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Mixture model

In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with "mixture distributions" relate to deriving the properties of the overall population from those of the sub-populations, "mixture models" are used to make statistical inferences about the properties of the sub-populations given only observations on the pooled population, without sub-population identity information. Mixture models are used for clustering, under the name model-based clustering, and also for density estimation.

Mixture models should not be confused with models for compositional data, i.e., data whose components are constrained to sum to a constant value (1, 100%, etc.). However, compositional models can be thought of as mixture models, where members of the population are sampled at random. Conversely, mixture models can be thought of as compositional models, where the total size reading population has been normalized to 1.

General mixture model
A typical finite-dimensional mixture model is a hierarchical model consisting of the following components:

 * N random variables that are observed, each distributed according to a mixture of K components, with the components belonging to the same parametric family of distributions (e.g., all normal, all Zipfian, etc.) but with different parameters
 * N random latent variables specifying the identity of the mixture component of each observation, each distributed according to a K-dimensional categorical distribution
 * A set of K mixture weights, which are probabilities that sum to 1.
 * A set of K parameters, each specifying the parameter of the corresponding mixture component. In many cases, each "parameter" is actually a set of parameters.  For example, if the mixture components are Gaussian distributions, there will be a mean and variance for each component. If the mixture components are categorical distributions (e.g., when each observation is a token from a finite alphabet of size V), there will be a vector of V probabilities summing to 1.

In addition, in a Bayesian setting, the mixture weights and parameters will themselves be random variables, and prior distributions will be placed over the variables. In such a case, the weights are typically viewed as a K-dimensional random vector drawn from a Dirichlet distribution (the conjugate prior of the categorical distribution), and the parameters will be distributed according to their respective conjugate priors.

Mathematically, a basic parametric mixture model can be described as follows:

\begin{array}{lcl} K &=& \text{number of mixture components} \\ N &=& \text{number of observations} \\ \theta_{i=1 \dots K} &=& \text{parameter of distribution of observation associated with component } i \\ \phi_{i=1 \dots K} &=& \text{mixture weight, i.e., prior probability of a particular component } i \\ \boldsymbol\phi &=& K\text{-dimensional vector composed of all the individual } \phi_{1 \dots K} \text{; must sum to 1} \\ z_{i=1 \dots N} &=& \text{component of observation } i \\ x_{i=1 \dots N} &=& \text{observation } i \\ F(x|\theta) &=& \text{probability distribution of an observation, parametrized on } \theta \\ z_{i=1 \dots N} &\sim& \operatorname{Categorical}(\boldsymbol\phi) \\ x_{i=1 \dots N}|z_{i=1 \dots N} &\sim& F(\theta_{z_i}) \end{array} $$

In a Bayesian setting, all parameters are associated with random variables, as follows:

\begin{array}{lcl} K,N &=& \text{as above} \\ \theta_{i=1 \dots K}, \phi_{i=1 \dots K}, \boldsymbol\phi &=& \text{as above} \\ z_{i=1 \dots N}, x_{i=1 \dots N}, F(x|\theta) &=& \text{as above} \\ \alpha &=& \text{shared hyperparameter for component parameters} \\ \beta &=& \text{shared hyperparameter for mixture weights} \\ H(\theta|\alpha) &=& \text{prior probability distribution of component parameters, parametrized on } \alpha \\ \theta_{i=1 \dots K} &\sim& H(\theta|\alpha) \\ \boldsymbol\phi &\sim& \operatorname{Symmetric-Dirichlet}_K(\beta) \\ z_{i=1 \dots N}|\boldsymbol\phi &\sim& \operatorname{Categorical}(\boldsymbol\phi) \\ x_{i=1 \dots N}|z_{i=1 \dots N},\theta_{i=1 \dots K} &\sim& F(\theta_{z_i}) \end{array} $$

This characterization uses F and H to describe arbitrary distributions over observations and parameters, respectively. Typically H will be the conjugate prior of F. The two most common choices of F are Gaussian aka "normal" (for real-valued observations) and categorical (for discrete observations). Other common possibilities for the distribution of the mixture components are:
 * Binomial distribution, for the number of "positive occurrences" (e.g., successes, yes votes, etc.) given a fixed number of total occurrences
 * Multinomial distribution, similar to the binomial distribution, but for counts of multi-way occurrences (e.g., yes/no/maybe in a survey)
 * Negative binomial distribution, for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs
 * Poisson distribution, for the number of occurrences of an event in a given period of time, for an event that is characterized by a fixed rate of occurrence
 * Exponential distribution, for the time before the next event occurs, for an event that is characterized by a fixed rate of occurrence
 * Log-normal distribution, for positive real numbers that are assumed to grow exponentially, such as incomes or prices
 * Multivariate normal distribution (aka multivariate Gaussian distribution), for vectors of correlated outcomes that are individually Gaussian-distributed
 * Multivariate Student's t-distribution, for vectors of heavy-tailed correlated outcomes
 * A vector of Bernoulli-distributed values, corresponding, e.g., to a black-and-white image, with each value representing a pixel; see the handwriting-recognition example below

Gaussian mixture model

A typical non-Bayesian Gaussian mixture model looks like this:

\begin{array}{lcl} K,N &=& \text{as above} \\ \phi_{i=1 \dots K}, \boldsymbol\phi &=& \text{as above} \\ z_{i=1 \dots N}, x_{i=1 \dots N} &=& \text{as above} \\ \theta_{i=1 \dots K} &=& \{ \mu_{i=1 \dots K}, \sigma^2_{i=1 \dots K} \} \\ \mu_{i=1 \dots K} &=& \text{mean of component } i \\ \sigma^2_{i=1 \dots K} &=& \text{variance of component } i \\ z_{i=1 \dots N} &\sim& \operatorname{Categorical}(\boldsymbol\phi) \\ x_{i=1 \dots N} &\sim& \mathcal{N}(\mu_{z_i}, \sigma^2_{z_i}) \end{array} $$

A Bayesian version of a Gaussian mixture model is as follows:

\begin{array}{lcl} K,N &=& \text{as above} \\ \phi_{i=1 \dots K}, \boldsymbol\phi &=& \text{as above} \\ z_{i=1 \dots N}, x_{i=1 \dots N} &=& \text{as above} \\ \theta_{i=1 \dots K} &=& \{ \mu_{i=1 \dots K}, \sigma^2_{i=1 \dots K} \} \\ \mu_{i=1 \dots K} &=& \text{mean of component } i \\ \sigma^2_{i=1 \dots K} &=& \text{variance of component } i \\ \mu_0, \lambda, \nu, \sigma_0^2 &=& \text{shared hyperparameters} \\ \mu_{i=1 \dots K} &\sim& \mathcal{N}(\mu_0, \lambda\sigma_i^2) \\ \sigma_{i=1 \dots K}^2 &\sim& \operatorname{Inverse-Gamma}(\nu, \sigma_0^2) \\ \boldsymbol\phi &\sim& \operatorname{Symmetric-Dirichlet}_K(\beta) \\ z_{i=1 \dots N} &\sim& \operatorname{Categorical}(\boldsymbol\phi) \\ x_{i=1 \dots N} &\sim& \mathcal{N}(\mu_{z_i}, \sigma^2_{z_i}) \end{array} $$$$$$

Multivariate Gaussian mixture model
A Bayesian Gaussian mixture model is commonly extended to fit a vector of unknown parameters (denoted in bold), or multivariate normal distributions. In a multivariate distribution (i.e. one modelling a vector $$\boldsymbol{x}$$ with N random variables) one may model a vector of parameters (such as several observations of a signal or patches within an image) using a Gaussian mixture model prior distribution on the vector of estimates given by

p(\boldsymbol{\theta}) = \sum_{i=1}^K\phi_i \mathcal{N}(\boldsymbol{\mu_i,\Sigma_i}) $$ where the ith vector component is characterized by normal distributions with weights $$\phi_i$$, means $$\boldsymbol{\mu_i}$$ and covariance matrices $$\boldsymbol{\Sigma_i}$$. To incorporate this prior into a Bayesian estimation, the prior is multiplied with the known distribution $$p(\boldsymbol{x | \theta})$$ of the data $$\boldsymbol{x}$$ conditioned on the parameters $$\boldsymbol{\theta}$$ to be estimated. With this formulation, the posterior distribution $$p(\boldsymbol{\theta | x})$$ is also a Gaussian mixture model of the form

p(\boldsymbol{\theta | x}) = \sum_{i=1}^K\tilde{\phi_i} \mathcal{N}(\boldsymbol{\tilde{\mu_i},\tilde{\Sigma_i}}) $$ with new parameters $$\tilde{\phi_i}, \boldsymbol{\tilde{\mu_i}}$$ and $$\boldsymbol{\tilde{\Sigma_i}}$$ that are updated using the EM algorithm. Although EM-based parameter updates are well-established, providing the initial estimates for these parameters is currently an area of active research. Note that this formulation yields a closed-form solution to the complete posterior distribution. Estimations of the random variable $$\boldsymbol{\theta}$$ may be obtained via one of several estimators, such as the mean or maximum of the posterior distribution.

Such distributions are useful for assuming patch-wise shapes of images and clusters, for example. In the case of image representation, each Gaussian may be tilted, expanded, and warped according to the covariance matrices $$\boldsymbol{\Sigma_i}$$. One Gaussian distribution of the set is fit to each patch (usually of size 8x8 pixels) in the image. Notably, any distribution of points around a cluster (see k-means) may be accurately given enough Gaussian components, but scarcely over K=20 components are needed to accurately model a given image distribution or cluster of data.

Categorical mixture model

A typical non-Bayesian mixture model with categorical observations looks like this:

 * $$K,N:$$ as above
 * $$\phi_{i=1 \dots K}, \boldsymbol\phi:$$ as above
 * $$z_{i=1 \dots N}, x_{i=1 \dots N}:$$ as above
 * $$V:$$ dimension of categorical observations, e.g., size of word vocabulary
 * $$\theta_{i=1 \dots K, j=1 \dots V}:$$ probability for component $$i$$ of observing item $$j$$
 * $$\boldsymbol\theta_{i=1 \dots K}:$$ vector of dimension $$V,$$ composed of $$\theta_{i,1 \dots V};$$ must sum to 1

The random variables:

\begin{array}{lcl} z_{i=1 \dots N} &\sim& \operatorname{Categorical}(\boldsymbol\phi) \\ x_{i=1 \dots N} &\sim& \text{Categorical}(\boldsymbol\theta_{z_i}) \end{array} $$

A typical Bayesian mixture model with categorical observations looks like this:

 * $$K,N:$$ as above
 * $$\phi_{i=1 \dots K}, \boldsymbol\phi:$$ as above
 * $$z_{i=1 \dots N}, x_{i=1 \dots N}:$$ as above
 * $$V:$$ dimension of categorical observations, e.g., size of word vocabulary
 * $$\theta_{i=1 \dots K, j=1 \dots V}:$$ probability for component $$i$$ of observing item $$j$$
 * $$\boldsymbol\theta_{i=1 \dots K}:$$ vector of dimension $$V,$$ composed of $$\theta_{i,1 \dots V};$$ must sum to 1
 * $$\alpha:$$ shared concentration hyperparameter of $$\boldsymbol\theta$$ for each component
 * $$\beta:$$ concentration hyperparameter of $$\boldsymbol\phi$$

The random variables:

\begin{array}{lcl} \boldsymbol\phi &\sim& \operatorname{Symmetric-Dirichlet}_K(\beta) \\ \boldsymbol\theta_{i=1 \dots K} &\sim& \text{Symmetric-Dirichlet}_V(\alpha) \\ z_{i=1 \dots N} &\sim& \operatorname{Categorical}(\boldsymbol\phi) \\ x_{i=1 \dots N} &\sim& \text{Categorical}(\boldsymbol\theta_{z_i}) \end{array} $$

A financial model

Financial returns often behave differently in normal situations and during crisis times. A mixture model for return data seems reasonable. Sometimes the model used is a jump-diffusion model, or as a mixture of two normal distributions. See and  for further context.

