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Khwaja Ghulam Farid

Khawaja Ghulam Farid (also romanized as Fareed; c. 1841/1845 – 24 July 1901) was a 19th-century Sufi poet and mystic from Bahawalpur, Punjab, belonging to the Chishti Order. Most of his work is in the local Multani, or what is now known as Saraiki. However, he also contributed to the Standard Punjabi, Urdu and Persian literature.

Life
Born into a Koreja family, Khawaja Farid traced descent from Umer ((r. 634 – 644)), the second Rashidun caliph. One of his ancestors had migrated to Sindh, and the family was established as saints associated with the Suhrawardī Sufi order. In the early 18th century, the family seat moved to Mithankot, and subsequently transferred their allegiance to the Chishtī order. Khawaja Farid was born in c. 1841/1845 at Chachran. Farid was orphaned around the age of eight when his father died. He was then brought up by his elder brother, Khawaja Fakhr al-Dīn, and grew up to become a scholar and writer. He received a fine formal education at the royal palace of Ṣādiq Muḥammad IV, the Nawab of Bahawalpur. His brother Fakhr al-Dīn, who had brought him up after their parents' deaths, also died when Farid was 26 years old. Farid performed hajj (pilgrimage to Mecca) in 1875, and then retired to the Cholistan Desert (also known as Rohi) for chilla (retreat) where he spent a total of eighteen years. He died at Chachran on 24 July, 1901, and was buried at Mithankot.

Works
His most significant works include:
 * Dīwān-i Farīd
 * Manāqib-i maḥbūbiyya (in Persian prose)
 * Fawāʾid-i Farīdiyya (in Persian prose)

Legacy

 * A literary award named after Farid –  the Khwaja Ghulam Farid Award  –  is awarded yearly by the Pakistan Academy of Letters in literature, its recipients including Ismail Ahmedani (in 2013) and Irshad Taunsvi (in 2007) among others.
 * Fareed Gate is the name of one of the historic gates surrounding the old city of Bahawalpur named in Farid's honour.
 * The Khawaja Fareed University of Engineering and Information Technology (KFUEIT) in Rahim Yar Khan District was named after Farid.
 * Shrine of Khawaja Ghulam Farid in Rajanpur, Punjab is among the 10 most visited shrines in Pakistan.

title: Khwaja Ghulam Farid


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Gibbs sampling

In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for sampling from a specified multivariate probability distribution when direct sampling from the joint distribution is difficult, but sampling from the conditional distribution is more practical. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables). Typically, some of the variables correspond to observations whose values are known, and hence do not need to be sampled.

Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference. It is a randomized algorithm (i.e. an algorithm that makes use of random numbers), and is an alternative to deterministic algorithms for statistical inference such as the expectation–maximization algorithm (EM).

As with other MCMC algorithms, Gibbs sampling generates a Markov chain of samples, each of which is correlated with nearby samples. As a result, care must be taken if independent samples are desired. Generally, samples from the beginning of the chain (the burn-in period) may not accurately represent the desired distribution and are usually discarded.

Introduction
Gibbs sampling is named after the physicist Josiah Willard Gibbs, in reference to an analogy between the sampling algorithm and statistical physics. The algorithm was described by brothers Stuart and Donald Geman in 1984, some eight decades after the death of Gibbs, and became popularized in the statistics community for calculating marginal probability distribution, especially the posterior distribution.

In its basic version, Gibbs sampling is a special case of the Metropolis–Hastings algorithm. However, in its extended versions (see below), it can be considered a general framework for sampling from a large set of variables by sampling each variable (or in some cases, each group of variables) in turn, and can incorporate the Metropolis–Hastings algorithm (or methods such as slice sampling) to implement one or more of the sampling steps.

Gibbs sampling is applicable when the joint distribution is not known explicitly or is difficult to sample from directly, but the conditional distribution of each variable is known and is easy (or at least, easier) to sample from. The Gibbs sampling algorithm generates an instance from the distribution of each variable in turn, conditional on the current values of the other variables. It can be shown that the sequence of samples constitutes a Markov chain, and the stationary distribution of that Markov chain is just the sought-after joint distribution.

Gibbs sampling is particularly well-adapted to sampling the posterior distribution of a Bayesian network, since Bayesian networks are typically specified as a collection of conditional distributions.

Implementation
Gibbs sampling, in its basic incarnation, is a special case of the Metropolis–Hastings algorithm. The point of Gibbs sampling is that given a multivariate distribution it is simpler to sample from a conditional distribution than to marginalize by integrating over a joint distribution. Suppose we want to obtain $$\left.k\right.$$ samples of $$\mathbf{X} = (x_1, \dots, x_n)$$ from a joint distribution $$ p(x_1, \dots, x_n) $$. Denote the $$i$$th sample by $$\mathbf{X}^{(i)} = \left(x_1^{(i)}, \dots, x_n^{(i)}\right)$$. We proceed as follows:

 * 1) We begin with some initial value $$\mathbf{X}^{(0)}$$.
 * 2) We want the next sample. Call this next sample $$\mathbf{X}^{(i+1)}$$. Since $$\mathbf{X}^{(i+1)} = \left(x_1^{(i+1)}, x_2^{(i+1)}, \dots, x_n^{(i+1)}\right)$$ is a vector, we sample each component of the vector, $$x_j^{(i+1)}$$, from the distribution of that component conditioned on all other components sampled so far. But there is a catch: we condition on $$\mathbf{X}^{(i+1)}$$'s components up to $$x_{j-1}^{(i+1)}$$, and thereafter condition on $$\mathbf{X}^{(i)}$$'s components, starting from $$x_{j+1}^{(i)}$$ to $$x_n^{(i)}$$. To achieve this, we sample the components in order, starting from the first component. More formally, to sample $$x_j^{(i+1)}$$, we update it according to the distribution specified by $$p\left(x_j^{(i+1)}|x_1^{(i+1)},\dots,x_{j-1}^{(i+1)},x_{j+1}^{(i)},\dots,x_n^{(i)}\right)$$. We use the value that the $$(j+1)$$th component had in the $$i$$th sample, not the $$(i+1)$$th sample.
 * 3) Repeat the above step $$k$$ times.

Properties
If such sampling is performed, these important facts hold:
 * The samples approximate the joint distribution of all variables.
 * The marginal distribution of any subset of variables can be approximated by simply considering the samples for that subset of variables, ignoring the rest.
 * The expected value of any variable can be approximated by averaging over all the samples.

When performing the sampling:
 * The initial values of the variables can be determined randomly or by some other algorithm such as expectation–maximization.
 * It is not actually necessary to determine an initial value for the first variable sampled.
 * It is common to ignore some number of samples at the beginning (the so-called burn-in period), and then consider only every $$n$$th sample when averaging values to compute an expectation. For example, the first 1,000 samples might be ignored, and then every 100th sample averaged, throwing away all the rest. The reason for this is that (1) the stationary distribution of the Markov chain is the desired joint distribution over the variables, but it may take a while for that stationary distribution to be reached; (2) successive samples are not independent of each other but form a Markov chain with some amount of correlation. Sometimes, algorithms can be used to determine the amount of autocorrelation between samples and the value of $$n$$ (the period between samples that are actually used) computed from this, but in practice there is a fair amount of "black magic" involved.
 * The process of simulated annealing is often used to reduce the "random walk" behavior in the early part of the sampling process (i.e. the tendency to move slowly around the sample space, with a high amount of autocorrelation between samples, rather than moving around quickly, as is desired). Other techniques that may reduce autocorrelation are collapsed Gibbs sampling, blocked Gibbs sampling, and ordered overrelaxation; see below.

Relation of conditional distribution and joint distribution
Furthermore, the conditional distribution of one variable given all others is proportional to the joint distribution:

 * $$p(x_j\mid x_1,\dots,x_{j-1},x_{j+1},\dots,x_n) = \frac{p(x_1,\dots,x_n)}{p(x_1,\dots,x_{j-1},x_{j+1},\dots,x_n)} \propto p(x_1,\dots,x_n)$$

"Proportional to" in this case means that the denominator is not a function of $$x_j$$ and thus is the same for all values of $$x_j$$; it forms part of the normalization constant for the distribution over $$x_j$$. In practice, to determine the nature of the conditional distribution of a factor $$x_j$$, it is easiest to factor the joint distribution according to the individual conditional distributions defined by the graphical model over the variables, ignore all factors that are not functions of $$x_j$$ (all of which, together with the denominator above, constitute the normalization constant), and then reinstate the normalization constant at the end, as necessary. In practice, this means doing one of three things:
 * 1) If the distribution is discrete, the individual probabilities of all possible values of $$x_j$$ are computed, and then summed to find the normalization constant.
 * 2) If the distribution is continuous and of a known form, the normalization constant will also be known.
 * 3) In other cases, the normalization constant can usually be ignored, as most sampling methods do not require it.

Inference
Gibbs sampling is commonly used for statistical inference (e.g. determining the best value of a parameter, such as determining the number of people likely to shop at a particular store on a given day, the candidate a voter will most likely vote for, etc.). The idea is that observed data is incorporated into the sampling process by creating separate variables for each piece of observed data and fixing the variables in question to their observed values, rather than sampling from those variables. The distribution of the remaining variables is then effectively a posterior distribution conditioned on the observed data.

The most likely value of a desired parameter (the mode) could then simply be selected by choosing the sample value that occurs most commonly; this is essentially equivalent to maximum a posteriori estimation of a parameter. (Since the parameters are usually continuous, it is often necessary to "bin" the sampled values into one of a finite number of ranges or "bins" in order to get a meaningful estimate of the mode.) More commonly, however, the expected value (mean or average) of the sampled values is chosen; this is a Bayes estimator that takes advantage of the additional data about the entire distribution that is available from Bayesian sampling, whereas a maximization algorithm such as expectation maximization (EM) is capable of only returning a single point from the distribution. For example, for a unimodal distribution the mean (expected value) is usually similar to the mode (most common value), but if the distribution is skewed in one direction, the mean will be moved in that direction, which effectively accounts for the extra probability mass in that direction. (If a distribution is multimodal, the expected value may not return a meaningful point, and any of the modes is typically a better choice.)

Although some of the variables typically correspond to parameters of interest, others are uninteresting ("nuisance") variables introduced into the model to properly express the relationships among variables. Although the sampled values represent the joint distribution over all variables, the nuisance variables can simply be ignored when computing expected values or modes; this is equivalent to marginalizing over the nuisance variables. When a value for multiple variables is desired, the expected value is simply computed over each variable separately. (When computing the mode, however, all variables must be considered together.)

