text:
\section{Introduction}
\label{Sec:Intro}

Considerable impact in speech recognition has been created in recent years using  fully-connected deep neural networks (DNN) that drastically cut errors in large vocabulary speech recognition \citep{DongDengDahl,dahl2011large,seide2011conversational,Dahl2012,kingsbury2012scalable,hinton2012deep,deng2013new,DengMicrosoft,Yu2013,dahl2013improving,sainath2013optimization}. However, the well-known problem of the previous state-of-the-art approach based on Gaussian Mixture Model (GMM)-HMMs has not been addressed by the DNNs in a principled way: missing temporal correlation structure that is prevalent in the speech sequence data. Recurrent neural networks (RNN) have shown their potential to address this problem \citep{robinson1994application,graves2013speech}, but the difficulty of learning RNNs due to vanishing or exploding gradients \citep{pascanu2012difficulty} or the complexity of the LSTM (long short-term memory) structure in RNNs \citep{graves2013speech} have so far slowed down the research progress in using RNNs to improve speech recognition and other sequence processing tasks.

In this paper, we propose an architecture of RNNs for supervised learning, where the input sequence to the RNN is computed by an independent feature extractor using a fully-connected DNN receiving its input from raw data sequences. We have formulated both autoregressive (AR) and autoregressive and moving-average (ARMA) versions of this RNN.  A new learning method is developed in this work, which is successfully applied to both AR and ARMA versions of the RNN. The new method frames the RNN learning problem as a constrained optimization one, where cross entropy is maximized subject to having the infinity norm of the recurrent matrix of the RNN to be less than a fixed value that provides a sufficient condition for the stability of RNN dynamics.  A primal-dual technique is devised to solve the resulting constrained optimization problem in a principled way. Experimental results on phone recognition demonstrate: 1) the primal-dual technique is effective in learning RNNs, with satisfactory performance on the TIMIT benchmark; 2) The ARMA version of the RNN produces higher recognition accuracy than the traditional AR version; 3) The use of a DNN to compute high-level features of speech data to feed into the RNN gives much higher accuracy than without using the DNN; and 4) The accuracy drops progressively as the DNN features are extracted from higher to lower hidden layers of the DNN.

\section{Related Work}
\label{Sec:RelatedWork}

The use of recurrent or temporally predictive forms of neural networks for speech recognition dated back to early 1990's \citep{robinson1994application,deng1994analysis}, with relatively low accuracy.
Since deep learning became popular in recent years, much more research has been devoted to the RNN \citep{graves2006connectionist,graves2012sequence,maas2012recurrent,mikolov2012statistical,vinyals2012revisiting,graves2013speech}.
Most work on RNNs made use of the method of Back Propagation Through Time (BPTT) to train the RNNs, and empirical tricks need to be exploited in order to make the training effective. The most notable trick is to truncate gradients when they become too large
\citep{mikolov2011strategies,pascanu2012difficulty,bengio2013advances}. Likewise, another empirical method, based on a regularization term that represents a ``preference for parameter values,'' was introduced to handle the gradient vanishing problem \citep{pascanu2012difficulty}.

The  method we propose for training RNN in this paper is based on optimization principles, capitalizing on the cause of difficulties in BPTT analyzed in \citep{pascanu2012difficulty}. Rather than using empirical ways to scale up or scale down the gradients, we formulate the RNN learning problem as an optimization one with inequality constraints and we call for a natural, primal-dual method to solve the constrained optimization problem in a principled way \citep{poliak1987introduction}. Our work also differs from the earlier work reported in \citep{sutskever2013training,martens2011learning}, which adopted a special way of initialization using echo state networks \citep{jaeger2001echostate} when carrying out the standard BPTT procedure, without using a formal constrained optimization framework.

This work is originally motivated by the echo state network \citep{jaeger2001echostate}, which carefully hand-designed the recurrent weights making use the
 the echo-state property. The weights are then fixed and not learned, due to the difficulty in learning them. Instead, in this work, we devise a method of learning these recurrent weights by a formal optimization framework which naturally incorporates the constraint derived from the echo-state property. The echo-state property proposed in  \citep{jaeger2001echostate} provides a sufficient condition for avoiding the exploding gradient problem. Although such a sufficient constraint looks restrictive, it allows the RNN to be trained in a relatively easy and principled way, and the trained RNN achieves satisfactory performance on the TIMIT benchmark.

As another main contribution of this paper, we build a ``deep'' version of the RNN by using an independent DNN to extract high-level features from the raw speech data, capitalizing on the well established evidence for the power of DNNs in carrying out automatic feature extraction \citep{hinton2012deep,dahl2011large,lecun2012learning}. Having the DNN as the feature extractor and the RNN as the classifier trained separately helps reduce overfitting in the training. This strategy of building a deep version of RNNs contrasts with other strategies in the literature, where the same RNN model is stacking up on top of each other and all layers of RNNs are trained jointly. Aside from using weight noise for regularization, the overfitting problem caused by joint training of many RNNs has been circumvented mainly by exploiting elaborate structures such as LSTM \citep{graves2013speech}, making the complexity of the overall model higher and the results more difficult to reproduce than our simpler approach to building the deep version of the RNN reported in this paper.

Finally, our method exploits the DNN features in a very different way than the ``tandem'' architecture discussed in \citep{Tuske12}, where posterior outputs  at the top layer of the DNN is concatenated with the acoustic features as new inputs to an HMM system. We take the hidden layer of the DNN as the features, which are shown experimentally in our work to be much better than the top-layer posterior outputs as in the tandem method. Further, rather than using the GMM-HMM as a separate sequence classifier in \citep{Tuske12}, we use the RNN as the sequence classifier.

\section{The Recurrent Neural Network}
\label{Sec:DRNN}

\subsection{Basic architecture}
\label{Sec:DRNN:Arch}

\begin{figure}
	\centering
	\includegraphics[width = 0.48\textwidth]{Fig_DeepRNN}
	\caption{Architecture of the recurrent neural network with DNN features, where one of the hidden layers of the DNN will be
	used as input for the RNN. Arrows of different colors from the DNN to the RNN indicate alternative ways of
	providing the inputs to RNN. }
	\label{Fig:DeepRNN}
\end{figure}

We consider a deep-RNN shown in Fig. \ref{Fig:DeepRNN}. $\mathbf{y}_t'$ denotes the output of the DNN that is trained over randomly permuted input sequence, and $\mathbf{y}_t$ denotes the output of RNN corresponding to the input sequence of the original order. The
network consists of two parts: (i) a lower-level DNN, and (ii) an upper-level RNN. The major task of the lower DNN
is to extract useful features from the raw data and feed them to the upper
RNN component, which replaces HMM as a sequence classifier. The RNN in the upper level captures the temporal contextual
information in its hidden states and generates the outputs that predict
the labels of the input data in the supervised sequential prediction task such as recognizing phones or words embedded in a sentence.

\subsection{Mathematical  formulation of the RNN}
\label{Sec:DRNN:Form}

In this section, we  focus on the RNN part of the deep network, given the DNN outputs that provide input vectors $\mathbf{v}_t$'s to the RNN.
A standard RNN is described by the following equations:
	\begin{align}
		\mathbf{h}_t 	&=	\mathbf{f}\left(\mathbf{W} \mathbf{h}_{t-1} + \mathbf{W}_I \mathbf{v}_t + \mathbf{b} \right)
		\label{Equ:DRNN:Model_hiddenEqu}
					\\
		\mathbf{y}_t	&=	\mathbf{g}\left(\mathbf{U} \mathbf{h}_t \right)
		\label{Equ:DRNN:Model_outputEqu}
	\end{align}
where $\mathbf{h}_t \in \mathbb{R}^N$, $\mathbf{v}_t \in \mathbb{R}^{N_I}$ and $\mathbf{y}_t \in \mathbb{R}^{N_o}$
are vectors at discrete time $t$ that represent the hidden states, the inputs, and the outputs, respectively,
and the matrices $\mathbf{W} \in \mathbb{R}^{N \times N}$, $\mathbf{W}_I \in \mathbb{R}^{N \times N_I}$,
$\mathbf{U} \in \mathbb{R}^{N_o \times N}$, and vector $\mathbf{b} \in \mathbb{R}^{N}$ collect the recurrent weights, input weights, the output weights and the bias. The function $\mathbf{f}(\mathbf{x})$ represents the nonlinearities that are applied to each entry of the vector
$\mathbf{x}$, i.e., the nonlinear operation that is applied to the vector component-by-component:
	\begin{align}
		\mathbf{f}(\mathbf{x})	=	\begin{bmatrix}
						f(x_1) & \cdots	&	f(x_N)
					\end{bmatrix}^T
					\nonumber
	\end{align}
where $x_k$ denotes the $k$-entry of the vector $\mathbf{x}$, and each $f(x_k)$ can be sigmoid, $\tanh$ or rectified. (We will use sigmoid nonlinearity through out this work as an example.) And $\mathbf{g}(\mathbf{x})$ represents the operation applied at the output units. Typical choices are linear function $\mathbf{g}(\mathbf{x})=\mathbf{x}$ or soft-max operation.

