Kodak Canada's centennial that Kodak closed in 2005 along with the company's entire "Kodak Heights" manufacturing campus in Mount Dennis, Toronto.


title: Kodak

text: On March 26, 2007, the Council of Better Business Bureaus (CBBB) announced that Eastman Kodak was resigning its national membership in the wake of expulsion proceedings initiated by the CBBB board of directors.


title: Kodak

text: In 2006, Kodak notified the BBB of Upstate New York that it would no longer accept or respond to consumer complaints submitted by them. In prior years, Kodak responded by offering consumers an adjustment or an explanation of the company's position. The BBB file contains consumer complaints of problems with repairs of Kodak digital cameras, as well as difficulty communicating with Kodak customer service. Among other complaints, consumers say that their cameras broke and they were charged for repairs when the failure was not the result of any damage or abuse. Some say their cameras failed again after being repaired.


title: Kodak

text: Kodak said its customer service and customer privacy teams concluded that 99% of all complaints forwarded by the BBB already were handled directly with the customer. Brian O’Connor, Kodak chief privacy officer, said the company was surprised by the news release distributed by the Better Business Bureau:


title: Kodak

text: In July 2021, Kodak removed a post on Xinjiang from its Instagram page. The photo was taken by the photographer Patrick Wack who describes the region as an "Orwellian dystopia" in a reference to the Uyghur genocide. In later statements on Instagram and WeChat, Kodak declared its Instagram page was not a "platform for political commentary" and affirmed their "close cooperation with various [Chinese] government departments".


title: Cell membrane

text: The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment (the extracellular space). The cell membrane consists of a lipid bilayer, made up of two layers of phospholipids with cholesterols (a lipid component) interspersed between them, maintaining appropriate membrane fluidity at various temperatures. The membrane also contains membrane proteins, including integral proteins that span the membrane and serve as membrane transporters, and peripheral proteins that loosely attach to the outer (peripheral) side of the cell membrane, acting as enzymes to facilitate interaction with the cell's environment. Glycolipids embedded in the outer lipid layer serve a similar purpose. The cell membrane controls the movement of substances in and out of cells and organelles, being selectively permeable to ions and organic molecules. In addition, cell membranes are involved in a variety of cellular processes such as cell adhesion, ion conductivity, and cell signalling and serve as the attachment surface for several extracellular structures, including the cell wall and the carbohydrate layer called the glycocalyx, as well as the intracellular network of protein fibers called the cytoskeleton. In the field of synthetic biology, cell membranes can be artificially reassembled.


title: Cell membrane

text: While Robert Hooke’s discovery of cells in 1665 led to the proposal of the Cell Theory, Hooke misled the cell membrane theory that all cells contained a hard cell wall since only plant cells could be observed at the time. Microscopists focused on the cell wall for well over 150 years until advances in microscopy were made. In the early 19th century, cells were recognized as being separate entities, unconnected, and bound by individual cell walls after it was found that plant cells could be separated. This theory extended to include animal cells to suggest a universal mechanism for cell protection and development. By the second half of the 19th century, microscopy was still not advanced enough to make a distinction between cell membranes and cell walls. However, some microscopists correctly identified at this time that while invisible, it could be inferred that cell membranes existed in animal cells due to intracellular movement of components internally but not externally and that membranes were not the equivalent of a cell wall to a plant cell. It was also inferred that cell membranes were not vital components to all cells. Many refuted the existence of a cell membrane still towards the end of the 19th century. In 1890, an update to the Cell Theory stated that cell membranes existed, but were merely secondary structures. It was not until later studies with osmosis and permeability that cell membranes gained more recognition. In 1895, Ernest Overton proposed that cell membranes were made of lipids.


title: Cell membrane

text: The lipid bilayer hypothesis, proposed in 1925 by and Grendel, created speculation in the description of the cell membrane bilayer structure based on crystallographic studies and soap bubble observations. In an attempt to accept or reject the hypothesis, researchers measured membrane thickness. These researchers extracted the lipid from human red blood cells and measured the amount of surface area the lipid would cover when spread over the surface of the water. Since mature mammalian red blood cells lack both nuclei and cytoplasmic organelles, the plasma membrane is the only lipid-containing structure in the cell. Consequently, all of the lipids extracted from the cells can be assumed to have resided in the cells’ plasma membranes. The ratio of the surface area of water covered by the extracted lipid to the surface area calculated for the red blood cells from which the lipid was 2:1(approx) and they concluded that the plasma membrane contains a lipid bilayer.


title: Cell membrane

text: In 1925 it was determined by Fricke that the thickness of erythrocyte and yeast cell membranes ranged between 3.3 and 4 nm, a thickness compatible with a lipid monolayer. The choice of the dielectric constant used in these studies was called into question but future tests could not disprove the results of the initial experiment. Independently, the leptoscope was invented in order to measure very thin membranes by comparing the intensity of light reflected from a sample to the intensity of a membrane standard of known thickness. The instrument could resolve thicknesses that depended on pH measurements and the presence of membrane proteins that ranged from 8.6 to 23.2 nm, with the lower measurements supporting the lipid bilayer hypothesis. Later in the 1930s, the membrane structure model developed in general agreement to be the paucimolecular model of Davson and Danielli (1935). This model was based on studies of surface tension between oils and echinoderm eggs. Since the surface tension values appeared to be much lower than would be expected for an oil–water interface, it was assumed that some substance was responsible for lowering the interfacial tensions in the surface of cells. It was suggested that a lipid bilayer was in between two thin protein layers. The paucimolecular model immediately became popular and it dominated cell membrane studies for the following 30 years, until it became rivaled by the fluid mosaic model of Singer and Nicolson (1972).