Supervised learning, unsupervised learning and semi-supervised learning (aka learning with missing values) can all be handled by simply fixing the values of all variables whose values are known, and sampling from the remainder.

For observed data, there will be one variable for each observation—rather than, for example, one variable corresponding to the sample mean or sample variance of a set of observations. In fact, there generally will be no variables at all corresponding to concepts such as "sample mean" or "sample variance". Instead, in such a case there will be variables representing the unknown true mean and true variance, and the determination of sample values for these variables results automatically from the operation of the Gibbs sampler.

Generalized linear models (i.e. variations of linear regression) can sometimes be handled by Gibbs sampling as well. For example, probit regression for determining the probability of a given binary (yes/no) choice, with normally distributed priors placed over the regression coefficients, can be implemented with Gibbs sampling because it is possible to add additional variables and take advantage of conjugacy. However, logistic regression cannot be handled this way. One possibility is to approximate the logistic function with a mixture (typically 7–9) of normal distributions. More commonly, however, Metropolis–Hastings is used instead of Gibbs sampling.

Mathematical background
Suppose that a sample $$\left.X\right.$$ is taken from a distribution depending on a parameter vector $$\theta \in \Theta \,\!$$ of length $$\left.d\right.$$, with prior distribution $$g(\theta_1, \ldots, \theta_d)$$. It may be that $$\left.d\right.$$ is very large and that numerical integration to find the marginal densities of the $$\left.\theta_i\right.$$ would be computationally expensive. Then an alternative method of calculating the marginal densities is to create a Markov chain on the space $$\left.\Theta\right.$$ by repeating these two steps:

 * 1) Pick a random index $$1 \leq j \leq d$$
 * 2) Pick a new value for $$\left.\theta_j\right.$$ according to $$g(\theta_1, \ldots, \theta_{j-1} , \, \cdot \, , \theta_{j+1} , \ldots , \theta_d )$$

These steps define a reversible Markov chain with the desired invariant distribution $$\left.g\right.$$. This can be proved as follows. Define $$x \sim_j y$$ if $$\left.x_i = y_i\right.$$ for all $$i \neq j$$ and let $$\left.p_{xy}\right.$$ denote the probability of a jump from $$x \in \Theta$$ to $$y \in \Theta$$. Then, the transition probabilities are

 * $$p_{xy} = \begin{cases}

\frac{1}{d}\frac{g(y)}{\sum_{z \in \Theta: z \sim_j x} g(z) } & x \sim_j y \\ 0 & \text{otherwise} \end{cases} $$

So

g(x) p_{xy} = \frac{1}{d}\frac{ g(x) g(y)}{\sum_{z \in \Theta: z \sim_j x} g(z) } = \frac{1}{d}\frac{ g(y) g(x)}{\sum_{z \in \Theta: z \sim_j y} g(z) } = g(y) p_{yx} $$

since $$x \sim_j y$$ is an equivalence relation. Thus the detailed balance equations are satisfied, implying the chain is reversible and it has invariant distribution $$\left.g\right.$$.

In practice, the index $$\left.j\right.$$ is not chosen at random, and the chain cycles through the indexes in order. In general this gives a non-stationary Markov process, but each individual step will still be reversible, and the overall process will still have the desired stationary distribution (as long as the chain can access all states under the fixed ordering).

Gibbs sampler in Bayesian inference and its relation to information theory
Let $$y$$ denote observations generated from the sampling distribution $$f(y|\theta)$$ and $$\pi(\theta)$$ be a prior supported on the parameter space $$\Theta$$. Then one of the central goals of the Bayesian statistics is to approximate the posterior density

 * $$\pi(\theta|y) = \frac{f(y|\theta) \cdot \pi(\theta)}{m(y)}$$

where the marginal likelihood $$ m(y) = \int_{\Theta} f(y|\theta) \cdot \pi(\theta) d\theta $$ is assumed to be finite for all $$y$$.

To explain the Gibbs sampler, we additionally assume that the parameter space $$\Theta$$ is decomposed as

 * $$\Theta = \prod_{i=1}^{K}\Theta_{i} = \Theta_1 \times \cdots \Theta_i \times \cdots \times \Theta_K, \quad\quad (K>1)$$,

where $$\times$$ represents the Cartesian product. Each component parameter space $$\Theta_i$$ can be a set of scalar components, subvectors, or matrices.

Define a set $$\Theta_{-i}$$ that complements the $$\Theta_i$$. Essential ingredients of the Gibbs sampler is the $$i$$-th full conditional posterior distribution for each $$i=1,\cdots, K$$
 * $$\pi(\theta_i|\theta_{-i},y)=\pi(\theta_i|\theta_1, \cdots, \theta_{i-1},\theta_{i+1},\cdots, \theta_{K},y)$$.

The following algorithm details a generic Gibbs sampler:

$$\text{Initialize: pick arbitrary starting value}\,\, \theta^{(1)} = (\theta_1^{(1)},\theta_2^{(1)},\cdots,\theta_i^{(1)},\theta_{i+1}^{(1)},\cdots,\theta_K^{(1)}) $$

$$\text{Iterate a Cycle:}\,$$

$$ \quad\quad \text{Step 1. draw}\,\, \theta_1^{(s+1)}\sim \pi(\theta_1|\theta_2^{(s)},\theta_3^{(s)},\cdots,\theta_K^{(s)},y )$$

$$ \quad\quad \text{Step 2. draw}\,\, \theta_2^{(s+1)}\sim \pi(\theta_2|\theta_1^{(s+1)},\theta_3^{(s)},\cdots,\theta_K^{(s)},y )$$

$$ \quad\quad\quad \vdots$$

$$ \quad\quad \text{Step i.     draw}\,\, \theta_i^{(s+1)}\sim \pi(\theta_i|\theta_1^{(s+1)},\theta_2^{(s+1)},\cdots, \theta_{i-1}^{(s+1)},\theta_{i+1}^{(s)} ,\cdots, \theta_K^{(s)},y )$$

$$ \quad \quad \text{Step i+1. draw}\,\, \theta_{i+1}^{(s+1)}\sim \pi(\theta_{i+1}|\theta_1^{(s+1)},\theta_2^{(s+1)},\cdots, \theta_{i}^{(s+1)},\theta_{i+2}^{(s)} ,\cdots, \theta_K^{(s)},y )$$

$$ \quad\quad\quad \vdots$$

$$ \quad\quad \text{Step K.     draw}\,\, \theta_K^{(s+1)}\sim \pi(\theta_K|\theta_1^{(s+1)},\theta_2^{(s+1)},\cdots,\theta_{K-1}^{(s+1)},y )$$

$$\text{end Iterate}$$

Note that Gibbs sampler is operated by the iterative Monte Carlo scheme within a cycle. The $$S$$ number of samples $$\{\theta^{(s)} \}_{s=1}^{S}$$ drawn by the above algorithm formulates Markov Chains with the invariant distribution to be the target density $$\pi(\theta|y)$$.

Now, for each $$i=1,\cdots,K$$, define the following information theoretic quantities:

$$I(\theta_i ; \theta_{-i}) = \text{KL}(\pi(\theta|y)||\pi(\theta_i|y) \cdot \pi(\theta_{-i}|y) ) =\int_{\Theta} \pi(\theta|y) \log \bigg(\frac{\pi(\theta|y)}{\pi(\theta_i|y) \cdot \pi(\theta_{-i}|y)}\bigg) d\theta, $$

$$H(\theta_{-i}) = -\int_{\Theta_{-i}} \pi(\theta_{-i}|y) \log \pi(\theta_{-i}|y) d\theta_{-i}, $$

$$H(\theta_{-i}|\theta_{i}) = -\int_{\Theta} \pi(\theta|y) \log \pi(\theta_{-i}|\theta_{i},y) d\theta, $$

namely, posterior mutual information, posterior differential entropy, and posterior conditional differential entropy, respectively. We can similarly define information theoretic quantities $$I(\theta_{-i} ; \theta_{i})$$, $$H(\theta_{i})$$, and $$H(\theta_{i}|\theta_{-i})$$ by interchanging the $$i$$ and $$-i$$ in the defined quantities. Then, the following $$K$$ equations hold.

$$I(\theta_i ; \theta_{-i}) = H(\theta_{-i}) - H(\theta_{-i}|\theta_{i}) = H(\theta_{i}) - H(\theta_{i}|\theta_{-i}) = I(\theta_{-i} ; \theta_{i}), \quad (i=1,\cdots,K) $$.

The mutual information $$I(\theta_i ; \theta_{-i}) $$ quantifies the reduction in uncertainty of random quantity $$\theta_{i}$$ once we know $$\theta_{-i}$$, a posteriori. It vanishes if and only if $$\theta_{i}$$ and $$\theta_{-i}$$ are marginally independent, a posterior. The mutual information $$I(\theta_i ; \theta_{-i})$$ can be interpreted as the quantity that is transmitted from the $$i$$-th step to the $$i+1$$-th step within a single cycle of the Gibbs sampler.

Variations and extensions
Numerous variations of the basic Gibbs sampler exist. The goal of these variations is to reduce the autocorrelation between samples sufficiently to overcome any added computational costs.

Blocked Gibbs sampler

 * A blocked Gibbs sampler groups two or more variables together and samples from their joint distribution conditioned on all other variables, rather than sampling from each one individually. For example, in a hidden Markov model, a blocked Gibbs sampler might sample from all the latent variables making up the Markov chain in one go, using the forward-backward algorithm.

Collapsed Gibbs sampler

 * A collapsed Gibbs sampler integrates out (marginalizes over) one or more variables when sampling for some other variable. For example, imagine that a model consists of three variables A, B, and C.  A simple Gibbs sampler would sample from p(A | B,C), then p(B | A,C), then p(C | A,B).  A collapsed Gibbs sampler might replace the sampling step for A with a sample taken from the marginal distribution p(A | C), with variable B integrated out in this case.  Alternatively, variable B could be collapsed out entirely, alternately sampling from p(A | C) and p(C | A) and not sampling over B at all.  The distribution over a variable A that arises when collapsing a parent variable B is called a compound distribution; sampling from this distribution is generally tractable when B is the conjugate prior for A, particularly when A and B are members of the exponential family.  For more information, see the article on compound distributions or Liu (1994).

