A paradox is a statement that apparently contradicts itself and yet might be true (or wrong at the same time). Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.
Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, are not yet resolved.
Examples outside logic include the Ship of Theseus from philosophy (questioning whether a ship repaired over time by replacing each of its wooden parts would remain the same ship). Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.
Paradox (1882–1890) was a British Thoroughbred racehorse and sire. In a career that lasted from October 1884 until October 1885 he ran eight times and won six races. Despite running only twice in 1884, he proved himself to be one of the best two-year-olds of his generation by winning the Dewhurst Plate. In the following year he won five of his six races including the 2,000 Guineas, the Grand Prix de Paris, the Sussex Stakes and the Champion Stakes. His only defeat came when he was narrowly beaten by Melton in the Epsom Derby.
The final phase of the colt's racing career was marked by controversy and recrimination following his withdrawal from the Cambridgeshire Handicap in the autumn of 1885 and he was retired from racing in 1886. Paradox had little opportunity to establish himself at stud, dying in 1890 at the age of eight.
Paradox was a strongly-built bay horse bred by the Graham brothers at the Yardley Stud near Birmingham. He was sired by the 2,000 Guineas runner-up Sterling out of Casuistry, an undistinguished racehorse who had been sold cheaply at the end of her racing career by Lord Rosebery. Casuistry became an important broodmare, being the direct female ancestor of notable thoroughbreds such as Humorist, Royal Palace and Spend a Buck. As a yearling Paradox was bought for 700 guineas by the trainer John Porter on behalf of his associate, Captain Bowling. Porter trained the colt at his stable at Kingsclere.
Paradox is the fourth studio album released by the Danish progressive metal band Royal Hunt. This is a concept album, with lyrics inspired by religion and divinity.
All songs written by André Andersen except where noted.
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Activin receptor type-1B is a protein that in humans is encoded by the ACVR1B gene.
ACVR1B or ALK-4 acts as a transducer of activin or activin like ligands (e.g., inhibin) signals. Activin binds to either ACVR2A or ACVR2B and then forms a complex with ACVR1B. These go on to recruit the R-SMADs SMAD2 or SMAD3. ACVR1B also transduces signals of nodal, GDF-1, and Vg1; however, unlike activin, they require other coreceptor molecules such as the protein Cripto.
Activins are dimeric growth and differentiation factors which belong to the transforming growth factor-beta (TGF-beta) superfamily of structurally related signaling proteins. Activins signal through a heteromeric complex of receptor serine kinases which include at least two type I (I and IB) and two type II (II and IIB) receptors. These receptors are all transmembrane proteins, composed of a ligand-binding extracellular domain with a cysteine-rich region, a transmembrane domain, and a cytoplasmic domain with predicted serine/threonine specificity. Type I receptors are essential for signaling, and type II receptors are required for binding ligands and for expression of type I receptors. Type I and II receptors form a stable complex after ligand binding, resulting in phosphorylation of type I receptors by type II receptors. This gene encodes activin A type IB receptor, composed of 11 exons. Alternative splicing and alternative polyadenylation result in 3 fully described transcript variants. The mRNA expression of variants 1, 2, and 3 is confirmed, and a potential fourth variant contains an alternative exon 8 and lacks exons 9 through 11, but its mRNA expression has not been confirmed.
Transforming growth factor, beta receptor I (activin A receptor type II-like kinase, 53kDa) is a TGF beta receptor. TGFBR1 is its human gene.
The protein encoded by this gene forms a heteromeric complex with type II TGF-β receptors when bound to TGF-β, transducing the TGF-β signal from the cell surface to the cytoplasm. The encoded protein is a serine/threonine protein kinase. Mutations in this gene have been associated with Loeys–Dietz aortic aneurysm syndrome (LDS, LDAS).
TGF beta receptor 1 has been shown to interact with: