text:
\section{introduction}
	In this paper, we consider the unconstrained optimization problem:
	\begin{align}\label{Newton:Problem}
	\mathop {\min }\limits_{x \in {\mathbb R^d}} f( x ) =
	\frac{1}{n}\sum\limits_{i = 1}^n {{f_i}( x )},
	\end{align}
	where $f_i(x)$ is smooth and not necessarily convex. Such finite-sum
	structure is increasingly popular in modern machine learning tasks,
	especially in deep learning, where each $f_i(\cdot)$ corresponds to the loss
	of a training sample. For large-scale problems, computing the full gradient and Hessian is
	prohibitive,  so Stochastic gradient descent (SGD) has
	become the most popular method.

	First order methods such as gradient descent and SGD are guaranteed to
	converge to stationary points, which can be a saddle point or a local
	minimum\footnote{Some recent analysis indicates SGD can escape from saddle
		points in certain cases~\cite{ge2017no,jin2017escape}, but SGD is not the focus of this
		paper. }.

	It is known that second-order methods, by utilizing the Hessian information,
	can more easily escape from saddle points.
	At each iteration, second-order methods typically build a quadratic
	approximation function around the current solution $x_k$ by
	\begin{align}\label{Newton:Definition_m}
	{m_k}( s) = f( {{x_k}} ) + \langle
	{{g(x_k)},s} \rangle  + \frac{1}{2}\langle {s,{B(x_k)}s}
	\rangle,
	\end{align}
	where $g(x_k)$ is the approximated gradient and $B(x_k)$ is
	the symmetric matrix. To update the current solution, a common strategy is to
	minimize this quadratic approximation within a small region. Algorithms based
	on this idea including Trust Region method (TR)~\cite{conn2000trust} and
	Adaptive Regularization using Cubics
	(ARC)~\cite{cartis2011adaptivea,cartis2011adaptiveb}
	have demonstrated good performance on small-scale non-convex problems.

	However, for large-scale optimization such as training deep neural networks, it is impossible
	to
	compute gradient and Hessian {\it exactly} for every update. As a result, stochastic
	second-order
	methods have been studied in the past few years.  \cite{xu2017newton, xu2017second} proposed
	TR and ARC methods with inexact Hessian, in which the second-order information is approximated
	by  the subsampled Hessian matrix, yet the gradient is still computed exactly.

	\cite{kohler2017sub} proposed a stochastic version of ARC, but they require a much stronger
	condition in both gradient and Hessian approximation, thus they need to keep increasing the
	sample size as iteration goes.

	More recently, \cite{tripuraneni2017stochastic} provide 	stochastic cubic regularization
	method, but they do not have an adaptive way 	to adjust the regularization parameters.

	In this paper, we consider a simple and practical stochastic version of trust region
	and cubic regularization methods (denoted as STR and SARC respectively). In the quadratic
	approximation~\eqref{Newton:Definition_m},
	we replace both $g(x_k)$ and $B(x_k)$ by the approximate gradient and Hessian
	with a fixed approximation error, which can be achieved using a fixed sample
	size.
	Furthermore, we consider the most general case where
	the trust region radius or cubic regularization parameter is adaptively adjusted
	by checking the {\it subsampled} objective function value.

	Note that we do
	not claim STR and SARC are ``new'' algorithms, since it is natural to transform TR
	and ARC to the stochastic setting. The question is whether this simple
	idea works in theory and in practice, and our contribution is to provide an affirmative
	answer to this question.
	Our contribution
	can be summarized as follows:

	%

	%
	%

	%

	\begin{itemize}
		\item We provide a theoretical analysis of convergence and iteration
		complexity for STR and SARC. Unlike~\cite{kohler2017sub}, we do not require
		the approximation error of Hessian and gradient estimation to be related
		to $s$ (the update step). Furthermore, even though the proof framework is similar to
		\cite{xu2017second}, we provide novel analysis to model the case when
		both gradient and Hessian are inexact, while \cite{xu2017second} does
		not allow inexact gradient.

		\item We use the operator-Bernstein inequality to bound the sub-sampled
		function value,
		which
		enables
		automatically adjusting trust region radius and cubic regularization parameter
		using subsamples. Even when function value, gradient  and Hessian
		are all inexact, we are able to show that the iteration complexity is in the same order
		with \cite{xu2017second,kohler2017sub}.

		\item We conduct experiments on CIFAR-10 data with VGG network and show that
		the proposed algorithms are faster than  the existing trust region and cubic
		regularization methods in terms of running time.
	\end{itemize}
	\subsection{Our results}
	We present the iteration complexity for both proposed methods under the  Assumptions in
	Preliminary where the parameters are defined as well.

	\textbf{{STR}} The total number of iterations is
	$\mathcal{O}( \max \{ (\varepsilon _{\nabla f} - \varepsilon _g)^{ -
		2},(\varepsilon _H - \varepsilon _B)^{ - 3} \} )$\footnote{We use
		$\mathcal{O}(\cdot)$ to hide constant factors.}.

	\textbf{{SARC}} The iteration complexity is the same order of  STR.
	If the condition of the terminal criterion is satisfied, then the total number of iterations is
	\[\mathcal{O}( \max \{ (\varepsilon _{\nabla f} - \varepsilon _g)^{ -
		3/2},(\varepsilon _H - \varepsilon _B)^{ - 3}\}  ),\]
	which is better than STR.

	\subsection{Related Work}
	With the increasing size of data and model, stochastic optimization becomes more and more
	popular since computing the gradient and Hessian are prohibitively
	expensive.

	For the stochastic first-order optimization, stochastic gradient descent (SGD)
	\cite{zhang2004solving, shalev2011pegasos, ghadimi2016accelerated} is
	absolutely the main
	method especially in training deep neural networks and other large-scale machine learning
	problems, due to its simplicity and effectiveness.

	However, the estimated gradient will induce the noise such that the
	variance of the gradient may not approximate zero even when converged
	to a stationary point.
	Stochastic variance reduction gradient (SVRG)
	\cite{johnson2013accelerating} and SGAG \cite{defazio2014saga} are two
	typical methods to reduce the variance of the gradient estimator, which lead to faster
	convergence especially in the convex setting.

	Several other related variance reduction methods are developed and analyzed
	for non-covex problems

	\cite{reddi2016stochastic,allen2016variance}. However,
	using only first-order information, the saddle point may not be escaped
	even though \cite{anandkumar2016efficient} prove that SGD with noise can
	escape but under certain conditions.

	For second-order optimization, Newton-typed methods rely on building a
	quadratic approximation around the current solution, and
	by exploring the curvature information it can better avoid saddle points in
	non-convex optimization.

	The negative eigenvector
	of the Hessian information provides the decrease direction for the updates.
	Using exact Hessian is often time consuming, so
	Broyden-Fletcher-Goldfarb-Shanno (BFGS) and
	Limited-BFGS \cite{nocedal1980updating} are two widely methods that approximate
	Hessian using first-order information.
	Another important technique for Hessian approximation is
	sub-sampling the function $f_i(\cdot)$ to obtain the estimated
	Hessian. Both \cite{byrd2011use} and \cite{erdogdu2015convergence} using
	the stochastic Hessian matrix to obtain the global convergence, while the
	former requires $f_i$ to be smooth and strongly convex.
	Furthermore, \cite{roosta2016suba,roosta2016subb} apply the
	sub-sampled gradient and Hessian to the quadratic model and give the
	convergence analysis of second-order methods thoroughly and
	quantitatively.

	Trust region Newton method is a classical second-order method that
	searches the update direction only within a trust region around the current
	point.
	The size of trust region is critical to the effectiveness of
	search direction. The region will be updated based on measuring whether
	the quadratic approximation is an adequate representation of the function or not.
	Following the sub-sampling for Hessian matrix as in
	\cite{roosta2016suba,roosta2016subb},
	\cite{xu2017newton, xu2017second} apply such inexact Hessian to trust
	region 	method and also provide the convergence and iteration complexity.
	Similar to the trust region method,
	\cite{cartis2011adaptivea,cartis2011adaptiveb}
	introduced adaptive
	cubic regularization methods for unconstrained optimization, in which the
	Hessian metrics can be replaced by the approximate matrix.
	\cite{kohler2017sub} apply the operator-Bernstein inequality to approximate
	the Hessian matrix and gradient into a quadratic function with cubic
	regularization.	However, the sample approximate condition is subject to the
	search direction $s$, thus they need to increase the sample size at each step.
	To overcome this issue, \cite{xu2017newton} provide
	another approximation condition of Hessian matrix that does not depend on the
	search step $s$. However, they assume gradient has to be computed exactly,
	which is not feasible in large-scale applications.
	Furthermore, each update of the $\rho$ that measure the adequacy
	of the function  will need the full computation of the objective function,
	which will lead to more computation cost.

	The rest of paper is organized as follows. Section
	\ref{Newton:Section:Preliminary}
	gives the  preliminary about the assumptions and definition. The
	sub-sampling method for estimating the corresponding function, gradient and
	Hessian is in Section \ref{Newton:Section:subsampling}.
	Section \ref{Newton:Section:STR} and  \ref{Newton:Section:SARC}
	respectively present the stochastic trust region method and cubic
	regularization method, and their convergence and iteration complexity.
	Section
	\ref{Newton:Section:Experiment} gives the experimental results. Section
	\ref{Newton:Section:Conclusion} concludes our paper.

