Cochlear implant Prosthesis A cochlear implant (CI) is a surgically implanted neuroprosthesis that provides a person who has moderate-to-profound sensorineural hearing loss with sound perception. With the help of therapy, cochlear implants may allow for improved speech understanding in both quiet and noisy environments.[1][2] A CI bypasses acoustic hearing by direct electrical stimulation of the auditory nerve.[2] Through everyday listening and auditory training, cochlear implants allow both children and adults to learn to interpret those signals as speech and sound.[3][4][5] The implant has two main components. The outside component is generally worn behind the ear, but could also be attached to clothing, for example, in young children. The surgical procedure is performed under general anesthesia. From the early days of implants in the 1970s and the 1980s, speech perception via an implant has steadily increased. History[edit] 1994 body-worn Cochlear Spectra processor. Parts[edit] External: Internal:
Complex dynamics Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions. Techniques[1][edit] Parts[edit] Holomorphic dynamics ( dynamics of holomorphic functions )[3]in one complex variablein several complex variablesConformal dynamics unites holomorphic dynamics in one complex variable with differentiable dynamics in one real variable. See also[edit] References[edit] Complex dynamics, Lennart Carleson, Theodore W. Complex quadratic polynomial Properties[edit] Quadratic polynomials have the following properties, regardless of the form: Forms[edit] When the quadratic polynomial has only one variable (univariate), one can distinguish its four main forms: The monic and centered form has been studied extensively, and has the following properties: The lambda form is: the simplest non-trivial perturbation of unperturbated system "the first family of dynamical systems in which explicit necessary and sufficient conditions are known for when a small divisor problem is stable"[4] Conjugation[edit] Between forms[edit] Since is affine conjugate to the general form of the quadratic polynomial it is often used to study complex dynamics and to create images of Mandelbrot, Julia and Fatou sets. When one wants change from to , the parameter transformation is[5] and the transformation between the variables in and is With doubling map[edit] There is semi-conjugacy between the dyadic transformation (the doubling map) and the quadratic polynomial case of c = –2. so
Complex adaptive system They are complex in that they are dynamic networks of interactions, and their relationships are not aggregations of the individual static entities. They are adaptive in that the individual and collective behavior mutate and self-organize corresponding to the change-initiating micro-event or collection of events.[1][2] Overview[edit] The term complex adaptive systems, or complexity science, is often used to describe the loosely organized academic field that has grown up around the study of such systems. Complexity science is not a single theory— it encompasses more than one theoretical framework and is highly interdisciplinary, seeking the answers to some fundamental questions about living, adaptable, changeable systems. The fields of CAS and artificial life are closely related. The study of CAS focuses on complex, emergent and macroscopic properties of the system.[3][11][12] John H. General properties[edit] Characteristics[edit] Robert Axelrod & Michael D. Modeling and Simulation[edit]
Closed-loop transfer function Overview[edit] The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop transfer function is shown below: The summing node and the G(s) and H(s) blocks can all be combined into one block, which would have the following transfer function: is called feedforward transfer function, is called feedback transfer function, and their product is called the Open loop transfer function. Derivation[edit] We define an intermediate signal Z (also known as error signal) shown as follows: Using this figure we write: Now, plug the second equation into the first to eliminate Z(s): Move all the terms with Y(s) to the left hand side, and keep the term with X(s) on the right hand side: Therefore, See also[edit] References[edit] This article incorporates public domain material from Federal Standard 1037C.
Computational irreducibility From Wikipedia, the free encyclopedia Concept proposed by Stephen Wolfram Computational irreducibility suggests certain computational processes cannot be simplified such that the only way to determine the outcome of such a process is to go through each step of its computation. It is one of the main ideas proposed by Stephen Wolfram in his 2002 book A New Kind of Science, although the concept goes back to studies from the 1980s.[1] Many physical systems are complex enough that they cannot be effectively measured. Computational irreducibility explains why many natural systems are hard to predict or simulate. There is no easy theory for any behavior that seems complex.Complex behavior features can be captured with models that have simple underlying structures.An overall system's behavior based on simple structures can still exhibit behavior indescribable by reasonably "simple" laws.
Classification of Fatou components Rational case[edit] If f is a rational function defined in the extended complex plane, and if it is a nonlinear function (degree > 1) of the Fatou set, exactly one of the following holds: Attracting periodic point[edit] The components of the map contain the attracting points that are the solutions to . by Newton–Raphson formula. Herman ring[edit] The map and t = 0.6151732... will produce a Herman ring.[2] It is shown by Shishikura that the degree of such map must be at least 3, as in this example. More than one type of component[edit] If degree d is greater than 2 then there is more than one critical point and then can be more than one type of component period 4 and 4 (2 attracting basins) Transcendental case[edit] Baker domain[edit] Wandering domain[edit] Transcendental maps may have wandering domains: these are Fatou components that are not eventually periodic. See also[edit] References[edit] Lennart Carleson and Theodore W.
Complex systems biology Complex systems biology (CSB) is a branch or subfield of mathematical and theoretical biology concerned with complexity of both structure and function in biological organisms, as well as the emergence and evolution of organisms and species, with emphasis being placed on the complex interactions of, and within, bionetworks,[1] and on the fundamental relations and relational patterns that are essential to life.[2][3][4][5][6] CSB is thus a field of theoretical sciences aimed at discovering and modeling the relational patterns essential to life that has only a partial overlap with complex systems theory,[7] and also with the systems approach to biology called systems biology; this is because the latter is restricted primarily to simplified models of biological organization and organisms, as well as to only a general consideration of philosophical or semantic questions related to complexity in biology. Network Representation of a Complex Adaptive System Telomerase structure and function