Collapsing Dirichlet distributions
In hierarchical Bayesian models with categorical variables, such as latent Dirichlet allocation and various other models used in natural language processing, it is quite common to collapse out the Dirichlet distributions that are typically used as prior distributions over the categorical variables. The result of this collapsing introduces dependencies among all the categorical variables dependent on a given Dirichlet prior, and the joint distribution of these variables after collapsing is a Dirichlet-multinomial distribution. The conditional distribution of a given categorical variable in this distribution, conditioned on the others, assumes an extremely simple form that makes Gibbs sampling even easier than if the collapsing had not been done. The rules are as follows:
 * 1) Collapsing out a Dirichlet prior node affects only the parent and children nodes of the prior. Since the parent is often a constant, it is typically only the children that we need to worry about.
 * 2) Collapsing out a Dirichlet prior introduces dependencies among all the categorical children dependent on that prior — but no extra dependencies among any other categorical children. (This is important to keep in mind, for example, when there are multiple Dirichlet priors related by the same hyperprior. Each Dirichlet prior can be independently collapsed and affects only its direct children.)
 * 3) After collapsing, the conditional distribution of one dependent children on the others assumes a very simple form: The probability of seeing a given value is proportional to the sum of the corresponding hyperprior for this value, and the count of all of the other dependent nodes assuming the same value. Nodes not dependent on the same prior must not be counted. The same rule applies in other iterative inference methods, such as variational Bayes or expectation maximization; however, if the method involves keeping partial counts, then the partial counts for the value in question must be summed across all the other dependent nodes.  Sometimes this summed up partial count is termed the expected count or similar. The probability is proportional to the resulting value; the actual probability must be determined by normalizing across all the possible values that the categorical variable can take (i.e. adding up the computed result for each possible value of the categorical variable, and dividing all the computed results by this sum).
 * 4) If a given categorical node has dependent children (e.g. when it is a latent variable in a mixture model), the value computed in the previous step (expected count plus prior, or whatever is computed) must be multiplied by the actual conditional probabilities (not a computed value that is proportional to the probability!) of all children given their parents. See the article on the Dirichlet-multinomial distribution for a detailed discussion.
 * 5) In the case where the group membership of the nodes dependent on a given Dirichlet prior may change dynamically depending on some other variable (e.g. a categorical variable indexed by another latent categorical variable, as in a topic model), the same expected counts are still computed, but need to be done carefully so that the correct set of variables is included.  See the article on the Dirichlet-multinomial distribution for more discussion, including in the context of a topic model.

Collapsing other conjugate priors
In general, any conjugate prior can be collapsed out, if its only children have distributions conjugate to it. The relevant math is discussed in the article on compound distributions. If there is only one child node, the result will often assume a known distribution. For example, collapsing an inverse-gamma-distributed variance out of a network with a single Gaussian child will yield a Student's t-distribution. (For that matter, collapsing both the mean and variance of a single Gaussian child will still yield a Student's t-distribution, provided both are conjugate, i.e. Gaussian mean, inverse-gamma variance.)

If there are multiple child nodes, they will all become dependent, as in the Dirichlet-categorical case. The resulting joint distribution will have a closed form that resembles in some ways the compound distribution, although it will have a product of a number of factors, one for each child node, in it.

In addition, and most importantly, the resulting conditional distribution of one of the child nodes given the others (and also given the parents of the collapsed node(s), but not given the children of the child nodes) will have the same density as the posterior predictive distribution of all the remaining child nodes. Furthermore, the posterior predictive distribution has the same density as the basic compound distribution of a single node, although with different parameters. The general formula is given in the article on compound distributions.

For example, given a Bayes network with a set of conditionally independent identically distributed Gaussian-distributed nodes with conjugate prior distributions placed on the mean and variance, the conditional distribution of one node given the others after compounding out both the mean and variance will be a Student's t-distribution. Similarly, the result of compounding out the gamma prior of a number of Poisson-distributed nodes causes the conditional distribution of one node given the others to assume a negative binomial distribution.

In these cases where compounding produces a well-known distribution, efficient sampling procedures often exist, and using them will often (although not necessarily) be more efficient than not collapsing, and instead sampling both prior and child nodes separately. However, in the case where the compound distribution is not well-known, it may not be easy to sample from, since it generally will not belong to the exponential family and typically will not be log-concave (which would make it easy to sample using adaptive rejection sampling, since a closed form always exists).

In the case where the child nodes of the collapsed nodes themselves have children, the conditional distribution of one of these child nodes given all other nodes in the graph will have to take into account the distribution of these second-level children. In particular, the resulting conditional distribution will be proportional to a product of the compound distribution as defined above, and the conditional distributions of all of the child nodes given their parents (but not given their own children). This follows from the fact that the full conditional distribution is proportional to the joint distribution. If the child nodes of the collapsed nodes are continuous, this distribution will generally not be of a known form, and may well be difficult to sample from despite the fact that a closed form can be written, for the same reasons as described above for non-well-known compound distributions. However, in the particular case that the child nodes are discrete, sampling is feasible, regardless of whether the children of these child nodes are continuous or discrete. In fact, the principle involved here is described in fair detail in the article on the Dirichlet-multinomial distribution.

Gibbs sampler with ordered overrelaxation

 * A Gibbs sampler with ordered overrelaxation samples a given odd number of candidate values for $$x_j^{(i)}$$ at any given step and sorts them, along with the single value for $$x_j^{(i-1)}$$ according to some well-defined ordering. If $$x_j^{(i-1)}$$ is the sth smallest in the sorted list then the $$x_j^{(i)}$$ is selected as the sth largest in the sorted list.  For more information, see Neal (1995).

Other extensions
It is also possible to extend Gibbs sampling in various ways. For example, in the case of variables whose conditional distribution is not easy to sample from, a single iteration of slice sampling or the Metropolis–Hastings algorithm can be used to sample from the variables in question. It is also possible to incorporate variables that are not random variables, but whose value is deterministically computed from other variables. Generalized linear models, e.g. logistic regression (aka "maximum entropy models"), can be incorporated in this fashion. (BUGS, for example, allows this type of mixing of models.)

Failure modes
There are two ways that Gibbs sampling can fail. The first is when there are islands of high-probability states, with no paths between them. For example, consider a probability distribution over 2-bit vectors, where the vectors (0,0) and (1,1) each have probability $1⁄2$, but the other two vectors (0,1) and (1,0) have probability zero. Gibbs sampling will become trapped in one of the two high-probability vectors, and will never reach the other one. More generally, for any distribution over high-dimensional, real-valued vectors, if two particular elements of the vector are perfectly correlated (or perfectly anti-correlated), those two elements will become stuck, and Gibbs sampling will never be able to change them.

The second problem can happen even when all states have nonzero probability and there is only a single island of high-probability states. For example, consider a probability distribution over 100-bit vectors, where the all-zeros vector occurs with probability $1⁄2$, and all other vectors are equally probable, and so have a probability of $$\frac{1}{2(2^{100}-1)}$$ each. If you want to estimate the probability of the zero vector, it would be sufficient to take 100 or 1000 samples from the true distribution. That would very likely give an answer very close to $1⁄2$. But you would probably have to take more than $$2^{100}$$ samples from Gibbs sampling to get the same result. No computer could do this in a lifetime.

This problem occurs no matter how long the burn-in period is. This is because in the true distribution, the zero vector occurs half the time, and those occurrences are randomly mixed in with the nonzero vectors. Even a small sample will see both zero and nonzero vectors. But Gibbs sampling will alternate between returning only the zero vector for long periods (about $$2^{99}$$ in a row), then only nonzero vectors for long periods (about $$2^{99}$$ in a row). Thus convergence to the true distribution is extremely slow, requiring much more than $$2^{99}$$ steps; taking this many steps is not computationally feasible in a reasonable time period. The slow convergence here can be seen as a consequence of the curse of dimensionality. A problem like this can be solved by block sampling the entire 100-bit vector at once. (This assumes that the 100-bit vector is part of a larger set of variables. If this vector is the only thing being sampled, then block sampling is equivalent to not doing Gibbs sampling at all, which by hypothesis would be difficult.)

Software

 * The OpenBUGS software (Bayesian inference Using Gibbs Sampling) does a Bayesian analysis of complex statistical models using Markov chain Monte Carlo.

 * JAGS (Just another Gibbs sampler) is a GPL program for analysis of Bayesian hierarchical models using Markov Chain Monte Carlo.

 * Church is free software for performing Gibbs inference over arbitrary distributions that are specified as probabilistic programs.

 * PyMC is an open source Python library for Bayesian learning of general Probabilistic Graphical Models.
 * Turing is an open source Julia library for Bayesian Inference using probabilistic programming.

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

title: Gibbs sampling


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Rotenone

Rotenone is an odorless, colorless, crystalline isoflavone used as a broad-spectrum insecticide, piscicide, and pesticide. It occurs naturally in the seeds and stems of several plants, such as the jicama vine, and in the roots of several other members of the Fabaceae. It was the first-described member of the family of chemical compounds known as rotenoids.

Discovery
The earliest written record of the now-known rotenone-containing plants used for killing leaf-eating caterpillars was in 1848; for centuries, these same plants had been used to poison fish. The active chemical component was first isolated in 1895 by a French botanist, Emmanuel Geoffroy, who called it nicouline, from a specimen of Robinia nicou, now called Deguelia utilis, while traveling in French Guiana. He wrote about this research in his thesis, published in 1895 after his death from a parasitic disease. In 1902 Kazuo Nagai, Japanese chemical engineer of the Government-General of Taiwan, isolated a pure crystalline compound from Derris elliptica which he called rotenone, after the Taiwanese name of the plant 蘆藤 translated into Japanese. By 1930, nicouline and rotenone were established to be chemically the same.

Uses
Rotenone is used as a pesticide, insecticide, and as a nonselective piscicide (fish killer). Rotenone has historically been used by indigenous peoples to catch fish. Typically, rotenone-containing plants in the legume family, Fabaceae, are crushed and introduced into a body of water, and as rotenone interferes with cellular respiration, the affected fish rise to the surface in an attempt to gulp air, where they are more easily caught.

In modern times it is frequently used as a tool to remove alien fish species, as it has a relatively short half-life (days) and is gone from rivers in the course of days and from lakes within a few months, depending on (seasonal) stirring, organic content, availability of sunlight and temperature. Rotenone has been used by government agencies to kill fish in rivers and lakes in the United States since 1952, and in Canada and Norway since the 1980s. It is less frequently used in EU countries, due to strict regulations, but has seen some use in selected countries such as the UK (Topmouth gudgeon), Sweden (pike and pumpkinseed), Spain (Topmouth gudgeon, Gambusia) and Hungary (Prussian carp).