	\section{Preliminary}\label{Newton:Section:Preliminary}

	For a
	vector $x$ and a matrix $X$,  we use $\|x\|$ and $\|X\|$ to denote the
	Euclidean norm and the matrix spectral norm, respectively. We use $\mathcal{S}$ to denote
	the set and $|\mathcal{S}|$ to denote its cardinality.
	For the matrix $X$, we use $\lambda_{\text{min}}(X)$ and $\lambda_{\text{max}
	}(X)$ to denote its smallest and largest eigenvalue.
	In the following, we give  assumptions and definition about the characteristic of function, the
	approximate conditions, related bounds, and optimality definition.

	\begin{assumption}(Lipschitz Continuous)\label{Newton:Assumption:function} For the function
		$f(x)$, we assume that ${\nabla ^2}f( x )$ and ${\nabla}f( x )$  are
		Lipschitz continuous
		satisfying $\| \nabla ^2f( x ) - {\nabla ^2}f( y ) \| \le L_H\| x - y\|$
		and $\| \nabla
		f( x ) - {\nabla}f( y ) \| \le L_{\nabla f}\| x - y\|$, $\forall x,y \in
		{\mathbb{R}^d}$.

	\end{assumption}

	\begin{assumption}(Approximate)\label{Newton:Assumption:approximation} For function $f(x)$,
	the
		approximate gradient $g(x)$ and Hessian matrix $B(x)$ satisfy
		\begin{align}\label{Newton:Assumption:approximation-gB}
		\left\| {\nabla f(x) - g(x)} \right\| \le {\varepsilon _g},
		\left\| {{\nabla ^2}f(x) - B(x)} \right\| \le {\varepsilon _B}.
		\end{align}
		with ${\varepsilon _g},{\varepsilon _B} > 0$. The approximated function $h(x)$ at
		$k$-iteration
		satisfies
		\begin{align}\label{Newton:Assumption:approximation-h}
		\color{black} \left\| {f(x_k) - h(x_k)} \right\| \le {\varepsilon _h}{\|s_k\|^2},{\varepsilon _h} > 0.

		\end{align}

	\end{assumption}

	\begin{assumption}(Bound)\label{Newton:Assumption:bound}
		For $i\in[n]$, the bound assumptions are the
		function $f_i(x)$ satisfies $\left\|
		{{f_i}({x})} \right\| \le {\kappa _f}$, $\left\| {\nabla {f_i}({x})} \right\| \le {\kappa
			_{\nabla f}}$, and $\left\| {{\nabla ^2}{f_i}({x})} \right\| \le {\kappa _H}$.
	\end{assumption}

	\begin{assumption} (Bound)\label{Newton:Assumption:Bound:Variance}
		We assume that $H_1$ and $H_2$ are the upper bounds on the variance of the $\nabla f_i(x)$
		and
		$\nabla^2f_i(x)$, that is
		\begin{center}
			$
			\frac{1}{n}\sum\limits_{i = 1}^n {{{\left\| {\nabla {f_i}\left( x \right) - \nabla
			f\left(
							x \right)} \right\|}^2}}  \le {H_1^2},\frac{1}{n}\sum\limits_{i = 1}^n
			{{{\left\|
						{{\nabla
								^2}{f_i}\left( x \right) - {\nabla ^2}f\left( x \right)}
								\right\|}^2}}  \le
			{H_2^2}.
			$
		\end{center}
	\end{assumption}
	The following lemmas are important tools for analyzing the convergence of the proposed
	algorithm,
	which are used to characterize the variance of random variable decreasing with the factor
	related
	to the set size.

	\begin{lemma}\label{Newton:Appendix:Tool:RandomSubset}
		If $v_1,...,v_n\in \mathbb{R}^d$ satisfy
		$\sum\nolimits_{i = 1}^n {{v_i}}  = \vec 0$, and $\cal A$ is a non-empty,
		uniform
		random subset of $[n]$, $A=|\mathcal{A}|$, then
		\begin{center}
			${\mathbb{E}_{\mathcal{A}}} {{{\left\| {\frac{1}{A}\sum\nolimits_{b \in
								{\mathcal{A}}}
							{{v_b}}
						}
						\right\|}^2}}  \le \frac{{\mathbb{I}\left( {A < n}
					\right)}}{A}\frac{1}{n}\sum\limits_{i = 1}^n {v_i^2}.$
		\end{center}
	\end{lemma}
	\begin{definition}(($\varepsilon_{{\nabla f}},\varepsilon _H$)-Optimality).
		Given
		${\varepsilon _{{\nabla f}}},{\varepsilon _H} \in [0,1]$, $x$ is an $(
		{{\varepsilon_{{\nabla f}}},{\varepsilon _H}}))$-Optimality solution to
		problem
		(\ref{Newton:Problem}), if
		\begin{align*}
		\| 	{\nabla f( {{x}} )} \| \le 	{\varepsilon _{\nabla
				f}},\,\lambda_\text{min} ({\nabla ^2}f( x
		)
		) 	\ge  - 	{\varepsilon_H }.
		\end{align*}
	\end{definition}
	Furthermore, we introduce three index sets
	\begin{align*}

	\mathcal{S}_{{\nabla f}}&\mathop  = \limits^\text{def}\{x: \,  \|{\nabla
		f( {{x}} )} \| \ge {\varepsilon _{\nabla f}}\}, \\

	\mathcal{S}_{H}&\mathop  = \limits^\text{def}\{x: \|{\nabla
		f( {{x}} )} \| \ge {\varepsilon _{\nabla f}} \,\text{and}
	\,\lambda_\text{min}
	({\nabla^2f(x )} ) \le - {\varepsilon_H }\}, \\

	\mathcal{S}_{*}&\mathop  = \limits^\text{def} \{x:\, \|
	\nabla f( {{x}} ) \| \le \varepsilon_{\nabla f}\,
	\text{and}\, \lambda_\text{min} (\nabla^2f( x )) \ge  -\varepsilon_H\}.
	\end{align*}
	where  {$ {\varepsilon _{\nabla f}}>\varepsilon_g$ and
		$\varepsilon_H>\varepsilon_B$}. In order to clearly classify three
	situations, we give a simple
	geometry
	illustration, as shown
	in Figure \ref{Newton:Figure3Situation}.
	\begin{figure*}[t]
		\centering
		\includegraphics[width=0.42\textwidth]{indexset2}
		\caption{Illustration of three situations in analyzing the convergence
			to first and second critical
			point.}\label{Newton:Figure3Situation}
	\end{figure*}

	\section{Sub-sampling for finite-sum
		minimization}\label{Newton:Section:subsampling}
	For the finite-sum problem~\eqref{Newton:Problem},
	we can estimate
	$f(x)$, $\nabla f(x)$, and $\nabla^2 f(x)$ by random sub-sampling,

	which can drastically reduce the computational complexity.
	Here, we use $\mathcal{S}_h$, $\mathcal{S}_g$ and $\mathcal{S}_B$ to denote the sample
	collections
	for estimating $f(x)$, $\nabla f(x)$ and $\nabla^2f(x)$, respectively, where $\mathcal{S}_h$,
	$\mathcal{S}_g$ and
	$\mathcal{S}_B\subseteq [n]$. The approximated functions are formed by
	\begin{align}
	\label{Newton:STR:Subsampling:h}
	h(x)&=\frac{1}{\left| {{\mathcal{S}_h}} \right|}\sum\nolimits_{i \in {\mathcal{S}_h}}
	{{f_i}\left(
		x \right)},\\
	\label{Newton:STR:Subsampling:g}
	g( {{x}} ) &= \frac{1}{{\left| {{\mathcal{S}_g}} \right|}}\sum\nolimits_{i \in
		{\mathcal{S}_g}}^{} {\nabla
		{f_i}\left(
		{{x}} \right)},\\
	\label{Newton:STR:Subsampling:B}
	B( {{x}} ) &= \frac{1}{{| {{\mathcal{S}_B}} |}}\sum\nolimits_{i \in {\mathcal{S}_B}}^{}
	{{\nabla
			^2}{f_i}( {{x}} )}.
	\end{align}
	Most papers use operator-Bernstein inequality to probabilistically guarantee such properties,
	such
	as \cite{drineas2006fast,mahoney2011randomized} use  approximate matrix multiplication results
	as a
	fundamental primitive
	in RandNLA  \cite{drineas2006fast,mahoney2011randomized} to control the
	approximation error of $\nabla f(x)$.  Furthermore,  the vector-Bernstein inequality
	\cite{candes2011probabilistic,gross2011recovering} is applied in \cite{ kohler2017sub} to
	obtain
	the of sub-sample bound of the gradient, which is different from 	\cite{drineas2006fast}.
	However,
	the number of sub-samples depend on the search direction $s$ in advance, which will affect the
	estimation of sub-sampling. 	Replacing the condition by
	(\ref{Newton:Assumption:approximation-gB}), we can have

	\begin{lemma}
		Suppose the Assumption \ref{Newton:Assumption:bound} holds,
		if $| {{\mathcal{S}_g}} | \ge 16\log (
		{{{2d}}/{\delta }}
		){{L_f^2}}/{{\varepsilon	_g^2}}$, then $g(x)$ formed by
		(\ref{Newton:STR:Subsampling:g})
		satisfies $\| \nabla f( x ) - g(x) \| \le {\varepsilon}_{g}$ with probability
		($1-\delta$).
	\end{lemma}
	Note that, we do not give the proof of above Lemmas as the difference lies on different
	conditions.
	We also obtain the approximate gradient $g(x)$ based on above results.

	\begin{lemma}
		Suppose the Assumption \ref{Newton:Assumption:bound} holds,
		If $| \mathcal{S}_B | \ge \log ( {{{2d}}/{\delta }} )
		{{16L_B^2}}/{{\varepsilon_B^2}}$, then  $B(x)$ formed by (\ref{Newton:STR:Subsampling:B})
		satisfies $\| {\nabla ^2}f( x ) -{B(x)}\| \le 	{\varepsilon}_B$ with probability
		($1-\delta$).
	\end{lemma}
	In order to reduce the computation cost for updating the $\rho$, we also use the sub-sampling
	combing with operator-Bernstein inequality to obtain the approximate function probabilistically
	satisfying (\ref{Newton:Assumption:approximation-h}). Note that, before obtain the approximate
	function $f(x)$, $s$ has been solved. Thus, we can use $\|s\|$ directly. Furthermore, if the
	approximate function $h(x)$ satisfies the condition in
	(\ref{Newton:Assumption:approximation-h}),
	but could not be guaranteed the bound of $\left\| {\nabla h\left( x \right) - \nabla f\left( x
		\right)}
	\right\|$ and $\| {{\nabla ^2}h( x ) - {\nabla ^2}f( x )} \|$,
	which will be later used to analyze the radius. Thus, we present a important assumption
	and use Lemma \ref{Newton:Appendix:Tool:RandomSubset} to derive the upper bound.

