title: Frock coat

text: The lounge suit was once only worn as smart leisure wear in the country or at the seaside but in the middle of the 19th century started to rise rapidly in popularity. It took on the role of a more casual alternative to the morning coat for town wear, moving the latter up in the scale of formality. The more the morning coat became fashionable as correct daytime full dress, the more the lounge suit became acceptable as an informal alternative. Finally the frock coat became relegated to the status of ultra-formal day wear, worn only by older men. At the most formal events during the signing of the Treaty of Versailles in 1919, heads of government wore the frock coat but at more informal meetings they wore morning coats or even a lounge suit. In 1926, George V hastened the demise of the frock coat when he shocked the public by appearing at the opening of the Chelsea Flower Show wearing a morning coat. The frock coat barely survived the 1930s only as an ultra-formal form of court dress, until being finally officially abolished in 1936 as official court dress by Edward VIII (who later abdicated to become the Duke of Windsor). It was replaced by the morning coat, thus consigning the frock coat protocol-wise to the status of historic dress at the British royal court.


title: Frock coat

text: Since that time it has been worn sparingly, albeit arguably not altogether vanished (see section on contemporary use further below).


title: Frock coat

text: Frock coats worn with waistcoat and formal striped trousers are still very occasionally worn as daytime formal wear, especially to weddings, as an alternative to morning coats, in order to give the wedding attire a Victorian flavour. They are today usually only worn by the wedding party, where elements of historical costume are more acceptable and even this practice is unusual, as its role as a formal ceremonial coat in daytime formal wear has been long supplanted in modern dress code by the morning coat. Like morning coats, frock coats are only worn for daytime formal events before 5pm. and no later than until around 7pm.


title: Frock coat

text: Prior to the establishment of morning dress around the turn of the century in 1900, the expression "morning dress" tended to refer to frock coat, while gradually extending to mean both the frock coat and "morning dress" in the contemporary sense.


title: Frock coat

text: Standard fibres used for the frock coat included wool and vicuña. The most common weaves were known as broadcloth and duffel, both so called "heavy wools" manufactured along a process originating from Flanders in the 11th century (Flemish cloth). The standard colour of a civilian frock coat was solid black but later, in the Victorian era, charcoal grey became an acceptable but less common alternative and Midnight Blue was an even rarer alternative colour. For business and festive occasions the revers was lined with black silk facings (either satin or grosgrain). For funerals black frock coats without self-faced revers were worn with a matching black waistcoat. In military uniforms a wider variety of colours was and is common, prompting colour names as "navy blue" and "cadet grey".


title: Frock coat

text: On more formal outings the coat was worn with a pair of cashmere striped morning trousers: ("cashmere stripes" refers to the muted design in black, silver and charcoal grey, not the fibres of the cloth.) However, trousers of muted checks were also worn in slightly more informal situations. In keeping with the rules set for morning dress, trousers matching the coat were considered a somewhat less formal alternative.


title: Frock coat

text: A matching black waistcoat was worn for more formal business or more solemn ceremonies. During the earlier Victorian period, colourful fancy waistcoats of silk were noted as being worn by gentlemen such as Charles Dickens. In summer a white or buff coloured linen waistcoat could be worn. For festive occasions a lighter coloured waistcoat such as light grey was permissible.


title: Frock coat

text: The length of the skirt of the frock coat varied during the Victorian era and Edwardian era according to fashion. The most conservative length became established as being to the knees but fashion conscious men would follow the latest trends to wear them either longer or shorter. Similarly, the height of the waist – the point of maximal waist suppression – changed according to fashion. During its heyday, the frock coat was cut following the 19th century ideal of flattering the natural elegance of the naked figure, based on the ideals of Neoclassicism that admired the depiction of the idealised nude in Classical Greco-Roman sculpture. The elegance of the form of the frock coat derived from its hourglass shape with a closely cut waist which at times around the 1830s-40's was reinforced further with padding to round out the chest. A cut with an ideal hourglass silhouette was achievable because coats during this era were all made bespoke, individually cut to the exact measurements of the customer. The 19th century aesthetics of tailoring contrasted markedly to the modern style of cutting suits which involves a greater degree of drape (fullness), as established by the great early 20th century Savile Row tailor Frederick Scholte. Caution needs to be exercised by modern tailors trained to create the drape cut style of modern lounge suits to minimise drape – particularly around the waist – when cutting a historically accurate frock coat. Sometimes, modern lounge suit coats with an unusually long skirt are referred to by ready-to-wear makers as a 'frock coat' but these lack the waist seam, resulting in the fuller drape more typical of a modern overcoat or a lounge suit jacket. The silhouette of the historically accurate frock coat has the waist seam precisely tailored to permit the classical and elongating hourglass figure with the strong waist suppression.


title: Frock coat

text: Another characteristic of frock coats was their lack of any outer pockets. Only late in the Victorian and Edwardian era were they ever made with a chest pocket to sport a pocket square, a feature more typical of the modern lounge suit. Oscar Wilde, a famous dandy of his time, was often seen in portraits wearing just such a model but this was rather rare on frock coats; while in keeping with the flamboyant nature of Wilde's dress, it was frowned upon by traditionalists. Side pockets were always absent from frock coats but pockets were provided on the inside of the chest or inside the top part of the tail.


title: Frock coat

text: The buttons on a frock coat were always covered in cloth, often to match the silk on the revers, showing in the triangle of lining wrapped over the inside of the lapels. Another common feature was the use of fancy buttons with a snow-flake or check pattern woven over it.


title: Frock coat

text: Through most of the Victorian era until towards the end, the lapels were cut separately and sewn on later, apparently because it made the lapel roll more elegantly from bottom up. The lapel revers from the inside of the coat wrapped over to the front, creating a small triangle of silk, while the outer half was cut from two strips of the body fabric. This was a feature of double-breasted frock coats used on all such coats but morning and dress coats, which had previously followed this practice, began to be made with attached lapels (wholecut) around the end of the Edwardian era. Through the Victorian era, a row of decorative button holes was created down the lapel edge but by Edwardian period these were reduced down to just the one lapel boutonnière button hole.


title: Frock coat

text: Turn back cuffs on the sleeves, similar to the turn ups (cuffs in American English) on modern trouser hems, were standard, with two buttons on the cuff.


title: Frock coat

text: Proper accessories to wear with the frock coat included a non-collapsible top hat and a boutonnière in the lapel. A Homburg hat was considered too informal to wear with proper formal morning dress. During the Victorian and Edwardian era, button boots with a single row of punching across the cap toe were worn along with a cane. On cold days, it was common to wear a frock overcoat, a type of overcoat cut exactly the same as the frock coat, with the waist seam construction only a little longer and fuller to permit it to be worn over the top of the frock coat. Patent leather dress boots were worn up until the Edwardian era with morning dress. The practice of wearing patent leather shoes is today reserved strictly for evening formalwear. Trousers are uncuffed and worn with braces to avoid the top of the trousers from showing underneath the waistcoat. Only white shirts were worn with frock coats. The shirt was worn with a standing detachable collar with either wingtips or "imperial" style (plain standing). The most standard neckwear was a formal cravat . The cravat was tied in the Ascot knot characterised by way the ends cross over in front or alternatively in a Ruche knot, tied like a four-in-hand knot of a modern necktie. A decorative cravat pin often adorned with a precious stone or pearl was used to keep the cravat tidy. The cravat was usual with a frock coat when worn in more formal occasions through the Victorian and Edwardian eras, although the long necktie came to be worn increasingly after the turn of the century in the same manner as it is today with morning dress. The practice of wearing bow ties as an acceptable alternative with formalwear fell away after the late Victorian to early Edwardian era and became relegated to eveningwear, as remains the case in the 21st century. As with a formal shirt for white tie, cuffs were single (rather than double) cuffed and made to close with cufflinks. The waistcoat was usually double-breasted with peaked lapels. Formal gloves in light grey suede, chamois or kid leather were also required.


title: Frock coat

text: The solid black garment described above was widely used but before the lounge suit became popular, there was a need for a more informal garment for smart casual wear. A version of the frock coat was used here too, with matching trousers and a more informal cloth, featuring stripes or the check shown in the plate opposite. The waistcoat, instead of being black as usual in the formal version, was matching or odd. Until the modern cut away morning coat was worn, the single breasted frock coat was called a morning coat and was used in such a less formal context and double breasted coats made this way would often not fasten, being held loosely together in much the same way the modern morning coat is, with a single link.


title: Frock coat

text: The accessories for the two styles depended on the intended use of the coat: for more formal settings, the outfit might still have striped trousers and demand a top hat and white gloves; for business, by the turn of the century, the morning coat was used (again, this referred to a single breasted frock coat then, not the modern morning coat). This last was accompanied by a business collar (such as winged collar, not a standing Imperial collar); a four in hand tie (as opposed to the formal cravat and puff) and a soft Derby or Homburg.


title: Frock coat

text: Although ceasing to be required by protocol as formal attire at the British royal court in 1936, at the order of the short-reigning King Edward VIII, the frock coat has not altogether vanished as modern civilian formal wear.


title: Frock coat

text: Frock coats, albeit often in other colours than black, survive until this day in the livery of hotel staff.


title: Frock coat

text: Examples of frock coats in fashion in the 21st century include Alexander McQueen in 2012, Prada's autumn edition in 2012, and Paul Smith in 2018.


title: Frock coat

text: Frock coats still appear in certain traditional Catholic processions, such as the Blutritt in Germany.


title: Frock coat

text: Some wedding grooms apply more or less creative civil or military variants of frock coats. In the civilian wear cases it is sometimes accompanied by the same creativity in terms of ascot ties. As a prominent example, when Prince Harry married Meghan Markle in 2018, he and his brother and best man Prince William opted for military full dress uniform variants of frock coats.


title: Frock coat

text: The cut of a frock coat with a waist seam flatters a man's figure, as opposed to a sack coat, and such frock coats remained part of some 21st-century military uniforms. They can either be single-breasted, as in some army uniforms, or double-breasted as in both army and navy uniforms. An example of the latter is seen in the modern gala dress of officers in the Spanish Navy. The British Army currently retains the frock coat for ceremonial wear by senior officers of Lieutenant-General rank and above, by officers of the Household Division, by some bandmasters and by holders of certain Royal appointments.