Rotenone decays through metabolites and its final product is reduced to water and carbon dioxide. Furthermore, its use is more benign for the environment (as compared to other piscicides) as most species are seen to recolonize aquatic systems within weeks to a year after application. Thus, it has also seen some use in other field studies in the marine environment needing only small quantities. Small-scale sampling with rotenone is used by fish researchers studying the biodiversity of marine fishes to collect cryptic, or hidden, fishes, which represent an important component of shoreline fish communities, since it has only minor and transient environmental side effects.

It is commercialized as cubé, tuba, or derris, in single preparation or in synergistic combination with other insecticides. In the United States and Canada, all uses of rotenone except as a piscicide are being phased out. It is currently banned in the United States for any use in organic farming. In the UK, rotenone insecticides (sold under the trade name Derris) were banned for sale in 2009.

Rotenone is also used in powdered form to treat scabies and head lice on humans, and parasitic mites on chickens, livestock, and pet animals.

In agriculture it is also unselective in action and kills potato beetles, cucumber beetles, flea beetles, cabbage worms, raspberry beetles, and asparagus beetles, as well as most other arthropods. It biodegrades rapidly in soil, with 90% degraded after 1–3 months at 20 C and three times faster at 30 C.

Mechanism of action
Rotenone works by interfering with the electron transport chain within complex I in mitochondria, which places it in IRAC MoA class 21 (by itself in 21B). It inhibits the transfer of electrons from iron-sulfur centers in complex I to ubiquinone. This interferes with NADH during the creation of usable cellular energy (ATP). Complex I is unable to pass off its electron to CoQ, creating a back-up of electrons within the mitochondrial matrix. Cellular oxygen is reduced to the radical, creating reactive oxygen species, which can damage DNA and other components of the mitochondria.

Rotenone also inhibits microtubule assembly.

Presence in plants
Rotenone is produced by extraction from the roots and stems of several tropical and subtropical plant species, especially those belonging to the genera Lonchocarpus and Derris.

Some of the plants containing rotenone:
 * Hoary pea or goat's rue (Tephrosia virginiana) – North America
 * Jícama (Pachyrhizus erosus) – North America
 * Cubé plant or lancepod (Lonchocarpus utilis) – South America
 * The root extract is referred to as cubé resin
 * Barbasco (Lonchocarpus urucu) – South America
 * The root extract is referred to as cubé resin
 * Tuba plant (Derris elliptica) – southeast Asia and southwest Pacific islands
 * The root extract is referred to as derris or derris root
 * Jewel vine (Derris involuta) – southeast Asia and southwest Pacific islands
 * The root extract is referred to as derris or derris root
 * Common Mullein (Verbascum thapsus L.)
 * Cork-bush (Mundulea sericea) – southern Africa
 * Florida fishpoison tree (Piscidia piscipula) – southern Florida, Caribbean
 * Several species of Millettia and Tephrosia in South-east Asian regions

Human toxicity
Rotenone is classified by the World Health Organization as moderately hazardous. It is mildly toxic to humans and other mammals, but extremely toxic to insects and aquatic life, including fish. This higher toxicity in fish and insects is because the lipophilic rotenone is easily taken up through the gills or trachea, but not as easily through the skin or the gastrointestinal tract. Rotenone is toxic to erythrocytes in vitro.

The lowest lethal dose for a child is not known, but death occurred in a 3.5-year-old child who had ingested 40 mg/kg rotenone solution. Human deaths from rotenone poisoning are rare because its irritating action causes vomiting. Deliberate ingestion of rotenone can be fatal.

The compound decomposes when exposed to sunlight and usually has an activity of six days in the environment. It oxidizes to rotenolone, which is about an order of magnitude less toxic than rotenone. In water, the rate of decomposition depends upon several factors, including temperature, pH, water hardness and sunlight. The half-life in natural waters ranges from half a day at 24 °C to 3.5 days at 0 °C.

A 2018 study, which examined the effects of rotenone administration on cell cultures that mimicked properties of developing brains, found that rotenone may be a developmental neurotoxicant; that is, that rotenone exposure in the developing fetus may impede proper human brain development, with potentially profound consequences later in life. The study found that rotenone was particularly damaging to dopaminergic neurons, consistent with prior findings.

Parkinson's disease
In 2000, injecting rotenone into rats was reported to cause the development of symptoms similar to those of Parkinson's disease (PD). Rotenone was continuously applied over a period of five weeks, mixed with DMSO and PEG to enhance tissue penetration, and injected into the jugular vein. The study does not directly suggest rotenone exposure is responsible for PD in humans, but is consistent with the belief that chronic exposure to environmental toxins increases the likelihood of the disease. In 2011, a US National Institutes of Health study showed a link between rotenone use and Parkinson's disease in farm workers, suggesting a link between neural damage and pulmonary uptake by not using protective gear. Exposure to the chemical in the field can be avoided by wearing a gas mask with filter, which is standard HSE procedure in modern application of the chemical.

Studies with primary cultures of rat neurons and microglia have shown low doses of rotenone (below 10 nM) induce oxidative damage and death of dopaminergic neurons, and it is these neurons in the substantia nigra that die in Parkinson's disease. Another study has also described toxic action of rotenone at low concentrations (5 nM) in dopaminergic neurons from acute rat brain slices. This toxicity was exacerbated by an additional cell stressor – elevated intracellular calcium concentration – adding support to the 'multiple hit hypothesis' of dopaminergic neuron death.

The neurotoxin MPTP had been known earlier to cause PD-like symptoms (in humans and other primates, though not in rats) by interfering with complex I in the electron transport chain and killing dopaminergic neurons in the substantia nigra. Further studies involving MPTP have failed to show development of Lewy bodies, a key component to PD pathology. However at least one study recently has found evidence of protein aggregation of the same chemical makeup as that which makes up Lewy bodies with similar pathology to Parkinson's disease in aged rhesus monkeys from MPTP. Therefore, the mechanism behind MPTP as it relates to Parkinson's disease is not fully understood. Because of these developments, rotenone was investigated as a possible Parkinson-causing agent. Both MPTP and rotenone are lipophilic and can cross the blood–brain barrier.

In 2010, a study was published detailing the progression of Parkinson's-like symptoms in mice following chronic intragastric ingestion of low doses of rotenone. The concentrations in the central nervous system were below detectable limits, yet still induced PD pathology.

Notable administrations
In 1992, Florida Fish and Wildlife Conservation Commission (FWC) officials used rotenone to eradicate an established population of invasive jaguar cichlids from a small pond in Miami-Dade County. Officials were successful in killing every jaguar cichlid (along with every other fish) in the pond, but unsuccessful in eradicating them from Florida; the cichlids had already spread throughout the Miami Canal and its connected waterways, and by 1994, jaguar cichlids had successfully established themselves throughout Southern and Central Florida.

In September 2010, Oregon Department of Fish and Wildlife officials used rotenone to kill an established population of invasive goldfish present in eastern Oregon's Mann Lake, with the intention of not disrupting the lake's native Lahontan cutthroat trout population. Rotenone successfully achieved these aims, killing between 179,000–197,000 goldfish and fathead minnows, and only three trout.

Beginning May 1, 2006, Panguitch Lake, a reservoir in the southeastern portion of the U.S. state of Utah, was treated with rotenone, to potentially eradicate and control the invasive population of Utah chub, which were probably introduced accidentally by anglers who used them as live bait. The lake was restocked with 20,000 rainbow trout in 2006; as of 2016, the lake's fish population has recovered.

In 2012, rotenone was used to kill all remaining fish in Stormy Lake (Alaska) due to invasive pike destroying native species, which were reintroduced once the treatment was concluded. In 2014, rotenone was used to kill all remaining fish in San Francisco's Mountain Lake, which is located in Mountain Lake Park, in order to rid it of invasive species introduced since the migration of European settlers to the region.

Rotenone is used in biomedical research to study the oxygen consumption rate of cells, usually in combination with antimycin A (an electron transport chain Complex III inhibitor), oligomycin (an ATP synthase inhibitor) and FCCP (a mitochondrial uncoupler).

Deactivation
Rotenone can be deactivated in water with the use of potassium permanganate to lower toxicity to acceptable levels.

title: Rotenone


text:
Glenorchy

Glenorchy may refer to:

 * Glen Orchy, a glen in Scotland containing the River Orchy
 * City of Glenorchy, a local government area of Tasmania, Australia
 * Glenorchy, Tasmania, the suburb contained within the local government area
 * Glenorchy, Victoria, a town in Australia
 * Glenorchy, New Zealand is a town bordering Lake Wakatipu in the South Island of New Zealand

Sports teams

 * Glenorchy Camanachd, a shinty club from Scotland
 * Glenorchy Football Club, an Australian Rules Football Club

title: Glenorchy


text:
Maya the Bee

Maya the Bee (Die Biene Maja) is the main character in The Adventures of Maya the Bee, a German book written by Waldemar Bonsels and published in 1912. The book has been published in many other languages and adapted into different media. The first American edition was published in 1922 by Thomas Seltzer and illustrated by Homer Boss. The latter's wife Adele Szold-Seltzer (1876-1940), the daughter of Benjamin Szold and younger sister of Henrietta Szold, was the translator.

The stories revolve around a little bee named Maya and her friends among bees, other insects and other creatures. The book depicts Maya's development from an adventurous youngster to a responsible adult member of bee society.

Plot
Bonsels' original book contains fewer than 200 pages. The storyline is centered on the relation of Maya and her many adventures.

Maya is a bee born in a bee hive during internal unrest: the hive is dividing itself into two new colonies. Maya is raised by her teacher, Miss Cassandra. Despite Miss Cassandra's warnings, Maya wants to explore the wide world and commits the unforgivable crime of leaving the hive. During her adventures, Maya, now in exile, befriends other insects and braves dangers with them. In the climax of the book, Maya is taken prisoner by hornets, the bees' sworn enemies.

Prisoner of the hornets, Maya learns of a hornet plan to attack her native hive. Maya is faced with the decision to either return to hive and suffer her due punishment, saving the hive, or leaving the plan unannounced, saving herself but destroying the hive. After severe pondering, she makes the decision to return. In the hive, she announces the coming attack and is unexpectedly pardoned. The forewarned bees triumph over the hornet attack force. Maya, now a heroine of the hive, becomes a teacher like Miss Cassandra and shares her experiences and wisdom with the future generation.