	\begin{lemma}\label{Newton:Subsample:Lemma}
		Suppose the Assumption \ref{Newton:Assumption:bound} and
		\ref{Newton:Assumption:Bound:Variance} hold,
		If 	 $|{{\cal S}_h}| \ge \log (2d/\delta )16\kappa _f^2/( {\varepsilon _h^2{{\| {{s_k}}
		\|}^4}}
		)$,
		then
		$h(x)$	formed by (\ref{Newton:STR:Subsampling:h}) satisfies $\|  f(x_k ) - h(x_k) \| \le
		{\varepsilon}{_h}\|s_k\|^2$ with probability
		($1-\delta$).
		Furthermore,  we can also have the upper bounds with the gradient and the Hessian of $h(x)$,
		\[ 	{\left\| {\nabla h\left( x \right) - \nabla f\left( x \right)} \right\|^2} \le
		\frac{{\mathbb{I}\left( {\left| {{\mathcal{S}_h}} \right| < n} \right)}}{{\left|
				{{\mathcal{S}_h}} \right|}}{H_1},
		{\left\| {{\nabla ^2}h\left( x \right) - {\nabla ^2}f\left( x \right)} \right\|^2} \le
		\frac{{\mathbb{I}\left( {\left| {{\mathcal{S}_h}} \right| < n} \right)}}{{\left|
				{{\mathcal{S}_h}} \right|}}{H_2}.\]
	\end{lemma}

	\section{Stochastic Trust Region method}\label{Newton:Section:STR}
	\begin{algorithm*}[t]
		\caption{STR  with Inexact Hessian and Gradient}
		\label{Newton:STR:Algorithm}
		\begin{algorithmic}[1]
			\Require given $x_0$, $r_2\ge 1> r_1$, $1>\eta>0$, $\varepsilon>0$ and
			$\Delta_0,\Delta_\text{max}>0$.
			\Ensure
			\For{$k$=1 to T }
			\State Compute the approximate gradient $g(x_k)$ and
			Hessian matrix 	$B(x_k)$ based on
			(\ref{Newton:STR:Subsampling:g})
			and (\ref{Newton:STR:Subsampling:B}).
			\State
			\Comment({\color{black} if

				$\|g\left( {{x_k}} \right)\| \le {\varepsilon 	_{\nabla 	f}}+ {\varepsilon _g}$,
				we set $\mathcal{S}_h=\mathcal{S}_g$})
			\State Compute the direction vector $s_k$
			\begin{align}\label{Newton:STR:Algorithm-solution}
			s_k=\text{Subproblem-Solver}(g_k,B_k,\Delta_k).
			\end{align}
			\State Compute the approximate  function $h(x_k)$ and $h(x_k+s_k)$ based on
			(\ref{Newton:STR:Subsampling:h}).
			\State 	Compute $
			{{\tilde \rho }_k} = \frac{{h\left( {{x_k}} \right) - h\left( {{x_k} + {s_k}}
					\right)}}{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right)}}
			$
			\State Set $\rho={{{\tilde \rho }_k} - \frac{{2{\varepsilon _f}{\color{black}\|s_k\|^2}}}
				{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right)}}}$
			\State set ${x_{k + 1}} = \left\{ {\begin{array}{*{20}{l}}
				{{x_k} + {s_k},}&{\rho  \ge \eta ,}\\
				{{x_k},}&{{\rm{otherwise}}{\rm{.}}}
				\end{array}} \right.$
			\State set
			${\Delta _{k + 1}} = \left\{ {\begin{array}{*{20}{l}}
				{\text{min} \left\{ {{\Delta _{\text{max} }},{r_2}{\Delta _k}} \right\},}&{\rho  >
				\eta
					,}\\
				{{r_1}{\Delta _k},}&{{\rm{otherwise}}.}
				\end{array}} \right.$
			\EndFor

		\end{algorithmic}
	\end{algorithm*}

	In this section, we consider the stochastic trust region method for
	solving the constrained optimization problem. At $k$-iteration, the
	objective function is approximated by a quadratic model within a trust
	region,
	\begin{align}\label{Newton:STR:Objective}
	\mathop {\min }\nolimits_{s\in \mathbb{R}^d} \,{m_k}( s
	),\,\,\,\,	\text{subject to}\,\| s \| \le {\Delta _k},
	\end{align}
	where $\Delta_k$ is the radius, and ${m_k}( s )$ is defined in (\ref{Newton:Definition_m}). The
	approximated gradient and Hessian
	are formed based on the conditions in Assumption \ref{Newton:Assumption:approximation}. The
	conditions of $\varepsilon_B $ in (\ref{Newton:Assumption:approximation-gB}) does not depend on
	the
	search direction $s$, which is the same as in
	\cite{xu2017newton,xu2017second}. Moreover, we also define a new parameter $\varepsilon_g$,
	which
	has the same characteristic as $\varepsilon_B$.    In addition, the computations of $f(x)$ and
	$f(x+s)$ are expensive as the objective function is finite-sum structure. Different from
	\cite{xu2017newton} and \cite{kohler2017sub}, we  replace $f(x)$ and $f(x+s)$ with the
	approximate
	function $h(x)$ and $h(x+s)$ under the condition (\ref{Newton:Assumption:approximation-h}).
	This
	condition is  subjected to the search direction $s$. However, the  approximate
	function $h(x)$ and $h(x+s)$ can be derived after obtaining the solution $s$ through
	Subproblem-Solver.  Algorithm
	\ref{Newton:STR:Algorithm} presents the process for updating the $x$ and $\Delta$.	This
	section consists of two parts: Firstly, we analyze the role of radius $\Delta$ to ensure that
	the
	radius has the lower bound. Secondly, we derive the corresponding iteration complexity under
	the
	assumptions we present in Preliminary \ref{Newton:Section:Preliminary}.

	\subsection{Bounds analysis  of radius }
	First of all, we present three important definition: $\rho_k$, $\tilde{\rho}$ and $\rho$. The
	first two terms are defined as

	\begin{align*}
	{\rho _k} = \frac{{f\left( {{x_k}} \right) - f\left( {{x_k} + {s_k}} \right)}}{{{m_k}\left( 0
			\right) - {m_k}\left( {{s_k}} \right)}},{{\tilde \rho }_k} = \frac{{h\left( {{x_k}}
			\right)
			-
			h\left( {{x_k} + {s_k}} \right)}}{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}}
			\right)}}.
	\end{align*}
	Based on the inequality (\ref{Newton:Assumption:approximation-h}) in Assumption
	\ref{Newton:Assumption:approximation}, we have

	\begin{align*}
	\left| {{\rho _k} - {{\tilde \rho }_k}} \right| =\left| {\frac{{f\left( {{x_k}} \right) -
				h\left( {{x_k}} \right) - \left( {f\left( {{x_k} + {s_k}} \right) - h\left( {{x_k}
						+
						{s_k}}
					\right)} \right)}}{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right)}}}
	\right|\le
	\frac{{2{\varepsilon _h}\|s_k\|^2}}{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right)}},
	\end{align*}
	that is
	\begin{align*}
	{{\tilde \rho }_k}- \frac{{2{\varepsilon _h}\|s_k\|^2}}{{{m_k}\left( 0 \right) - {m_k}\left(
			{{s_k}} \right)}} \le
	{\rho _k}  \le \frac{{2{\varepsilon _h}{\|s_k\|^2}}}{{{m_k}\left( 0 \right) -
			{m_k}\left( {{s_k}}
			\right)}}+ {{\tilde \rho }_k}.
	\end{align*}

	Then, define $\rho={{\tilde \rho }_k} - \frac{{2{\varepsilon
				_h}{\|s_k\|^2}}}{{{m_k}\left( 0 \right) -
			{m_k}\left(
			{{s_k}} \right)}} $.  If $\rho \ge {\eta}$, we can obtain ${\rho _k} \ge {\eta}$. Thus,
			in
	the following analysis, we consider the size of $\rho$ that derive the desired lower bound
	of the radius.

	Before giving the analyses, we briefly present the processing that why the $\Delta$ do not
	approximate to zero. If  ${\rho} > {\eta
	}$, the current iteration will be  successful and the radius $\Delta$
	will increase by a factor of $r_2$. Thus, we consider that whether there is a constant $C$ such
	that
	$\Delta<C$ and the current iteration is successful simultaneously. Then we can see that such
	constant $C$ is our desired bound of $\Delta$ due to the fact that $\Delta$ will increase again
	under the successful iteration. What's more, such constant plays a critical role in determining
	the iteration complexity.

