1.
DNA sequencing
–
DNA sequencing is the process of determining the precise order of nucleotides within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases—adenine, guanine, cytosine, the advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. The first DNA sequences were obtained in the early 1970s by academic researchers using laborious methods based on two-dimensional chromatography, following the development of fluorescence-based sequencing methods with a DNA sequencer, DNA sequencing has become easier and orders of magnitude faster. DNA sequencing may be used to determine the sequence of genes, larger genetic regions, full chromosomes or entire genomes. DNA sequencing is also the most efficient way to sequence RNA or proteins, in fact, DNA sequencing has become a key technology in many areas of biology and other sciences such as medicine, forensics, or anthropology. Sequencing is used in biology to study genomes and the proteins they encode. Information obtained using sequencing allows researchers to identify changes in genes, associations with diseases and phenotypes, the field of metagenomics involves identification of organisms present in a body of water, sewage, dirt, debris filtered from the air, or swab samples from organisms. Knowing which organisms are present in an environment is critical to research in ecology, epidemiology, microbiology. Sequencing enables researchers to determine which types of microbes may be present in a microbiome, medical technicians may sequence genes from patients to determine if there is risk of genetic diseases. This is a form of testing, though some genetic tests may not involve DNA sequencing. DNA sequencing may be used along with DNA profiling methods for forensic identification, the canonical structure of DNA has four bases, thymine, adenine, cytosine, and guanine. DNA sequencing is the determination of the order of these bases in a molecule of DNA. However, there are other bases that may be present in a molecule. In some viruses, cytosine may be replaced by hydroxy methyl or hydroxy methyl glucose cytosine, in mammalian DNA, variant bases with methyl groups or phosphosulfate may be found. Depending on the technique, a particular modification, e. g. the 5mC common in humans. This situation changed after 1944 as a result of experiments by Oswald Avery, Colin MacLeod. This was the first time that DNA was shown capable of transforming the properties of cells, in 1953, James Watson and Francis Crick put forward their double-helix model of DNA, based on crystallized X-ray structures being studied by Rosalind Franklin. According to the model, DNA is composed of two strands of nucleotides coiled around each other, linked together by bonds and running in opposite directions
2.
Convergent evolution
–
Convergent evolution is the independent evolution of similar features in species of different lineages. Convergent evolution creates analogous structures that have similar form or function but were not present in the last common ancestor of those groups, the cladistic term for the same phenomenon is homoplasy. The recurrent evolution of flight is an example, as flying insects, birds. Functionally similar features that have arisen through convergent evolution are analogous, whereas homologous structures or traits have a common origin, bird, bat and pterosaur wings are analogous structures, but their forelimbs are homologous, sharing an ancestral state despite serving different functions. The opposite of convergence is divergent evolution, where related species evolve different traits, convergent evolution is similar to but different from parallel evolution. Many instances of convergent evolution are known in plants, including the development of C4 photosynthesis, seed dispersal by fleshy fruits adapted to be eaten by animals. In morphology, analogous traits arise when different species live in similar ways and/or a similar environment, when occupying similar ecological niches similar problems can lead to similar solutions. The British anatomist Richard Owen was the first to identify the difference between analogies and homologies. In biochemistry, physical and chemical constraints on mechanisms have caused some active site arrangements such as the triad to evolve independently in separate enzyme superfamilies. In his 1989 book Wonderful Life, Stephen Jay Gould argued that if one could rewind the tape of life the same conditions were encountered again, evolution could take a very different course. In cladistics, a homoplasy is a trait shared by two or more taxa for any other than that they share a common ancestry. Taxa which do share ancestry are part of the same clade, homoplastic traits caused by convergence are therefore, from the point of view of cladistics, confounding factors which could lead to an incorrect analysis. In some cases, it is difficult to tell whether a trait has been lost and then re-evolved convergently, or whether a gene has simply been switched off, such a re-emerged trait is called an atavism. From a mathematical standpoint, a gene has a steadily decreasing probability of retaining potential functionality over time. When two species are similar in a character, evolution is defined as parallel if the ancestors were also similar. When the ancestral forms are unspecified or unknown, or the range of traits considered is not clearly specified, the enzymology of proteases provides some of the clearest examples of convergent evolution. These examples reflect the intrinsic chemical constraints on enzymes, leading evolution to converge on equivalent solutions independently and repeatedly, serine and cysteine proteases use different amino acid functional groups as a nucleophile. In order to activate that nucleophile, they orient an acidic, the chemical and physical constraints on enzyme catalysis have caused identical triad arrangements to evolve independently more than 20 times in different enzyme superfamilies
3.
