Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
SignalIn signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The IEEE Transactions on Signal Processing includes audio, video, speech, , sonar, and radar as examples of signals. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information.
Computational physicsComputational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics - an area of study which supplements both theory and experiment.
DefibrillationDefibrillation is a treatment for life-threatening cardiac arrhythmias, specifically ventricular fibrillation (V-Fib) and non-perfusing ventricular tachycardia (V-Tach). A defibrillator delivers a dose of electric current (often called a counter-shock) to the heart. Although not fully understood, this process depolarizes a large amount of the heart muscle, ending the arrhythmia. Subsequently, the body's natural pacemaker in the sinoatrial node of the heart is able to re-establish normal sinus rhythm.
ArrhythmiaArrhythmias, also known as cardiac arrhythmias, heart arrhythmias, or dysrhythmias, are irregularities in the heartbeat, including when it is too fast or too slow. A resting heart rate that is too fast – above 100 beats per minute in adults – is called tachycardia, and a resting heart rate that is too slow – below 60 beats per minute – is called bradycardia. Some types of arrhythmias have no symptoms. Symptoms, when present, may include palpitations or feeling a pause between heartbeats.
ElectrocardiographyElectrocardiography is the process of producing an electrocardiogram (ECG or EKG ), a recording of the heart's electrical activity through repeated cardiac cycles. It is an electrogram of the heart which is a graph of voltage versus time of the electrical activity of the heart using electrodes placed on the skin. These electrodes detect the small electrical changes that are a consequence of cardiac muscle depolarization followed by repolarization during each cardiac cycle (heartbeat).
Artificial cardiac pacemakerAn artificial cardiac pacemaker (artificial pacemaker, and sometimes just pacemaker, although the term is also used to refer to the body's natural cardiac pacemaker) is a medical device, nowadays always implanted, that generates electrical pulses delivered by electrodes to one or more of the chambers of the heart, the upper atria or lower ventricles. Each pulse causes the targeted chamber(s) to contract and pump blood, thus regulating the function of the electrical conduction system of the heart.
Computational neuroscienceComputational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous.
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.
Computational chemistryComputational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form.
Ventricular fibrillationVentricular fibrillation (V-fib or VF) is an abnormal heart rhythm in which the ventricles of the heart quiver. It is due to disorganized electrical activity. Ventricular fibrillation results in cardiac arrest with loss of consciousness and no pulse. This is followed by sudden cardiac death in the absence of treatment. Ventricular fibrillation is initially found in about 10% of people with cardiac arrest. Ventricular fibrillation can occur due to coronary heart disease, valvular heart disease, cardiomyopathy, Brugada syndrome, long QT syndrome, electric shock, or intracranial hemorrhage.
Computational anatomyComputational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, machine learning, computational mechanics, computational science, biological imaging, neuroscience, physics, probability, and statistics; it also has strong connections with fluid mechanics and geometric mechanics.
