Differential operatorIn mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist, such as the Schwarzian derivative.
Treatment of cancerCancer can be treated by surgery, chemotherapy, radiation therapy, hormonal therapy, targeted therapy (including immunotherapy such as monoclonal antibody therapy) and synthetic lethality, most commonly as a series of separate treatments (e.g. chemotherapy before surgery). The choice of therapy depends upon the location and grade of the tumor and the stage of the disease, as well as the general state of the patient (performance status). Cancer genome sequencing helps in determining which cancer the patient exactly has for determining the best therapy for the cancer.
Merkel-cell carcinomaMerkel cell carcinoma (MCC) is a rare and aggressive skin cancer occurring in about 3 people per 1,000,000 members of the population. It is also known as cutaneous APUDoma, primary neuroendocrine carcinoma of the skin, primary small cell carcinoma of the skin, and trabecular carcinoma of the skin. Factors involved in the development of MCC include the Merkel cell polyomavirus (MCPyV or MCV), a weakened immune system, and exposure to ultraviolet radiation.
Pattern formationThe science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. In developmental biology, pattern formation refers to the generation of complex organizations of cell fates in space and time. The role of genes in pattern formation is an aspect of morphogenesis, the creation of diverse anatomies from similar genes, now being explored in the science of evolutionary developmental biology or evo-devo.
Patterns in naturePatterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.
Turing patternThe Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. The pattern arises due to Turing instability which in turn arises due to the interplay between differential diffusion (i.e., different values of diffusion coefficients) of chemical species and chemical reaction.
Germ layerA germ layer is a primary layer of cells that forms during embryonic development. The three germ layers in vertebrates are particularly pronounced; however, all eumetazoans (animals that are sister taxa to the sponges) produce two or three primary germ layers. Some animals, like cnidarians, produce two germ layers (the ectoderm and endoderm) making them diploblastic. Other animals such as bilaterians produce a third layer (the mesoderm) between these two layers, making them triploblastic.
Differential (mathematics)In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity.
P16p16 (also known as p16INK4a, cyclin-dependent kinase inhibitor 2A, CDKN2A, multiple tumor suppressor 1 and numerous other synonyms), is a protein that slows cell division by slowing the progression of the cell cycle from the G1 phase to the S phase, thereby acting as a tumor suppressor. It is encoded by the CDKN2A gene. A deletion (the omission of a part of the DNA sequence during replication) in this gene can result in insufficient or non-functional p16, accelerating the cell cycle and resulting in many types of cancer.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
P14arfp14ARF (also called ARF tumor suppressor, ARF, p14ARF) is an alternate reading frame protein product of the CDKN2A locus (i.e. INK4a/ARF locus). p14ARF is induced in response to elevated mitogenic stimulation, such as aberrant growth signaling from MYC and Ras (protein). It accumulates mainly in the nucleolus where it forms stable complexes with NPM or Mdm2. These interactions allow p14ARF to act as a tumor suppressor by inhibiting ribosome biogenesis or initiating p53-dependent cell cycle arrest and apoptosis, respectively.
