The approaches to machine learning are many, but are often split into two main categories. In supervised learning we know the answer to a problem, and let the computer deduce the logic behind it. On the other hand, unsupervised learning is a method for finding patterns and relationship in data sets without any prior knowledge of the system. Some authours also operate with a third category, namely reinforcement learning. This is a paradigm of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, solely from rewards and punishment.
Another way to categorize machine learning tasks is to consider the desired output of a system. Some of the most common tasks are:
What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. One of the major reasons is that they can be stacked layer-wise to build deep neural networks that capture complicated statistics.
The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images.
Furthermore, they have been used to solve complicated quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models.
More material on Hopfield networks will come here later.
The Markov process is used repeatedly in Monte Carlo simulations in order to generate new random states.
The reason for choosing a Markov process is that when it is run for a long enough time starting with a random state, we will eventually reach the most likely state of the system.
In thermodynamics, this means that after a certain number of Markov processes we reach an equilibrium distribution.
This mimicks the way a real system reaches its most likely state at a given temperature of the surroundings.
To reach this distribution, the Markov process needs to obey two important conditions, that of ergodicity and detailed balance. These conditions impose then constraints on our algorithms for accepting or rejecting new random states.
The Metropolis algorithm discussed here abides to both these constraints.
The Metropolis algorithm is widely used in Monte Carlo simulations and the understanding of it rests within the interpretation of random walks and Markov processes.
In a random walk one defines a mathematical entity called a walker, whose attributes completely define the state of the system in question.
The state of the system can refer to any physical quantities, from the vibrational state of a molecule specified by a set of quantum numbers, to the brands of coffee in your favourite supermarket.
The walker moves in an appropriate state space by a combination of deterministic and random displacements from its previous position.
This sequence of steps forms a chain.
The list of applications is endless.
A Markov process allows in principle for a microscopic description of Brownian motion. As with the random walk studied in the previous section, we consider a particle which moves along the \( x \)-axis in the form of a series of jumps with step length \( \Delta x = l \). Time and space are discretized and the subsequent moves are statistically independent, i.e., the new move depends only on the previous step and not on the results from earlier trials. We start at a position \( x=jl=j\Delta x \) and move to a new position \( x =i\Delta x \) during a step \( \Delta t=\epsilon \), where \( i\ge 0 \) and \( j\ge 0 \) are integers. The original probability distribution function (PDF) of the particles is given by \( w_i(t=0) \) where \( i \) refers to a specific position on the grid in
For the Markov process we have a transition probability from a position \( x=jl \) to a position \( x=il \) given by $$ \begin{equation*} W_{ij}(\epsilon)=W(il-jl,\epsilon)=\left\{\begin{array}{cc}\frac{1}{2} & |i-j| = 1\\ 0 & \mathrm{else} \end{array} \right. , \end{equation*} $$ where \( W_{ij} \) is normally called the transition probability and we can represent it, see below, as a matrix. Here we have specialized to a case where the transition probability is known.
Our new PDF \( w_i(t=\epsilon) \) is now related to the PDF at \( t=0 \) through the relation $$ \begin{equation*} w_i(t=\epsilon) =\sum_{j} W(j\rightarrow i)w_j(t=0). \end{equation*} $$
This equation represents the discretized time-development of an original PDF with equal probability of jumping left or right.
Since both \( W \) and \( w \) represent probabilities, they have to be normalized, i.e., we require that at each time step we have $$ \begin{equation*} \sum_i w_i(t) = 1, \end{equation*} $$ and $$ \begin{equation*} \sum_j W(j\rightarrow i) = 1, \end{equation*} $$ which applies for all \( j \)-values. The further constraints are \( 0 \le W_{ij} \le 1 \) and \( 0 \le w_{j} \le 1 \). Note that the probability for remaining at the same place is in general not necessarily equal zero.
The time development of our initial PDF can now be represented through the action of the transition probability matrix applied \( n \) times. At a time \( t_n=n\epsilon \) our initial distribution has developed into $$ \begin{equation*} w_i(t_n) = \sum_jW_{ij}(t_n)w_j(0), \end{equation*} $$ and defining $$ \begin{equation*} W(il-jl,n\epsilon)=(W^n(\epsilon))_{ij} \end{equation*} $$ we obtain $$ \begin{equation*} w_i(n\epsilon) = \sum_j(W^n(\epsilon))_{ij}w_j(0), \end{equation*} $$ or in matrix form $$ \begin{equation} \label{eq:wfinal} \hat{w}(n\epsilon) = \hat{W}^n(\epsilon)\hat{w}(0). \end{equation} $$
The following simple example may help in understanding the meaning of the transition matrix \( \hat{W} \) and the vector \( \hat{w} \). Consider the \( 4\times 4 \) matrix \( \hat{W} \) $$ \begin{equation*} \hat{W} = \left(\begin{array}{cccc} 1/4 & 1/9 & 3/8 & 1/3 \\ 2/4 & 2/9 & 0 & 1/3\\ 0 & 1/9 & 3/8 & 0\\ 1/4 & 5/9& 2/8 & 1/3 \end{array} \right), \end{equation*} $$ and we choose our initial state as $$ \begin{equation*} \hat{w}(t=0)= \left(\begin{array}{c} 1\\ 0\\ 0 \\ 0 \end{array} \right). \end{equation*} $$
We note that both the vector and the matrix are properly normalized. Summing the vector elements gives one and summing over columns for the matrix results also in one. Furthermore, the largest eigenvalue is one. We act then on \( \hat{w} \) with \( \hat{W} \). The first iteration is $$ \begin{equation*} \hat{w}(t=\epsilon) = \hat{W}\hat{w}(t=0), \end{equation*} $$
resulting in $$ \begin{equation*} \hat{w}(t=\epsilon)= \left(\begin{array}{c} 1/4\\ 1/2 \\ 0 \\ 1/4 \end{array} \right). \end{equation*} $$
The next iteration results in $$ \begin{equation*} \hat{w}(t=2\epsilon) = \hat{W}\hat{w}(t=\epsilon), \end{equation*} $$
resulting in $$ \begin{equation*} \hat{w}(t=2\epsilon)= \left(\begin{array}{c} 0.201389\\ 0.319444 \\ 0.055556 \\ 0.423611 \end{array} \right). \end{equation*} $$ Note that the vector \( \hat{w} \) is always normalized to \( 1 \).
We find the steady state of the system by solving the set of equations $$ \begin{equation*} w(t=\infty) = Ww(t=\infty), \end{equation*} $$ which is an eigenvalue problem with eigenvalue equal to one! This set of equations reads $$ \begin{align} W_{11}w_1(t=\infty) +W_{12}w_2(t=\infty) +W_{13}w_3(t=\infty)+ W_{14}w_4(t=\infty)=&w_1(t=\infty) \nonumber \\ W_{21}w_1(t=\infty) + W_{22}w_2(t=\infty) + W_{23}w_3(t=\infty)+ W_{24}w_4(t=\infty)=&w_2(t=\infty) \nonumber \\ W_{31}w_1(t=\infty) + W_{32}w_2(t=\infty) + W_{33}w_3(t=\infty)+ W_{34}w_4(t=\infty)=&w_3(t=\infty) \nonumber \\ W_{41}w_1(t=\infty) + W_{42}w_2(t=\infty) + W_{43}w_3(t=\infty)+ W_{44}w_4(t=\infty)=&w_4(t=\infty) \nonumber \\ \label{_auto1} \end{align} $$ with the constraint that $$ \begin{equation*} \sum_i w_i(t=\infty) = 1, \end{equation*} $$ yielding as solution $$ \begin{equation*} \hat{w}(t=\infty)= \left(\begin{array}{c}0.244318 \\ 0.319602 \\ 0.056818 \\ 0.379261 \end{array} \right). \end{equation*} $$
The table here demonstrates the convergence as a function of the number of iterations or time steps. After twelve iterations we have reached the exact value with six leading digits.
| Iteration | \( w_1 \) | \( w_2 \) | \( w_3 \) | \( w_4 \) |
|---|---|---|---|---|
| 0 | 1.000000 | 0.000000 | 0.000000 | 0.000000 |
| 1 | 0.250000 | 0.500000 | 0.000000 | 0.250000 |
| 2 | 0.201389 | 0.319444 | 0.055556 | 0.423611 |
| 3 | 0.247878 | 0.312886 | 0.056327 | 0.382909 |
| 4 | 0.245494 | 0.321106 | 0.055888 | 0.377513 |
| 5 | 0.243847 | 0.319941 | 0.056636 | 0.379575 |
| 6 | 0.244274 | 0.319547 | 0.056788 | 0.379391 |
| 7 | 0.244333 | 0.319611 | 0.056801 | 0.379255 |
| 8 | 0.244314 | 0.319610 | 0.056813 | 0.379264 |
| 9 | 0.244317 | 0.319603 | 0.056817 | 0.379264 |
| 10 | 0.244318 | 0.319602 | 0.056818 | 0.379262 |
| 11 | 0.244318 | 0.319602 | 0.056818 | 0.379261 |
| 12 | 0.244318 | 0.319602 | 0.056818 | 0.379261 |
| \( \hat{w}(t=\infty) \) | 0.244318 | 0.319602 | 0.056818 | 0.379261 |
We have after \( t \)-steps $$ \begin{equation*} \hat{w}(t) = \hat{W}^t\hat{w}(0), \end{equation*} $$ with \( \hat{w}(0) \) the distribution at \( t=0 \) and \( \hat{W} \) representing the transition probability matrix.
We can always expand \( \hat{w}(0) \) in terms of the right eigenvectors \( \hat{v} \) of \( \hat{W} \) as $$ \begin{equation*} \hat{w}(0) = \sum_i\alpha_i\hat{v}_i, \end{equation*} $$ resulting in $$ \begin{equation*} \hat{w}(t) = \hat{W}^t\hat{w}(0)=\hat{W}^t\sum_i\alpha_i\hat{v}_i= \sum_i\lambda_i^t\alpha_i\hat{v}_i, \end{equation*} $$ with \( \lambda_i \) the \( i^{\mathrm{th}} \) eigenvalue corresponding to the eigenvector \( \hat{v}_i \).
If we assume that \( \lambda_0 \) is the largest eigenvector we see that in the limit \( t\rightarrow \infty \), \( \hat{w}(t) \) becomes proportional to the corresponding eigenvector \( \hat{v}_0 \). This is our steady state or final distribution.
Let us recapitulate some of our results about Markov chains and random walks.
This equation represents the discretized time-development of an original PDF. We can rewrite this as a $$ \begin{equation*} w_i(t=\epsilon) = W_{ij}w_j(t=0). \end{equation*} $$ with the transition matrix \( W \) for a random walk given by $$ \begin{equation*} W_{ij}(\epsilon)=W(il-jl,\epsilon)=\left\{\begin{array}{cc}\frac{1}{2} & |i-j| = 1\\ 0 & \mathrm{else} \end{array} \right. \end{equation*} $$
We call \( W_{ij} \) for the transition probability and we represent it as a matrix.
The further constraints are \( 0 \le W_{ij} \le 1 \) and \( 0 \le w_{j} \le 1 \).
Another way of phrasing this is $$ \begin{equation} w(t=\infty) = Ww(t=\infty). \label{_auto2} \end{equation} $$
The question then is how can we model anything under such a severe lack of knowledge? The Metropolis algorithm comes to our rescue here. Since \( W(j\rightarrow i) \) is unknown, we model it as the product of two probabilities, a probability for accepting the proposed move from the state \( j \) to the state \( j \), and a probability for making the transition to the state \( i \) being in the state \( j \). We label these probabilities \( A(j\rightarrow i) \) and \( T(j\rightarrow i) \), respectively. Our total transition probability is then $$ \begin{equation*} W(j\rightarrow i)=T(j\rightarrow i)A(j\rightarrow i). \end{equation*} $$ The algorithm can then be expressed as
We wish to derive the required properties of the probabilities \( T \) and \( A \) such that \( w_i^{(t\rightarrow \infty)} \rightarrow w_i \), starting from any distribution, will lead us to the correct distribution.
We can now derive the dynamical process towards equilibrium. To obtain this equation we note that after \( t \) time steps the probability for being in a state \( i \) is related to the probability of being in a state \( j \) and performing a transition to the new state together with the probability of actually being in the state \( i \) and making a move to any of the possible states \( j \) from the previous time step.
We can express this as, assuming that \( T \) and \( A \) are time-independent, $$ \begin{equation*} w_i(t+1) = \sum_j \left [ w_j(t)T_{j\rightarrow i} A_{j\rightarrow i} +w_i(t)T_{i\rightarrow j}\left ( 1- A_{i\rightarrow j} \right) \right ] \,. \end{equation*} $$
All probabilities are normalized, meaning that \( \sum_j T_{i\rightarrow j} = 1 \). Using the latter, we can rewrite the previous equation as $$ \begin{equation*} w_i(t+1) = w_i(t) + \sum_j \left [ w_j(t)T_{j\rightarrow i} A_{j\rightarrow i} -w_i(t)T_{i\rightarrow j}A_{i\rightarrow j}\right ] \,, \end{equation*} $$ which can be rewritten as $$ \begin{equation*} w_i(t+1)-w_i(t) = \sum_j \left [w_j(t)T_{j\rightarrow i} A_{j\rightarrow i} -w_i(t)T_{i\rightarrow j}A_{i\rightarrow j}\right ] . \end{equation*} $$
The last equation is very similar to the so-called Master equation, which relates the temporal dependence of a PDF \( w_i(t) \) to various transition rates. The equation can be derived from the so-called Chapman-Einstein-Enskog-Kolmogorov equation. The equation is given as $$ \begin{equation} \label{eq:masterequation} \frac{d w_i(t)}{dt} = \sum_j\left[ W(j\rightarrow i)w_j-W(i\rightarrow j)w_i\right], \end{equation} $$ which simply states that the rate at which the systems moves from a state \( j \) to a final state \( i \) (the first term on the right-hand side of the last equation) is balanced by the rate at which the system undergoes transitions from the state \( i \) to a state \( j \) (the second term). If we have reached the so-called steady state, then the temporal development is zero. This means that in equilibrium we have $$ \begin{equation*} \frac{d w_i(t)}{dt} = 0. \end{equation*} $$
