Gödel's incompleteness theoremsGödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.
Stem cellIn multicellular organisms, stem cells are undifferentiated or partially differentiated cells that can differentiate into various types of cells and proliferate indefinitely to produce more of the same stem cell. They are the earliest type of cell in a cell lineage. They are found in both embryonic and adult organisms, but they have slightly different properties in each. They are usually distinguished from progenitor cells, which cannot divide indefinitely, and precursor or blast cells, which are usually committed to differentiating into one cell type.
Gödel numberingIn mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was developed by Kurt Gödel for the proof of his incompleteness theorems. () A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols.
Optimal designIn the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design.
Locus (genetics)In genetics, a locus (: loci) is a specific, fixed position on a chromosome where a particular gene or genetic marker is located. Each chromosome carries many genes, with each gene occupying a different position or locus; in humans, the total number of protein-coding genes in a complete haploid set of 23 chromosomes is estimated at 19,000–20,000. Genes may possess multiple variants known as alleles, and an allele may also be said to reside at a particular locus.
MutagenIn genetics, a mutagen is a physical or chemical agent that permanently changes genetic material, usually DNA, in an organism and thus increases the frequency of mutations above the natural background level. As many mutations can cause cancer in animals, such mutagens can therefore be carcinogens, although not all necessarily are. All mutagens have characteristic mutational signatures with some chemicals becoming mutagenic through cellular processes. The process of DNA becoming modified is called mutagenesis.
Estimation theoryEstimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
Somatic evolution in cancerSomatic evolution is the accumulation of mutations and epimutations in somatic cells (the cells of a body, as opposed to germ plasm and stem cells) during a lifetime, and the effects of those mutations and epimutations on the fitness of those cells. This evolutionary process has first been shown by the studies of Bert Vogelstein in colon cancer. Somatic evolution is important in the process of aging as well as the development of some diseases, including cancer. Cells in pre-malignant and malignant neoplasms (tumors) evolve by natural selection.
Design of experimentsThe design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.
NeoplasmA neoplasm (ˈniː.oʊˌplæzəm,_ˈniː.ə-) is a type of abnormal and excessive growth of tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tissue, and persists in growing abnormally, even if the original trigger is removed. This abnormal growth usually forms a mass, when it may be called a tumour or tumor. ICD-10 classifies neoplasms into four main groups: benign neoplasms, in situ neoplasms, malignant neoplasms, and neoplasms of uncertain or unknown behavior.