House prices
Assume that we observe the prices of N different houses. Different types of houses in different neighborhoods will have vastly different prices, but the price of a particular type of house in a particular neighborhood (e.g., three-bedroom house in moderately upscale neighborhood) will tend to cluster fairly closely around the mean. One possible model of such prices would be to assume that the prices are accurately described by a mixture model with K different components, each distributed as a normal distribution with unknown mean and variance, with each component specifying a particular combination of house type/neighborhood. Fitting this model to observed prices, e.g., using the expectation-maximization algorithm, would tend to cluster the prices according to house type/neighborhood and reveal the spread of prices in each type/neighborhood. (Note that for values such as prices or incomes that are guaranteed to be positive and which tend to grow exponentially, a log-normal distribution might actually be a better model than a normal distribution.)

Topics in a document
Assume that a document is composed of N different words from a total vocabulary of size V, where each word corresponds to one of K possible topics. The distribution of such words could be modelled as a mixture of K different V-dimensional categorical distributions. A model of this sort is commonly termed a topic model. Note that expectation maximization applied to such a model will typically fail to produce realistic results, due (among other things) to the excessive number of parameters. Some sorts of additional assumptions are typically necessary to get good results. Typically two sorts of additional components are added to the model:
 * 1) A prior distribution is placed over the parameters describing the topic distributions, using a Dirichlet distribution with a concentration parameter that is set significantly below 1, so as to encourage sparse distributions (where only a small number of words have significantly non-zero probabilities).
 * 2) Some sort of additional constraint is placed over the topic identities of words, to take advantage of natural clustering.
 * For example, a Markov chain could be placed on the topic identities (i.e., the latent variables specifying the mixture component of each observation), corresponding to the fact that nearby words belong to similar topics. (This results in a hidden Markov model, specifically one where a prior distribution is placed over state transitions that favors transitions that stay in the same state.)
 * Another possibility is the latent Dirichlet allocation model, which divides up the words into D different documents and assumes that in each document only a small number of topics occur with any frequency.

Handwriting recognition
The following example is based on an example in Christopher M. Bishop, Pattern Recognition and Machine Learning.

Imagine that we are given an N×N black-and-white image that is known to be a scan of a hand-written digit between 0 and 9, but we don't know which digit is written. We can create a mixture model with $$K=10$$ different components, where each component is a vector of size $$N^2$$ of Bernoulli distributions (one per pixel). Such a model can be trained with the expectation-maximization algorithm on an unlabeled set of hand-written digits, and will effectively cluster the images according to the digit being written. The same model could then be used to recognize the digit of another image simply by holding the parameters constant, computing the probability of the new image for each possible digit (a trivial calculation), and returning the digit that generated the highest probability.

Assessing projectile accuracy (a.k.a. circular error probable, CEP)
Mixture models apply in the problem of directing multiple projectiles at a target (as in air, land, or sea defense applications), where the physical and/or statistical characteristics of the projectiles differ within the multiple projectiles. An example might be shots from multiple munitions types or shots from multiple locations directed at one target. The combination of projectile types may be characterized as a Gaussian mixture model. Further, a well-known measure of accuracy for a group of projectiles is the circular error probable (CEP), which is the number R such that, on average, half of the group of projectiles falls within the circle of radius R about the target point. The mixture model can be used to determine (or estimate) the value R. The mixture model properly captures the different types of projectiles.

Direct and indirect applications
The financial example above is one direct application of the mixture model, a situation in which we assume an underlying mechanism so that each observation belongs to one of some number of different sources or categories. This underlying mechanism may or may not, however, be observable. In this form of mixture, each of the sources is described by a component probability density function, and its mixture weight is the probability that an observation comes from this component.

In an indirect application of the mixture model we do not assume such a mechanism. The mixture model is simply used for its mathematical flexibilities. For example, a mixture of two normal distributions with different means may result in a density with two modes, which is not modeled by standard parametric distributions. Another example is given by the possibility of mixture distributions to model fatter tails than the basic Gaussian ones, so as to be a candidate for modeling more extreme events. When combined with dynamical consistency, this approach has been applied to financial derivatives valuation in presence of the volatility smile in the context of local volatility models. This defines our application.

Predictive Maintenance
The mixture model-based clustering is also predominantly used in identifying the state of the machine in predictive maintenance. Density plots are used to analyze the density of high dimensional features. If multi-model densities are observed, then it is assumed that a finite set of densities are formed by a finite set of normal mixtures. A multivariate Gaussian mixture model is used to cluster the feature data into k number of groups where k represents each state of the machine. The machine state can be a normal state, power off state, or faulty state. Each formed cluster can be diagnosed using techniques such as spectral analysis. In the recent years, this has also been widely used in other areas such as early fault detection.

Fuzzy image segmentation
In image processing and computer vision, traditional image segmentation models often assign to one pixel only one exclusive pattern. In fuzzy or soft segmentation, any pattern can have certain "ownership" over any single pixel. If the patterns are Gaussian, fuzzy segmentation naturally results in Gaussian mixtures. Combined with other analytic or geometric tools (e.g., phase transitions over diffusive boundaries), such spatially regularized mixture models could lead to more realistic and computationally efficient segmentation methods.

Point set registration
Probabilistic mixture models such as Gaussian mixture models (GMM) are used to resolve point set registration problems in image processing and computer vision fields. For pair-wise point set registration, one point set is regarded as the centroids of mixture models, and the other point set is regarded as data points (observations). State-of-the-art methods are e.g. coherent point drift (CPD) and Student's t-distribution mixture models (TMM). The result of recent research demonstrate the superiority of hybrid mixture models (e.g. combining Student's t-distribution and Watson distribution/Bingham distribution to model spatial positions and axes orientations separately) compare to CPD and TMM, in terms of inherent robustness, accuracy and discriminative capacity.

Identifiability
Identifiability refers to the existence of a unique characterization for any one of the models in the class (family) being considered. Estimation procedures may not be well-defined and asymptotic theory may not hold if a model is not identifiable.

Example
Let J be the class of all binomial distributions with. Then a mixture of two members of J would have

 * $$p_0=\pi(1-\theta_1)^2+(1-\pi)(1-\theta_2)^2$$
 * $$p_1=2\pi\theta_1(1-\theta_1)+2(1-\pi)\theta_2(1-\theta_2)$$

and. Clearly, given p0 and p1, it is not possible to determine the above mixture model uniquely, as there are three parameters (π, θ1, θ2) to be determined.

Definition
Consider a mixture of parametric distributions of the same class. Let

 * $$J=\{f(\cdot ; \theta):\theta\in\Omega\}$$

be the class of all component distributions. Then the convex hull K of J defines the class of all finite mixture of distributions in J:

 * $$K=\left\{p(\cdot):p(\cdot)=\sum_{i=1}^n a_i f_i(\cdot ; \theta_i), a_i>0, \sum_{i=1}^n a_i=1, f_i(\cdot ; \theta_i)\in J\ \forall i,n\right\}$$

K is said to be identifiable if all its members are unique, that is, given two members p and p′ in K, being mixtures of k distributions and k′ distributions respectively in J, we have if and only if, first of all,  and secondly we can reorder the summations such that  and  for all i.

Parameter estimation and system identification
Parametric mixture models are often used when we know the distribution Y and we can sample from X, but we would like to determine the ai and θi values. Such situations can arise in studies in which we sample from a population that is composed of several distinct subpopulations.

It is common to think of probability mixture modeling as a missing data problem. One way to understand this is to assume that the data points under consideration have "membership" in one of the distributions we are using to model the data. When we start, this membership is unknown, or missing. The job of estimation is to devise appropriate parameters for the model functions we choose, with the connection to the data points being represented as their membership in the individual model distributions.

A variety of approaches to the problem of mixture decomposition have been proposed, many of which focus on maximum likelihood methods such as expectation maximization (EM) or maximum a posteriori estimation (MAP). Generally these methods consider separately the questions of system identification and parameter estimation; methods to determine the number and functional form of components within a mixture are distinguished from methods to estimate the corresponding parameter values. Some notable departures are the graphical methods as outlined in Tarter and Lock and more recently minimum message length (MML) techniques such as Figueiredo and Jain and to some extent the moment matching pattern analysis routines suggested by McWilliam and Loh (2009).

Expectation maximization (EM)
Expectation maximization (EM) is seemingly the most popular technique used to determine the parameters of a mixture with an a priori given number of components. This is a particular way of implementing maximum likelihood estimation for this problem. EM is of particular appeal for finite normal mixtures where closed-form expressions are possible such as in the following iterative algorithm by Dempster et al. (1977)

 * $$ w_s^{(j+1)} = \frac{1}{N} \sum_{t =1}^N h_s^{(j)}(t) $$
 * $$ \mu_s^{(j+1)} =  \frac{\sum_{t =1}^N h_s^{(j)}(t) x^{(t)}}{\sum_{t =1}^N h_s^{(j)}(t)} $$
 * $$ \Sigma_s^{(j+1)} =  \frac{\sum_{t =1}^N h_s^{(j)}(t) [x^{(t)}-\mu_s^{(j+1)}][x^{(t)}-\mu_s^{(j+1)}]^{\top}}{\sum_{t =1}^N h_s^{(j)}(t)} $$

with the posterior probabilities
 * $$ h_s^{(j)}(t) = \frac{w_s^{(j)} p_s(x^{(t)}; \mu_s^{(j)},\Sigma_s^{(j)}) }{ \sum_{i = 1}^n w_i^{(j)} p_i(x^{(t)}; \mu_i^{(j)}, \Sigma_i^{(j)})}. $$

Thus on the basis of the current estimate for the parameters, the conditional probability for a given observation x(t) being generated from state s is determined for each ; N being the sample size. The parameters are then updated such that the new component weights correspond to the average conditional probability and each component mean and covariance is the component specific weighted average of the mean and covariance of the entire sample.

Dempster also showed that each successive EM iteration will not decrease the likelihood, a property not shared by other gradient based maximization techniques. Moreover, EM naturally embeds within it constraints on the probability vector, and for sufficiently large sample sizes positive definiteness of the covariance iterates. This is a key advantage since explicitly constrained methods incur extra computational costs to check and maintain appropriate values. Theoretically EM is a first-order algorithm and as such converges slowly to a fixed-point solution. Redner and Walker (1984) make this point arguing in favour of superlinear and second order Newton and quasi-Newton methods and reporting slow convergence in EM on the basis of their empirical tests. They do concede that convergence in likelihood was rapid even if convergence in the parameter values themselves was not. The relative merits of EM and other algorithms vis-à-vis convergence have been discussed in other literature.