	Instead of computing the $\rho$ directly, we consider another relationship, that is
	\begin{align}\label{Newton:STR:1-p}
	1 - \rho  = \frac{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right) - \left( {h\left(
				{{x_k}} \right) - h\left( {{x_k} + {s_k}} \right)} \right) + 2{\varepsilon
				_h}{\|s_k\|^2}}}{{{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right)}}
	\end{align}
	As long as $1-\rho<1-\eta$, we can see that $\rho>\eta$. Here, we consider the upper and lower
	bound of denominator and numerator in (\ref{Newton:STR:1-p}) in Lemma
	\ref{Newton:STR:Lemma:Upperbound_mx-msx} and Lemma \ref{Newton:STR:Lemma:Upperbound_fxs-msx},
	respectively. Moreover, we separately give the corresponding bound under the index sets
	$\mathcal{S}_{\nabla f}$ and $\mathcal{S}_H$.

	\begin{lemma}\label{Newton:STR:Lemma:Upperbound_mx-msx}
		Suppose the Assumption
		\ref{Newton:Assumption:approximation} and
		\ref{Newton:Assumption:bound} hold,  $m_k(s)$ is defined in
		(\ref{Newton:Definition_m}). For the case of
		$x_k\in\mathcal{S}_{\nabla f}$, if $m_k(s_k)\le m_k(s_k^C)$, where $s_k^C$ is the Cauchy
		point,
		then we
		have
		\[{m_k}(0) - {m_k}({s_k}) \ge \frac{1}{2}({\varepsilon _{\nabla f}} - {\varepsilon _g})\min
		\left\{ {{\Delta _k},({{{\varepsilon _{\nabla f}} - {\varepsilon _g}}})/{{{\kappa _H}}}}
		\right\},\]
		For the case of $x_k\in \mathcal{S}_H$,
		that is
		${\lambda _{\text{min} }}( {\nabla^2f(x_k)} ) \le  -
		{\varepsilon _H}$,
		there exist a vector $s_k$ such that $\langle
		{ g({x_k}),{s_k}} \rangle \le 0$, $ {s_k^T\nabla^2f(x_k){s_k}}<-v_{0}
		\Delta_k^2$, and $\left\| {{s_k}} \right\| = {\Delta
			_k}$, where $v_{0}\ge\varepsilon_H$,	then we have
		\begin{align*}
		m_k( 0) - {m_k}(s_k )\ge \frac{1}{2} ( {{\varepsilon
				_H} - {\varepsilon _B}})\Delta _k^2.
		\end{align*}
	\end{lemma}
	The solution $S_k$ for the \textit{Subproblem-Solver} is based on subproblem in
	(\ref{Newton:Definition_m}). For the case of $x_k\in\mathcal{S}_{\nabla f}$, we use the Cauchy
	point \cite{conn2000trust}; while for the case of $x_k\in\mathcal{S}_{H}$, there are many
	methods
	to derive the solution, such as Shift-and-invert \cite{garber2016faster},  Lanczos
	\cite{kuczynski1992estimating} and Negative-Curvature \cite{carmon2018accelerated}.  We do not
	present the
	details information, which beyond our scope of this paper.

	\begin{lemma}\label{Newton:STR:Lemma:Upperbound_fxs-msx}
		Suppose  the Assumption
		\ref{Newton:Assumption:function},
		\ref{Newton:Assumption:approximation} and \ref{Newton:Assumption:Bound:Variance} hold,
		based
		on the definition of $m_k(s)$ in
		(\ref{Newton:Definition_m}),  we have
		\begin{align*}
		{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right) - \left( {h\left( {{x_k}} \right) -
			h\left( {{x_k} + {s_k}} \right)} \right) \le 2\left(
		{\frac{{\mathbb{I}\left(
					{\left| {{\mathcal{S}_h}} \right| < n} \right)}}{{\left| {{\mathcal{S}_h}}
					\right|}}H_1 +
			{\varepsilon _g}}
		\right){\Delta _k} + \frac{3}{2}\left( {\frac{{\mathbb{I}\left( {\left| {{\mathcal{S}_h}}
						\right| <
						n}
					\right)}}{{\left| {{\mathcal{S}_h}} \right|}}{H_2} + L_H{\Delta _k} +
			{\varepsilon
				_B}}
		\right)\Delta
		_k^2.
		\end{align*}
		If $\mathcal{S}_h=\mathcal{S}_g$, we have
		\begin{align*}
		{m_k}\left( 0 \right) - {m_k}\left( {{s_k}} \right) - \left( {h\left( {{x_k}} \right) -
			h\left( {{x_k} + {s_k}} \right)} \right) \le\frac{3}{2}\left( {\frac{{\mathbb{I}\left(
					{\left| {{\mathcal{S}_h}} \right| <
						n}
					\right)}}{{\left| {{\mathcal{S}_h}} \right|}}{H_2} + L_H{\Delta _k} +
			{\varepsilon
				_B}}
		\right)\Delta
		_k^2.
		\end{align*}

	\end{lemma}

	Note that, in Algorithm
	\ref{Newton:STR:Algorithm}, for the case of $\|g\left( {{x_k}} \right)\| \le {\varepsilon
		_{\nabla 	f}}+ {\varepsilon _g}$, that is
	\begin{center}
		$\left\| {\nabla f\left( {{x_k}} \right)} \right\| \le
		\left\| {g\left( {{x_k}} \right)} \right\| + \left\| {\nabla f\left( {{x_k}} \right) -
		g\left(
			{{x_k}} \right)} \right\| \le {\varepsilon _{\nabla f}} + {\varepsilon _g} +
			{\varepsilon
			_g} =
		{\varepsilon _{\nabla f}} + 2{\varepsilon _g}$,
	\end{center}
	we set $\mathcal{S}_h=\mathcal{S}_g$.
	$x\in\mathcal{S}_H$, in which $\left\| {\nabla f\left( {{x_k}} \right)} \right\| \le
	{\varepsilon _{\nabla f}}$, satisfies such case\footnote{In the case of $\varepsilon_{\nabla
			f}+2\varepsilon_{g}>\nabla f(x_k)>\varepsilon_{\nabla f}$, we have
		$\mathcal{S}_h=\mathcal{S}_g$
		such that the equality (\ref{Newton:STR:Lemma:Bound:Radius-3}) in Appendix become
		$\frac{{4{\varepsilon _g} +
				\frac{3}{2}\left( {{L_H}{\Delta _k} + 2{\varepsilon _B} +
					\frac{4}{3}{\varepsilon
						_h}} \right){\Delta _k}}}{{\frac{1}{2}\left( {{\varepsilon _{\nabla f}} -
					{\varepsilon _g}}
				\right)}}$, which is smaller than equality (\ref{Newton:STR:Lemma:Bound:Radius-3}),
		thus
		$\Delta_{{\rm{min1}}}$ is also satisfying such case. In this paper, in order to simply the
		analysis, we  consider the
		case $\nabla f(x)>\varepsilon_{\nabla f}$ without the requirement of $\mathcal{S}_{\nabla
			f}=\mathcal{S}_H$.}.
	Thus, we give the $\Delta_{\text{min2}}$ in
	(\ref{Newton:STR:Lemma:Bound:Radius-equality}) based on such implementation, which is key for
	analyses. The reason we make such implementation is to
	ensure that there is lower bound of radius. What's more, the parameters' setting is more
	simple.
	Based on above lemmas, we analyze the minimal radius.

	\begin{lemma}\label{Newton:STR:Lemma:Bound:Radius}
		In Algorithm \ref{Newton:STR:Algorithm}, suppose the Assumption
		\ref{Newton:Assumption:function}-
		\ref{Newton:Assumption:Bound:Variance} hold,  let $| {{\mathcal{S}_h}} | = \min
		\{ n,\max \{ H_1/\varepsilon_g,H_2/\varepsilon_B
		\} \}$, $1>r_1>0$, there
		will be a  non-zero radium
		\begin{align}\label{Newton:STR:Lemma:Bound:Radius-equality}
		{\Delta _\text{min}} = \min \left\{ {{\Delta _\text{min1}},{\Delta
				_\text{min2}}}
		\right\},
		\end{align}
		where the parameters satisfy
		\begin{align}
		\label{Newton:STR:Lemma:Bound:Radius-equality1}
		{\Delta _\text{min1}} =& {\kappa _1}\left( {{\varepsilon _{\nabla f}} -
			{\varepsilon _g}}
		\right),{\kappa _1} = {r_1}\min \left\{ {\frac{1}{{{\kappa _H}}},\frac{1}{{40}}\left( {1 -
				\eta
			} \right),\sqrt {\frac{1}{{12{L_H}}}\left( {1 - \eta } \right)} } \right\},\\
		\label{Newton:STR:Lemma:Bound:Radius-equality2}
		{\Delta _\text{min2}} =& {\kappa _2}\left( {{\varepsilon _H} -
			{\varepsilon _B}}
		\right),{\kappa _2} = {r_1}\frac{1}{{6{L_H}}}\left( {1 - \eta } \right),\\
		{\varepsilon _g} =& \frac{1}{{16}}\left( {1 - \eta } \right)\left( {{\varepsilon _{\nabla
					f}} - {\varepsilon _g}} \right),\nonumber\\
		{\varepsilon _B} =& {\varepsilon _h} = \frac{1}{{10}}\left( {1 - \eta } \right)\left(
		{{\varepsilon _H} - {\varepsilon _B}} \right).\nonumber
		\end{align}
		In particular, 	$\Delta_\text{min1}$ belongs to the case of $x\in
		\mathcal{S}_{\nabla f}$ and $\Delta_\text{min2}$ belongs to the case of
		$x\in
		\mathcal{S}_{H}$.
	\end{lemma}

	\subsection{Convergence and iteration complexity}
	In this section, we  present the successful and
	unsuccessful iteration complexity based on Lemma
	\ref{Newton:STR:Lemma:Bound:Radius} including
	$x\in \mathcal{S}_{\nabla f}$ and $k\in \mathcal{S}_H$, and then provide the total number of
	iterations.