title: Frock coat

text: The 19th century polish frock coat with hood and toggle-and-tow fastenings stood model for the overcoat used by the Royal Navy and British Army from 1890 on, known as Duffel coat or Monty coat.


title: Frock coat

text: In the Lithuanian yeshiva world, many prominent figures wear a black frock coat also known as a kapotteh (accompanied by either a Homburg or fedora hat) as formal wear. In recent years many Sefardi rabbis also wear a similar frock coat. The frock coat amongst non-Hassidic Jews is usually reserved for a rosh yeshiva, (maybe also the mashgiach and other senior rabbis of the yeshiva) and other rabbis such as important communal rabbis and some chief rabbis.


title: Frock coat

text: Most married male Lubavitcher Hasidim also don frock coats on Shabbat. All Hasidim also wear a gartel (belt) over their outer coats during prayer services.


title: Frock coat

text: Most Hasidim wear long coats called rekelekh during the week, which are often mistaken for frock coats but are really very long suit jackets. On Shabbat, Hasidim wear bekishes, which are usually silk or polyester as opposed to the woollen frock coat. The bekishe and the rekel both lack the waist seam construction of the frock coat. Additionally, bekishes can be distinguished from frock coats by the additional two buttons on front and a lack of a slit in the back.


title: Frock coat

text: Part of the slit hem in the back of the frock coat is rounded so as to not require tzitzit. The buttons are usually made to go right over left on most Jewish frock coats, particularly those worn by Hasidic Jews.


title: Frock coat

text: The Teddy Boys, a 1950s UK youth movement, named for their use of Edwardian-inspired clothing, briefly revived the frock coat, which they often referred to as a "drape".


title: Gaussian beam

text: In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or TEM) transverse Gaussian mode describes the intended output of most (but not all) lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse "phase" dependence is altered; this results in a "different" Gaussian beam. The electric and magnetic field amplitude profiles along any such circular Gaussian beam (for a given wavelength and polarization) are determined by a single parameter: the so-called waist . At any position relative to the waist (focus) along a beam having a specified , the field amplitudes and phases are thereby determined as detailed below.


title: Gaussian beam

text: The equations below assume a beam with a circular cross-section at all values of ; this can be seen by noting that a single transverse dimension, , appears. Beams with elliptical cross-sections, or with waists at different positions in for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of and of the location for the two transverse dimensions and .


title: Gaussian beam

text: Arbitrary solutions of the paraxial Helmholtz equation can be expressed as combinations of Hermite–Gaussian modes (whose amplitude profiles are separable in and using Cartesian coordinates) or similarly as combinations of Laguerre–Gaussian modes (whose amplitude profiles are separable in and using cylindrical coordinates). At any point along the beam these modes include the same Gaussian factor as the fundamental Gaussian mode multiplying the additional geometrical factors for the specified mode. However different modes propagate with a different Gouy phase which is why the net transverse profile due to a superposition of modes evolves in , whereas the propagation of any "single" Hermite–Gaussian (or Laguerre–Gaussian) mode retains the same form along a beam.


title: Gaussian beam

text: Although there are other possible modal decompositions, these families of solutions are the most useful for problems involving compact beams, that is, where the optical power is rather closely confined along an axis. Even when a laser is "not" operating in the fundamental Gaussian mode, its power will generally be found among the lowest-order modes using these decompositions, as the spatial extent of higher order modes will tend to exceed the bounds of a laser's resonator (cavity). "Gaussian beam" normally implies radiation confined to the fundamental (TEM) Gaussian mode.


title: Gaussian beam

text: The Gaussian beam is a transverse electromagnetic (TEM) mode. The mathematical expression for the electric field amplitude is a solution to the paraxial Helmholtz equation. Assuming polarization in the direction and propagation in the direction, the electric field in phasor (complex) notation is given by:


title: Gaussian beam

text: There is also an understood time dependence multiplying such phasor quantities; the actual field at a point in time and space is given by the real part of that complex quantity. This time factor involves an arbitrary sign convention, as discussed at .


title: Gaussian beam

text: Since this solution relies on the paraxial approximation, it is not accurate for very strongly diverging beams. The above form is valid in most practical cases, where .


title: Gaussian beam

text: where the constant is the wave impedance of the medium in which the beam is propagating. For free space, ≈ 377 Ω. is the intensity at the center of the beam at its waist.


title: Gaussian beam

text: At a position along the beam (measured from the focus), the spot size parameter is given by a hyperbolic relation:


title: Gaussian beam

text: is called the Rayleigh range as further discussed below, and formula_6 is the refractive index of the medium.


title: Gaussian beam

text: The radius of the beam , at any position along the beam, is related to the full width at half maximum (FWHM) of the intensity distribution at that position according to:


title: Gaussian beam

text: The curvature of the wavefronts is largest at the Rayleigh distance, , on either side of the waist, crossing zero at the waist itself. Beyond the Rayleigh distance, , it again decreases in magnitude, approaching zero as . The curvature is often expressed in terms of its reciprocal, , the "radius of curvature"; for a fundamental Gaussian beam the curvature at position is given by:


title: Gaussian beam

text: Being the reciprocal of the curvature, the radius of curvature reverses sign and is infinite at the beam waist where the curvature goes through zero.


title: Gaussian beam

text: The "Gouy phase" is a phase advance gradually acquired by a beam around the focal region. At position the Gouy phase of a fundamental Gaussian beam is given by


title: Gaussian beam

text: The Gouy phase results in an increase in the apparent wavelength near the waist (). Thus the phase velocity in that region formally exceeds the speed of light. That paradoxical behavior must be understood as a near-field phenomenon where the departure from the phase velocity of light (as would apply exactly to a plane wave) is very small except in the case of a beam with large numerical aperture, in which case the wavefronts' curvature (see previous section) changes substantially over the distance of a single wavelength. In all cases the wave equation is satisfied at every position.


title: Gaussian beam

text: The sign of the Gouy phase depends on the sign convention chosen for the electric field phasor. With dependence, the Gouy phase changes from to , while with dependence it changes from to along the axis.


title: Gaussian beam

text: For a fundamental Gaussian beam, the Gouy phase results in a net phase discrepancy with respect to the speed of light amounting to radians (thus a phase reversal) as one moves from the far field on one side of the waist to the far field on the other side. This phase variation is not observable in most experiments. It is, however, of theoretical importance and takes on a greater range for higher-order Gaussian modes.


title: Gaussian beam

text: Many laser beams have an elliptical cross-section. Also common are beams with waist positions which are different for the two transverse dimensions, called astigmatic beams. These beams can be dealt with using the above two evolution equations, but with distinct values of each parameter for and and distinct definitions of the point. The Gouy phase is a single value calculated correctly by summing the contribution from each dimension, with a Gouy phase within the range contributed by each dimension.


title: Gaussian beam

text: An elliptical beam will invert its ellipticity ratio as it propagates from the far field to the waist. The dimension which was the larger far from the waist, will be the smaller near the waist.


title: Gaussian beam

text: The geometric dependence of the fields of a Gaussian beam are governed by the light's wavelength ("in" the dielectric medium, if not free space) and the following beam parameters, all of which are connected as detailed in the following sections.


title: Gaussian beam

text: The shape of a Gaussian beam of a given wavelength is governed solely by one parameter, the "beam waist" . This is a measure of the beam size at the point of its focus ( in the above equations) where the beam width (as defined above) is the smallest (and likewise where the intensity on-axis () is the largest). From this parameter the other parameters describing the beam geometry are determined. This includes the Rayleigh range and asymptotic beam divergence , as detailed below.


title: Gaussian beam

text: Here is the wavelength of the light, is the index of refraction. At a distance from the waist equal to the Rayleigh range , the width of the beam is larger than it is at the focus where , the beam waist. That also implies that the on-axis () intensity there is one half of the peak intensity (at ). That point along the beam also happens to be where the wavefront curvature () is greatest.


title: Gaussian beam

text: The distance between the two points is called the "confocal parameter" or "depth of focus" of the beam.


title: Gaussian beam

text: Although the tails of a Gaussian function never actually reach zero, for the purposes of the following discussion the "edge" of a beam is considered to be the radius where . That is where the intensity has dropped to of its on-axis value. Now, for the parameter increases linearly with . This means that far from the waist, the beam "edge" (in the above sense) is cone-shaped. The angle between that cone (whose ) and the beam axis () defines the "divergence" of the beam:


title: Gaussian beam

text: where is the refractive index of the medium the beam propagates through, and is the free-space wavelength. The total angular spread of the diverging beam, or "apex angle" of the above-described cone, is then given by


title: Gaussian beam

text: Because the divergence is inversely proportional to the spot size, for a given wavelength , a Gaussian beam that is focused to a small spot diverges rapidly as it propagates away from the focus. Conversely, to "minimize" the divergence of a laser beam in the far field (and increase its peak intensity at large distances) it must have a large cross-section () at the waist (and thus a large diameter where it is launched, since is never less than ). This relationship between beam width and divergence is a fundamental characteristic of diffraction, and of the Fourier transform which describes Fraunhofer diffraction. A beam with any specified amplitude profile also obeys this inverse relationship, but the fundamental Gaussian mode is a special case where the product of beam size at focus and far-field divergence is smaller than for any other case.


title: Gaussian beam

text: Since the Gaussian beam model uses the paraxial approximation, it fails when wavefronts are tilted by more than about 30° from the axis of the beam. From the above expression for divergence, this means the Gaussian beam model is only accurate for beams with waists larger than about .


title: Gaussian beam

text: Laser beam quality is quantified by the beam parameter product (BPP). For a Gaussian beam, the BPP is the product of the beam's divergence and waist size . The BPP of a real beam is obtained by measuring the beam's minimum diameter and far-field divergence, and taking their product. The ratio of the BPP of the real beam to that of an ideal Gaussian beam at the same wavelength is known as ("M squared"). The for a Gaussian beam is one. All real laser beams have values greater than one, although very high quality beams can have values very close to one.


title: Gaussian beam

text: The numerical aperture of a Gaussian beam is defined to be , where is the index of refraction of the medium through which the beam propagates. This means that the Rayleigh range is related to the numerical aperture by


title: Gaussian beam

text: With a beam centered on an aperture, the power passing through a circle of radius in the transverse plane at position is


title: Gaussian beam

text: Similarly, about 90% of the beam's power will flow through a circle of radius , 95% through a circle of radius , and 99% through a circle of radius .