title: Cell membrane

text: Despite the numerous models of the cell membrane proposed prior to the fluid mosaic model, it remains the primary archetype for the cell membrane long after its inception in the 1970s. Although the fluid mosaic model has been modernized to detail contemporary discoveries, the basics have remained constant: the membrane is a lipid bilayer composed of hydrophilic exterior heads and a hydrophobic interior where proteins can interact with hydrophilic heads through polar interactions, but proteins that span the bilayer fully or partially have hydrophobic amino acids that interact with the non-polar lipid interior. The fluid mosaic model not only provided an accurate representation of membrane mechanics, it enhanced the study of hydrophobic forces, which would later develop into an essential descriptive limitation to describe biological macromolecules.


title: Cell membrane

text: For many centuries, the scientists cited disagreed with the significance of the structure they were seeing as the cell membrane. For almost two centuries, the membranes were seen but mostly disregarded as an important structure with cellular function. It was not until the 20th century that the significance of the cell membrane as it was acknowledged. Finally, two scientists Gorter and Grendel (1925) made the discovery that the membrane is “lipid-based”. From this, they furthered the idea that this structure would have to be in a formation that mimicked layers. Once studied further, it was found by comparing the sum of the cell surfaces and the surfaces of the lipids, a 2:1 ratio was estimated; thus, providing the first basis of the bilayer structure known today. This discovery initiated many new studies that arose globally within various fields of scientific studies, confirming that the structure and functions of the cell membrane are widely accepted.


title: Cell membrane

text: The structure has been variously referred to by different writers as the ectoplast (de Vries, 1885), "Plasmahaut" (plasma skin, Pfeffer, 1877, 1891), "Hautschicht" (skin layer, Pfeffer, 1886; used with a different meaning by Hofmeister, 1867), plasmatic membrane (Pfeffer, 1900), plasma membrane, cytoplasmic membrane, cell envelope and cell membrane. Some authors who did not believe that there was a functional permeable boundary at the surface of the cell preferred to use the term plasmalemma (coined by Mast, 1924) for the external region of the cell.


title: Cell membrane

text: Cell membranes contain a variety of biological molecules, notably lipids and proteins. Composition is not set, but constantly changing for fluidity and changes in the environment, even fluctuating during different stages of cell development. Specifically, the amount of cholesterol in human primary neuron cell membrane changes, and this change in composition affects fluidity throughout development stages.


title: Cell membrane

text: The cell membrane consists of three classes of amphipathic lipids: phospholipids, glycolipids, and sterols. The amount of each depends upon the type of cell, but in the majority of cases phospholipids are the most abundant, often contributing for over 50% of all lipids in plasma membranes. Glycolipids only account for a minute amount of about 2% and sterols make up the rest. In red blood cell studies, 30% of the plasma membrane is lipid. However, for the majority of eukaryotic cells, the composition of plasma membranes is about half lipids and half proteins by weight.


title: Cell membrane

text: The fatty chains in phospholipids and glycolipids usually contain an even number of carbon atoms, typically between 16 and 20. The 16- and 18-carbon fatty acids are the most common. Fatty acids may be saturated or unsaturated, with the configuration of the double bonds nearly always "cis". The length and the degree of unsaturation of fatty acid chains have a profound effect on membrane fluidity as unsaturated lipids create a kink, preventing the fatty acids from packing together as tightly, thus decreasing the melting temperature (increasing the fluidity) of the membrane. The ability of some organisms to regulate the fluidity of their cell membranes by altering lipid composition is called homeoviscous adaptation.


title: Cell membrane

text: The entire membrane is held together via non-covalent interaction of hydrophobic tails, however the structure is quite fluid and not fixed rigidly in place. Under physiological conditions phospholipid molecules in the cell membrane are in the liquid crystalline state. It means the lipid molecules are free to diffuse and exhibit rapid lateral diffusion along the layer in which they are present. However, the exchange of phospholipid molecules between intracellular and extracellular leaflets of the bilayer is a very slow process. Lipid rafts and caveolae are examples of cholesterol-enriched microdomains in the cell membrane. Also, a fraction of the lipid in direct contact with integral membrane proteins, which is tightly bound to the protein surface is called annular lipid shell; it behaves as a part of protein complex.


title: Cell membrane

text: In animal cells cholesterol is normally found dispersed in varying degrees throughout cell membranes, in the irregular spaces between the hydrophobic tails of the membrane lipids, where it confers a stiffening and strengthening effect on the membrane. Additionally, the amount of cholesterol in biological membranes varies between organisms, cell types, and even in individual cells. Cholesterol, a major component of animal plasma membranes, regulates the fluidity of the overall membrane, meaning that cholesterol controls the amount of movement of the various cell membrane components based on its concentrations. In high temperatures, cholesterol inhibits the movement of phospholipid fatty acid chains, causing a reduced permeability to small molecules and reduced membrane fluidity. The opposite is true for the role of cholesterol in cooler temperatures. Cholesterol production, and thus concentration, is up-regulated (increased) in response to cold temperature. At cold temperatures, cholesterol interferes with fatty acid chain interactions. Acting as antifreeze, cholesterol maintains the fluidity of the membrane. Cholesterol is more abundant in cold-weather animals than warm-weather animals. In plants, which lack cholesterol, related compounds called sterols perform the same function as cholesterol.


title: Cell membrane

text: Lipid vesicles or liposomes are approximately spherical pockets that are enclosed by a lipid bilayer. These structures are used in laboratories to study the effects of chemicals in cells by delivering these chemicals directly to the cell, as well as getting more insight into cell membrane permeability. Lipid vesicles and liposomes are formed by first suspending a lipid in an aqueous solution then agitating the mixture through sonication, resulting in a vesicle. By measuring the rate of efflux from that of the inside of the vesicle to the ambient solution, allows researcher to better understand membrane permeability. Vesicles can be formed with molecules and ions inside the vesicle by forming the vesicle with the desired molecule or ion present in the solution. Proteins can also be embedded into the membrane through solubilizing the desired proteins in the presence of detergents and attaching them to the phospholipids in which the liposome is formed. These provide researchers with a tool to examine various membrane protein functions.