While the standard RNN model described by \eqref{Equ:DRNN:Model_hiddenEqu} updates the hidden states $\mathbf{h}_t$ from its summary of the history $\mathbf{h}_{t-1}$ and the current input $\mathbf{v}_t$, which we call the autoregressive (AR) version, we can have a more general ARMA version described by
	\begin{align}
		\mathbf{h}_t	&=	\mathbf{f}\left(
							\mathbf{W} \mathbf{h}_{t-1}
							+
							\sum_{\tau = -\Delta_1}^{\Delta_2}
							\mathbf{W}_{I,\tau}
							\mathbf{v}_{t-\tau}
							+
							\mathbf{b}
					\right)
		\label{Equ:DRNN:Model_hiddenEqu_contextwindow}
	\end{align}
where $\Delta_1$ and $\Delta_2$ denote the number of inputs that the network looks forward and backwards. If $\Delta_1=0$, then it only looks backwards into the past history and if $\Delta_2=0$, it only looks into future. The models described by \eqref{Equ:DRNN:Model_hiddenEqu} and \eqref{Equ:DRNN:Model_hiddenEqu_contextwindow} are parallel to the vector AR and ARMA models, respectively,  in time series analysis except that the classical AR and ARMA models are linear:
	\begin{align}
		\mathrm{[AR]:~}
		\mathbf{h}_t	&=	\mathbf{W} \mathbf{h}_{t-1} + \mathbf{W}_I \mathbf{v}_t					\\
		\mathrm{[ARMA]:~}
		\mathbf{h}_t	&=	\mathbf{W} \mathbf{h}_{t-1} + \sum_{\tau = -\Delta_1}^{\Delta_2} \mathbf{W}_{I,\tau} \mathbf{v}_{t-\tau}
	\end{align}
In the context of ARMA version of the RNN, $\mathbf{W} \mathbf{h}_{t-1}$ is called AR part, and the term $\sum_{\tau = -\Delta_1}^{\Delta_2} \mathbf{W}_{I,\tau} \mathbf{v}_{t-\tau}$ is called MA part. Depending on the nature of the time sequence, some tasks are easier to be modeled by AR, and some others by MA, or jointly ARMA. Just as AR model is a special case of ARMA model ($\Delta_1=\Delta_2=0$), model \eqref{Equ:DRNN:Model_hiddenEqu} is a special case of \eqref{Equ:DRNN:Model_hiddenEqu_contextwindow}. Due to its generality, the ARMA version of the RNN \eqref{Equ:DRNN:Model_hiddenEqu_contextwindow} is expected to be more powerful than the AR version \eqref{Equ:DRNN:Model_hiddenEqu}. Indeed, our experimental results presented in Section 5 have confirmed this expectation.

A key observation we make is that in order to develop a unified learning method, \eqref{Equ:DRNN:Model_hiddenEqu_contextwindow} can be converted back to the form of \eqref{Equ:DRNN:Model_hiddenEqu} by defining some extra augmented variables. Let $\overline{\mathbf{v}}_t$ and $\overline{\mathbf{W}}_I$ be defined as
	\begin{align}
		\overline{\mathbf{v}}_t	&\triangleq		\begin{bmatrix}
										\mathbf{v}_{t-\Delta_2}^T & \cdots & \mathbf{v}_{t+\Delta_1}^T
									\end{bmatrix}^T
								\\
		\overline{\mathbf{W}}_I	&\triangleq		\begin{bmatrix}
										\mathbf{W}_{I, -\Delta_2} & \cdots & \mathbf{W}_{I, \Delta_1}
									\end{bmatrix}
	\end{align}
Then, \eqref{Equ:DRNN:Model_hiddenEqu_contextwindow} can be written in the following equivalent form:
	\begin{align}
		\mathbf{h}_t	&=	\mathbf{f}\left(
						\mathbf{W} \mathbf{h}_{t-1} + \overline{\mathbf{W}}_I \overline{\mathbf{v}}_t + \mathbf{b}
					\right)
	\end{align}
In other words, the ARMA version of the RNN model in \eqref{Equ:DRNN:Model_hiddenEqu_contextwindow} can be implemented in an equivalent manner by having a context window that slides through several input samples and deliver them as an augmented input sample. From now on, we will proceed with the simple AR model \eqref{Equ:DRNN:Model_hiddenEqu}--\eqref{Equ:DRNN:Model_outputEqu} since the general ARMA version can be reduced to the AR version by the above conversion and hence the learning method will stay unchanged from the AR version to the ARMA version. Note that another approach to letting the model look into future is the bi-directional recurrent neural network\citep{graves2013speech}, which uses information from future by letting its hidden layers depend on the hidden states at future. On the other hand, the ARMA is made to depend on future by letting its input include future. So these two methods uses information from future in two different ways and our ARMA method is relatively easier to implement and also effectively capture the future information. Furthermore, by incorporating past and future information into the inputs, the ARMA-RNN also provides a relative easy way of enhancing the amount of memory in the RNN.

\subsection{Learning the RNN and its difficulties}
\label{Sec:DRNN:Difficulties}
The standard BPTT method for learning RNNs ``unfolds'' the network in time and propagates
error signals backwards through time.
Let $J(\Theta)$ denote the cost function that measures how good the RNN predicts
the target, where $\Theta \triangleq \{ \mathbf{W}, \mathbf{W}_I, \mathbf{U}, \mathbf{b}\}$ is the set of all the parameters
to be trained. In general, the cost can be written as an average of costs over different
time instants:
	\begin{align}
		J(\Theta)	=	\frac{1}{T}\sum_{t=1}^T J_t(\mathbf{y}_t, \mathbf{d}_t)
		\label{Equ:DRNN:J_def}
	\end{align}
where $\mathbf{d}_t$ denotes the desired signal (also called target) at time $t$, and $J_t(\mathbf{y}_t,\mathbf{d}_t)$ characterizes the cost at time $t$. The cost $J_t(\mathbf{y}_t,\mathbf{d}_t)$ depends on the model parameters $\Theta$ through $\mathbf{y}_t$, which, as shown in \eqref{Equ:DRNN:Model_hiddenEqu}--\eqref{Equ:DRNN:Model_outputEqu}, further depends on $\{\mathbf{W},\mathbf{W}_I,\mathbf{U}, \mathbf{b}\}$. Typical choices of $J_t(\mathbf{y}_t, \mathbf{d}_t)$ includes squared-error and cross entropy, etc. The gradient formula for $J(\Theta)$ with respect to $\Theta \triangleq \{ \mathbf{W}, \mathbf{W}_I, \mathbf{U}, \mathbf{b}\}$ can be computed by back propagation through time (BPTT), which are given in sections \ref{Appendix:FormulaBPTT}--\ref{Appendix:Proof_BPTT} of the supplementary material.

It is well known that training RNNs is difficult
because of the exploding and vanishing gradient problems  \citep{pascanu2012difficulty}. Let
	\begin{align}
		\gamma	\triangleq		\| \mathbf{D}_f \|
	\end{align}
where $\mathbf{D}_f$ is a diagonal matrix constructed from the element-wise derivative of $\mathbf{f}(\mathbf{x})$:
	\begin{align}
		\mathbf{D}_f	\triangleq	\mathrm{diag}\{ \mathbf{f}'(\mathbf{p}_t) \}
	\end{align}
and $\|\mathbf{X}\|$ denotes the $2-$norm (the largest singular value) of the matrix $X$. For sigmoid function $\mathbf{f}(\mathbf{x})$, $\gamma = 1/4$, and for $\tanh$, $\gamma = 1$. The argument in \citep{pascanu2012difficulty} pointed out that a sufficient condition for vanishing gradient problem to occur is
	\begin{align}
		\| \mathbf{W} \| = \|\mathbf{W}^T\|	< 	\frac{1}{\gamma}
		\label{Equ:DRNN:VanishingGradient}
	\end{align}
and a necessary condition for exploding gradient to occur is that
	\begin{align}
		\| \mathbf{W} \| = \|\mathbf{W}^T\|	>	\frac{1}{\gamma}
		\label{Equ:DRNN:ExplodingGradient}
	\end{align}
Therefore, the properties of the recurrent matrix $\mathbf{W}$ is essential for the performance of the RNN. In previous work \citep{pascanu2012difficulty,mikolov2011strategies}, the way to solve the exploding gradient problem is to empirically clip the gradient if the norm of the gradient exceeds a certain threshold, and the way to avoid the vanishing gradient is also empirical --- either to add a regularization term to push up the gradient or exploit the information about the curvature of the objective function \citep{maas2012recurrent}. Below, we describe an alternative primal-dual approach for training RNN, which is based on the echo-state property, a sufficient condition for avoiding the exploding gradient problem.

\section{A New Algorithm for Learning the RNN}
\label{Sec:NewLearning}

In this section, we first discuss an essential property for the model of the kind in \eqref{Equ:DRNN:Model_hiddenEqu} --- the echo-state property, and provide a sufficient condition for it. Then, we formulate the problem of training the RNN that preserves the echo-state property as a constrained optimization problem. Finally, we develop a primal-dual method to solve the problem.