title: Gaussian beam

text: The peak intensity at an axial distance from the beam waist can be calculated as the limit of the enclosed power within a circle of radius , divided by the area of the circle as the circle shrinks:


title: Gaussian beam

text: The spot size and curvature of a Gaussian beam as a function of along the beam can also be encoded in the complex beam parameter given by:


title: Gaussian beam

text: Introducing this complication leads to a simplification of the Gaussian beam field equation as shown below. It can be seen that the reciprocal of contains the wavefront curvature and relative on-axis intensity in its real and imaginary parts, respectively:


title: Gaussian beam

text: The complex beam parameter simplifies the mathematical analysis of Gaussian beam propagation, and especially in the analysis of optical resonator cavities using ray transfer matrices.


title: Gaussian beam

text: Then using this form, the earlier equation for the electric (or magnetic) field is greatly simplified. If we call the relative field strength of an elliptical Gaussian beam (with the elliptical axes in the and directions) then it can be separated in and according to:


title: Gaussian beam

text: When a gaussian beam propagates through a thin lens, the outgoing beam is also a (different) gaussian beam, provided that the beam travels along the cylindrical symmetry axis of the lens. The focal length of the lens formula_26, the beam waist radius formula_27, and beam waist position formula_28 of the incoming beam can be used to determine the beam waist radius formula_29 and position formula_30 of the outgoing beam.


title: Gaussian beam

text: As derived by Saleh and Teich, the relationship between the ingoing and outgoing beams can be found by considering the phase that is added to each point formula_31 of the gaussian beam as it travels through the lens. An alternative approach due to Self is to consider the effect of a thin lens on the gaussian beam wavefronts.


title: Gaussian beam

text: This last expression makes clear that the ray optics thin lens equation is recovered in the limit that formula_40. It can also be noted that if formula_41 then the incoming beam is "well collimated" so that formula_42.


title: Gaussian beam

text: In some applications it is desirable to use a converging lens to focus a laser beam to a very small spot. Mathematically, this implies minimization of the magnification formula_32. If the beam size is constrained by the size of available optics, this is typically best achieved by sending the largest possible collimated beam through a small focal length lens, i.e. by maximizing formula_44 and minimizing formula_26. In this situation, it is justifiable to make the approximation formula_46, implying that formula_47 and yielding the result formula_48. This result is often presented in the form


title: Gaussian beam

text: which is found after assuming that the medium has index of refraction formula_51 and substituting formula_52. The factors of 2 are introduced because of a common preference to represent beam size by the beam waist diameters formula_53 and formula_54, rather than the waist radii formula_29 and formula_27.


title: Gaussian beam

text: As a special case of electromagnetic radiation, Gaussian beams (and the higher-order Gaussian modes detailed below) are solutions to the wave equation for an electromagnetic field in free space or in a homogeneous dielectric medium, obtained by combining Maxwell's equations for the curl of and the curl of , resulting in:


title: Gaussian beam

text: where is the speed of light "in the medium", and could either refer to the electric or magnetic field vector, as any specific solution for either determines the other. The Gaussian beam solution is valid only in the paraxial approximation, that is, where wave propagation is limited to directions within a small angle of an axis. Without loss of generality let us take that direction to be the direction in which case the solution can generally be written in terms of which has no time dependence and varies relatively smoothly in space, with the main variation spatially corresponding to the wavenumber in the direction:


title: Gaussian beam

text: Using this form along with the paraxial approximation, can then be essentially neglected. Since solutions of the electromagnetic wave equation only hold for polarizations which are orthogonal to the direction of propagation (), we have without loss of generality considered the polarization to be in the direction so that we now solve a scalar equation for .


title: Gaussian beam

text: Substituting this solution into the wave equation above yields the paraxial approximation to the scalar wave equation:


title: Gaussian beam

text: Writing the wave equations in the light-cone coordinates returns this equation without utilizing any approximation. Gaussian beams of any beam waist satisfy the paraxial approximation to the scalar wave equation; this is most easily verified by expressing the wave at in terms of the complex beam parameter as defined above. There are many other solutions. As solutions to a linear system, any combination of solutions (using addition or multiplication by a constant) is also a solution. The fundamental Gaussian happens to be the one that minimizes the product of minimum spot size and far-field divergence, as noted above. In seeking paraxial solutions, and in particular ones that would describe laser radiation that is "not" in the fundamental Gaussian mode, we will look for families of solutions with gradually increasing products of their divergences and minimum spot sizes. Two important orthogonal decompositions of this sort are the Hermite–Gaussian or Laguerre-Gaussian modes, corresponding to rectangular and circular symmetry respectively, as detailed in the next section. With both of these, the fundamental Gaussian beam we have been considering is the lowest order mode.


title: Gaussian beam

text: It is possible to decompose a coherent paraxial beam using the orthogonal set of so-called "Hermite-Gaussian modes", any of which are given by the product of a factor in and a factor in . Such a solution is possible due to the separability in and in the paraxial Helmholtz equation as written in Cartesian coordinates. Thus given a mode of order referring to the and directions, the electric field amplitude at may be given by:


title: Gaussian beam

text: where in this case the combined mode number . As before, the transverse amplitude variations are contained in the last two factors on the upper line of the equation, which again includes the basic Gaussian drop off in but now multiplied by a Laguerre polynomial. The effect of the rotational mode number , in addition to affecting the Laguerre polynomial, is mainly contained in the "phase" factor , in which the beam profile is advanced (or retarded) by complete phases in one rotation around the beam (in ). This is an example of an optical vortex of topological charge , and can be associated with the orbital angular momentum of light in that mode.


title: Gaussian beam

text: In elliptic coordinates, one can write the higher-order modes using Ince polynomials. The even and odd Ince-Gaussian modes are given by


title: Gaussian beam

text: There is another important class of paraxial wave modes in cylindrical coordinates in which the complex amplitude is proportional to a confluent hypergeometric function.


title: Gaussian beam

text: These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. Their intensity profiles are characterized by a single brilliant ring; like Laguerre–Gaussian modes, their intensities fall to zero at the center (on the optical axis) except for the fundamental (0,0) mode. A mode's complex amplitude can be written in terms of the normalized (dimensionless) radial coordinate and the normalized longitudinal coordinate as follows:


title: American Theater (World War II)

text: The American Theater was a theater of operations during World War II including all continental American territory, and extending into the ocean.


title: American Theater (World War II)

text: Owing to North and South America's geographical separation from the central theaters of conflict (in Europe, the Mediterranean and Middle East, and the Pacific) the threat of an invasion of the continental U.S. or other areas in the Americas by the Axis Powers was negligible and the theater saw relatively little conflict.


title: American Theater (World War II)

text: However, despite the relative unimportance of the American Theater, some battles took place within it, including the Battle of the River Plate, submarine attacks off the East Coast, the Aleutian Islands campaign, the Battle of the St. Lawrence, and the attacks on Newfoundland. Espionage efforts included Operation Bolívar.


title: American Theater (World War II)

text: The first naval battle during the war was fought on December 13, 1939, off the Atlantic coast of South America. The German "pocket battleship" (acting as a commerce raider) encountered one of the British naval units searching for her. Composed of three Royal Navy cruisers, , , and , the unit was patrolling off the River Plate estuary of Argentina and Uruguay. In a bloody engagement, "Admiral Graf Spee" successfully repulsed the British attacks. Captain Hans Langsdorff then brought his damaged ship to shelter in neutral Uruguay for repairs. However, British intelligence successfully deceived Langsdorff into believing that a much superior British force had now gathered to wait for him, and he scuttled his ship at Montevideo to save his crew's lives before committing suicide. German combat losses were 96 killed or wounded, against 72 British sailors killed and 28 wounded. Two Royal Navy cruisers had been severely damaged.


title: American Theater (World War II)

text: U-boat operations in the region (centered in the Atlantic Narrows between Brazil and West Africa) began in autumn 1940. After negotiations with Brazilian Foreign Minister Osvaldo Aranha (on behalf of dictator Getúlio Vargas), the U.S. introduced its Air Force along Brazil's coast in the second half of 1941. Germany and Italy subsequently extended their submarine attacks to include Brazilian ships wherever they were, and from April 1942 were found in Brazilian waters. On 22 May 1942, the first Brazilian attack (although unsuccessful) was carried out by Brazilian Air Force aircraft on the . After a series of attacks on merchant vessels off the Brazilian coast by , Brazil officially entered the war on 22 August 1942, offering an important addition to the Allied strategic position in the South Atlantic. Although the Brazilian Navy was small, it had modern minelayers suitable for coastal convoy escort and aircraft which needed only small modifications to become suitable for maritime patrol. During its three years of war, mainly in Caribbean and South Atlantic, alone and in conjunction with the U.S., Brazil escorted 3,167 ships in 614 convoys, totalling 16,500,000 tons, with losses of 0.1%. Brazil saw three of its warships sunk and 486 men killed in action (332 in the cruiser "Bahia"); 972 seamen and civilian passengers were also lost aboard the 32 Brazilian merchant vessels attacked by enemy submarines. American and Brazilian air and naval forces worked closely together until the end of the Battle. One example was the sinking of in July 1943, by a coordinated action of Brazilian and American aircraft. Only in Brazilian waters, eleven other Axis submarines were known sunk between January and September 1943—the Italian and ten German boats: , , , , , , , , , and .


title: American Theater (World War II)

text: By late 1943, the decreasing number of Allied shipping losses in South Atlantic coincided with the increasing elimination of Axis submarines operating there. From then, the battle in the region was lost for Germans, even with the most of remaining submarines in the region receiving official order of withdrawal only in August of the following year, and with ("Baron Jedburgh") the last Allied merchant ship sunk by a U-boat ("U-532") there, on 10 March 1945.


