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Hyperbolastic Functions
The hyperbolastic functions, also known as hyperbolastic growth models, are Function (mathematics), 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 w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 *Figure–ground (perception), the distinction between a visually perceived object and its surroundings 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Probability Distributions
In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events 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). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Brownian Motion
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical sources. This motion pattern typically consists of Randomness, 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 momentum, linear and Angular momentum, angular momenta remain null over time. The Kinetic energy, 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 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Diffusion Process
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes. It is used heavily in statistical physics, statistical analysis, information theory, data science, neural networks, finance and marketing. 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 a convection–diffusion equation. Mathematical definition A ''diffusion process'' is a Markov process with continuous sample paths for which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, 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 function, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 Mitosis () is a part of the cell cycle in eukaryote, euka ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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3D Hyperbolastic Graph Of Phytoplankton Biomass
3D, 3-D, 3d, or Three D may refer to: Science, technology, and mathematics * A three-dimensional space in mathematics Relating to three-dimensionality * 3D computer graphics, computer graphics that use a three-dimensional representation of geometric data * 3D display, a type of information display that conveys depth to the viewer * 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 television, television that conveys depth perception to the viewer * 3D projection * 3D rendering * 3D scanning, making a digital representation of three-dimensional objects * 3D video game * Stereoscopy, any technique capable of recording three-dimensional visual information or creating the illusion of depth in an image * Three-dimensional space Other uses in science and technology * 3-D Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 describing the time to failure. If T has cumulative distribution function F(t) and probability density function f(t) on the interval [0,\infty), then the ''survival function'' or ''reliability function'' is: S(t) = P(T > t) = 1-F(t) = 1 - \int_0^t f(u)\,du Examples of survival functions The graphs below show examples of hypot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Hazard Function
A hazard is a potential source of harm. Substances, events, or circumstances can constitute hazards when their nature would potentially allow them to cause damage to health, life, property, or any other interest of value. The probability of that harm being realized in a specific ''incident'', combined with the magnitude of potential harm, make up its risk. This term is often used synonymously in colloquial speech. Hazards can be classified in several ways which are not mutually exclusive. They can be classified by ''causing actor'' (for example, natural or anthropogenic), by ''physical nature'' (e.g. biological or chemical) or by ''type of damage'' (e.g., health hazard or environmental hazard). Examples of natural disasters with highly harmful impacts on a society are floods, droughts, earthquakes, tropical cyclones, lightning strikes, volcanic activity and wildfires. Technological and anthropogenic hazards include, for example, structural collapses, transport accidents, acciden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Probability Density Function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), 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 equal 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. More precisely, the PDF is used to specify the probability of the random variable falling ''within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |