Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
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.
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 ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
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.
AmitriptylineAmitriptyline, sold under the brand name Elavil among others, is a tricyclic antidepressant primarily used to treat major depressive disorder, a variety of pain syndromes such as neuropathic pain, fibromyalgia, migraine and tension headaches. Due to the frequency and prominence of side effects, amitriptyline is generally considered a second-line therapy for these indications. The most common side effects are dry mouth, drowsiness, dizziness, constipation, and weight gain. Of note is sexual dysfunction, observed primarily in males.
T cellT cells are one of the important types of white blood cells of the immune system and play a central role in the adaptive immune response. T cells can be distinguished from other lymphocytes by the presence of a T-cell receptor (TCR) on their cell surface. T cells are born from hematopoietic stem cells, found in the bone marrow. Developing T cells then migrate to the thymus gland to develop (or mature). T cells derive their name from the thymus. After migration to the thymus, the precursor cells mature into several distinct types of T cells.
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).
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
MDMA3,4-Methylenedioxymethamphetamine (MDMA), commonly known as ecstasy (tablet form); and molly or mandy (crystal form), is a potent empathogen–entactogen with stimulant and minor psychedelic properties primarily used for recreational purposes. The beneficial pharmacological effects include altered sensations, increased energy, empathy, and pleasure. When taken by mouth, effects begin in 30 to 45 minutes and last three to six hours. MDMA was first developed in 1912 by Merck.
FluoxetineFluoxetine, sold under the brand name Prozac, among others, is an antidepressant of the selective serotonin reuptake inhibitor (SSRI) class. It is used for the treatment of major depressive disorder, obsessive–compulsive disorder (OCD), bulimia nervosa, panic disorder, and premenstrual dysphoric disorder. It is also approved for treatment of major depressive disorder in adolescents and children 8 years of age and over. It has also been used to treat premature ejaculation. Fluoxetine is taken by mouth.
Golgi apparatusThe Golgi apparatus (ˈɡɒldʒi), also known as the Golgi complex, Golgi body, or simply the Golgi, is an organelle found in most eukaryotic cells. Part of the endomembrane system in the cytoplasm, it packages proteins into membrane-bound vesicles inside the cell before the vesicles are sent to their destination. It resides at the intersection of the secretory, lysosomal, and endocytic pathways. It is of particular importance in processing proteins for secretion, containing a set of glycosylation enzymes that attach various sugar monomers to proteins as the proteins move through the apparatus.
T helper cellThe T helper cells (Th cells), also known as CD4+ cells or CD4-positive cells, are a type of T cell that play an important role in the adaptive immune system. They aid the activity of other immune cells by releasing cytokines. They are considered essential in B cell antibody class switching, breaking cross-tolerance in dendritic cells, in the activation and growth of cytotoxic T cells, and in maximizing bactericidal activity of phagocytes such as macrophages and neutrophils.
BupropionBupropion, sold under the brand name Wellbutrin among others, is an atypical antidepressant primarily used to treat major depressive disorder and to support smoking cessation. It is also popular as an add-on medication in the cases of "incomplete response" to the first-line selective serotonin reuptake inhibitor (SSRI) antidepressant. Bupropion has several features that distinguish it from other antidepressants: it does not usually cause sexual dysfunction; it is not associated with weight gain and sleepiness, and it is more effective than SSRIs at improving symptoms of hypersomnia and fatigue.
B cellB cells, also known as B lymphocytes, are a type of white blood cell of the lymphocyte subtype. They function in the humoral immunity component of the adaptive immune system. B cells produce antibody molecules which may be either secreted or inserted into the plasma membrane where they serve as a part of B-cell receptors. When a naïve or memory B cell is activated by an antigen, it proliferates and differentiates into an antibody-secreting effector cell, known as a plasmablast or plasma cell.
SertralineSertraline, sold under the brand name Zoloft among others, is an antidepressant of the selective serotonin reuptake inhibitor (SSRI) class. The efficacy of sertraline for depression is similar to that of other antidepressants, and the differences are mostly confined to side effects. Sertraline is better tolerated than the older tricyclic antidepressants, and it may work better than fluoxetine for some subtypes of depression. Sertraline is effective for panic disorder, social anxiety disorder, generalized anxiety disorder (GAD), and obsessive–compulsive disorder (OCD).
CeramideCeramides are a family of waxy lipid molecules. A ceramide is composed of sphingosine and a fatty acid joined by an amide bond. Ceramides are found in high concentrations within the cell membrane of eukaryotic cells, since they are component lipids that make up sphingomyelin, one of the major lipids in the lipid bilayer. Contrary to previous assumptions that ceramides and other sphingolipids found in cell membrane were purely supporting structural elements, ceramide can participate in a variety of cellular signaling: examples include regulating differentiation, proliferation, and programmed cell death (PCD) of cells.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
Cell cultureCell culture or tissue culture is the process by which cells are grown under controlled conditions, generally outside of their natural environment. The term "tissue culture" was coined by American pathologist Montrose Thomas Burrows. This technique is also called micropropagation. After the cells of interest have been isolated from living tissue, they can subsequently be maintained under carefully controlled conditions. They need to be kept at body temperature (37 °C) in an incubator.