title: American Theater (World War II)

text: Even before the war, a large Nazi spy ring was found operating in the United States. The Duquesne Spy Ring is still the largest espionage case in United States history that ended in convictions. The 33 German agents who formed the Duquesne spy ring were placed in key jobs in the United States to get information that could be used in the event of war and to carry out acts of sabotage. One man opened a restaurant and used his position to get information from his customers; another worked at an airline so he could report Allied ships crossing the Atlantic Ocean; others in the ring worked as deliverymen so they could deliver secret messages alongside normal messages. The ring was led by Captain Fritz Joubert Duquesne, a South African Boer who spied for Germany in both World Wars and is best known as "The man who killed Kitchener" after he was awarded the Iron Cross for his key role in the sabotage and sinking of in 1916. William G. Sebold, a double agent for the United States, was a major factor in the FBI's successful resolution of this case. For nearly two years, Sebold ran a secret radio station in New York for the ring. Sebold provided the FBI with information on what Germany was sending to its spies in the United States while allowing the FBI to control the information that was being transmitted to Germany. On June 29, 1941, six months before the U.S. declared war, the FBI acted. All 33 spies were arrested, found or pled guilty, and sentenced to serve a total of over 300 years in prison.


title: American Theater (World War II)

text: After declaring war on the United States following the attack on Pearl Harbor, Adolf Hitler ordered the remaining German saboteurs to wreak havoc on America. The responsibility for carrying this out was given to German Intelligence (Abwehr). In the spring of 1942, nine agents were recruited (one eventually dropping out) and divided into two teams. The first, commanded by George John Dasch, included Ernst Peter Burger, Heinrich Heinck, and Richard Quirin; the second, under command of Edward Kerling, included Hermann Neubauer, Werner Thiel, and Herbert Haupt.


title: American Theater (World War II)

text: On June 12, 1942, the landed Dasch's team with explosives and plans at Amagansett, New York. Their mission was to destroy power plants at Niagara Falls and three Aluminum Company of America (ALCOA) factories in Illinois, Tennessee, and New York. However, Dasch instead turned himself in to the FBI, providing them with a complete list of his team members and an account of the planned missions, which led to their arrests.


title: American Theater (World War II)

text: On June 17, Kerling's team landed from "U-584" at Ponte Vedra Beach, south-east of Jacksonville, Florida. They were ordered to place mines in four areas: the Pennsylvania Railroad in Newark, New Jersey; canal sluices in both St. Louis, Missouri, and Cincinnati, Ohio; and New York City's water supply pipes. The team members made their way to Cincinnati and then split up, two going to Chicago, Illinois, and the others to New York. Dasch's confession led to the arrest of all of the men by July 10.


title: American Theater (World War II)

text: Because the German agents were captured in civilian clothes (though they had landed in uniforms), they were tried by a military tribunal in Washington D.C., with six of them sentenced to death for spying. President Franklin D. Roosevelt approved the sentences. The constitutionality of military tribunals was upheld by the U.S. Supreme Court in "Ex parte Quirin" on July 31, and the six men were executed by electrocution at the D.C. jail on August 8. Dasch and Burger were given thirty-year prison sentences because they had turned themselves in to the FBI and provided information about the others. Both were released in 1948 and deported to Germany. Dasch (aka George Davis), who had been a longtime American resident before the war, suffered a difficult life in Germany after his return from U.S. custody because he had betrayed his comrades to the U.S. authorities. As a condition of his deportation, he was not permitted to return to the United States, even though he spent many years writing letters to prominent American authorities (J. Edgar Hoover, President Eisenhower, etc.) seeking permission to return. He eventually moved to Switzerland and wrote a book, titled "Eight Spies Against America".


title: American Theater (World War II)

text: In 1944 another attempt at infiltration was made, codenamed Operation Elster ("Magpie"). Elster involved Erich Gimpel and German-American defector William Colepaugh. Their mission's objective was to gather intelligence on a variety of military subjects and transmit it back to Germany by a radio to be constructed by Gimpel. They sailed from Kiel on and landed at Hancock Point, Maine, on November 29, 1944. Both then made their way to New York, but the operation soon collapsed. Colepaugh lost his nerve and turned himself in to the FBI on December 26, confessing the whole plan and naming Gimpel. Gimpel was then arrested four days later in New York. Both men were sentenced to death, but eventually their sentences were commuted. Gimpel spent 10 years in prison, while Colepaugh was released in 1960 and operated a business in King of Prussia, Pennsylvania, before he retired to Florida.


title: American Theater (World War II)

text: One month earlier than the Dasch operation (on May 14, 1942), a solitary Abwehr agent, Marius A. Langbein, was landed by a U-boat () near St. Martins, New Brunswick, Canada. His mission, codenamed Operation Grete, after the name of the agent's wife, was to observe and report shipping movements at Montreal and Halifax, Nova Scotia (the main departure port for North Atlantic convoys). Langbein, who had lived in Canada before the war, changed his mind and moved to Ottawa, where he lived off his Abwehr funds until he surrendered to the Canadian authorities in December 1944. A jury found Langbein not guilty of spying, since he had never committed any hostile acts against Canada during the war.


title: American Theater (World War II)

text: In November 1942, sank two iron ore freighters and damaged another off Bell Island in Conception Bay, Newfoundland, en route to the Gaspé Peninsula where, despite an attack by a Royal Canadian Air Force aircraft, it successfully landed a spy, Werner von Janowski, four miles (6.5 km) from New Carlisle, Quebec, at around 5am on November 9, 1942.


title: American Theater (World War II)

text: Von Janowski showed up at the New Carlisle Hotel at 06:30 and checked in under the alias of William Brenton. The son of the hotel owner, Earle Annett Jr., grew suspicious of him, because of inconsistencies with the German spy's story. He used an out-of-circulation Canadian note when paying his bill to the owner's son and when he left to wait at the train station the suspicious son of the hotelier followed him.


title: American Theater (World War II)

text: There Annett grew more suspicious and he alerted a Quebec Provincial Police constable, Alfonse Duchesneau, who quickly boarded the train as it pulled away from the station and began searching for the stranger. Duchesneau located von Janowski, who said he was a radio salesman from Toronto. He stuck with this story until the policeman asked to search his bags; the stranger then confessed: "That will not be necessary. I am a German officer who serves his country as you do yourself." Inspection of von Janowski's personal effects upon his arrest revealed that he was carrying a powerful radio transmitter, among other things.


title: American Theater (World War II)

text: Von Janowski spent the next year as a double agent, codenamed "WATCHDOG" by the Allies and "Bobbi" by the Abwehr, sending false messages to Germany under the joint control of the RCMP and MI5, with spymaster Cyril Mills having been seconded to Canada to assist in the double cross initiative. The effectiveness and honesty of his "turn" is a matter of some dispute. For example, John Cecil Masterman wrote in "The Double Cross System": "In November, WATCHDOG was landed from a U-boat in Canada together with a wireless set and an extensive questionnaire. This move on the part of the Germans threatened an extension of our activities to other parts of the world, but in fact the case did not develop very satisfactorily... WATCHDOG was closed down in the summer [of 1943]."


title: American Theater (World War II)

text: Accurate weather reporting was important to the sea war and on September 18, 1943, sailed from Kiel, via Bergen, Norway, with a meteorological team led by Professor Kurt Sommermeyer. They landed at Martin Bay, a remote location near the northern tip of Labrador on October 22, 1943, and successfully set up an automatic weather station ("Weather Station Kurt" or ""Wetter-Funkgerät Land-26""), despite the constant risk of Allied air patrols. The station was powered by batteries that were expected to last about three months. At the beginning of July 1944, left Bergen to replace the equipment, but was sunk en route. The weather station remained at the site until it was recovered in the 1980s and placed in the Canadian War Museum.


title: American Theater (World War II)

text: The Atlantic Ocean was a major strategic battle zone (the "Battle of the Atlantic") and when Germany declared war on the U.S., the East Coast of the United States offered easy pickings for German U-boats (referred to as the "Second Happy Time"). After a highly successful foray by five Type IX long-range U-boats, the offensive was maximized by the use of short-range Type VII U-boats, with increased fuel stores, replenished from supply U-boats called "Milchkühe" (milk cows). From February to May 1942, 348 ships were sunk, for the loss of two U-boats during April and May. U.S. naval commanders were reluctant to introduce the convoy system that had protected trans-Atlantic shipping and, without coastal blackouts, shipping was silhouetted against the bright lights of American towns and cities such as Atlantic City until a dim-out was ordered in May.


title: American Theater (World War II)

text: The cumulative effect of this campaign was severe; a quarter of all wartime sinkings – 3.1 million tons. There were several reasons for this. The American naval commander, Admiral Ernest King, as an apparent anglophobe, was averse to taking British recommendations to introduce convoys, U.S. Coast Guard and Navy patrols were predictable and could be avoided by U-boats, inter-service co-operation was poor, and the U.S. Navy did not possess enough suitable escort vessels (British and Canadian warships were transferred to the U.S. east coast).


title: American Theater (World War II)

text: Several ships were torpedoed within sight of East Coast cities such as New York and Boston. The only documented World War II sinking of a U-boat close to New England shores occurred on May 5, 1945, when the torpedoed and sank the collier off Newport, Rhode Island. When "Black Point" was hit, the U.S. Navy immediately chased down the sub and began dropping depth charges. In recent years, "U-853" has become a popular dive site. Its intact hull, with open hatches, is located in of water off Block Island, Rhode Island. A wreck discovered in 1991 off the New Jersey coast was concluded in 1997 to be that of . Previously, "U-869" had been thought to have been sunk off Rabat, Morocco.


title: American Theater (World War II)

text: Once convoys and air cover were introduced in the Atlantic, sinking numbers were reduced and the U-boats shifted to attack shipping in the Gulf of Mexico. During 1942 and 1943, more than 20 U-boats operated in the Gulf of Mexico. They attacked tankers transporting oil from ports in Texas and Louisiana, successfully sinking 56 vessels. By the end of 1943, the U-boat attacks diminished as the merchant ships began to travel in armed convoys.


title: American Theater (World War II)

text: In one instance, the tanker "Virginia" was torpedoed in the mouth of the Mississippi River by the on May 12, 1942, killing 26 crewmen. There were 14 survivors. Again, when defensive measures were introduced, ship sinkings decreased.