In the limit \( t\rightarrow \infty \) we require that the two distributions \( w_i(t+1)=w_i \) and \( w_i(t)=w_i \) and we have $$ \begin{equation*} \sum_j w_jT_{j\rightarrow i} A_{j\rightarrow i}= \sum_j w_iT_{i\rightarrow j}A_{i\rightarrow j}, \end{equation*} $$ which is the condition for balance when the most likely state (or steady state) has been reached. We see also that the right-hand side can be rewritten as $$ \begin{equation*} \sum_j w_iT_{i\rightarrow j}A_{i\rightarrow j}= \sum_j w_iW_{i\rightarrow j}, \end{equation*} $$ and using the property that \( \sum_j W_{i\rightarrow j}=1 \), we can rewrite our equation as $$ \begin{equation*} w_i= \sum_j w_jT_{j\rightarrow i} A_{j\rightarrow i}= \sum_j w_j W_{j\rightarrow i}, \end{equation*} $$ which is nothing but the standard equation for a Markov chain when the steady state has been reached.
However, the condition that the rates should equal each other is in general not sufficient to guarantee that we, after many simulations, generate the correct distribution. We may risk to end up with so-called cyclic solutions. To avoid this we therefore introduce an additional condition, namely that of detailed balance $$ \begin{equation*} W(j\rightarrow i)w_j= W(i\rightarrow j)w_i. \end{equation*} $$ These equations were derived by Lars Onsager when studying irreversible processes. At equilibrium detailed balance gives thus $$ \begin{equation*} \frac{W(j\rightarrow i)}{W(i\rightarrow j)}=\frac{w_i}{w_j}. \end{equation*} $$ Rewriting the last equation in terms of our transition probabilities \( T \) and acceptance probobalities \( A \) we obtain $$ \begin{equation*} w_j(t)T_{j\rightarrow i}A_{j\rightarrow i}= w_i(t)T_{i\rightarrow j}A_{i\rightarrow j}. \end{equation*} $$
Since we normally have an expression for the probability distribution functions \( w_i \), we can rewrite the last equation as $$ \begin{equation*} \frac{T_{j\rightarrow i}A_{j\rightarrow i}}{T_{i\rightarrow j}A_{i\rightarrow j}}= \frac{w_i}{w_j}. \end{equation*} $$
In statistical physics this condition ensures that it is e.g., the Boltzmann distribution which is generated when equilibrium is reached.
We introduce now the Boltzmann distribution $$ \begin{equation*} w_i= \frac{\exp{(-\beta(E_i))}}{Z}, \end{equation*} $$ which states that the probability of finding the system in a state \( i \) with energy \( E_i \) at an inverse temperature \( \beta = 1/k_BT \) is \( w_i\propto \exp{(-\beta(E_i))} \). The denominator \( Z \) is a normalization constant which ensures that the sum of all probabilities is normalized to one. It is defined as the sum of probabilities over all microstates \( j \) of the system $$ \begin{equation*} Z=\sum_j \exp{(-\beta(E_i))}. \end{equation*} $$
From the partition function we can in principle generate all interesting quantities for a given system in equilibrium with its surroundings at a temperature \( T \).
With the probability distribution given by the Boltzmann distribution we are now in a position where we can generate expectation values for a given variable \( A \) through the definition $$ \begin{equation*} \langle A \rangle = \sum_jA_jw_j= \frac{\sum_jA_j\exp{(-\beta(E_j)}}{Z}. \end{equation*} $$ In general, most systems have an infinity of microstates making thereby the computation of \( Z \) practically impossible and a brute force Monte Carlo calculation over a given number of randomly selected microstates may therefore not yield those microstates which are important at equilibrium. To select the most important contributions we need to use the condition for detailed balance. Since this is just given by the ratios of probabilities, we never need to evaluate the partition function \( Z \).
For the Boltzmann distribution, detailed balance results in $$ \begin{equation*} \frac{w_i}{w_j}= \exp{(-\beta(E_i-E_j))}. \end{equation*} $$
Let us now specialize to a system whose energy is defined by the orientation of single spins. Consider the state \( i \), with given energy \( E_i \) represented by the following \( N \) spins $$ \begin{equation*} \begin{array}{cccccccccc} \uparrow&\uparrow&\uparrow&\dots&\uparrow&\downarrow&\uparrow&\dots&\uparrow&\downarrow\\ 1&2&3&\dots& k-1&k&k+1&\dots&N-1&N\end{array} \end{equation*} $$
We are interested in the transition with one single spinflip to a new state \( j \) with energy \( E_j \) $$ \begin{equation*} \begin{array}{cccccccccc} \uparrow&\uparrow&\uparrow&\dots&\uparrow&\uparrow&\uparrow&\dots&\uparrow&\downarrow\\ 1&2&3&\dots& k-1&k&k+1&\dots&N-1&N\end{array} \end{equation*} $$ This change from one microstate \( i \) (or spin configuration) to another microstate \( j \) is the configuration space analogue to a random walk on a lattice. Instead of jumping from one place to another in space, we 'jump' from one microstate to another.
However, the selection of states has to generate a final distribution which is the Boltzmann distribution. This is again the same we saw for a random walker, for the discrete case we had always a binomial distribution, whereas for the continuous case we had a normal distribution. The way we sample configurations should result, when equilibrium is established, in the Boltzmann distribution. Else, our algorithm for selecting microstates is wrong.
As stated above, we do in general not know the closed-form expression of the transition rate and we are free to model it as \( W(i\rightarrow j)=T(i\rightarrow j)A(i\rightarrow j) \). Our ratio between probabilities gives us $$ \begin{equation*} \frac{A_{j\rightarrow i}}{A_{i\rightarrow j}}= \frac{w_iT_{i\rightarrow j}}{w_jT_{j\rightarrow i}}. \end{equation*} $$ The simplest form of the Metropolis algorithm (sometimes called for brute force Metropolis) assumes that the transition probability \( T(i\rightarrow j) \) is symmetric, implying that \( T(i\rightarrow j)=T(j\rightarrow i) \).
We obtain then (using the Boltzmann distribution) $$ \begin{equation*} \frac{A(j\rightarrow i)}{A(i\rightarrow j)}= \exp{(-\beta(E_i-E_j))} . \end{equation*} $$ We are in this case interested in a new state \( E_j \) whose energy is lower than \( E_i \), viz., \( \Delta E = E_j-E_i \le 0 \). A simple test would then be to accept only those microstates which lower the energy. Suppose we have ten microstates with energy \( E_0 \le E_1 \le E_2 \le E_3 \le \dots \le E_9 \). Our desired energy is \( E_0 \).
At a given temperature \( T \) we start our simulation by randomly choosing state \( E_9 \). Flipping spins we may then find a path from \( E_9\rightarrow E_8 \rightarrow E_7 \dots \rightarrow E_1 \rightarrow E_0 \). This would however lead to biased statistical averages since it would violate the ergodic hypothesis discussed in the previous section. This principle states that it should be possible for any Markov process to reach every possible state of the system from any starting point if the simulations is carried out for a long enough time.
Any state in a Boltzmann distribution has a probability different from zero and if such a state cannot be reached from a given starting point, then the system is not ergodic. This means that another possible path to \( E_0 \) could be \( E_9\rightarrow E_7 \rightarrow E_8 \dots \rightarrow E_9 \rightarrow E_5 \rightarrow E_0 \) and so forth. Even though such a path could have a negligible probability it is still a possibility, and if we simulate long enough it should be included in our computation of an expectation value.
Thus, we require that our algorithm should satisfy the principle of detailed balance and be ergodic. The problem with our ratio $$ \begin{equation*} \frac{A(j\rightarrow i)}{A(i\rightarrow j)}= \exp{(-\beta(E_i-E_j))}, \end{equation*} $$ is that we do not know the acceptance probability. This equation only specifies the ratio of pairs of probabilities. Normally we want an algorithm which is as efficient as possible and maximizes the number of accepted moves. Moreover, we know that the acceptance probability has \( 0 \) as its smallest value and \( 1 \) as its largest. If we assume that the largest possible acceptance probability is \( 1 \), we adjust thereafter the other acceptance probability to this constraint.
To understand this better, assume that we have two energies, \( E_i \) and \( E_j \), with \( E_i < E_j \). This means that the largest acceptance value must be \( A(j\rightarrow i) \) since we move to a state with lower energy. It follows from also from the fact that the probability \( w_i \) is larger than \( w_j \). The trick then is to fix this value to \( A(j\rightarrow i)=1 \). It means that the other acceptance probability has to be $$ \begin{equation*} A(i\rightarrow j)= \exp{(-\beta(E_j-E_i))}. \end{equation*} $$
One possible way to encode this equation reads $$ \begin{equation*} A(j\rightarrow i)=\left\{\begin{array}{cc} \exp{(-\beta(E_i-E_j))} & E_i-E_j > 0 \\ 1 & else \end{array} \right., \end{equation*} $$ implying that if we move to a state with a lower energy, we always accept this move with acceptance probability \( A(j\rightarrow i)=1 \). If the energy is higher, we need to check this acceptance probability with the ratio between the probabilities from our PDF. From a practical point of view, the above ratio is compared with a random number. If the ratio is smaller than a given random number we accept the move to a higher energy, else we stay in the same state.
Nothing hinders us obviously in choosing another acceptance ratio, like a weighting of the two energies via $$ \begin{equation*} A(j\rightarrow i)=\exp{(-\frac{1}{2}\beta(E_i-E_j))}. \end{equation*} $$ However, it is easy to see that such an acceptance ratio would result in fewer accepted moves.
The Monte Carlo approach, combined with the theory for Markov chains can be summarized as follows: A Markov chain Monte Carlo method for the simulation of a distribution \( w \) is any method producing an ergodic Markov chain of events \( x \) whose stationary distribution is \( w \). The Metropolis algorithm can be phrased as
More text to come.
Why use a generative model rather than the more well known discriminative deep neural networks (DNN)?
A BM is what we would call an undirected probabilistic graphical model with stochastic continuous or discrete units.
It is interpreted as a stochastic recurrent neural network where the state of each unit(neurons/nodes) depends on the units it is connected to. The weights in the network represent thus the strength of the interaction between various units/nodes.
It turns into a Hopfield network if we choose deterministic rather than stochastic units. In contrast to a Hopfield network, a BM is a so-called generative model. It allows us to generate new samples from the learned distribution.
A standard BM network is divided into a set of observable and visible units \( \hat{x} \) and a set of unknown hidden units/nodes \( \hat{h} \).
Additionally there can be bias nodes for the hidden and visible layers. These biases are normally set to \( 1 \).
BMs are stackable, meaning they cwe can train a BM which serves as input to another BM. We can construct deep networks for learning complex PDFs. The layers can be trained one after another, a feature which makes them popular in deep learning
However, they are often hard to train. This leads to the introduction of so-called restricted BMs, or RBMS. Here we take away all lateral connections between nodes in the visible layer as well as connections between nodes in the hidden layer. The network is illustrated in the figure below.
The network layers:
The goal of the hidden layer is to increase the model's expressive power. We encode complex interactions between visible variables by introducing additional, hidden variables that interact with visible degrees of freedom in a simple manner, yet still reproduce the complex correlations between visible degrees in the data once marginalized over (integrated out).
Examples of this trick being employed in physics:
The function \( E(\mathbf{x},\mathbf{h}) \) gives the energy of a configuration (pair of vectors) \( (\mathbf{x}, \mathbf{h}) \). The lower the energy of a configuration, the higher the probability of it. This function also depends on the parameters \( \mathbf{a} \), \( \mathbf{b} \) and \( W \). Thus, when we adjust them during the learning procedure, we are adjusting the energy function to best fit our problem.
An expression for the energy function is $$ E(\hat{x},\hat{h}) = -\sum_{ia}^{NA}b_i^a \alpha_i^a(x_i)-\sum_{jd}^{MD}c_j^d \beta_j^d(h_j)-\sum_{ijad}^{NAMD}b_i^a \alpha_i^a(x_i)c_j^d \beta_j^d(h_j)w_{ij}^{ad}. $$
Here \( \beta_j^d(h_j) \) and \( \alpha_i^a(x_j) \) are so-called transfer functions that map a given input value to a desired feature value. The labels \( a \) and \( d \) denote that there can be multiple transfer functions per variable. The first sum depends only on the visible units. The second on the hidden ones. Note that there is no connection between nodes in a layer.
The quantities \( b \) and \( c \) can be interpreted as the visible and hidden biases, respectively.
The connection between the nodes in the two layers is given by the weights \( w_{ij} \).