\subsection{The echo-state property}
\label{Sec:DRNN:ESN_Property}
We now show that conditions of the form \eqref{Equ:DRNN:VanishingGradient}--\eqref{Equ:DRNN:ExplodingGradient} are closely related to whether the model \eqref{Equ:DRNN:Model_hiddenEqu}--\eqref{Equ:DRNN:Model_outputEqu} satisfies the echo-state property \citep{jaeger2002tutorial}, which states that ``if the network has been run for a very long time [from minus infinity time in the definition], the current network state is uniquely determined by the history of the input and the (teacher-forced) output''. It is also shown in \citep{jaeger2001short} that this echo-state property is  equivalent to the ``state contracting'' property. Since we do not consider the case with feedback from output in the model \eqref{Equ:DRNN:Model_hiddenEqu}, we here describe the ``state contracting'' property slightly different from \citep{jaeger2001short}:
	\begin{definition}[State contracting]
		\label{Def:StateContracting}
		The network is state contracting if for all right-infinite input sequences
		$\{\mathbf{v}_t\}$, where $t = 0,1,2,\ldots$, there exists a null sequence $(\epsilon_t)_{t \ge 0}$
		such that for all starting states $\mathbf{h}_0$ and $\mathbf{h}_0'$ and for all $t > 0$ it holds that
		$\|\mathbf{h}_t - \mathbf{h}_t'\| < \epsilon_t$, where $\mathbf{h}_t$ [resp. $\mathbf{h}_t'$] is the hidden state vector
		at time $t$ obtained when the network is driven by $\mathbf{v}_t$ up to time $t$ after having been
		stated in $\mathbf{v}_0$, [resp. in $\mathbf{h}_0'$].
	\end{definition}

It is shown in \citep{jaeger2001echostate} that a sufficient condition for the \emph{non-existence}, i.e., a necessary condition for the \emph{existence}, of the echo-state property is that the spectral radius of the recurrent matrix $\mathbf{W}$ is greater than one (resp. four) when $\tanh$ (resp. sigmoid) units are used. And it is further conjectured that for a weight matrix $\mathbf{W}$ that is randomly generated by sampling the weights over uniform distribution over $[-1,1]$ and normalized such that $\rho(\mathbf{W}) = 1-\delta$ would satisfy the echo-state property with high probability, where $\delta$ is a small positive number.

In echo-state networks, the reservoir or the recurrent weights  are randomly generated and normalized according to the rule above and will be fixed over time in the training. The  input weights are fixed as well. Instead, in this paper, \emph{we learn the recurrent weights together with the input and output weights subject to the constraint that the network satisfies the echo-state property.} To this end, we propose the following sufficient condition for the echo-state property, which will be shown to be easily handled in the training procedure. The proof of the following proposition can be found in Appendix \ref{Appendix:Proof_SufficientESP}.
	\begin{proposition}[Echo-state: a sufficient condition]
		\label{Prop:ESN_sufficient}
		Let $\gamma \triangleq \max_{x}  |f'(x)|$.
		The network model \eqref{Equ:DRNN:Model_hiddenEqu} satisfies the echo-state property if
			\begin{align}
				\|\mathbf{W}\|_{\infty}		<	\frac{1}{\gamma}
				\label{Equ:Prop:ESN_sufficient}
			\end{align}
		where $\| \mathbf{W} \|_{\infty}$ denote the $\infty$-norm of the matrix $\mathbf{W}$
		(maximum absolute row sum), and $\gamma=1$ for $\tanh$ units, and
		$\gamma=1/4$
		for sigmoid units.
	\end{proposition}

The echo state property is typically assumed to capture a short-term memory in the data. However, it is reasonable for many applications, such as speech recognition, using RNNs since each phone typically lasts for fewer than 60 frames, requiring relatively short memory. Suppose we have two RNNs that run on different input sequences up to some time t so that they have different hidden states at time $t$. Afterwards, if the input acoustic sequences to the two RNNs become identical, the echo state property requires that the hidden states of these two RNNs be close to each other in order to produce the same predicted labels. Another important consequence of condition \eqref{Equ:Prop:ESN_sufficient} is that it also provides a sufficient condition to avoid the exploding gradient problem in a more principled manner. This can be shown by following the same argument as \citep{pascanu2012difficulty} except that the $2$-norm is replaced by $\infty$-norm. Thus, if the condition \eqref{Equ:Prop:ESN_sufficient} can be enforced in the training process, there is no need to clip the gradient. We will show in next section that the $\infty$-norm constraint on $\mathbf{W}$ is convenient to handle in optimization. Therefore, our proposed method below provides a relatively easy way to train RNN in a principled manner, especially on tasks that requires short memory. Learning RNN under refined characterization of its dynamics, such as \citep{manjunath2013echo}, is left as future work.

\subsection{Formal formulation of the learning problem}
\label{Sec:NewLearning:Form}
Based on the previous discussion, we can formulate the problem of training the RNN that preserves the echo-state property as the following constrained optimization problem:
	\begin{align}
		\min_{\Theta}	&	\quad J(\Theta) = J(\mathbf{W}, \mathbf{W}_I, \mathbf{U}, \mathbf{b})			\\
		\mathrm{s.t.}	&	\quad \|\mathbf{W}\|_{\infty} \le \frac{1}{\gamma}
	\end{align}
In other words, we need to find the set of model parameters that best predict the target while preserving the echo-state property. Recall that $\|\mathbf{W}\|_{\infty}$ is defined as the maximum absolute row sum. Therefore, the above optimization problem is equivalent to the following constrained optimization problem (since $\max\{x_1,\ldots, x_N\} \le 1/\gamma$ is equivalent to $x_i \le 1/\gamma, \; i=1,\ldots,N$):
	\begin{align}
		\min_{\Theta}	&	\quad J(\Theta) = J(\mathbf{W}, \mathbf{W}_I, \mathbf{U}, \mathbf{b})
		\label{Equ:NewLearn:Optimization_Objective}
							\\
		\mathrm{s.t.}	&	\quad \sum_{j=1}^N |W_{ij}|	\le 	\frac{1}{\gamma}, \quad i = 1,\ldots,N
		\label{Equ:NewLearn:Optimization_Constraint}
	\end{align}
where $W_{ij}$ denotes the $(i,j)$-th entry of the matrix $\mathbf{W}$. Next, we will proceed to derive the learning algorithm that can achieve this objective.

\subsection{Primal-dual method for optimizing RNN parameters}
\label{Sec:NewLearning:PD}
We solve the constrained optimization problem \eqref{Equ:NewLearn:Optimization_Objective}--\eqref{Equ:NewLearn:Optimization_Constraint} by primal-dual method. The Lagrangian of the problem can be written as
	\begin{align}
		\mathcal{L}(\Theta, \bm{\lambda})
			=	J(\mathbf{W}, \mathbf{W}_I, \mathbf{U}, \mathbf{b})
				\!+\!
				\sum_{i=1}^N \lambda_i \left(\sum_{j=1}^N |W_{ij}| \!-\! \frac{1}{\gamma}\right)
		\label{Equ:NewLearn:Lagrangian}
	\end{align}
where $\lambda_i$ denotes the $i$th entry of the Lagrange vector $\bm{\lambda}$ (or dual variable) and is required to be non-negative. Let the dual function $q(\bm{\lambda})$ be defined as the following \emph{unconstrained} optimization problem:
	\begin{align}
		q(\bm{\lambda})	=	\min_{\Theta} \mathcal{L}(\Theta,\bm{\lambda})
		\label{Equ:NewLearn:DualFunc_def}
	\end{align}
It is shown that the dual function $q(\bm{\lambda})$ obtained from the above unconstrained optimization problem is always concave, even when the original cost $J(\Theta)$ is not convex \citep{boyd2004convex}. And the dual function is always a lower bound of the original constrained optimization problem \eqref{Equ:NewLearn:Optimization_Objective}--\eqref{Equ:NewLearn:Optimization_Constraint}: $q(\bm{\lambda}) \le J(\Theta^{\star})$. Maximizing $q(\bm{\lambda})$ subject to the constraint $\lambda_i \ge 0$, $i=1,\ldots, N$ will be the best lower bound that can be obtained from the dual function \citep{boyd2004convex}. This new problem is called the dual problem of the original optimization problem \eqref{Equ:NewLearn:Optimization_Objective}--\eqref{Equ:NewLearn:Optimization_Constraint}:
	\begin{align}
		\max_{\bm{\lambda}}	&	\quad q(\bm{\lambda})
		\label{Equ:NewLearn:OptimizationDual_Objective}
							\\
		\mathrm{s.t.}	&	\quad \lambda_i \ge 0, \quad i = 1,\ldots,N
		\label{Equ:NewLearn:OptimizationDual_Constraint}
	\end{align}
which is a convex optimization problem since we are maximizing a concave objective with linear inequality constraints. After solving $\bm{\lambda}^{\star}$ from \eqref{Equ:NewLearn:OptimizationDual_Objective}--\eqref{Equ:NewLearn:OptimizationDual_Constraint}, we can substitute the corresponding $\bm{\lambda}^{\star}$ into the Lagrangian \eqref{Equ:NewLearn:Lagrangian} and then solve the correponding set of parameters $\Theta^o=\{\mathbf{W}^o, \mathbf{W}_I^o, \mathbf{U}^o, \mathbf{b}^o\}$ that minimizes $\mathcal{L}(\Theta,\bm{\lambda})$ for this given $\bm{\lambda}^{\star}$:
	\begin{align}
		\Theta^o		=	\arg\min_{\Theta} \mathcal{L}(\Theta, \bm{\lambda}^{\star})
	\end{align}
Then, the obtained $\Theta^o=\{\mathbf{W}^o, \mathbf{W}_I^o, \mathbf{U}^o, \mathbf{b}^o\}$ will be an approximation to the optimal solutions. In convex optimization problems, this approximate solution will be the same global optimal solution under some mild conditions \citep{boyd2004convex}. This property is called strong duality. However, in general non-convex problems, it will not be the exact solution. But since finding the globally optimal solution to the original problem \eqref{Equ:NewLearn:Optimization_Objective}--\eqref{Equ:NewLearn:Optimization_Constraint} is not realistic, it would be satisfactory if it can provide a good approximation.