Bat
–
Bats are mammals of the order Chiroptera whose forelimbs form webbed wings, making them the only mammals naturally capable of true and sustained flight. By contrast, other mammals said to fly, such as flying squirrels, gliding possums, Bats do not flap their entire forelimbs, as birds do, but instead flap their spread-out digits, which are very long and covered with a thin membrane or patagium. About 70% of bat species are insectivores, most of the rest are frugivores, or fruit eaters. A few species, such as the bat, feed from animals other than insects, with the vampire bats being hematophagous. Bats are present throughout most of the world, with the exception of cold regions. They perform the vital roles of pollinating flowers and dispersing fruit seeds. Bats are economically important, as they consume insect pests, reducing the need for pesticides, the smallest bat is the Kittis hog-nosed bat, measuring 29–34 mm in length,15 cm across the wings and 2–2.6 g in mass. It is also arguably the smallest extant species of mammal, with the Etruscan shrew being the other contender. The largest species of bat are a few species of Pteropus, the Mexican free-tailed bat is the fastest flying animal in horizontal flight. An older English name for bats is flittermouse, which matches their name in other Germanic languages, middle English had bakke, most likely cognate with Old Swedish natbakka, which may have undergone a shift from -k- to -t- influenced by Latin blatta, moth, nocturnal insect. They were formerly grouped in the superorder Archonta, along with the treeshrews, colugos, genetic studies have now placed bats in the superorder Laurasiatheria, along with carnivorans, pangolins, odd-toed ungulates, even-toed ungulates, and cetaceans. A recent study by Zhang et al. places Chiroptera as a taxon to the clade Perissodactyla. The phylogenetic relationships of the different groups of bats have been the subject of much debate and this hypothesis recognized differences between microbats and megabats and acknowledged that flight has only evolved once in mammals. Most molecular biological evidence supports the view that bats form a single or monophyletic group, in the 1980s, a hypothesis based on morphological evidence was offered that stated the Megachiroptera evolved flight separately from the Microchiroptera. The so-called flying primate hypothesis proposes that, when adaptations to flight are removed, one example is that the brains of megabats show a number of advanced characteristics that link them to primates. Although recent genetic studies support the monophyly of bats, debate continues as to the meaning of available genetic. Genetic evidence indicates that megabats originated during the early Eocene and should be placed within the four lines of microbats. Consequently, two new suborders based on molecular data have been proposed and these two new suborders are strongly supported by statistical tests
4.
Anatomy
–
Anatomy is the branch of biology concerned with the study of the structure of organisms and their parts. Anatomy is inherently tied to embryology, comparative anatomy, evolutionary biology, Human anatomy is one of the basic essential sciences of medicine. The discipline of anatomy is divided into macroscopic and microscopic anatomy, macroscopic anatomy, or gross anatomy, is the examination of an animals body parts using unaided eyesight. Gross anatomy also includes the branch of superficial anatomy, microscopic anatomy involves the use of optical instruments in the study of the tissues of various structures, known as histology, and also in the study of cells. The history of anatomy is characterized by an understanding of the functions of the organs. Anatomy and physiology, which study the structure and function of organisms and their parts, make a pair of related disciplines. Derived from the Greek ἀνατομή anatomē dissection, anatomy is the study of the structure of organisms including their systems, organs. It includes the appearance and position of the parts, the materials from which they are composed, their locations. Anatomy is quite distinct from physiology and biochemistry, which deal respectively with the functions of those parts, the discipline of anatomy can be subdivided into a number of branches including gross or macroscopic anatomy and microscopic anatomy. Gross anatomy is the study of large enough to be seen with the naked eye, and also includes superficial anatomy or surface anatomy. Microscopic anatomy is the study of structures on a scale, including histology. Anatomy can be studied using both invasive and non-invasive methods with the goal of obtaining information about the structure and organization of organs, angiography using X-rays or magnetic resonance angiography are methods to visualize blood vessels. The term anatomy is commonly taken to refer to human anatomy, however, substantially the same structures and tissues are found throughout the rest of the animal kingdom and the term also includes the anatomy of other animals. The term zootomy is also used to specifically refer to animals. The structure and tissues of plants are of a dissimilar nature, the kingdom Animalia or metazoa, contains multicellular organisms that are heterotrophic and motile. Most animals have bodies differentiated into separate tissues and these animals are known as eumetazoans. They have a digestive chamber, with one or two openings, the gametes are produced in multicellular sex organs, and the zygotes include a blastula stage in their embryonic development. Metazoans do not include the sponges, which have undifferentiated cells, unlike plant cells, animal cells have neither a cell wall nor chloroplasts
5.