	\begin{theorem}\label{Newton:STR:Theorem:Iteration}
		In Algorithm \ref{Newton:STR:Algorithm}, suppose the Assumption
		\ref{Newton:Assumption:function}-
		\ref{Newton:Assumption:Bound:Variance} hold, let $| {{\mathcal{S}_h}} | = \min
		\{ n,\max \{ H_1/\varepsilon_g,H_2/\varepsilon_B
		\} \}$, $\{ {f( {{x_k}} )} \}$ is
		bounded below by $f_{\text{low}}$, the number of successful iterations ${T_\text{suc}}$  is
		no large than
		\[{\kappa _3}{\rm{max}}\{ {{{( {{\varepsilon _{\nabla f}} - {\varepsilon _g}}
					)}^{ - 2}},{{({\varepsilon _H} - {\varepsilon _B})}^{ - 3}}} \},\]
		where ${\kappa _3} = 2\left( {f\left( {{x_0}} \right) - {f_{low}}} \right){\rm{max}}\left\{
		{1/\left( {\eta {\kappa _1}} \right),1/\left( {\eta \kappa _2^2} \right)} \right\}$,
		$\kappa_1$
		and $\kappa_2$ are defined in (\ref{Newton:STR:Lemma:Bound:Radius-equality1}) and
		(\ref{Newton:STR:Lemma:Bound:Radius-equality2}). The number of unsuccessful iterations
		$T_\text{unsuc}$ is at
		most
		\[ \frac{1}{{ - \log {r_1}}}\left( {\log \left( {\frac{{{\Delta
							_{{\text{max}}}}}}{{{\Delta _{{\text{min}}}}}}} \right) - T\log {r_2}}
		\right).\]
		where ${\Delta _{\text{max}}}$ and ${\Delta _{\text{min} }}$ are defined in
		(\ref{Newton:STR:Lemma:Bound:Radius-equality}) and Algorithm \ref{Newton:STR:Algorithm},
		$1>{r}_1>0$ and
		$r_2\ge
		1$. Thus, the total
		number of iterations is
		\[\mathcal{O}\left( {\max \{ {{{({\varepsilon _{\nabla f}} - {\varepsilon _g})}^{ -
						2}},{{({\varepsilon _H} - {\varepsilon _B})}^{ - 3}}} \}} \right)\]

	\end{theorem}

	After the $|T_\text{suc}|+|T_\text{unsuc}|$ iterations, it will fall into $\mathcal{S}_*$ and
	converge to the
	stationary point. As can be seen from above Theorems, we make two conclusions: the first is the
	order of iteration complexities are the same as \cite{cartis2011adaptiveb} and
	\cite{xu2017second}
	if the parameters $\varepsilon_g$ and $\varepsilon_B$ are set properly according to
	$\varepsilon_{\nabla f}$ and $\varepsilon_H$ respectively;
	the second is that when $| {{\mathcal{S}_h}} |<n$, the total number of computation iteration
	including computing the function is less than that of \cite{cartis2011adaptiveb} and
	\cite{xu2017second}; when  $| {{\mathcal{S}_h}} |=n$, our result is equal
	to\cite{cartis2011adaptiveb} and
	\cite{xu2017second}. Thus, our proposed algorithm is more general.

	\section{Stochastic Adaptive Regularization using Cubics}\label{Newton:Section:SARC}

	\begin{algorithm*}[t]
		\caption{SARC  with the Inexact Hessian and Gradient}
		\label{Newton:SARC:Algorithm}
		\begin{algorithmic}[1]
			\Require given $x_0$, $r_2\ge 1> r_1$, $1>\eta>0$, $\varepsilon>0$ and
			$\sigma_\text{min}>0$.
			\Ensure
			\For{$k$=1 to T }
			\State Compute the approximate gradient $g(x_k)$ and
			Hessian matrix 	$B(x_k)$ based on
			(\ref{Newton:STR:Subsampling:g})
			and (\ref{Newton:STR:Subsampling:B}).
			\State \Comment({\color{black} if

				$||g\left( {{x_k}} \right)|| \le {\varepsilon 	_{\nabla 	f}} + {\varepsilon
				_g}$,
				we set $\mathcal{S}_h=\mathcal{S}_g$})
			\State Compute the direction vector $s_k$
			\begin{align}\label{Newton:SARC:Algorithm-solution}
			s_k=\text{Subproblem-Solver}(g(x_k),B(x_k),\sigma_k).
			\end{align}
			\State Compute the approximate function $h(x_k)$ and $h(x_k+s_k)$ based on
			(\ref{Newton:STR:Subsampling:h}).
			\State 	Compute $
			{{\tilde \rho }_k} = \frac{{h\left( {{x_k}} \right) - h\left( {{x_k} + {s_k}}
					\right)}}{{{p_k}\left( 0 \right) - {p_k}\left( {{s_k}} \right)}}
			$
			\State Set $\rho={{{\tilde \rho }_k} - \frac{{2{\varepsilon _f}/{\color{black}\sigma^
							2_k}}}{{{p_k}\left( 0
						\right) - {p_k}\left( {{s_k}} \right)}}}$
			\State set ${x_{k + 1}} = \left\{ {\begin{array}{*{20}{l}}
				{{x_k} + {s_k},}&{\rho  \ge \eta ,}\\
				{{x_k},}&{{\rm{otherwise}}{\rm{.}}}
				\end{array}} \right.$
			\State set
			${\sigma _{k + 1}} = \left\{ {\begin{array}{*{20}{l}}
				{\max \left\{ {{\sigma _{\text{min} }},{r_1}{\sigma _k}} \right\},}&{\rho  > \eta
				,}\\
				{{r_2}{\sigma _k},}&{{\rm{otherwise}}.}
				\end{array}} \right.$
			\EndFor
		\end{algorithmic}
	\end{algorithm*}

	In this section, we consider the stochastic adaptive regularization using
	Cubics (SARC) method, which solves the following unconstrained minimization
	problem at each iteration:
	\begin{align}\label{Newton:SARC:definition_P}
	\mathop {\min }\nolimits_{s\in \mathbb{R}^d}  p_k( s ) := m_k(s) + \frac{{{\sigma _k}}}{3}{\| s
		\|^3},
	\end{align}
	where $m_k(s)$ is defined in (\ref{Newton:Definition_m}), and $\sigma_k$
	is an adaptive parameter that can be considered as the reciprocal of the
	trust-region radius. Algorithm \ref{Newton:SARC:Algorithm} presents the process for
	updating the $x_k$ and $\sigma_k$. Similar to the analysis as in \cite{cartis2011adaptivea},
	$\sigma_k$ in the
	cubic term actually performs one more task, besides accounting for the
	discrepancy between the objective function and its corresponding
	second-order Taylor expansion, but also for the difference between   the exact and approximate
	function, gradient and Hessian. The update rules of $\sigma$ is analogous to stochastic region
	method. $\sigma$ will decrease if sufficient decrease is obtained in some measure of relative
	objective chance, but increase otherwise. Following the framework of STR, we analyze SARC
	including
	two parts: To ensure the existence of the maximal bound of $\sigma$ and present the iterative
	complexity.

	\subsection{Bounds analysis of  the adaptive parameter}
	Similar to STR, we present the definition of $\rho$ directly,
	\begin{align}\label{Newton:SARC:1-p}
	1 - \rho  =& \frac{{{p_k}\left( 0 \right) - {p_k}\left( {{s_k}} \right) - \left( {h\left(
				{{x_k}} \right) - h\left( {{x_k} + {s_k}} \right)} \right) + 2{\varepsilon
				_h}\|s_k\|^2}} {{{p_k}\left( 0 \right) - {p_k}\left( {{s_k}} \right)}}
	\end{align}
	In order to satisfy inequality (\ref{Newton:SARC:1-p}), we
	need to obtain the lower bound of the numerator in
	(\ref{Newton:SARC:1-p}). Firstly, we derived the lower bound
	from the view of a Cauchy pint, but subject to ${p_k}\left( {{s_k}} \right)
	\le {p_k}\left( {s_k^C} \right)$. Note that the lower bound is almost the
	same
	as in \cite{cartis2011adaptivea} and \cite{xu2017newton}, but give the
	proof
	from the geometrical explanation.

	\begin{lemma}\label{Newton:SARC:Lemma:UpperboundOfP0Ps}
		Suppose that the step size $s_k$ satisfying ${p_k}\left( {{s_k}}
		\right)
		\le {p_k}\left( {s_k^C} \right)$, where $s_k^C$ is a Cauchy point, 	defined
		as
		\begin{align*}
		s_k^C =&  - {\alpha _k}g\left( {{x_k}} \right),

		{\alpha _k} =

		\mathop {\arg \min }\nolimits_{\alpha  \in {\mathbb{R}_ +
		}}
		\left\{ {{p_k}\left( x_k{ - \alpha g\left( {{x_k}} \right)} \right)}
		\right\},
		\end{align*}
		for all $k\ge 0$,
		we have that

		\begin{center}
			$p_k(0) - {p_k}( s_k)
			\ge
			\frac{1}{10}\left\| {{g_k}} \right\|\min \left\{
			{{\left\| {{g_k}} \right\|}/{{\left\| {{B_k}} \right\|}},\sqrt {{{\left\| {{g_k}}
							\right\|}}/(\sigma _k)} }
			\right\}.$
		\end{center}
		Specifically, we set ${\alpha} = 2/(\| B_k
		\| + \sqrt
		{{\| B_k \|}^2 + 4{\sigma _k}\| g_k
			\|} )$ and $s_k=-\alpha g(x_k)$ that satisfy above inequality. Furthermore, we
		can also obtain the upper bound of the step
		$\| s_k \|$, $k>0$, satisfies
		$\| s_k \| \le {{11}}/{4}\max \{ {{{\|
					{B({x_k})} \|}}/{{{\sigma _k}}},\sqrt {{{\|
						{g({x_k})}
						\|}}/{{{\sigma _k}}}} } \}.$