Back to the problem \eqref{Equ:NewLearn:OptimizationDual_Objective}--\eqref{Equ:NewLearn:OptimizationDual_Constraint}, we are indeed solving the following problem
	\begin{align}
		\max_{\bm{\lambda} \succeq \bm{0}} \min_{\Theta} \mathcal{L}(\Theta, \bm{\lambda})
	\end{align}
where the notation $\bm{\lambda} \succeq \bm{0}$ means that each entry of the vector $\bm{\lambda}$ is greater than or equal to zero. \emph{Now, to solve the problem, what we need to do is to minimize the Lagrangian $\mathcal{L}(\Theta, \bm{\lambda})$ with respect to $\Theta$, and in the mean time, maximize the dual variable $\bm{\lambda}$ subjected to the constraint that $\bm{\lambda} \succeq \bm{0}$}. Therefore, as we will see soon, updating the RNN parameters consists of two steps: \emph{primal update} (minimization of $\mathcal{L}$ with respect to $\Theta$) and \emph{dual update} (maximization of $\mathcal{L}$ with respect to $\bm{\lambda}$).

First, we provide the primal update rule.
To minimize the Lagrangian $\mathcal{L}(\Theta,\bm{\lambda})$ with respect to $\Theta$, we may apply gradient descent to $\mathcal{L}(\Theta,\bm{\lambda})$ with respect to $\Theta$. However, note that $\mathcal{L}(\Theta,\bm{\lambda})$ consists of two parts: $J(\Theta)$ that measures the prediction quality, and the part that penalizes the violation of the constraint \eqref{Equ:NewLearn:Optimization_Constraint}. Indeed, the second part is a sum of many $\ell_1$ regularization terms on the rows of the matrix $\mathbf{W}$:
	\begin{align}
		\sum_{j=1}^N |W_{ij}|	=	\| \mathbf{w}_i \|_{1}
	\end{align}
where $\mathbf{w}_i$ denotes the $i$th row vector of the matrix $\mathbf{W}$. With such observations, the Lagrangian in \eqref{Equ:NewLearn:Lagrangian} can be written in the following equivalent form:
	\begin{align}
		\mathcal{L}(\Theta, \bm{\lambda})
			=	J(\mathbf{W}, \mathbf{W}_I, \mathbf{U}, \mathbf{b}) + \sum_{i=1}^N \lambda_i \left(\|\mathbf{w}_i\|_1 - \frac{1}{\gamma}\right)
	\end{align}
To Minimize $\mathcal{L}(\Theta,\bm{\lambda})$ of the above structure with respect to $\Theta = \{\mathbf{W},\mathbf{W}_I,\mathbf{U}, \mathbf{b}\}$, we can apply an argument similar to the one made in \citep{beck2009fast} to derive the following iterative soft-thresholding algorithm for the primal update of $\mathbf{W}$:
	\begin{align}
		\mathbf{W}_k		&=	\mathcal{T}_{\bm{\lambda} \mu_k}\!
					\left\{
						\mathbf{W}_{k-1} \!-\! \mu_k \frac{\partial J(\mathbf{W}_{k\!-\!1},\mathbf{W}_{I,{k\!-\!1}},\mathbf{U}_{k\!-\!1}, \mathbf{b}_{k\!-\!1})}{\partial \mathbf{W}}
					\right\}
		\label{Equ:NewLearn:primalUpdate_W}
	\end{align}
where $\mathcal{T}_{\bm{\lambda} \mu_k}(\mathbf{X})$ denote a component-wise shrinkage (soft-thresholding) operator on a matrix $\mathbf{X}$, defined as
	\begin{align}
		[\mathcal{T}_{\bm{\lambda} \mu_k}(\mathbf{X})]_{ij}
				=	\begin{cases}
						X_{ij} - \lambda_i \mu_k	&	X_{ij} \ge \lambda_i \mu_k			\\
						X_{ij} + \lambda_i \mu_k	&	X_{ij} \le -\lambda_i \mu_k			\\
						0						& 	\mathrm{otherwise}
					\end{cases}
	\end{align}
Note that the primal update for $\mathbf{W}$ is implemented by a standard (stochastic) gradient descent followed by a shrinkage operator.
On the other hand, the primal updates for $\mathbf{W}_I$, $\mathbf{U}$ and $\mathbf{b}$ follow the standard (stochastic) gradient descent rule:
	\begin{align}
		\mathbf{W}_{I,k}	&=	\mathbf{W}_{I,k-1} - \mu_k \frac{\partial J(\mathbf{W}_{k-1},\mathbf{W}_{I,k-1},\mathbf{U}_{k-1}, \mathbf{b}_{k-1})}{\partial \mathbf{W}_I}
		\label{Equ:NewLearn:primalUpdate_WI}
					\\
		\mathbf{U}_{k}		&=	\mathbf{U}_{k-1} - \mu_k \frac{\partial J(\mathbf{W}_{k-1},\mathbf{W}_{I,k-1},\mathbf{U}_{k-1}, \mathbf{b}_{k-1})}{\partial \mathbf{U}}
		\label{Equ:NewLearn:primalUpdate_U}
					\\
		\mathbf{b}_k			&=	\mathbf{b}_{k-1} - \mu_k \frac{\partial J(\mathbf{W}_{k-1},\mathbf{W}_{I,k-1},\mathbf{U}_{k-1}, \mathbf{b}_{k-1})}{\partial \mathbf{b}}
		\label{Equ:NewLearn:primalUpdate_b}
	\end{align}
In order to accelerate the convergence of the algorithm, we can, for example, add momentum or use Nesterov method \citep{sutskever2013importance} to replace the gradient descent steps in \eqref{Equ:NewLearn:primalUpdate_W}--\eqref{Equ:NewLearn:primalUpdate_U}. In our experiments reported in Section 5, we adopted Nesterov method to accelerate the training process.

Next, we describe the dual update, which aims to maximize $\mathcal{L}$ with respect to $\bm{\lambda}$ subject to the constraint that $\bm{\lambda}\succeq \bm{0}$. To this end, we use the following rule of gradient ascent with projection, which increases the function value of $\mathcal{L}$ while enforcing the constraint:
	\begin{align}
		\lambda_{i,k}	=	\left[
								\lambda_{i,k-1}
								+
								\mu_k
								\left(
									\|\mathbf{w}_{i,k-1}\|_1 - \frac{1}{\gamma}
								\right)
							\right]_{+}
		\label{Equ:NewLearn:DualUpdate}
	\end{align}
where $[x]_{+} \triangleq \max\{0,x\}$. Note that $\lambda_i$ is indeed a regularization factor in $\mathcal{L}(\Theta,\bm{\lambda})$ that penalizes the violation of constraint \eqref{Equ:NewLearn:Optimization_Constraint} for the $i$th row of $\mathbf{W}$. The dual update can be interpreted as a rule to adjust the regularization factor in an adaptive manner. When the sum of the absolute values of the $i$th row of $\mathbf{W}$ exceeds $1/\gamma$, i.e., violating the constraint, the recursion \eqref{Equ:NewLearn:DualUpdate} will increase the regularization factor $\lambda_{i,k}$ on the $i$th row in \eqref{Equ:NewLearn:Lagrangian}. On the other hand, if the constraint \eqref{Equ:NewLearn:Optimization_Constraint} for a certain $i$ is not violated, i.e., $\|\mathbf{w}_i\|_1 < 1/\gamma$, then the dual update \eqref{Equ:NewLearn:DualUpdate} will decrease the value of the corresponding $\lambda_i$ so that $\|\mathbf{w}_i\|_1 - 1/\gamma$ is less penalized in \eqref{Equ:NewLearn:Lagrangian}. This process will repeat itself until the constraints \eqref{Equ:NewLearn:Optimization_Constraint} are satisfied. The projection operator $[x]_{+}$ makes sure that once the regularization factor $\lambda_i$ is decreased below zero, it will be set to zero and the constraint for the $i$th row in \eqref{Equ:NewLearn:OptimizationDual_Constraint} will not be penalized in \eqref{Equ:NewLearn:Lagrangian}. An alternative choice to enhance the constraint is to apply projection operator to $\mathbf{W}$ after each stochastic gradient descent update \eqref{Equ:NewLearn:primalUpdate_WI}--\eqref{Equ:NewLearn:primalUpdate_b}.