Analysis of the book
Sulevi Riukulehto suggested that the book may have carried a political message. This view depicts the beehive as a well-organised militarist society and Maya as an ideal citizen. Elements of nationalism also appear when Maya gets angry at a grasshopper for failing to distinguish between bees and wasps (whom she calls "a useless gang of bandits" [Räubergeschlecht] that have no "home or faith" [Heimat und Glauben]) and at a insulting fly, whom Maya threatens to teach "respect for bees" and with her stinger. Riukulehto interprets this to mean that respect is based on the threat of violence. Collectivism versus individualism is also a theme. Maya's independence and departure from the beehive is seen as reproachable, but it is atoned by her warning of the hornets' attack. This show of loyalty restores her position in the society. In the hornet attack part of the story, the bees' will to defend the hive and the heroic deaths of bee officers are glorified, often in overtly militarist tones.

After World War II, adaptations toned down the militarist element considerably, reduced the hornets' role. The 1975 anime added the character of Willy, a lazy and quite un-warlike drone bee. In the cartoon series, the briskly marching, but ridiculously incompetent ant armies provide a parody of militarism.

Main characters

 * Maya – Bee. The series main protagonist. She loves freedom and living in the meadow by herself, unlike other bees who live in the hive. She is good, fair, happy and willing to help everybody.
 * Miss Cassandra – Bee, Teacher at the Bee-School.

The following characters only appear in the animated series and films:
 * Willy – Bee. Lazy, clumsy, and cowardly, sometimes a showoff, but generally good-natured – not featured in the original Bonsels story, but a major character in all adaptations other than the 1926 film. His relationship to Maya is depicted inconsistently: in most adaptations, he's her best friend, who is secretly in love with her, prone to jealousy when Maya's attentions turn to others. Often reluctantly dragged into adventures by Maya.
 * Flip (or Philip) – Grasshopper. A wise friend of Maya and Willy. Introduced first in the animated series. Whether he is meant to be identical with the unnamed grasshopper of the book is unclear.
 * Alexander (or Aleksander) – Mouse. Intellectual, whose level of respect among the other creatures, and close friendship with Maya, often sends Willy into jealous rages. Appears only in the second season of the older animated series (1978).

1926 film
German director Wolfram Junghans made a 1926 silent version ("starring" real insects). The film was lost for a decade until the only original copy of the film was found in Finland. The material was restored in 2005 with a new musical score and released on DVD in 2012, in collaboration with the KAVI and the Bundesarchiv-Filmarchiv, and the film was screened in both Hamburg and Helsinki.

1975 anime
Perhaps the most popular and widely known adaptation of the story is the Japanese anime Maya the Honey Bee (みつばちマーヤの冒険). Originally aired on Japanese TV in 1975, the anime has been dubbed into 42 languages and screened on television in various territories. The Japanese TV series was preceded by Tokyo Kodomo Club's musical play based on the short story, presented as Mitsubachi Māya ("Maya the Honeybee"), distributed on an LP album.

The original theme was composed by Karel Svoboda and sung by Karel Gott in the German, Czech and Slovak versions; Zbigniew Wodecki in the Polish version.

2012 TV series
In 2012 Studio 100 Animation produced a 78-episode, 13-minute TV series. The series was rendered in CGI animation. A second 52 episode season aired in 2017.

Film series
A 2014 film adaptation based upon the 2012 series was released. In 2018, a sequel to the 2014 film, titled Maya the Bee: The Honey Games, released on March 1, 2018, in Germany and May 1, 2018, in United States.

In 2021, third film, titled Maya the Bee: The Golden Orb was released on January 7, 2021, in Australia. It was delayed from its original 2020 release date due to the COVID-19 pandemic.

Opera
Maya the Bee also served as the basis for a children's opera written by the Croatian composer Bruno Bjelinski in 1963. In 2008 it was staged in Villach, Austria, as part of their Carinthian Summer Music Festival. This performance was distinguished by having the "bees" played by children and not professional opera singers as it is usually the case.

Puppet musical
Singer-songwriter Nancy Harrow created a jazz-musical version of the story, called The Adventures of Maya the Bee, that featured puppets by Zofia Czechlewska. Harrow's adaptation was produced in New York City by The Culture Project in 2000, and was revived in 2012.

Musical
On October 10, 2016, Belgian company Studio 100 (the current owners of the series) created a Flemish stage musical called "Maya en de Pollenbollen" based on the 2012 series that has the people dressed in costumes for the characters from the show. The show contains songs made by Studio 100 with a few news songs created exclusively for the show. The musical centers around Maya alongside Flip and Beatrice celebrating Willy's birthday. The musical later returned in the Spring of 2017.

Since 2016, live actors from the original stage show make numerous appearances at numerous stage shows and special events held by Studio 100. Notably Studio 100's annual "De Grote Sinterklaasshow" held from late November till early December featuring Sinterklaas and Zwarte Pieten watching various Studio 100 Characters such as Kabouter Plop, and Piet Piraat (including Maya and friends) perform musical numbers on stage. The same actress that portrayed Maya in the musical is also the official Flemish voice of the character and reprised her role for Studio 100's "De Liedjestuin" where Maya is singing various Dutch children's songs and nursery rhymes. In The French and Walloon version "Le Jardin des Refrains", Maya is played by a different actress.

Amusement parks
After Studio 100's acquisition of the franchise, Plopsa began expanding the franchise to its own theme parks. Plopsaland De Panne opened an indoor children's area called "Mayaland" on July 3, 2011, before the CGI incarnation's begun airing on numerous television stations across Europe. Maya alongside Flip, and Willy would also appear at other Plopsa owned parks such as Plopsa Coo and Plopsa Indoor Hasselt. In Poland, Plopsa opened an indoor theme park called "Majaland Kownaty" which opened to the public on September 28, 2018, which is mostly themed to Maya the Bee but features other Studio 100's IPs (such as Bumba and Piet Piraat).

A year after Mayaland opened in Plopsaland, Holiday Park, Germany, opened a similar Maya the Bee children's area called "Majaland" which opened March 31, 2012.

Video game background
The origins of the Maya the Bee video games originated from a South Park video game for the Game Boy Color developed by Crawfish Interactive in development in 1998. But was eventually cancelled due to South Park creators Matt Stone and Trey Parker stating that the game would not be fitting on the Game Boy Color as that console was marketed towards children. A year later in 1999, the unreleased game's engine and assets were reused for two additional Game Boy Color titles from Crawfish and Acclaim - Maya the Bee & Her Friends, based on the Maya the Bee franchise which was released in Europe, and The New Adventures of Mary-Kate and Ashley, based on Mary-Kate and Ashley Olsen and was released in North America, being the first of the various video games based on the duo.

Games released
Developed by Crawfish, published by Acclaim. Developed by Neon Studios and Kiloo, published by Acclaim and Plan-B Media. Developed by Junior Interactive, published by Tivola. Developed by Shin'en Multimedia, published by Acclaim. Developed by The Web Production, published by Tivola. Developed by Shin'en Multimedia, published by Midway. Developed by Kiloo and co-published by Plan-B Media. The Bee Game is an adventure video game released for Nintendo DS and Game Boy Advance, developed by German studio Independent Arts Software. The game lets players experience the adventures of Maya the Bee and her friend Willie as they search for their friends, lost from a strong storm that has blown through Corn Poppy Meadow. Developed by Studio 100 and Engine Software, published by Bandai Namco Games Europe. Mobile racing game. Developed by Midnight Pigeon in cooperation with Studio 100.
 * Maya the Bee & Her Friends (Game Boy Color – 1999)
 * Maya the Bee: Garden Adventures (Game Boy Color – 2000)
 * Maya the Bee: What a Thunderstorm (PC – 2001)
 * Maya the Bee: The Great Adventure (Game Boy Advance – 2002)
 * Maya the Bee: A Wonderful Surprise! (PC – 2004)
 * Maya the Bee: Sweet Gold (Game Boy Advance – 2005)
 * Maya the Bee and Friends (mobile – 2006)
 * The Bee Game (Game Boy Advance, Nintendo DS – 2007)
 * Maya (Nintendo DS – 2013)
 * Maya the Bee: The Nutty Race (iOS and Android – 2019)

Merchandising
Many companies contributed worldwide to the success of the character by producing and selling merchandising. Most of them were drawn between 1976 and 1986 by the French licensed characters specialist André Roche. His works have included motifs for textiles, porcelain, books, comics and games, including a campaign for Kinder Surprise Eggs.

title: Maya the Bee


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Ruth Aylett

Ruth S. Aylett (born 1951) is a British author, computer scientist, professor, poet and political activist. She is a professor of computer science at Heriot-Watt University in Edinburgh, where she specialises in affective computing, social computing, software agents, and human–robot interaction.

Research
Aylett's research involves affective computing, social computing, software agents, and human–robot interaction. She is the leader of Socially Competent Robots (SoCoRo), a project of the Engineering and Physical Sciences Research Council that studies whether robots can assist autistic people in learning to recognize facial expressions and other social cues.

She has also studied the use of "emotionally literate" robots for tutoring schoolchildren, developed interactive role-playing software intended to combat bullying, and performed with a robot poet named Sarah the Poetic Robot as part of the Edinburgh Free Fringe.

Education and career
Aylett earned a degree in mathematical economics at the London School of Economics, and began her career in computing by working in technical support at International Computers Limited for three years, before moving to the University of Sheffield to work in computing and robotics. She became a lecturer at Sheffield Hallam University for five years, and then moved to the University of Edinburgh in 1989, as part of the Artificial Intelligence Applications Institute there. She moved again to the University of Salford in 1992, first as part of the IT Institute there and later in the Centre for Virtual Environments. There, she became Professor of Intelligent Virtual Environments in 2000. In 2004, she moved to her present position at Heriot-Watt University.

Publications
Aylett's book Robots: Bringing Intelligent Machines to Life? (2002) is a historical exploration on robots, on the history of robotics, and on research problems confronting roboticists. Aimed at high-school age students, it consists of a sequence of two-page illustrated spreads on each of its topics.

She is the coauthor, with Judy Robertson, Lisa Gjedde, Rose Luckin and Paul Brna, of the self-published book Inside Stories: A Narrative Journey (2008), on the use of story-telling in education and the use of technology to assist in storytelling.

Aylett is also the coauthor of the poetry pamphlet Handfast: Poetry Duets with Beth McDonough (Mothers Milk, 2016). It has a challenge-response format, in which a poem by one of the authors inspires a poem by the other author exploring the same theme.

Family and politics
Aylett was born in London. She is the mother of writer and activist Owen Jones. She met her husband, union organiser Robert Jones, through their membership in the Militant tendency, a Trotskyist group within the Labour Party. He developed prostate cancer, and died in 2018.