Cladistics
–
Therefore, members of a group are assumed to share a common history and are considered to be closely related. The techniques and nomenclature of cladistics have been applied to other disciplines, Cladistics in the original sense refers to a particular set of methods used in phylogenetic analysis, although it is now sometimes used to refer to the whole field. What is now called the cladistic method appeared as early as 1901 with a work by Peter Chalmers Mitchell for birds and subsequently by Robert John Tillyard in 1921, Hennig referred to his own approach as phylogenetic systematics. Phenetics was championed at this time by the numerical taxonomists Peter Sneath and Robert Sokal, originally conceived, if only in essence, by Willi Hennig in a book published in 1950, cladistics did not flourish until its translation into English in 1966. Today, cladistics is the most popular method for constructing phylogenies from morphological, unlike phenetics, cladistics is specifically aimed at reconstructing evolutionary histories. The way for computational phylogenetics was paved by phenetics, a set of commonly used from the 1950s to 1980s. Phenetics did not try to reconstruct phylogenetic trees, rather, it tried to build dendrograms from similarity data, the cladistic method interprets each character state transformation implied by the distribution of shared character states among taxa as a potential piece of evidence for grouping. The outcome of an analysis is a cladogram – a tree-shaped diagram that is interpreted to represent the best hypothesis of phylogenetic relationships. Cladists contend that these models are unjustified, every cladogram is based on a particular dataset analyzed with a particular method. Different datasets and different methods, not to mention violations of the mentioned assumptions, only scientific investigation can show which is more likely to be correct. Since the cladograms provide competing accounts of events, at most one of them is correct. Within the primates, all anthropoids are hypothesized to have had a common ancestor all of whose descendants were anthropoids, the prosimians, on the other hand, form a paraphyletic taxon. When two or more taxa that are not nested within each other share a plesiomorphy, it is a symplesiomorphy, symplesiomorphies do not mean that the taxa that exhibit that character state are necessarily closely related. For example, Reptilia is traditionally characterized by being cold-blooded, whereas birds are warm-blooded, an apomorphy or derived state is an innovation. It can thus be used to diagnose a clade – or even to help define a clade name in phylogenetic nomenclature, features that are derived in individual taxa are called autapomorphies. Autapomorphies express nothing about relationships among groups, clades are identified by synapomorphies, for example, the possession of digits that are homologous with those of Homo sapiens is a synapomorphy within the vertebrates. The tetrapods can be singled out as consisting of the first vertebrate with such digits homologous to those of Homo sapiens together with all descendants of this vertebrate and it is therefore inferred to have evolved by convergence or reversal. Both mammals and birds are able to maintain a constant body temperature
6.
DNA
–
Deoxyribonucleic acid is a molecule that carries the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses. DNA and RNA are nucleic acids, alongside proteins, lipids and complex carbohydrates, most DNA molecules consist of two biopolymer strands coiled around each other to form a double helix. The two DNA strands are termed polynucleotides since they are composed of simpler units called nucleotides. Each nucleotide is composed of one of four nitrogen-containing nucleobases—cytosine, guanine, adenine, or thymine —a sugar called deoxyribose, and a phosphate group. The nucleotides are joined to one another in a chain by covalent bonds between the sugar of one nucleotide and the phosphate of the next, resulting in an alternating sugar-phosphate backbone. The nitrogenous bases of the two polynucleotide strands are bound together, according to base pairing rules, with hydrogen bonds to make double-stranded DNA. The total amount of related DNA base pairs on Earth is estimated at 5.0 x 1037, in comparison the total mass of the biosphere has been estimated to be as much as 4 trillion tons of carbon. The DNA backbone is resistant to cleavage, and both strands of the double-stranded structure store the same biological information and this information is replicated as and when the two strands separate. A large part of DNA is non-coding, meaning that these sections do not serve as patterns for protein sequences, the two strands of DNA run in opposite directions to each other and are thus antiparallel. Attached to each sugar is one of four types of nucleobases and it is the sequence of these four nucleobases along the backbone that encodes biological information. RNA strands are created using DNA strands as a template in a process called transcription, under the genetic code, these RNA strands are translated to specify the sequence of amino acids within proteins in a process called translation. Within eukaryotic cells DNA is organized into structures called chromosomes. During cell division these chromosomes are duplicated in the process of DNA replication, eukaryotic organisms store most of their DNA inside the cell nucleus and some of their DNA in organelles, such as mitochondria or chloroplasts. In contrast prokaryotes store their DNA only in the cytoplasm, within the eukaryotic chromosomes, chromatin proteins such as histones compact and organize DNA. These compact structures guide the interactions between DNA and other proteins, helping control which parts of the DNA are transcribed, DNA was first isolated by Friedrich Miescher in 1869. DNA is used by researchers as a tool to explore physical laws and theories, such as the ergodic theorem. The unique material properties of DNA have made it an attractive molecule for material scientists and engineers interested in micro-, among notable advances in this field are DNA origami and DNA-based hybrid materials. DNA is a polymer made from repeating units called nucleotides
7.
