Madison Avenue is a north-south avenue in the borough of Manhattan in New York City, United States, that carries northbound one-way traffic. It runs from Madison Square to meet the southbound Harlem River Drive at 142nd Street. In doing so, it passes through Midtown, the Upper East Side, East Harlem, Harlem, it is named after and arises from Madison Square, itself named after James Madison, the fourth President of the United States. Madison Avenue was not part of the original Manhattan street grid established in the Commissioners' Plan of 1811, was carved between Park Avenue and Fifth Avenue in 1836, due to the effort of lawyer and real estate developer Samuel B. Ruggles, who had purchased and developed New York's Gramercy Park in 1831, convinced the authorities to create Lexington Avenue and Irving Place between Fourth Avenue and Third Avenue in order to service it; the street's name has been metonymous with the American advertising industry since the 1920s. Thus, the term "Madison Avenue" refers to the agencies and methodology of advertising.

"Madison Avenue techniques" refers, according to William Safire, to the "gimmicky, slick use of the communications media to play on emotions." Madison Avenue carries one-way traffic uptown from East 23rd Street to East 135th Street, with the changeover from two-way traffic taking place on January 14, 1966, at which time Fifth Avenue was changed to one-way downtown. Between East 135th Street and East 142nd Street, Madison Avenue carries southbound traffic only, runs parallel to the Harlem River Drive; the term "Madison Avenue" is used metonymically to stand for the American advertising industry. Madison Avenue became identified with advertising after that sector's explosive growth in this area in the 1920s. According to "The Emergence of Advertising in America", by the year 1861, there were twenty advertising agencies in New York City. Among various depictions in popular culture, the portion of the advertising industry which centers on Madison Avenue serves as a backdrop for the AMC television drama Mad Men, which focuses on industry activities during the 1960s.

In recent decades, many agencies have left Madison Avenue, with some moving further downtown and others moving west. The continued presence of large agencies in the city made New York the third-largest job market per capita in the U. S. in 2016, according to a study by marketing recruitment firm MarketPro. Today, several agencies are still located in the old business cluster on Madison Avenue, including StrawberryFrog, TBWA Worldwide, Inc. and DDB Worldwide. However, the term is still used to describe the agency business as a whole and large, New York–based agencies in particular. Madison Square Park is a 6.2-acre public park which runs along Madison Avenue from East 26th Street to East 23rd Street. It is bordered on the west by Fifth Broadway as they cross; the park was named for James Madison, fourth President of the United States. Madison Square Garden took its name from the location of the first building of that name, located on the northeast corner of Madison Avenue at 26th Street, across from the Park.

The first Garden was a former railroad terminal for the Park Avenue main line, converted into an open-air circus venue by P. T. Barnum in 1871 and was renamed "Madison Square Garden" in 1879; the original Garden was demolished in 1889 and replaced by a new indoor arena designed by Stanford White that opened the following year. The second Garden had a bronze statue of the Roman goddess Diana on the tower of the sports arena; when it moved to a new building at 50th Street and Eighth Avenue in 1925 it kept its old name. Madison Square Garden is now located at Eighth Avenue between 33rd Street. Retail brands with locations on Madison Avenue include: Burberry, Brooks Brothers, Alexander McQueen, Hermès, Tom Ford, Céline, Proenza Schouler, Valentino, Stuart Weitzman, Emporio Armani, Chloé, Roberto Cavalli, Dolce & Gabbana, Calvin Klein, Christian Louboutin, La Perla, Jimmy Choo, Mulberry, Victoria's Secret, Barneys New York, Rolex, Giorgio Armani, Oliver Peoples, Vera Wang, Anne Fontaine, Carolina Herrera,Manrico Cashmere, Ralph Lauren and others.

Madison Avenue is served by M2, M3, M4 and Q32 local New York City Transit buses. These buses use a double exclusive bus lane between 42nd and 59th Streets, which comprise the only exclusive bus lane along the avenue. Although no New York City Subway stations are named after Madison Avenue, the Fifth Avenue/53rd Street station on the E and ​M trains has an entrance on Madison Avenue. Pursuant to Section 4-12 of the New York City Traffic Rules, driving a vehicle other than a bus in the bus lane on Madison Avenue to turn right during the restricted hours specified by sign between 42nd Street and 59th Street is prohibited permitted at 60th Street, but a taxicab carrying a passenger may use the bus lane to turn right at 46th Street. Bikes are excluded from this prohibition. In July 1987, then-New York City Mayor Edward Koch proposed banning bicycling on Fifth and Madison Avenues during weekdays, but many bicyclists protested and

An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances in the plane that cannot be extended by any additional points. Equivalently, it can be described as a complete graph with vertices located on the integer square grid Z 2 such that all mutual distances between the vertices are integers, while all other grid points have a non-integer distance to at least one vertex. Erdős–Diophantine graphs are named after Paul Erdős and Diophantus of Alexandria, they form a subset of the set of Diophantine figures, which are defined as complete graphs in the Diophantine plane for which the length of all edges are integers. Thus, Erdős–Diophantine graphs are the Diophantine figures that cannot be extended; the existence of Erdős–Diophantine graphs follows from the Erdős–Anning theorem, according to which infinite Diophantine figures must be collinear in the Diophantine plane. Hence, any process of extending a non-collinear Diophantine figure by adding vertices must reach a figure that can no longer be extended.

Any set of zero or one point can be trivially extended, any Diophantine set of two points can be extended by more points on the same line. Therefore, all Diophantine sets with fewer than three nodes can be extended, so Erdős–Diophantine graphs on fewer than three nodes cannot exist. By numerical search, Kohnert & Kurz have shown; the smallest Erdős–Diophantine triangle is characterised by edge lengths 2066, 1803, 505. The next larger Erdős–Diophantine triangle has edges 2549, 2307 and 1492. In both cases, the sum of the three edge-lengths is even. Brancheva has proven. More the total length of any closed path in an Erdős–Diophantine graph is always even. An example of a 4-node Erdős–Diophantine graph is provided by the complete graph formed by the four nodes located on the vertices of a rectangle with sides 4 and 3. Kohnert, Axel.

Sadwavirus is a genus of viruses in the order Picornavirales, in the family Secoviridae. Plants serve as natural hosts. There is only one species in this genus: the type species Satsuma dwarf virus. Diseases associated with this genus include: satsuma dwarf virus disease which causes spoon-shaped leaves on citrus tree. Symptoms are enations, multiple flushing, stunting or dwarfing, reduction in number and size of leaves and fruits; the name of this genus comes from its type species: Satsuma dwarf virus. Group: ssRNA Viruses in Sadwavirus are non-enveloped, with icosahedral geometries, T=pseudo3 symmetry; the diameter is around 25-30 nm. The genome is segmented into two parts of linear, positive-sense, single-stranded RNA, 11000-12000 nucleotides in length, where one segment is about 7kb and the second segment is 4.6 to 5.4kb. Viral replication is cytoplasmic, is lysogenic. Entry into the host cell is achieved by penetration into the host cell. Replication follows the positive stranded RNA virus replication model.

Positive stranded RNA virus transcription is the method of transcription. The virus exits the host cell by tubule-guided viral movement. Plants serve as the natural host; the virus is transmitted via a vector. Transmission routes are vector, seed borne, grafting. Viralzone: Sadwavirus ICTV UniProt Taxonomy