RBMs were first developed using binary units in both the visible and hidden layer. The corresponding energy function is defined as follows: $$ \begin{align} E(\mathbf{x}, \mathbf{h}) = - \sum_i^M x_i a_i- \sum_j^N b_j h_j - \sum_{i,j}^{M,N} x_i w_{ij} h_j, \label{_auto5} \end{align} $$ where the binary values taken on by the nodes are most commonly 0 and 1.
Another varient is the RBM where the visible units are Gaussian while the hidden units remain binary: $$ \begin{align} E(\mathbf{x}, \mathbf{h}) = \sum_i^M \frac{(x_i - a_i)^2}{2\sigma_i^2} - \sum_j^N b_j h_j - \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma_i^2}. \label{_auto6} \end{align} $$
Metropolis sampling starts by suggesting a new configuration \( \boldsymbol{x}^{k+1} \). In the brute force method this is done by some random change of the visible units. The new configuration is then accepted with the acceptance probability $$ \begin{align} A(\boldsymbol{x}^k \rightarrow \boldsymbol{x}^{k+1}) = \text{min} (1, \frac{P(\boldsymbol{x}^{k+1})}{P(\boldsymbol{x}^k)}), \label{_auto7} \end{align} $$ where we need the marginalized probability $$ \begin{align} P(\boldsymbol{x}) &= \sum_\mathbf{h} P_{rbm}(\mathbf{x}, \mathbf{h}) \label{_auto8}\\ &= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}. \label{_auto9} \end{align} $$
In this method we sample from the joint probability \( P_{rbm} (\mathbf{x}, \mathbf{h}) \) by way of a two step sampling process. We alternately update the visible and hidden units. New samples are generated according to the conditional probabilities \( P(x_i|\mathbf{h}) \) and \( P(h_j|\mathbf{x}) \) respectively and accepted with the probability of \( 1 \). While the the visible nodes are dependent on the hidden nodes and vice versa, the nodes are independent of other nodes within the same layer. This is due to there being no intra layer interactions in the restricted Boltzmann machine.
The conditional probabilities are often referred to as the activitation functions in the neural networks context due to their role in determining the node outputs. For the binary-binary RBM they are $$ \begin{align} P(h_j = 1 | \boldsymbol{x}) &= \frac{1}{1 + e^{-b_j - \sum_i x_i w_{ij}}} \label{_auto10}\\ P(x_i = 1 | \boldsymbol{h}) &= \frac{1}{1 + e^{-a_j - \sum_j h_j w_{ij}}}, \label{_auto11} \end{align} $$ where we recognize the logistic sigmoid function \( \sigma (x) = 1/(1+exp(-x)) \).
When working with a training dataset, the most common training approach is maximizing the log-likelihood of the training data. The log likelihood characterizes the log-probability of generating the observed data using our generative model. Using this method our cost function is chosen as the negative log-likelihood. The learning then consists of trying to find parameters that maximize the probability of the dataset, and is known as Maximum Likelihood Estimation (MLE). Denoting the parameters as \( \boldsymbol{\theta} = a_1,...,a_M,b_1,...,b_N,w_{11},...,w_{MN} \), the log-likelihood is given by $$ \begin{align} \mathcal{L}(\{ \theta_i \}) &= \langle \text{log} P_\theta(\boldsymbol{x}) \rangle_{data} \label{_auto14}\\ &= - \langle E(\boldsymbol{x}; \{ \theta_i\}) \rangle_{data} - \text{log} Z(\{ \theta_i\}), \label{_auto15} \end{align} $$ where we used that the normalization constant does not depend on the data, \( \langle \text{log} Z(\{ \theta_i\}) \rangle = \text{log} Z(\{ \theta_i\}) \) Our cost function is the negative log-likelihood, \( \mathcal{C}(\{ \theta_i \}) = - \mathcal{L}(\{ \theta_i \}) \)
The training procedure of choice often is Stochastic Gradient Descent (SGD). It consists of a series of iterations where we update the parameters according to the equation $$ \begin{align} \boldsymbol{\theta}_{k+1} = \boldsymbol{\theta}_k - \eta \nabla \mathcal{C} (\boldsymbol{\theta}_k) \label{_auto16} \end{align} $$ at each \( k \)-th iteration. There are a range of variants of the algorithm which aim at making the learning rate \( \eta \) more adaptive so the method might be more efficient while remaining stable.
We now need the gradient of the cost function in order to minimize it. We find that $$ \begin{align} \frac{\partial \mathcal{C}(\{ \theta_i\})}{\partial \theta_i} &= \langle \frac{\partial E(\boldsymbol{x}; \theta_i)}{\partial \theta_i} \rangle_{data} + \frac{\partial \text{log} Z(\{ \theta_i\})}{\partial \theta_i} \label{_auto17}\\ &= \langle O_i(\boldsymbol{x}) \rangle_{data} - \langle O_i(\boldsymbol{x}) \rangle_{model}, \label{_auto18} \end{align} $$ where in order to simplify notation we defined the "operator" $$ \begin{align} O_i(\boldsymbol{x}) = \frac{\partial E(\boldsymbol{x}; \theta_i)}{\partial \theta_i}, \label{_auto19} \end{align} $$ and used the statistical mechanics relationship between expectation values and the log-partition function: $$ \begin{align} \langle O_i(\boldsymbol{x}) \rangle_{model} = \text{Tr} P_\theta(\boldsymbol{x})O_i(\boldsymbol{x}) = - \frac{\partial \text{log} Z(\{ \theta_i\})}{\partial \theta_i}. \label{_auto20} \end{align} $$
The data-dependent term in the gradient is known as the positive phase of the gradient, while the model-dependent term is known as the negative phase of the gradient. The aim of the training is to lower the energy of configurations that are near observed data points (increasing their probability), and raising the energy of configurations that are far from observed data points (decreasing their probability).
The gradient of the negative log-likelihood cost function of a Binary-Binary RBM is then $$ \begin{align} \frac{\partial \mathcal{C} (w_{ij}, a_i, b_j)}{\partial w_{ij}} =& \langle x_i h_j \rangle_{data} - \langle x_i h_j \rangle_{model} \label{_auto21}\\ \frac{\partial \mathcal{C} (w_{ij}, a_i, b_j)}{\partial a_{ij}} =& \langle x_i \rangle_{data} - \langle x_i \rangle_{model} \label{_auto22}\\ \frac{\partial \mathcal{C} (w_{ij}, a_i, b_j)}{\partial b_{ij}} =& \langle h_i \rangle_{data} - \langle h_i \rangle_{model}. \label{_auto23}\\ \label{_auto24} \end{align} $$ To get the expecation values with respect to the data, we set the visible units to each of the observed samples in the training data, then update the hidden units according to the conditional probability found before. We then average over all samples in the training data to calculate expectation values with respect to the data.
To get the expectation values with respect to the model, we use Gibbs sampling. We can either initialize the \( \boldsymbol{x} \) randomly or with a training sample. While we ideally want a large number of Gibbs iterations \( n\rightarrow n \), one might decide to truncate it earlier for efficiency. Doing this while having intialized \( \boldsymbol{x} \) with a training data vector is referred to as contrastive divergence (CD), because one is then closer to approximating the gradient of this function than the negative log-likelihood. The contrastive divergence function is the difference between two Kullback-Leibler divergences (also called relative entropy), which measure how one probability distribution diverges from a second, expected probability distribution (in this case the estimated one from the ground truth one).
When the goal of the training is to approximate a probability distribution, as it is in generative modeling, another relevant measure is the Kullback-Leibler divergence, also known as the relative entropy or Shannon entropy. It is a non-symmetric measure of the dissimilarity between two probability density functions \( p \) and \( q \). If \( p \) is the unkown probability which we approximate with \( q \), we can measure the difference by $$ \begin{align} \text{KL}(p||q) = \int_{-\infty}^{\infty} p (\boldsymbol{x}) \log \frac{p(\boldsymbol{x})}{q(\boldsymbol{x})} d\boldsymbol{x}. \label{_auto25} \end{align} $$
Thus, the Kullback-Leibler divergence between the distribution of the training data \( f(\boldsymbol{x}) \) and the model distribution \( p(\boldsymbol{x}| \boldsymbol{\theta}) \) is $$ \begin{align} \text{KL} (f(\boldsymbol{x})|| p(\boldsymbol{x}| \boldsymbol{\theta})) =& \int_{-\infty}^{\infty} f (\boldsymbol{x}) \log \frac{f(\boldsymbol{x})}{p(\boldsymbol{x}| \boldsymbol{\theta})} d\boldsymbol{x} \label{_auto26}\\ =& \int_{-\infty}^{\infty} f(\boldsymbol{x}) \log f(\boldsymbol{x}) d\boldsymbol{x} - \int_{-\infty}^{\infty} f(\boldsymbol{x}) \log p(\boldsymbol{x}| \boldsymbol{\theta}) d\boldsymbol{x} \label{_auto27}\\ %=& \mathbb{E}_{f(\boldsymbol{x})} (\log f(\boldsymbol{x})) - \mathbb{E}_{f(\boldsymbol{x})} (\log p(\boldsymbol{x}| \boldsymbol{\theta})) =& \langle \log f(\boldsymbol{x}) \rangle_{f(\boldsymbol{x})} - \langle \log p(\boldsymbol{x}| \boldsymbol{\theta}) \rangle_{f(\boldsymbol{x})} \label{_auto28}\\ =& \langle \log f(\boldsymbol{x}) \rangle_{data} + \langle E(\boldsymbol{x}) \rangle_{data} + \log Z \label{_auto29}\\ =& \langle \log f(\boldsymbol{x}) \rangle_{data} + \mathcal{C}_{LL} . \label{_auto30} \end{align} $$
The first term is constant with respect to \( \boldsymbol{\theta} \) since \( f(\boldsymbol{x}) \) is independent of \( \boldsymbol{\theta} \). Thus the Kullback-Leibler Divergence is minimal when the second term is minimal. The second term is the log-likelihood cost function, hence minimizing the Kullback-Leibler divergence is equivalent to maximizing the log-likelihood.
To further understand generative models it is useful to study the gradient of the cost function which is needed in order to minimize it using methods like stochastic gradient descent.
The partition function is the generating function of expectation values, in particular there are mathematical relationships between expectation values and the log-partition function. In this case we have $$ \begin{align} \langle \frac{ \partial E(\boldsymbol{x}; \theta_i) } { \partial \theta_i} \rangle_{model} = \int p(\boldsymbol{x}| \boldsymbol{\theta}) \frac{ \partial E(\boldsymbol{x}; \theta_i) } { \partial \theta_i} d\boldsymbol{x} = -\frac{\partial \log Z(\theta_i)}{ \partial \theta_i} . \label{_auto31} \end{align} $$
Here \( \langle \cdot \rangle_{model} \) is the expectation value over the model probability distribution \( p(\boldsymbol{x}| \boldsymbol{\theta}) \).
Using the previous relationship we can express the gradient of the cost function as $$ \begin{align} \frac{\partial \mathcal{C}_{LL}}{\partial \theta_i} =& \langle \frac{ \partial E(\boldsymbol{x}; \theta_i) } { \partial \theta_i} \rangle_{data} + \frac{\partial \log Z(\theta_i)}{ \partial \theta_i} \label{_auto32}\\ =& \langle \frac{ \partial E(\boldsymbol{x}; \theta_i) } { \partial \theta_i} \rangle_{data} - \langle \frac{ \partial E(\boldsymbol{x}; \theta_i) } { \partial \theta_i} \rangle_{model} \label{_auto33}\\ %=& \langle O_i(\boldsymbol{x}) \rangle_{data} - \langle O_i(\boldsymbol{x}) \rangle_{model} \label{_auto34} \end{align} $$
This expression shows that the gradient of the log-likelihood cost function is a difference of moments, with one calculated from the data and one calculated from the model. The data-dependent term is called the positive phase and the model-dependent term is called the negative phase of the gradient. We see now that minimizing the cost function results in lowering the energy of configurations \( \boldsymbol{x} \) near points in the training data and increasing the energy of configurations not observed in the training data. That means we increase the model's probability of configurations similar to those in the training data.
The gradient of the cost function also demonstrates why gradients of unsupervised, generative models must be computed differently from for those of for example FNNs. While the data-dependent expectation value is easily calculated based on the samples \( \boldsymbol{x}_i \) in the training data, we must sample from the model in order to generate samples from which to caclulate the model-dependent term. We sample from the model by using MCMC-based methods. We can not sample from the model directly because the partition function \( Z \) is generally intractable.
As in supervised machine learning problems, the goal is also here to perform well on unseen data, that is to have good generalization from the training data. The distribution \( f(x) \) we approximate is not the true distribution we wish to estimate, it is limited to the training data. Hence, in unsupervised training as well it is important to prevent overfitting to the training data. Thus it is common to add regularizers to the cost function in the same manner as we discussed for say linear regression.
The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.
Some of their motivation included
Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.
Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS) $$ \begin{align} \Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x}) \label{_auto38}\\ &= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})} \label{_auto39}\\ &= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_\ {i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}} \label{_auto40}\\ &= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x\ _i w_{ij}}{\sigma^2}}). \label{_auto41}\\ \label{_auto42} \end{align} $$
You can find the codes for the simple two-electron case at the Github repository https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src. Python codes to come, only c++ as of now.
The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines.
The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below.


