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Hyperbolastic Functions
The hyperbolastic functions, also known as hyperbolastic growth models, are mathematical functions that are used in medical statistical modeling. These models were originally developed to capture the growth dynamics of multicellular tumor spheres, and were introduced in 2005 by Mohammad Tabatabai, David Williams, and Zoran Bursac. The precision of hyperbolastic functions in modeling real world problems is somewhat due to their flexibility in their point of inflection. These functions can be used in a wide variety of modeling problems such as tumor growth, stem cell proliferation, pharma kinetics, cancer growth, sigmoid activation function in neural networks, and epidemiological disease progression or regression. The ''hyperbolastic functions'' can model both growth and decay curves until it reaches carrying capacity. Due to their flexibility, these models have diverse applications in the medical field, with the ability to capture disease progression with an intervening trea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figure 1 - Hyperbolastic Type I
Figure may refer to: General *A shape, drawing, depiction, or geometric configuration *Figure (wood), wood appearance *Figure (music), distinguished from musical motif *Noise figure, in telecommunication *Dance figure, an elementary dance pattern *A person's figure, human physical appearance Arts *Figurine, a miniature statuette representation of a creature *Action figure, a posable jointed solid plastic character figurine *Figure painting, realistic representation, especially of the human form *Figure drawing *Model figure, a scale model of a creature Writing *figure, in writing, a type of floating block (text, table, or graphic separate from the main text) *Figure of speech, also called a rhetorical figure *Christ figure, a type of character * in typesetting, text figures and lining figures Accounting *Figure, a synonym for number *Significant figures in a decimal number Science *Figure of the Earth, the size and shape of the Earth in geodesy Sports *Figure (horse), a sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distributions
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall linear and angular momenta remain null over time. The kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's internal energy (the equipartition theorem). This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking throu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion Process
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes. A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion. The position of the particle is then random; its probability density function as a function of space and time is governed by an advection– diffusion equation. Mathematical definition A ''diffusion process'' is a Markov process with continuous sample paths for which the Kolmogorov forward equation is the Fokker–Planck equation. See also *Diffusion *Itô diffusion *Jump diffusion *Sample-continuous process In mathematics, a sample-continuous process is a stochastic process whose sample paths are almost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when all observed outcomes are assumed to have Normal distributions with the same variance. From the perspective of Bayesian inference, M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Diffusion
Stochastic diffusion search (SDS) was first described in 1989 as a population-based, pattern-matching algorithm. It belongs to a family of swarm intelligence and naturally inspired search and optimisation algorithms which includes ant colony optimization, particle swarm optimization and genetic algorithms; as such SDS was the first Swarm Intelligence metaheuristic. Unlike stigmergetic communication employed in ant colony optimization, which is based on modification of the physical properties of a simulated environment, SDS uses a form of direct (one-to-one) communication between the agents similar to the tandem calling mechanism employed by one species of ants, ''Leptothorax acervorum''. In SDS agents perform cheap, partial evaluations of a hypothesis (a candidate solution to the search problem). They then share information about hypotheses (diffusion of information) through direct one-to-one communication. As a result of the diffusion mechanism, high-quality solutions can be ident ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrlich Carcinoma
Ehrlich-Lettre ascites carcinoma (EAC) is also known as Ehrlich cell. It was originally established as an ascites tumor in mice. Ehrlich cell The tumor was cultured ''in vivo'', which became known as the Ehrlich cell. After 1948 Ehrlich cultures spread around research institutes all over the world. The Ehrlich cell became popular because it could be expanded by ''in vivo'' passage. This made it useful for biochemical studies involving large amounts of tissues. It could also be maintained ''in vitro'' for more carefully controlled studies. Culture techniques in large-scale, mice passage is less attractive, due to the contamination of the tumor with multifarious host inflammatory cells. Properties EAC is referred to as undifferentiated carcinoma, and is originally hyper-diploid. The permeability to water is highest at the initiation of the S phase and progressively decreases to its lowest value just after mitosis In cell biology, mitosis () is a part of the cell cycle i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Hyperbolastic Graph Of Phytoplankton Biomass
3-D, 3D, or 3d may refer to: Science, technology, and mathematics Relating to three-dimensionality * Three-dimensional space ** 3D computer graphics, computer graphics that use a three-dimensional representation of geometric data ** 3D film, a motion picture that gives the illusion of three-dimensional perception ** 3D modeling, developing a representation of any three-dimensional surface or object ** 3D printing, making a three-dimensional solid object of a shape from a digital model ** 3D display, a type of information display that conveys depth to the viewer ** 3D television, television that conveys depth perception to the viewer ** Stereoscopy, any technique capable of recording three-dimensional visual information or creating the illusion of depth in an image Other uses in science and technology or commercial products * 3D projection * 3D rendering * 3D scanning, making a digital representation of three-dimensional objects * 3D video game (other) * 3-D Secure, a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Survival Function
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The survival function is also known as the survivor function or reliability function. The term ''reliability function'' is common in engineering while the term ''survival function'' is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime. Sometimes complementary cumulative distribution functions are called survival functions in general. Definition Let the lifetime ''T'' be a continuous random variable with cumulative distribution function ''F''(''t'') on the interval [0,∞). Its ''survival function'' or ''reliability function'' is: :S(t) = P(\) = \int_t^ f(u)\,du = 1-F(t). Examples of survival functions The graphs below show examples of hypothetical survival functions. The x-axis is time. The y-axis is the proportion o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hazard Function
Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system. For example, an automobile's failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service. One does not expect to replace an exhaust pipe, overhaul the brakes, or have major transmission problems in a new vehicle. In practice, the mean time between failures (MTBF, 1/λ) is often reported instead of the failure rate. This is valid and useful if the failure rate may be assumed constant – often used for complex units / systems, electronics – and is a general agreement in some reliability standards (Military and Aerospace). It does in this case ''only'' relate to the flat region of the ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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