title: Discrete Fourier transform

text: where formula_166 and formula_167 are the variances of formula_168 and formula_169 respectively, with the equality attained in the case of a suitably normalized Gaussian distribution. Although the variances may be analogously defined for the DFT, an analogous uncertainty principle is not useful, because the uncertainty will not be shift-invariant. Still, a meaningful uncertainty principle has been introduced by Massar and Spindel.


title: Discrete Fourier transform

text: However, the Hirschman entropic uncertainty will have a useful analog for the case of the DFT. The Hirschman uncertainty principle is expressed in terms of the Shannon entropy of the two probability functions.


title: Discrete Fourier transform

text: The equality is obtained for formula_173 equal to translations and modulations of a suitably normalized Kronecker comb of period formula_174 where formula_174 is any exact integer divisor of formula_8. The probability mass function formula_177 will then be proportional to a suitably translated Kronecker comb of period formula_178.


title: Discrete Fourier transform

text: There is also a well-known deterministic uncertainty principle that uses signal sparsity (or the number of non-zero coefficients). Let formula_179 and formula_180 be the number of non-zero elements of the time and frequency sequences formula_181 and formula_182, respectively. Then,


title: Discrete Fourier transform

text: As an immediate consequence of the inequality of arithmetic and geometric means, one also has formula_184. Both uncertainty principles were shown to be tight for specifically-chosen "picket-fence" sequences (discrete impulse trains), and find practical use for signal recovery applications.


title: Discrete Fourier transform

text: It follows that for even formula_8 formula_190 and formula_191 are real-valued, and the remainder of the DFT is completely specified by just formula_192 complex numbers.


title: Discrete Fourier transform

text: It is possible to shift the transform sampling in time and/or frequency domain by some real shifts "a" and "b", respectively. This is sometimes known as a generalized DFT (or GDFT), also called the shifted DFT or offset DFT, and has analogous properties to the ordinary DFT:


title: Discrete Fourier transform

text: While the ordinary DFT corresponds to a periodic signal in both time and frequency domains, formula_199 produces a signal that is anti-periodic in frequency domain (formula_200) and vice versa for formula_201.


title: Discrete Fourier transform

text: Thus, the specific case of formula_202 is known as an "odd-time odd-frequency" discrete Fourier transform (or O DFT).


title: Discrete Fourier transform

text: Such shifted transforms are most often used for symmetric data, to represent different boundary symmetries, and for real-symmetric data they correspond to different forms of the discrete cosine and sine transforms.


title: Discrete Fourier transform

text: Another interesting choice is formula_203, which is called the centered DFT (or CDFT). The centered DFT has the useful property that, when "N" is a multiple of four, all four of its eigenvalues (see above) have equal multiplicities (Rubio and Santhanam, 2005)


title: Discrete Fourier transform

text: The term GDFT is also used for the non-linear phase extensions of DFT. Hence, GDFT method provides a generalization for constant amplitude orthogonal block transforms including linear and non-linear phase types. GDFT is a framework


title: Discrete Fourier transform

text: to improve time and frequency domain properties of the traditional DFT, e.g. auto/cross-correlations, by the addition of the properly designed phase shaping function (non-linear, in general) to the original linear phase functions (Akansu and Agirman-Tosun, 2010).


title: Discrete Fourier transform

text: The discrete Fourier transform can be viewed as a special case of the z-transform, evaluated on the unit circle in the complex plane; more general z-transforms correspond to "complex" shifts "a" and "b" above.


title: Discrete Fourier transform

text: The ordinary DFT transforms a one-dimensional sequence or array formula_42 that is a function of exactly one discrete variable "n". The multidimensional DFT of a multidimensional array formula_205 that is a function of "d" discrete variables formula_206 for formula_207 in formula_208 is defined by:


title: Discrete Fourier transform

text: where formula_210 as above and the "d" output indices run from formula_211. This is more compactly expressed in vector notation, where we define formula_212 and formula_213 as "d"-dimensional vectors of indices from 0 to formula_214, which we define as formula_215:


title: Discrete Fourier transform

text: where the division formula_217 is defined as formula_218 to be performed element-wise, and the sum denotes the set of nested summations above.


title: Discrete Fourier transform

text: As the one-dimensional DFT expresses the input formula_42 as a superposition of sinusoids, the multidimensional DFT expresses the input as a superposition of plane waves, or multidimensional sinusoids. The direction of oscillation in space is formula_221. The amplitudes are formula_222. This decomposition is of great importance for everything from digital image processing (two-dimensional) to solving partial differential equations. The solution is broken up into plane waves.


title: Discrete Fourier transform

text: The multidimensional DFT can be computed by the composition of a sequence of one-dimensional DFTs along each dimension. In the two-dimensional case formula_223 the formula_224 independent DFTs of the rows (i.e., along formula_225) are computed first to form a new array formula_226. Then the formula_227 independent DFTs of "y" along the columns (along formula_228) are computed to form the final result formula_229. Alternatively the columns can be computed first and then the rows. The order is immaterial because the nested summations above commute.


title: Discrete Fourier transform

text: An algorithm to compute a one-dimensional DFT is thus sufficient to efficiently compute a multidimensional DFT. This approach is known as the "row-column" algorithm. There are also intrinsically multidimensional FFT algorithms.


title: Discrete Fourier transform

text: For input data formula_205 consisting of real numbers, the DFT outputs have a conjugate symmetry similar to the one-dimensional case above:


title: Discrete Fourier transform

text: where the star again denotes complex conjugation and the formula_207-th subscript is again interpreted modulo formula_233 (for formula_234).


title: Discrete Fourier transform

text: The DFT has seen wide usage across a large number of fields; we only sketch a few examples below (see also the references at the end). All applications of the DFT depend crucially on the availability of a fast algorithm to compute discrete Fourier transforms and their inverses, a fast Fourier transform.


title: Discrete Fourier transform

text: When the DFT is used for signal spectral analysis, the formula_45 sequence usually represents a finite set of uniformly spaced time-samples of some signal formula_236, where formula_237 represents time. The conversion from continuous time to samples (discrete-time) changes the underlying Fourier transform of formula_238 into a discrete-time Fourier transform (DTFT), which generally entails a type of distortion called aliasing. Choice of an appropriate sample-rate (see "Nyquist rate") is the key to minimizing that distortion. Similarly, the conversion from a very long (or infinite) sequence to a manageable size entails a type of distortion called "leakage", which is manifested as a loss of detail (a.k.a. resolution) in the DTFT. Choice of an appropriate sub-sequence length is the primary key to minimizing that effect. When the available data (and time to process it) is more than the amount needed to attain the desired frequency resolution, a standard technique is to perform multiple DFTs, for example to create a spectrogram. If the desired result is a power spectrum and noise or randomness is present in the data, averaging the magnitude components of the multiple DFTs is a useful procedure to reduce the variance of the spectrum (also called a periodogram in this context); two examples of such techniques are the Welch method and the Bartlett method; the general subject of estimating the power spectrum of a noisy signal is called spectral estimation.


title: Discrete Fourier transform

text: A final source of distortion (or perhaps "illusion") is the DFT itself, because it is just a discrete sampling of the DTFT, which is a function of a continuous frequency domain. That can be mitigated by increasing the resolution of the DFT. That procedure is illustrated at .


title: Discrete Fourier transform

text: The discrete Fourier transform is widely used with spatial frequencies in modeling the way that light, electrons, and other probes travel through optical systems and scatter from objects in two and three dimensions. The dual (direct/reciprocal) vector space of three dimensional objects further makes available a three dimensional reciprocal lattice, whose construction from translucent object shadows (via the Fourier slice theorem) allows tomographic reconstruction of three dimensional objects with a wide range of applications e.g. in modern medicine.


title: Discrete Fourier transform

text: The field of digital signal processing relies heavily on operations in the frequency domain (i.e. on the Fourier transform). For example, several lossy image and sound compression methods employ the discrete Fourier transform: the signal is cut into short segments, each is transformed, and then the Fourier coefficients of high frequencies, which are assumed to be unnoticeable, are discarded. The decompressor computes the inverse transform based on this reduced number of Fourier coefficients. (Compression applications often use a specialized form of the DFT, the discrete cosine transform or sometimes the modified discrete cosine transform.)


title: Discrete Fourier transform

text: Some relatively recent compression algorithms, however, use wavelet transforms, which give a more uniform compromise between time and frequency domain than obtained by chopping data into segments and transforming each segment. In the case of JPEG2000, this avoids the spurious image features that appear when images are highly compressed with the original JPEG.


title: Discrete Fourier transform

text: Discrete Fourier transforms are often used to solve partial differential equations, where again the DFT is used as an approximation for the Fourier series (which is recovered in the limit of infinite "N"). The advantage of this approach is that it expands the signal in complex exponentials formula_239, which are eigenfunctions of differentiation: formula_240. Thus, in the Fourier representation, differentiation is simple—we just multiply by formula_241. (However, the choice of formula_22 is not unique due to aliasing; for the method to be convergent, a choice similar to that in the trigonometric interpolation section above should be used.) A linear differential equation with constant coefficients is transformed into an easily solvable algebraic equation. One then uses the inverse DFT to transform the result back into the ordinary spatial representation. Such an approach is called a spectral method.


title: Discrete Fourier transform

text: Suppose we wish to compute the polynomial product "c"("x") = "a"("x") · "b"("x"). The ordinary product expression for the coefficients of "c" involves a linear (acyclic) convolution, where indices do not "wrap around." This can be rewritten as a cyclic convolution by taking the coefficient vectors for "a"("x") and "b"("x") with constant term first, then appending zeros so that the resultant coefficient vectors a and b have dimension . Then,


title: Discrete Fourier transform

text: Where c is the vector of coefficients for "c"("x"), and the convolution operator formula_244 is defined so


title: Discrete Fourier transform

text: Here the vector product is taken elementwise. Thus the coefficients of the product polynomial "c"("x") are just the terms 0, ..., deg("a"("x")) + deg("b"("x")) of the coefficient vector


title: Discrete Fourier transform

text: With a fast Fourier transform, the resulting algorithm takes "O"("N" log "N") arithmetic operations. Due to its simplicity and speed, the Cooley–Tukey FFT algorithm, which is limited to composite sizes, is often chosen for the transform operation. In this case, "d" should be chosen as the smallest integer greater than the sum of the input polynomial degrees that is factorizable into small prime factors (e.g. 2, 3, and 5, depending upon the FFT implementation).