title: Cell membrane

text: Plasma membranes also contain carbohydrates, predominantly glycoproteins, but with some glycolipids (cerebrosides and gangliosides). Carbohydrates are important in the role of cell-cell recognition in eukaryotes; they are located on the surface of the cell where they recognize host cells and share information, viruses that bind to cells using these receptors cause an infection For the most part, no glycosylation occurs on membranes within the cell; rather generally glycosylation occurs on the extracellular surface of the plasma membrane. The glycocalyx is an important feature in all cells, especially epithelia with microvilli. Recent data suggest the glycocalyx participates in cell adhesion, lymphocyte homing, and many others. The penultimate sugar is galactose and the terminal sugar is sialic acid, as the sugar backbone is modified in the Golgi apparatus. Sialic acid carries a negative charge, providing an external barrier to charged particles.


title: Cell membrane

text: The cell membrane has large content of proteins, typically around 50% of membrane volume These proteins are important for the cell because they are responsible for various biological activities. Approximately a third of the genes in yeast code specifically for them, and this number is even higher in multicellular organisms. Membrane proteins consist of three main types: integral proteins, peripheral proteins, and lipid-anchored proteins.


title: Cell membrane

text: As shown in the adjacent table, integral proteins are amphipathic transmembrane proteins. Examples of integral proteins include ion channels, proton pumps, and g-protein coupled receptors. Ion channels allow inorganic ions such as sodium, potassium, calcium, or chlorine to diffuse down their electrochemical gradient across the lipid bilayer through hydrophilic pores across the membrane. The electrical behavior of cells (i.e. nerve cells) are controlled by ion channels. Proton pumps are protein pumps that are embedded in the lipid bilayer that allow protons to travel through the membrane by transferring from one amino acid side chain to another. Processes such as electron transport and generating ATP use proton pumps. A G-protein coupled receptor is a single polypeptide chain that crosses the lipid bilayer seven times responding to signal molecules (i.e. hormones and neurotransmitters). G-protein coupled receptors are used in processes such as cell to cell signaling, the regulation of the production of cAMP, and the regulation of ion channels.


title: Cell membrane

text: The cell membrane, being exposed to the outside environment, is an important site of cell–cell communication. As such, a large variety of protein receptors and identification proteins, such as antigens, are present on the surface of the membrane. Functions of membrane proteins can also include cell–cell contact, surface recognition, cytoskeleton contact, signaling, enzymatic activity, or transporting substances across the membrane.


title: Cell membrane

text: Most membrane proteins must be inserted in some way into the membrane. For this to occur, an N-terminus "signal sequence" of amino acids directs proteins to the endoplasmic reticulum, which inserts the proteins into a lipid bilayer. Once inserted, the proteins are then transported to their final destination in vesicles, where the vesicle fuses with the target membrane.


title: Cell membrane

text: The cell membrane surrounds the cytoplasm of living cells, physically separating the intracellular components from the extracellular environment. The cell membrane also plays a role in anchoring the cytoskeleton to provide shape to the cell, and in attaching to the extracellular matrix and other cells to hold them together to form tissues. Fungi, bacteria, most archaea, and plants also have a cell wall, which provides a mechanical support to the cell and precludes the passage of larger molecules.


title: Cell membrane

text: The cell membrane is selectively permeable and able to regulate what enters and exits the cell, thus facilitating the transport of materials needed for survival. The movement of substances across the membrane can be achieved by either passive transport, occurring without the input of cellular energy, or by active transport, requiring the cell to expend energy in transporting it. The membrane also maintains the cell potential. The cell membrane thus works as a selective filter that allows only certain things to come inside or go outside the cell. The cell employs a number of transport mechanisms that involve biological membranes:


title: Cell membrane

text: 1. Passive osmosis and diffusion: Some substances (small molecules, ions) such as carbon dioxide (CO) and oxygen (O), can move across the plasma membrane by diffusion, which is a passive transport process. Because the membrane acts as a barrier for certain molecules and ions, they can occur in different concentrations on the two sides of the membrane. Diffusion occurs when small molecules and ions move freely from high concentration to low concentration in order to equilibrate the membrane. It is considered a passive transport process because it does not require energy and is propelled by the concentration gradient created by each side of the membrane. Such a concentration gradient across a semipermeable membrane sets up an osmotic flow for the water. Osmosis, in biological systems involves a solvent, moving through a semipermeable membrane similarly to passive diffusion as the solvent still moves with the concentration gradient and requires no energy. While water is the most common solvent in cell, it can also be other liquids as well as supercritical liquids and gases.


title: Cell membrane

text: 2. Transmembrane protein channels and transporters: Transmembrane proteins extend through the lipid bilayer of the membranes; they function on both sides of the membrane to transport molecules across it. Nutrients, such as sugars or amino acids, must enter the cell, and certain products of metabolism must leave the cell. Such molecules can diffuse passively through protein channels such as aquaporins in facilitated diffusion or are pumped across the membrane by transmembrane transporters. Protein channel proteins, also called "permeases", are usually quite specific, and they only recognize and transport a limited variety of chemical substances, often limited to a single substance. Another example of a transmembrane protein is a cell-surface receptor, which allow cell signaling molecules to communicate between cells.


title: Cell membrane

text: 3. Endocytosis: Endocytosis is the process in which cells absorb molecules by engulfing them. The plasma membrane creates a small deformation inward, called an invagination, in which the substance to be transported is captured. This invagination is caused by proteins on the outside on the cell membrane, acting as receptors and clustering into depressions that eventually promote accumulation of more proteins and lipids on the cytosolic side of the membrane. The deformation then pinches off from the membrane on the inside of the cell, creating a vesicle containing the captured substance. Endocytosis is a pathway for internalizing solid particles ("cell eating" or phagocytosis), small molecules and ions ("cell drinking" or pinocytosis), and macromolecules. Endocytosis requires energy and is thus a form of active transport.