title: American Theater (World War II)

text: From the start of the war in 1939 until VE Day, several of Canada's Atlantic coast ports became important to the resupply effort for the United Kingdom and later for the Allied land offensive on the Western Front. Halifax and Sydney, Nova Scotia, became the primary convoy assembly ports, with Halifax being assigned the fast or priority convoys (largely troops and essential material) with the more modern merchant ships, while Sydney was given slow convoys which conveyed bulkier material on older and more vulnerable merchant ships. Both ports were heavily fortified with shore radar emplacements, searchlight batteries, and extensive coastal artillery stations all manned by RCN and Canadian Army regular and reserve personnel. Military intelligence agents enforced strict blackouts throughout the areas and anti-torpedo nets were in place at the harbor entrances, making a direct attack on those facilities unfeasible because it was impossible for Germany to provide air support. Even though no landings of German personnel took place near these ports, there were frequent attacks by U-boats on convoys departing for Europe once these had reached the mouth of the St. Lawrence. Less extensively used, but no less important, was the port of Saint John which also saw matériel funneled through the port, largely after the United States entered the war in December 1941. The port's location within the protected waters of the Bay of Fundy made it a difficult target for attack. The Canadian Pacific Railway mainline from central Canada (which crossed the state of Maine) could be used to transport in aid of the war effort.


title: American Theater (World War II)

text: Although not crippling to the Canadian war effort, given the country's rail network to the east coast ports, but possibly more destructive to the morale of the Canadian public, was the Battle of the St. Lawrence, when U-boats began to venture upriver and attack domestic coastal shipping along Canada's east coast in the St. Lawrence River and Gulf of St. Lawrence from early 1942 through to the end of the shipping season in late 1944. From a German perspective this area contained most of the military assets in North America that could realistically be targeted for attack, and therefore the St. Lawrence was the only zone that saw consistent warfare—albeit on a limited scale—in North America during World War II. Residents along the Gaspé coast and the St. Lawrence River and Gulf of St. Lawrence were startled at the sight of maritime warfare off their shores, with ships on fire and explosions rattling their communities, while bodies and debris floated ashore. The number of military losses is not known, although loose estimates can be made based on the number of surface units and submarines sunk.


title: American Theater (World War II)

text: Five significant attacks on Newfoundland took place in 1942. On 3 March 1942, launched three torpedoes at St. John's; one hit Fort Amherst and two more hit the cliffs of Signal Hill below Cabot Tower. In autumn German U-boats attacked four iron ore carriers serving the DOSCO iron mine at Wabana on Bell Island in Newfoundland's Conception Bay. The ships SS "Saganaga" and SS "Lord Strathcona" were sunk by on 5 September 1942, while SS "Rose Castle" and "P.L.M 27" were sunk by on 2 November with the loss of 69 lives. After the sinkings the submarine fired a torpedo that missed its target, the 3,000-ton collier "Anna T", and struck the DOSCO loading pier and exploded. On 14 October 1942, the Newfoundland Railway ferry was torpedoed by and sunk in the Cabot Strait south of Port aux Basques. "Caribou" was carrying 45 crew and 206 civilian and military passengers. One hundred thirty-seven lost their lives, many of them Newfoundlanders.


title: American Theater (World War II)

text: Half a dozen U-boat wrecks lie in waters around Newfoundland and Labrador, destroyed by Canadian patrols.


title: American Theater (World War II)

text: A German submarine shelled the American Standard Oil refinery at the San Nicolas harbour and the "Arend"/"Eagle" Maatschappij (from the Dutch/British Shell Co.) near the Oranjestad harbour situated on the Island of Aruba (a Dutch colony) and some ships that were near the entrance to Lake Maracaibo on February 16, 1942. Three tankers, including the Venezuelan "Monagas", were sunk. A Venezuelan gunboat, , assisted in rescuing the crews.


title: American Theater (World War II)

text: Before 1941, the Central American nations had various diplomatic ties with Nazi Germany and the Empire of Japan. After the attack on Pearl Harbor, they declared war on the Axis nations. The Central American nations joined the Allied side, broke diplomatic relations with the Axis nations, and initiated persecutions of German and Italian immigrants.


title: American Theater (World War II)

text: During the course of the war, several merchant ships were sunk in the Caribbean by German submarines, for example the Tela, a Honduran cargo ship sunk by a U-504 submarine in 1942. This led the country to carry out constant air patrols over the coasts under fear of the approach of more German submarines or the general fear of an attack by Germany. Other Central American cargo ships sunk by U-boats are the "Olancho," the "Comayagua", and the "Bluefields", of Honduran and Nicaraguan origins. Central American volunteers in the United States Army participated in both the European and Asia Pacific theater.


title: American Theater (World War II)

text: Before Operation MI could be carried out, the Japanese decided to take the Aleutian Islands. On June 3–4, 1942, Japanese planes from two light carriers and struck the U.S. against the city of Unalaska, Alaska, at Dutch Harbor in the Aleutian Islands. Originally, the Japanese planned to attack Dutch Harbor simultaneously with its attack on Midway, but the Midway attack was delayed by one day. The attack only did moderate damage on Dutch Harbor, but 43 Americans were killed and 50 others wounded in the attack.


title: American Theater (World War II)

text: On June 6, two days after the bombing of Dutch Harbor, 500 Japanese marines landed on Kiska, one of the Aleutian Islands of Alaska. Upon landing, they killed two and captured eight United States Navy officers, then seized control of American soil for the first time. The next day, a total of 1,140 Japanese infantrymen landed on Attu via Holtz Bay, eventually reaching Massacre Bay and Chichagof Harbor. Attu's population at the time consisted of 45 Alaska Native Aleuts, and two white Americans – Charles Foster Jones, a 60-year-old ham radio operator and weather observer, and his 62-year-old wife Etta, a teacher and nurse. The Japanese killed Charles Jones after interrogating him, while Etta Jones and the Aleut population were sent to Japan, where 16 of the Aleuts died and Etta survived the war.


title: American Theater (World War II)

text: A year after Japan's occupation of Kiska and Attu, U.S. troops invaded Attu on May 11, 1943 and successfully retook the island after three weeks of fighting, killing 2,351 Japanese combatants and taking only 28 as prisoners of war at the cost of 549 lives. Three months later on August 15, U.S. and Canadian forces landed on Kiska expecting the same resistance like Attu; they later found the entire island empty, as most of the Japanese forces secretly evacuated weeks before the landing. In spite of enemy absence on the island, over 313 Allied casualties were sustained nonetheless through car accidents, booby traps, landmines, and friendly fire, in which 28 Americans and four Canadians were killed in the exchange of fire between the two forces.


title: American Theater (World War II)

text: Several ships were torpedoed within sight of West Coast Californian cities such as Los Angeles, Santa Barbara, San Diego, and Santa Monica. During 1941 and 1942, more than 10 Japanese submarines operated in the West Coast and Baja California. They attacked American, Canadian, and Mexican ships, successfully sinking over 10 vessels including the Soviet Navy submarine "L-16" on October 11, 1942.


title: American Theater (World War II)

text: The United States continent was first shelled by the Axis on February 23, 1942, when the attacked the Ellwood Oil Field west of Goleta, near Santa Barbara, California. Although only a pumphouse and catwalk at one oil well were damaged, "I-17" Captain Nishino Kozo radioed Tokyo that he had left Santa Barbara in flames. No casualties were reported and the total cost of the damage was officially estimated at approximately $500–1,000. News of the shelling triggered an invasion scare along the West Coast.


title: American Theater (World War II)

text: More than five Japanese submarines operated in Western Canada during 1941 and 1942. On June 20, 1942, the , under the command of Yokota Minoru, fired 25–30 rounds of 5.5-inch shells at the Estevan Point lighthouse on Vancouver Island in British Columbia, but failed to hit its target. Though no casualties were reported, the subsequent decision to turn off the lights of outer stations caused difficulties for coastal shipping activity.


title: American Theater (World War II)

text: In what became the second attack on a continental American military installation during World War II, the , under the command of Tagami Akiji, surfaced near the mouth of the Columbia River in Oregon on the night of June 21 and June 22, 1942, and fired shells toward Fort Stevens. The only damage officially recorded was to a baseball field's backstop. Probably the most significant damage was a shell that damaged some large phone cables. The Fort Stevens gunners were refused permission to return fire for fear of revealing the guns' location and/or range limitations to the sub. American aircraft on training flights spotted the submarine, which was subsequently attacked by a U.S. bomber, but escaped.


title: American Theater (World War II)

text: The Lookout Air Raids occurred on September 9, 1942. The second location to be subject to aerial bombing in the continental United States by a foreign power occurred when an attempt to start a forest fire was made by a Japanese Yokosuka E14Y1 "Glen" seaplane dropping two incendiary bombs over Mount Emily, near Brookings, Oregon.


title: American Theater (World War II)

text: The seaplane, piloted by Nobuo Fujita, had been launched from the Japanese submarine aircraft carrier "I-25". No significant damage was officially reported following the attack, nor after a repeat attempt on September 29.


title: American Theater (World War II)

text: Between November 1944 and April 1945, the Japanese Navy launched over 9,000 fire balloons toward North America. Carried by the recently discovered Pacific jet stream, they were to sail over the Pacific Ocean and land in North America, where the Japanese hoped they would start forest fires and cause other damage. About three hundred were reported as reaching North America, but little damage was caused.


title: American Theater (World War II)

text: Near Bly, Oregon, six people (five children and a woman) became the only deaths due to an enemy balloon bomb attack in the United States when a balloon bomb exploded. The site is marked by a stone monument at the Mitchell Recreation Area in the Fremont-Winema National Forest.


title: American Theater (World War II)

text: A fire balloon is also considered to be a possible cause of the third fire in the Tillamook Burn in Oregon. One member of the 555th Parachute Infantry Battalion died while responding to a fire in the Umpqua National Forest near Roseburg, Oregon, on August 6, 1945; other casualties of the 555th were two fractures and 20 other injuries.


title: American Theater (World War II)

text: In 1940, the German Air Ministry secretly requested designs from the major German aircraft companies for its "Amerikabomber" program, in which a long-range strategic bomber would strike the continental United States from the Azores (more than away). Planning was complete in 1942 with the submittal of the program to Goering's RLM offices in March 1942, resulting in cogent piston-engined designs from Focke-Wulf, Heinkel, Junkers and Messerschmitt (who had built the ultra-long-range Messerschmitt Me 261 before WW II), but by mid-1944 the project had been abandoned as too expensive, with a serious increase in the need for defensive fighters, needing to come from Nazi Germany's by-then rapidly diminishing aviation production capacity.