title: Discrete Fourier transform

text: The fastest known algorithms for the multiplication of very large integers use the polynomial multiplication method outlined above. Integers can be treated as the value of a polynomial evaluated specifically at the number base, with the coefficients of the polynomial corresponding to the digits in that base (ex. formula_248). After polynomial multiplication, a relatively low-complexity carry-propagation step completes the multiplication.


title: Discrete Fourier transform

text: When data is convolved with a function with wide support, such as for downsampling by a large sampling ratio, because of the Convolution theorem and the FFT algorithm, it may be faster to transform it, multiply pointwise by the transform of the filter and then reverse transform it. Alternatively, a good filter is obtained by simply truncating the transformed data and re-transforming the shortened data set.


title: Discrete Fourier transform

text: The DFT can be interpreted as a complex-valued representation of the finite cyclic group. In other words, a sequence of formula_22 complex numbers can be thought of as an element of formula_22-dimensional complex space formula_251 or equivalently a function formula_252 from the finite cyclic group of order formula_22 to the complex numbers, formula_254. So formula_252 is a class function on the finite cyclic group, and thus can be expressed as a linear combination of the irreducible characters of this group, which are the roots of unity.


title: Discrete Fourier transform

text: From this point of view, one may generalize the DFT to representation theory generally, or more narrowly to the representation theory of finite groups.


title: Discrete Fourier transform

text: More narrowly still, one may generalize the DFT by either changing the target (taking values in a field other than the complex numbers), or the domain (a group other than a finite cyclic group), as detailed in the sequel.


title: Discrete Fourier transform

text: Many of the properties of the DFT only depend on the fact that formula_256 is a primitive root of unity, sometimes denoted formula_257 or formula_258 (so that formula_259). Such properties include the completeness, orthogonality, Plancherel/Parseval, periodicity, shift, convolution, and unitarity properties above, as well as many FFT algorithms. For this reason, the discrete Fourier transform can be defined by using roots of unity in fields other than the complex numbers, and such generalizations are commonly called "number-theoretic transforms" (NTTs) in the case of finite fields. For more information, see number-theoretic transform and discrete Fourier transform (general).


title: Discrete Fourier transform

text: The standard DFT acts on a sequence "x", "x", ..., "x" of complex numbers, which can be viewed as a function {0, 1, ..., "N" − 1} → C. The multidimensional DFT acts on multidimensional sequences, which can be viewed as functions


title: Discrete Fourier transform

text: This suggests the generalization to Fourier transforms on arbitrary finite groups, which act on functions "G" → C where "G" is a finite group. In this framework, the standard DFT is seen as the Fourier transform on a cyclic group, while the multidimensional DFT is a Fourier transform on a direct sum of cyclic groups.


title: Discrete Fourier transform

text: There are various alternatives to the DFT for various applications, prominent among which are wavelets. The analog of the DFT is the discrete wavelet transform (DWT). From the point of view of time–frequency analysis, a key limitation of the Fourier transform is that it does not include "location" information, only "frequency" information, and thus has difficulty in representing transients. As wavelets have location as well as frequency, they are better able to represent location, at the expense of greater difficulty representing frequency. For details, see comparison of the discrete wavelet transform with the discrete Fourier transform.


title: Brachiosaurus

text: Brachiosaurus () is a genus of sauropod dinosaur that lived in North America during the Late Jurassic, about 154to 150million years ago. It was first described by American paleontologist Elmer S. Riggs in 1903 from fossils found in the Colorado River valley in western Colorado, United States. Riggs named the dinosaur Brachiosaurus altithorax; the generic name is Greek for "arm lizard", in reference to its proportionately long arms, and the specific name means "deep chest". "Brachiosaurus" is estimated to have been between 18 and 22 meters (59 and 72ft) long; body mass estimates of the subadult holotype specimen range from 28.3 to 46.9 metric tons (31.2 and 51.7 short tons). It had a disproportionately long neck, small skull, and large overall size, all of which are typical for sauropods. Atypically, "Brachiosaurus" had longer forelimbs than hindlimbs, which resulted in a steeply inclined trunk, and a proportionally shorter tail.


title: Brachiosaurus

text: "Brachiosaurus" is the namesake genus of the family Brachiosauridae, which includes a handful of other similar sauropods. Most popular depictions of "Brachiosaurus" are in fact based on "Giraffatitan", a genus of brachiosaurid dinosaur from the Tendaguru Formation of Tanzania. "Giraffatitan" was originally described by German paleontologist Werner Janensch in 1914 as a species of "Brachiosaurus", "B. brancai", but moved to its own genus in 2009. Three other species of "Brachiosaurus" have been named based on fossils found in Africa and Europe; two are no longer considered valid, and a third has become a separate genus, "Lusotitan".


title: Brachiosaurus

text: The type specimen of "B. altithorax" is still the most complete specimen, and only a few other specimens are thought to belong to the genus, making it one of the rarer sauropods of the Morrison Formation. It is regarded as a high browser, possibly cropping or nipping vegetation as high as off the ground. Unlike other sauropods, it was unsuited for rearing on its hindlimbs. It has been used as an example of a dinosaur that was most likely ectothermic because of its large size and the corresponding need for sufficient forage, but more recent research suggests it was warm-blooded. Among the most iconic and initially thought to be one of the largest dinosaurs, "Brachiosaurus" has appeared in popular culture, notably in the 1993 film "Jurassic Park".


title: Brachiosaurus

text: The genus "Brachiosaurus" is based on a partial postcranial skeleton discovered in 1900 in the valley of the Colorado River near Fruita, Colorado. This specimen, which was later declared the holotype, comes from rocks of the Brushy Basin Member of the Morrison Formation, and therefore is late Kimmeridgian in age, about 154to 153million years old. Discovered by American paleontologist Elmer S. Riggs and his crew from the Field Columbian Museum (now the Field Museum of Natural History) of Chicago, it is currently cataloged as FMNHP25107.


title: Brachiosaurus

text: Riggs and company were working in the area as a result of favorable correspondence between Riggs and Stanton Merill Bradbury, a dentist in nearby Grand Junction. In the spring of 1899 Riggs had sent letters to mayors in western Colorado, inquiring after possible trails leading from railway heads into northeastern Utah, where he hoped to find fossils of Eocene mammals. To his surprise, he was informed by Bradbury, an amateur collector himself and president of the Western Colorado Academy of Science, that dinosaur bones had been collected near Grand Junction since 1885. Riggs was skeptical of this claim, but his superior, curator of geology Oliver Cummings Farrington, was very eager to add a large sauropod skeleton to the collection to outdo other institutions, and convinced the museum management to invest five hundred dollars in an expedition. Arriving on June 20, 1900 they set camp at the abandoned Goat Ranch. During a prospecting trip on horseback, Riggs's field assistant Harold William Menke found the humerus of FMNHP25107, on July 4, exclaiming it was "the biggest thing yet!". Riggs at first took the find for a badly preserved "Brontosaurus" specimen and gave priority to excavating Quarry 12, which held a more promising "Morosaurus" skeleton. Having secured that, on July 26 he returned to the humerus in Quarry 13, which soon proved to be of enormous size, convincing a puzzled Riggs that he had discovered the largest land animal ever.


title: Brachiosaurus

text: The site, Riggs Quarry 13, is located on a small hill later known as Riggs Hill; it is today marked by a plaque. More "Brachiosaurus" fossils are reported on Riggs Hill, but other fossil finds on the hill have been vandalized. During excavation of the specimen, Riggs misidentified the humerus as a deformed femur due to its great length, and this seemed to be confirmed when an equally-sized, well-preserved real femur of the same skeleton was discovered. In 1904 Riggs noted: "Had it not been for the unusual size of the ribs found associated with it, the specimen would have been discarded as an Apatosaur, too poorly preserved to be of value." It was only after preparation of the fossil material in the laboratory that the bone was recognized as a humerus. The excavation attracted large numbers of visitors, delaying the work and forcing Menke to guard the site to prevent bones from being looted. On August 17, the last bone was jacketed in plaster. After a concluding ten-day prospecting trip, the expedition returned to Grand Junction and hired a team and wagon to transport all fossils to the railway station, during five days; another week was spent to pack them in thirty-eight crates with a weight of . On September 10, Riggs left for Chicago by train, arriving on the 15th; the railroad companies let both passengers and cargo travel for free, as a public relations gesture.


title: Brachiosaurus

text: The holotype skeleton consists of the right humerus (upper arm bone), the right femur (thigh bone), the right ilium (a hip bone), the right coracoid (a shoulder bone), the sacrum (fused vertebrae of the hip), the last seven thoracic (trunk) and two caudal (tail) vertebrae, and several ribs. Riggs described the coracoid as from the left side of the body, but restudy has shown it to be a right coracoid. At the time of discovery, the lower end of the humerus, the underside of the sacrum, the ilium and the preserved caudal vertebrae were exposed to the air and thus partly damaged by weathering. The vertebrae were only slightly shifted out of their original anatomical position; they were found with their top sides directed downward. The ribs, humerus, and coracoid, however, were displaced to the left side of the vertebral column, indicating transportation by a water current. This is further evidenced by an isolated ilium of "Diplodocus" that apparently had drifted against the vertebral column, as well as by a change in composition of the surrounding rocks. While the specimen itself was embedded in fine-grained clay, indicating low-energy conditions at the time of deposition, it was cut off at the seventh presacral vertebra by a thick layer of much coarser sediments consisting of pebbles at its base and sandstone further up, indicating deposition under stronger currents. Based on this evidence, Riggs in 1904 suggested that the missing front part of the skeleton was washed away by a water current, while the hind part was already covered by sediment and thus got preserved.


title: Brachiosaurus

text: Riggs published a short report of the new find in 1901, noting the unusual length of the humerus compared to the femur and the extreme overall size and the resulting giraffe-like proportions, as well as the lesser development of the tail, but did not publish a name for the new dinosaur. In 1903, he named the type species "Brachiosaurus altithorax". Riggs derived the genus name from the Greek "brachion"/βραχίων meaning "arm" and "sauros"/ meaning "lizard", because he realized that the length of the arms was unusual for a sauropod. The specific epithet was chosen because of the unusually deep and wide chest cavity, from Latin "altus" "deep" and Greek "thorax"/θώραξ, "breastplate, cuirass, corslet". Latin "thorax" was derived from the Greek and had become a usual scientific designation for the chest of the body. The titles of Riggs's 1901 and 1903 articles emphasized that the specimen was the "largest known dinosaur". Riggs followed his 1903 publication with a more detailed description in a monograph in 1904.