	\end{lemma}

	Following the subspace analysis in the cubic model as in
	\cite{cartis2011adaptivea}
	and \cite{cartis2011adaptiveb}, in order to widen the scope of convergence
	analysis and iteration complexity, we also consider the step size $s_k$ on
	the
	following conditions
	\begin{align}
	\label{Newton:SARC:Assumption_s1}
	&\left\langle {g\left( {{x_k}} \right),{s_k}} \right\rangle  +
	s_k^T{B_k}{s_k} +
	{\sigma _k}{\left\| {{s_k}} \right\|^3} = 0,\\
	\label{Newton:SARC:Assumption_s2}
	&s_k^T{B_k}{s_k} + {\sigma _k}{\left\| {{s_k}} \right\|^3} \ge 0,\\
	\label{Newton:SARC:Assumption_s3}
	&\left\| {\nabla {p_k}\left( {{s_k}} \right)} \right\| \le {\theta _k}\left\| {\nabla g\left(
		{{x_k}} \right)} \right\|,{\theta _k} \le {\kappa _\theta }\text{min}\left\{ {1,\left\|
		{{s_k}}
		\right\|} \right\},{\kappa _\theta } < 1.
	\end{align}
	Thus, we can also obtain lower bound of the numerator in
	(\ref{Newton:SARC:1-p}), which will be used for analyzing the
	convergence and
	iteration complexity in the case of the saddle point.

	\begin{lemma}\label{Newton:SARC:Lemma:UpperboundOfP0Ps-2} Given the
		conditions of
		$s_k$ in
		(\ref{Newton:SARC:Assumption_s1}) and
		(\ref{Newton:SARC:Assumption_s2}),
		we have

		\begin{align*}
		p( 0) - {p_k}( s_k ) \ge
		\frac{{{\sigma_k}}}{6}{\| {{s_k}} \|^3}.
		\end{align*}
		Furthermore, 	suppose
		Assumption \ref{Newton:Assumption:function} and
		\ref{Newton:Assumption:approximation},  and the condition (\ref{Newton:SARC:Assumption_s3})
		hold, for $\left\| {g\left( {{x_{k + 1}}} \right)} \right\| \ge {\varepsilon _{\nabla f}} -
		{\varepsilon _g}$, we have
		\begin{align}\label{Newton:SARC:Lemma:UpperboundOfP0Ps-2-1}
		\left\| {g\left( {{x_{k + 1}}} \right)} \right\| \le {\kappa
			_s}{\left\| {{s_k}}
			\right\|^2},
		\end{align}
		where
		\[\begin{array}{l}
		{\kappa _s} = \min \left\{ {\frac{{2{\varepsilon _B} + \left(
					{{L_H} + {\sigma _k}}
					\right) + 2{\kappa _\theta }{\varepsilon _g} + {\kappa _\theta
					}{L_{\nabla f}}}}{{\left( {1 -
						{\theta
							_k}} \right)}},\frac{{{L_H} + {\sigma _k} + {\kappa _\theta }{L_{\nabla
							f}}}}{{1 - {\theta _k}
					- {\zeta
						_1} - {\zeta _2}}}} \right\}, {\zeta _1},{\zeta _2} < 1\\
		{\varepsilon _B} \le {\zeta _1}\left( {{\varepsilon _{\nabla f}} - {\varepsilon _g}}
		\right),{\varepsilon _g} \le {\zeta _2}\left( {{\varepsilon _{\nabla f}} - {\varepsilon
		_g}}
		\right)
		\end{array}\]
	\end{lemma}
	Different from the STR, we can also derive the relationship between $g(x_{k+1})$ and $\|s_k\|$.
	The
	core process of the proof is based on cubic regularization of Newton method
	\cite{nesterov2006cubic}. Such a relationship leads to the improved iteration complexity.
	Besides
	lower bound of the numerator in (\ref{Newton:SARC:1-p}), we can also obtain the corresponding
	upper bound of the denominator, which is similar to Lemma
	\ref{Newton:STR:Lemma:Upperbound_fxs-msx}.
	Thus, we do not provide the proof.

	\begin{lemma}\label{Newton:SARC:Lemma:Upperbound_p-h}
		Suppose the Assumption \ref{Newton:Assumption:function},
		\ref{Newton:Assumption:approximation} and \ref{Newton:Assumption:Bound:Variance} hold, at
		$k$-iteration, we have
		\begin{align*}
		&{p_k}\left( 0 \right) - {p_k}\left( {{s_k}} \right) - \left( {h\left( {{x_k}} \right) -
			h\left(
			{{x_k} + {s_k}} \right)} \right)\\
		\le& 2\left( {\frac{\mathbb{I}{\left( {\left| {{{\cal S}_h}} \right| < n} \right)}}{{\left|
					{{{\cal
								S}_h}}
					\right|}}{H_1} + {\varepsilon _g}} \right)\left\| {{s_k}} \right\| +
		\frac{3}{2}\left(
		{\frac{\mathbb{I}{\left( {\left| {{{\cal S}_h}} \right| < n} \right)}}{{\left| {{{\cal
								S}_h}}
					\right|}}{H_2} + {\varepsilon _B}} \right){\left\| {{s_k}} \right\|^2} + \left(
		{\frac{3}{2}{L_H} - \frac{1}{3}{\sigma _k}} \right){\left\| {{s_k}} \right\|^3}
		\end{align*}
		If $\mathcal{S}_h=\mathcal{S}_g$, we have
		\begin{align*}
		{p_k}\left( 0 \right) - {p_k}\left( {{s_k}} \right) - \left( {h\left( {{x_k}} \right) -
			h\left(
			{{x_k} + {s_k}} \right)} \right)\le\frac{3}{2}\left(
		{\frac{\mathbb{I}{\left( {\left| {{{\cal S}_h}} \right| < n} \right)}}{{\left| {{{\cal
		S}_h}}
					\right|}}{H_2} + {\varepsilon _B}} \right){\left\| {{s_k}} \right\|^2} + \left(
		{\frac{3}{2}{L_H} - \frac{1}{3}{\sigma _k}} \right){\left\| {{s_k}} \right\|^3}.
		\end{align*}
	\end{lemma}

	Based on the above lemmas, we can derive the upper bound of adaptive parameter $\sigma$, which
	is
	used to analyze the iteration complexity. Furthermore, the parameters' setting, such as
	$\varepsilon_g$, $\varepsilon_B$ and $\varepsilon_h$ are similar
	to that of Lemma \ref{Newton:STR:Lemma:Bound:Radius}.
	\begin{lemma}\label{Newton:SARC:Lemma:bound_sigmal}In Algorithm \ref{Newton:SARC:Algorithm},
		suppose Assumption
		\ref{Newton:Assumption:function}-\ref{Newton:Assumption:Bound:Variance} hold, let $|
		{{\mathcal{S}_h}} | = \min
		\{ n,\max \{ H_1/\varepsilon_g,H_2/\varepsilon_B
		\} \}$, $r_2>1$, the parameter
		$\sigma$ is bounded by
		\begin{align}\label{Newton:SARC:Lemma:bound_sigmal-1}
		{\sigma _{\text{max}}} = \max  \left\{ {{\sigma _\text{max1}},{\sigma
				_\text{max2}}}
		\right\},
		\end{align}
		where
		\begin{align}
		{\sigma _{{\text{max1}}}} =& {\kappa
			_4}\frac{1}{{({\varepsilon _{\nabla f}} - {\varepsilon _g})}},{\sigma _{\text{max2}}} =
		\frac{9}{2}{r_2}{L_H},\nonumber\\
		\label{Newton:SARC:Lemma:bound_sigmal-2}
		{\kappa _4} =& {r_2}\left\{ {\kappa _H^2,\frac{{{{\left( {304\left( {3{\varepsilon _B} +
									2{\varepsilon _h}} \right)} \right)}^2}}}{{\left( {1 - \eta }
					\right)}},\frac{9}{2}({\varepsilon _{\nabla f}} - {\varepsilon _g}){L_H}}
		\right\},\\
		{\varepsilon _g} =&
		\frac{1}{{220}}\left( {1 - \eta } \right)({\varepsilon _{\nabla f}} -
		{\varepsilon _g}),\nonumber\\
		{\varepsilon _B} =& {\varepsilon _h} =\frac{1}{{36}}\left( {1 - \eta } \right)\left(
		{{\varepsilon _H} -
			{\varepsilon _B}} \right).\nonumber
		\end{align}
		In particular, 	$\sigma_\text{min1}$ belongs to the case of $x\in
		\mathcal{S}_{\nabla f}$ and $\sigma_\text{min2}$ belongs to the case of
		$x\in
		\mathcal{S}_{H}$.
	\end{lemma}

	\subsection{Analysis of convergence and iteration complexity}
	Based on above lemmas, we present the iteration complexity. Different from STR, we derive two
	kinds of complexity. The first one has the same order as STR while the second is better or
	equal to
	STR. The difference lies that if the criterion conditions in (\ref{Newton:SARC:Assumption_s3})
	is
	satisfied, the iteration
	complexity to the stationary point is improved.

	\begin{theorem}\label{Newton:SARC:theorem:Iteration}
		In Algorithm \ref{Newton:SARC:Algorithm}, suppose the Assumption
		\ref{Newton:Assumption:function}-
		\ref{Newton:Assumption:Bound:Variance} hold, let $| {{\mathcal{S}_h}} | = \min
		\{ n,\max \{ H_1/\varepsilon_g,H_2/\varepsilon_B
		\} \}$, $\{ {f( {{x_k}} )} \}$ is
		bounded below by $f_{\text{low}}$, the number of successful iterations ${T_\text{suc}}$  is
		no large than
		\[{\kappa _5}\max \{ {{{({\varepsilon _{\nabla f}} - {\varepsilon _g})}^{ - 2}},{{(
					{{\varepsilon _H} - {\varepsilon _B}} )}^{ - 3}}} \},\]
		where ${\kappa _5} = ( {f( {{x_0}} ) - {f_{{\rm{low}}}}} )\max \{
		{5/( \eta \kappa _4^{ - 1/2} ),6{\sigma _{{\rm{max2}}}}/\eta } \}$,
		$\kappa_4$  is defined in (\ref{Newton:SARC:Lemma:bound_sigmal-2}). If the conditions
		(\ref{Newton:SARC:Assumption_s1})-(\ref{Newton:SARC:Assumption_s3}) are satisfied, then the
		number of successful 	iterations
		$T_\text{unsuc}$ is at
		most
		\[{\kappa _6}\max \{ {{{({\varepsilon _{\nabla f}} - {\varepsilon _g})}^{ - 3/2}},{{(
					{{\varepsilon _H} - {\varepsilon _B}} )}^{ - 3}}} \},\]
		where ${\kappa _6} = ( {f( {{x_0}} ) - {f_{{\text{low}}}}} )\max \{
		{6\kappa _s^{3/2}/( {\eta {\sigma _{{\text{min}}}}} ),6{\sigma _{{\text{max2}}}}/\eta }
		\}$, $\kappa_s$ is defined (\ref{Newton:SARC:Lemma:UpperboundOfP0Ps-2-1}).
	\end{theorem}
	As can be seen above results, our proposed method has the same order of iteration complexity as
	in
	\cite{xu2017newton} and \cite{xu2017second}. However, our algorithm does not require the full
	computation of function and gradient with the finite-sum structure such that reduce the
	computation
	cost properly.