External Code Formatter is a plugin for integrating Eclipse's code formatter, as well as any other command line tools for code formatting, into IntelliJ IDEA. This solves the problem of maintaining a common code style in a team, where both IDEA and Eclipse are used.


---
layout: main
hero-message: PIONEERS IN ENGINEERING
Bringing STEM education to the Bay Area
title: Pioneers in Engineering
hero-button: Join Us!
hero-button-url: ../get-involved/
---
Looking for an engineering outreach club to join for the spring semester? Learn about what PiE does and the work you can do here.
Join PiE StaffLooking for a DeCal that combines learning robotics with a fun teaching experience to high school students? Check out the PiE RC DeCal.
DeCal MentorsOur capstone robotics competition for Bay Area high school students, 10th year in the running. Learn more about the competition, the timeline, and resources for students.
2018 Spring Robotics CompetitionBringing high school students together to challenge themselves in new ways through robotics
Connecting mentors to Bay Area high school students through PIE PREP and promoting STEM awareness throughout the community
Developing our own software and hardware to give students the best experience for $100 per team


Ugandans worried after a million condoms are recalled over quality concerns
Ugandans have expressed sexual reproductive health concerns following Wednesday’s confirmation by global health charity Marie Stopes that it had recalled hundreds of thousands of faulty condoms on sale in Uganda.
The recall followed a warning from Uganda’s National Drug Authority (NDA) that the Life Guard brand condoms had failed manufacturing “quality tests” because they contained holes and may burst.
The affected condoms were manufactured by India-based MHL Healthcare in April 2019 and have an expiry date of April 2024, the government regulator said.
Marie Stopes Uganda spokesman David Kamu told AFP on Wednesday that the two affected batches each contained “around 400,000” condoms.
Earlier reports had suggested millions of condoms could have been involved but NDA spokesman Fred Ssekyana told AFP the figure was below one million.
Marie Stopes Uganda said more than half of the condoms of concern had been recalled.
“While the LifeGuard brand follows strict quality controls, unfortunately two recent batches have fallen short of the quality we demand,” the charity’s country director, Carole Sekimpi, said in a statement Tuesday.
Marie Stopes is the largest and most specialised sexual reproductive health organisation in Uganda, the charity says on its website.
According to UNAIDS, 1.4 million Ugandans are living with HIV.
Last year 53,000 people were newly infected with the disease in the East African country, the UN agency said.


version
Astral Sorcery Perk Planner
Perk Tree planner for HellFirePVP's awesome Astral Sorcery mod for Minecraft.
Updated on 02/06/2021: Added equipment perks. Note that builds may not match exactly because attribute values on gems and equipment display as rounded in game.
Updated on 02/04/2021: Added some touch support for mobile.
Updated on 02/03/2021: Added version 1.16 perk tree.
- grite


In the United States April is Sexual Assault Awareness Month (SAAM). The goal of SAAM is to raise public awareness about sexual violence and to educate communities on how to prevent it. Click on the tabs below to see how the nation is participating in #saam.
Trigger Warning: Content is not monitored or filtered.  For more resource centers, check out nsvrc.org
Location: 44 Merrimon Ave, Asheville, NC 28801
Our VOICE, Inc. is a non-profit crisis intervention and prevention agency which serves victims of sexual violence, age 13 through adult, in Buncombe County. Learn more here.
 Options provides empowerment services and emergency shelter to Burke County families in crisis. Learn more here.
Location: 225 Birch St, Boone, NC 28607
OASIS (Opposing Abuse with Service, Information, and Shelter) is a private, non-profit organization serving survivors of domestic violence and sexual assault in Watauga, Avery and surrounding counties. Learn more here.
Location: 628 Summit Ave Greensboro, NC 27405
Women's Resource Center is women helping women to navigate life's hurdles, to access community services, to develop new skill sets, to move lives forward. Whatever the challenge, find the help you need - whether you are dealing with divorce, returning to work, starting a business, dealing with financial difficulties, or coping with family or health problems. Learn more here.
Location: 407 W Warren St, Shelby, NC 28150
Located in Shelby, NC, the Cleveland County Abuse Prevention Council, Inc. provides confidential services to survivors of domestic violence, rape, and sexual assault, and homeless women and children. They do so by providing safe shelter, advocacy, support services, and preventive education. Learn more here.
Location: 601 E 5th St, Charlotte, NC 28202
Previously United Family Services, Safe Alliance assists over 12,000 people in sexual assault and domestic violence services annually throughout Mecklenburg County and Lake Norman. Learn more here.
Location: 1206 Vaughn Rd, Burlington, NC 27217
Crossroads serves child and adult victims of sexual assault and trauma through confidential counseling, advocacy, child medical treatment, education, and community awareness. Learn more here.
Location: 1506 E Franklin St #302, Chapel Hill, NC 27514
The Orange County Rape Crisis Center is a non-profit agency. They serve the Chapel Hill, Carrboro, Hillsborough, and surrounding communities and provide 24-hour crisis intervention services to survivors of sexual violence. Services include 24-Hour Help Line, advocacy and accompaniment, support groups, workshops, therapy referrals and educational programs. Learn more here.
Location: 206 N Dillard St, Durham, NC 27701
The Durham Crisis Response Center has been the sole provider of comprehensive shelter and support services in the Durham area, providing counseling, legal advocacy, support groups, and shelter to survivors and their families in the aftermath of domestic and sexual violence. DCRC’s services include a 24-hour, confidential crisis line, short-term emergency shelter, hospital and court accompaniment, legal clinics with local attorneys, support groups, counseling, and referrals for job training, housing, childcare and other community services free of charge. Learn more here.
Location: 811 Spring Forest Rd, Raleigh, NC 27609
The North Carolina Coalition Against Sexual Assault is an inclusive, statewide alliance working to end sexual violence through education, advocacy, and legislation. NCCASA works on a local, state and national level to help the North Carolina community. Learn more here.
Location: 1012 Oberlin Rd, Raleigh, NC 27605
InterAct is a private, non-profit, United Way agency that provides safety, support, and awareness to victims and survivors of domestic violence and rape/sexual assault. InterAct also promotes violence-free relationships and communities through collaboration, public information, education, and advocacy. Learn more here.
 Learn more here.
Location: 609 Shipyard Blvd #106, Wilmington, NC 28412
Coastal Horizons Center, Inc. is a private, non-profit service delivery Corporation servicing Eastern North Carolina and Durham. The Rape Crisis Center provides 24 hour crisis response, counseling, information and referrals, court advocacy and accompaniment, and support groups for victims of sexual assault. Learn more here.
Location: 133 Fifth Avenue West, Hendersonville, NC 28739
Previously The Healing Place, Safelight is a nonprofit agency that provides support for victims of interpersonal violence, sexual assault and child abuse. Over time, the organization has evolved from a strictly crisis-driven agency to one striving to develop longer-term services addressing community needs such as low-income housing and the unavailability of medical, mental health and substance abuse resources. Learn more here.