As a political activist, Aylett has advocated for the Labour Party, for improved labour security for university staff, for permanent residency for European Union citizens already in the UK at the time of Brexit, for academic freedom for faculty and students in the face of the 'Counter-terrorism and security bill' legislation by signing a letter claiming the bill ran counter to universities mission to foster free speech as well as being 'unenforceable' and 'unlawful', as well as support for transgender rights. She has served as one of the leaders of the Labour Party in Edinburgh Southern.

title: Ruth Aylett


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Glenorchy, Tasmania

Glenorchy is a suburb of Hobart, in the state of Tasmania, Australia. Glenorchy is bound by the River Derwent to the east, Mount Wellington to the west, Hobart City to the south and to the north. The city officially begins at Creek Road New Town, in Hobart's northern suburbs, and includes, Moonah, Derwent Park, Lutana, Goodwood, Montrose, Rosetta, Berriedale, Chigwell, Claremont and Austins Ferry. It is the seat of the local government area of the same name, the City of Glenorchy.

Glenorchy draws its name from Glen Orchy, Scotland, meaning "Glen of tumbling waters".

Overview
Glenorchy was first occupied in the year 1804, being mostly agricultural land from the 1820s onward, with orchards being the prime commercial industry for the area. Becoming a municipality in 1864 and then officially a city in 1964, Glenorchy is now a largely suburban, working class area, which grew quickly after WWII when a great number of returning soldiers settled in the northern suburbs.

Glenorchy has entertainment facilities including the Glenorchy Pool, a Village Cinemas complex, KGV Oval which houses the Glenorchy Football Club, and a bowls club. Glenorchy is also home to the Tasmanian Transport Museum and Glenorchy Art and Sculpture Park.

Schools in the area include Glenorchy Primary School, Cosgrove High School, Guilford Young College and Dominic College.

Glenorchy is passed through by the Main Road of Greater Hobart, and the Brooker Highway which is the main connection to surrounding councils. When the Brooker Highway was built in 1952, it extended from Hobart to Berriedale. During this time, areas of Glenorchy and Moonah undertook street widening works in order to cope with increased traffic from the south.

Significant areas of Glenorchy include:
 * Elwick is the name given to the area east of the Brooker Highway, including the Elwick Racecourse (where the Hobart Cup is raced) and the Hobart Showground, which represents all of Southern Tasmania.
 * Merton refers to the Barossa Road area, and the surrounding bushlands between Glenorchy and Lenah Valley.
 * O'Brien's Bridge is the name given to the site of first settlement in 1809.

At the 2016 Australian census, the suburban Glenorchy area had a population of 10,828, with the Glenorchy City population totalling 46,397.

Retail
The Glenorchy Central business district has three major indoor shopping centres, Northgate Shopping Centre, Glenorchy Central (Centro), and Glenorchy Plaza. Leading retail stores in Glenorchy include Best & Less, Coles, Woolworths, Big W, and Target, as well as a Bunnings located on the eastern edge of the Hobart show grounds on the Brooker Highway near Goodwood, with access via Howard Rd.

Glenorchy has the second largest shopping district in Tasmania, following the Hobart CBD. Glenorchy CBD is one of the three main commercial districts in Glenorchy City, as well as those in Moonah and Claremont.

Smelter contamination
The Risdon Zinc Works (trading as Nyrstar Hobart) at nearby Lutana, which has been in operation since 1917, continues to produce heavy metal contaminants affecting the air, land and estuary waters surrounding Greater Hobart.

Drawing from data complied in the National Pollutant Inventory, a report by the Australian Conservation Foundation placed Hobart at number 6 of Australia's most polluted cities in 2018. The data identified medium levels of air pollution in postcodes 7009 (Lutana, Derwent Park, Moonah, West Moonah) and 7010 (Glenorchy, Rosetta, Montrose, Goodwood, Dowsing Point) with average air contaminate readings of 40% (nitric oxide  and nitrogen dioxide ), and sulfur dioxide (SO2) contributing 57% of airborne emissions.

The Tasmanian Planning Scheme does not mandate the Glenorchy City Council to notify prospective buyers about potential land contamination within the City of Glenorchy.

title: Glenorchy, Tasmania


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Baron Mostyn

Baron Mostyn, of Mostyn in the County of Flint, is a title in the Peerage of the United Kingdom.

History
The title was created in 1831 for Sir Edward Lloyd, 2nd Baronet, who had earlier represented Flint Boroughs and Beaumaris in the House of Commons. His son, the second Baron, sat as a Member of Parliament for Flintshire and Lichfield and served as Lord Lieutenant of Merionethshire.

In 1831 Lord Mostyn assumed by Royal licence the additional surname of Mostyn. His eldest son and heir the Hon. Thomas Lloyd-Mostyn, who also represented Flintshire in Parliament, predeceased his father. Lord Mostyn was therefore succeeded by his grandson, the third Baron (the son of Hon. Thomas Lloyd-Mostyn). The 6th Baron died on 22 March 2011 and was succeeded by his only son.

The Baronetcy of Pengwerra in the County of Flint, was created in the Baronetage of Great Britain in 1778 for Edward Lloyd, with remainder to his nephews. He was succeeded according to the special remainder by his eldest nephew, the aforementioned second Baronet, who was elevated to the peerage in 1831.

The family seat is Mostyn Hall, near Mostyn.

Lloyd Baronets, of Pengwerra (1778)

 * Sir Edward Pryce Lloyd, 1st Baronet (c. 1710–1795)
 * Sir Edward Pryce Lloyd, 2nd Baronet (1768–1854) (created Baron Mostyn in 1831)

Barons Mostyn (1831)

 * Edward Pryce Lloyd, 1st Baron Mostyn (1768–1854)
 * Edward Mostyn Lloyd-Mostyn, 2nd Baron Mostyn (1795–1884)
 * Hon. Thomas Edward Lloyd-Mostyn (1830–1861)
 * Llewelyn Nevill Vaughan Lloyd-Mostyn, 3rd Baron Mostyn (1856–1929)
 * Edward Llewellyn Roger Lloyd-Mostyn, 4th Baron Mostyn (1885–1965)
 * Roger Edward Lloyd Lloyd-Mostyn, 5th Baron Mostyn (1920–2000)
 * Llewellyn Roger Lloyd Lloyd-Mostyn, 6th Baron Mostyn (1948–2011)
 * Gregory Philip Roger Lloyd-Mostyn, 7th Baron Mostyn (b. 1984)

The heir presumptive is the present holder's third cousin twice removed, Roger Hugh Lloyd-Mostyn (born 1941), great-great-grandson of the 2nd Baron.

The heir presumptive's heir is his eldest son, Christopher Edward Lloyd-Mostyn (b. 1968)

The heir presumptive's heir's heir is his son Alexander James Lloyd-Mostyn (b. 2000)

title: Baron Mostyn


text:
Alan Silvestri

Alan Anthony Silvestri (born March 26, 1950) is an American composer and conductor of film and television scores. He has been associated with director Robert Zemeckis since 1984, composing music for nearly all of his feature films including the Back to the Future film series, Who Framed Roger Rabbit, Forrest Gump, Cast Away, and The Polar Express. Silvestri also scored many other popular movies, including Predator, The Abyss, Father of the Bride, The Bodyguard, Eraser, The Parent Trap, Stuart Little, The Mummy Returns, Lilo & Stitch, The Wild, Night at the Museum trilogy, G.I. Joe: The Rise of Cobra, The Croods, Ready Player One, and several Marvel Cinematic Universe films, including the Avengers films.

He is a two-time Academy Award and Golden Globe Award nominee, and a three-time Saturn Award and two-time Primetime Emmy Award recipient.

Early life and education
Silvestri was born March 26, 1950. His grandparents emigrated in 1909 from the Italian town of Castell'Alfero, and settled in Teaneck, New Jersey. He grew up in Teaneck, and graduated in 1968 from Teaneck High School. He attended Berklee College of Music for two years. He was a drummer for a short time in 1966 with Teaneck-based rock band the Wildcats.

Career
Silvestri moved to Los Angeles in 1970. "I came to Hollywood in 1970 broke.... I didn't even have any goals or plans. I didn't even go to movies. And I knew nothing about composers or composing," he said. In 1972, while he was working intermittently as a session guitarist, the producer of the low-budget action film The Doberman Gang asked him to score the picture. Silvestri agreed, despite a lack of experience: "I went out and bought a how-to-compose book by Earl Hagen.... At one point, I was using beer cans for percussion."

From 1978 to 1983, Silvestri was the main composer for the television series CHiPs, writing music for 95 of the show's 139 episodes.

Silvestri met film director Robert Zemeckis when they worked together on Zemeckis's film Romancing the Stone (1984). Since then, he has composed the music for all of Zemeckis's movies, including the Back to the Future trilogy (1985–1990), Who Framed Roger Rabbit (1988), Death Becomes Her (1992), Forrest Gump (1994), Contact (1997), Cast Away (2000), The Polar Express (2004), Beowulf (2007), A Christmas Carol (2009), Flight (2012), and The Walk (2015).

In 1989, Silvestri composed the score for the James Cameron-directed film The Abyss. Since 2001, he has also collaborated regularly with director Stephen Sommers, scoring the films The Mummy Returns (2001), Van Helsing (2004), and G.I. Joe: The Rise of Cobra (2009).

Silvestri has composed the scores for four Marvel Cinematic Universe films: Captain America: The First Avenger (2011), The Avengers (2012), Avengers: Infinity War (2018), and Avengers: Endgame (2019). His themes and motifs from those films have been referenced and reprised by other composers in multiple other MCU films.

Silvestri has also composed music for television series, including T. J. Hooker (one episode), Starsky & Hutch (three episodes), and Tales from the Crypt (seven episodes). In 2014, he composed the award-winning music for the science documentary series Cosmos: A Spacetime Odyssey. He wrote new songs with Glen Ballard for the live-action film adaptation of Disney's Pinocchio.

Personal life
Silvestri and his wife Sandra own a vineyard, Silvestri Vineyards, in Carmel Valley, California. He also has a wine tasting room for his vineyards on the ground floor of the Enchanted Oaks Building. He has a daughter and two sons. A licensed pilot, he flies his own jet aircraft.

Awards
Silvestri has received two Academy Award nominations: Best Original Score for Forrest Gump (1994); and Best Original Song for "Believe" on The Polar Express soundtrack. He also received two Golden Globe nominations: Best Score for Forrest Gump and Best Song for The Polar Express.

Silvestri received an honorary Doctorate of Music from Berklee College of Music in 1995.