Other common objections to the use of EM are that it has a propensity to spuriously identify local maxima, as well as displaying sensitivity to initial values. One may address these problems by evaluating EM at several initial points in the parameter space but this is computationally costly and other approaches, such as the annealing EM method of Udea and Nakano (1998) (in which the initial components are essentially forced to overlap, providing a less heterogeneous basis for initial guesses), may be preferable.

Figueiredo and Jain note that convergence to 'meaningless' parameter values obtained at the boundary (where regularity conditions breakdown, e.g., Ghosh and Sen (1985)) is frequently observed when the number of model components exceeds the optimal/true one. On this basis they suggest a unified approach to estimation and identification in which the initial n is chosen to greatly exceed the expected optimal value. Their optimization routine is constructed via a minimum message length (MML) criterion that effectively eliminates a candidate component if there is insufficient information to support it. In this way it is possible to systematize reductions in n and consider estimation and identification jointly.

The expectation step
With initial guesses for the parameters of our mixture model, "partial membership" of each data point in each constituent distribution is computed by calculating expectation values for the membership variables of each data point. That is, for each data point xj and distribution Yi, the membership value yi, j is:

 * $$ y_{i,j} = \frac{a_i f_Y(x_j;\theta_i)}{f_{X}(x_j)}.$$

The maximization step
With expectation values in hand for group membership, plug-in estimates are recomputed for the distribution parameters.

The mixing coefficients ai are the means of the membership values over the N data points.

 * $$ a_i = \frac{1}{N}\sum_{j=1}^N y_{i,j}$$

The component model parameters θi are also calculated by expectation maximization using data points xj that have been weighted using the membership values. For example, if θ is a mean μ

 * $$ \mu_{i} = \frac{\sum_{j} y_{i,j}x_{j}}{\sum_{j} y_{i,j}}.$$

With new estimates for ai and the θi's, the expectation step is repeated to recompute new membership values. The entire procedure is repeated until model parameters converge.

Markov chain Monte Carlo
As an alternative to the EM algorithm, the mixture model parameters can be deduced using posterior sampling as indicated by Bayes' theorem. This is still regarded as an incomplete data problem whereby membership of data points is the missing data. A two-step iterative procedure known as Gibbs sampling can be used.

The previous example of a mixture of two Gaussian distributions can demonstrate how the method works. As before, initial guesses of the parameters for the mixture model are made. Instead of computing partial memberships for each elemental distribution, a membership value for each data point is drawn from a Bernoulli distribution (that is, it will be assigned to either the first or the second Gaussian). The Bernoulli parameter θ is determined for each data point on the basis of one of the constituent distributions. Draws from the distribution generate membership associations for each data point. Plug-in estimators can then be used as in the M step of EM to generate a new set of mixture model parameters, and the binomial draw step repeated.

Moment matching
The method of moment matching is one of the oldest techniques for determining the mixture parameters dating back to Karl Pearson's seminal work of 1894. In this approach the parameters of the mixture are determined such that the composite distribution has moments matching some given value. In many instances extraction of solutions to the moment equations may present non-trivial algebraic or computational problems. Moreover, numerical analysis by Day has indicated that such methods may be inefficient compared to EM. Nonetheless, there has been renewed interest in this method, e.g., Craigmile and Titterington (1998) and Wang.

McWilliam and Loh (2009) consider the characterisation of a hyper-cuboid normal mixture copula in large dimensional systems for which EM would be computationally prohibitive. Here a pattern analysis routine is used to generate multivariate tail-dependencies consistent with a set of univariate and (in some sense) bivariate moments. The performance of this method is then evaluated using equity log-return data with Kolmogorov–Smirnov test statistics suggesting a good descriptive fit.

Spectral method
Some problems in mixture model estimation can be solved using spectral methods. In particular it becomes useful if data points xi are points in high-dimensional real space, and the hidden distributions are known to be log-concave (such as Gaussian distribution or Exponential distribution).

Spectral methods of learning mixture models are based on the use of Singular Value Decomposition of a matrix which contains data points. The idea is to consider the top k singular vectors, where k is the number of distributions to be learned. The projection of each data point to a linear subspace spanned by those vectors groups points originating from the same distribution very close together, while points from different distributions stay far apart.

One distinctive feature of the spectral method is that it allows us to prove that if distributions satisfy certain separation condition (e.g., not too close), then the estimated mixture will be very close to the true one with high probability.

Graphical Methods
Tarter and Lock describe a graphical approach to mixture identification in which a kernel function is applied to an empirical frequency plot so to reduce intra-component variance. In this way one may more readily identify components having differing means. While this λ-method does not require prior knowledge of the number or functional form of the components its success does rely on the choice of the kernel parameters which to some extent implicitly embeds assumptions about the component structure.

Other methods
Some of them can even probably learn mixtures of heavy-tailed distributions including those with infinite variance (see links to papers below). In this setting, EM based methods would not work, since the Expectation step would diverge due to presence of outliers.

A simulation
To simulate a sample of size N that is from a mixture of distributions Fi, i=1 to n, with probabilities pi (sum= pi = 1):
 * 1) Generate N random numbers from a categorical distribution of size n and probabilities pi for i= 1= to n.  These tell you which of the Fi each of the N values will come from.  Denote by mi the quantity of random numbers assigned to the ith category.
 * 2) For each i, generate mi random numbers from the Fi distribution.

Extensions
In a Bayesian setting, additional levels can be added to the graphical model defining the mixture model. For example, in the common latent Dirichlet allocation topic model, the observations are sets of words drawn from D different documents and the K mixture components represent topics that are shared across documents. Each document has a different set of mixture weights, which specify the topics prevalent in that document. All sets of mixture weights share common hyperparameters.

A very common extension is to connect the latent variables defining the mixture component identities into a Markov chain, instead of assuming that they are independent identically distributed random variables. The resulting model is termed a hidden Markov model and is one of the most common sequential hierarchical models. Numerous extensions of hidden Markov models have been developed; see the resulting article for more information.

History
Mixture distributions and the problem of mixture decomposition, that is the identification of its constituent components and the parameters thereof, has been cited in the literature as far back as 1846 (Quetelet in McLachlan, 2000) although common reference is made to the work of Karl Pearson (1894) as the first author to explicitly address the decomposition problem in characterising non-normal attributes of forehead to body length ratios in female shore crab populations. The motivation for this work was provided by the zoologist Walter Frank Raphael Weldon who had speculated in 1893 (in Tarter and Lock ) that asymmetry in the histogram of these ratios could signal evolutionary divergence. Pearson's approach was to fit a univariate mixture of two normals to the data by choosing the five parameters of the mixture such that the empirical moments matched that of the model.

While his work was successful in identifying two potentially distinct sub-populations and in demonstrating the flexibility of mixtures as a moment matching tool, the formulation required the solution of a 9th degree (nonic) polynomial which at the time posed a significant computational challenge.

Subsequent works focused on addressing these problems, but it was not until the advent of the modern computer and the popularisation of Maximum Likelihood (MLE) parameterisation techniques that research really took off. Since that time there has been a vast body of research on the subject spanning areas such as fisheries research, agriculture, botany, economics, medicine, genetics, psychology, palaeontology, electrophoresis, finance, geology and zoology.

Mixture

 * Mixture density
 * Mixture (probability)
 * Flexible Mixture Model (FMM)
 * Subspace Gaussian mixture model

Hierarchical models

 * Graphical model
 * Hierarchical Bayes model

Outlier detection

 * RANSAC

title: Mixture model


text:
Face the Music

Face the Music may refer to:

Film and television

 * Face the Music (film), a 1954 British crime film directed by Terence Fisher
 * Face the Music, a 1993 film starring Molly Ringwald and Patrick Dempsey
 * Face the Music, a 2000 film featuring Tyler Christopher
 * Face the Music (American game show), a 1980–1981 music quiz show
 * Face the Music (British game show), a 1967–1984 music quiz show
 * Face the Music (New Zealand game show), a 1992–1994 music quiz show
 * Bill & Ted Face the Music, the third film of the Bill & Ted franchise (2020)

Literature

 * Face the Music, a 1954 novel by Ernest Bornemann, basis for the 1954 film
 * Face the Music, a 2014 novel by Greg Anton
 * Face the Music, a Hannah Montana television series novelization
 * Face the Music: A Life Exposed, a 2014 memoir by Paul Stanley

Music

 * Face the Music (music ensemble), a classical youth ensemble from New York City
 * Face the Music (musical), a 1932 Broadway musical

Albums

 * Face the Music (Avant album), 2013
 * Face the Music (Burning Rain album) or the title song, 2019
 * Face the Music (Electric Light Orchestra album), 1975
 * Face the Music (Melody Club album), 2004
 * Face the Music (New Kids on the Block album) or the title song, 1994
 * Face the Music (EP), by Marianas Trench, 2013
 * Face the Music, by Meg Christian, 1977
 * Face the Music, by George Duke, 2002
 * Face the Music, by Sinne Eeg, 2014
 * Face the Music, by Nils Lofgren, 2014
 * Face the Music, by Rick Moses, 1978

Songs

 * "Face the Music", by Conjure One from Extraordinary Ways, 2005
 * "Face the Music", by Crazy Town from The Gift of Game, 1999
 * "Face the Music", by Louis Tomlinson from Faith in the Future, 2022
 * "Face the Music", by Wyld Stallyns from the film Bill & Ted Face the Music, 2020

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Face the Music


text: Talk:Face the Music

title: Talk:Face the Music


text: Category:The Velvet Underground albums

title: Category:The Velvet Underground albums


text:
Category:Prehistoric birds

This is a category for birds that are only known from fossil evidence or oral traditions.

Several early taxa are not unequivocally classified as birds or non-avian dinosaurs; for these, both inclusion in this category and Category:Feathered dinosaurs is feasible. As soon as a taxon is generally accepted to be a bird or a non-avian dinosaur, it should only be listed in one of the aforementioned categories as appropriate.

A note on the use of subcategories and page listings:

A page should be listed here if it deals with:
 * a taxon above the rank of genus
 * a genus or species which occurred over several geologic periods.

Other genera, species and subspecies should be listed under the appropriate subcategory.

title: Category:Prehistoric birds


text:
Killing spinor

Killing spinor is a term used in mathematics and physics.

Definition
By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates those twistor spinors which are also eigenspinors of the Dirac operator. The term is named after Wilhelm Killing.

Another equivalent definition is that Killing spinors are the solutions to the Killing equation for a so-called Killing number.

More formally:

 * A Killing spinor on a Riemannian spin manifold M is a spinor field $$\psi$$ which satisfies

 * $$\nabla_X\psi=\lambda X\cdot\psi$$

 * for all tangent vectors X, where $$\nabla$$ is the spinor covariant derivative, $$\cdot$$ is Clifford multiplication and $$\lambda \in \mathbb{C}$$ is a constant, called the Killing number of $$\psi$$. If $$\lambda=0$$ then the spinor is called a parallel spinor.

Applications
In physics, Killing spinors are used in supergravity and superstring theory, in particular for finding solutions which preserve some supersymmetry. They are a special kind of spinor field related to Killing vector fields and Killing tensors.