The Apostle (1997) * * * * A movie review by Serdar Yegulalp Copyright 1999 by Serdar Yegulalp
"The Apostle" is one of the very few American movies I know of that is not only about religion but seems to be informed by the very spirit of what it studies. It doesn't make its subjects into easy, hypocritical targets or strawmen. Many people do believe in God without being the kind of Bible-clutching psychotic characters that Hollywood loves to indulge in. The movie, which was written and directed by Robert Duvall as a labor of love, does not indulge in such easy cliches.
Duvall's Euliss Dewey, or "Sonny" as he's known -- the apostle of the title -- isn't just a man who talks to God. He has out-and-out shouting matchines with Him. One of the early scenes of "The Apostle" has him pacing in his room like a prisoner in solitary, bellowing at God, begging Him to let him have his wife and children and ministry back. His wife, you see, has been cheating on him with another man, a youth minister, and she's now using underhanded tactics to get Sonny voted out of the church. Then the phone rings and Sonny's mother answers, telling the angry neighbor on the other end of the line that Sonny's been talking to God ever since he was a boy, and she sees no reason to tell him to stop now.
There's some symmetry here with an earlier scene, where Sonny and his mother stop at the scene of a roadside accident. Sonny pokes his head in the driver's- side window of a car where a young man lies bleeding, and gently asks him if he's ready to accept Jesus as his savior. The man agrees. In any other movie this would be farce, caricature, borderline bad taste. But the way it's seen and played and directed here tells us, gently, that everyone involved, from the victim to the cop who comes to shoo Sonny away, takes this seriously.
Sonny is a charismatic Pentecostal preacher who tours and shouts and whips up his congregations into jubilation. He's fond of wild metaphors: "Tonight we're going to short-circuit the Devil! We're going to plug into a power line that's wired straight into the Pearly Gates!" But his marriage is troubled, and his wife (a neurasthenic Farrah Fawcett) fears something in him. We get a hint of what that might be one day when Sonny confronts the youth minister one day during a softball game and smashes him over the head with a bat.
Sonny flees, heads to another state down South, and changes his name to "the Apostle E.F.". In one of the best scenes in the movie, he ingratiates himself with a black man who lets him sleep in a pup tent on his property. One of that man's friends is a retired preacher, and E.F. hooks up with him to start a small congregation of his own.
The congregation is tiny, but E.F. gets it going with sheer sweat -- working odd jobs at the local garage (one of the mechanics dotes on him), getting promoted on the local FM station ("We have a pay-before-you-preach policy here," the program director informs him, having been stiffed too many times before), and putting together Thanksgiving baskets for the poorer families. He's redeeming himself -- not just in the eyes of the characters, but in OUR eyes as well, because at first we're not really sure if he's just putting on a good front of change, or is really changing.
Then other things start to happen, so casually we barely notice them creeping up on us. E.F. has a showdown with an almost compulsively angry bully (Billy Bob Thornton) that does not end in the way we would anticipate. E.F.'s family back at home starts to ask about him. And then there is the matter of the youth preacher, for which E.F. will eventually have to answer.
The film is shot in a quasidocumentary style that feels almost like eavesdropping. No one reaches for affect or "acts". The actors are all unknowns, aside from Duvall himself, playing the preacher as though born to the role, Fawcett, and Miranda Richardson as the radio station secretary. Because of this, we don't see a bunch of "Jesus freaks"; we just see people with a deep and abiding faith that gives them a genuine community and togetherness. The whole film feels alive and spontaneous; it isn't just another plot out of the Hollywood shrink-wrap factory.
Duvall's movie works on almost too many levels to list. It's spiritual without being smarmy or cloying; it's an affecting character study (E.F. is far from being one-sided); it's great fun. It only seems appropriate, in today's climate, that he would have had no choice but to make the movie himself.
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Nyzo version 477 (commit on GitHub) modifies NewVerifierQueueManager to continue voting for a verifier until it becomes the top-voted verifier.
In NewVerifierQueueManager, the consecutiveBlocksVotingForSameVerifier field was renamed to consecutiveBlocksVotingForTopVerifier to reflect its new use.
In NewVerifierQueueManager.updateVote(), the outer condition now only checks if the vote is null. Some of the inner logic must be performed even if the vote is unchanged.
If the vote has changed, the new vote is registered, stored, and broadcast. With the exception of removal of an assignment of consecutiveBlocksVotingForSameVerifier and different nesting of conditions, this code is unchanged.
If the current vote is for the top-voted new verifier, the consecutiveBlocksVotingForTopVerifier counter is incremented. If this verifier is voting for the top-voted new verifier for too long, that verifier is demoted to give another verifier a chance to join.


R functions for handling, processing, and analyzing geographic data on species' distributions and environmental variables.
| Version: | 3.1 |
| Depends: | R (≥ 3.1.0), raster, maps |
| Imports: | XML, geosphere, fields, maptools, sp, rgdal, rgeos, methods |
| Suggests: | testthat, devtools |
| Published: | 2018-01-24 |
| Author: | Bruno Vilela & Fabricio Villalobos |
| Maintainer: | Bruno Vilela <brunovilelasilva at hotmail.com> |
| BugReports: | https://github.com/macroecology/letsR/issues |
| License: | GPL-2 |
| URL: | http://onlinelibrary.wiley.com/doi/10.1111/2041-210X.12401/abstract, https://github.com/macroecology/letsR |
| NeedsCompilation: | no |
| Citation: | letsR citation info |
| Materials: | README |
| CRAN checks: | letsR results |
| Reference manual: | letsR.pdf |
| Package source: | letsR_3.1.tar.gz |
| Windows binaries: | r-devel: letsR_3.1.zip, r-release: letsR_3.1.zip, r-oldrel: letsR_3.1.zip |
| OS X binaries: | r-release: letsR_3.1.tgz, r-oldrel: letsR_3.1.tgz |
| Old sources: | letsR archive |
Please use the canonical form https://CRAN.R-project.org/package=letsR to link to this page.


| Top |
GObject ╰── GInitiallyUnowned ╰── GtkWidget ╰── GtkContainer ╰── GtkBin ╰── GtkWindow ╰── GtkOffscreenWindow
GtkOffscreenWindow is strictly intended to be used for obtaining snapshots of widgets that are not part of a normal widget hierarchy. Since GtkOffscreenWindow is a toplevel widget you cannot obtain snapshots of a full window with it since you cannot pack a toplevel widget in another toplevel.
The idea is to take a widget and manually set the state of it, add it to a GtkOffscreenWindow and then retrieve the snapshot as a cairo_surface_t or GdkPixbuf.
GtkOffscreenWindow derives from GtkWindow only as an implementation detail. Applications should not use any API specific to GtkWindow to operate on this object. It should be treated as a GtkBin that has no parent widget.
When contained offscreen widgets are redrawn, GtkOffscreenWindow will emit a “damage-event” signal.
GtkWidget *
gtk_offscreen_window_new (void
);
Creates a toplevel container widget that is used to retrieve snapshots of widgets without showing them on the screen.
Since: 2.20
cairo_surface_t *
gtk_offscreen_window_get_surface (GtkOffscreenWindow *offscreen
);
Retrieves a snapshot of the contained widget in the form of a cairo_surface_t. If you need to keep this around over window resizes then you should add a reference to it.
Since: 2.20
GdkPixbuf *
gtk_offscreen_window_get_pixbuf (GtkOffscreenWindow *offscreen
);
Retrieves a snapshot of the contained widget in the form of a GdkPixbuf. This is a new pixbuf with a reference count of 1, and the application should unreference it once it is no longer needed.
Since: 2.20


2 Samuel 1:7
And when he looked behind him, he saw me, and called unto me. And I answered, Here am I.


@(project: String, task: String, referenceLinks: de.fuberlin.wiwiss.silk.evaluation.ReferenceLinks)
@header = {
}
@toolbar = {
}
@content = {
@if(referenceLinks.isDefined) {
There are already @referenceLinks.positive.size positive and @referenceLinks.positive.size negative reference links.
Start learning a linkage rules from existing reference links:
Start with existing reference links but find new reference links:
} else {
Start active learning:
}
}
@main(Some(project), Some(task), "learn")(header)(toolbar)(content)


Welcome <% user_details.name%>!
<%user_details.name%> <%user_details.email%>
This is your dashboard, soon you will be able to see all the tasks asigned to you and much more!
INDEPENDENT CONTRACTOR AGREEMENT
Please follow these instructions so we can properly pay you when you perform a task:
1. Download the document from: https://www.irs.gov/pub/irs-pdf/fw9.pdf
2. – Fill out the form
3.- Upload your filled form to Phocus.io.
Your form was uploaded:


Allowing www and ssh:
Allow all outbound trafic from established connection (outbound new connections are note allowed):
iptables -A OUTPUT -p tcp -o eth0 -m state --state ESTABLISHED,RELATED -j ACCEPT
Allow incoming to port 22 and 80:
iptables -A INPUT -p tcp -i eth0 --dport 80 --sport 1024:65535 -m state \
--state NEW -j ACCEPT
iptables -A INPUT -p tcp -i eth0 --dport 22 --sport 1024:65535 -m state \
--state NEW -j ACCEPT
Allowing the firewall to browse the internet:
Open outbound traffic for port 80 and 443:
iptables -A OUTPUT -p tcp -j ACCEPT -o eth0 -m state \
--state NEW,ESTABLISHED,RELATED -m multiport --dport 80,443 \
--sport 1024:65535
Allow previously established connections
iptables -A INPUT -p tcp -i eth0 -m state --state ESTABLISHED,RELATED -j ACCEPT
One could also allow all outbound tcp traffic
iptables -A OUTPUT -p tcp -o eth0 -j ACCEPT -m state \
--state NEW,ESTABLISHED,RELATED
Masquerading (also known as many to one NAT):
First you must make sure the iptables_nat module is loaded (use modprobe) or put it in the /etc/sysconfig/iptables (for redhaters)
Enable IP forwarding and routing: echo 1 > /proc/sys/net/ipv4/ip_forward
Now Masquerade:
iptables -A POSTROUTING -t nat -o eth0 -s <IP_ADDRESS>/24 -s 0/0 -j MASQUERADE
Port forwarding with DNAT:
Assuming that you’ve loaded the iptables_nat module and have enabled the IP forwarding as in the Masquerading example above:
iptables -A PREROUTING -t nat -d (external IP) --dport 80 \
-j DNAT --to <IP_ADDRESS>:8080
You should also forward trafic among the two interface:
1 iptables -A FORWARD -t filter -p tcp -i eth0 -o eth1 -d <IP_ADDRESS> \
--dport 8080 -m state --state NEW -j ACCEPT
2 iptables -A FORWARD -t filter -p tcp -m state \
--sate ESTABLISHED,RELATED -j ACCEPT


|
Bullet Collision Detection & Physics Library
|
Public Member Functions | |
| ConvertBodiesLoop (btSequentialImpulseConstraintSolverMt *solver, btCollisionObject **bodies, int numBodies, const btContactSolverInfo &infoGlobal) | |
| void | forLoop (int iBegin, int iEnd) const BT_OVERRIDE |
| Public Member Functions inherited from btIParallelForBody | |
| virtual | ~btIParallelForBody () |
Public Attributes | |
| btSequentialImpulseConstraintSolverMt * | m_solver |
| btCollisionObject ** | m_bodies |
| int | m_numBodies |
| const btContactSolverInfo & | m_infoGlobal |
Definition at line 780 of file btSequentialImpulseConstraintSolverMt.cpp.
|
inline |
Definition at line 787 of file btSequentialImpulseConstraintSolverMt.cpp.
|
inlinevirtual |
Implements btIParallelForBody.
Definition at line 796 of file btSequentialImpulseConstraintSolverMt.cpp.
| btCollisionObject** ConvertBodiesLoop::m_bodies |
Definition at line 783 of file btSequentialImpulseConstraintSolverMt.cpp.
| const btContactSolverInfo& ConvertBodiesLoop::m_infoGlobal |
Definition at line 785 of file btSequentialImpulseConstraintSolverMt.cpp.
| int ConvertBodiesLoop::m_numBodies |
Definition at line 784 of file btSequentialImpulseConstraintSolverMt.cpp.
| btSequentialImpulseConstraintSolverMt* ConvertBodiesLoop::m_solver |
Definition at line 782 of file btSequentialImpulseConstraintSolverMt.cpp.