\section{Experiments and Results }
\label{Sec:ExperimentSetup}

\begin{table*
   \centering
    \caption{Phone recognition error (percent) on the TIMIT core test set using DNN-top feature sequences as the input to the RNNs. The results are shown as a function
of two hyperparameters: the size of the RNN's hidden layer and the moving-average order of the RNN. }
\begin{tabular}{|c|c|c|c|c|c|c|c|c| }
            \hline
           HiddenSz& Order=0 &Order=2   & Order =4  & Order=6  &Order=8   & Order=10  & Order=12 \ \\
            \hline \hline
            100       &  19.85     & 19.83      &  19.80      &    19.65   &  19.50      &  19.44       & 19.42        \  \\
            200       &  19.86     & 19.72      &  19.65      &    19.60   &  19.45      &  19.35       & 19.31        \  \\
            300       &  20.02     & 19.72      &  19.60      &    19.56   &  19.40      &  19.23       & 19.16        \  \\
            500       &  20.00     & 19.73      &  19.56      &    19.44   &  19.34      &  19.06       & 18.91        \  \\
          1000       &  20.44     & 19.83      &  19.60      &    19.49   &  19.24      &  19.10       & 18.98        \  \\
          2000       &  20.70     & 20.34      &  20.10      &    19.65   &  19.45      &  19.30       & 19.12        \  \\
            \hline
        \end{tabular}
    \label{tab:Accuracy}
\end{table*}

\begin{table*}
\renewcommand{\arraystretch}{1.3}
	\centering
	\caption{Phone recognition error as a function of the clipping threshold (\citep{mikolov2011strategies}; \citep{pascanu2012difficulty}). The lowest error 19.05\% around threshold 1.0 is nevertheless higher than 18.91\% obtained by the new primal-dual method without tuning parameters.}
	\label{Tab:BPTT_gradclip}

	\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
		\hline
		Threshold & 1 & 2 & 0.5 & 9 & 1.0 & 1.1 & 1.5 & 2 & 10 \\
		\hline
		Phone error (\%) & 19.65 & 19.50 & 19.25 & 19.10 & 19.05 & 19.08 & 19.15 & 19.54 & 20.5 \\
		\hline
	\end{tabular}

\end{table*}

We use the TIMIT phone recognition task to evaluate the deep-RNN architecture and the primal-dual optimization method for training the
RNN part of the network.  The standard 462-speaker training set is used and all SA sentences are removed conforming to the standard protocol \citep{lee1989speaker,hinton2012deep,deng2013deep}. A separate development set of 50 speakers is used
for tuning all hyper parameters. Results are reported using the 24-speaker core
test set, which has no overlap with the development set.

In our experiments, standard signal processing techniques are used for the raw speech waveforms, and 183 target class labels are used with three states for each of 61 phones.  After decoding, the original 61 phone classes are mapped to a set of 39 classes for final scoring according to the standard evaluation protocol.  In our experiments, a bi-gram language model over
phones, estimated from the training set, is used in decoding. To prepare the DNN and RNN targets, a high-quality tri-phone HMM model is trained on the training data set, which is then used to generate state-level labels based on HMM forced alignment.

The DNN as part of the baseline described in \citep{deng2013deep} is used in this work to extract the high-level features from raw speech features. That is, the DNN features are discriminatively learned.
In our experiments, we use a DNN with three hidden layers, each having 2000 units. Each hidden layer's output vector, with a dimensionality of 2000, can be utilized as the DNN features. Thus, we have three sets of high-level features: DNN-top, DNN-middle, and DNN-bottom, indicated in Figure 1 with three separate colors of arrows pointing from DNN to RNN.

We first report the phone recognition error performance of the deep-RNN using the DNN-top features. In Table \ref{tab:Accuracy},
the percent error results are shown as a function of the RNN hidden layer's size, varying from 100 to 2000, and also as a function of the moving average (MA) order in the RNN.
Note when MA order is zero, the ARMA version of the RNN reverts to the traditional AR version.

The above results are obtained using the fixed insertion penalty of zero and the fixed bi-phone ``language model'' weight of one.
When the language model's weight is tuned slightly over the development set, the core test set error further drops to
18.86\%,
which is close to the best numbers reported recently
on this benchmark task in \citep{deng2013deep} using deep  convolutional neural networks with special design of the pooling strategy (18.70\%) and in \citep{graves2013speech} using a bi-directional RNN with special design of the memory structure (17.7\%). No bi-directionality and no special design on any structure are used in the RNN reported in this paper.
The confusion matrix of this best result is shown in Section \ref{Appendix:ConfusionMatrix} of the supplementary document.

We next compare the new primal-dual training method with the classical BPTT using gradient clipping as described in \citep{pascanu2012difficulty}. Table \ref{Tab:BPTT_gradclip} shows the the phone recognition error of the classical BPTT with gradient clipping on the TIMIT benchmark. We found that the error rate is sensitive to the threshold value. The best phone error rate on the test set is found to be between 19.05\%-20.5\% over a wide range of the threshold values where the best tuned clipping threshold is around 1.0 which corresponds to the error rate of 19.05\%. This is higher than the 18.91\% from our primal-dual method (without tuning the language model weights). Thus, using the new method presented in the paper, we do not need to tune the hyper-parameter of clipping threshold while obtaining lower errors.

We finally show the phone recognition error (percent) results for the features of DNN-middle, DNN-bottom, and of raw filter-bank data.
The size of the RNN's hidden layer is fixed at 500. And the results for four different MA orders are shown in Table \ref{tab:methods}.

\begin{table
  \centering
    \caption{Phone recognition error (percent) on the TIMIT core test set using DNN-middle and DNN-bottom features, as well as the raw filter-bank features. }
\begin{tabular}{|c|c|c|c|c| }
            \hline
         Features              & Order0 &Order4   & Order8  & Order12   \ \\
            \hline \hline
            DNN-Middle       &  20.70     & 20.30      &  19.96      &    19.65          \  \\
            DNN-Bottom      &  23.10     & 22.65      &  22.00      &    21.50          \  \\
            Filter-Banks       &  30.50     & 30.15      &  29.40      &    28.15          \  \\
            \hline
        \end{tabular}
    \label{tab:methods}
\end{table}

Comparisons among the results in Tables \ref{tab:Accuracy} and \ref{tab:methods} on phone recognition provide strong evidence that the high-level features extracted by DNNs are extremely useful for lowering recognition errors by the RNN. Further, the higher hidden layers in the DNN are more useful than the lower ones, given the same dimensionality of the features (fixed at 2000 as reported in this paper but we have the same conclusion for all other dimensions we have experimented). In addition, the introduction of MA components in the traditional AR version of the RNN also contributes significantly to reducing recognition errors.

\section{Discussion and Conclusion}
\label{Sec:Discussion}

The main contribution of the work described in this paper is a formulation of the RNN that lends itself to effective learning using a formal optimization
framework with a natural inequality constraint that provides a sufficient condition to guarantee the stability of the RNN dynamics during learning. This new learning method overcomes the
challenge of the earlier echo-state networks that typically fixed the recurrent weights due to the well-known difficulty in learning them. During the development of our new method, we propose a sufficient condition for the echo-state property, which is shown to be easily incorporated in the training procedure. We also make contributions to a new deep-RNN architecture, where the MA part is added to the original AR-only version of the RNN. The learning of both AR and ARMA versions of the RNN is unified after re-formulation of the model, and hence the same learning method developed can be applied to both versions.

The experimental contributions of this work are of four folds. First, we successfully apply the new learning method for the RNN to achieve close-to-record low error rates in phone recognition in the TIMIT benchmark. Second, we demonstrate the effectiveness of using DNNs to extract high-level features from the speech signal for providing the inputs to the RNN. With a combination of the DNN and RNN, we form a novel architecture of the deep-RNN, which, when trained separately, mitigates the overfitting problem. Third, on the same TIMIT benchmark task, we demonstrate clear superiority of the ARMA version of the RNN over the traditional AR version. The same efficient learning procedure is applied to both versions, with the only difference in the additional need to window the DNN outputs in the ARMA version of the RNN. Fourth, we show experimentally that the new training method motivated by optimization methodology achieves satisfactory performance as a sequence classifier on TIMIT benchmark task. Compared to the previous methods \citep{mikolov2011strategies,pascanu2012difficulty} of learning RNNs using heuristic rules of truncating gradients during the BPTT procedure,  our new method reports slightly lower phone recognition errors on the TIMIT benchmark and no longer needs to tune the threshold parameter as in the previous methods.

redpajama_set_name: RedPajamaArXiv


text:
<?php

namespace Respect\Validation\Exceptions\CountrySubdivision;

use Respect\Validation\Exceptions\CountrySubdivisionException;

/**
 * Exception class for Cape Verde country subdivision.
 *
 * ISO 3166-1 alpha-2: CV
 */
class CvCountrySubdivisionException extends CountrySubdivisionException
{
    public static $defaultTemplates = array(
        self::MODE_DEFAULT => array(
            self::STANDARD => '{{name}} must be a country subdivision of Cape Verde',
        ),
        self::MODE_NEGATIVE => array(
            self::STANDARD => '{{name}} must not be a country subdivision of Cape Verde',
        ),
    );
}

redpajama_set_name: RedPajamaGithub


Blood is a specialized bodily fluid that contains red blood cells, white blood cells, plasma, and platelets. It is essential for transporting nutrients, oxygen, and waste as well as fighting infection and regulating body temperature. In addition, fetal DNA is present in maternal blood and is used to screen for genetic disorders such as aneuploidy.
Whole human maternal blood is collected from aneuploidy positive pregnancies verified by chorionic villus sampling (CVS) or an amniocentesis at varying gestations and demographics in 10 mL aliquots containing the anticoagulant Na-heparin. Maternal donors are recallable after 8 weeks of prior donation. IDS testing can be requested for each donor.