title: Brachiosaurus

text: Preparation of the holotype began in the fall of 1900 shortly after it was collected by Riggs for the Field Museum. First the limb elements were processed. In the winter of 1904, the badly weathered vertebrae of the back and hip were prepared by James B. Abbott and C.T. Kline. As the preparation of each bone was finished, it was put on display in a glass case in Hall 35 of the Fine Arts Palace of the Worlds Columbian Exposition, the Field Museum's first location. All the bones were, solitarily, still on display by 1908 in Hall 35 when the Field Museum's newly mounted "Apatosaurus" was unveiled, the very specimen Riggs had found in Quarry 12, today catalogued as FMNH P25112 and identified as a "Brontosaurus" exemplar. No mount of "Brachiosaurus" was attempted because only twenty percent of the skeleton had been recovered. In 1993, the holotype bones were molded and cast, and the missing bones were sculpted based on material of the related "Brachiosaurus brancai" (now "Giraffatitan") in Museum für Naturkunde, Berlin. This plastic skeleton was mounted and, in 1994, put on display at the north end of Stanley Field Hall, the main exhibit hall of the Field Museum's current building. The real bones of the holotype were put on exhibit in two large glass cases at either end of the mounted cast. The mount stood until 1999, when it was moved to the BConcourse of United Airlines' Terminal One in O'Hare International Airport to make room for the museum's newly acquired tyrannosaurus skeleton, "Sue". At the same time, the Field Museum mounted a second plastic cast of the skeleton (designed for outside use) which is on display outside the museum on the NW terrace.


title: Brachiosaurus

text: Another outdoor cast was sent to Disney's Animal Kingdom to serve as a gateway icon for the "DinoLand, U.S.A." area, known as the "Oldengate Bridge" that connects the two halves of the fossil quarry themed Boneyard play area.


title: Brachiosaurus

text: Further discoveries of "Brachiosaurus" material in North America have been uncommon and consist of a few bones. To date, material can be unambiguously ascribed only to the genus when overlapping with the holotype material, and any referrals of elements form the skull, neck, anterior dorsal region, or distal limbs or feet remain tentative. Nevertheless, material has been described from Colorado, Oklahoma, Utah, and Wyoming, and undescribed material has been mentioned from several other sites.


title: Brachiosaurus

text: In 1883, farmer Marshall Parker Felch, a fossil collector for the American paleontologist Othniel Charles Marsh, reported the discovery of a sauropod skull in Felch Quarry 1, near Garden Park, Colorado. The skull was found in yellowish white sandstone, near a cervical vertebra, which was destroyed during an attempt to collect it. The skull was cataloged as YPM 1986, and sent to Marsh at the Peabody Museum of Natural History, who incorporated it into his 1891 skeletal restoration of "Brontosaurus" (perhaps because Felch had identified it as belonging to that dinosaur). The Felch Quarry skull consists of the cranium, the maxillae, the right postorbital, part of the left maxilla, the left squamosal, the dentaries, and a possible partial pterygoid. The bones were roughly prepared for Marsh, which led to some damage. Felch also collected several postcranial fossils, including a partial cervical vertebra and partial forelimb. Most of the specimens collected by Felch were sent to the National Museum of Natural History in 1899 after Marsh's death, including the skull, which was then cataloged as USNM 5730.


title: Brachiosaurus

text: In 1975 the American paleontologists Jack McIntosh and David Berman investigated the historical issue of whether Marsh had assigned an incorrect skull to "Brontosaurus" (at the time thought to be a junior synonym of "Apatosaurus"), and found the Felch Quarry skull to be of "the general "Camarasaurus" type", while suggesting that the vertebra found near it belonged to "Brachiosaurus". They concluded that if Marsh had not arbitrarily assigned the Felch quarry skull and another "Camarasaurus"-like skull to "Brontosaurus", it would have been recognized earlier that the actual skull of "Brontosaurus" and "Apatosaurus" was more similar to that of "Diplodocus". McIntosh later tentatively recognized the Felch Quarry skull as belonging to "Brachiosaurus", and brought it to the attention of the American paleontologists Kenneth Carpenter and Virginia Tidwell, while urging them to describe it. They brought the skull to the Denver Museum of Natural History, where they further prepared it and made a reconstruction of it based on casts of the individual bones, with the skulls of "Giraffatitan" and "Camarasaurus" acting as templates for the missing bones.


title: Brachiosaurus

text: In 1998 Carpenter and Tidwell described the Felch Quarry skull, and formally assigned it to "Brachiosaurus" sp. (of uncertain species), since it is impossible to determine whether it belonged to the species "B. altithorax" itself (as there is no overlapping material between the two specimens). They based the skull's assignment to "Brachiosaurus" on its similarity to that of "B. brancai", later known as "Giraffatitan". In 2019, American paleontologists Michael D. D'Emic and Matthew T. Carrano re-examined the Felch Quarry skull after having it further prepared and CT-scanned (while consulting historical illustrations that showed earlier states of the bones), and concluded that a quadrate bone and dentary tooth considered part of the skull by Carpenter and Tidwell did not belong to it. The quadrate is too large to articulate with the squamosal, is preserved differently from the other bones, and was found several meters away. The tooth does not resemble those within the jaws (as revealed by CT data), is larger, and was therefore assigned to "Camarasaurus" sp. (other teeth assignable to that genus are known from the quarry). They also found it most parsimonious to assign the skull to "B. altithorax" itself rather than an unspecified species, as there is no evidence of other brachiosaurid taxa in the Morrison Formation (and adding this and other possible elements to a phylogenetic analysis did not change the position of "B. altithorax").


title: Brachiosaurus

text: A shoulder blade with coracoid from Dry Mesa Quarry, Colorado, is one of the specimens at the center of the "Supersaurus"/"Ultrasauros" issue of the 1980s and 1990s. In 1985 James A. Jensen described disarticulated sauropod remains from the quarry as belonging to several exceptionally large taxa, including the new genera "Supersaurus" and "Ultrasaurus", the latter renamed "Ultrasauros" shortly thereafter because another sauropod had already received the name. Later study showed that the "ultrasaur" material mostly belonged to "Supersaurus", though the shoulder blade did not. Because the holotype of "Ultrasauros", a dorsal vertebra, was one of the specimens that was actually from "Supersaurus", the name "Ultrasauros" is a synonym of "Supersaurus". The shoulder blade, specimen BYU 9462 (previously BYU 5001), was in 1996 assigned to a "Brachiosaurus" sp. (of uncertain species) by Brian Curtice and colleagues; in 2009 Michael P. Taylor concluded that it could not be referred to "B. altithorax". The Dry Mesa "ultrasaur" was not as large as had been thought; the dimensions of the shoulder's coracoid bone indicate that the animal was smaller than Riggs's original specimen of "Brachiosaurus".


title: Brachiosaurus

text: Several additional specimens were briefly described by Jensen in 1987. One of these finds, the humerus USNM 21903, was discovered in ca. 1943 by uranium prospectors Vivian and Daniel Jones in the Potter Creek Quarry in western Colorado, and donated to the Smithsonian Institution. Originally, this humerus was part of a poorly preserved partial skeleton that was not collected. According to Taylor in 2009, it is not clearly referable to "Brachiosaurus" despite its large size of . Jensen himself worked at the Potter Creek site in 1971 and 1975, excavating the disarticulated specimen BYU 4744, which contains a mid-dorsal vertebra, an incomplete left ilium, a left radius and a right metacarpal. According to Taylor in 2009, this specimen can be confidently referred to "B. altithorax", as far as it is overlapping with its type specimen. Jensen further mentioned a specimen discovered near Jensen, Utah, that includes a rib in length, an anterior cervical vertebra, part of a scapula, and a coracoid, although he did not provide a description. In 2001, Curtice and Stadtman ascribed two articulated dorsal vertebrae (specimen BYU 13023) from Dry Mesa Quarry to "Brachiosaurus". Taylor, in 2009, noted that these vertebrae are markedly shorter than those of the "B. altithorax" holotype, although otherwise being similar.


title: Brachiosaurus

text: In 2012, José Carballido and colleagues reported a nearly complete postcranial skeleton of a small juvenile approximately in length. This specimen, nicknamed "Toni" and cataloged as SMA 0009, stems from the Morrison Formation of the Bighorn Basin in north-central Wyoming. Although originally thought to belong to a diplodocid, it was later reinterpreted as a brachiosaurid, probably belonging to "B. altithorax". In 2018, the largest sauropod foot ever found was reported from the Black Hills of Weston County, Wyoming. The femur is not preserved but comparisons suggest that it was about two percent longer than that of the "B. altithorax" holotype. Though possibly belonging to "Brachiosaurus", the authors cautiously classified it as an indeterminate brachiosaurid. However, the assignment of these two specimens to their respective clades was later questioned by D'Emic and Carrano in 2019. They considered the referral of "Toni" to "B. altithorax" be based on mistaken interpretations of the species' unique features or of the specimen itself, and deemed it worthy of further study. Analyzing photos of the large foot, D'Emic and Carrano noted that the only feature that allowed referral to Brachiosauridae may have been influenced by damage to the bone it was found on, but did state that "general similarities" with "Sonorasaurus" and "Giraffatitan" suggested brachiosaurid affinities, but this, the authors stated, would be confirmed only through further study.


title: Brachiosaurus

text: Between 1909 and 1912, large-scale paleontological expeditions in German East Africa unearthed a considerable amount of brachiosaurid material from the Tendaguru Formation. In 1914, German paleontologist Werner Janensch listed differences and commonalities between these fossils and "B. altithorax", concluding they could be referred to the genus "Brachiosaurus". From this material Janensch named two species: "Brachiosaurus brancai" for the larger and more complete taxon, and "Brachiosaurus fraasi" for the smaller and more poorly known species. In three further publications in 1929, 1950 and 1961, Janensch compared the species in more detail, listing thirteen shared characters between "Brachiosaurus brancai" (which he now considered to include "B. fraasi") and "B. altithorax". Taylor, in 2009, considered only four of these characters as valid; six pertain to groups more inclusive than the Brachiosauridae, and the rest are either difficult to assess or refer to material that is not "Brachiosaurus".


title: Brachiosaurus

text: There was ample material referred to "B. brancai" in the collections of the Museum für Naturkunde in Berlin, some of which was destroyed during World War II. Other material was transferred to other institutions throughout Germany, some of which was also destroyed. Additional material was collected by the British Museum of Natural History's Tendaguru expedition, including a nearly complete skeleton (BMNH R5937) collected by F.W.H. Migeod in 1930. This specimen is now believed to represent a new species, awaiting description.