	\section{Experiment}\label{Newton:Section:Experiment}

	\begin{figure*}[t]
		\centering
		\includegraphics[width=0.7\linewidth]{experiment_result.eps}
		\caption{Training loss/accuracy vs running time for different schemes of
			second-order methods. Note that TR-full and ARC-full only finish 1 epoch
			after 3000 seconds, so we omit them in the plot. }
		\label{fig:experiment_result}
	\end{figure*}

	In this section, we give a comprehensive comparison among trust region and ARC
	algorithms. Our goal is not to show TR/ARC methods are state-of-the-art
	compared with other solvers; we are trying to present different variances of TR and
	ARC, and show using a fixed batch size to estimate both gradient and Hessian
	is the best choice for large-scale optimization.
	We compare following variants:
	\begin{itemize}
		\item Stochastic TR with fixed batch size (TR, fixed): Both Hessian and
		gradient are estimated through a fixed batch size at each iteration. In our
		experiment, we choose batch size $|B_g|=|B_H|=256$.
		\item Stochastic TR with growing batch size (TR, inc): As above, both
		Hessian and gradient are estimated through a batch of samples, except
		that the sample size is increasing with epochs: At the early stage we feed
		a crude estimation of $\nabla f(x)$ and $\nabla^2 f(x)$ on small batch,
		then gradually increase the batch size to give better gradient and Hessian
		information. In practice we multiply the batch size by a factor of $2$ for
		every $10$ epochs until memory is used up.
		\item Stochastic TR with exact gradient and subsampled Hessian (TR, full): We use
		implementation similar with \cite{xu2017newton,xu2017second}. At each iteration the
		gradient is
		exact, while the Hessian is approximated on a batch of $256$ samples.
		\item Stochastic ARC with fixed batch size (Cubic, fixed): This is similar to stochastic
		TR,
		the batch size is fixed to $|B_g|=|B_H|=256$.
		\item Stochastic ARC with growing batch size (Cubic, inc): Similar to stochastic TR with
		increasing batch size, we double the batch size once every $10$ epochs to estimate both
		Hessian
		and gradient.
		\item ARC with exact gradient and subsampled Hessian (Cubic, full): The
		gradient is exactly computed while the Hessian is approximated on a batch
		of $256$ samples.
	\end{itemize}
	Note that the ARC-inc algorithm is proposed in~\cite{kohler2017sub}; TR-inc is
	a generalization of that to the trust region case; TR-full and ARC-full are
	proposed in~\cite{xu2017newton}; TR-fixed and ARC-fixed are our method
	analyzed in this paper.

	We train a VGG16 network\footnote{Publically available at
		\url{https://raw.githubusercontent.com/kuangliu/pytorch-cifar/master/models/vgg.py}} on
		CIFAR10
	dataset using the above algorithms and evaluate the performance according to
	training loss and test accuracy with respect to training time. All the
	experiments are run on a machine with 1 Titan Xp GPU.
	The result is reported in Figure~\ref{fig:experiment_result}.

	Note that TR-full and ARC-full take 3500 seconds  while
	TR-fixed and ARC-fixed only take 40 seconds for each epoch. Thus we omit the
	full gradient versions on the plot since there will be only one point there.
	This shows that calculating the full gradient for each update is
	too expensive for solving large-scale problems like deep learning.
	Apart from that we notice both Cubic and TR on fixed batch size are faster
	than their growing batch size version, this validates our guess that sampling
	a fixed number of data to estimate gradient and Hessian is sufficient to make
	trust region and ARC work, and this scheme turns out to be more efficient than
	sample a growing batch over time. Moreover, in our task, the trust region
	algorithm is faster than ARC algorithm. However, we are not sure whether this
	phenomenon also applies to other tasks.

	\section{Conclusion}\label{Newton:Section:Conclusion}
	In this paper, we present a family of stochastic trust region method and
	stochastic cubic regularization method under inexact gradient and Hessian
	matrix. Furthermore, in order to reduce the computation cost for the function
	value of $f(x)$ in evaluating the role of $\rho$, we also present a
	sub-sample technique to estimate the function.  We provide the theoretical
	analysis of convergence and iteration complexity and obtain that we keep the
	same order of iteration complexity but reduce the computation cost per
	iteration. We apply our proposed method to deep learning application which
	outperforms  the previous second-order methods.
	{\small

		\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
Home > Journals > Journal of Literary & Cultural Disability Studies > Volume 13 (2019), Issue 4 > Sexy Like Us
Journal of Literary & Cultural Disability Studies
Sexy Like Us
Expanding Notions of Disability and Sexuality Through Burlesque Performance
Milbrodt, Teresa
Journal of Literary & Cultural Disability Studies (2019), 13, (4), 377–392.
I thought you would find this interesting: Journal of Literary & Cultural Disability Studies, Volume 13, Issue 4 Sexy Like Us Milbrodt, Teresa Editors: David Bolt Journal of Literary & Cultural Disability Studies (2019), 13, (4), 377–392.
https://doi.org/10.3828/jlcds.2019.29
People with disabilities often have their sexuality denied or dismissed in mainstream culture, which prohibits disabled bodies from being considered sexy bodies. The article explores how burlesque performance can open a space for people with disabilities to display their bodies onstage and expand the notion of what kinds of bodies and performances can be considered sexy and sexual. This type of stage performance allows for a prolonged stare that helps audience members normalize body variability, while the storytelling element allows disabled actors to create spaces of identification with the audience through narrative. By using burlesque techniques to perform disability in innovative ways, disabled actors can create a space for individuals to be considered sexual beings because of disability, not in spite of their embodiment, thereby expanding notions of sexuality and sexual practice for all bodies.
Allen, Robert C. Horrible Prettiness: Burlesque and American Culture. Chapel Hill: U of North Carolina P, 1991. Print. Google Scholar
Baynton, Douglas. "Disability and the Justification of Inequality in American History." The Disability Studies Reader. Ed. Lennard J. Davis. New York: Routledge, 2017. 17–34. Print. Google Scholar
Berne, Patricia, Jamal T. Lewis, Stacey Milbern, Malcolm Shanks, Alok Vaid, and Alice Wong. "'Beauty Always Recognizes Itself': A Roundtable on Sins Invalid." WSQ: Women's Studies Quarterly 46.1–2 (2018): 241–50. Web. 1 May 2018. Google Scholar
"Brave Sheffield Woman Performs Burlesque Routine in Wheelchair and Wearing Stoma Bag." The Star, Sheffield, UK. 20 Dec. 2015. Web. 2 Feb. 2017. Google Scholar
Butler, Alexis. "Re-Vamping History: Neo-Burlesque and Historical Tradition." Canadian Theater Review 158 (2014): 44–47. Web. 2 Feb. 2017. Google Scholar
Clare, Eli. Exile and Pride: Disability, Queerness, and Liberation. Boston, MA: South End Press, 1999. Print. Cohen, Rena. 9 Feb. 2017. Personal interview. Google Scholar
Disman, Adriana. "The Politics of Burlesque: A Dialogue Among Dancers." Canadian Theater Review 158 (2014): s1–s16. Web. 2 Feb. 2017. Google Scholar
Dodds, Sherril. "Embodied Transformations in Neo-Burlesque Striptease." Dance Research Journal 45.3 (2013): 75–90. Web. 2 Feb. 2017. Google Scholar
Fraser, Mat. "Mat 'Seal Boy' Fraser Burlesque Performance." 12 Jan. 2012. YouTube. Web. 1 May 2018. Google Scholar
Garland-Thomson, Rosemarie. Extraordinary Bodies: Figuring Physical Disability in American Culture and Literature. New York: Columbia UP, 1996. Print. Google Scholar
Garland-Thomson, Rosemarie. Staring. New York: Oxford UP, 2009. Print. Google Scholar
Graves, Cassidy Dawn. "An Interview With Disabled Burlesque Performer Cerebral Pussy." NYU Local. 15 Oct. 2015. Web. 2 Feb. 2017. Google Scholar
Henry, Elsa S. "Self Casting and Burlesque." Feminist Sonar. 10 Sep. 2012. Web. 2 Feb. 2017. Google Scholar
Kafaim, Shayda. "Reclaiming and Honoring: Sins Invalid's Cultivation of Crip Beauty." WSQ: Women's Studies Quarterly 46.1–2 (2018): 231–35. Web. 2 May 2018. Google Scholar
Kafer, Alison. "Desire and Disgust: My Ambivalent Adventures in Devoteeism." Sex and Disability. Ed. Robert McRuer and Anna Mallow. Durham: Duke UP, 2012. 331–54. Print. Google Scholar
Kafer, Alison. Feminist, Queer, Crip. Bloomington, IN: Indiana UP, 2013. Print. Google Scholar
Kuppers, Petra. Disability Culture and Community Performance: Find a Strange and Twisted Shape. New York: Palgrave/MacMillan, 2011. Print. Google Scholar
Lewis, Bradley. "A Mad Fight: Psychiatry and Disability Activism." The Disability Studies Reader. Ed. Lennard J. Davis. New York: Routledge, 2017. 103–16. Print. Google Scholar
Lorde, Audre. The Cancer Journals. Special Edition. San Francisco: Aunt Lute Books, 1997. Print. Google Scholar
Mairs, Nancy. "Sex and Death and the Crippled Body: A Meditation." Disability Studies: Enabling the Humanities. Ed. Sharon L. Snyder and Brenda Jo Bruggeman. New York: Modern Language Association of America, 2002. 156–70. Print. Google Scholar
McRuer, Robert. Crip Theory: Cultural Signs of Queerness and Disability. New York: New York UP, 2006. Print. Google Scholar
McRuer, Robert and Anna Mallow. "Introduction." Sex and Disability. Ed. Robert McRuer and Anna Mallow. Durham, NC: Duke UP, 2012. 1–34. Print. Google Scholar
Mossman, Mark. "Visible Disability in the College Classroom." College English 64.6 (2002): 645–59. Web. 15 Oct. 2015. Google Scholar
Muñoz, José. Disidentifications: Queers of Color and the Performance of Politics. Minneapolis: U of Minnesota P, 1999. Print. Google Scholar
Nelson, Adiba. "She's Sitting Pretty." 3 Story Magazine. May 2015. Web. 2 Feb. 2017. Google Scholar
Sandahl, Carrie. "The Tyranny of Neutral: Disability and Actor Training." Bodies in Commotion: Disability and Performance. Ed. Carrie Sandahl and Philip Auslander. Ann Arbor: U of Michigan P, 2005. 255–68. Print. Google Scholar
Sexy Voices. Realwheels Theatre Company. Dir. Rachel Peake. Vancouver, BC. 12–14 May 2016. Video performance. Google Scholar
Shakespeare, Tom. "Joking a Part." Body & Society 5.4 (1999): 47–52. Sagepub.com. Web. 15 Oct. 2015. Google Scholar
Siebers, Tobin. Disability Theory. Ann Arbor: U of Michigan P, 2008. Print. Google Scholar
Snyder, Sharon L. and David T. Mitchell. Cultural Locations of Disability. Chicago: U of Chicago P, 2006. Print. Google Scholar
Takemoto, Tina. "Love Is Still Possible in this Junky World: Conversation with Sheree Rose about Her Life with Bob Flanagan." Women & Performance: A Journal of Feminist Theory 19.1 (2009): 95–111. Web. 2 May 2018. Google Scholar
Wilson, Jacki. The Happy Stripper: Pleasures and Politics of the New Burlesque. London: I.B. Tauris, 2008. Print. Google Scholar