Properties
If $$\mathcal{M}$$ is a manifold with a Killing spinor, then $$\mathcal{M}$$ is an Einstein manifold with Ricci curvature $$Ric=4(n-1)\alpha^2 $$, where $$\alpha$$ is the Killing constant.

Types of Killing spinor fields
If $$\alpha$$ is purely imaginary, then $$\mathcal{M}$$ is a noncompact manifold; if $$\alpha$$ is 0, then the spinor field is parallel; finally, if $$\alpha$$ is real, then $$\mathcal{M}$$ is compact, and the spinor field is called a ``real spinor field."

title: Killing spinor


text:
Yourself or Someone Like You

Yourself or Someone Like You is the debut album by American rock band Matchbox 20. It was released on October 1, 1996, by Lava Records and Atlantic Records. The album was certified 12× Platinum by the Recording Industry Association of America.

Composition and release
The album features a sound similar to traditional rock and post-grunge. The album features themes of adolescence, adultery, loneliness, domestic violence, psychological abuse, humiliation, depression, anger, and alcoholism.

According to Rob Thomas, the album's title was originally to be Woodshed Diaries. However, that changed when Thomas and Paul Doucette were at a woman's musical performance at Café Largo when the singer said "this song is for you, or someone like you". They loved the phrase so much that they insisted on changing the album's title, despite the fact that 3,500 copies of the album with the original title had already been made. Their labels agreed, however the name change resulted in the album's release being delayed.

The album sold a mere 610 copies in its first week, but eventually went on to sell several million copies in the United States. Yourself or Someone Like You became one of the few albums to achieve the prestigious Diamond certification, and it was also certified multi-platinum in Australia, Canada and New Zealand. To date, the album has sold more than 15 million copies worldwide.

Artwork lawsuit
In 2005, almost a decade after the album's release, the band was sued by Frank Torres, the man on the album's cover. Torres claimed the band never asked for his permission to use his image on the sleeve. In the litigation, Torres claimed the photo was taken as he was walking down the street after being asked to pose. He also claimed the photo had caused him emotional distress. Torres justified the delay in suing Matchbox 20 by claiming he had first seen the album photo within two years of the litigation. Torres died in 2016 at age 73.

Personnel
Matchbox 20
 * Rob Thomas – lead vocals; acoustic guitar on "Hang"
 * Kyle Cook – lead guitar, backing vocals, co-lead vocals on "Hang"
 * Adam Gaynor – rhythm guitar, backing vocals
 * Brian Yale – bass
 * Paul Doucette – drums

Additional musicians
 * Matt Serletic – keyboards, percussion
 * Elizabeth Burkhardt – bassoon and woodwind leader on "Back 2 Good"
 * Amy Porter – flute on "Back 2 Good"
 * Yvonne Powers – oboe on "Back 2 Good"
 * Ted Gurch – clarinet on "Back 2 Good"
 * Douglas Smith – bass clarinet on "Back 2 Good"

Production
 * Matt Serletic – producer, mixing engineer
 * Jeff Tomei – engineer
 * Travis McGehee – engineer/mixing engineer
 * John Nielsen – assistant engineer
 * Greg Archilla – mixing engineer
 * Malcolm Springer – assistant mixing engineer
 * Stephen Marcussen – mastering engineer
 * Don C. Tyler – digital editing
 * Tony Adams – drum tech
 * Craig Poole – guitar tech
 * Jan Smith – vocal coach
 * Valerie Wagner – art direction, graphic design
 * Katrin Thomas – photography
 * Chris Cuffaro – band photo

title: Yourself or Someone Like You


text:
Jody Lynn Nye

Jody Lynn Nye (born 1957) is an American science fiction writer. She is the author or co-author of approximately forty published novels and more than 100 short stories. She has specialized in science fiction or fantasy action novels and humor. Her humorous series range from contemporary fantasy (The Magic Touch and Mythology 101) to military science fiction (Strong Arm Tactics and a new series beginning with View from the Imperium). About one-third of her novels are collaborations, either as a co-author or as the author of a sequel. She has been an instructor of the Fantasy Writing Workshop at Columbia College Chicago (2007) and she teaches the annual Science Fiction Writing Workshop at DragonCon.

Nye began collaborating with Robert Lynn Asprin on the MythAdventures series in 2003 with the publication of the collection Myth-told Tales and the novel Myth Alliances. Since Asprin's death in 2008 she has continued that humorous fantasy series and she is now also writing sequels to his Dragons, or Griffen McCandles, contemporary fantasy series.

In 2008 she donated her archive to the department of Rare Books and Special Collections at Northern Illinois University Libraries.

Career
Born 1957 in Chicago, Illinois, Nye says that she "always told stories" to her younger brothers, cousins, and friends, and as a junior camp counselor. Her first published writings were technical articles on broadcasting in the magazine "Video Action" during the 1980s. She first wrote fiction for the "Ellery Queen Mystery Magazine game" and the Role-Aids line of game supplements published by Mayfair Games.

Late in the eighties Nye wrote six companion books for the Dragonriders of Pern series by Anne McCaffrey and the Magic of Xanth series by Piers Anthony. The first four were "branching-path" gamebooks in the Crossroads Adventure series, two set on Pern and two in Xanth. Then simultaneously November 1989, Ballantine Books published The Dragonlover's Guide to Pern by Nye with McCaffrey and Avon Books published Piers Anthony's Visual Guide to Xanth by Nye and Anthony. Todd Cameron Hamilton and James Clouse were the illustrators for both Guides, as Hamilton had been for Roger Zelazny's Visual Guide to Amber published by Avon one year earlier.

For the Pern guide, Nye explained in its introduction, her team (without Clouse) had visited McCaffrey two years earlier, for ten days during October 1987. In the living room Nye, editor Bill Fawcett (Nye's husband), illustrator Hamilton, and McCaffrey's son Todd Johnson discussed Pern with its creator and Hamilton sketched under her direction. They produced "a companion volume to her work, intended to help you visualize the setting and background for her chronicles."

Before The Dragonlover's Guide was finished, McCaffrey and Nye were working together on a novel, presumably The Death of Sleep (1990) in the Planet Pirates trilogy. In the early 1990s they collaborated in three series based on McCaffrey stories from the 1960s and 1970s. Meanwhile, McCaffrey completed five more Pern books, after which they revised The Dragonlover's Guide.

Late in the 1990s Nye began work with Robert Asprin to extend the Myth Adventures series he had started in 1978. After his 2008 death she continued to write books they had planned. Meanwhile, three of Nye's book series were "adrift" since Meisha Merlin Publishing went out of business in 2007.

Among other projects, Nye is continuing to write the Myth Adventures series and her military SF/humor series begun with View from the Imperium (2011).

Series

 * Mythology
 * 1) Mythology 101 (1990)
 * 2) Mythology Abroad (1991)
 * 3) Higher Mythology (1993)
 * 4) Advanced Mythology (2001)
 * Applied Mythology (2000) – omnibus edition of books 1–3

Asprin alone wrote 12 novels in the MythAdventures series that were published from 1978 to 2002.
 * MythAdventures
 * Myth-told Tales (2003), by Robert Lynn Asprin and Nye
 * Myth Alliances (2003), Asprin and Nye
 * Myth-taken Identity (2004), Asprin and Nye
 * Class Dis-Mythed (2005), Asprin and Nye
 * Myth-Gotten Gains (2006), Asprin and Nye
 * Myth-Chief (2008), Asprin and Nye
 * Myth-Fortunes (2011), Asprin and Nye
 * Myth-Quoted (2012) (Advertised as Robert Asprin's Myth-Quoted but authored by Nye alone.)
 * Myth-Fits (2016) (Advertised as Robert Asprin's Myth-Fits but authored by Nye alone.)

 * Imperium (or Lord Thomas Kinago)
 * 1) View from the Imperium (2011)
 * 2) Fortunes of the Imperium (September 2014)
 * 3) Rhythm of the Imperium (November, 2015)

 * Dreamland
 * 1) Waking in Dreamland (1998)
 * 2) School of Light (1999)
 * 3) The Grand Tour (2000)

McCaffrey alone wrote two Dinosaur Planet novels that were published in 1978 and 1984. She and Elizabeth Moon inaugurated the Planet Pirates subseries in a novel that was published a few months before McCaffrey and Nye's.
 * Ireta (or Dinosaur Planet; or Planet Pirates)
 * The Death of Sleep (1990), by Anne McCaffrey and Nye
 * The Planet Pirates (1993), McCaffrey, Elizabeth Moon and Nye – omnibus edition of the 3-volume subseries

McCaffrey alone wrote one Doona novel that was published in 1969.
 * Doona
 * Crisis on Doona (1992), McCaffrey and Nye
 * Treaty at Doona (1994), McCaffrey and Nye; also titled Treaty Planet

 * Taylor's Ark
 * 1) Taylor's Ark (1993)
 * 2) Medicine Show (1994)
 * 3) The Lady and the Tiger (2003)

McCaffrey alone wrote The Ship Who Sang, a collection published in 1969. She wrote three Ship novels in collaboration with three different women that were published in 1992 and 1993.
 * The Ship Who Sang (or Brain and Brawn Ship)
 * The Ship Who Won (1994), McCaffrey and Nye
 * The Ship Errant (1996)
 * The Ship Who Saved the Worlds (2003), McCaffrey and Nye – omnibus comprising The Ship who Won and The Ship Errant

Asprin alone wrote two novels in the Griffen McCandles series, published 2008 and 2009.
 * Dragons, or Griffen McCandles
 * 1) Dragons Deal (2010), by Robert Lynn Asprin and Nye
 * 2) Dragons Run (2013)

Anne McCaffrey inaugurated the long-running Pern series in 1967; Piers Anthony the long-running Xanth series in 1977. ISFDB catalogs the four Crossroads Adventures as novels, the two Guides as reference books, and all six as contributions to the Pern and Xanth series.
 * Crossroads Adventure game books (copyright Bill Fawcett and Associates)
 * Dragonharper (Tor Books, Aug 1987), illus. Todd Cameron Hamilton – set in the world of Pern
 * Encyclopedia of Xanth (1987) – set in the world of Xanth
 * Dragonfire (Tor, Jul 1988), illus. Todd Cameron Hamilton – set in the world of Pern
 * Ghost of a Chance (1988) – set in the world of Xanth

Novels

 * The Magic Touch (1996)
 * License Invoked (2001), by Robert Lynn Asprin and Nye
 * Strong-Arm Tactics (2005)
 * An Unexpected Apprentice (2007)
 * A Forthcoming Wizard (2009)

Anthologies (as editor)

 * Don't Forget Your Spacesuit, Dear (1996); (includes the short story What's the Magic Word?)

