Airborne transmissionAirborne transmission or aerosol transmission is transmission of an infectious disease through small particles suspended in the air. Infectious diseases capable of airborne transmission include many of considerable importance both in human and veterinary medicine. The relevant infectious agent may be viruses, bacteria, or fungi, and they may be spread through breathing, talking, coughing, sneezing, raising of dust, spraying of liquids, flushing toilets, or any activities which generate aerosol particles or droplets.
Conjugate transposeIn mathematics, the conjugate transpose, also known as the Hermitian transpose, of an complex matrix is an matrix obtained by transposing and applying complex conjugate on each entry (the complex conjugate of being , for real numbers and ). It is often denoted as or or and very commonly in physics as . For real matrices, the conjugate transpose is just the transpose, . The conjugate transpose of an matrix is formally defined by where the subscript denotes the -th entry, for and , and the overbar denotes a scalar complex conjugate.
Transient stateA system is said to be transient or in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state. The time taken for the circuit to change from one steady state to another steady state is called the transient time. When a chemical reactor is being brought into operation, the concentrations, temperatures, species compositions, and reaction rates are changing with time until operation reaches its nominal process variables.
Steady stateIn systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so: In discrete time, it means that the first difference of each property is zero and remains so: The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Symmetric matrixIn linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
Energy flow (ecology)Energy flow is the flow of energy through living things within an ecosystem. All living organisms can be organized into producers and consumers, and those producers and consumers can further be organized into a food chain. Each of the levels within the food chain is a trophic level. In order to more efficiently show the quantity of organisms at each trophic level, these food chains are then organized into trophic pyramids.
Emerging infectious diseaseAn emerging infectious disease (EID) is an infectious disease whose incidence has increased recently (in the past 20 years), and could increase in the near future. The minority that are capable of developing efficient transmission between humans can become major public and global concerns as potential causes of epidemics or pandemics. Their many impacts can be economic and societal, as well as clinical. EIDs have been increasing steadily since at least 1940.
Matrix exponentialIn mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as .
Disease vectorIn epidemiology, a disease vector is any living agent that carries and transmits an infectious pathogen to another living organism; agents regarded as vectors are organisms, such as parasites or microbes. The first major discovery of a disease vector came from Ronald Ross in 1897, who discovered the malaria pathogen when he dissected a mosquito. Arthropods form a major group of pathogen vectors with mosquitoes, flies, sand flies, lice, fleas, ticks, and mites transmitting a huge number of pathogens.