Compare Marda Loop real estate reviews, community reviews, Top real estate agents. Browse our Marda Loop real estate reviews directory of user generated reviews, REALTORS® & Marda Loop real estate agents.
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text:
<?xml version="1.0" ?>

<container xmlns="http://symfony.com/schema/dic/services"
           xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
           xsi:schemaLocation="http://symfony.com/schema/dic/services http://symfony.com/schema/dic/services/services-1.0.xsd">
    <services>
        <service id="Integrated\Bundle\StorageBundle\DataFixtures\MongoDB\LoadFixtureData" autowire="true" autoconfigure="true">
            <argument type="service" id="nelmio_alice.files_loader.simple" on-invalid="null" />
            <tag name="doctrine.fixture.odm" />
        </service>

        <service id="integrated_storage.data_fixtures.faker.image_provider" class="Integrated\Bundle\StorageBundle\DataFixtures\Faker\Provider\ImageProvider">
            <argument type="service" id="integrated_storage.manager" />
            <tag name="nelmio_alice.faker.provider" />
        </service>

        <service id="integrated_storage.data_fixtures.faker.video_provider" class="Integrated\Bundle\StorageBundle\DataFixtures\Faker\Provider\VideoProvider">
            <argument type="service" id="integrated_storage.manager" />
            <tag name="nelmio_alice.faker.provider" />
        </service>
    </services>
</container>


Park Operating hours are subjected to changes without prior notice, guest may visit www.rwsentosa.com for updates prior.
Please print and present e-ticket to exchange admission ticket(s) at Kindly present your Universal Studios Singapore® Redemption Voucher at Resorts World Sentosa, Kiosk No. 9 Location (***Basement 1 coach bay drop off area ) to exchange your Admission tickets.


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One of the most common reasons for heating repair service in New Jersey is a gas furnace that won't ignite. In New Jersey's frigid winter climate, it's nearly impossible to go without a working heater for very long at all. A failing ignition can make your gas furnace unusable, creating a serious problem for you and your family. There are several different reasons why your electric ignition or pilot light might not be working correctly. In most cases, you'll probably have to call a professional for heating repair service.
Gas furnaces can use a couple of different kinds of devices to provide the ignition source that allows the gas to burn, warming the air in your home. These mechanisms can be either flame-based, or electrical.
Pilot lights. The pilot light may be the most familiar type of gas furnace ignition. A pilot light is a small, gas-powered flame, which ignites another, more powerful gas burner.
Intermittent pilot switches. These use a small electric spark to ignite the gas.
Hot surface switches. As the name suggests, hot surface switches use an electric heating element that causes the gas to ignite.
A gas furnace from manufacturers like Trane, York, and Carrier may use any of these types of ignition systems, and it's useful to know whether yours has a pilot light or an electrical ignition switch.
End of lifecycle. Although a gas furnace itself can last for up to fifteen years with occasional furnace repairs, some elements will need to be replaced sooner. One of these elements is a hot surface ignition switch. These are only designed to last for about three years before they fail, at which point a heating repair contractor will need to install a replacement part.
Improper handling. If you mess with the ignition switch without knowing what you're doing, you could damage it accidentally. Heating repair and furnace maintenance are best handled by a trained HVAC professional.
Running the ignition switch too high. This can damage the electric ignition, causing it to fail prematurely.
Dust and dirt buildup. Over time, dust, dirt, and debris can build up on your furnace's electric ignition. If the problem gets severe enough, it can impede your furnace's ability to ignite.
Faulty control boards. Sometimes, the problem isn't the ignition itself, but your gas furnace's control board. This component is complicated to fix, so you'll almost certainly need professional heating repairs.
Faulty safety switch. The safety switch is a very important safety feature, since a natural gas leak is both highly toxic, and a serious fire hazard. If something's wrong with the safety switch, your gas furnace may fail to ignite.
Tripped circuit breaker. Fortunately for homeowners, this is fairly simple to fix.
Thermostat problems. If the problem isn't your electrical ignition, it might be a faulty thermostat. If so, you may want to replace it with an energy-saving programmable thermostat.
Problems with the thermocouple. A thermocouple is a safety mechanism that detects whether or not the pilot light is lit, using a metal rod connected to the gas valve. This is responsible for lighting the burners. If the pilot light is out, the thermocouple will shut off the gas supply, so that natural gas can't build up inside the furnace and explode when reignited. Thermocouples can come loose and malfunction, in which case they'll need to be tightened. They can also be compromised by dirt and dust buildup, which causes it to take mistaken readings about the status of the pilot light.
Faulty gas valve. The gas valve opens up to release natural gas into the burners. If it's malfunctioning, your pilot light won't ignite– a crucial safety mechanism. You'll probably need professional heating repairs to fix it safely.
Cracked heat exchanger. This furnace component separates the warming flame from your household air supply. It's important for containing the dangerous fumes, such as carbon monoxide, that are released during the combustion of natural gas, propane, and other fossil fuels. A cracked heat exchanger is a serious problem, since it creates the potential for a fire or deadly carbon monoxide leak. Cracks usually result either from overheating, or from rusting and corrosion over time. Either way, a furnace repair technician will need to replace the heat exchanger to restore heating to your home, as well as ensuring your safety.
When your pilot light or electric ignition fails on your gas furnace, it can be a miserable experience. It doesn't take long for the warmth in your indoor air to dissipate, leaving your home freezing cold and incredibly uncomfortable. During very low temperatures, this can even become dangerous. If you can't successfully relight your pilot light, or your electric ignition isn't working, you shouldn't try to fix it yourself. Gas furnaces are complex devices, as well as presenting potential dangers in the form of fires, explosions, and carbon monoxide.
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text:
9 Facts Proving Slavery Was Responsible for American and European Economic Success
Curtis Bunn
Cotton Drove U.S. Economic Growth
According to the Gilder Lehrman Institute of American History, cotton provided over half of all U.S. export earnings. By 1840, the South grew 60 percent of the world's cotton and provided some 70 percent of the cotton used by the British textile industry. Thus, according to the institute, slavery paid for a substantial share of the capital, iron, and manufactured goods that laid the basis for American economic growth.
Enslaved Africans Represented a Significant Amount of Wealth in the Southern U.S.
When Abraham Lincoln signed the Emancipation Proclamation — which freed enslaved Africans only in the rebellious states and territories of the U.S. — approximately $10 trillion in today's money was eliminated from the American economy with a stroke of his pen, according to MeasuringWorth.com. The Three-Fifths Compromise in the U.S. Constitution allowed the Southern states to count enslaved people as three-fifths of a person for the purpose of calculating states' representation in the U.S. Congress. And so, the balance of power between slaveholding and non-slaveholding states turned, in part, on the three-fifths presence of enslaved Africans in the census. Slaveholders were taxed on the same three-fifths principle. Taxes paid on the enslaved supported the national treasury. So, the slavery system in the United States was a national system that touched the very core of its economic and political life.
Benefits of Slavery
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Mississippi Cemetery Crews Find 119 Unmarked Graves of Enslaved Africans During Maintenance Work
'We're Not a Broke Country': Congresswoman Jackson Alleviates Concerns About Who's Responsible for Slavery Reparations
Research by Black Female Professor Reveals Startling Truth That White Women Made Up 40% of Slaveowners

redpajama_set_name: RedPajamaCommonCrawl


text:
The story of A Rock in the Water is quite simple. After a lengthy and bloody civil war, the new King (Creon) is trying to heal a broken country. There were two rival brothers who caused the war and they are now both dead. He decrees that the brother who led the winning faction should be buried with full honours and the other brother must rot outside the city walls. The King has decreed and the law is the law – and must be obeyed by everybody. Creon's niece Antigone is the sister of the two slain brothers. Her family and moral duty is to bury her traitorous brother. So here we have the immovable object (Creon) and the irresistible force (Antigone).
Scholars believe that when Sophocles first wrote the Tale of Antigone in the fourth century BC it was an attack on Pericles and the new democracy of Athens. For Pericles' democracy to work it had to override both local and family traditions. The success of the play reflected that Sophocles was not alone with that thought. Since then the story of Antigone has been a constant source for interpretation. Theatre, Dance and Opera have all explored her story.
Simon Denver
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Drama, Historical
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This is a story as old as time. Conscience versus State. There are some that could argue that in our modern times both Julian Assange and Aung San Suu Kyi are still dancing this eternal dance. We all face this dilemma in both minor and major incarnations – what to do when you believe you are right even when the government, your peer group and your family and friends tell you that you are wrong?
Simon Denver's adaption of this classic Greek tale has won awards at every theatre festival it's been entered in to, and with good reason. It's not only challenging for the actors but causes ripples in the audience for them to contemplate – if they were in such a horrible situation as Antigone, would they follow their heads, or their hearts?
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Sample: How the West Was Warped


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Q: Did Sauron ever find out that Isengard was attacked? Did Sauron ever find out that Isengard was attacked?  Saruman would probably be reluctant to tell him.  Sauron was probably watching more important things at the time, like the Battle of Helm's Deep, preparing the attack on Minas Tirith, and later the battle at the Black Gate.  Did Sauron find out that Isengard had been defeated before the ring was destroyed?