Others

 * The Dragonlover's Guide to Pern (Ballantine, 1989), with Anne McCaffrey. Illustrated by Todd Cameron Hamilton and James Clouse. ISBN 0-345-35424-9. xi + 178 pages. — Pern geography, society, flora, fauna, etc., including information not in the previously published fiction
 * The Dragonlover's Guide to Pern, second edition (Ballantine, 1997). ISBN 0-345-41274-5. xi + 260 pages.
 * Piers Anthony's Visual Guide to Xanth (Harper, 1989), with Piers Anthony. Illustrated by Todd Cameron Hamilton and James Clouse. ISBN 0-380-75749-4

Short stories in anthologies

 * The Fleet, "Bolthole", Ace Books (1988)
 * The Fleet II: Counterattack, "Lab Rats", Ace (1988)
 * The Fleet III: Breakthrough, "Crossing the Line", Ace (1989)
 * The Fleet IV: Sworn Allies, "Full Circle", Ace (1990)
 * The Fleet V: Total War "Change Partners and Dance", Ace (1990)
 * The Fleet VI: Crisis, "The Mosquito", Ace (1991)
 * The War Years I: Far Stars War, "Volunteers", New American Library (1990)
 * The War Years II: Siege of Arista, "Unreality", NAL (1991)
 * The War Years III: Jupiter War, "Gold-digging", NAL (1991)
 * The Crafters, "The Seeing Stone", Ace (1991)
 * The Crafters II: Blessings & Curses, "Miss Crafter's School For Girls", Ace (1992)
 * Halflings, Hobbits, Wee Folk and Warrows; "Moon Shadows", Warner Books (1991)
 * Alternate Presidents edited by Mike Resnick, "The Father of His Country", TOR Books (1992)
 * Space Cats, "Well Worth the Money", Baen Books (1992)
 * Battlestation, "Star Light", Ace (1992)
 * Battlestation II, "Shooting Star", Ace (1993)
 * The Gods of War, "Order in Heaven", Baen (1992)
 * More Whatdunits, "Way Out" (by Bill Fawcett and Nye), TOR (1993)
 * Quest to Riverworld, "If the King Like Not the Comedy", Warner (1993)
 * Alien Pregnant By Elvis! "Psychic Bats 1000 for Accuracy", DAW (1994)
 * Dragon’s Eye, "The Stuff of Legends", Baen (1994)
 * Deals With The Devil, "The Party of the First Part", DAW (1994)
 * Elric, Tales of the White Wolf, "The White Child", White Wolf Publishing (1994)
 * Superheroes, "Theme Music Man", Ace (1995)
 * Excalibur, "Sword Practice"—Warner Aspect (1995)
 * Chicks in Chainmail, "The Growling"—Baen (Sept 1995)
 * The Day The Magic Stopped, "Flicker"—Baen (Oct 1995)
 * Fantastic Alice, "Muchness"—Ace (December 1995)
 * Dante’s Disciples, "The Bridge on the River Styx"—White Wolf (1996)
 * Lammas Night, "Sunflower"—Baen (February 1996)
 * Otherwere, "What? And Give Up Show Business?"—Ace (1996)
 * Future Net, "Souvenirs and Photographs"—DAW (1996)
 * Many Faces of Fantasy, "Sidhe Who Must Be Obeyed" -- World Fantasy Convention (Oct 1996)
 * Space Opera, "Calling Them Home"—DAW (1996)
 * Elf Fantastic, "The Dancing Ring"—DAW (1997)
 * First Contact, "Take Me to Your Leader"—DAW (1997)
 * Acorna, "Pony Girl"—BIG Entertainment (1997)
 * Zodiac Fantastic, "The Billion-Year Boys' Club" – DAW (1997)
 * Wizard Fantastic, "Bird Bones"—DAW (1997)
 * Urban Nightmares, "The Bicycle Messenger From Hell"—Baen (1997)
 * Did You Say ‘Chicks’?, "The Old Fire" – Baen (1998)
 * Alternate Generals, "Queen of the Amazons" – Baen (1998)
 * The Quintessential World of Darkness, "The Muse" -- HarperCollins (1998)
 * Mob Magic, "Power Corrupts" – DAW (1998)
 * Tails From the Pet Shop, "A Cat's Chance" – 11th Hour Productions (1999)
 * Twice Upon a Time, "Spinning A Yarn" – DAW (1999)
 * Chicks and Chained Males, "Don’t Break the Chain!" – Baen (1999)
 * Stardates, "The Stars in Their Courses" – Dreams-Unlimited.com (Dec 1999)
 * Flights of Fantasy, "Eagle's Eye" – DAW (Jan 2000)
 * Perchance to Dream, "The Piper" – DAW (2000)
 * Daughter of Dangerous Dames, "Riddle of the Sphinx" – 11th Hour (May 2000)
 * Such a Pretty Face, "Casting Against Type" – Meisha Merlin Publishing (Jun 2000)
 * 100 Crafty Little Cat Crimes, "Land Rush" – Barnes & Noble (2000)
 * Guardian Angels, "Desperation Gulch" – Cumberland House (2000)
 * Warrior Fantastic, "Conscript" – DAW (2000)
 * Blood and Donuts, "The Haunted Patrol Car" – 11th Hour (2001)
 * Murder Most Romantic, "Night Hawks" – Cumberland (2001)
 * Conjuration 2001 program book, "Shore Excursion" (Jun 2001)
 * The Mutant Files, "Rite of Passage" – DAW (2001)
 * Past Imperfect, "Theory of Relativity" – DAW(2001)
 * Creature Fantastic, "Father Noe’s Bestiary" – DAW (2001)
 * Dracula’s London, "Everything to Order" – Ace (2001)
 * Oceans of Space, "Pyrats" – DAW (2001)
 * Xena, Warrior Princess, "As Fate Would Have It" – DAW (2001)
 * Silicon Dreams, "Sacrifices" – DAW (2001)
 * Constellation of Cats, "Purr Power" – DAW (2002)
 * Heaven and Hell, "The Fiber of Being" – Speculation Press (2002)
 * Something M.Y.T.H., Inc. "M.Y.T.H., Inc. Instructions" – Meisha Merlin (2002)
 * Turning Points (Thieves’ World 2K I), "Doing the Gods' Work" – TOR (2003)
 * Vengeance Fantastic, "Even Tempo" – DAW (2002)
 * Pharaoh Fantastic, "The Voice of Authority" – DAW (2002)
 * Familiars Fantastic, "And So, Ad Infinitum" – DAW (2002)
 * The Repentant, "The Salem Trial" – DAW (Oct 2003)
 * Low Port, "Bottom of the Food Chain" – Meisha Merlin (2003)
 * The Sorcerer’s Academy, "Field Trip" – DAW (Sep 2003)
 * The Magic Shop, "For Whom the Bell Tolled" – DAW (2004)
 * Little Red Riding Hood in the Big Bad City, "Keeping It Real" – DAW (2004)
 * Rotten Relations, "Cuckoo’s Egg" – DAW (2004)
 * Turn the Other Chick, "Defender of the Small" – Baen (2004)
 * Masters of Fantasy, "Mything in Dreamland" (by Asprin and Nye) – Baen (2004)
 * Enemies of Fortune (Thieves’ World 2K II), "Consequences" – TOR (Dec 2004)
 * Time After Time, "Wait Until Next Year" – DAW (2005)
 * Magic Tails, "Sleeping Beauties" – DAW (2005)
 * Maiden, Matron, Crone, "The Gift" – DAW (2005)
 * International House of Bubbas, "Bubba Suey" – Yard Dog Press (2005)
 * LiftPort, "Going Up?" – Meisha Merlin (Jan 2006)
 * Children of Magic, "Nethan’s Magic" – DAW (2006)
 * This Is My Funniest, reprint of "The Growling", ed. Mike Resnick, BenBella Books (2006)
 * The Magic Toybox, "The Revenge of Chatty Cathy" – DAW (2006)
 * Furry Fantastic, "Superstition" – DAW (2006)
 * Army of the Fantastic, "Airborne" – DAW (2007)
 * If I Were an Evil Overlord, "Ensuring the Succession" – DAW (2007)
 * Tales of the Red Lion, "Kindred Spirits" – Twilight Tales (2007)
 * Front Lines, "The Battle for Trehinnick's Garden" – DAW (2008)
 * Fellowship Fantastic, "Sweet Threads" – DAW (Jan 2008)
 * Mystery Date, "Venus in Blue Jeans" – DAW (Feb 2008)
 * Witch High, "Another Learning Experience" – DAW (2008)
 * Here Be Dragons, "Pat the Magic Dragon" – DragonCon (Aug 2008)
 * Enchantment Place, "Altar Ego" – DAW (2008)
 * The Dimension Next Door, "Waiting for Evolution" – DAW (Jul 2008)
 * Terribly Twisted Tales, "No Good Deed" – DAW (2008)
 * Witch Way to the Mall, "There’s No ‘I’ in Coven" – DAW (2009)
 * Zombie Raccoons and Killer Bunnies, "Death Mask" – DAW (2009)
 * Gamer Fantastic, "Roles We Play" – DAW (2009)
 * Strip-Mauled, "Howl!" – Baen (2009)
 * Timeshares, "Time Sharing" – DAW (Mar 2010)
 * Gateways, "Virtually, A Cat" (reprint) – TOR (Jul 2010)
 * Fangs for the Mammaries, "Overbite" – Baen (Sep 2010)
 * Steampunk’d, "Portrait of a Lady in a Monocle" – DAW (Nov 2010)
 * Love and Rockets, "Dance of Life" – DAW (TBA)
 * Hot and Steamy, "Clockworks" – DAW (Jun 2011)
 * Untold Adventures: A D&D Anthology, "To Chaos and Back Again" (Jun 2011)
 * Westward Weird, "Lone Wolf" – DAW (2011)
 * Exiled: Clan of the Claw, "Cata" (by John Ringo and Nye) – Baen (hc 2011, pb 2012)
 * Human for a Day, "The Very Next Day" – DAW (2012)
 * Cast of Characters, "Small Sacrifices" – Fiction Studio Books (2012)
 * Baker Street Irregulars: Thirteen Authors with New Takes on Sherlock Holmes, "The Scent of Truth" - Diversion Publishing (Mar 2017)

Teleplays

 * Dinosaucers animated TV series, "Toy-ranosaurus Store Wars" script – DIC Entertainment

Non-fiction

 * "Dungeon Etiquette", The Dragon #130, TSR Inc (1988)
 * It Seemed Like a Good Idea at the Time, various articles – Avon Books (2000)
 * You Did What?, various articles – Avon (2004)
 * Alias Assumed, "Why Sydney Has No Social Life" – BenBella Books (Aug 2005)
 * FarScape Forever, "My Imaginary Friend" – BenBella (Oct 2005)
 * Charmed, "Talent and the Socialism of Fear" – BenBella (Nov 2005)
 * Battle of Azeroth, "Advice for the Warlorn" – BenBella (2006)
 * So Say We All, "Report to Congress" – BenBella (2006)
 * Nebula Awards 2010 anthology, "Medium with a Message" – (2010)
 * Chicks Dig Time Lords, "Hopelessly Devoted to Who" – Mad Norwegian Press (2010)
 * SFWA Bulletin, "Being a convention literary guest" (vol 4 iss 3, Aug-Sep 2010)
 * SFWA Bulletin, "Conventional Wisdom: DragonCon" (Spring 2011)
 * SFWA Bulletin, "Conventional Wisdom: GenCon" (Summer 2011)
 * SFWA Bulletin, "Conventional Wisdom: Small Cons" (Fall 2011)
 * SFWA Bulletin, "Conventional Wisdom: Interview Gene Wolfe" (Winter 2012)
 * SFWA Bulletin, "Conventional Wisdom: Writers Workshops" (Spring 2012)
 * SFWA Bulletin, "Conventional Wisdom: 1,000 Cons" (Summer 2012)

title: Jody Lynn Nye


text:
Face the Music (British game show)

Face the Music is a British panel game show that originally aired on BBC2 from 3 August 1967 to 2 January 1977 and then moved to BBC1 from 17 April 1983 to 16 December 1984 with Joseph Cooper hosting the entire run.