title: American Theater (World War II)

text: Hitler had ordered that biological warfare should be studied only for the purpose of defending against it. The head of the Science Division of the Wehrmacht, Erich Schumann, lobbied for Hitler to be persuaded otherwise: "America must be attacked simultaneously with various human and animal epidemic pathogens, as well as plant pests." The plans were never adopted because they were opposed by Hitler.


title: American Theater (World War II)

text: An Italian naval commander Junio Valerio Borghese devised a plan to attack New York harbor with midget submarines; however, as the tides of war changed against Italy, the plan was postponed and later scrapped.


title: American Theater (World War II)

text: Just after the attack on Pearl Harbor, a force of seven Japanese submarines patrolled the United States West Coast. The Wolfpack made plans to bombard targets in California on Christmas Eve or Christmas Day of 1941. However, the attack was postponed to December 27 in order to avoid attacking during the Christian festival and offending German and Italian allies. Eventually the plan was canceled altogether for fears of American reprisal. In 1946, an unexploded Japanese torpedo was found near the Golden Gate Bridge, and it has been interpreted as evidence of an attack, potentially targeting the bridge itself, in late December of 1941.


title: American Theater (World War II)

text: The Japanese constructed a plan early in the Pacific War to attack the Panama Canal, a vital water passage in Panama, used during World War II primarily for the Allied supply effort. The Japanese attack was never launched because Japan suffered crippling naval losses at the beginning of conflict with the United States and United Kingdom (See: Aichi M6A).


title: American Theater (World War II)

text: The Imperial Japanese Army launched Project Z (also called the Z Bombers Project) in 1942, similar to the Nazi German Amerika Bomber project, to design an intercontinental bomber capable of reaching North America. The Project Z plane was to have six engines of 5,000 horsepower each; the Nakajima Aircraft Company quickly began developing engines for the plane, and proposed doubling HA-44 engines (the most powerful engine available in Japan) into a 36-cylinder engine. Designs were presented to the Imperial Japanese Army, including the Nakajima G10N, Kawasaki Ki-91, and Nakajima G5N. None developed beyond prototypes or wind tunnel models, save for the G5N. In 1945, the Z project and other heavy bomber projects were cancelled.


title: American Theater (World War II)

text: During the final months of World War II, Japan had planned to use bubonic plague as a biological weapon against U.S. civilians in San Diego, California, during Operation Cherry Blossoms at Night. The plan was set to launch at night on September 22, 1945. However, it was shelved because Japan surrendered on August 15, 1945.


title: American Theater (World War II)

text: These false alarms have generally been attributed to military and civilian inexperience with war and poor radars of the era. Critics have theorized they were a deliberate attempt by the Army to frighten the public in order to stimulate interest in war preparations.


title: American Theater (World War II)

text: On December 8, 1941, "rumors of an enemy carrier off the coast led to the closing of schools in Oakland, California," a blackout enforced by local wardens and radio silence followed that evening. The reports reaching Washington of an attack on San Francisco were regarded as credible. The affair was described as a test but Lt. Gen. John L. DeWitt of the Western Defense Command said "Last night there were planes over this community. They were enemy planes! I mean Japanese planes! And they were tracked out to sea. You think it was a hoax? It is damned nonsense for sensible people to assume that the Army and Navy would practice such a hoax on San Francisco." Rumors continued on the West Coast in the following days. An alert of a similar nature occurred in the Northeast on December 9. "At noon advices were received that hostile planes were only two hours' distance away." Although there was no general hysteria, fighter aircraft from Mitchel Field on Long Island took the air to intercept the "raiders". Wall Street had its worst sell off since the Fall of France, school children in New York City were sent home and several radio stations left the air. In Boston police shifted heavy stores of guns and ammunition from storage vaults to stations throughout the city, and industrial establishments were advised to prepare for a raid.


title: American Theater (World War II)

text: The Battle of Los Angeles, also known as "The Great Los Angeles Air Raid", is the name given by contemporary sources to the imaginary enemy attack and subsequent anti-aircraft artillery barrage which took place in 1942 from February 24 and early on February 25 over Los Angeles, California. Initially, the target of the aerial barrage was thought to be an attacking force from Japan, but Secretary of the Navy Frank Knox speaking at a press conference shortly afterward called the incident a "false alarm." Newspapers of the time published a number of sensational reports and speculations of a cover-up to conceal an actual invasion by enemy airplanes. When documenting the incident in 1983, the U.S. Office of Air Force History attributed the event to a case of "war nerves" likely triggered by a lost weather balloon and exacerbated by stray flares and shell bursts from adjoining batteries.


title: Saikhom Mirabai Chanu

text: Saikhom Mirabai Chanu (Meitei pronunciation: /sái.kʰom mi.ra.bái cə.nu/; born 8 August, 1994) is an Indian weightlifter. 27-year-old Mirabai Chanu lifted a total of 201 kg to win the Gold Medal which was also India's third medal after at the ongoing CWG 2022. She won the silver medal at the 2020 Tokyo Olympics in Women's 49 kg category. Mirabai Chanu has won the World Championships and multiple medals at the Commonwealth Games. She was awarded the Padma Shri by the Government of India for her contributions to the sport. She was awarded the sporting honour Major Dhyan Chand Khel Ratna by the Government of India in 2018.


title: Saikhom Mirabai Chanu

text: Chanu won the silver medal in the women's 48 kg weight class at the 2014 Commonwealth Games, Glasgow; she went on to break the games record en route to the gold medal at the 2018 edition of the event held in Gold Coast. Prior to the 2020 Summer Olympics, her biggest achievement came in 2017, when she won the gold medal at World Weightlifting Championships held in Anaheim, California. She is the current world record holder in Clean & Jerk in the 49 kg category.


title: Saikhom Mirabai Chanu

text: Saikhom Mirabai Chanu was born on 8 August 1994 in Nongpok Kakching about 30 km away from Imphal city, Manipur to a Meitei family, a warrior clan of that region. Chanu identified herself as a follower of Sanamahism but also stated she worships Hindu deities as well. Her family identified her strength when she was just 12. She could easily carry a huge bundle of firewood home when her elder brother found it hard to even pick it up.


title: Saikhom Mirabai Chanu

text: Mirabai trained at the Sports Academy in Manipur. She hitched rides with truck drivers carrying sand. After winning the Olympic medal, she invited the truck drivers to offer her gratitude and touched their feet as a sign of respect.


title: Saikhom Mirabai Chanu

text: Chanu's first major breakthrough came at the Glasgow edition of the Commonwealth Games; she won the silver medal in the 48 kg weight category.


title: Saikhom Mirabai Chanu

text: Chanu qualified for the 2016 Rio Olympics in the women's 48 kg category. However, she failed to complete the event, owing to no successful lifts in any of her three attempts in the clean & jerk section.


title: Saikhom Mirabai Chanu

text: In 2017, she won the gold medal in the Women's 48 kg category by lifting a competition record 194 kg in total (85 kg snatch and 109 kg clean & jerk) in the 2017 World Weightlifting Championships held at Anaheim, California, United States.


title: Saikhom Mirabai Chanu

text: Chanu lifted a total of 196 kg, 86 kg in Snatch and 110 kg in Clean and Jerk to win the first gold medal for India in the 2018 Commonwealth Games. En route to the medal, she broke the games record for her weight category; the effort also marked her personal best performance. She missed out on a bronze medal in 49 kg category at 2019 Asian Weightlifting Championships with a total lift of 199 kg, her personal best, as her Snatch weight was lower than the third place athlete, both of whom had identical totals.


title: Saikhom Mirabai Chanu

text: At the 2019 World Weightlifting Championships, Mirabai lifted a total of 201 kg (87 kg Snatch and 114 kg Clean & Jerk) to finish fourth. This personal best total also created a new national record in the 49 kg category. She broke her personal record again four months later when she lifted 203 kg (88 kg in Snatch and 115 kg in Clean & Jerk,) in the 49 kg category to win the gold medal at the 2020 Senior National Weightlifting Championships.


title: Saikhom Mirabai Chanu

text: In April 2021, she won the bronze medal at the 2020 Asian Weightlifting Championships in Tashkent where she lifted 86 kg in snatch and then created the world record by lifting 119 kg in the clean and jerk, for a total of 205 kg. In June 2021, Chanu became the only Indian woman weightlifter to qualify for the 2020 Summer Olympics by securing second position on the Absolute Rankings for 49 kg category.


title: Saikhom Mirabai Chanu

text: Chanu won the silver medal in 49 kg division at the 2020 Summer Olympics in Tokyo with a total lift of 202 kg, becoming the first Indian weightlifter to win silver at the Olympics, the second Indian weightlifter after Karnam Malleswari to win an Olympic medal, and the second Indian woman after P. V. Sindhu to win an Olympic silver. A new Olympic record was registered by Chanu with a successful lift of 115 kg in clean and jerk. Her win ensured India its first medal at the Tokyo Olympics.


title: Saikhom Mirabai Chanu

text: Aftermath of Tokyo Olympic Manipur Chief Minister N. Biren Singh announced an award of 1 crore for her. Indian Railway Minister Ashwini Vaishnaw announced an award of ₹2 crore, a promotion and more for her.


title: Saikhom Mirabai Chanu

text: Chanu won gold medal in 49 kg category at Commonwealth Games 2022 held at Birmingham, England. She lifted a total of 201 kg in snatch and clean and jerk.


title: Saikhom Mirabai Chanu

text: "Mei Iklaba Thamoi" is a Meitei language Shumang Kumhei play based on the life of Mirabai Chanu, directed by Shougrakpam Hemanta, released on 19 September 2021.


title: Saikhom Mirabai Chanu

text: A biographical Manipuri feature film on Mirabai Chanu was also announced by Seuti Films. The movie will be directed by OC Meira and screenplay by Manaobi MM.


title: Propensity score matching

text: In the statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment, policy, or other intervention by accounting for the covariates that predict receiving the treatment. PSM attempts to reduce the bias due to confounding variables that could be found in an estimate of the treatment effect obtained from simply comparing outcomes among units that received the treatment versus those that did not. Paul R. Rosenbaum and Donald Rubin introduced the technique in 1983.