title: Cell membrane

text: 4. Exocytosis: Just as material can be brought into the cell by invagination and formation of a vesicle, the membrane of a vesicle can be fused with the plasma membrane, extruding its contents to the surrounding medium. This is the process of exocytosis. Exocytosis occurs in various cells to remove undigested residues of substances brought in by endocytosis, to secrete substances such as hormones and enzymes, and to transport a substance completely across a cellular barrier. In the process of exocytosis, the undigested waste-containing food vacuole or the secretory vesicle budded from Golgi apparatus, is first moved by cytoskeleton from the interior of the cell to the surface. The vesicle membrane comes in contact with the plasma membrane. The lipid molecules of the two bilayers rearrange themselves and the two membranes are, thus, fused. A passage is formed in the fused membrane and the vesicles discharges its contents outside the cell.


title: Cell membrane

text: Prokaryotes are divided into two different groups, Archaea and Bacteria, with bacteria dividing further into gram-positive and gram-negative. Gram-negative bacteria have both a plasma membrane and an outer membrane separated by periplasm, however, other prokaryotes have only a plasma membrane. These two membranes differ in many aspects. The outer membrane of the gram-negative bacteria differ from other prokaryotes due to phospholipids forming the exterior of the bilayer, and lipoproteins and phospholipids forming the interior. The outer membrane typically has a porous quality due to its presence of membrane proteins, such as gram-negative porins, which are pore-forming proteins. The inner, plasma membrane is also generally symmetric whereas the outer membrane is asymmetric because of proteins such as the aforementioned. Also, for the prokaryotic membranes, there are multiple things that can affect the fluidity. One of the major factors that can affect the fluidity is fatty acid composition. For example, when the bacteria "Staphylococcus aureus" was grown in 37C for 24h, the membrane exhibited a more fluid state instead of a gel-like state. This supports the concept that in higher temperatures, the membrane is more fluid than in colder temperatures. When the membrane is becoming more fluid and needs to become more stabilized, it will make longer fatty acid chains or saturated fatty acid chains in order to help stabilize the membrane. Bacteria are also surrounded by a cell wall composed of peptidoglycan (amino acids and sugars). Some eukaryotic cells also have cell walls, but none that are made of peptidoglycan. The outer membrane of gram negative bacteria is rich in lipopolysaccharides, which are combined poly- or oligosaccharide and carbohydrate lipid regions that stimulate the cell's natural immunity. The outer membrane can bleb out into periplasmic protrusions under stress conditions or upon virulence requirements while encountering a host target cell, and thus such blebs may work as virulence organelles. Bacterial cells provide numerous examples of the diverse ways in which prokaryotic cell membranes are adapted with structures that suit the organism's niche. For example, proteins on the surface of certain bacterial cells aid in their gliding motion. Many gram-negative bacteria have cell membranes which contain ATP-driven protein exporting systems.


title: Cell membrane

text: According to the fluid mosaic model of S. J. Singer and G. L. Nicolson (1972), which replaced the earlier model of Davson and Danielli, biological membranes can be considered as a two-dimensional liquid in which lipid and protein molecules diffuse more or less easily. Although the lipid bilayers that form the basis of the membranes do indeed form two-dimensional liquids by themselves, the plasma membrane also contains a large quantity of proteins, which provide more structure. Examples of such structures are protein-protein complexes, pickets and fences formed by the actin-based cytoskeleton, and potentially lipid rafts.


title: Cell membrane

text: Lipid bilayers form through the process of self-assembly. The cell membrane consists primarily of a thin layer of amphipathic phospholipids that spontaneously arrange so that the hydrophobic "tail" regions are isolated from the surrounding water while the hydrophilic "head" regions interact with the intracellular (cytosolic) and extracellular faces of the resulting bilayer. This forms a continuous, spherical lipid bilayer. Hydrophobic interactions (also known as the hydrophobic effect) are the major driving forces in the formation of lipid bilayers. An increase in interactions between hydrophobic molecules (causing clustering of hydrophobic regions) allows water molecules to bond more freely with each other, increasing the entropy of the system. This complex interaction can include noncovalent interactions such as van der Waals, electrostatic and hydrogen bonds.


title: Cell membrane

text: Lipid bilayers are generally impermeable to ions and polar molecules. The arrangement of hydrophilic heads and hydrophobic tails of the lipid bilayer prevent polar solutes (ex. amino acids, nucleic acids, carbohydrates, proteins, and ions) from diffusing across the membrane, but generally allows for the passive diffusion of hydrophobic molecules. This affords the cell the ability to control the movement of these substances via transmembrane protein complexes such as pores, channels and gates.


title: Cell membrane

text: Flippases and scramblases concentrate phosphatidyl serine, which carries a negative charge, on the inner membrane. Along with NANA, this creates an extra barrier to charged moieties moving through the membrane.


title: Cell membrane

text: Membranes serve diverse functions in eukaryotic and prokaryotic cells. One important role is to regulate the movement of materials into and out of cells. The phospholipid bilayer structure (fluid mosaic model) with specific membrane proteins accounts for the selective permeability of the membrane and passive and active transport mechanisms. In addition, membranes in prokaryotes and in the mitochondria and chloroplasts of eukaryotes facilitate the synthesis of ATP through chemiosmosis.


title: Cell membrane

text: The apical membrane of a polarized cell is the surface of the plasma membrane that faces inward to the lumen. This is particularly evident in epithelial and endothelial cells, but also describes other polarized cells, such as neurons. The basolateral membrane of a polarized cell is the surface of the plasma membrane that forms its basal and lateral surfaces. It faces outwards, towards the interstitium, and away from the lumen. Basolateral membrane is a compound phrase referring to the terms "basal (base) membrane" and "lateral (side) membrane", which, especially in epithelial cells, are identical in composition and activity. Proteins (such as ion channels and pumps) are free to move from the basal to the lateral surface of the cell or vice versa in accordance with the fluid mosaic model. Tight junctions join epithelial cells near their apical surface to prevent the migration of proteins from the basolateral membrane to the apical membrane. The basal and lateral surfaces thus remain roughly equivalent to one another, yet distinct from the apical surface.