title: Brachiosaurus

text: Janensch based his description of "B. brancai" on "Skelett S" (skeleton S) from Tendaguru, but later realized that it comprised two partial individuals: SI and SII. He at first did not designate them as a syntype series, but in 1935 made SI (presently MB.R.2180) the lectotype. Taylor in 2009, unaware of this action, proposed the larger and more complete SII (MB.R.2181) as the lectotype. It includes, among other bones, several dorsal vertebrae, the left scapula, both coracoids, the breastbones, both humeri, both ulnae and radii (lower arm bones), a right hand, a partial left hand, both hip bones and the right femur, tibia and fibula (shank bones). Later in 2011, Taylor realized that Janensch had designated the smaller skeleton SI as the lectotype in 1935.


title: Brachiosaurus

text: In 1988 Gregory S. Paul published a new reconstruction of the skeleton of "B. brancai", highlighting differences in proportion between it and "B. altithorax". Chief among them was a distinction in the way the trunk vertebrae vary: they are fairly uniform in length in the African material, but vary widely in "B. altithorax". Paul believed that the limb and girdle elements of both species were very similar, and therefore suggested they be separated not at genus, but only at subgenus level, as "Brachiosaurus (Brachiosaurus) altithorax" and "Brachiosaurus (Giraffatitan) brancai". "Giraffatitan" was raised to full genus level by George Olshevsky in 1991, while referring to the vertebral variation. Between 1991 and 2009, the name "Giraffatitan" was almost completely disregarded by other researchers.


title: Brachiosaurus

text: A detailed 2009 study by Taylor of all material, including the limb and girdle bones, found that there are significant divergences between "B. altithorax" and the Tendaguru material in all elements known from both species. Taylor found twenty-six distinct osteological (bone-based) characters, a larger difference than between "Diplodocus" and "Barosaurus", and therefore argued that the African material should indeed be placed in its own genus ("Giraffatitan") as "Giraffatitan brancai". An important contrast between the two genera is their overall body shape, with "Brachiosaurus" having a 23 percent longer dorsal vertebral series and a 20 to 25 percent longer and also taller tail. The split was rejected by Daniel Chure in 2010, but from 2012 onward most studies recognized the name "Giraffatitan".


title: Brachiosaurus

text: In 1947, at Atalaia in Portugal, brachiosaurid remains were found in layers dating from the Tithonian. Albert-Félix de Lapparent and Georges Zbyszewski named them as the species "Brachiosaurus atalaiensis" in 1957. Its referral to "Brachiosaurus" was doubted in the 2004 edition of "The Dinosauria" by Paul Upchurch, Barret, and Peter Dodson who listed it as an as yet unnamed brachiosaurid genus. Shortly before the publication of the 2004 book, the species had been placed in its own genus "Lusotitan" by Miguel Telles Antunes and Octávio Mateus in 2003. De Lapparent and Zbyszewski had described a series of remains but did not designate a type specimen. Antunes and Mateus selected a partial postcranial skeleton (MIGM4978, 4798, 4801–4810, 4938, 4944, 4950, 4952, 4958, 4964–4966, 4981–4982, 4985, 8807, 8793–87934) as the lectotype; this specimen includes twenty-eight vertebrae, chevrons, ribs, a possible shoulder blade, humeri, forearm bones, partial left pelvis, lower leg bones, and part of the right ankle. The low neural spines, the prominent deltopectoral crest of the humerus (a muscle attachment site on the upper arm bone), the elongated humerus (very long and slender), and the long axis of the ilium tilting upward indicate that "Lusotitan" is a brachiosaurid, which was confirmed by some later studies, such as an analysis in 2013.


title: Brachiosaurus

text: In 1958 French petroleum geologist F. Nougarède reported to have discovered fragmentary brachiosaurid remains in eastern Algeria, in the Sahara Desert. Based on these, Albert-Félix de Lapparent described and named the species "Brachiosaurus nougaredi" in 1960. He indicated the discovery locality as being in the Late Jurassic-age Taouratine Series. He assigned the rocks to this age in part because of the presumed presence of "Brachiosaurus". A more recent review placed it in the "Continental intercalaire," which is considered to belong to the Albian age of the late Early Cretaceous, significantly younger.


title: Brachiosaurus

text: The type material moved to Paris consisted of a sacrum, weathered out at the desert surface, and some of the left metacarpals and phalanges. Found at the discovery site but not collected, were partial bones of the left forearm, wrist bones, a right shin bone, and fragments that may have come from metatarsals.


title: Brachiosaurus

text: "B. nougaredi" was in 2004 considered to represent a distinct, unnamed brachiosaurid genus, but a 2013 analysis by Philip D. Mannion and colleagues found that the remains possibly belong to more than one species, as they were collected far apart. The metacarpals were concluded to belong to some indeterminate titanosauriform. The sacrum was reported lost in 2013. It was not analyzed and provisionally considered to represent an indeterminate sauropod, until such time that it could be relocated in the collections of the "Muséum national d'histoire naturelle". Only four out of the five sacral vertebrae are preserved. The total original length was in 1960 estimated at , compared to with "B. altithorax". This would make it larger than any other sauropod sacrum ever found, except those of "Argentinosaurus" and "Apatosaurus".


title: Brachiosaurus

text: Most estimates of "Brachiosaurus altithorax" size are based on the related brachiosaurid "Giraffatitan" (formerly known as "B. brancai"), which is known from much more complete material than "Brachiosaurus". The two species are the largest brachiosaurids of which relatively extensive remains have been discovered. There is another element of uncertainty for the North American "Brachiosaurus" because the type (and most complete) specimen appears to represent a subadult, as indicated by the unfused suture between the coracoid, a bone of the shoulder girdle that forms part of the shoulder joint, and the scapula (shoulder blade). Over the years, the mass of the holotype specimen has been estimated within the range of . Benson et al. suggested a maximum body mass of , but these estimates were questioned due to a very large error range and lack of precision. The length of "Brachiosaurus" has been estimated at 20–22 meters (66–72ft) per Paul and , and its height at and 12–13 meters (39–43ft).


title: Brachiosaurus

text: While the limb bones of the most complete "Giraffatitan" skeleton (MB.R.2181) were very similar in size to those of the "Brachiosaurus" type specimen, the former was somewhat lighter than the "Brachiosaurus" specimen given its proportional differences. In studies including estimates for both genera, "Giraffatitan" was estimated at , , , , and . As with the main "Brachiosaurus" specimen, "Giraffatitan" specimen MB.R.2181 likely does not reflect the maximum size of the genus, as a fibula (specimen HMXV2) is thirteen percent longer than that of MB.R.2181.


title: Brachiosaurus

text: Like all sauropod dinosaurs, "Brachiosaurus" was a quadruped with a small skull, a long neck, a large trunk with a high-ellipsoid cross section, a long, muscular tail and slender, columnar limbs. Large air sacs connected to the lung system were present in the neck and trunk, invading the vertebrae and ribs by bone resorption, greatly reducing the overall density of the body. The neck is not preserved in the holotype specimen, but was very long even by sauropod standards in the closely related "Giraffatitan", consisting of thirteen elongated cervical (neck) vertebrae. The neck was held in a slight S-curve, with the lower and upper sections bent and a straight middle section. "Brachiosaurus" likely shared with "Giraffatitan" the very elongated neck ribs, which ran down the underside of the neck, overlapping several preceding vertebrae. These bony rods were attached to neck muscles at their ends, allowing these muscles to operate distal portions of the neck while themselves being located closer to the trunk, lightening the distal neck portions.


title: Brachiosaurus

text: "Brachiosaurus" and "Giraffatitan" probably had a small shoulder hump between the third and fifth dorsal (back) vertebra, where the sideward- and upward-directed vertebral processes were longer, providing additional surface for neck muscle attachment. The ribcage was deep compared to other sauropods. Though the humerus (upper arm bone) and femur (thigh bone) were roughly equal in length, the entire forelimb would have been longer than the hindlimb, as can be inferred from the elongated forearm and metacarpus of other brachiosaurids. This resulted in an inclined trunk with the shoulder much higher than the hips, and the neck exiting the trunk at a steep angle. The overall build of "Brachiosaurus" resembles a giraffe more than any other living animal. In contrast, most other sauropods had a shorter forelimb than hindlimb; the forelimb is especially short in contemporaneous diplodocoids.


title: Brachiosaurus

text: "Brachiosaurus" differed in its body proportions from the closely related "Giraffatitan". The trunk was about 25 to 30 percent longer, resulting in a dorsal vertebral column longer than the humerus. Only a single complete caudal (tail) vertebra has been discovered, but its great height suggests that the tail was larger than in "Giraffatitan". This vertebra had a much greater area for ligament attachment due to a broadened neural spine, indicating that the tail was also longer than in "Giraffatitan", possibly by 20 to 25percent. In 1988, paleontologist Gregory S. Paul suggested that the neck of "Brachiosaurus" was shorter than that of "Giraffatitan", but in 2009, paleontologist Mike P. Taylor pointed out that two cervical vertebrae likely belonging to "Brachiosaurus" had identical proportions. Unlike "Giraffatitan" and other sauropods, which had vertically oriented forelimbs, the arms of "Brachiosaurus" appear to have been slightly sprawled at the shoulder joints, as indicated by the sideward orientation of the joint surfaces of the coracoids. The humerus was less slender than that of "Giraffatitan", while the femur had similar proportions. This might indicate that the forelimbs of "Brachiosaurus" supported a greater fraction of the body weight than is the case for "Giraffatitan".


title: Brachiosaurus

text: Though the vertebral column of the trunk or torso is incompletely known, the back of "Brachiosaurus" most likely comprised twelve dorsal vertebrae; this can be inferred from the complete dorsal vertebral column preserved in an unnamed brachiosaurid specimen, BMNH R5937. Vertebrae of the front part of the dorsal column were slightly taller but much longer than those of the back part. This is in contrast to "Giraffatitan", where the vertebrae at the front part were much taller but only slightly longer. The centra (vertebral bodies), the lower part of the vertebrae, were more elongated and roughly circular in cross-section, while those of "Giraffatitan" were broader than tall. The foramina (small openings) on the sides of the centra, which allowed for the intrusion of air sacs, were larger than in "Giraffatitan". The diapophyses (large projections extending sideways from the neural arch of the vertebrae) were horizontal, while those of "Giraffatitan" were inclined upward. At their ends, these projections articulated with the ribs; the articular surface was not distinctly triangular as in "Giraffatitan". In side view, the upward-projecting neural spines stood vertically and were twice as wide at the base than at the top; those of "Giraffatitan" tilted backward and did not broaden at their base. When seen in front or back view, the neural spines widened toward their tops.