The theme music for the show was the Popular Song from the Façade suite by Sir William Walton (who was a guest on the programme in his 70th birthday year). During its most popular period the programme had a weekly audience of over 4 million.

Format
The programme, chaired by Joseph Cooper, took the form of a quiz, with a panel of three music-loving celebrities, but without scoring or any winner. Each week there would be a special guest, who would also have to answer questions – with the focus being on topics that related to the guest's life and career, so as to lead to amusing anecdotes. The questions to the panel were asked in a series of rounds, each with a theme, such as "The Face, The Music", where the panel would have to identify a composer from their picture, as well as the composer of the music played along with it.

The most demanding round was the "Dummy Keyboard", where Cooper would play a famous piece on a dummy (soundless) instrument, requiring the panel to identify it from hand movements alone. For the benefit of the audience at home, the music in question – which Cooper was hearing through earphones for the purpose of synchronisation – would be slowly faded in as the piece progressed.

Another round was "Hidden Melody" where Cooper would perform a popular tune in the style of a famous composer, while including extracts of works by that composer to help the listeners. Robin Ray, if a member of that week's panel, would typically identify the opus number of the quoted works.

For opera lovers, the panel were shown a filmed performance of one opera with the soundtrack of a different one, and asked to identify both.

title: Face the Music (British game show)


text:
Joseph Hare

Rear Admiral Joseph C. Hare is a Pennsylvania native, a 1972 graduate of the Naval ROTC program of Villanova University, and a 1978 graduate of the Villanova University School of Law.

Following his training in naval communications and cryptography, he served as communications officer, electronic material officer, and cryptographic security officer in U.S. Atlantic Fleet destroyers Lowry (DD-770) and Corry (DD-817).

Afloat tours in the Naval Reserve have included deck watch officer in Emory S. Land (AS-39), weapons officer in Harold J. Ellison (DD-864), and selected reserve coordinator in Oliver Hazard Perry (FFG-7).

Shore billets have included executive officer of Shore Intermediate Maintenance Activity (SIMA) Philadelphia, Surface Group Four Squadron liaison officer, and plans officer of Naval Reserve Readiness Command Region Four.

Major staff billets have included assistant chief of staff to commander, Naval Base Philadelphia, and assistant deputy to commander, Iceland Defense Force.

Hare was promoted to flag rank in October 1996. His notable assignments in flag rank included serving as commander of Military Sealift Command Atlantic, commander of Military Sealift Command Europe, commander of Naval Reserve Readiness Command Region Four, deputy commander of Naval Surface Force, U.S. Atlantic Fleet, and deputy for Training Integration at Naval Education and Training Command. Hare retired on March 1, 2005.

Hare was the president of AgraCo Technologies International, LLC, a defense industry contractor, as well as a private consultant in legal and defense-industry-related matters. He has formerly served as the chief operating officer and general counsel of Granary Associates, Inc., a health-care-facility design and development company in Philadelphia, Pa. He has formerly served as a partner in the law firm of Weir & Partners, as the CEO of a 200-bed acute care hospital, as general counsel of a hospital system, and as treasurer and general counsel of a member firm of the Philadelphia Stock Exchange. Hare is a member of the boards of various professional organizations, including the Philadelphia Council of the Navy League of the United States, the Philadelphia Chapter of the Surface Navy Association, the USO Of Pennsylvania and South Jersey, and the Armed Services Committee of the Union League of Philadelphia.

Hare resides in the suburbs of Philadelphia. He has a daughter named Casey and a son named Joe.

Awards and decorations
Hare has been the recipient of the Distinguished Service Medal, the Legion of Merit (three awards), the Meritorious Service Medal (two awards), the Navy Commendation Medal (three awards), and various other service medals and ribbons.

title: Joseph Hare


text:
Talk:Amphibious warfare ship

LSL
Can you make an article titled LSL (Amphibious Assault Ship)? I made a disambiguation page for LSL...

 * Try Landing Ship Logistics. - BillCJ 16:33, 15 November 2007 (UTC)

Needs a lot of work
This article is very confusing and is in need of a lot of work. The fundamental problem seems to be that there is no single definition of what an "Amphibious assault ship" actually is. For instance, while the opening paragraph states that such ships "grossly resembl[e] aircraft carriers" and seems to refer to ships capable of operating large numbers of troop carrying helicopters, the body of the article includes ships which cannot operate helicopters and only land their embarked troops through beaching. The article also contains a very strong US and British bias. --Nick Dowling 08:12, 8 June 2006 (UTC)

I think we should partly merge it with landing craft (aren't landing craft only smallest type of amphibious assault ships? Or are they wider term?) Pibwl ←« 19:40, 11 September 2006 (UTC)

 * I agree that some work is needed, though there is much value in the article. Specifically, the LCM and LCVP are boats, not ships, but are listed among the various types of ships. Lou Sander 13:10, 16 November 2007 (UTC)

Operation Atilla?
I believe Operation Atilla can also be considered as a large scale amphibious assault, therefore I added it to the first paragraph. —The preceding unsigned comment was added by 88.254.132.8 (talk) 19:11, 5 March 2007 (UTC).

Hi All, I've just searched a bit in Wikipedia, and apparently the unknown contributor was right in that "Operation Attila" (or "Atilla"?) was in its first stage an amphibious operation conducted by teh Turkish (see more in: Military operations during the Invasion of Cyprus (1974)). What I'm not sure is if it should bem linked/mentioned in this article or elsewhere. Any suggestions? Thanks & regards, DPdH (talk) 06:03, 14 October 2008 (UTC)

Revamp/split article
For a long time, I've thought this article is a mess. The Tarawa class amphibious assault ship page, for example, links to Amphibious assault ship, but instead of an aricle on the type of ships the LHA/LHDs are (large-deck ampibs), you get a narrow opening definition of the ships (reworked some, but it was much worse before), and the the article wanders all over discussing every type of amphibious warfare ship and boat. Perhaps the more-general information, including the "boats", could go to Amphibious warfare vessel, with the Amphibious assault ship page covering LHDs, LHAs, LPH, LSDs, and those that are more properly called ships. These are just my random opening thoughts - I welcome any other ideas/comments. - BillCJ 16:28, 15 November 2007 (UTC)

 * Per the USN's page on amphibious assault ships, this term is specifically applied only to LHAs and LHDs by the USN. I do believe that was the original scope of this article, but it was expanded to cover more vessels over time, without any apparent concept of the strict meaning of the term. As such, I have moved this page to Amphibious warfare ship, the broadest term I can find. I will be re-doing the Amphibious assault ship page, probably using the early versions of the page, to focus on LHAs and LHDs, though I'm not sure how fast I will accomplish this. - BillCJ (talk) 17:01, 19 November 2007 (UTC)

Possible bias towards US and UK amphibious doctrine?
Hi, I concur with Nick Dowling's comment (on 08:12, 8 June 2006) that most of the information of the article is (still) related to Amphibious Warfare as conducted by the United States Navy and the Royal Navy, as for example: the List of Types is all USN (AFAIK). But I feel that is a good basis for a great atricle, it just needs expansion. I'll try to find out hot to properly tag this article, then if time available will try to search for other navies' amphibious doctrine. Can anybody else please help? Thanks & regards, DPdH (talk) 05:46, 14 October 2008 (UTC)

 * I'm not sure exactly what you mean by "doctrine", but this article is primarily about amphibious ship types, and an overview of their history. Doctrine as such should be discussed in the Amphibious warfare aritcle, not here. If you can add historical examples of amphibious warfare ships used by other nations, then that would be good. Reliable sources on ships of other nations are often hard to come by in English, while there is an abundance of data on US and UK ships, for variaous reasons. As for the list of types, most other nations (Western at least) don't have their own type codes (they usually don't even have as many amphib ships as the code is long!), and use the USN codes when describing their own ships. A good example is "LHD", as the Spanish ship Juan Carlos I (L61) was known as "LHD1" (not BPE1) until ITS NATO pennant number was assigned. Additionally, most reference works will descripe sthe ships of other nations using the US codes, even if the nations don't. Again, if you can find sourced lists from other nations, feel free to add them. - BillCJ (talk) 06:40, 14 October 2008 (UTC)

 * I've renamed "List of Types" to "List of USN hull classification symbols" to make it clear exactly what the list is and where it is from. If we add other lists, we can restore the "List of types" as a first-level heading, and make each list a second-level heading. - BillCJ (talk) 07:04, 14 October 2008 (UTC)

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was not done. Skomorokh, barbarian   03:27, 15 November 2009 (UTC)

Amphibious warfare ship → Amphibious warfare vessel —. Changing this article's name to Amphibious warfare vessel makes the article more inclusive (avoiding the potentially contentious ship vs. boat debate) and helps it to match the consensus category structure which uses "Amphibious warfare vessels of …". (Redirect with history prevented a direct move.) — Bellhalla (talk) 18:16, 26 October 2009 (UTC)

Oppose as stated - Not sure what "boats" are covered here, as Landing craft are barely mentioned, and are covered elsewhere. - BilCat (talk) 22:32, 26 October 2009 (UTC)
 * Sorry, I didn't see the discussion above. I was primarily trying to get an article—rather than just a redirect, as Amphibious warfare vessel is—under the de facto consensus name used in categories. I agree that "Amphibious warfare vessel" should be a separate article that gives an overview of different type of amphibious vessels, kind of like an expanded dab page. — Bellhalla (talk) 09:54, 29 October 2009 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Self explanatory really
The uncited purple prose at the beginning has to go or get some proper editing, it's not encyclopaedic. 70.55.59.182 (talk) 11:42, 25 April 2010 (UTC)

 * No, not really. I haven't a clue what you're objecting to - could you be more specific without using vague labels? Thanks. - BilCat (talk) 17:44, 25 April 2010 (UTC)

 * They maybe meant this statement at the beginning of the history section
 * Amphibious assaults need such fine control and such a large degree of coordination that it is only the top tier powers that have the ability to even attempt them seriously, let alone pull them off. The two nations that have made by far the most amphibious assaults during the past century are the United States and the United Kingdom. From the great assaults of World War II to the recent attack on the Al-Faw Peninsula in Iraq, both countries have been at the forefront of developing amphibious assault doctrine and shipping.
 * I have removed that whole part as unsourced and unneccessary speculation and/or POV. Weakopedia (talk) 11:16, 29 June 2010 (UTC)

Amphibious?
i guess i'm just stupid, but, none of these ship appear to be Amphibious. shouldn't somewhere, some point be made that it means '"Amphibious-warfare" Ships', and not 'Amphibious "Warfare-ships"', you know, for stupid people like me?· Lygophile   has   spoken  20:40, 14 March 2012 (UTC)

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title: Talk:Amphibious warfare ship


text:
Talk:Ferdinand IV, King of the Romans

Wrong Picture
The picture on the right shows Ferdinand III, the father of Ferdinand IV. PNM 23:10, 25 May 2015 (UTC)