title: Cell membrane

text: Cell membrane can form different types of "supramembrane" structures such as caveola, postsynaptic density, podosome, invadopodium, focal adhesion, and different types of cell junctions. These structures are usually responsible for cell adhesion, communication, endocytosis and exocytosis. They can be visualized by electron microscopy or fluorescence microscopy. They are composed of specific proteins, such as integrins and cadherins.


title: Cell membrane

text: The cytoskeleton is found underlying the cell membrane in the cytoplasm and provides a scaffolding for membrane proteins to anchor to, as well as forming organelles that extend from the cell. Indeed, cytoskeletal elements interact extensively and intimately with the cell membrane. Anchoring proteins restricts them to a particular cell surface — for example, the apical surface of epithelial cells that line the vertebrate gut — and limits how far they may diffuse within the bilayer. The cytoskeleton is able to form appendage-like organelles, such as cilia, which are microtubule-based extensions covered by the cell membrane, and filopodia, which are actin-based extensions. These extensions are ensheathed in membrane and project from the surface of the cell in order to sense the external environment and/or make contact with the substrate or other cells. The apical surfaces of epithelial cells are dense with actin-based finger-like projections known as microvilli, which increase cell surface area and thereby increase the absorption rate of nutrients. Localized decoupling of the cytoskeleton and cell membrane results in formation of a bleb.


title: Cell membrane

text: The content of the cell, inside the cell membrane, is composed of numerous membrane-bound organelles, which contribute to the overall function of the cell. The origin, structure, and function of each organelle leads to a large variation in the cell composition due to the individual uniqueness associated with each organelle.


title: Cell membrane

text: The cell membrane has different lipid and protein compositions in distinct types of cells and may have therefore specific names for certain cell types.


title: Cell membrane

text: The permeability of a membrane is the rate of passive diffusion of molecules through the membrane. These molecules are known as permeant molecules. Permeability depends mainly on the electric charge and polarity of the molecule and to a lesser extent the molar mass of the molecule. Due to the cell membrane's hydrophobic nature, small electrically neutral molecules pass through the membrane more easily than charged, large ones. The inability of charged molecules to pass through the cell membrane results in pH partition of substances throughout the fluid compartments of the body.


title: Kilroy was here

text: Kilroy was here is a meme that became popular during World War II, typically seen in graffiti. Its origin is debated, but the phrase and the distinctive accompanying doodle became associated with GIs in the 1940s: a bald-headed man (sometimes depicted as having a few hairs) with a prominent nose peeking over a wall with his fingers clutching the wall.


title: Kilroy was here

text: "Mr Chad" or just "Chad" was the version that became popular in the United Kingdom. The character of Chad may have been derived from a British cartoonist in 1938, possibly pre-dating "Kilroy was here". According to Dave Wilton, "Some time during the war, Chad and Kilroy met, and in the spirit of Allied unity merged, with the British drawing appearing over the American phrase." Other names for the character include Smoe, Clem, Flywheel, Private Snoops, Overby, Eugene the Jeep, Scabooch, and Sapo.


title: Kilroy was here

text: According to Charles Panati, "The outrageousness of the graffiti was not so much what it said, but where it turned up." It is not known if there was an actual person named Kilroy who inspired the graffiti, although there have been claims over the years.


title: Kilroy was here

text: The phrase may have originated through United States servicemen who would draw the picture and the text "Kilroy was here" on the walls and other places where they were stationed, encamped, or visited. An ad in "Life" magazine noted that WWII-era servicemen were fond of claiming that "whatever beach-head they stormed, they always found notices chalked up ahead of them, that 'Kilroy was here. "Brewer's Dictionary of Phrase and Fable" notes that it was particularly associated with the Air Transport Command, at least when observed in the United Kingdom. At some point, the graffiti (Chad) and slogan (Kilroy was here) must have merged.


title: Kilroy was here

text: Many sources claim origin as early as 1939. Earlier examples of the phrase dating from 1937 are unverified.


title: Kilroy was here

text: According to one story, German intelligence found the phrase on captured American equipment. This led Adolf Hitler to believe that Kilroy could be the name or codename of a high-level Allied spy. At the time of the Potsdam Conference in 1945, it was rumored that Stalin found "Kilroy was here" written in the VIP bathroom, prompting him to ask his aides who Kilroy was. War photographer Robert Capa noted a use of the phrase at Bastogne during the Battle of the Bulge in December 1944: "On the black, charred walls of an abandoned barn, scrawled in white chalk, was the legend of Gen. Anthony McAuliffe's soldiers: KILROY WAS STUCK HERE."


title: Kilroy was here

text: "Digger History, the Unofficial history of the Australian & New Zealand Armed Services", says of Foo that "He was chalked on the side of railway carriages, appeared in probably every camp that the 1st AIF World War I served in and generally made his presence felt". If this is the case, then "Foo was here" predates the American version of World War II, "Kilroy was here", by about 25 years. "Foo" was thought of as a gremlin by the Royal Australian Air Force. It has been claimed that Foo came from the acronym for Forward Observation Officer.


title: Kilroy was here

text: One theory identifies James J. Kilroy (1902–1962), an American shipyard inspector, as the man behind the signature. James Kilroy had served on the Boston City Council and represented the Roxbury district in the Massachusetts Legislature during the 1930s. He worked at the Fore River Shipyard in Quincy during the war checking the work of riveters paid by how many rivets they installed. Usually, inspectors made a small chalk mark which riveters used to erase, so that they would be paid double for their work. To prevent this, Kilroy marked work he had inspected and approved with the phrase "Kilroy was here" in more durable crayon.


title: Kilroy was here

text: More than 40 candidates claimed to have originated the phrase and cartoon in response to a 1946 contest conducted by the American Transit Association to establish the origin of the phenomenon. James Kilroy was credited after his claim was verified by shipyard officials and the riveters whose work he inspected. While Kilroy's marks might normally have been painted over, interior painting was a low priority in the rush to launch ships, so Kilroy's marks were seen by thousands of servicemen who sailed aboard troopships built at Quincy. A "The New York Times" article noted that Kilroy had marked the ships as they were being built as a way to be sure that he had inspected a compartment, and the phrase would be found chalked in places that nobody could have reached for graffiti, such as inside sealed hull spaces. "Brewer's Dictionary of Phrase and Fable" notes this as a possible origin, but suggests that "the phrase grew by accident."