Occam's razor
–
Occams razor is a problem-solving principle attributed to William of Ockham, who was an English Franciscan friar, scholastic philosopher and theologian. The principle can be interpreted as stating Among competing hypotheses, the one with the fewest assumptions should be selected, in science, Occams razor is used as a heuristic technique to guide scientists in the development of theoretical models, rather than as an arbiter between published models. The term Occams razor did not appear until a few centuries after William of Ockhams death in 1347, libert Froidmont, in his On Christian Philosophy of the Soul, takes credit for the phrase, speaking of novacula occami. Ockham did not invent this principle, but the association with him may be due to the frequency. The origins of what has come to be known as Occams razor are traceable to the works of philosophers such as John Duns Scotus, Robert Grosseteste, Maimonides. Aristotle writes in his Posterior Analytics, We may assume the superiority ceteris paribus of the demonstration which derives from fewer postulates or hypotheses, ptolemy stated, We consider it a good principle to explain the phenomena by the simplest hypothesis possible. Phrases such as It is vain to do more what can be done with fewer. Robert Grosseteste, in Commentary on the Posterior Analytics Books, declares, That is better, similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal. The Summa Theologica of Thomas Aquinas states that it is superfluous to suppose that what can be accounted for by a few principles has been produced by many. Aquinas uses this principle to construct an objection to Gods existence, an objection that he in turn answers and refutes generally, hence, Aquinas acknowledges the principle that today is known as Occams razor, but prefers causal explanations to other simple explanations. The Indian Hindu philosopher Madhva in verse 400 of his Vishnu-Tattva-Nirnaya says, William of Ockham was an English Franciscan friar and theologian, an influential medieval philosopher and a nominalist. His popular fame as a great logician rests chiefly on the maxim attributed to him, the term razor refers to distinguishing between two hypotheses either by shaving away unnecessary assumptions or cutting apart two similar conclusions. This principle is sometimes phrased as pluralitas non est ponenda sine necessitate, in his Summa Totius Logicae, i. 12, Ockham cites the principle of economy, Frustra fit per plura quod potest fieri per pauciora, to quote Isaac Newton, We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the natural effects we must, as far as possible. Bertrand Russell offers a version of Occams razor, Whenever possible. The only assumption is that the environment follows some unknown but computable probability distribution and this theory is a mathematical formalization of Occams razor. Another technical approach to Occams razor is ontological parsimony, the widespread laymans formulation that the simplest explanation is usually the correct one appears to have been derived from Occams razor
8.
