Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Heart transplantationA heart transplant, or a cardiac transplant, is a surgical transplant procedure performed on patients with end-stage heart failure or severe coronary artery disease when other medical or surgical treatments have failed. , the most common procedure is to take a functioning heart, with or without both lungs, from a recently deceased organ donor (brain death is the standard) and implant it into the patient.
Heart rateHeart rate (or pulse rate) is the frequency of the heartbeat measured by the number of contractions of the heart per minute (beats per minute, or bpm). The heart rate can vary according to the body's physical needs, including the need to absorb oxygen and excrete carbon dioxide, but is also modulated by numerous factors, including (but not limited to) genetics, physical fitness, stress or psychological status, diet, drugs, hormonal status, environment, and disease/illness as well as the interaction between and among these factors.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Ventricle (heart)A ventricle is one of two large chambers toward the bottom of the heart that collect and expel blood towards the peripheral beds within the body and lungs. The blood pumped by a ventricle is supplied by an atrium, an adjacent chamber in the upper heart that is smaller than a ventricle. Interventricular means between the ventricles (for example the interventricular septum), while intraventricular means within one ventricle (for example an intraventricular block).
Artificial heart valveAn artificial heart valve is a one-way valve implanted into a person's heart to replace a heart valve that is not functioning properly (valvular heart disease). Artificial heart valves can be separated into three broad classes: mechanical heart valves, bioprosthetic tissue valves and engineered tissue valves. The human heart contains four valves: tricuspid valve, pulmonary valve, mitral valve and aortic valve. Their main purpose is to keep blood flowing in the proper direction through the heart, and from the heart into the major blood vessels connected to it (the pulmonary artery and the aorta).
Uncertainty quantificationUncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if the speed was exactly known, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc.
Inverse problemAn inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects.
Irreducible complexityIrreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts were removed, so supposedly could not have evolved by successive small modifications from earlier less complex systems through natural selection, which would need all intermediate precursor systems to have been fully functional. This negative argument is then complemented by the claim that the only alternative explanation is a "purposeful arrangement of parts" inferring design by an intelligent agent.
Mathematical beautyMathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. Mathematicians describe an especially pleasing method of proof as elegant.
Review articleA review article is an article that summarizes the current state of understanding on a topic within a certain discipline. A review article is generally considered a secondary source since it may analyze and discuss the method and conclusions in previously published studies. It resembles a survey article or, in news publishing, overview article, which also surveys and summarizes previously published primary and secondary sources, instead of reporting new facts and results.