title: Kilroy was here

text: The "Lowell Sun" reported in November 1945 that Sgt. Francis J. Kilroy Jr. from Everett, Massachusetts, wrote "Kilroy will be here next week" on a barracks bulletin board at a Boca Raton, Florida, airbase while ill with flu, and the phrase was picked up by other airmen and quickly spread abroad. The Associated Press similarly reported Sgt. Kilroy's account of being hospitalized early in World War II, and his friend Sgt. James Maloney wrote the phrase on a bulletin board. Maloney continued to write the shortened phrase when he was shipped out a month later, according to the AP account, and other airmen soon picked it up. Francis Kilroy only wrote the phrase a couple of times.


title: Kilroy was here

text: The figure was initially known in the United Kingdom as "Mr Chad" and would appear with the slogan "Wot, no sugar" or a similar phrase bemoaning shortages and rationing. He often appeared with a single curling hair that resembled a question mark and with crosses in his eyes. The phrase "Wot, no —?" pre-dates "Chad" and was widely used separately from the doodle. Chad was used by the RAF and civilians; he was known in the army as Private Snoops, and in the navy he was called The Watcher. Chad might have first been drawn by British cartoonist George Edward Chatterton in 1938. Chatterton was nicknamed "Chat", which may then have become "Chad". "Life Magazine" wrote in 1946 that the RAF and army were competing to claim him as their own invention, but they agreed that he had first appeared around 1944. The character resembles Alice the Goon, a character in Popeye who first appeared in 1933, and another name for Chad was "The Goon".


title: Kilroy was here

text: A spokesman for the Royal Air Force Museum London suggested in 1977 that Chad was probably an adaptation of the Greek letter omega, used as the symbol for electrical resistance; his creator was probably an electrician in a ground crew. "Life" suggested that Chad originated with REME, and noted that a symbol for alternating current resembles Chad (a sine wave through a straight line), that the plus and minus signs in his eyes represent polarity, and that his fingers are symbols of electrical resistors. The character is usually drawn in Australia with pluses and minuses as eyes and the nose and eyes resemble a distorted sine wave. "The Guardian" suggested in 2000 that "Mr. Chad" was based on a diagram representing an electrical circuit. One correspondent said that a man named Dickie Lyle was at RAF Yatesbury in 1941, and he drew a version of the diagram as a face when the instructor had left the room and wrote "Wot, no leave?" beneath it. This idea was repeated in a submission to the BBC in 2005 which included a story of a 1941 radar lecturer in Gainsborough, Lincolnshire, who drew the circuit diagram with the words "WOT! No electrons?" The RAF Cranwell Apprentices Association says that the image came from a diagram of how to approximate a square wave using sine waves, also at RAF Yatesbury and with an instructor named Chadwick. This version was initially called Domie or Doomie, and "Life" noted that Doomie was used by the RAF. REME claimed that the name came from their training school, nicknamed "Chad's Temple"; the RAF claimed that it arose from Chadwick House at a Lancashire radio school; and the Desert Rats claimed that it came from an officer in El Alamein.


title: Kilroy was here

text: It is unclear how Chad gained widespread popularity or became conflated with Kilroy. It was, however, widely in use by the late part of the war and in the immediate post-war years, with slogans ranging from the simple "What, no bread?" or "Wot, no char?" to the plaintive; one sighting was on the side of a British 1st Airborne Division glider in Operation Market Garden with the complaint "Wot, no engines?" The "Los Angeles Times" reported in 1946 that Chad was "the No. 1 doodle", noting his appearance on a wall in the Houses of Parliament after the 1945 Labour election victory, with "Wot, no Tories?" Trains in Austria in 1946 featured Mr. Chad along with the phrase "Wot—no Fuehrer?"


title: Kilroy was here

text: As rationing became less common, so did the joke. The cartoon is occasionally seen today as "Kilroy was here", but "Chad" and his complaints have long fallen from popular use, although they continue to be seen occasionally on walls and in references in popular culture.


title: Kilroy was here

text: Writing about the Kilroy phenomenon in 1946, " The Milwaukee Journal" describes the doodle as the European counterpart to "Kilroy was here", under the name Smoe. It also says that Smoe was called Clem in the African theater. It noted that next to "Kilroy was here" was often added "And so was Smoe". While Kilroy enjoyed a resurgence of interest after the war due to radio shows and comic writers, the name Smoe had already disappeared by the end of 1946. A B-24 airman writing in 1998 also noted the distinction between the character of Smoe and Kilroy (who he says was never pictured), and suggested that Smoe stood for "Sad men of Europe". Correspondents to "Life" magazine in 1962 also insisted that Clem, Mr. Chad or Luke the Spook was the name of the figure, and that Kilroy was unpictured. The editor suggested that the names were all synonymous early in the war, then later separated into separate characters.


title: Kilroy was here

text: Similar drawings appear in many countries. Herbie (Canada), Overby (Los Angeles, late 1960s), Flywheel, Private Snoops, The Jeep, and Clem (Canada) are alternative names. An advertisement in "Billboard" in November 1946 for plastic "Kilroys" also used the names Clem, Heffinger, Luke the Spook, Some, and Stinkie. "Luke the Spook" was the name of a B-29 bomber, and its nose-art resembles the doodle and is said to have been created at the Boeing factory in Seattle. In Chile, the graphic is known as a "sapo" (slang for nosy).


title: Kilroy was here

text: In Poland, Kilroy is replaced with "" or "M. Pulina". In Russia, the phrase "Vasya was here" () is a notorious piece of graffiti.


title: Kilroy was here

text: Kilroy is seen scrawling "Kilroy is here" on a wall in Tennessee Williams's 1953 play "Camino Real", which he revises to "was" before his final departure. Kilroy functions in the play as "a folk character...who here is a sort of Everyman." The graffiti appears on the cover of the first edition published by New Directions. Isaac Asimov's short story "The Message" (1955) depicts a time-travelling George Kilroy from the 30th century as the writer of the graffiti.