RNA
–
Ribonucleic acid is a polymeric molecule essential in various biological roles in coding, decoding, regulation, and expression of genes. RNA and DNA are nucleic acids, and, along with proteins and carbohydrates, like DNA, RNA is assembled as a chain of nucleotides, but unlike DNA it is more often found in nature as a single-strand folded onto itself, rather than a paired double-strand. Cellular organisms use messenger RNA to convey information that directs synthesis of specific proteins. Many viruses encode their genetic information using an RNA genome, some RNA molecules play an active role within cells by catalyzing biological reactions, controlling gene expression, or sensing and communicating responses to cellular signals. One of these processes is protein synthesis, a universal function where RNA molecules direct the assembly of proteins on ribosomes. This process uses transfer RNA molecules to deliver amino acids to the ribosome, analysis of these RNAs has revealed that they are highly structured. Unlike DNA, their structures do not consist of long double helices, in this fashion, RNAs can achieve chemical catalysis. For instance, determination of the structure of the enzyme that catalyzes peptide bond formation—revealed that its active site is composed entirely of RNA. Each nucleotide in RNA contains a sugar, with carbons numbered 1 through 5. A base is attached to the 1 position, in general, adenine, cytosine, guanine, adenine and guanine are purines, cytosine and uracil are pyrimidines. A phosphate group is attached to the 3 position of one ribose, the phosphate groups have a negative charge each, making RNA a charged molecule. The bases form hydrogen bonds between cytosine and guanine, between adenine and uracil and between guanine and uracil, however, other interactions are possible, such as a group of adenine bases binding to each other in a bulge, or the GNRA tetraloop that has a guanine–adenine base-pair. An important structural feature of RNA that distinguishes it from DNA is the presence of a group at the 2 position of the ribose sugar. The A-form geometry results in a deep and narrow major groove. RNA is transcribed with only four bases, but these bases, pseudouridine, in which the linkage between uracil and ribose is changed from a C–N bond to a C–C bond, and ribothymidine are found in various places. Another notable modified base is hypoxanthine, a deaminated adenine base whose nucleoside is called inosine, inosine plays a key role in the wobble hypothesis of the genetic code. The specific roles of many of these modifications in RNA are not fully understood, the functional form of single-stranded RNA molecules, just like proteins, frequently requires a specific tertiary structure. The scaffold for this structure is provided by secondary structural elements that are hydrogen bonds within the molecule and this leads to several recognizable domains of secondary structure like hairpin loops, bulges, and internal loops
9.
Mutation
–
In biology, a mutation is the permanent alteration of the nucleotide sequence of the genome of an organism, virus, or extrachromosomal DNA or other genetic elements. Mutations may also result from insertion or deletion of segments of DNA due to mobile genetic elements, mutations may or may not produce discernible changes in the observable characteristics of an organism. Mutations play a part in normal and abnormal biological processes including, evolution, cancer, and the development of the immune system. The genomes of RNA viruses are based on RNA rather than DNA, the RNA viral genome can be double stranded or single stranded. In some of these viruses replication occurs quickly and there are no mechanisms to check the genome for accuracy and this error-prone process often results in mutations. Mutation can result in different types of change in sequences. Mutations in genes can either have no effect, alter the product of a gene, mutations can also occur in nongenic regions. Mutations can involve the duplication of large sections of DNA, usually through genetic recombination and these duplications are a major source of raw material for evolving new genes, with tens to hundreds of genes duplicated in animal genomes every million years. Most genes belong to larger families of shared ancestry, known as homology. Here, protein domains act as modules, each with a particular and independent function, that can be mixed together to produce genes encoding new proteins with novel properties. For example, the eye uses four genes to make structures that sense light. Another advantage of duplicating a gene is that this increases engineering redundancy, other types of mutation occasionally create new genes from previously noncoding DNA. Changes in chromosome number may involve even larger mutations, where segments of the DNA within chromosomes break and then rearrange. For example, in the Homininae, two fused to produce human chromosome 2, this fusion did not occur in the lineage of the other apes. Sequences of DNA that can move about the genome, such as transposons, make up a fraction of the genetic material of plants and animals. For example, more than a million copies of the Alu sequence are present in the genome. Another effect of these mobile DNA sequences is that when they move within a genome, they can mutate or delete existing genes, nonlethal mutations accumulate within the gene pool and increase the amount of genetic variation. The abundance of some changes within the gene pool can be reduced by natural selection, while other more favorable mutations may accumulate
10.