Support Tool download links
Please note:
- Be sure to have all your documents saved and closed before starting the remote session.
- You will need to provide the Access Code and Password before the technician may connect.
- The Password is case sensitive, please make sure to specify each letter exactly as it appears.
- If you receive a virus alert about this program, please ignore it. It is a false positive.
- If your firewall attempts to block the program, please allow the program access through your firewall.
If you are running Windows Vista 64-bit or newer:
Download: CRU-RT-v2-Vista64.exe (895K)
If you are running Windows Vista 32-bit or newer:
Download: CRU-RT-v2-Vista32.exe (862K)
If you are running Windows 2000, XP, or Server 2003:
Download: CRU-RT-v2-XP32.exe (854K)


Attribute Master Yin:
You haven't found them yet? Why not?
"Tell me again what to do."
"The device disappeared. Can you give me another one?"


About Me
I am a full-stack web developer, with interest in back-end architecture and development, leveraging five years of experience as a practicing general dentist to best serve clients and users in developing interactive and engaging programs. Having graduated from the Full Stack Web Development Coding Bootcamp at Rice University, I developed the skills to use JavaScript, jQuery, Bootstrap, React and other tools to develop responsive, mobile-friendly applications.
I am passionate about precision in my work, solving complex problems, and working with others to build concise, highly functional code. I am excited to continue to expand my skill sets, obtain additional certifications, and grow as a team-player and developer. In my free time I like to play golf, watch sports, play video games, and traverse the internet in search of ways to better myself as a programmer.
Projects
Galleria
An e-commerce website for buying and selling art. The website employs the Handlebars engine to render gallery content, MySQL to store data, and Express for routing.
Click to go to deployed site
Gooberville-Foods
A website where users can search for recipes and save recipes and comments for later. Application makes use of third-part APIs to find recipes and local storage for saving recipes and comments.
Click to go to deployed site
Tech Blog
A simple full-stack blog website built using MVC convention. User accounts and posts are stored in MySQL database, with Sequelize as the ORM, and the Handlebars engine is used to dynamically update content.
Click to go to deployed site


all games
all games
(current)
Profile
Start Game
Design Game
Users
filters
time of design
score
game numbers
game numbers per day
...
...
...
...
ali
score: 100
played: 4
saeid
score: 200
played: 2
hamid
score: 300
played: 1
ali
score: 100
played: 4
saeid
score: 200
played: 2
hamid
score: 300
played: 1


Life is Beautiful reveals dates for 2020 festival in Las Vegas
by Jason BracelinLife is Beautiful is officially back.
The three-day music and arts festival has announced its return Sept. 18-20, 2020.
Back for its eighth year, Life is Beautiful will once again take over 18 blocks downtown after drawing 170,000 attendees in 2019.
“It’s a good day when you get to announce the return of Life Is Beautiful,” Life is Beautiful CEO Justin Weniger said in a press release. “Each year, we look forward to aiding the positive transformation of our community and infusing art and culture into the vibrant walls of downtown Las Vegas. We are very excited to be back again for the 2020 edition of the festival and already have some great things in store.”
Ticket sale information will be announced later.


Regions of Ruin Map v0.7
Filters
Groups:
Contain:
Search:
Info
Location:
Type:
Contain:
Comment:
Usage
- Click on location to get info
- Double click on location to mark it
- You can copy location link
- Select an item from contain dropbox to see amount
- Keep a mouse over location to see the name
- If you spot a mistake report to the Steam
Discussion


data class ConversionResult
A result of an exchange rate conversion. |
|
class Currency
Currency representation. tagId is used as unique identifier; always uppercase. |
|
class CurrencyConverter
Main point for using this module. Given an ExchangeRateProvider, calculates exchange rates. |
|
data class ExchangeRateData
|
|
interface ExchangeRateProvider
Source of data for the CurrencyConverter. |
|
data class FromToCurrencyPair
A FROM -> TO pair of currencies. Used for convenience. |
|
sealed class Rate
Base class for representing an exchange rate. The rate can be basic containing only the middleRate or extended containing the buying and selling rate. |
class RateNotAvailableException : RuntimeException
Thrown when a rate can not be calculated. |
infix fun Currency.convertTo(that: Currency): FromToCurrencyPair
Creates a FromToCurrencyPair. |


Luca Foschini
Data Scientist, Engineer.
Professional
I'm a co-founder and Head of Data Science at Evidation Health.
In the past, I worked on aggregation of news articles at Ask.com, on community detection in social networks at Google and on low-latency web caching at the CERN.
Research
My research focuses on designing efficient algorithms for finding approximate solutions to problems for which computing an exact solution would require an impractical amount of resources.
Simply put, a recurrent pattern you'd find in my research papers is "This theorem proves that this problems can't be solved exactly on large inputs within a reasonable amount of time or memory, but if you're willing to settle for a slightly suboptimal solution, here's an algorithm that can compute that efficiently."
The problems I studied include detecting outliers on large streams of network packets in real time; quickly finding shortest paths in road networks under heavy traffic conditions; and efficiently partitioning large graphs into balanced components.
During my Ph.D. I was lucky enough to spend time visiting prestigious research institutions such as Google Research, ETH Zurich, and UIUC. That allowed me to collaborate with scholars from many different fields of study, including computational geometry, computer security, data compression, and computer vision.
You can find a complete list of my publications here.
Education
- Ph.D., Computer Science, UCSB (2012), Dean's Fellowship.
- M.S., Computer Science, UCSB (2011), GPA 4.0
- Diploma di Licenza Specialistica, Sant'Anna School of Advanced Studies (2007), Magna cum Laude.
- M.E., Computer Engineering, University of Pisa (2007), Summa cum Laude.
- Diploma di Licenza, Sant'Anna School of Advanced Studies (2005), Summa cum Laude.
- B.E., Computer Engineering, University of Pisa (2004), Summa cum Laude.
Personal
I live in Santa Barbara, CA, where I spend most of my spare time at a small or negative distance from the Pacific Ocean.
I grew up on Cappelletti and Piadina on a farm near Ravenna, Italy.
Resume
See my full resume here.


This is the configure speed page, where you're able to set how fast you want the packets to be sent out. Specifically, you set how many packets per seconds you want to be sent out. There's also an informational progress bar that tells you what the calculated bandwidth will be. Keep in mind that this bar uses both the pps that is entered and the currently configured packet on the C side, so if there's no packet on the C side, then it will just display 0.
The maximum line rate is around 100 Mbps, however, due to the (lack of) power in a Raspberry Pi, in reality you will probably be getting far less than that with smaller packets (down to about 5 Mbps with 64 byte packets). If you want to increase the actual bandwidth, try increasing the size of the packets.
The Pi currently does not have a packet configured, and as such the bandwidth calculation will not work until you have configured a packet for the Pi to send.


On a boring weekend while trying to kill some time, a friend of mine recommended me a video1 on YouTube which inspired me to write some code to make patterns like below.
This is called Modular Multiplication on a Circle(Times table). Here I’ll walk through a tutorial on how you can make this yourself.
To make these patterns, the circle is first divided into n equal parts. They’re numbered from 0 to n — 1.
Each part is then joined with its kth multiple. The pattern shown below is made with k = 7. Which means that 1 is connected with 7, 2 with 14, 3 with 21 and so on. Doing this for above setup, gives the following pattern.
Doing the above procedure for a large number of parts give rise to some beautiful patterns. Let’s make them using HTML Canvas.
First lets initialize the canvas and draw the main circle.
Circles are drawn with .arc()
method.
The first checkpoint of the code would be to divide the circle in n-parts and get their coordinates for later use.
And the final part to join the points with their index multiplied by k. .moveTo()
and .lineTo()
are used to specify start and end points. And finally .stroke()
method to draw it.
Also added some random colors for visual appeal ;). Take a look at my version here2.
You can read more about HTML Canvas here3.
Hope you liked this! Give this some claps on Medium.


{% extends 'base.html' %} {% block content %}
File uploaded successfully. You have uploaded an image of {{ pred }}! Confidence: {{ prob }}%


{% extends 'base_email.html' %} {% block content %}
You are {{ rank }} on the general waitlist for {{ register.program.name }} with the following time slots:
{% endblock %} {% block footer %}Currently, the class can only accept {{ capacity }} Googlers. Should there be a vacated spot in the class, you will be automatically enrolled from the waitlist and receive an email confirmation.
If you no longer want to be enrolled, go to the Activity page to cancel your enrollment.
{% endblock %}


CS 392 - Game AI
Spring 2001
Course Information
Course Information Page
Presentations
Homework Assignments
Assignment Submissions Instructions
Project #1
Online Resources
Text Home Page:
Tom Mitchell,
Machine Learning
Stuart Russell and Peter Norvig,
Artificial Intelligence: a modern approach
Game AI: State of the Industry articles from Gamasutra (Nov. 1,8 2000):
http://www.gamasutra.com/features/20001101/woodcock_pfv.htm
http://www.gamasutra.com/features/20001108/laird_pfv.htm
www.gameai.com
Department Account Resources Page
Lecture Examples