title: Brachiosaurus

text: In "Brachiosaurus", this widening occurred gradually, resulting in a paddle-like shape, while in "Giraffatitan" the widening occurred abruptly and only in the uppermost portion. At both their front and back sides, the neural spines featured large, triangular and rugose surfaces, which in "Giraffatitan" were semicircular and much smaller. The various vertebral processes were connected by thin sheets or ridges of bone, which are called "laminae". "Brachiosaurus" lacked postspinal laminae, which were present in "Giraffatitan", running down the back side of the neural spines. The spinodiapophyseal laminae, which stretched from the neural spines to the diapophyses, were conflated with the spinopostzygapophyseal laminae, which stretched between the neural spines and the articular processes at the back of the vertebrae, and therefore terminated at mid-height of the neural spines. In "Giraffatitan", both laminae were not conflated, and the spinodiapophyseal laminae reached up to the top of the neural spines. "Brachiosaurus" is further distinguished from "Giraffatitan" in lacking three details in the laminae of the dorsal vertebrae that are unique to the latter genus.


title: Brachiosaurus

text: Air sacs not only invaded the vertebrae but also the ribs. In "Brachiosaurus", the air sacs invaded through a small opening on the front side of the rib shafts, while in "Giraffatitan" openings were present on both the front and back sides of the tuberculum, a bony projection articulating with the diapophyses of the vertebrae. Paul, in 1988, stated that the ribs of "Brachiosaurus" were longer than in "Giraffatitan", which was questioned by Taylor in 2009. Behind the dorsal vertebral column, the sacrum consisted of five co-ossified sacral vertebrae. As in "Giraffatitan", the sacrum was proportionally broad and featured very short neural spines. Poor preservation of the sacral material in "Giraffatitan" precludes detailed comparisons between both genera. Of the tail, only the second caudal vertebra is well preserved.


title: Brachiosaurus

text: As in "Giraffatitan", this vertebra was slightly amphicoelous (concave on both ends), lacked openings on the sides, and had a short neural spine that was rectangular and tilted backward. In contrast to the second caudal vertebra of "Giraffatitan", that of "Brachiosaurus" had a proportionally taller neural arch, making the vertebra about thirty percent taller. The centrum lacked depressions on its sides, in contrast to "Giraffatitan". In front or back view, the neural spine broadened toward its tip to approximately three times its minimum width, but no broadening is apparent in "Giraffatitan". The neural spines were also inclined backward by about 30°, more than in "Giraffatitan" (20°). The caudal ribs projected laterally and were not tilted backward as in "Giraffatitan". The articular facets of the articular processes at the back of the vertebra were directed downward, while those of "Giraffatitan" faced more toward the sides. Besides the articular processes, the hyposphene-hypantrum articulation formed an additional articulation between vertebrae, making the vertebral column more rigid; in "Brachiosaurus", the hyposphene was much more pronounced than in "Giraffatitan".


title: Brachiosaurus

text: The coracoid was semicircular and taller than broad. Differences from "Giraffatitan" are related to its shape in side view, including the straighter suture with the scapula. Moreover, the articular surface that forms part of the shoulder joint was thicker and directed more sideward than in "Giraffatitan" and other sauropods, possibly indicating a more sprawled forelimb. The humerus, as preserved, measures in length, though part of its lower end was lost to erosion; its original length is estimated at . This bone was more slender in "Brachiosaurus" than in most other sauropods, measuring only in width at its narrowest part. It was, however, more robust than that of "Giraffatitan", being about ten percent broader at the upper and lower ends. At its upper end, it featured a low bulge visible in side view, which is absent in "Giraffatitan".


title: Brachiosaurus

text: Distinguishing features can also be found in the ilium of the pelvis. In "Brachiosaurus", the ischiadic peduncle, a downward projecting extension connecting to the ischium, reaches farther downward than in "Giraffatitan". While the latter genus had a sharp notch between the ischiadic peduncle and the back portion of the ilium, this notch is more rounded in "Brachiosaurus". On the upper surface of the hind part of the ilium, "Brachiosaurus" had a pronounced tubercle that is absent in other sauropods. Of the hindlimb, the femur was very similar to that of "Giraffatitan" although slightly more robust, and measured long. As in "Giraffatitan", it was strongly elliptical in cross-section, being more than twice as wide in front or back view than in side view. The fourth trochanter, a prominent bulge on the back side of the femoral shaft, was more prominent and located further downward. This bulge served as anchor point for the most important locomotory muscle, the caudofemoralis, which was situated in the tail and pulled the upper thigh backward when contracted. At the lower end of the femur, the pair of condyles did not extend backward as strongly as in "Giraffatitan"; the two condyles were similar in width in "Brachiosaurus" but unequal in "Giraffatitan".


title: Brachiosaurus

text: As reconstructed by Carpenter and Tidwell, the assigned Felch Quarry skull was about long from the occipital condyle at the back of the skull to the front of the premaxillae (the front bones of the upper jaw), making it the largest sauropod skull from the Morrison Formation. D'Emic and Carrano instead estimated the skull to have been long, and if proportionally similar to that of "Giraffatitan", about tall, and wide. Overall, the skull was tall as in "Giraffatitan", with a snout that was long (about 36 percent of the skull length according to Carpenter and Tidwell) in front of the nasal bar between the nostrilsypical of brachiosaurids. The snout was somewhat blunt when seen from above (as in "Giraffatitan"), and since it was set at an angle relative to the rest of the skull, gave the impression of pointing downward.


title: Brachiosaurus

text: The dorsal and lateral temporal fenestrae (openings at the upper rear and sides of the skull) were large, perhaps due to the force imparted there by the massive jaw adductor musculature. The frontal bones on top of the skull were short and wide (similar to "Giraffatitan"), fused and connected by a suture to the parietal bones, which were also fused together. The surface of the parietals between the dorsal fenestrae was wider than that of "Giraffatitan", but narrower than that of "Camarasaurus". The skull differed from that of "Giraffatitan" in its U-shaped (instead of W-shaped) suture between frontal and nasal bones, a shape which appears more pronounced by the frontal bones extending forward over the orbits (eye sockets). Similar to "Giraffatitan", the neck of the occipital condyle was very long.


title: Brachiosaurus

text: The premaxilla appears to have been longer than that of "Camarasaurus", sloping more gradually toward the nasal bar, which created the very long snout. "Brachiosaurus" had a long and deep maxilla (the main bone of the upper jaw), which was thick along the margin where the alveoli (tooth sockets) were placed, thinning upward. The interdental plates of the maxilla were thin, fused, porous, and triangular. There were triangular nutrient foramina between the plates, each containing the tip of an erupting tooth. The narial fossa (depression) in front of the bony nostril was long, relatively shallow, and less developed than that of "Giraffatitan". It contained a subnarial fenestra, which was much larger than those of "Giraffatitan" and "Camarasaurus". The dentaries (the bones of the lower jaws that contained the teeth) were robust, though less than in "Camarasaurus". The upper margin of the dentary was arched in profile, but not as much as in "Camarasaurus". The interdental plates of the dentary were somewhat oval, with diamond shaped openings between them. The dentary had a Meckelian groove that was open until below the ninth alveolus, continuing thereafter as a shallow trough.


title: Brachiosaurus

text: Each maxilla had space for fourteen or fifteen teeth, whereas "Giraffatitan" had eleven and "Camarasaurus" eight to ten. The maxillae contained replacement teeth that had rugose enamel, similar to "Camarasaurus", but lacked the small denticles (serrations) along the edges. Since the maxilla was wider than that of "Camarasaurus", "Brachiosaurus" would have had larger teeth. The replacement teeth in the premaxilla had crinkled enamel, and the most complete of these teeth did not have denticles. It was somewhat spatulate (spoon-shaped), and had a longitudinal ridge. Each dentary had space for about fourteen teeth. The maxillary tooth rows of "Brachiosaurus" and "Giraffatitan" ended well in front of the antorbital fenestra (the opening in front of the orbit), whereas they ended just in front of and below the fenestra in "Camarasaurus" and "Shunosaurus".


title: Brachiosaurus

text: Riggs, in his preliminary 1903 description of the not yet fully prepared holotype specimen, considered "Brachiosaurus" to be an obvious member of the Sauropoda. To determine the validity of the genus, he compared it to the previously named genera "Camarasaurus", "Apatosaurus", "Atlantosaurus", and "Amphicoelias", whose validity he questioned given the lack of overlapping fossil material. Because of the uncertain relationships of these genera, little could be said about the relationships of "Brachiosaurus" itself. In 1904, Riggs described the holotype material of "Brachiosaurus" in more detail, especially the vertebrae. He admitted that he originally had assumed a close affinity with "Camarasaurus", but now decided that "Brachiosaurus" was more closely related to "Haplocanthosaurus". Both genera shared a single line of neural spines on the back and had wide hips. Riggs considered the differences from other taxa significant enough to name a separate family, Brachiosauridae, of which "Brachiosaurus" is the namesake genus. According to Riggs, "Haplocanthosaurus" was the more primitive genus of the family while "Brachiosaurus" was a specialized form.


title: Brachiosaurus

text: When describing "Brachiosaurus brancai" and "B. fraasi" in 1914, Janensch observed that the unique elongation of the humerus was shared by all three "Brachiosaurus" species as well as the British "Pelorosaurus". He also noted this feature in "Cetiosaurus", where it was not as strongly pronounced as in "Brachiosaurus" and "Pelorosaurus". Janensch concluded that the four genera must have been closely related to each other, and in 1929 assigned them to a subfamily Brachiosaurinae within the family Bothrosauropodidae.