title: Propensity score matching

text: The possibility of bias arises because a difference in the treatment outcome (such as the average treatment effect) between treated and untreated groups may be caused by a factor that predicts treatment rather than the treatment itself. In randomized experiments, the randomization enables unbiased estimation of treatment effects; for each covariate, randomization implies that treatment-groups will be balanced on average, by the law of large numbers. Unfortunately, for observational studies, the assignment of treatments to research subjects is typically not random. Matching attempts to reduce the treatment assignment bias, and mimic randomization, by creating a sample of units that received the treatment that is comparable on all observed covariates to a sample of units that did not receive the treatment.


title: Propensity score matching

text: For example, one may be interested to know the consequences of smoking. An observational study is required since it is unethical to randomly assign people to the treatment 'smoking.' The treatment effect estimated by simply comparing those who smoked to those who did not smoke would be biased by any factors that predict smoking (e.g.: gender and age). PSM attempts to control for these biases by making the groups receiving treatment and not-treatment comparable with respect to the control variables.


title: Propensity score matching

text: PSM is for cases of causal inference and simple selection bias in non-experimental settings in which: (i) few units in the non-treatment comparison group are comparable to the treatment units; and (ii) selecting a subset of comparison units similar to the treatment unit is difficult because units must be compared across a high-dimensional set of pretreatment characteristics.


title: Propensity score matching

text: In normal matching, single characteristics that distinguish treatment and control groups are matched in an attempt to make the groups more alike. But if the two groups do not have substantial overlap, then substantial error may be introduced. For example, if only the worst cases from the untreated "comparison" group are compared to only the best cases from the treatment group, the result may be regression toward the mean, which may make the comparison group look better or worse than reality.


title: Propensity score matching

text: PSM employs a predicted probability of group membership—e.g., treatment versus control group—based on observed predictors, usually obtained from logistic regression to create a counterfactual group. Propensity scores may be used for matching or as covariates, alone or with other matching variables or covariates.


title: Propensity score matching

text: 2. Match each participant to one or more nonparticipants on propensity score, using one of these methods:


title: Propensity score matching

text: 3. Check that covariates are balanced across treatment and comparison groups within strata of the propensity score.


title: Propensity score matching

text: The basic case is of two treatments (numbered 1 and 0), with "N" independent and identically distributed random variables subjects. Each subject "i" would respond to the treatment with formula_1 and to the control with formula_2. The quantity to be estimated is the average treatment effect: formula_3. The variable formula_4 indicates if subject "i" got treatment (formula_5) or control (formula_6). Let formula_7 be a vector of observed pretreatment measurements (or covariates) for the "i"th subject. The observations of formula_7 are made prior to treatment assignment, but the features in formula_7 may not include all (or any) of the ones used to decide on the treatment assignment. The numbering of the units (i.e.: "i" = 1, ..., "N") are assumed to not contain any information beyond what is contained in formula_7. The following sections will omit the "i" index while still discussing the stochastic behavior of some subject.


title: Propensity score matching

text: Let some subject have a vector of covariates "X" (i.e.: conditionally unconfounded), and some potential outcomes "r" and "r" under control and treatment, respectively. Treatment assignment is said to be strongly ignorable if the potential outcomes are independent of treatment ("Z") conditional on background variables "X". This can be written compactly as


title: Propensity score matching

text: A balancing score "b"("X") is a function of the observed covariates "X" such that the conditional distribution of "X" given "b"("X") is the same for treated ("Z" = 1) and control ("Z" = 0) units:


title: Propensity score matching

text: A propensity score is the probability of a unit (e.g., person, classroom, school) being assigned to a particular treatment given a set of observed covariates. Propensity scores are used to reduce selection bias by equating groups based on these covariates.


title: Propensity score matching

text: Suppose that we have a binary treatment indicator "Z", a response variable "r", and background observed covariates "X". The propensity score is defined as the conditional probability of treatment given background variables:


title: Propensity score matching

text: In the context of causal inference and survey methodology, propensity scores are estimated (via methods such as logistic regression, random forests, or others), using some set of covariates. These propensity scores are then used as estimators for weights to be used with Inverse probability weighting methods.


title: Propensity score matching

text: If we think of the value of "Z" as a parameter of the population that impacts the distribution of "X" then the balancing score serves as a sufficient statistic for "Z". Furthermore, the above theorems indicate that the propensity score is a minimal sufficient statistic if thinking of "Z" as a parameter of "X". Lastly, if treatment assignment "Z" is strongly ignorable given "X" then the propensity score is a minimal sufficient statistic for the joint distribution of formula_22.


title: Propensity score matching

text: Judea Pearl has shown that there exists a simple graphical test, called the back-door criterion, which detects the presence of confounding variables. To estimate the effect of treatment, the background variables X must block all back-door paths in the graph. This blocking can be done either by adding the confounding variable as a control in regression, or by matching on the confounding variable.


title: Propensity score matching

text: PSM has been shown to increase model "imbalance, inefficiency, model dependence, and bias," which is not the case with most other matching methods. The insights behind the use of matching still hold but should be applied with other matching methods; propensity scores also have other productive uses in weighting and doubly robust estimation.


title: Propensity score matching

text: Like other matching procedures, PSM estimates an average treatment effect from observational data. The key advantages of PSM were, at the time of its introduction, that by using a linear combination of covariates for a single score, it balances treatment and control groups on a large number of covariates without losing a large number of observations. If units in the treatment and control were balanced on a large number of covariates one at a time, large numbers of observations would be needed to overcome the "dimensionality problem" whereby the introduction of a new balancing covariate increases the minimum necessary number of observations in the sample geometrically.


title: Propensity score matching

text: One disadvantage of PSM is that it only accounts for observed (and observable) covariates and not latent characteristics. Factors that affect assignment to treatment and outcome but that cannot be observed cannot be accounted for in the matching procedure. As the procedure only controls for observed variables, any hidden bias due to latent variables may remain after matching. Another issue is that PSM requires large samples, with substantial overlap between treatment and control groups.


title: Propensity score matching

text: General concerns with matching have also been raised by Judea Pearl, who has argued that hidden bias may actually increase because matching on observed variables may unleash bias due to dormant unobserved confounders. Similarly, Pearl has argued that bias reduction can only be assured (asymptotically) by modelling the qualitative causal relationships between treatment, outcome, observed and unobserved covariates. Confounding occurs when the experimenter is unable to control for alternative, non-causal explanations for an observed relationship between independent and dependent variables. Such control should satisfy the "backdoor criterion" of Pearl.


title: Nivolumab

text: Nivolumab, sold under the brand name Opdivo, is a medication used to treat a number of types of cancer. This includes melanoma, lung cancer, malignant pleural mesothelioma, renal cell carcinoma, Hodgkin lymphoma, head and neck cancer, urothelial carcinoma, colon cancer, esophageal squamous cell carcinoma, liver cancer, gastric cancer, and esophageal or gastroesophageal junction (GEJ) cancer. It is used by slow injection into a vein.


title: Nivolumab

text: The most common side effects include fatigue, rash, musculoskeletal pain, pruritus, diarrhea, nausea, asthenia, cough, dyspnea, constipation, decreased appetite, back pain, arthralgia, upper respiratory tract infection, pyrexia, headache, abdominal pain, and vomiting. Use during pregnancy may harm the baby and use when breastfeeding is not recommended. Nivolumab is a human IgG4 monoclonal antibody that blocks PD-1. It is a type of immunotherapy and works as a checkpoint inhibitor, blocking a signal that prevents activation of T cells from attacking the cancer. The most common side effects when used in combination with chemotherapy include peripheral neuropathy (damage to the nerves outside of the brain and spinal cord), nausea, fatigue, diarrhea, vomiting, decreased appetite, abdominal pain, constipation and musculoskeletal pain.


title: Nivolumab

text: Nivolumab was approved for medical use in the United States in 2014. It is on the World Health Organization's List of Essential Medicines. It is made using Chinese hamster ovary cells.


title: Nivolumab

text: Nivolumab is the second FDA-approved systemic therapy for mesothelioma and is the first FDA-approved immunotherapy for the first-line treatment of gastric cancer.


title: Nivolumab

text: Nivolumab is used as a first-line treatment for inoperable or metastatic melanoma in combination with ipilimumab if the cancer does not have a mutation in BRAF, and as a second-line treatment for inoperable or metastatic melanoma following treatment of ipilimumab and, if the cancer has a BRAF mutation, a BRAF inhibitor. It is also used to treat metastatic squamous non-small cell lung cancer with progression with or after platinum-based drugs and for treatment of small cell lung cancer It also used as a second-line treatment for renal cell carcinoma after anti-angiogenic treatment has failed.


title: Nivolumab

text: Nivolumab is used for primary or metastatic urothelial carcinoma, the most common form of bladder cancer. It can be prescribed for locally advanced or metastatic form of the condition that experience disease progression during or following platinum-containing chemotherapy or have progression within 12 months of neoadjuvant or adjuvant treatment with platinum-containing chemotherapy.


title: Nivolumab

text: Nivolumab is indicated for the adjuvant treatment of people with melanoma with involvement of lymph nodes or in people with metastatic disease who have undergone complete resection.


title: Nivolumab

text: The combination of nivolumab with ipilimumab is used for the first-line treatment of adults with malignant pleural mesothelioma (MPM) that cannot be removed by surgery.


title: Nivolumab

text: In April 2021, the U.S. Food and Drug Administration (FDA) approved nivolumab, in combination with certain types of chemotherapy, for the initial treatment of people with advanced or metastatic gastric cancer, gastroesophageal junction cancer and esophageal adenocarcinoma.


title: Nivolumab

text: In May 2021, the U.S. FDA approved nivolumab for people with completely resected esophageal or gastroesophageal junction (GEJ) cancer with residual pathologic disease who have received neoadjuvant chemoradiotherapy.


title: Nivolumab

text: In August 2021, the U.S. FDA approved nivolumab for the adjuvant treatment of people with urothelial carcinoma (UC) who are at high risk of recurrence after undergoing radical resection.


title: Nivolumab

text: In May 2022, the U.S. FDA expanded the indication to include the first-line treatment of patients with advanced or metastatic esophageal squamous cell carcinoma (ESCC).