21 details you might have missed in ‘Frozen 2’
by Kim Renfro- Warning: Spoilers ahead for Disney’s “Frozen 2.”
- The new sequel to “Frozen” is packed with small details and references you might not have noticed.
- From Disney Easter eggs of other characters and movies like “The Little Mermaid” to neat costume parallels, keep reading to see all the things you might have missed.
- Visit Insider’s homepage for more stories.
Disney’s new animated movie sequel “Frozen 2” has several key moments you might not see upon a first viewing of the movie. We watched the new film twice to try and catch all of the best Disney references (like nods to “Big Hero Six,” “The Little Mermaid,” and more), plus cool examples of foreshadowing.
Keep reading to see 21 details you might have missed in “Frozen 2.”
In the opening flashback, Anna and Elsa are playing with small snow figurines.
Young Elsa and Queen Iduna together at the start of “Frozen 2.”
Disney
The two young princesses have an array of little snow people and creatures, and there were some Disney characters among them.
One of the figures is Baymax, the lovable robot from Disney’s 2014 animated movie “Big Hero Six.”
We’re also pretty sure we spotted a little “Bolt” dog among the snow figures.
“Bolt” was a 2008 Walt Disney Animation Studios movie, and marked a new phase for the studio’s direction in animated feature films that led to “Frozen” in 2013.
Both “Bolt” and “Big Hero Six” were codirected by Chris Williams — the same man who voices Oaken in the “Frozen” movies.
Williams is used to wearing many different hats at Walt Disney Animation Studio. He’s an animator, story artist/screenwriter, director, and actor.
When Anna and Elsa hear the story of the enchanted forest for the first time, there’s a small horse figurine sitting on Elsa’s bedside table.
Later in the movie, it’s revealed that the water spirit is a mythical horse (called the Nokk). Elsa tames it and rides it to Ahtohallan. The horse’s presence in her childhood flashback was a neat little bit of foreshadowing.
Our first hint that Iduna was the one who saved Agnarr came when little Anna reacted to her father’s story.
“Whoever saved you, I love them!” young Anna cries out in the movie before falling into her mother’s lap.
Upon a rewatch, this is a pretty direct foreshadowing of the reveal that Queen Iduna’s played a key role in saving King Agnarr’s life.
Starting in those flashbacks, we see a lot of important repeating patterns.
The most important of these is of course the four-sided diamond pattern on Queen Iduna’s scarf, which is later revealed to show the four spirit symbols and the “fifth spirit” sign.
That diamond patter was also on King Agnarr’s coat trim, and we saw it back in the first “Frozen” movie.
That repeating diamond pattern, which later becomes the foundation of Elsa’s new “fifth spirit” symbol, appeared frequently throughout the first movie (usually in connection to Elsa).
That new symbol was shown in the very first poster for “Frozen 2.”
Back when the poster and teaser trailer debuted, fans began speculating about the meaning of the small symbols in the middle of each diamond.
But it turns out the real clue was the entire four-sided “fifth spirit” design.
Anna and Elsa’s first dresses and necklaces we see them wear in “Frozen 2” were hints at how they’d separate by the end of the movie.
Throughout “Frozen 2,” Anna is the only one of the two sisters who has distinct Arendelle iconography on her clothes. The small detailing on her dress and the bronze necklace she’s wearing at the beginning of the movie are all pulled from the flags you see around Arendelle.
In contrast, Elsa is wearing a necklace with her signature half-snowflake design.
You can see the Arendelle sigil clearly on Lieutenant Mattias’ shield here:
The little floral design is everywhere in Arendelle, and used in the detailing of Anna’s clothing, but it’s never seen on Elsa in “Frozen 2.”
Anna was always more connected to Arendelle, both emotionally and literally (through her costuming), so it makes sense she winds up being the Queen.
And her costuming in “Frozen 2” is inextricably linked to Elsa’s journey, too.
Now let’s take a closer look at Anna’s traveling cloak, which also tells part of the story about her relationship to Elsa and Kristoff.
When they set out on their journey, Anna is wearing a magenta cape over her black and gold outfit.
The cape Anna wears for the first two acts in “Frozen 2” is a similar color to Elsa’s cape from the first movie.
The cape Elsa wore and then discarded during the iconic “Let It Go” number had an Arendelle sigil on it – further showing her disconnect from the kingdom.
Anna wearing a cape of the similar color in “Frozen 2” shows a link between her and her sister, and how much Anna is trying to hold onto a way of life that is becoming increasingly untenable.
It’s only when Elsa literally pushes Anna away and on a different path that the younger princess stops wearing the magenta cape.
After Elsa decides to go to find Ahtohollan alone, Anna and Olaf find themselves in a dark cave. Anna’s cape is lost when they fall into the dark river, revealing her black and gold outfit underneath.
Anna is more focused on Elsa than Kristoff for the first part of the movie, and this was reflected in the couples’ costumes.
The side story of “Frozen 2” is all about how Anna and Kristoff are having trouble communicating and getting on the same page, largely due to Anna’s focus on her sister.
When Anna is wearing her traveling cloak, she’s more visually connected to Elsa.
But once the cloak is gone, Anna’s outfit actually matches the one Kristoff has been wearing the whole time.
They were synced up the whole time, just underneath some communication problems that needed to be sorted out.
When Kristoff is singing in “Some Things Never Change,” you can briefly little statues made in the likeness of two Disney animators.
As Insider learned during a press event for the movie, two “Frozen 2” creators – Mike Giaimo, the production designer, and David Womersley, the art director of environments – were turned into wooden statuettes for the background of this scene.
Giaimo and Womersley had no idea they were in the film until just a couple of months before it premiered.
You can spot the two statues in the background a little over halfway through the song at the beginning of the movie, when Kristoff and Sven meet up with Anna on the streets of Arendelle.
There’s a hidden Mickey somewhere in the scene when Olaf sings “When I Am Older.”
“There’s one Mickey mouse hidden in there,” the head of animation of “Frozen 2,” Becky Bresee, told Insider. “You have to find it though.”
So far we haven’t spotted it, but fans should keep an eye out during this song in case they can spot the hidden Mickey.
You might have noticed that a scene shown in the trailer for “Frozen 2” never appeared in the movie.
The very first teaser for “Frozen 2” was released in February, and it ended with a dramatic moment showing Anna grabbing a sword from Kristoff and swinging it towards the camera.
That original scene had already been cut from the movie by the time the teaser premiered, but the fan reaction to it convinced the directors to add it back in somehow.
Jennifer Lee and Chris Buck, the film’s codirectors, told Insider about how people’s love for that moment made them rework it into the movie again.
“That [scene] was in [the movie] at one point, and then it was out,” Buck said. “We were like, ‘Uh oh, people love that scene.’ So we made it work, but it’s different.”
The final version of the Anna-sword moment shows her grabbing an ice-sword from a statue instead of a real sword from Kristoff.
You can read more about this moment and people’s reactions to it here.
Kristoff’s song “Lost in the Woods” was invoking lots of ’80s rock ballads, and also gave a nod to “Bohemian Rhapsody.”
At one point during “Lost in the Woods,” we see Kristoff surrounded by singing reindeer in the exact same arrangement as the above music video from Queen for their seminal hit “Bohemian Rhapsody.”
Jonathan Groff was singing the voices of 18 different reindeer for “Lost in the Woods.”
As revealed in a Vanity Fair feature written by Joanna Robinson, actor Jonathan Groff brought to life close to a 20 reindeer for his big ballad.
When Elsa sees all the snow memories in Ahtohollan, there’s a reference to “The Little Mermaid.”
Elsa sees young Iduna ask young Agnarr what he’s reading, and he replies: “Some new Danish author.” On the cover of his book, you can just make out the silhouette of Ariel from “The Little Mermaid.”
Hans Christian Anderson was the Danish author of both “The Little Mermaid” and “The Snow Queen.”
This could be taken as a hint about what year the “Frozen” take place in.
“The Little Mermaid” was published in 1837, and “The Snow Queen” came afterwards in 1844. If young Agnarr was reading the “new” book by Anderson in 1837 as a boy, then that means the current timeframe in the “Frozen” movies could be around the late 1860s or 1870s.
When Olaf “dies,” his snow is gathered by Gale and dotted with purple flowers.
This is likely reference to the scene at the end of “Frozen” when Olaf is finally experiencing warm weather in Arendelle and smells two buckets of purple flowers.
When Anna is revealed as Queen of Arendelle, her hairstyle when matches Elsa’s original coronation style.
Anna has a whole new gown (again, dotted with the Arendelle insignia), but her hair is distinctly mirroring the updo Elsa had for her coronation. And both queen’s looks also happen to match their mother’s style we saw in both movies.
The snow goblin in the post-credits scene is wearing Elsa’s crown from the first movie she threw away.
During the post-credits scene, we get a quick look at Elsa’s snow goblin as he listens to Olaf retell the events of “Frozen 2.” Perched on top of the goblin’s head is the little crown Elsa tossed away at the end of “Let it Go” during the first movie.
- Read more:
- The directors explain why Elsa doesn’t have a love story, gay or otherwise, in ‘Frozen 2’
- What the cast of ‘Frozen 2’ looks like in real life
- How the fan response to the first ‘Frozen 2’ teaser wound up saving Anna’s sword-swinging scene
- What the ‘Frozen 2’ creators think about making a trilogy


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The El Farol Bar Problem¶
The El Farol Bar Problem is a tought experiment proposed by Brian-Arthur in 1994 that intends to show the emergent properties of a complex system.
The patrons of a bar (The El Farol Bar, in Santa Fe, New Mexico) want to go to the bar, but are not happy if the bar is crowded. So, each agent have multiple forecast models that she/he/they uses to estimate the probable bar attendance and decide to go (or not) to the bar.
The concurrent methods of forecast compete and the method that have the best fitness is chosen, so the agents change the forecast methods according with the accuracy of the observed predictions.
This problem was later generalized by In 1997 Damien Challet and Yi-Cheng Zhang into game form as the Minority Game.
We have implemented an example of the El Farol Bar problem.
The model is executed using a .sh file el_farol_classic.sh that runs the model and the R markdown file El_Farol.rmd that generates the report with the simulation results that can be seen in this html file as a sample of a typical run of the simulation
To execute the model go to the El Farol Bar Model folder (examples/el_farol_bar_model) Open a bash console and write:
$ ./el_farol_classic.sh
The results will be show in a browser (look for the file El_Farol.html in the folder ‘results’)


Exercise 1 (1/2)
Consider the list v1 below:
v1 = [2,3,1]
What is v1[1]
Exercise 1 (2/2)
Consider the dictionary v2 below:
v2 = {2:0, 4:1, 1:3}
What is v2[1]?
Exercise 2 (1/2)
Consider the list people below:
people = [{'name':'Alice', 'gender':'F', 'age':15},
{'name':'Bob', 'gender':'M', 'age':20},
{'name':'Claire', 'gender':'F', 'age':25},
{'name':'David', 'gender':'M', 'age':30}]
Write a function names() that takes in a list like this and returns just the names of the players such that
names(people) = ['Alice', 'Bob', 'Claire', 'David']
Exercise 2 (2/2)
Consider the same list people below:
people = [{'name':'Alice', 'gender':'F', 'age':15},
{'name':'Bob', 'gender':'M', 'age':20},
{'name':'Claire', 'gender':'F', 'age':25},
{'name':'David', 'gender':'M', 'age':30}]
Write a function filter_adult() that returns just the people over 18 years such that
filter_adult(people) = [{'name':'Bob', 'gender':'M', 'age':20},
{'name':'Claire', 'gender':'F', 'age':25},
{'name':'David', 'gender':'M', 'age':30}]
Exercise 3
- Write a function odd_even() that takes as input an integer and prints a message stating whether the number is even or odd
- Write a function even_divide that takes as input two numbers: one number to check (call it num) and one number to divide by (call it div) if div divides evenly into num, print an appropriate message. If not, print a different appropriate message
Exercise 4
- Define the following list li:
li = [1,1,2,3,5,8,13,21,34,55,89]
- Write a piece of code that prints out all the elements of the list that are strictly less than 13
- Make a new list other_li that has all the elements strictly less that 13 from li in it and print out this new list