title: Brachiosaurus

text: During the twentieth century, several sauropods were assigned to Brachiosauridae, including "Astrodon", "Bothriospondylus", "Pelorosaurus", "Pleurocoelus", and "Ultrasauros". These assignments were often based on broad similarities rather than unambiguous synapomorphies, shared new traits, and most of these genera are currently regarded as dubious. In 1969, in a study by R.F. Kingham, "B. altithorax", "B. brancai" and "B. atalaiensis", along with many species now assigned to other genera, were placed in the genus "Astrodon", creating an "Astrodon altithorax". Kingham's views of brachiosaurid taxonomy have not been accepted by many other authors. Since the 1990s, computer-based cladistic analyses allow for postulating detailed hypotheses on the relationships between species, by calculating those trees that require the fewest evolutionary changes and thus are the most likely to be correct. Such cladistic analyses have cast doubt on the validity of the Brachiosauridae. In 1993, Leonardo Salgado suggested that they were an unnatural group into which all kinds of unrelated sauropods had been combined. In 1997, he published an analysis in which species traditionally considered brachiosaurids were subsequent offshoots of the stem of a larger grouping, the Titanosauriformes, and not a separate branch of their own. This study also pointed out that "B. altithorax" and "B. brancai" did not have any synapomorphies, so that there was no evidence to assume they were particularly closely related.


title: Brachiosaurus

text: Many cladistic analyses have since suggested that at least some genera can be assigned to the Brachiosauridae, and that this group is a basal branch within the Titanosauriformes. The exact status of each potential brachiosaurid varies from study to study. For example, a 2010 study by Chure and colleagues recognized "Abydosaurus" as a brachiosaurid together with "Brachiosaurus", which in this study included "B. brancai". In 2009, Taylor noted multiple anatomical differences between the two "Brachiosaurus" species, and consequently moved "B. brancai" into its own genus, "Giraffatitan". In contrast to earlier studies, Taylor treated both genera as distinct units in a cladistic analysis, finding them to be sister groups. Another 2010 analysis focusing on possible Asian brachiosaurid material found a clade including "Abydosaurus", "Brachiosaurus", "Cedarosaurus", "Giraffatitan", and "Paluxysaurus", but not "Qiaowanlong", the putative Asian brachiosaurid. Several subsequent analyses have found "Brachiosaurus" and "Giraffatitan" not to be sister groups, but instead located at different positions on the evolutionary tree. A 2012 study by D'Emic placed "Giraffatitan" in a more basal position, in an earlier branch, than "Brachiosaurus", while a 2013 study by Philip Mannion and colleagues had it the other way around.


title: Brachiosaurus

text: Cladistic analyses also allow scientists to determine which new traits the members of a group have in common, their synapomorphies. According to the 2009 study by Taylor, "B. altithorax" shares with other brachiosaurids the classic trait of having an upper arm bone that is at least nearly as long as the femur (ratio of humerus length to femur length of at least 0.9). Another shared character is the very flattened femur shaft, its transverse width being at least 1.85 times the width measured from front to rear.


title: Brachiosaurus

text: It was believed throughout the nineteenth and early twentieth centuries that sauropods like "Brachiosaurus" were too massive to support their own weight on dry land, and instead lived partly submerged in water. Riggs, affirming observations by John Bell Hatcher, was the first to defend in length that most sauropods were fully terrestrial animals in his 1904 account on "Brachiosaurus", pointing out that their hollow vertebrae have no analogue in living aquatic or semiaquatic animals, and their long limbs and compact feet indicate specialization for terrestrial locomotion. "Brachiosaurus" would have been better adapted than other sauropods to a fully terrestrial lifestyle through its slender limbs, high chest, wide hips, high ilia and short tail. In its dorsal vertebrae the zygapophyses were very reduced while the hyposphene-hypanthrum complex was extremely developed, resulting in a stiff torso incapable of bending sideways. The body was fit for only quadrupedal movement on land. Though Riggs's ideas were gradually forgotten during the first half of the twentieth century, the notion of sauropods as terrestrial animals has gained support since the 1950s, and is now universally accepted among paleontologists. In 1990 the paleontologist Stephen Czerkas stated that "Brachiosaurus" could have entered water occasionally to cool off (thermoregulate).


title: Brachiosaurus

text: Ongoing debate revolves around the neck posture of brachiosaurids, with estimates ranging from near-vertical to horizontal orientations. The idea of near-vertical postures in sauropods in general was popular until 1999, when Stevens and Parrish argued that the sauropod neck was not flexible enough to be held in an upright, S-curved pose, and instead was held horizontally. Reflecting this research, various newspapers ran stories criticizing the Field Museum "Brachiosaurus" mount for having an upward curving neck. Museum paleontologists Olivier Rieppel and Christopher Brochu defended the posture in 1999, noting the long forelimbs and upward sloping backbone. They also stated that the most developed neural spines for muscle attachment being positioned in the region of the shoulder girdle would have permitted the neck to be raised in a giraffe-like posture. Furthermore, such a pose would have required less energy than lowering its neck, and the inter-vertebral discs would not have been able to counter the pressure caused by a lowered head for extended periods of time (though lowering its neck to drink must have been possible). Some recent studies also advocated a more upward directed neck. Christian and Dzemski (2007) estimated that the middle part of the neck in "Giraffatitan" was inclined by sixty to seventy degrees; a horizontal posture could be maintained only for short periods of time.


title: Brachiosaurus

text: With their heads held high above the heart, brachiosaurids would have had stressed cardiovascular systems. It is estimated that the heart of "Brachiosaurus" would have to pump double the blood pressure of a giraffe to reach the brain, and possibly weighed . The distance between head and heart would have been reduced by the S-curvature of the neck by more than in comparison to a totally vertical posture. The neck may also have been lowered during locomotion by twenty degrees. In studying the inner ear of "Giraffatitan", Gunga & Kirsch (2001) concluded that brachiosaurids would have moved their necks in lateral directions more often than in dorsal-ventral directions while feeding.


title: Brachiosaurus

text: "Brachiosaurus" is thought to have been a high browser, feeding on foliage well above the ground. Even if it did not hold its neck near vertical, and instead had a less inclined neck, its head height may still have been over above the ground. It probably fed mostly on foliage above . This does not preclude the possibility that it also fed lower at times, between up. Its diet likely consisted of ginkgos, conifers, tree ferns, and large cycads, with intake estimated at of plant matter daily in a 2007 study. Brachiosaurid feeding involved simple up-and-down jaw motion. As in other sauropods, animals would have swallowed plant matter without further oral processing, and relied on hindgut fermentation for food processing. The teeth were somewhat spoon-shaped and chisel-like. Such teeth are optimized for non-selective nipping, and the relatively broad jaws could crop large amounts of plant material. Even if a "Brachiosaurus" of forty tonnes would have needed half a tonne of fodder, its dietary needs could have been met by a normal cropping action of the head. If it fed sixteen hours per day, biting off between a tenth and two-thirds of a kilogram, taking between one and six bites per minute, its daily food intake would have equaled roughly 1.5 percent of its body mass, comparable to the requirement of a modern elephant.


title: Brachiosaurus

text: As "Brachiosaurus" shared its habitat, the Morrison, with many other sauropod species, its specialization for feeding at greater heights would have been part of a system of niche partitioning, the various taxa thus avoiding direct competition with each other. A typical food tree might have resembled "Sequoiadendron". The fact that such tall conifers were relatively rare in the Morrison might explain why "Brachiosaurus" was much less common in its ecosystem than the related "Giraffatitan", which seems to have been one of the most abundant sauropods in the Tendaguru. "Brachiosaurus", with its shorter arms and lower shoulders, was not as well-adapted to high-browsing as "Giraffatitan".


title: Brachiosaurus

text: It has been suggested that "Brachiosaurus" could rear on its hind legs to feed, using its tail for extra ground support. A detailed physical modelling-based analysis of sauropod rearing capabilities by Heinrich Mallison showed that while many sauropods could rear, the unusual body shape and limb length ratio of brachiosaurids made them exceptionally ill-suited for rearing. The forward position of its center of mass would have led to problems with stability, and required unreasonably large forces in the hips to obtain an upright posture. "Brachiosaurus" would also have gained only 33 percent more feeding height, compared to other sauropods, for which rearing may have tripled the feeding height. A bipedal stance might have been adopted by "Brachiosaurus" in exceptional situations, like male dominance fights.


title: Brachiosaurus

text: The downward mobility of the neck of "Brachiosaurus" would have allowed it to reach open water at the level of its feet, while standing upright. Modern giraffes spread their forelimbs to lower the mouth in a relatively horizontal position, to more easily gulp down the water. It is unlikely that "Brachiosaurus" could have attained a stable posture this way, forcing the animal to plunge the snout almost vertically into the surface of a lake or stream. This would have submerged its fleshy nostrils if they were located at the tip of the snout as Witmer hypothesized. Hallett and Wedel therefore in 2016 rejected his interpretation and suggested that they were in fact placed at the top of the head, above the bony nostrils, as traditionally thought. The nostrils might have evolved their retracted position to allow the animal to breathe while drinking.


title: Brachiosaurus

text: The bony nasal openings of neosauropods like "Brachiosaurus" were large and placed on the top of their skulls. Traditionally, the fleshy nostrils of sauropods were thought to have been placed likewise on top of the head, roughly at the rear of the bony nostril opening, because these animals were erroneously thought to have been amphibious, using their large nasal openings as snorkels when submerged. The American paleontologist Lawrence M. Witmer rejected this reconstruction in 2001, pointing out that all living vertebrate land animals have their external fleshy nostrils placed at the front of the bony nostril. The fleshy nostrils of such sauropods would have been placed in an even more forward position, at the front of the narial fossa, the depression which extended far in front of the bony nostril toward the snout tip.


title: Brachiosaurus

text: Czerkas speculated on the function of the peculiar brachiosaurid nose, and pointed out that there was no conclusive way to determine where the nostrils where located, unless a head with skin impressions was found. He suggested that the expanded nasal opening would have made room for tissue related to the animal's ability to smell, which would have helped smell proper vegetation. He also noted that in modern reptiles, the presence of bulbous, enlarged, and uplifted nasal bones can be correlated with fleshy horns and knobby protuberances, and that "Brachiosaurus" and other sauropods with large noses could have had ornamental nasal crests.


title: Brachiosaurus

text: It has been proposed that sauropods, including "Brachiosaurus", may have had proboscises (trunks) based on the position of the bony narial orifice, to increase their upward reach. Fabien Knoll and colleagues disputed this for "Diplodocus" and "Camarasaurus" in 2006, finding that the opening for the facial nerve in the braincase was small. The facial nerve was thus not enlarged as in elephants, where it is involved in operating the sophisticated musculature of the proboscis. However, Knoll and colleagues also noted that the facial nerve for "Giraffatitan" was larger, and could therefore not discard the possibility of a proboscis in this genus.