title: Kilroy was here

text: Thomas Pynchon's novel "V." (1963) includes the proposal that the Kilroy doodle originated from a band-pass filter diagram. Ken Young wrote a parody of "'Twas the Night Before Christmas" which was transmitted to Apollo 8 on December 25, 1968. It featured the lines "When what to his wondering eyes should appear, but a Burma-Shave sign saying, 'Kilroy was here'."


title: Kilroy was here

text: In the 1975 "M*A*S*H" episode "The Bus", Hawkeye Pierce (Alan Alda) writes "Kilroy" in a dust-encrusted bus window as B.J. Hunnicutt (Mike Farrell) peers out from behind the window, his hands and nose resting on its top edge.


title: Kilroy was here

text: In the opening credits of the 2009 American sitcom "Community", two Kilroys are drawn in blue ink on the inside of a paper fortune teller, their noses forming the L's of lead actor Joel McHale's name.


title: Graph theory

text: In mathematics, graph theory is the study of "graphs", which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of "vertices" (also called "nodes" or "points") which are connected by "edges" (also called "links" or "lines"). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.


title: Graph theory

text: Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures.


title: Graph theory

text: In one restricted but very common sense of the term, a graph is an ordered pair formula_1 comprising:


title: Graph theory

text: In the edge formula_4, the vertices formula_5 and formula_6 are called the endpoints of the edge. The edge is said to join formula_5 and formula_6 and to be incident on formula_5 and on formula_6. A vertex may exist in a graph and not belong to an edge. Multiple edges, not allowed under the definition above, are two or more edges that join the same two vertices.


title: Graph theory

text: In one more general sense of the term allowing multiple edges, a graph is an ordered triple formula_11 comprising:


title: Graph theory

text: A loop is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex formula_5 to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) formula_16 which is not in formula_17. So to allow loops the definitions must be expanded. For undirected simple graphs, the definition of formula_13 should be modified to formula_19. For undirected multigraphs, the definition of formula_20 should be modified to formula_21. To avoid ambiguity, these types of objects may be called undirected simple graph permitting loops and undirected multigraph permitting loops (sometimes also undirected pseudograph), respectively.


title: Graph theory

text: formula_2 and formula_13 are usually taken to be finite, and many of the well-known results are not true (or are rather different) for infinite graphs because many of the arguments fail in the infinite case. Moreover, formula_2 is often assumed to be non-empty, but formula_13 is allowed to be the empty set. The order of a graph is formula_26, its number of vertices. The size of a graph is formula_27, its number of edges. The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices.


title: Graph theory

text: In an undirected simple graph of order "n", the maximum degree of each vertex is and the maximum size of the graph is .


title: Graph theory

text: The edges of an undirected simple graph permitting loops formula_28 induce a symmetric homogeneous relation formula_29 on the vertices of formula_28 that is called the adjacency relation of formula_28. Specifically, for each edge formula_32, its endpoints formula_5 and formula_6 are said to be adjacent to one another, which is denoted formula_35.


title: Graph theory

text: In one restricted but very common sense of the term, a directed graph is an ordered pair formula_1 comprising:


title: Graph theory

text: In the edge formula_39 directed from formula_5 to formula_6, the vertices formula_5 and formula_6 are called the "endpoints" of the edge, formula_5 the "tail" of the edge and formula_6 the "head" of the edge. The edge is said to "join" formula_5 and formula_6 and to be "incident" on formula_5 and on formula_6. A vertex may exist in a graph and not belong to an edge. The edge formula_50 is called the "inverted edge" of formula_39. "Multiple edges", not allowed under the definition above, are two or more edges with both the same tail and the same head.


title: Graph theory

text: In one more general sense of the term allowing multiple edges, a directed graph is an ordered triple formula_11 comprising:


title: Graph theory

text: A "loop" is an edge that joins a vertex to itself. Directed graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex formula_5 to itself is the edge (for a directed simple graph) or is incident on (for a directed multigraph) formula_57 which is not in formula_58. So to allow loops the definitions must be expanded. For directed simple graphs, the definition of formula_13 should be modified to formula_60. For directed multigraphs, the definition of formula_20 should be modified to formula_62. To avoid ambiguity, these types of objects may be called precisely a directed simple graph permitting loops and a directed multigraph permitting loops (or a "quiver") respectively.


title: Graph theory

text: The edges of a directed simple graph permitting loops formula_28 is a homogeneous relation ~ on the vertices of formula_28 that is called the "adjacency relation" of formula_28. Specifically, for each edge formula_32, its endpoints formula_5 and formula_6 are said to be "adjacent" to one another, which is denoted formula_5 ~ formula_6.


title: Graph theory

text: Graphs can be used to model many types of relations and processes in physical, biological, social and information systems. Many practical problems can be represented by graphs. Emphasizing their application to real-world systems, the term "network" is sometimes defined to mean a graph in which attributes (e.g. names) are associated with the vertices and edges, and the subject that expresses and understands real-world systems as a network is called network science.


title: Graph theory

text: Within computer science, cybernetics uses graphs to represent networks of communication, data organization, computational devices, the flow of computation, etc. For instance, the link structure of a website can be represented by a directed graph, in which the vertices represent web pages and directed edges represent links from one page to another. A similar approach can be taken to problems in social media, travel, biology, computer chip design, mapping the progression of neuro-degenerative diseases, and many other fields. The development of algorithms to handle graphs is therefore of major interest in computer science. The transformation of graphs is often formalized and represented by graph rewrite systems. Complementary to graph transformation systems focusing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data.


title: Graph theory

text: Graph-theoretic methods, in various forms, have proven particularly useful in linguistics, since natural language often lends itself well to discrete structure. Traditionally, syntax and compositional semantics follow tree-based structures, whose expressive power lies in the principle of compositionality, modeled in a hierarchical graph. More contemporary approaches such as head-driven phrase structure grammar model the syntax of natural language using typed feature structures, which are directed acyclic graphs.