|
Drake
|
Represents symbolic rational function.
A function f(x) is a rational function, if f(x) = p(x) / q(x), where both p(x) and q(x) are polynomials of x. Note that rational functions are closed under (+, -, x, /). One application of rational function is in polynomial optimization, where we represent (or approximate) functions using rational functions, and then convert the constraint f(x) = h(x) (where h(x) is a polynomial) to a polynomial constraint p(x) - q(x) * h(x) = 0, or convert the inequality constraint f(x) >= h(x) as p(x) - q(x) * h(x) >= 0 if we know q(x) > 0.
This class represents a special subset of the symbolic::Expression. While a symbolic::Expression can represent a rational function, extracting the numerator and denominator, generally, is quite difficult; for instance, from p1(x) / q1(x) + p2(x) / q2(x) + ... + pn(x) / qn(x). This class's explicit structure facilitates this decomposition.
#include <drake/common/symbolic_rational_function.h>
Public Member Functions | |
| RationalFunction () | |
| Constructs a zero rational function 0 / 1. More... | |
| RationalFunction (const Polynomial &numerator, const Polynomial &denominator) | |
| Constructs the rational function: numerator / denominator. More... | |
| RationalFunction (const Polynomial &p) | |
| Constructs the rational function: p / 1. More... | |
| RationalFunction (double c) | |
| Constructs the rational function: c / 1. More... | |
| ~RationalFunction ()=default | |
| const Polynomial & | numerator () const |
| Getter for the numerator. More... | |
| const Polynomial & | denominator () const |
| Getter for the denominator. More... | |
| RationalFunction & | operator+= (const RationalFunction &f) |
| RationalFunction & | operator+= (const Polynomial &p) |
| RationalFunction & | operator+= (double c) |
| RationalFunction & | operator-= (const RationalFunction &f) |
| RationalFunction & | operator-= (const Polynomial &p) |
| RationalFunction & | operator-= (double c) |
| RationalFunction & | operator *= (const RationalFunction &f) |
| RationalFunction & | operator *= (const Polynomial &p) |
| RationalFunction & | operator *= (double c) |
| RationalFunction & | operator/= (const RationalFunction &f) |
| RationalFunction & | operator/= (const Polynomial &p) |
| RationalFunction & | operator/= (double c) |
| bool | EqualTo (const RationalFunction &f) const |
| Returns true if this rational function and f are structurally equal. More... | |
| Formula | operator== (const RationalFunction &f) const |
Returns a symbolic formula representing the condition where this rational function and f are the same. More... | |
| Formula | operator!= (const RationalFunction &f) const |
Returns a symbolic formula representing the condition where this rational function and f are not the same. More... | |
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable | |
| RationalFunction (const RationalFunction &)=default | |
| RationalFunction & | operator= (const RationalFunction &)=default |
| RationalFunction (RationalFunction &&)=default | |
| RationalFunction & | operator= (RationalFunction &&)=default |
Friends | |
| std::ostream & | operator<< (std::ostream &, const RationalFunction &f) |
| RationalFunction | ( | ) |
Constructs a zero rational function 0 / 1.
|
default |
|
default |
| RationalFunction | ( | const Polynomial & | numerator, |
| const Polynomial & | denominator | ||
| ) |
Constructs the rational function: numerator / denominator.
| numerator | The numerator of the fraction. |
| denominator | The denominator of the fraction. |
| std::logic_error | if the precondition is not satisfied. |
|
explicit |
Constructs the rational function: p / 1.
Note that we use 1 as the denominator.
| p | The numerator of the rational function. |
|
explicit |
Constructs the rational function: c / 1.
Note that we use 1 as the denominator.
| c | The numerator of the rational function. |
|
default |
| const Polynomial& denominator | ( | ) | const |
Getter for the denominator.
| bool EqualTo | ( | const RationalFunction & | f | ) | const |
Returns true if this rational function and f are structurally equal.
| const Polynomial& numerator | ( | ) | const |
Getter for the numerator.
| RationalFunction& operator *= | ( | const RationalFunction & | f | ) |
| RationalFunction& operator *= | ( | const Polynomial & | p | ) |
| RationalFunction& operator *= | ( | double | c | ) |
| Formula operator!= | ( | const RationalFunction & | f | ) | const |
Returns a symbolic formula representing the condition where this rational function and f
are not the same.
| RationalFunction& operator+= | ( | const RationalFunction & | f | ) |
| RationalFunction& operator+= | ( | const Polynomial & | p | ) |
| RationalFunction& operator+= | ( | double | c | ) |
| RationalFunction& operator-= | ( | const RationalFunction & | f | ) |
| RationalFunction& operator-= | ( | const Polynomial & | p | ) |
| RationalFunction& operator-= | ( | double | c | ) |
| RationalFunction& operator/= | ( | const RationalFunction & | f | ) |
| RationalFunction& operator/= | ( | const Polynomial & | p | ) |
| RationalFunction& operator/= | ( | double | c | ) |
|
default |
|
default |
| Formula operator== | ( | const RationalFunction & | f | ) | const |
Returns a symbolic formula representing the condition where this rational function and f
are the same.
If f1 = p1 / q1, f2 = p2 / q2, then f1 == f2 <=> p1 * q2 == p2 * q1
|
friend |


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FILTERDIFF(1) Man pages FILTERDIFF(1) NAME filterdiff - extract or exclude diffs from a diff file SYNOPSIS filterdiff [[-i PATTERN] | [--include=PATTERN]] [[-I FILE] | [--include-from-file=FILE]] [[-p n] | [--strip-match=n]] [--strip=n] [--addprefix=PREFIX] [--addoldprefix=PREFIX] [--addnewprefix=PREFIX] [[-x PATTERN] | [--exclude=PATTERN]] [[-X FILE] | [--exclude-from-file=FILE]] [[-v] | [--verbose]] [--clean] [[-z] | [--decompress]] [[-# RANGE] | [--hunks=RANGE]] [--lines=RANGE] [--files=RANGE] [--annotate] [--format=FORMAT] [--as-numbered-lines=WHEN] [--remove-timestamps] [file...] filterdiff {[--help] | [--version] | [--list] | [--grep ...]} DESCRIPTION You can use filterdiff to obtain a patch that applies to files matching the shell wildcard PATTERN from a larger collection of patches. For example, to see the patches in patch-2.4.3.gz that apply to all files called lp.c: filterdiff -z -i '*/lp.c' patch-2.4.3.gz If neither -i nor -x options are given, -i '*' is assumed. This way filterdiff can be used to clean up an existing diff file, removing redundant lines from the beginning (eg. the text from the mail body) or between the chunks (eg. in CVS diffs). To extract pure patch data, use a command like this: filterdiff message-with-diff-in-the-body > patch Note that the interpretation of the shell wildcard pattern does not count slash characters or periods as special (in other words, no flags are given to fnmatch). This is so that “*/basename”-type patterns can be given without limiting the number of pathname components. You can use both unified and context format diffs with this program. OPTIONS -i PATTERN, --include=PATTERN Include only files matching PATTERN. All other lines in the input are suppressed. -I FILE, --include-from-file=FILE Include only files matching any pattern listed in FILE, one pattern per line. All other lines in the input are suppressed. -x PATTERN, --exclude=PATTERN Exclude files matching PATTERN. All other lines in the input are displayed. -X FILE, --exclude-from-file=FILE Exclude files matching any pattern listed in FILE, one pattern per line. All other lines in the input are displayed. -p n, --strip-match=n When matching, ignore the first n components of the pathname. -# RANGE, --hunks=RANGE Only include hunks within the specified RANGE. Hunks are numbered from 1, and the range is a comma-separated list of numbers or “first-last” spans; either the first or the last in the span may be omitted to indicate no limit in that direction. --lines=RANGE Only include hunks that contain lines from the original file that lie within the specified RANGE. Lines are numbered from 1, and the range is a comma-separated list of numbers or “first-last” spans; either the first or the last in the span may be omitted to indicate no limit in that direction. --files=RANGE Only include files indicated by the specified RANGE. Files are numbered from 1 in the order they appear in the patch input, and the range is a comma-separated list of numbers or “first-last” spans; either the first or the last in the span may be omitted to indicate no limit in that direction. --annotate Annotate each hunk with the filename and hunk number. --format=unified|context Use specified output format. --strip=n Remove the first n components of pathnames in the output. --addprefix=PREFIX Prefix pathnames in the output by PREFIX. This will override any individual settings specified with the --addoldprefix or --addnewprefix options. --addoldprefix=PREFIX Prefix pathnames for old or original files in the output by PREFIX. --addnewprefix=PREFIX Prefix pathnames for updated or new files in the output by PREFIX. --as-numbered-lines=before|after Instead of a patch fragment, display the lines of the selected hunks with the line number of the file before (or after) the patch is applied, followed by a TAB character and a colon, at the beginning of each line. Each hunk except the first will have a line consisting of “...” before it. --remove-timestamps Do not include file timestamps in the output. -v, --verbose Always show non-diff lines in the output. By default, non-diff lines are only shown when excluding a filename pattern. --clean Always remove all non-diff lines from the output. Even when excluding a filename pattern. -z, --decompress Decompress files with extensions .gz and .bz2. --help Display a short usage message. --version Display the version number of filterdiff. --list Behave like lsdiff(1) instead. --grep Behave like grepdiff(1) instead. EXAMPLES To see all patch hunks that affect the first five lines of a C file: filterdiff -i '*.c' --lines=-5 < patch To see the first hunk of each file patch, use: filterdiff -#1 patchfile To see patches modifying a ChangeLog file in a subdirectory, use: filterdiff -p1 Changelog To see the complete patches for each patch that modifies line 1 of the original file, use: filterdiff --lines=1 patchfile | lsdiff | \ xargs -rn1 filterdiff patchfile -i To see all but the first hunk of a particular patch, you might use: filterdiff -p1 -i file.c -#2- foo-patch If you have a very specific list of hunks in a patch that you want to see, list them: filterdiff -#1,2,5-8,10,12,27- To see the lines of the files that would be patched as they will appear after the patch is applied, use: filterdiff --as-numbered-lines=after patch.file You can see the same context before the patch is applied with: filterdiff --as-numbered-lines=before patch.file Filterdiff can also be used to convert between unified and context format diffs: filterdiff -v --format=unified context.diff SEE ALSO lsdiff(1), grepdiff(1) AUTHOR Tim Waugh<EMAIL_ADDRESS>Package maintainer patchutils 23 Jan 2009 FILTERDIFF(1)


helloldap.cli¶
Tools to assist CLI scripts.
-
helloldap.cli.
add_parser_args
(parser, which=None)[source]¶ Adds default arguments to given parser instance.
Parameters: - parser – Instance of a parser
- which – List of 2-Tuples. 1st elem tells which argument to add, 2nd elem tells requiredness.
-
helloldap.cli.
build_rc
(args, default_rc, config='config')[source]¶ Builds map of settings.
Settings are taken from default_rc, optionally overridden by settings in the config file specified on command line, optionally overridden by explicit command line arguments.
Parameters: - args – Namespace with CLI arguments
- default_rc – Dict with default settings
- config – Key in args that gives path to external config file
Returns: ChainMap with settings
-
helloldap.cli.
init_cli_locale
(locale_name, detach_stdout=True)[source]¶ Initialises CLI locale and encoding.
Sets a certain locale. Ensures that output is correctly encoded, whether it is send directly to a console or piped.
Parameters: - locale_name – A locale name, e.g. “de_DE.utf8”.
- detach_stdout – If True (default), and we are not in a TTY (meaning, output is piped somewhere), we replace original STDOUT with a writer from the codecs module. If you do not want that (e.g. in PyCharm test runner), set this to False.
Returns: active locale as 2-tuple (lang_code, encoding)