title: Nivolumab

text: The drug label contains warnings with regard to increased risks of severe immune-mediated inflammation of the lungs, the colon, the liver, the kidneys (with accompanying kidney dysfunction), as well as immune-mediated hypothyroidism and hyperthyroidism. Hypothyroidism may affect 8.5% and hyperthyroidism 3.7%. Autoimmune diabetes similar to diabetes mellitus type 1 may occur in approximately 2% of people treated with nivolumab. Colitis may occur due to nivolumab.


title: Nivolumab

text: In trials for melanoma, the following side effects occurred in more than 10% of subjects and more frequently than with chemotherapy alone: rash and itchy skin, cough, upper respiratory tract infections, and peripheral edema. Other clinically important side effects with less than 10% frequency were ventricular arrhythmia, inflammation of parts of the eye (iridocyclitis), infusion-related reactions, dizziness, peripheral and sensory neuropathy, peeling skin, erythema multiforme, vitiligo, and psoriasis.


title: Nivolumab

text: In trials for lung cancer, the following side effects occurred in more than 10% of subjects and more frequently than with chemotherapy alone: fatigue, weakness, edema, fever, chest pain, generalized pain, shortness of breath, cough, muscle and joint pain, decreased appetite, abdominal pain, nausea and vomiting, constipation, weight loss, rash, and itchy skin.


title: Nivolumab

text: Use during pregnancy may harm the baby; it is not known if nivolumab is secreted in breast milk but use during breastfeeding is not recommended.


title: Nivolumab

text: Based on data from 909 patients, the terminal half-life of nivolumab is 26.7 days and steady-state concentrations were reached by 12 weeks when administered at 3 mg/kg every 2 weeks. Age, gender, race, baseline LDH, PD-L1 expression, tumor type, tumor size, renal impairment, and mild hepatic impairment do not affect clearance of the drug.


title: Nivolumab

text: T cells protect the body from cancer by killing certain cancer cells. But cancer cells evolve proteins to protect themselves from T cells. Nivolumab blocks those protective proteins. Thus, the T cells can kill the cancer cells. This is an example of immune checkpoint blockade.


title: Nivolumab

text: PD-1 is a protein on the surface of activated T cells. If another molecule, called programmed cell death 1 ligand 1 or programmed cell death 1 ligand 2 (PD-L1 or PD-L2), binds to PD-1, the T cell becomes inactive. This is one way that the body regulates the immune system, to avoid an overreaction. Many cancer cells make PD-L1, which inhibits T cells from attacking the tumor. Nivolumab blocks PD-L1 from binding to PD-1, allowing the T cell to work. PD-L1 is expressed on 40–50% of melanomas and has limited expression otherwise in most visceral organs with the exception of respiratory epithelium and placental tissue.


title: Nivolumab

text: Nivolumab is a fully human monoclonal immunoglobulin G4 antibody to PD-1. The gamma 1 heavy chain is 91.8% unmodified human design while the kappa light chain is 98.9%.


title: Nivolumab

text: Nivolumab was generated under intellectual property of Ono Pharmaceutical regarding PD-1 and under a research collaboration entered in 2005 between Ono and Medarex.


title: Nivolumab

text: Through the research collaboration with Ono, it was invented by Dr. Changyu Wang and his team of scientists at Medarex using its transgenic mice with a humanized immune system; the discovery and "in vitro" characterization of the antibody, originally called MDX-1106/ONO-4538, was published (much later) in 2014. Under the agreement between the companies in 2005, Medarex held an exclusive right of nivolumab in North America, and Ono retained the right in all other countries except North America.


title: Nivolumab

text: Bristol-Myers Squibb acquired Medarex in 2009, for $2.4B, largely on the strength of its checkpoint inhibitor program.


title: Nivolumab

text: Promising clinical trial results made public in 2012, caused excitement among industry analysts and in the mainstream media; PD-1 was being avidly pursued as a biological target at that time, with companies including Merck with pembrolizumab (Keytruda), Roche (via its subsidiary Genentech) with atezolizumab, GlaxoSmithKline in collaboration with the Maryland biotech company Amplimmune; and Teva in collaboration with the Israeli biotech company CureTech competing.


title: Nivolumab

text: Ono received approval from Japanese regulatory authorities to use nivolumab to treat unresectable melanoma in July 2014, which was the first regulatory approval of a PD-1 inhibitor anywhere in the world.


title: Nivolumab

text: Merck received its first FDA approval for its PD-1 inhibitor, pembrolizumab (Keytruda), in September 2014.


title: Nivolumab

text: Nivolumab received FDA approval for the treatment of melanoma in December 2014. In April 2015, the Committee for Medicinal Products for Human Use of the European Medicines Agency recommended approval of Nivolumab for metastatic melanoma as a monotherapy.


title: Nivolumab

text: On 19 June 2015, the European Medicines Agency (EMA) granted a marketing authorization valid throughout the European Union.


title: Nivolumab

text: In November 2015, the FDA approved nivolumab as a second-line treatment for renal cell carcinoma after having granted the application breakthrough therapy designation, fast track designation, and priority review status.


title: Nivolumab

text: In May 2016, the FDA approved nivolumab for the treatment of patients with classical Hodgkin lymphoma (cHL) who have relapsed or progressed after autologous hematopoietic stem cell transplantation (auto-HSCT) and post-transplantation brentuximab vedotin.


title: Nivolumab

text: On 20 December 2017, the FDA granted approval to nivolumab for adjuvant treatment of melanoma with involvement of lymph nodes or for metastatic disease with complete resection.


title: Nivolumab

text: On 16 April 2018, the FDA granted approval to nivolumab in combination with ipilimumab for the first-line treatment of intermediate and poor risk advanced renal cell carcinoma patients.


title: Nivolumab

text: On 15 June 2018, China's Drug Administration approved nivolumab, the country's first immuno-oncology and the first PD-1 therapy.


title: Nivolumab

text: In October 2020, the U.S. Food and Drug Administration (FDA) approved the combination of nivolumab with ipilimumab for the first-line treatment of adults with malignant pleural mesothelioma (MPM) that cannot be removed by surgery.


title: Nivolumab

text: In April 2021, the FDA approved nivolumab, in combination with certain types of chemotherapy, for the initial treatment of people with advanced or metastatic gastric cancer, gastroesophageal junction cancer and esophageal adenocarcinoma.


title: Nivolumab

text: Nivolumab, and other PD-1 inhibitors, appear to be effective in people with brain metastases and for cancer in people with autoimmune diseases.


title: Nivolumab

text: In Hodgkin's lymphoma, Reed–Sternberg cells harbor amplification of chromosome 9p24.1, which encodes PD-L1 and PD-L2 and leads to their constitutive expression. In a small clinical study published in 2015, nivolumab elicited an objective response rate of 87% in a cohort of 20 patients.


title: Nivolumab

text: The evidence is very uncertain about the effect of Nivolumab for patients with a Hodgkin's lymphoma on the overall survival, the quality of life, the survival without a progression, the response rate (=complete disappear) and grade 3 or 4 serious adverse events.


title: Nivolumab

text: Each company pursuing mAbs against PD-1 as drugs developed assays to measure PD-L1 levels as a potential biomarker using their drugs as the analyte-specific reagent in the assay. BMS partnered with Dako on a nivolumab-based assay. However, as of 2015 the complexity of the immune response had hindered efforts to identify people who would be likely to respond well to PD-1 inhibitors; in particular PD-L1 levels appear to be dynamic and modulated by several factors, and efforts to correlate PD-L1 levels before or during treatment with treatment response or duration of response had failed to reveal any useful correlations as of 2015.


title: Nivolumab

text: In 2016, BMS announced the results of a clinical trial in which nivolumab failed to achieve its endpoint and was no better than traditional chemotherapy at treating newly diagnosed lung cancer. BMS went on to attempt to win approval for a combination therapy against lung cancer which included nivolumab and BMS's older drug ipilimumab. The application was withdrawn in early 2019 following disappointing clinical trial data.


title: Nivolumab

text: Infusion times of 60 minutes and 30 minutes appear to have similar pharmacokinetics (absorption, distribution, metabolism, and elimination) of the treatment.


title: Nivolumab

text: Nivolumab is indicated for the treatment of people with metastatic squamous non small cell lung cancer (NSCLC) with progression on or after platinum-based chemotherapy. CHECKMATE-227 tested the combination of nivolumab and ipilimumab in patients with stage IV or recurrent NSCLC without previous treatment. Patients with a PD-L1 expression level of 1% or more were randomized in a 1:1:1 ratio to receive nivolumab plus ipilimumab, nivolumab alone, or chemotherapy. The chemotherapy used was cisplatin or carboplatin, combined with Gemcitabine for patient with squamous cell NSCLC, or pemetrexed for patients with nonsquamous disease. The overall survival was 17.1, 15.7 and 14.9 months, respectively. The patients who had a PD-L1 expression level of less than 1% were randomly assigned in a 1:1:1 ratio to receive nivolumab plus ipilimumab, nivolumab plus chemotherapy, or chemotherapy. The OS was 17.2, 15.2 and 12.2 months, respectively


title: Nivolumab

text: PD-L1 is expressed in 40-50% of melanomas. Phase I and II clinical trials have shown nivolumab as a promising and durable treatment option in melanoma as a single agent and in combination with ipilimumab. Phase III trials are ongoing.


title: Nivolumab

text: In October 2022, the results of a Phase 3 trial, CheckMate -76K, showed that Opdivo reduced the risk of death by 58% as an adjuvant therapy in patients with completely resected stage two melanoma, the most serious type of skin cancer.


title: Maroon 5 discography

text: American pop rock band Maroon 5 has released seven studio albums, three live albums, two compilation albums, one remix album, six extended plays (EPs), 33 singles, seven promotional singles, and 38 music videos. The group originally formed in 1994 as Kara's Flowers while they were still attending high school. With a line-up of Adam Levine, Jesse Carmichael, Mickey Madden and Ryan Dusick, they released their independent album, "We Like Digging?" in 1995. In 1997, they signed to Reprise Records and released an album, "The Fourth World". After a tepid response to the album, the band parted with their record label and attended college. In 2001, the band regrouped and added James Valentine to the lineup, and pursued a new direction under the name Maroon 5.