Untitled
The suffix "of Germany" is rather imprecise, given that those lands weren't "Germany" at the time, and besides, his earlier Bohemian and Hungarian domain was likely larger or at least comparable to the one referred to as "Germany"... --Shallot 20:14, 1 Aug 2004 (UTC)

Ferdinand IV
Ferdinand IV was the King of Naples 1760, I been trying to find it on Wikipedia but can't seem to —Preceding unsigned comment added by Zylog79 (talk • contribs) 22:52, 14 November 2010 (UTC)
 * see Ferdinand I of the Two Sicilies.--Yopie (talk) 00:19, 15 November 2010 (UTC)

title: Talk:Ferdinand IV, King of the Romans


text:
Talk:Alfred Brehm

Thierleben
Both the 1st and 2nd edition of Thierleben were translated to Swedish. The 1st Swedish edition appeared in 3 volumes in 1874-76 and the 2nd edition in 4 volumes in 1882-88. The title page of the first volume of the 2nd edition clearly says 1882. This makes me think that the German 2nd edition didn't appear 1883-1887, but already in the late 1870s? Could anybody with access to this German 2nd edition (or a good library catalog) please check this? Items for sale at Zvab.com indicate the 2nd German edition appeared in 10 volumes 1876-1879 (Säugethiere 1 1876; Säugethiere 2, Insekten 1877; Vögel, Kriechthiere, Niederen Thiere 1878; Fische 1879), then again 1883-1884. Brehm died in 1884 so the 3rd edition (1890-1893) was the first that wasn't edited by himself. --LA2

Not zookeeper?
This person is categorized as zookeeper, but doesn't seem to have been a zookeeper at all? Dan Koehl (talk) 17:38, 2 February 2017 (UTC)

 * He was a Zoo director, and a Zoo director employs staff to look after the animals, they are referred to as zookeepers. Dan Koehl (talk) 22:38, 3 February 2017 (UTC)

title: Talk:Alfred Brehm


text:
Minister of the Interior (France)

Minister of the Interior (Ministre de l'Intérieur; ) is a prominent position in the Government of France. The position is equivalent to the interior minister in other countries, like the Home Secretary in the United Kingdom, the Minister of Public Safety in Canada, or the Minister of Home Affairs in Australia.

Responsibilities
The Minister of the Interior is responsible for the following:
 * The general interior security of the country, with respect to criminal acts or natural catastrophes
 * including the major law-enforcement forces
 * the National Police
 * the National Gendarmerie for its police operations since 2009; as a part of the French Armed Forces, the Gendarmerie is administratively under the purview of the Ministry of Armed Forces
 * General directorate for civil defence and crisis management (Sécurité Civile)
 * the directorate of Firefighters (Sapeurs-Pompiers)
 * the granting of identity documents (passports, identity cards) and driving licenses through the network of prefectures and subprefectures
 * relations between the central government and local governments
 * logistics and organisation of political elections, at the national and prefectoral levels; the results of the elections are overseen by the Constitutional Council or the administrative courts
 * regulation of immigration and preventing illegal immigration
 * integration of legal immigrants (professionally, linguistically, housing)
 * all regional and departmental prefects and subprefects are subordinate to the Minister of the Interior

The Minister of the Interior also takes on the role of the former Minister of Worship and is formally consulted in the process of appointment of Catholic diocesan bishops (Briand-Ceretti Agreement). The Minister of Worship used to be a fully-fledged position; the office was abolished in 1912.

While the Ministry of the Interior supervises police forces, it does not supervise criminal enquiries. Those enquiries are conducted under the supervision of the judiciary.

History
The Minister for the Maison du Roi under the Ancien Régime is considered to be the precursor of the position of Minister of the Interior, which was officially established on 7 August 1790, during the French Revolution, when François-Emmanuel Guignard, comte de Saint-Priest became the inaugural officeholder. Although his tasks included the organisation of elections, relations with local authorities, agriculture, as well as trade, the Minister of the Interior's main duty was to oversee the functioning of police forces. This has been the case since then, with the exception of the period from 1796 to 1818, when a Ministry of Police was in use, which was also briefly restored under the Second Empire.

During the First Empire, the Interior Ministry's tasks were reduced; in 1824, the Ministry of Public Instruction was established to oversee France's education policy. In 1832, the Interior Ministry was primarily occupied with the holding of elections and maintenance of the firefighters force, as the Institut de France and national public libraries were transferred to the Public Instruction Ministry. In 1836, the Ministry of Public Works, Agriculture and Commerce was established.

In 1911, the Directorate of Penitentiary Administration, established in 1858 in the Interior Ministry to oversee prison conditions, was placed under the authority of the Minister of Justice. Nine years later, the Interior Ministry lost its public health policy department to the newly established Ministry of Hygiene, Assistance and Social Security.

Location
The ministry's headquarters have been located on Place Beauvau, facing the Élysée Palace, since 1861. "Place Beauvau" is often used as a metonym for the ministry.

Organisation
The Minister of the Interior has been Gérald Darmanin since 6 July 2020. He succeeded Christophe Castaner, who was appointed to the office on 16 October 2018. Darmanin is assisted by Marlène Schiappa, who holds the junior title of Minister for Citizenship in the government of Prime Minister Jean Castex.

title: Minister of the Interior (France)


text:
Baron Darcy

Baron Darcy may refer to the following baronies:

 * Baron Darcy of Nocton, created 1299, abeyant circa 1350
 * Baron Darcy de Knayth, created 1332, presently extant
 * Baron Darcy de Darcy (also known as Baron Darcy of Temple Hurst), created 1509, extinct in 1635
 * Baron Darcy of Chiche, created 1551, extinct in 1640; reversion granted 1613, extinct in 1737
 * Baron Darcy de Meinill, created 1641, extinct in 1778
 * Baron Darcy of Navan in the Peerage of Ireland, created 1721, extinct in 1733

title: Baron Darcy


text:
Wikipedia:Articles for deletion/Intact Day

The following is a current tally on votes. For those who have yet to make their vote please add only your name to this list, save the discussion/reasoning for below. I realize that your reasoning is generally found next to your vote, but that encourages debate and the purpose of this list is to make it easyer to weed out the comments from the votes. Note that votes to Delete/Redirect have been placed under redirect; please move your name if you feel another option better suits your views. Also I have made no attempts to weed out sock puppets, moderators are encouraged to be aware of that as well as to check the integrity of this list to guard against any tampering. --Starx 22:06, 5 Aug 2004 (UTC)

Keep

Redirect Delete
 * syntax recorded syntax
 * Michael Glass
 * Elf-friend
 * Denni ☯
 * RickK
 * Cyrius|✎
 * Hayford Peirce
 * Gary D
 * Lucky 6.9
 * [[User:dpbsmith|dpbsmith (talk)]]
 * Geogre
 * Andrewa
 * Rhobite
 * Starx
 * Acegikmo1
 * Fire Star
 * UtherSRG
 * Sean Curtin
 * Ŭalabio

Can't find this one on any of my calendars. And how does one celebrate it...? Denni ☯ 20:21, 2004 Aug 1 (UTC)

It is for opposing the Feast of the Circumcision  (the sexual mutilation of Jesus Christ),  which is on the first of January. Intactivists celebrate Intactness. This has occurred since the 1990s. ¿Is Intact Day any less real than the Feast of the Circumcision?

¡Keep!

Ŭalabio 20:58, 2004 Aug 1 (UTC)
 * Note that the above is the creator, who's creating several of these silly articles which could all be placed under Intactivism. Move this one to BJAODN and delete.  RickK 20:59, Aug 1, 2004 (UTC)
 * Let's snip this one (article) off! Move information to Intactivism and delete. Elf-friend 21:09, 1 Aug 2004 (UTC) (Addition: Elf-friend 21:50, 1 Aug 2004 (UTC).)
 * Under that (elf-friend's) argument, shouldn't "easter" be placed under christianity? Keep! syntax recorded syntax
 * Hmmm ... Google hits for "Intact Day" is 183, most of which are not even references to this day. Most of the rest are hits for Wikipedia or its mirrors. Hits for "Easter" is 7,440,000 which I think does justify a separate article (among other reasons, such as article length). Every activist group can declare some kind of feast day, that does not necessarily mean automatic inclusion in Wikipedia as a separate article. Also note that the reputed Christian equivalent (Feast of the Circumcision) actually does not have an article in Wikipedia. Elf-friend 21:39, 1 Aug 2004 (UTC)
 * P.S. I'm happy to defend any vote of mine, but what argument of mine are you referring to? I just voted - the other "delete" voters had much more of an "argument" in their posts. Elf-friend 21:46, 1 Aug 2004 (UTC)
 * Delete neologism. -- Cyrius|✎ 22:26, 1 Aug 2004 (UTC)

 * deleteHayford Peirce 22:36, 1 Aug 2004 (UTC)

 * Denni ☯ is biased against Intactivism:

 * ¿What do you have against Genital Integrity and Intact Day?

 * Nothing, except the high-pitched shrieking of those who believe that having one's foreskin removed is like having one's brain removed. I have seen you before, Walabio, and all I can say is that I hope I never find myself so one-track-minded on an issue as you. While I am neutral in the circumcision debate, I see intact Day as a huge joke (what are you going to do - wave your foreskin about?). Neither of these articles is acceptable for Wikipedia, either because they are (genital integrity) a neologism, and (Intact Day), a singularly unrecognised celebration. Did you not bother to read my comments? Denni ☯ 23:21, 2004 Aug 1 (UTC)

The person wanting deletion has a bias against those trying to stop child-abuse, and possibly me personally.

Ŭalabio 23:35, 2004 Aug 1 (UTC)

 * Delete. --Gary D 23:38, 1 Aug 2004 (UTC)

 * Delete this one as well. As for Walabio, get that chip off of your shoulder and stop hurling accusations of child abuse, for crying out loud.  Your comments are unwarrranted. - Lucky 6.9 01:00, 2 Aug 2004 (UTC)

 * Delete. No evidence yet presented that this day is celebrated by more than a handful of people. You will see in Talk:Rice pudding that I considered mentioning National RIce Pudding Day, August 9th, in the article, but thought better of it because I could not verify that it really exists. Yet "National Rice Pudding Day" August gets 25 Google hits, all relevant, and from a wide variety of sources. "Intact Day" July gets 36. As nearly as I can tell, all of these are either from Wikipedia, Wikipedia mirrors, Walabio's postings elsewhere, or irrelevant ("The intact Day 14 and Day 15 embryos may represent a population...") [[User:dpbsmith|dpbsmith (talk)]] 01:12, 2 Aug 2004 (UTC)

 * If you go to Google and type in +"hayford peirce" +birthday you will get 29 hits. I think that I'll write a separate article about my birthday, what I like to eat on it, and what presents I'd like to receive....Hayford Peirce 01:55, 2 Aug 2004 (UTC)

 * He's not making it up. Again, I find this group annoying.  They take a legitimate matter like female genital mutilation and co-opt it into a private gripe, IMO.  Delete this, though, as I doubt Clean Up is going to fix it any, and this is uninformative. Geogre 02:21, 2 Aug 2004 (UTC)

 * Snip. I mean delete. Politically motivated neologism. No useful content. Andrewa 09:16, 2 Aug 2004 (UTC)

