Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
Neuroendocrine tumorNeuroendocrine tumors (NETs) are neoplasms that arise from cells of the endocrine (hormonal) and nervous systems. They most commonly occur in the intestine, where they are often called carcinoid tumors, but they are also found in the pancreas, lung, and the rest of the body. Although there are many kinds of NETs, they are treated as a group of tissue because the cells of these neoplasms share common features, including a similar histological appearance, having special secretory granules, and often producing biogenic amines and polypeptide hormones.
Elliptic partial differential equationSecond-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form where A, B, C, D, E, F, and G are functions of x and y and where , and similarly for . A PDE written in this form is elliptic if with this naming convention inspired by the equation for a planar ellipse.
Hyperbolic partial differential equationIn mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation.
ApoptosisApoptosis (from apóptōsis) is a form of programmed cell death that occurs in multicellular organisms and in some eukaryotic, single-celled microorganisms such as yeast. Biochemical events lead to characteristic cell changes (morphology) and death. These changes include blebbing, cell shrinkage, nuclear fragmentation, chromatin condensation, DNA fragmentation, and mRNA decay. The average adult human loses between 50 and 70 billion cells each day due to apoptosis.
Bone tumorA bone tumor is an abnormal growth of tissue in bone, traditionally classified as noncancerous (benign) or cancerous (malignant). Cancerous bone tumors usually originate from a cancer in another part of the body such as from lung, breast, thyroid, kidney and prostate. There may be a lump, pain, or neurological signs from pressure. A bone tumor might present with a pathologic fracture. Other symptoms may include fatigue, fever, weight loss, anemia and nausea. Sometimes there are no symptoms and the tumour is found when investigating another problem.
Convection–diffusion equationThe convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.
Method of characteristicsIn mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation. The method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data given on a suitable hypersurface.
DiscretizationIn applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification).
Dimensional analysisIn engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.
Renal cell carcinomaRenal cell carcinoma (RCC) is a kidney cancer that originates in the lining of the proximal convoluted tubule, a part of the very small tubes in the kidney that transport primary urine. RCC is the most common type of kidney cancer in adults, responsible for approximately 90–95% of cases. RCC occurrence shows a male predominance over women with a ratio of 1.5:1. RCC most commonly occurs between 6th and 7th decade of life. Initial treatment is most commonly either partial or complete removal of the affected kidney(s).
Stochastic simulationA stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values. These steps are repeated until a sufficient amount of data is gathered. In the end, the distribution of the outputs shows the most probable estimates as well as a frame of expectations regarding what ranges of values the variables are more or less likely to fall in.