A: Gandalf believed Sauron did not immediately learn of the fall of Isengard.
In the books, after Pippin looked into the Palantir which Grima Wormtongue had thrown down from Orthanc, Gandalf surmised that Sauron believed Pippin had been taken prisoner by Saruman and made to look into the Palantir as an act of cruelty.
From this, we can guess that Sauron was unable, or unwilling, to simply look through his own Palantir and see what had happened to Isengard.
The question was not explicitly raised again -- the main characters were focused on more urgent matters, just as Sauron was. (Edit: This is incorrect, as noted in other answers -- it was discussed, and Sauron sent a Nazgul to Isengard to investigate.)
However, it was not in Sauron's nature to trust Saruman. He almost certainly had spies in Isengard. One of these would eventually report back. It might only take a day or two if the agent had a fast way of sending messages (through birds like Saruman's crows, or by making contact with one of the Nazgul). On the other hand, travelling overland from Isengard to Mordor would have taken some weeks, especially since the agent would have to be wary of patrols from Rohan or Gondor.
So Sauron probably learned of the fall of Isengard before the destruction of the Ring, but it is plausible that word might not have reached him in time.

A: Yes. At the Black Gate (The Black Gate Opens, the Return of the King), the Mouth of Sauron says

West of the Anduin as far as the Misty Mountains and the Gap of Rohan
  shall be tributary to Mordor, and men there shall bear no weapons, but
  shall have leave to govern their own affairs. But they shall help to
  rebuild Isengard which they have wantonly destroyed...

A: Yes.
In The Two Towers, Book 3 Chaper 11 (The Palantir) a Nazgul travels to Isengard shortly after Pippin looks into the Palantir:

'Nazgul!' he cried. 'The messenger of Mordor. The storm is coming. The Nazgul have crossed the River! Ride, ride! Wait not for the dawn! Let not the swift wait for the slow! Ride!'

Later in the same chapter Gandalf confirms the purpose of this messenger:

A messenger has been sent to find out what he is doing. And after what has happened tonight another will come, I think, and swiftly. So Saruman will come to the last pinch of the vice that he has put his hand in. He has no captive to send. He has no Stone to see with, and cannot answer the summons. Sauron will only believe that he is withholding the captive and refusing to use the Stone. It will not help Saruman to tell the truth to the messenger. For Isengard may be ruined, yet he is still safe in Orthanc.

He also speculates some on other information that the Nazgul might learn:

It may be that the counsels of the Enemy will be confused, or hindered by his wrath with Saruman. It may be that he will learn that I was there and stood upon the stairs of Orthanc – with hobbits at my tail. Or that an heir of Elendil lives and stood beside me.

So Sauron certainly knew that Isengard had been destroyed at some point during or, at latest, shortly after Gandalf's and Pippin's ride to Minas Tirith, and may have even had more information.

redpajama_set_name: RedPajamaStackExchange


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Roman Emperor Elagabalus paper
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Roman Emperor ElagabalusAmor Diaz
Roman Emperor Elagabalus When we think about Rome the first thing that usually comes to mind is gladiators, power, emperor and many stories that fascinates us but when you do research in to it you will find that there is a part of their history that is not so glamorous. A history full of what many will call evil acts against humanity preform by does who were in charge of the safety of the people, the emperors them self. Acts that went anywhere from rape to virgins to using innocent children as human sacrifices. An example of this is one of Rome's youngest emperors Elagabalus.
Elagabalus is considered by many as one of the most bizarre Emperor s of Rome history. He was the nephew of Emperor Caracalla and was raise by his grandmother after his mother and her lover where caught plotting against the throne in an effort to make him Rome's Emperor. Ha His original name was Varius Avitus Bassianus, he began to be known as Elagabalus after he became the priest of the deity El-Gabal, a Syrian phallic-oriented cult which he attempted to introduce in Rome once he became emperor this was one of many crazy ideas and ideologies that his ruling will bring. His sexuality has been a source of debate since he was known to be a transvestite and a masochist, who often toyed with the idea of castrating himself but ultimately opted for only having himself circumcise.
He was also well known for his sexual excesses an example of this was that he broke into the secret sanctuary of Vesta and raped Aquilia Severa, a chaste Vestal Virgin. By Roman law any Vestal who had any sexual interaction had to be buried alive, but Elagabalus decided to married her, in hopes for 'god-like children'. They divorce soon after although he will go on to married four other women also ending their relationships in divorce, many say his sexuality play a role in this decision. He enjoyed dressing as a woman and used make up to paint his eyes and rouge his cheeks and he also used to depilate all over his body. It was also knowing that Elagabalus was bisexual and, something that was not uncommon back in does days since Emperors in that era were well known to associated them self with boys young age as a sideline to their heterosexual activities.
He was also known as an evil man because of the terrible and evil nature crimes supposedly committed by him like used of children as human sacrifice. There are allegations that Elagabalus had claimed that he did not killed kids for his own benefit but instead he did it to get the favor of the gods for everyone who was part of Roman Empire. Other crimes were allowing the practice of gladiatorial games instead of banding the use of this barbaric activity. Another practice he allowed Romans to have was slavery, instead he allowed slave owners to continue buying new slaves without any consequences. And last but not least, he had no problems allowing parents to kill their own children whenever they felt like it especially if the child was an unwanted one.
In March 13 of 222, after four years of cruelty Romans had enough of Elagabalus evilness and had him and his mother executed, they were beheaded, dragged through the streets of Rome and subsequently dumped into the Tiber. He was only eighteen-years-old and at the time. (Donald 2013)
1. Wasson D. (October, 2013) Elagabalus, Ancient History Encyclopedia
2. Weingarten J. (November 2011) The crimes of Elagabalus:
The life and legacy of Rome's decadent boy emperor, The World University Ranking
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Q: What's the correct way to marshal a const float**? I'm trying to read an array that's created by pinvoking a dll function from C#. When I print out the array's contents it's actually full of junk.
I suspect this is happening because I am incorrectly marshalling a const float** to an out IntPtr. How do you properly marshal a const float**?
DLL C++ Interface
int Foo(void *objPtr, uint64_t *resultLen, const float **result);

DLL Import Statement
[DllImport("foo.dll", CharSet = CharSet.Auto)]
public static extern int Foo(IntPtr objPtr, out ulong resultLen, out IntPtr result);

Calling Code
IntPtr objPtr = getObj();
IntPtr result;
ulong resultLen;
int output = Foo(objPtr, out resultLen, out result);

A: Because there is no way to tell the marshaler the size of the array ahead of time you will have to copy the array manually. So out IntPtr is correct.
Note you will have a problem with very large arrays. See https://msdn.microsoft.com/en-us/library/hh285054(v=vs.110).aspx and How to get around Marshal.Copy (32bit) length limit? . This snippet will use int as the resulting array length. You will need to figure out what to do in your particular case.
Also note your DLL must be responsible for releasing the memory it allocates. See Release unmanaged memory from managed C# with pointer of it .
IntPtr objPtr = getObj();
IntPtr result;
int resultLen;

// call your external function
int output = Foo(objPtr, out resultLen, out result);

// create an array to hold the output data
float[] array = new float[resultLen];

// copy the data
Marshal.Copy(result, array, 0, resultLen);

// since the memory was allocated by the DLL only it knows how to free it
// so call the free function exported by the DLL
FreeBufferAfterFoo(result);


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Middleburgh Central School District > Athletics > Concussions
The Middleburgh Central School District recognizes that concussions and head injuries are the most commonly reported injuries in children and adolescents who participate in sports and recreational activities. The physical and mental well-being of our students is a primary concern. Therefore, the Middleburgh Central School District adopts the following Policy to support the proper evaluation and management of concussion injuries.
A concussion is a mild traumatic brain injury (MTBI). A concussion occurs when normal brain functioning is disrupted by a blow or jolt to the head or body that causes the head and brain to move rapidly back and forth. Recovery from concussion and its symptoms will vary. Avoiding re-injury and over-exertion until fully recovered are the cornerstones of proper concussion management. Concussions can impact a student's academics as well as their athletic pursuits.
Concussion Management Team (CMT)
In accordance with the Concussion Management and Awareness Act, the District is authorized, at its discretion, to establish a Concussion Management Team (CMT) which may be composed of the certified athletic director, a school nurse, the school physician, a coach of an interscholastic team, a certified athletic trainer or such other appropriate personnel as designated by the District. The Concussion Management Team shall oversee and implement the District's concussion policy and regulations, including the requirement that all school coaches, physical education teachers, nurses and certified athletic trainers who work with and/or provide instruct ion to pupils engaged in school-sponsored athletic activities complete training relating to mild traumatic brain injuries. Furthermore, every concussion management team may establish and implement a program which provides information on mild traumatic brain injuries to parents and persons in parental relation throughout each school year.
Staff Training/Course of Instruction
Each school coach, physical education teacher, school nurse and certified athletic trainer who works with and/or provides instruction to students in school-sponsored athletic activities (including physical education class and recess) shall complete a course of instruction every two (2) years relating to recognizing the symptoms of concussions or MTBIs and monitoring and seeking proper medical treatment for students who suffer from a concussion or MTBI.
Components of the training will include:
The definition of MTBI;
Signs and symptoms of MTBI;
How MTBIs may occur;
Practices regarding prevention; and
Guidelines for the return to school and school activities for a student who has suffered an MTBI, even if the injury occurred outside of school.
The course can be completed by means of instruction approved by SED which include, but are not limited to, courses provided online and by teleconference.
Information to Parents
The District shall include the following information on concussion in any permission or consent form or similar document that may be required from a parent/person in parental relation for a student's participation in interscholastic sports. Information will include:
Identification of Concussion and Removal from Athletic Activities
The District shall require the immediate removal from all athletic activities of any student who has sustained, or is believed to have sustained, a mild traumatic brain injury (MTBI) or concussion. Any student demonstrating signs, symptoms or behaviors consistent with a concussion while participating in a class, extracurricular activity, or interscholastic athletic activity shall be removed from the class, game or activity and must be evaluated as soon as possible by an appropriate health care professional. Such removal must occur based on display of symptoms regardless of whether such injury occurred inside or outside of school. If there is any doubt as to whether the student has sustained a concussion, it shall be presumed that the student has been injured until proven otherwise. The District shall notify the student's parents or guardians and recommend appropriate evaluation and monitoring.
The School District may choose to allow credentialed District staff to use validated Neuro-cognitive computerized testing as a concussion assessment tool to obtain baseline and post-concussion performance data. These tools are not a replacement for a medical evaluation to diagnose and treat a concussion.
Return to School Activities and Athletics
The student shall not return to physical activity (including athletics, physical education class and recess) until he/she has been symptom-free for not less than twenty-four (24) hours, and has been evaluated and received written authorization from a licensed physician. In accordance with Commissioner's Regulations, the School District's Medical Director will give final clearance on a return to activity for extra-class athletics. All such authorizations shall be kept on file in the student's permanent health record. The standards for return to athletic activity will also apply to injuries that occur outside of school. School staff should be aware that students may exhibit concussion symptoms caused by injuries from outside activities and that these visible symptoms also indicate a removal from play.
The District shall follow any directives issued by the student's treating physician with regard to limitations and restrictions on school and athletic activities for the student. The District's Medical Director may also formulate a standard protocol for treatment of students with concussions during the school day.
In accordance with NYSED guidelines, this Policy shall be reviewed periodically and updated as necessary in accordance with New York State Education Department guidelines. The Superintendent, in consultation with the District's Medical Director and other appropriate staff, may develop regulations and protocols for strategies to prevent concussions, the identification of concussions, and procedures for removal from and return to activities or academics.
Athletics Information
Athletics Handbook
Athletic Placement Policy
Indoor Livestreaming
NYSED Guidelines for Concussion Management in a School Setting
NYSDOH Sports-related Concussion resources
NYSDOH Concussion Fact Sheet for Parents and Caregivers
Middleburgh Board of Education Concussion Management Policy