title: Brachiosaurus

text: Like other sauropods, "Brachiosaurus" was probably homeothermic (maintaining a stable internal temperature) and endothermic (controlling body temperature through internal means) at least while growing, meaning that it could actively control its body temperature ("warm-blooded"), producing the necessary heat through a high basic metabolic rate of its cells. Russel (1989) used "Brachiosaurus" as an example of a dinosaur for which endothermy is unlikely, because of the combination of great size (leading to overheating) and great caloric needs to fuel endothermy. Sander (2010) found that these calculations were based on incorrect body mass estimates and faulty assumptions on the available cooling surfaces, as the presence of large air sacs was unknown at the time of the study. These inaccuracies resulted in the overestimation of heat production and the underestimation of heat loss. The large nasal arch has been postulated as an adaptation for cooling the brain, as a surface for evaporative cooling of the blood.


title: Brachiosaurus

text: The respiration system of sauropods, like that of birds, made use of air sacs. There was not a bidirectional airflow as with mammals, in which the lungs function as bellows, first inhaling and then exhaling air. Instead the air was sucked from the trachea into an abdominal air sac in the belly which then pumped it forward through the parabranchi, air loops, of the stiff lung. Valves prevented the air from flowing backward when the abdominal air sac filled itself again; at the same time a cervical air sac at the neck base sucked out the spent air from the lung. Both air sacs contracted simultaneously to pump the used air out of the trachea. This procedure guaranteed a unidirectional airflow, the air always moving in a single forward direction in the lung itself. This significantly improved the oxygen intake and the release of carbon dioxide. Not only was dead air removed quickly but also the blood flow in the lung was counterdirectional in relation to the airflow, leading to a far more effective gas exchange.


title: Brachiosaurus

text: In sauropods, the air sacs did not simply function as an aid for respiration; by means of air channels they were connected to much of the skeleton. These branches, the "diverticula", via pneumatic openings invaded many bones and strongly hollowed them out. It is not entirely clear what the evolutionary benefit of this phenomenon was but in any case it considerably lightened the skeleton. They might also have removed excess heat to aid thermoregulation.


title: Brachiosaurus

text: In 2016, Mark Hallett and Mathew Wedel for the first time reconstructed the entire air sac system of a sauropod, using "B. altithorax" as an example of how such a structure might have been formed. In their reconstruction a large abdominal air sac was located between the pelvis and the outer lung side. As with birds, three smaller sacs assisted the pumping process from the underside of the breast cavity: at the rear the posterior thoracic air sac, in the middle the anterior thoracic air sac and in front the clavicular air sac, in that order gradually diminishing in size. The cervical air sac was positioned under the shoulder blade, on top of the front lung. The air sacs were via tubes connected with the vertebrae. Diverticula filled the various fossae and pleurocoels that formed depressions in the vertebral bone walls. These were again connected with inflexible air cells inside the bones.


title: Brachiosaurus

text: The ontogeny of "Brachiosaurus" has been reconstructed by Carballido and colleagues in 2012 based on Toni (SMA 0009), a postcranial skeleton of a young juvenile with an estimated total body length of just . This skeleton shares some unique traits with the "B. altithorax" holotype, indicating it is referable to this species. These commonalities include an elevation on the rear blade of the ilium; the lack of a postspinal lamina; vertical neural spines on the back; an ilium with a subtle notch between the appendage for the ischium and the rear blade; and the lack of a side bulge on the upper thighbone. There are also differences; these might indicate that the juvenile is not a "B. altithorax" individual after all, but belongs to a new species. Alternatively, they might be explained as juvenile traits that would have changed when the animal matured.


title: Brachiosaurus

text: Such ontogenetic changes are especially to be expected in the proportions of an organism. The middle neck vertebrae of SMA 0009 are remarkably short for a sauropod, being just 1.8 times longer than high, compared with a ratio of 4.5 in "Giraffatitan". This suggests that the necks of brachiosaurids became proportionally much longer while their backs, to the contrary, experienced relative negative growth. The humerus of SMA 0009 is relatively robust: it is more slender than that of most basal titanosauriforms but thicker than the upper arm bone of "B. altithorax". This suggests that it was already lengthening in an early juvenile stage and became even more slender during growth. This is in contrast to diplodocoids and basal macronarians, whose slender humeri are not due to such allometric growth. "Brachiosaurus" also appears to have experienced an elongation of the metacarpals, which in juveniles were shorter compared to the length of the radius; SMA 0009 had a ratio of just 0.33, the lowest known in the entire Neosauropoda.


title: Brachiosaurus

text: Another plausible ontogenetic change is the increased pneumatization of the vertebrae. During growth, the diverticula of the air sacs invaded the bones and hollowed them out. SMA 0009 already has pleurocoels, pneumatic excavations, at the sides of its neck vertebrae. These are divided by a ridge but are otherwise still very simple in structure, compared with the extremely complex ridge systems typically shown by adult derived sauropods. Its dorsal vertebrae still completely lack these.


title: Brachiosaurus

text: Two traits are not so obviously linked to ontogeny. The neural spines of the rear dorsal vertebrae and the front sacral vertebrae are extremely compressed transversely, being eight times longer from front to rear than wide from side to side. The spinodiapophyseal lamina or "SPOL", the ridge normally running from each side of the neural spine toward each diapophysis, the transverse process bearing the contact facet for the upper rib head, is totally lacking. Both traits could be autapomorphies, unique derived characters proving that SMA 0009 represents a distinct species, but there are indications that these traits are growth-related as well. Of the basal sauropod "Tazoudasaurus" a young juvenile is known that also lacks the spinodiapophyseal lamina, whereas the adult form has an incipient ridge. Furthermore, a very young juvenile of "Europasaurus" had a weak SPOL but it is well developed in mature individuals. These two cases represent the only finds in which the condition can be checked; they suggest that the SPOL developed during growth. As this very ridge widens the neural spine, its transverse compression is not an independent trait and the development of the SPOL plausibly precedes the thickening of the neural spine with more mature animals.


title: Brachiosaurus

text: Sauropods were likely able to sexually reproduce before they attained their maximum individual size. The maturation rate differed between species. Its bone structure indicates that "Brachiosaurus" was able to reproduce when it reached forty percent of its maximal size.


title: Brachiosaurus

text: "Brachiosaurus" is known only from the Morrison Formation of western North America (following the reassignment of the African species). The Morrison Formation is interpreted as a semiarid environment with distinct wet and dry seasons, and flat floodplains. Several other sauropod genera were present in the Morrison Formation, with differing body proportions and feeding adaptations. Among these were "Apatosaurus", "Barosaurus", "Camarasaurus", "Diplodocus", "Haplocanthosaurus", and "Supersaurus". "Brachiosaurus" was one of the less abundant Morrison Formation sauropods. In a 2003 survey of more than two hundred fossil localities, John Foster reported 12 specimens of the genus, comparable to "Barosaurus" (13) and "Haplocanthosaurus" (12), but far fewer than "Apatosaurus" (112), "Camarasaurus" (179), and "Diplodocus" (98). "Brachiosaurus" fossils are found only in the lower-middle part of the expansive Morrison Formation (stratigraphic zones 2–4), dated to about 154to 153million years ago, unlike many other types of sauropod which have been found throughout the formation. If the large foot reported from Wyoming (the northernmost occurrence of a brachiosaurid in North America) did belong to "Brachiosaurus", the genus would have covered a wide range of latitudes. Brachiosaurids could process tough vegetation with their broad-crowned teeth, and might therefore have covered a wider range of vegetational zones than for example diplodocids. Camarasaurids, which were similar in tooth morphology to brachiosaurids, were also widespread and are known to have migrated seasonally, so this might have also been true for brachiosaurids.


title: Brachiosaurus

text: Other dinosaurs known from the Morrison Formation include the predatory theropods "Koparion", "Stokesosaurus", "Ornitholestes", "Ceratosaurus", "Allosaurus", "Torvosaurus", and "Saurophaganax", as well as the herbivorous ornithischians "Camptosaurus", "Dryosaurus", "Othnielia", "Gargoyleosaurus" and "Stegosaurus". "Allosaurus" accounted for 70 to 75 percent of theropod specimens and was at the top trophic level of the Morrison food web. "Ceratosaurus" might have specialized in attacking large sauropods, including smaller individuals of "Brachiosaurus". Other vertebrates that shared this paleoenvironment included ray-finned fishes, frogs, salamanders, turtles like "Dorsetochelys", sphenodonts, lizards, terrestrial and aquatic crocodylomorphans such as "Hoplosuchus", and several species of pterosaur like "Harpactognathus" and "Mesadactylus". Shells of bivalves and aquatic snails are also common. The flora of the period has been revealed by fossils of green algae, fungi, mosses, horsetails, cycads, ginkgoes, and several families of conifers. Vegetation varied from river-lining forests in otherwise treeless settings (gallery forests) with tree ferns, and ferns, to fern savannas with occasional trees such as the "Araucaria"-like conifer "Brachyphyllum".


title: Brachiosaurus

text: Riggs in the first instance tried to limit public awareness of the find. When reading a lecture to the inhabitants of Grand Junction, illustrated by lantern slides, on July 27, 1901, he explained the general evolution of dinosaurs and the exploration methods of museum field crews but did not mention that he had just found a spectacular specimen. He feared that teams of other institutions might soon learn of the discovery and take away the best of the remaining fossils. A week later, his host Bradbury published an article in the local "Grand Junction News" announcing the find of one of the largest dinosaurs ever. On August 14, "The New York Times" brought the story. At the time sauropod dinosaurs appealed to the public because of their great size, often exaggerated by sensationalist newspapers. Riggs in his publications played into this by emphasizing the enormous magnitude of "Brachiosaurus".


title: Brachiosaurus

text: "Brachiosaurus" has been called one of the most iconic dinosaurs, but most popular depictions are based on the African species "B. brancai" which has since been moved to its own genus, "Giraffatitan". A main belt asteroid, , was named 9954 Brachiosaurus in honor of the genus in 1991. "Brachiosaurus" was featured in the 1993 movie "Jurassic Park", as the first computer generated dinosaur shown. These effects were considered ground-breaking at the time, and the awe of the movie's characters upon seeing the dinosaur for the first time was mirrored by audiences. The movements of the movie's "Brachiosaurus" were based on the gait of a giraffe combined with the mass of an elephant. A scene later in the movie used an animatronic head and neck, for when a "Brachiosaurus" interacts with human characters. The digital model of "Brachiosaurus" used in "Jurassic Park" later became the starting point for the ronto models in the 1997 special edition of the film "".