He has also received nine Grammy Award nominations, winning two awards: Best Song Written for a Motion Picture, Television or Other Visual Media for "Believe" from The Polar Express in 2004; and Best Instrumental Composition for "Cast Away End Credits" from Cast Away in 2002. His other nominations were for Best Album of Original Score Written for a Motion Picture or a Television Special and Best Instrumental Composition, for Back to the Future in 1985, Best Album of Original Instrumental Background Score Written for a Motion Picture or Television, for Who Framed Roger Rabbit in 1988, Best Instrumental Composition, for "Who Framed Roger Rabbit Suite" in 1989, Best Pop Instrumental Performance, for "I'm Forrest...Forrest Gump (The Feather Theme)" in 1994, Best Instrumental Composition, for Avengers: Infinity War in 2018, and Best Score Soundtrack For Visual Media, for Avengers: Endgame in 2019. During the 2005 Grammy Awards, Josh Groban performed "Believe".

He has won two Emmys, both for Cosmos: A Spacetime Odyssey – Outstanding Main Title Theme Music and Outstanding Music Composition for a Series for the episode "Standing Up in the Milky Way".

He has won the Saturn Award for Best Music three times, for his scores for Predator (1987), Back to the Future Part III (1989/90), and Van Helsing (2004).

On September 23, 2011, he received the Max Steiner Film Music Achievement Award from the City of Vienna the yearly film-music gala concert Hollywood in Vienna.

title: Alan Silvestri


text:
Ruritania

Ruritania is a fictional country, originally located in Central Europe as a setting for novels by Anthony Hope, such as The Prisoner of Zenda (1894). Nowadays, the term connotes a quaint minor European country or is used as a placeholder name for an unspecified country in academic discussions. The first known use of the demonym Ruritanian was in 1896.

Hope's setting lent its name to a literary genre involving fictional countries, which is known as Ruritanian romance.

Fictional country
Jurists specialising in international law and private international law use Ruritania and other fictional countries when describing a hypothetical case illustrating some legal point. Examples include:

 * For example, writes in a legal textbook:
 * ″[t]he question whether $A$ obtained good title to a camera which he bought in Ruritania is governed by Ruritanian law, even if the camera had been delivered on hire purchase terms, or under a conditional sale to $A’$s seller in England.″

 * In another legal textbook, frequently use “Ruritania” as a placeholder-name when referring to a generic country in hypothetical scenarios in international law.

 * Australian foreign minister Alexander Downer cited “Ruritania” as a fictional enemy when illustrating a security treaty between Australia and Indonesia signed on 8 November 2006:
 * "We do not need to have a security agreement with Indonesia so both of us will fight off the “Ruritanians”. That's not what the relationship is about," he said. "It is all about working together on the threats that we have to deal with, which are different types of threats."

 * A British court, when contemplating a publication ban relating to a childhood sexual assault case, referred to the country of origin of the child as “Ruritania”, further explaining, "The boy was described in the judgment as having 'dual British and “Ruritanian” nationality'."

M. Rothbard – a former student of von Mises – similarly used the fictional country in his own works.
 * The well-known economist L. von Mises used “Ruritania” to discuss currency reform and other issues in economics,
 * Polish politician and historiographer Janusz Korwin-Mikke often uses "Poronia" and "Rurytania" to compare Poland to some Western or Utopian country, e.g. | https://twitter.com/JkmMikke/status/1781649204579856741 |
 * BBC radio used “Ruritania” in 1956, as a euphemism for Egypt during the Suez Crisis for on-air discussions of the crisis, in order to circumvent the terms of an agreement with the British government that prevented broadcasting details of the events before they were discussed in parliament.

Central and southeastern Europe
Ruritania has also been used to describe the stereotypical development of nationalism in 19th-century Eastern Europe, by Ernest Gellner in Nations and Nationalism, in a pastiche of the historical narratives of nationalist movements among Poles, Czechs, Serbians, Romanians, etc. In this story, peasant Ruritanians living in the "Empire of Megalomania" developed national consciousness through the elaboration of a Ruritanian high culture by a small group of intellectuals responding to industrialization and labor migration.

Author and royal historian Theo Aronson, in his book Crowns in Conflict (1986), used the term to describe the semi-romantic and even tribal-like conditions of the Balkan and Romanian cultures before World War I. Walter Lippmann used the word to describe the stereotype that characterized the vision of international relations during and after the War.

Vesna Goldsworthy of Kingston University, in her book Inventing Ruritania: the imperialism of the imagination (Yale University Press, 1998), addresses the question of the impact of the work of novelists and film-makers in shaping international perceptions of the Balkans in the framework of an anti-Western type of modernism which has received much criticism from other academics. Goldsworthy's theories consider stories and movies about Ruritania to be a form of "literary exploitation" or "narrative colonization" of the peoples of the Balkans.

While discussing how new revolutionary leadership consciously or unconsciously may inherit certain elements of the previous regime, Benedict Anderson, in his book Imagined Communities, mentions among other examples "Josip Broz's revival of Ruritanian pomp and ceremony."

title: Ruritania


text:
Marc Shaiman

Marc Shaiman (born October 22, 1959) is an American composer and lyricist for films, television, and theatre, best known for his collaborations with lyricist and director Scott Wittman, actor Billy Crystal, and director Rob Reiner. Shaiman has received numerous accolades including two Grammy Awards, a Primetime Emmy Award, and a Tony Award. He has also received seven Academy Awards nominations.

Early life, family and education
Shaiman was born to a Jewish family in Newark, New Jersey, the son of Claire (née Goldfein) and William Robert Shaiman. He grew up in Scotch Plains, New Jersey.

He attended Scotch Plains-Fanwood High School, but he left school at age 16 to start working in New York's theaters; he later obtained a GED.

Career
Shaiman started his career as a theatre/cabaret musical director. He started working at Saturday Night Live as an arranger/writer. He portrayed Skip St. Thomas, the accompanying pianist for The Sweeney Sisters, a singing duo played by Nora Dunn and Jan Hooks, which earned him an Emmy nomination; he returned for an appearance on The Saturday Night Live 40th Anniversary Special, having co-created Martin Short and Maya Rudolph's salute to musical sketch characters. He began his professional relationships with Billy Crystal and Martin Short during his tenure at the show. He also was a vocal arranger for Bette Midler, eventually becoming her musical director and co-producer of many of her recordings, including "The Wind Beneath My Wings" and "From a Distance." He helped create the material for her performance on the penultimate The Tonight Show Starring Johnny Carson. His work with both Midler and Billy Crystal led to his involvement on their films. He later produced Midler's album It's the Girls, which had the highest debut of Midler's recording career on the Billboard Album charts, and co-wrote Crystal's farewell to Jay Leno which featured Carol Burnett and Oprah Winfrey among others.

His film credits include Broadcast News, Beaches, When Harry Met Sally..., City Slickers, The Addams Family, Sister Act, Sleepless in Seattle, A Few Good Men, The American President, The First Wives Club, George of the Jungle, In & Out, Patch Adams, South Park: Bigger, Longer & Uncut, Team America: World Police, Hairspray, Flipped, Mary Poppins Returns and HBO's From the Earth to the Moon and 61*. On television, he worked on the final performances for Johnny Carson's Tonight Show (with Bette Midler), Conan O'Brien's Late Night (with Nathan Lane), both of Jay Leno's final Tonight Show broadcasts, and Nathan Lane's farewell to David Letterman called "Dead Inside."

Shaiman has earned seven Academy Award nominations, a Tony Award and a Grammy Award for his work on the musical Hairspray, and an Emmy Award for co-writing Billy Crystal's Academy Award performances. He has also been Grammy-nominated for his arrangements for Harry Connick Jr.'s recordings When Harry Met Sally... and We Are in Love as well as Hairspray and Smash and Emmy-nominated for his work on Saturday Night Live and Smash. In 2002, he was honored with the "Outstanding Achievement in Music-In-Film" award at The Hollywood Film Festival, and in 2007 he was honored with ASCAP's Henry Mancini Award in recognition of his outstanding achievements and contributions to the music of film and television. He is the first recipient of the Film & TV Music Award for Best Score for a Comedy Feature Film. He wrote and sang the song "Yes" for his agent's film Finding Kraftland, and co-wrote (with partner Scott Wittman) songs for Neil Patrick Harris when Harris hosted the 63rd Tony Awards (2009) and the 61st Primetime Emmy Awards (2009), and was Emmy-nominated for musical directing and co-writing the 82nd Academy Awards (2010).

Shaiman co-produced and co-wrote cuts on Mariah Carey's 2010 Christmas album Merry Christmas II You. He and Wittman wrote original songs for the musical-based television show for NBC, Smash, which ran from 2012 to 2013, and served as executive producers. For their song "Let Me Be Your Star," Shaiman and co-lyricist Wittman were nominated for both an Emmy Award and a Grammy Award, and as executive producers they were nominated for the Golden Globe Award for Best Television Series - Comedy or Musical.

Shaiman and Wittman were honored on April 28, 2014, by The New York Pops Orchestra at Carnegie Hall. The following year, Jennifer Hudson sang the Smash song "I Can't Let Go" at the 87th Academy Awards during the in memoriam tribute, featuring revised lyrics. The duo's Broadway musical Charlie and the Chocolate Factory ran on Broadway at the Lunt-Fontanne Theatre, after finishing a four-year run on London's West End at The Royal Drury Lane Theater. Shaiman was Tony-nominated for his orchestrations for their previous Broadway musical Catch Me If You Can. In 2021, they wrote a song titled "Save the City" for the Marvel Cinematic Universe (MCU) in-universe Broadway production titled Rogers: The Musical featured in the first episode of Hawkeye, "Never Meet Your Heroes". It was released as a single on November 24, the day the episode became available on Disney+.

In February 2021, it was announced that Shaiman and Wittman were writing songs for a new musical adaptation of Some Like It Hot, which premiered on Broadway in 2022 with a book by Amber Ruffin and Matthew Lopez.

Activism
In 2008, a controversy erupted nationwide when California Musical Theatre's then artistic director Scott Eckern resigned over the revelation of his personal donation of $1,000 to a political campaign to support California Proposition 8, which was an amendment to change the California Constitution to eliminate the right of same-sex couples to marry in California. After the amendment was passed, donor information became public. Shaiman and other Broadway artists who had previously worked with the director became critical and called for a boycott of the theatre by all gay artists and performers, ending in the director's resignation days later.