Phylogenetic tree
–
The taxa joined together in the tree are implied to have descended from a common ancestor. Phylogenetic trees are central to the field of phylogenetics, each node is called a taxonomic unit. Internal nodes are generally called hypothetical taxonomic units, as they cannot be directly observed, Trees are useful in fields of biology such as bioinformatics, systematics, and phylogenetic comparative methods. Unrooted trees illustrate only the relatedness of the nodes and do not require the ancestral root to be known or inferred. The idea of a tree of life arose from ancient notions of a progression from lower to higher forms of life. Charles Darwin also produced one of the first illustrations and crucially popularized the notion of a tree in his seminal book The Origin of Species. Over time, species classification has become static and more dynamic. A rooted phylogenetic tree is a tree with a unique node corresponding to the most recent common ancestor of all the entities at the leaves of the tree. The most common method for rooting trees is the use of an uncontroversial outgroup—close enough to allow inference from trait data or molecular sequencing, unrooted trees illustrate the relatedness of the leaf nodes without making assumptions about ancestry. They do not require the ancestral root to be known or inferred, unrooted trees can always be generated from rooted ones by simply omitting the root. By contrast, inferring the root of an unrooted tree requires some means of identifying ancestry, both rooted and unrooted phylogenetic trees can be either bifurcating or multifurcating, and either labeled or unlabeled. In contrast, a rooted multifurcating tree may have more than two children at some nodes and an unrooted multifurcating tree may have more than three neighbors at some nodes. A labeled tree has specific values assigned to its leaves, while a tree, sometimes called a tree shape. The last distinction is the most biologically relevant, it arises because there are places on an unrooted tree to put the root. For labeled bifurcating trees, there are,2 n −2. for n ≥2 total rooted trees and. 2 n −3. for n ≥3 total unrooted trees, among labeled bifurcating trees, the number of unrooted trees with n leaves is equal to the number of rooted trees with n −1 leaves. A dendrogram is a term for the diagrammatic representation of a phylogenetic tree. A cladogram is a phylogenetic tree formed using cladistic methods and this type of tree only represents a branching pattern, i. e. its branch spans do not represent time or relative amount of character change
11.
Simulated annealing
–
Simulated annealing is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a search space. It is often used when the space is discrete. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals, both are attributes of the material that depend on its thermodynamic free energy. Heating and cooling the material both the temperature and the thermodynamic free energy. Khachaturyan, Svetlana V. Semenovskaya, Boris K. Vainshtein in 1979 and by Armen G. Khachaturyan, Svetlana V. Semenovskaya and these authors used computer simulation mimicking annealing and cooling of such a system to find its global minimum. This notion of slow cooling implemented in the Simulated Annealing algorithm is interpreted as a decrease in the probability of accepting worse solutions as the solution space is explored. The method is an adaptation of the Metropolis–Hastings algorithm, a Monte Carlo method to sample states of a thermodynamic system. Rosenbluth and published by N. Metropolis et al. in 1953, the state of some physical systems, and the function E to be minimized is analogous to the internal energy of the system in that state. The goal is to bring the system, from an initial state. At each step, the SA heuristic considers some neighbouring state s of the current state s and these probabilities ultimately lead the system to move to states of lower energy. Typically this step is repeated until the system reaches a state that is enough for the application. Optimization of a solution involves evaluating the neighbours of a state of the problem, the well-defined way in which the states are altered to produce neighbouring states is called a move, and different moves give different sets of neighbouring states. These moves usually result in alterations of the last state. States with a smaller energy are better than those with a greater energy, the probability function P must be positive even when e ′ is greater than e. This feature prevents the method from becoming stuck at a minimum that is worse than the global one. When T tends to zero, the probability P must tend to zero if e ′ > e, for sufficiently small values of T, the system will then increasingly favor moves that go downhill, and avoid those that go uphill. With T =0 the procedure reduces to the greedy algorithm, which makes only the downhill transitions
12.
Algorithm
–
In mathematics and computer science, an algorithm is a self-contained sequence of actions to be performed. Algorithms can perform calculation, data processing and automated reasoning tasks, an algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. The transition from one state to the next is not necessarily deterministic, some algorithms, known as randomized algorithms, giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem. In English, it was first used in about 1230 and then by Chaucer in 1391, English adopted the French term, but it wasnt until the late 19th century that algorithm took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu and it begins thus, Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as, Algorism is the art by which at present we use those Indian figures, the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals. An informal definition could be a set of rules that precisely defines a sequence of operations, which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually, but humans can do something equally useful, in the case of certain enumerably infinite sets, They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. An enumerably infinite set is one whose elements can be put into one-to-one correspondence with the integers, the concept of algorithm is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a set of axioms. In logic, the time that an algorithm requires to complete cannot be measured, from such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete and abstract usage of the term. Algorithms are essential to the way computers process data, thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system. Although this may seem extreme, the arguments, in its favor are hard to refute. Gurevich. Turings informal argument in favor of his thesis justifies a stronger thesis, according to Savage, an algorithm is a computational process defined by a Turing machine. Typically, when an algorithm is associated with processing information, data can be read from a source, written to an output device. Stored data are regarded as part of the state of the entity performing the algorithm. In practice, the state is stored in one or more data structures, for some such computational process, the algorithm must be rigorously defined, specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be dealt with, case-by-case
Media related to Cladograms at Wikimedia Commons