title: Arian Moayed

text: Arian Moayed (, born April 15, 1980) is an Iranian-American actor, writer, and director. Moayed received a Tony Award nomination for Best Featured Actor in a Play for his performance in "Bengal Tiger at the Baghdad Zoo" and also starred in the Tony Award-winning "The Humans." Moayed gained prominence for his role as Stewy Hosseini in HBO's "Succession" and Todd Spodek in Netflix’s "Inventing Anna", as well as his portrayal of Agent P. Cleary in the Marvel Cinematic Universe film "" and Disney+ series "Ms. Marvel".


title: Arian Moayed

text: Moayed was born in Tehran, Iran. His father is a banker by profession. His parents emigrated from Iran in 1986. The family settled in Glenview, Illinois, a suburb of Chicago, when Moayed was five years old. He speaks Persian.


title: Arian Moayed

text: Moayed graduated from Glenbrook South High School in 1998. He then received a bachelor's degree from Indiana University in 2002. During college, he appeared in plays by Samuel Beckett, Carlo Goldoni and William Shakespeare.


title: Arian Moayed

text: Moayed moved to Manhattan after college. In 2002, Moayed and director Tom Ridgely, who was Moayed's roommate at Indiana University, co-founded the Waterwell, a theater, education and film company based out of New York. Waterwell has produced more than a dozen stage productions and shows since the theater was established.


title: Arian Moayed

text: He portrayed the character of Musa in Rajiv Joseph's "Bengal Tiger at the Baghdad Zoo," where Moayed appeared opposite Robin Williams. Moayed received a Tony Award nomination for Best Featured Actor in a Play for his portrayal of Musa at the 65th Tony Awards in 2011. He also received a Drama League Award nomination and received a Theater World Award.


title: Arian Moayed

text: As a writer/director, Moayed wrote and directed his first short "Overdue", which premiered at the Cinequest Film Festival and was released on The Business of Being Born website. His second film, "Day Ten," stars Omar Metwally and is about the days after September 11, 2001, premiering at the Tribeca Film Festival.


title: Arian Moayed

text: In 2016, he starred as Babur, one of two characters in "Guards at the Taj", a play written by Rajiv Joseph, alongside Omar Metwally as Humayun. For his performance, he received a 2016 Obie Award presented by the American Theatre Wing and The Village Voice.


title: Arian Moayed

text: In 2017, Moayed starred as Richard Saad in Stephen Karam's "The Humans", which performed at the Roundabout Theater off-Broadway, Helen Hayes Theater and Gerald Schoenfeld Theater on Broadway as well as the Hampstead Theater in London, United Kingdom. The production was directed by Joe Mantello and produced by Scott Rudin and garnered Moayed a Drama Desk Award, Drama League Award and a Tony Award for Best Play.


title: Arian Moayed

text: Waterwell focuses on socially conscious and civic minded approach to theater, education, and film. Waterwell mission states, "empower its audience to change their lives and the world in which they live."


title: Arian Moayed

text: As the co-founder of Waterwell, Moayed has helped devise over a dozen original productions including most recently a dual-language "Hamlet" (played the title role) to critical acclaim. Also with Waterwell, Moayed produced a forgotten war musical called "Blueprint Specials", produced on board of the Intrepid with a cast of veterans.


title: Arian Moayed

text: With Waterwell Films, he has written and directed the Emmy nominated and Webby nominated "The Accidental Wolf", a premium short form series starring Kelli O'Hara, Laurie Metcalf, Denis O'Hare, Brandon Dirden, Ben McKenzie, Judith Ivey, Reed Birney, Marsha Stephanie Blake and a cast of over 70 Tony nominations on its own platform, theaccidentalwolf.com.


title: Radiocarbon dating

text: Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.


title: Radiocarbon dating

text: The method was developed in the late 1940s at the University of Chicago by Willard Libby. It is based on the fact that radiocarbon () is constantly being created in the Earth's atmosphere by the interaction of cosmic rays with atmospheric nitrogen. The resulting combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire by eating the plants. When the animal or plant dies, it stops exchanging carbon with its environment, and thereafter the amount of it contains begins to decrease as the undergoes radioactive decay. Measuring the amount of in a sample from a dead plant or animal, such as a piece of wood or a fragment of bone, provides information that can be used to calculate when the animal or plant died. The older a sample is, the less there is to be detected, and because the half-life of (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to approximately 50,000 years ago, although special preparation methods occasionally make accurate analysis of older samples possible. Libby received the Nobel Prize in Chemistry for his work in 1960.


title: Radiocarbon dating

text: Research has been ongoing since the 1960s to determine what the proportion of in the atmosphere has been over the past fifty thousand years. The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age. Other corrections must be made to account for the proportion of in different types of organisms (fractionation), and the varying levels of throughout the biosphere (reservoir effects). Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s. Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its to decay below detectable levels, fossil fuels contain almost no . As a result, beginning in the late 19th century, there was a noticeable drop in the proportion of as the carbon dioxide generated from burning fossil fuels began to accumulate in the atmosphere. Conversely, nuclear testing increased the amount of in the atmosphere, which reached a maximum in about 1965 of almost double the amount present in the atmosphere prior to nuclear testing.


title: Radiocarbon dating

text: Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying atoms in a sample. More recently, accelerator mass spectrometry has become the method of choice; it counts all the atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly. The development of radiocarbon dating has had a profound impact on archaeology. In addition to permitting more accurate dating within archaeological sites than previous methods, it allows comparison of dates of events across great distances. Histories of archaeology often refer to its impact as the "radiocarbon revolution". Radiocarbon dating has allowed key transitions in prehistory to be dated, such as the end of the last ice age, and the beginning of the Neolithic and Bronze Age in different regions.


title: Radiocarbon dating

text: In 1939, Martin Kamen and Samuel Ruben of the Radiation Laboratory at Berkeley began experiments to determine if any of the elements common in organic matter had isotopes with half-lives long enough to be of value in biomedical research. They synthesized using the laboratory's cyclotron accelerator and soon discovered that the atom's half-life was far longer than had been previously thought. This was followed by a prediction by Serge A. Korff, then employed at the Franklin Institute in Philadelphia, that the interaction of thermal neutrons with in the upper atmosphere would create . It had previously been thought that would be more likely to be created by deuterons interacting with . At some time during World War II, Willard Libby, who was then at Berkeley, learned of Korff's research and conceived the idea that it might be possible to use radiocarbon for dating.


title: Radiocarbon dating

text: In 1945, Libby moved to the University of Chicago, where he began his work on radiocarbon dating. He published a paper in 1946 in which he proposed that the carbon in living matter might include as well as non-radioactive carbon. Libby and several collaborators proceeded to experiment with methane collected from sewage works in Baltimore, and after isotopically enriching their samples they were able to demonstrate that they contained . By contrast, methane created from petroleum showed no radiocarbon activity because of its age. The results were summarized in a paper in "Science" in 1947, in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin.


title: Radiocarbon dating

text: Libby and James Arnold proceeded to test the radiocarbon dating theory by analyzing samples with known ages. For example, two samples taken from the tombs of two Egyptian kings, Zoser and Sneferu, independently dated to 2625 BC plus or minus 75 years, were dated by radiocarbon measurement to an average of 2800 BC plus or minus 250 years. These results were published in "Science" in December 1949. Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide. In 1960, Libby was awarded the Nobel Prize in Chemistry for this work.


title: Radiocarbon dating

text: In nature, carbon exists as three isotopes, two stable, nonradioactive: carbon-12 (), and carbon-13 (), and radioactive carbon-14 (), also known as "radiocarbon". The half-life of (the time it takes for half of a given amount of to decay) is about 5,730 years, so its concentration in the atmosphere might be expected to decrease over thousands of years, but is constantly being produced in the lower stratosphere and upper troposphere, primarily by galactic cosmic rays, and to a lesser degree by solar cosmic rays. These cosmic rays generate neutrons as they travel through the atmosphere which can strike nitrogen-14 () atoms and turn them into . The following nuclear reaction is the main pathway by which is created:


title: Radiocarbon dating

text: Once produced, the quickly combines with the oxygen (O) in the atmosphere to form first carbon monoxide (), and ultimately carbon dioxide ().


title: Radiocarbon dating

text: Carbon dioxide produced in this way diffuses in the atmosphere, is dissolved in the ocean, and is taken up by plants via photosynthesis. Animals eat the plants, and ultimately the radiocarbon is distributed throughout the biosphere. The ratio of to is approximately 1.25 parts of to 10 parts of . In addition, about 1% of the carbon atoms are of the stable isotope .


title: Radiocarbon dating

text: By emitting a beta particle (an electron, e) and an electron antineutrino (), one of the neutrons in the nucleus changes to a proton and the nucleus reverts to the stable (non-radioactive) isotope .


title: Radiocarbon dating

text: During its life, a plant or animal is in equilibrium with its surroundings by exchanging carbon either with the atmosphere or through its diet. It will, therefore, have the same proportion of as the atmosphere, or in the case of marine animals or plants, with the ocean. Once it dies, it ceases to acquire , but the within its biological material at that time will continue to decay, and so the ratio of to in its remains will gradually decrease. Because decays at a known rate, the proportion of radiocarbon can be used to determine how long it has been since a given sample stopped exchanging carbon – the older the sample, the less will be left.


title: Radiocarbon dating

text: where "N" is the number of atoms of the isotope in the original sample (at time "t" = 0, when the organism from which the sample was taken died), and "N" is the number of atoms left after time "t". "λ" is a constant that depends on the particular isotope; for a given isotope it is equal to the reciprocal of the mean-life – i.e. the average or expected time a given atom will survive before undergoing radioactive decay. The mean-life, denoted by "τ", of is 8,267 years, so the equation above can be rewritten as:


title: Radiocarbon dating

text: The sample is assumed to have originally had the same / ratio as the ratio in the atmosphere, and since the size of the sample is known, the total number of atoms in the sample can be calculated, yielding "N", the number of atoms in the original sample. Measurement of "N", the number of atoms currently in the sample, allows the calculation of "t", the age of the sample, using the equation above.


title: Radiocarbon dating

text: The half-life of a radioactive isotope (usually denoted by t) is a more familiar concept than the mean-life, so although the equations above are expressed in terms of the mean-life, it is more usual to quote the value of 's half-life than its mean-life. The currently accepted value for the half-life of is 5,700 ± 30 years. This means that after 5,700 years, only half of the initial will remain; a quarter will remain after 11,400 years; an eighth after 17,100 years; and so on.