title: Graph theory

text: Within lexical semantics, especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words; semantic networks are therefore important in computational linguistics. Still, other methods in phonology (e.g. optimality theory, which uses lattice graphs) and morphology (e.g. finite-state morphology, using finite-state transducers) are common in the analysis of language as a graph. Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as TextGraphs, as well as various 'Net' projects, such as WordNet, VerbNet, and others.


title: Graph theory

text: Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics, the three-dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms. Also, "the Feynman graphs and rules of calculation summarize quantum field theory in a form in close contact with the experimental numbers one wants to understand." In chemistry a graph makes a natural model for a molecule, where vertices represent atoms and edges bonds. This approach is especially used in computer processing of molecular structures, ranging from chemical editors to database searching. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such


title: Graph theory

text: systems. Similarly, in computational neuroscience graphs can be used to represent functional connections between brain areas that interact to give rise to various cognitive processes, where the vertices represent different areas of the brain and the edges represent the connections between those areas. Graph theory plays an important role in electrical modeling of electrical networks, here, weights are associated with resistance of the wire segments to obtain electrical properties of network structures. Graphs are also used to represent the micro-scale channels of porous media, in which the vertices represent the pores and the edges represent the smaller channels connecting the pores. Chemical graph theory uses the molecular graph as a means to model molecules.


title: Graph theory

text: Graphs and networks are excellent models to study and understand phase transitions and critical phenomena.


title: Graph theory

text: Removal of nodes or edges leads to a critical transition where the network breaks into small clusters which is studied as a phase transition. This breakdown is studied via percolation theory.


title: Graph theory

text: Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. Acquaintanceship and friendship graphs describe whether people know each other. Influence graphs model whether certain people can influence the behavior of others. Finally, collaboration graphs model whether two people work together in a particular way, such as acting in a movie together.


title: Graph theory

text: Likewise, graph theory is useful in biology and conservation efforts where a vertex can represent regions where certain species exist (or inhabit) and the edges represent migration paths or movement between the regions. This information is important when looking at breeding patterns or tracking the spread of disease, parasites or how changes to the movement can affect other species.


title: Graph theory

text: Graphs are also commonly used in molecular biology and genomics to model and analyse datasets with complex relationships. For example, graph-based methods are often used to 'cluster' cells together into cell-types in single-cell transcriptome analysis. Another use is to model genes or proteins in a pathway and study the relationships between them, such as metabolic pathways and gene regulatory networks. Evolutionary trees, ecological networks, and hierarchical clustering of gene expression patterns are also represented as graph structures.


title: Graph theory

text: Graph theory is also used in connectomics; nervous systems can be seen as a graph, where the nodes are neurons and the edges are the connections between them.


title: Graph theory

text: In mathematics, graphs are useful in geometry and certain parts of topology such as knot theory. Algebraic graph theory has close links with group theory. Algebraic graph theory has been applied to many areas including dynamic systems and complexity.


title: Graph theory

text: A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road. There may be several weights associated with each edge, including distance (as in the previous example), travel time, or monetary cost. Such weighted graphs are commonly used to program GPS's, and travel-planning search engines that compare flight times and costs.


title: Graph theory

text: The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory. This paper, as well as the one written by Vandermonde on the "knight problem," carried on with the "analysis situs" initiated by Leibniz. Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy and L'Huilier, and represents the beginning of the branch of mathematics known as topology.


title: Graph theory

text: More than one century after Euler's paper on the bridges of Königsberg and while Listing was introducing the concept of topology, Cayley was led by an interest in particular analytical forms arising from differential calculus to study a particular class of graphs, the "trees". This study had many implications for theoretical chemistry. The techniques he used mainly concern the enumeration of graphs with particular properties. Enumerative graph theory then arose from the results of Cayley and the fundamental results published by Pólya between 1935 and 1937. These were generalized by De Bruijn in 1959. Cayley linked his results on trees with contemporary studies of chemical composition. The fusion of ideas from mathematics with those from chemistry began what has become part of the standard terminology of graph theory.


title: Graph theory

text: In particular, the term "graph" was introduced by Sylvester in a paper published in 1878 in "Nature", where he draws an analogy between "quantic invariants" and "co-variants" of algebra and molecular diagrams:


title: Graph theory

text: The first textbook on graph theory was written by Dénes Kőnig, and published in 1936. Another book by Frank Harary, published in 1969, was "considered the world over to be the definitive textbook on the subject", and enabled mathematicians, chemists, electrical engineers and social scientists to talk to each other. Harary donated all of the royalties to fund the Pólya Prize.


title: Graph theory

text: One of the most famous and stimulating problems in graph theory is the four color problem: "Is it true that any map drawn in the plane may have its regions colored with four colors, in such a way that any two regions having a common border have different colors?" This problem was first posed by Francis Guthrie in 1852 and its first written record is in a letter of De Morgan addressed to Hamilton the same year. Many incorrect proofs have been proposed, including those by Cayley, Kempe, and others. The study and the generalization of this problem by Tait, Heawood, Ramsey and Hadwiger led to the study of the colorings of the graphs embedded on surfaces with arbitrary genus. Tait's reformulation generated a new class of problems, the "factorization problems", particularly studied by Petersen and Kőnig. The works of Ramsey on colorations and more specially the results obtained by Turán in 1941 was at the origin of another branch of graph theory, "extremal graph theory".


title: Graph theory

text: The four color problem remained unsolved for more than a century. In 1969 Heinrich Heesch published a method for solving the problem using computers. A computer-aided proof produced in 1976 by Kenneth Appel and Wolfgang Haken makes fundamental use of the notion of "discharging" developed by Heesch. The proof involved checking the properties of 1,936 configurations by computer, and was not fully accepted at the time due to its complexity. A simpler proof considering only 633 configurations was given twenty years later by Robertson, Seymour, Sanders and Thomas.