To protest the passage of California Proposition 8 in November 2008, Shaiman wrote a satiric mini-musical Prop 8 – The Musical. The three-minute video was distributed on the internet at FunnyOrDie.com, beginning on December 3, 2008. It was written and produced in just a few days. The cast includes Jack Black (who plays Jesus), Neil Patrick Harris, John C. Reilly, Allison Janney, Andy Richter, Maya Rudolph, Margaret Cho, and Rashida Jones. Shaiman plays the piano and appears briefly in the video. It received 1.2 million internet hits in its first day.

Personal life
He is openly gay, and married Louis Mirabal, a retired lieutenant commander in the U.S. Navy, on March 26, 2016. He lives in both Manhattan and upstate New York.

Theatre
Broadway
 * Peter Allen: Up in One (1979)
 * Bette! Divine Madness (1980)
 * André De Shields' Haarlem Nocturne (1984)
 * Leader of the Pack (1985)
 * An Evening with Harry Connick Jr. and Orchestra (1990)
 * Patti LuPone on Broadway (1995)
 * Hairspray (2002)
 * The Odd Couple (2005)
 * Martin Short: Fame Becomes Me (2006)
 * Catch Me If You Can (2009)
 * Charlie and the Chocolate Factory (2017)
 * Some Like It Hot (2022)
 * Smash (2024–25 Broadway season)

West End
 * Charlie and the Chocolate Factory (2013)

Off-Broadway
 * Dementos - The Production Company
 * Livin' Dolls - Manhattan Theatre Club
 * Legends - Ahmanson Theatre
 * The Sound of Muzak - Club 82
 * Trilogy of Terror - Club 57
 * Non Pasquale - Delacorte Theatre

Disney Parks
 *  Rogers: The Musical - Hyperion Theatre

Internet

 * Prop 8 - The Musical (2008) (composer, lyricist, pianist) - 2009 "Webby" winner for Best Comedy: Short or Individual Episode
 * Soundtrack of Our Lives: A Celebration for the Film and TV Music Community ("The End Titles" song) (2020)

Discography
Mariah Carey
 * Merry Christmas II You

Bette Midler
 * Thighs and Whispers
 * Mud Will Be Flung Tonight
 * Some People's Lives
 * Experience the Divine
 * Bette
 * Bathhouse Betty
 * It's the Girls!

Harry Connick Jr.
 * We Are in Love

Peter Allen
 * Making Every Moment Count

Original Broadway cast recordings
 * Hairspray
 * Martin Short: Fame Becomes Me
 * Catch Me If You Can
 * Charlie and the Chocolate Factory the Musical (West End musical)
 * Charlie and the Chocolate Factory the Musical (Broadway musical)

Soundtracks
 * The Addams Family
 * Addams Family Values
 * Beaches
 * When Harry Met Sally...
 * Heart and Souls
 * For the Boys
 * City Slickers
 * A Few Good Men
 * Sister Act
 * Sleepless in Seattle
 * Hocus Pocus
 * North
 * The American President
 * The Out-of-Towners
 * South Park: Bigger, Longer & Uncut
 * Mr. Hankey's Christmas Classics
 * The Story of Us
 * Alex & Emma
 * Rumor Has It...
 * Hairspray
 * The Bucket List
 * Smash Season One
 * Smash Season Two
 * Bombshell
 * Hairspray Live!
 * The Star
 * Mary Poppins Returns
 * Hocus Pocus 2

Concert/cabaret work

 * Peter Allen
 * Jack Black & Will Ferrell
 * Kristin Chenoweth
 * Rosemary Clooney
 * Harry Connick Jr.
 * Billy Crystal
 * Christine Ebersole
 * Ellen Foley
 * Whoopi Goldberg
 * Annie Golden
 * The Harlettes
 * The High-Heeled Women
 * Lauryn Hill
 * Jennifer Holliday
 * Allison Janney
 * Laura Kenyon
 * Nathan Lane
 * Ute Lemper
 * Jenifer Lewis
 * Darlene Love
 * Patti LuPone
 * Lypsinka
 * Ann Magnuson
 * Andrea Martin
 * Lonette McKee
 * Bette Midler
 * Catherine O'Hara
 * Sarah Jessica Parker
 * Zora Rasmussen
 * Ann Reinking
 * Debbie Shapiro Gravitte
 * Martin Short
 * Barbra Streisand
 * Donald Trump
 * Tracey Ullman
 * Luther Vandross
 * Bruce Vilanch
 * Steven Weber
 * Raquel Welch
 * Robin Williams

Accolades
For his work as a composer and lyricist for films, television, and theatre, Shaiman has received numerous accolades including a Emmy Award, two Grammy Awards and a Tony Award as well as nominations for seven Academy Awards, two BAFTA Awards and two Golden Globe Awards. He earned the Hollywood Film Award for Outstanding Contribution to Music and Film in 2002.

title: Marc Shaiman


text:
Complex manifold

In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in the complex coordinate space $$\mathbb{C}^n$$, such that the transition maps are holomorphic.

The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold.

Implications of complex structure
Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds.

For example, the Whitney embedding theorem tells us that every smooth n-dimensional manifold can be embedded as a smooth submanifold of R2n, whereas it is "rare" for a complex manifold to have a holomorphic embedding into Cn. Consider for example any compact connected complex manifold M: any holomorphic function on it is constant by the maximum modulus principle. Now if we had a holomorphic embedding of M into Cn, then the coordinate functions of Cn would restrict to nonconstant holomorphic functions on M, contradicting compactness, except in the case that M is just a point. Complex manifolds that can be embedded in Cn are called Stein manifolds and form a very special class of manifolds including, for example, smooth complex affine algebraic varieties.

The classification of complex manifolds is much more subtle than that of differentiable manifolds. For example, while in dimensions other than four, a given topological manifold has at most finitely many smooth structures, a topological manifold supporting a complex structure can and often does support uncountably many complex structures. Riemann surfaces, two dimensional manifolds equipped with a complex structure, which are topologically classified by the genus, are an important example of this phenomenon. The set of complex structures on a given orientable surface, modulo biholomorphic equivalence, itself forms a complex algebraic variety called a moduli space, the structure of which remains an area of active research.

Since the transition maps between charts are biholomorphic, complex manifolds are, in particular, smooth and canonically oriented (not just orientable: a biholomorphic map to (a subset of) Cn gives an orientation, as biholomorphic maps are orientation-preserving).

Examples of complex manifolds

 * Riemann surfaces.
 * Calabi–Yau manifolds.
 * The Cartesian product of two complex manifolds.
 * The inverse image of any noncritical value of a holomorphic map.

Smooth complex algebraic varieties
Smooth complex algebraic varieties are complex manifolds, including:
 * Complex vector spaces.
 * Complex projective spaces, Pn(C).
 * Complex Grassmannians.
 * Complex Lie groups such as GL(n, C) or Sp(n, C).

Simply connected
The simply connected 1-dimensional complex manifolds are isomorphic to either: Note that there are inclusions between these as Δ ⊆ C ⊆ Ĉ, but that there are no non-constant holomorphic maps in the other direction, by Liouville's theorem.
 * Δ, the unit disk in C
 * C, the complex plane
 * Ĉ, the Riemann sphere

Disc vs. space vs. polydisc
The following spaces are different as complex manifolds, demonstrating the more rigid geometric character of complex manifolds (compared to smooth manifolds):
 * complex space $$\mathbb{C}^n$$.
 * the unit disc or open ball
 * $$\left \{ z \in \mathbb{C}^n : \|z\| < 1 \right \}.$$

 * the polydisc
 * $$\left \{z = (z_1, \dots, z_n) \in \mathbb{C}^n : \vert z_j \vert < 1\ \forall j = 1,\dots,n \right \}.$$

Almost complex structures
An almost complex structure on a real 2n-manifold is a GL(n, C)-structure (in the sense of G-structures) – that is, the tangent bundle is equipped with a linear complex structure.

Concretely, this is an endomorphism of the tangent bundle whose square is −I; this endomorphism is analogous to multiplication by the imaginary number i, and is denoted J (to avoid confusion with the identity matrix I). An almost complex manifold is necessarily even-dimensional.

An almost complex structure is weaker than a complex structure: any complex manifold has an almost complex structure, but not every almost complex structure comes from a complex structure. Note that every even-dimensional real manifold has an almost complex structure defined locally from the local coordinate chart. The question is whether this almost complex structure can be defined globally. An almost complex structure that comes from a complex structure is called integrable, and when one wishes to specify a complex structure as opposed to an almost complex structure, one says an integrable complex structure. For integrable complex structures the so-called Nijenhuis tensor vanishes. This tensor is defined on pairs of vector fields, X, Y by

 * $$N_J(X,Y) = [X,Y] + J[JX,Y] + J[X,JY]-[JX,JY]\ .$$

For example, the 6-dimensional sphere S6 has a natural almost complex structure arising from the fact that it is the orthogonal complement of i in the unit sphere of the octonions, but this is not a complex structure. (The question of whether it has a complex structure is known as the Hopf problem, after Heinz Hopf. ) Using an almost complex structure we can make sense of holomorphic maps and ask about the existence of holomorphic coordinates on the manifold. The existence of holomorphic coordinates is equivalent to saying the manifold is complex (which is what the chart definition says).

Tensoring the tangent bundle with the complex numbers we get the complexified tangent bundle, on which multiplication by complex numbers makes sense (even if we started with a real manifold). The eigenvalues of an almost complex structure are ±i and the eigenspaces form sub-bundles denoted by T0,1M and T1,0M. The Newlander–Nirenberg theorem shows that an almost complex structure is actually a complex structure precisely when these subbundles are involutive, i.e., closed under the Lie bracket of vector fields, and such an almost complex structure is called integrable.

Kähler and Calabi–Yau manifolds
One can define an analogue of a Riemannian metric for complex manifolds, called a Hermitian metric. Like a Riemannian metric, a Hermitian metric consists of a smoothly varying, positive definite inner product on the tangent bundle, which is Hermitian with respect to the complex structure on the tangent space at each point. As in the Riemannian case, such metrics always exist in abundance on any complex manifold. If the skew symmetric part of such a metric is symplectic, i.e. closed and nondegenerate, then the metric is called Kähler. Kähler structures are much more difficult to come by and are much more rigid.

Examples of Kähler manifolds include smooth projective varieties and more generally any complex submanifold of a Kähler manifold. The Hopf manifolds are examples of complex manifolds that are not Kähler. To construct one, take a complex vector space minus the origin and consider the action of the group of integers on this space by multiplication by exp(n). The quotient is a complex manifold whose first Betti number is one, so by the Hodge theory, it cannot be Kähler.

A Calabi–Yau manifold can be defined as a compact Ricci-flat Kähler manifold or equivalently one whose first Chern class vanishes.

title: Complex manifold