 * Delete. Not a notable holiday. Also be sure to remove the reference from July 1. Rhobite 18:21, Aug 2, 2004 (UTC)
 * Delete. I don't know if this is a valid holiday; if it is then a mention in inactivism is sufficient, if it isn't then no mention, either way it doesn't need it's own article. --Starx 02:25, 3 Aug 2004 (UTC)
 * Delete. Either very unknown or made up. Acegikmo1 03:19, 3 Aug 2004 (UTC)

 * Ŭalabio removed my DELETE vote, so here it is again. Not a good way to win an argument, Ŭalabio. Fire Star 04:02, 3 Aug 2004 (UTC)
 * Deleted nothing. It was an editconflict.  Trying to win an argument by deleting votes is bound to fail on a wiki.  A sysops should look at the logs.  I would like to know when the edits started  --  not just when they finished.
 * Ŭalabio 04:34, 2004 Aug 3 (UTC)

 * Delete. - UtherSRG 17:14, 3 Aug 2004 (UTC)

 * Keep. While I admit that the term "Genital Integrity" is controversial, it is still significant, because it points to a change in thinking about the whole area of genital modifications. It is therefore important to keep it. However, it is very important to expand the article so that the issues that it raises and the connections it makes can be examined and discussed. In that way the article will have something to say to all who see the slogan, whether they are pro circumcision or pro genital integrity

 * 1) Michael Glass (presumably): you probably meant to type four tildes, which would have signed your comment, rather than the four hyphens you did type. On most keyboards the tilde is near the top left, just below the esc key.
 * 2) This article isn't about Circumcision or various debates regarding circumcision, it is an article about a day which is said to celebrate "intactivism." The day is not widely celebrated even among those opposing circumcision. I believe it is recognized only by a handful of people, and that the purpose of this article is to promote this holiday and thereby advance their cause. I believe there can be meaningful articles exploring different views regarding circumcision, by I can't imagine a meaningful article debating whether or not "intact day" should be celebrate. My own vote to delete applies to this specific article on this specific topic, "intact day." [[User:dpbsmith|dpbsmith (talk)]] 15:24, 4 Aug 2004 (UTC)

 * Delete, not notable and possibly original research. -Sean Curtin 20:20, 5 Aug 2004 (UTC)

Full Disclosure

Since the circumsiophiliacs, to use a medical term, seem to be trying to remove all pages devoted to Genital Integrity, Intactivism, et cetera, by voting in a block for deletion, I informed Intactivists that it mighht be a good idea to join the debate before we are cast out of Encyclopædia WikiPedia.Org.

Also, I suggested that Intactivist try to improve and expand Genital Integrity and Intact Day so that WikiPædists who might vote for deletion just because the articles are small and poorly written, might say:

 * "¡Hey! I want to keep this because it is significant and well written."

Since people actively try to improve the articles, I ask that one read the articles one last time on the last day of voting before finalizing your votes.

I also ask that you ask yourselves why to articles, written at different times, both with no controversy, should both be listed by the same user at the same time for deletion. I quote Denni ☯ :

 * ¿What do you have against Genital Integrity and Intact Day?

 * Nothing, except the high-pitched shrieking of those who believe that having one's foreskin removed is like having one's brain removed.
 * Denni ☯ 23:21, 2004 Aug 1 (UTC)
 * Denni ☯ 23:21, 2004 Aug 1 (UTC)

Denni ☯ seems to have an axe to grind.

Hugh Young suggests that we should give up Intact Day for Genital Integrity as long as Intact Day remains listed on July 1. Technically, I have no authority to speak for anyone else, but since time is of the essence, I will concede Intact Day, if we can keep Genital Integrity. I suspect that other Intactivists will find this acceptable.

¿Is this acceptable to you?

Ŭalabio 00:26, 2004 Aug 3 (UTC)

Just because someone does support believe in Genital Integrity and support Intactivism does not mean the person opposes child-advocacy. The person may just believe that circumcision is good for health:

Doctor Benjamin Spock, the famous "baby-doctor" heard in medical school the lies supporting circumcision. He did not realize that these lies exist for protecting the circumcision-fee. In early editions of Baby and Child Care, he supported circumcision. He learned the truth:

Doctor Benjamin Spock, the famous "baby-doctor" oppose circumcision in later editions of Baby and Child Care. He wrote:

 * "My own preference, if I had the good fortune to have another son, would be to leave his little penis alone."

I withdraw my claim that Denni ☯ opposes child-advocacy and apologize for making the claim.

Ŭalabio 12:15, 2004 Aug 11 (UTC)

No. Intact Day is a nonexistant event and a neologism, and whether there is a page or not, there should not be an entry on any Wikipedia page for it. And who's Hugh Young? RickK

 * I've just looked at the "Genital Integrity" so-called article. I can't believe that no one has put this up for deletion!  Has anyone else here ever looked at it?  It is surely the most POV article I've ever seen about anything on any subject.  Surely it ought to be listed for deletion! If no one else does it, I'll certainly figure out how to do it myself. Hayford Peirce 19:40, 8 Aug 2004 (UTC)

 * I read it today. It's irrelevant to this discussion, because the two articles, and my judgements on them are completely independent, as I hope everyone else's will be. I'm voting to delete Intact Day because I believe it to be an all-but-nonexistent holiday, regardless of what it celebrates. I haven't formed a judgement on the size or notability of the group that uses the term "Genital Integrity." If it is a tiny group of people trying to promote their point of view, I will vote to delete Genital Integrity. If the group exists and their point of view is being reported accurately, and properly identified as such, and opposing points of view recognized, the article can be kept. In its present form Genital Integrity is not acceptable, but that doesn't necessarily mean it should be deleted. And I am very sorry to tell you this, but if you keep reading Wikipedia you will find that it is not by any means the most POV article you will ever see. Wikipedia contains large numbers of such articles but amazingly enough the Wiki-process keeps them down to a small percentage.  [[User:Dpbsmith|Dpbsmith (talk)]] 21:41, 8 Aug 2004 (UTC)
 * Well, it is, of course, irrelevant to this discussion, but someone keeps bringing it up as a trade. Keep one, delete the other. I think that of the two, Intact Day actually has more fact to it -- it says that there's a day, on a certain date, to celebrate this event (or non-event, bien sur).  The other one is just pure opinion in the form of an article.  But I do agree with you, it could, I suppose, be rewritten to acceptable form.  If, as you say, it is not the most POV article ever to be found in the Wikipedia, please do not point me in the direction of the others! Hayford Peirce 21:54, 8 Aug 2004 (UTC)
 * Genital Integrity has been listed for deletion since August 1. Its VfD lifetime is about to expire.  RickK 21:44, Aug 8, 2004 (UTC)
 * I thought that it had been, but I can't seen to find the deletion-vote page.... Hayford Peirce 21:54, 8 Aug 2004 (UTC)

It's right here: Votes for deletion/Genital Integrity. It looks like somebody who seems to be worried that their arguments aren't good enough has deleted it from the VfD page. I'll restore it. RickK 21:57, Aug 8, 2004 (UTC)


text:
Don Hastings

Donald Francis Michael Hastings (born April 1, 1934) is an American actor, singer, and writer best known for his 50-year role as Dr. Robert "Bob" Hughes on the CBS soap opera As the World Turns. Hastings was the third actor to portray Hughes and is the longest serving living cast member of an American television soap opera, after the death of matriarch Helen Wagner of the same series.

Hastings was active in show business from 1940 and on television from 1947, primarily in soap operas. A rare exception was his appearance as Dave Carter in the 1958 episode "The Savage Payoff" of Beverly Garland's groundbreaking crime drama, Decoy.

Career
Born on April 1, 1934, in Brooklyn, New York, to Charles and Hazel Hastings, he lived his earliest years in the Bedford-Stuyvesant district. He started working in radio at the age of six, as a member of the "Bus Bunny" chorus on the serial Coast to Coast on a Bus. From 1944 to 1948, he acted in four Broadway plays. From 1949 to 1955, Hastings played Captain Video's teenaged companion, the Video Ranger, on the DuMont television series, Captain Video and His Video Rangers. He portrayed one of television's first superheroes designed to appeal to children.

Hastings was cast from 1956 to 1960 as Jack Lane on the CBS soap opera, The Edge of Night. He played Bob Hughes on As the World Turns from October 1960 until the show's final airing on September 17, 2010, and spoke the series' final line: "Good Night."

Hastings previously held the record as the longest continuous actor in the history of television serials until November 2010, shortly after As the World Turns ended. Guinness World Records stated that the non-continuous record was held by Hastings' co-star Helen Wagner, who played Nancy Hughes on As the World Turns, from April 2,1956, until her death in May 2010. Wagner departed from the cast of the program, or had only appeared on a recurring basis, between 1981 and 1985.

Hastings is also a screenwriter, and he wrote dialogue for both As the World Turns and Guiding Light under the name J. J. Matthews.

Personal life
Hastings and his first wife, Nan, had three children, Jennifer, Julie, and Matthew. Hastings lives in upstate New York with his second wife, actress Leslie Denniston. They married in 1980 and have a daughter, Kate. His son Matthew has been active in show business since 1999 as a writer, director, and producer.

Hastings is the younger brother of veteran radio and television actor Bob Hastings, who died in 2014, aged 89.

title: Don Hastings


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Limequat

The limequat (Citrus × floridana) is a citrus hybrid that is the result of a cross between the Key lime and the kumquat, hybridized by Walter Tennyson Swingle in 1909.

Description
It is a small tree that grows into a contained bushy form. The leaves are characteristically citrus-like. The limequat produces an abundance of fruit even at a young age. The fruit is small, oval, greenish-yellow and contains seeds or pips. It has a sweet-tasting skin and a bitter-sweet pulp with a flavor similar to limes. The fruit can be eaten whole or the juice and rind can be used to flavor drinks and dishes. It has considerable amounts of vitamin C and is highly acidic.

This plant is now grown in Japan, Israel, Spain, Malaysia, South Africa, the United Kingdom and the United States in California, Arizona, Florida, and Texas. The fruit can be found, in small quantities, during the fall and winter months in the United States, India and Japan.

Limequats can be grown indoors or outdoors providing the temperature stays between 10 and 30 C. They are fairly small and can be planted in containers or pots, in well-drained fertile soil. Plants grow fairly slowly and flower and fruit for 5–7 months, then rest for 5–7 months.

Limequats are more cold-hardy than limes but less cold-hardy than kumquats.

Limequats are used in cocktails and fruit salads, and can be candied whole. They can be cooked if the seeds are removed, as they impart a bitter taste, and they can also be made into conserves.

Varieties
There are three different named cultivars of limequats:
 * Eustis (Citrus japonica (synonym Fortunella japonica) × Citrus aurantiifolia) - Key lime crossed with round kumquat, the most common limequat. It was named after the city of Eustis, Florida.
 * Lakeland (Citrus japonica × Citrus aurantiifolia) - Key lime crossed with round kumquat, different seed from same hybrid parent as Eustis. Fruit is slightly larger and contains a few fewer seeds than Eustis. It was named after the city of Lakeland, Florida.
 * Tavares (Citrus japonica 'Margarita' × Citrus aurantiifolia) - Key lime crossed with oval kumquat (though there is some speculation that it is actually a lemon/kumquat hybrid), fruit is larger and more elongated and color at maturity is more orange than other limequats. It was named after the city of Tavares, Florida.

title: Limequat