A few months ago I jumped on the pre-order impluse buy for the Freescale Freedom-KL25Z. Thankfully I had forgotten about it until I recieved shipment notification. It was nice that I didn't have to wait too long. Today it as arrived. Here are some close-up pictures – thought it would be nice to have some since there doesn't seem to be any up yet.
If you would like to get one, I ordered it from element14newark.com.
Here are the specifications as listed on Newark's website. I cannot wait to start playing with it!
FYI: If you order it now, I am pretty sure you don't get the headers. The orginal listing was a prototype board with headers and when they released the final version, it didn't have headers, so they included them with the pre-orders at no extra cost.


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October 01, 2014 Opinion » Commentaries
'I have decided to pursue new opportunities elsewhere'
Arroyo Grande City Manager Steve Adams reveals and explains his decision to leave the position
By Steve Adams
It is with regret that I announce my plans to step down as city manager with the city of Arroyo Grande. After much deliberation, I have determined that the current events have created too much distraction for me to lead the future of our organization as effectively as I would like. To be involved in something divisive to the community would be the ultimate contradiction of everything I have tried to stand for in bringing the community together during these past 14 years. As a result, my family and I have decided to pursue new opportunities elsewhere. I cannot begin to express how much I appreciate the support I have received from so many kind people in our community.
My resignation will become effective once my replacement has been hired and starts work. Therefore, I intend to remain in my position throughout the recruitment process in order to ensure a smooth transition and enable me to complete a number of important efforts underway. I will continue to cooperate fully with the investigation. My primary motivation is to serve the best interests of this community that I cherish so much.
I want to emphasize to the community how fortunate it is to have such an amazing mayor and City Council. I have had the distinct honor to work with each of them on a day-to-day basis for many years. I never cease to be amazed at their level of dedication to the entire community. The effort they take to respond to the concerns of every individual that contacts them is extraordinary.
They took the July 3 incident very seriously, responded quickly, and handled it in the best way possible based on the information they had. Everything was handled consistently with how similar incidents are dealt with involving other staff. An initial review is first completed to identify if any policies are violated and to determine whether a formal investigation is warranted. There seems to be some confusion from people unfamiliar with government procedures who are comparing the situation to an incident involving a potential criminal action or when a formal personnel complaint is filed, neither of which apply in this case.
There was no so-called "cover-up." I actually called a meeting of my executive team the first work day following the incident to inform them of what had happened. Personnel matters are not publicized, which is not the same as a cover-up.
It is reprehensible that negative criticism has been made toward the city attorney's office. Their level of expertise, hard work, and dedication to effectively protect the city's and community's interests day in and day out is something unparalleled to anything I have witnessed anywhere in my career. They handled this incident in that same consistent and professional manner.
I have also witnessed the city clerk and her staff work tirelessly and with the utmost professionalism to respond to a barrage of public records requests, only to have wild, unfounded insinuations made about altering records and tapes. Our citizens would agree what a travesty this is if they had the opportunity as I do to witness the seriousness with which they take their integrity as it relates to their professional responsibilities. The so-called "missing 80 minutes" of tape resulted because the representative of the website that requested the tape submitted a flash drive that was too small to hold the entire file. Once they submitted a new flash drive, they received the remainder of the tape. However, these background facts were never reported.
The impact on Ms. McClish's reputation is an even greater travesty. She has consistently treated everyone she comes in contact with in a kind, professional, and responsive manner. She has served this community with great distinction and does not deserve the meanness that has been directed toward her.
I have consistently expressed my deepest respect for the important work our officers do in protecting our community. I also fully support the officers that responded to the July 3 incident and early on issued a public apology to them for the uncomfortable position my actions put them in, as well as to the rest of the organization and community. I have never accused any of them of lying, and it has never been my belief that they said anything with the intent of harming me.
I have tried to focus on my job, stay out of the press, and let the investigation process take its course. However, given the amount of accusations that have been made publicly, I believe I must now speak out to provide clarification regarding some of the statements.
First, I never lied about Ms. McClish being in the building. When I asked why the officers were there, I was twice told they were looking for someone with the name of an employee that until recently worked in City Hall. When one of the officers used Ms. McClish's correct name, I responded that she was there. Later reports on a website that they were using her nickname are false, although I acknowledge that they may have thought that was the case.
Second, the building was reported as being dark, which is an accurate statement given that most the lights were off. However, it is also important to clarify for the public that there are lights at each end of the building that automatically remain on at all times. Therefore, there would be no reason to turn on additional lights in other portions of the building.
Third, due to the extent of the activity by the officers in the building, our belief was that they could be responding to a serious threat. Therefore, Ms. McClish was standing out of view in response to her fear for her safety.
Lastly, I continue to confirm my earlier statements that nobody was at any time unclothed or partially clothed.
With regard to the actions of the Arroyo Grande Police Officers' Association, I continue to provide them the benefit of the doubt that their motivations are sincere. However, given that they are still not satisfied now that the City Council complied with their request for an outside investigation, I believe it is important that the public be provided pertinent background information regarding the city's labor relations.
I will be the first to recognize that I have failed to maintain a positive relationship with the POA. I acknowledge that there were things I could have done and/or communicated better to improve this relationship. However, it is important to also acknowledge that we have been through the worst economic period since the Great Depression. We are proud of the fact that during this period, we actually increased reserves, maintained important capital projects to improve our streets and other infrastructure, and maintained key service levels despite skyrocketing pension costs and plummeting revenues. This could not have been accomplished without some tough decisions and tough labor negotiations.
During this time, the POA hired an attorney to represent them who was a partner with a law firm that posted on its website a "playbook" for negotiations. Among other questionable tactics, it advocated "public ridicule" of blunders by the city manager, mayor, and City Council. It also recommended to "focus on a city manager, councilperson, mayor or police chief and keep the pressure up until that person assures you his loyalty and then move on to the next victim." They have since gone out of business amongst a variety of their own legal problems, but the POA has continued the services from the same attorney, now with a new firm.
I am confident that our extraordinary and dedicated staff will carry on to do more great things for this wonderful community that I love so much. I believe my greatest legacy is the effective team we have assembled over the years and am extremely proud of all that they have accomplished. The state of the city's infrastructure, finances, and economic vitality are at their highest level ever due to their hard work, the council's leadership, and the community's support and involvement. My wish is that my departure will remove this distraction and allow them to return their full focus to these important efforts. I cherish all my time serving the city of Arroyo Grande, I bear no ill will to anyone who has opposed me in this matter, and I hope everyone can now seek a new level of cooperation in addressing some major challenges ahead for our community. Meanwhile, I look forward to spending more time with my incredible family who has been so supportive of me throughout this ordeal and my life.
Steven Adams is currently the city manager of Arroyo Grande. Send comments to the executive editor at rmiller@newtimesslo.com.
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Teen dating violence is defined as the physical, sexual, psychological, or emotional violence within a dating relationship, including stalking. Dating violence is widespread with serious long-term and short-term effects. If you or someone you know is experiencing teen dating violence, please contact the Deans' Office or our social worker, Ms. Zachary at 708-585-2041 or azachary@tfd215.org.