redpajama_set_name: RedPajamaCommonCrawl


text:
The Best Laid Plans by Terry Fallis wins Canada Reads 2011!
Submitted by erin on February 9, 2011 - 3:26pm
This year's CBC Canada Reads was a big one...and the panelists proved themselves up to the challenge with heated debates, surprising twists, a confession — and of course, a winner. Terry Fallis's The Best Laid Plans (McClelland & Stewart), which initially couldn't even find a publisher, has been crowned Canada's book of the decade. The Best Laid Plans was championed by CNN broadcaster Ali Velshi.
There's still time to weigh in with your opinion: visit the CBC Canada Reads website to vote in the Canada Reads People's Choice poll.
Thu March 11, 2010
Deborah Ellis and Eric Walters Receive OLA President's Award
View more items filed under "Awards" in our Open Book Archives.
Submitted by clelia on March 11, 2010 - 6:01pm
Eric Walters and former Open Book writer in residence Deborah Ellis have been awarded the Ontario Library Association's 2010 President's Award for Exceptional Achievement. The award "acknowledges an outstanding action or contribution that has in a major or unique way enhanced or furthered librarianship in Ontario." Find out more about the award at the OLA website.


Bill Tibbles spent 30+ years directing creative and running one of Toronto's most successful boutique marketing and communications studios. Two years after attending the Ontario College of Art, Bill opened his own company where he masterminded projects that included the design of 24 Canadian postage stamps and campaigns for Volkswagen, Tyco Electronics and RBC Royal Bank. Bill has a reputation for building long term relationships with clients and will continue to bring clients full agency services at Rapport.


text:
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    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:fitsSystemWindows="true"

    app:layout_behavior="@string/action_settings"

    tools:context="com.st33fo.glideforktt.Feed">
    <android.support.design.widget.CoordinatorLayout
        xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:app="http://schemas.android.com/apk/res-auto"
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        android:layout_width="match_parent"
        android:layout_height="match_parent">

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        android:layout_width="match_parent"
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        app:elevation="4dp"
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        app:layout_scrollFlags="scroll|enterAlways|snap"
        android:theme="@style/MyToolbarStyle"

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redpajama_set_name: RedPajamaGithub


In a second opinion today, the Federal Circuit affirmed a district court's finding of inequitable conduct based on the nondisclosure of three pieces of information to the USPTO. The patentee had two similar pending applications at the USPTO, and in fact had cited the same prior art in both applications via information disclosure statements. In addition, a continuation-in-part (CIP) was filed based on the first application, and several claims were allowed in that application. In the other, however, the examiner made additional rejections and discovered another relevant prior art reference.
In the first application, the prosecuting attorney did not disclose the prior art reference or the rejection in the second application. Similarly, the attorney did not disclose the notice of allowance from the CIP. The district court found each of these nondisclosures material, and the fact that the applications were so related, along with the proximity in time (17 days) between when the prosecuting attorney found out about the new prior art reference and arguments made that were arguably inconsistent with the state of the prior art given the teachings of that reference. While there was some evidence that these omissions were made without deceptive intent, the court ultimately found that the evidence as a whole, showed the necessary intent. Accordingly, the court found that substantial evidence supported the district court's determination of inequitable conduct, and affirmed the finding of unenforceability.
Judge Newman dissented. Although only two pages in length, her dissent expresses her belief that this case is a return to "the 'plague' of encouraging unwarranted charges of inequitable conduct" that the court cautioned against in the Kingsdown case.
More detail regarding McKesson Info. Solutions, Inc. v. Bridge Med., Inc. after the jump.
The patent at issue relates to a patient identification system that uses a three-point communication architecture. Generally, the system is made up of a computer system, a base station, and a portable handheld terminal; the court refers to this as the "three node" approach to the system. While the application that led to the '716 patent was pending, there was another, similar application pending at the same time, directed toward a very similar invention and with very similar claims. The prosecuting attorney disclosed the existence of this second application to the examiner in the first application (Examiner Trafton), and the same prior art was disclosed to the USPTO in both applications via information disclosure statements. In response to a first rejection, the prosecuting attorney stated that the cited prior art references did not, either alone or in combination, teach the "three node" system. In response, on December 8, 1987, Examiner Trafton rejected several claims over two different prior art references, Blum and Pejas, but indicated that one claim would be allowable if rewritten in independent form. The patentee accepted this offer, filed a continuation with the appropriate amendment on June 8, 1988. The claims were allowed on February 27, 1989. While this application was pending, a CIP was also filed, and the CIP had nine claims allowed on December 16, 1988.
On February 26, 1987, the examiner in the second application, Examiner Lev, rejected the claims in that application based on the combination of Blum and Pejas. The prosecuting attorney did not disclose this rejection to Examiner Trafton, although, as noted previously, he made a similar rejection in December 1987. In response to an amendment, on October 23, 1987, Examiner Lev had a telephone interview with the prosecuting attorney, where they discussed a previously unknown reference, a prior art patent to Baker. This conversation took place 17 days after the argument in the first application that the prior art did not disclose the "three node" system, but the Baker patent was not disclosed in the first application. Also, although the claims in the two applications were quite similar, the notice of allowance in the first application was not disclosed to Examiner Lev in the second case to be considered for possible double patenting issues.
Based on these three nondisclosures, (1) the Baker patent in the first application, (2) the February 26, 1987 office action from the second application in the first application, and (3) the CIP application's notice of allowance in the first application, the district court found inequitable conduct. Specifically, the court found all three of these nondisclosures material under the "reasonable examiner" standard, and that there was intent to deceive based on circumstantial evidence surrounding the prosecution of the two applications, such as the short time between when the attorney found out about the Baker patent and when prior action had been taken in the first application, the high degree of materiality of the various items not disclosed, and the implausibility of the various explanations given by the prosecuting attorney at trial.
The court affirmed in all respects. First, the court rejected the contention that the Baker reference was cumulative to other prior art of record, finding that it more clearly described the "three node" system that the art of record. With regard to intent to deceive, the court found that it was within the district court's discretion to find the testimony of the prosecuting attorney not credible. The attorney had no independent recollection of the prosecution of the '716 patent, so the court could properly discount this testimony as "the product of newly developed hindsight." If the attorney had considered Baker and found it not to be material, he should have made a reference stating such in the prosecution file, including the reason for discarding it. See MPEP § 2004(18). As a result, based on the circumstantial evidence of intent, such as the relatedness of the applications and claims and the short period of time between the attorney's knowledge of the Baker reference and action in the application, the court found the lower court's conclusions supported by substantial evidence.
The court made similar findings with regard to the other two nondisclosures. For example, the court held that while the attorney disclosed the existence of the related applications, this was not a constructive disclosure of the office actions taken in the similar applications. It was also insufficient to overcome the circumstantial evidence of intent that the same examiner examined both the patent-in-suit and the application whose notice of allowance was not disclosed, because there was no evidence that the examiner actually remembered the allowance in the other application and realized its materiality. Further, the MPEP explicitly stated at the time that an attorney should not assume that an examiner "retains details of every pending file in his mind when he is reviewing a particular application." Therefore, the lower court's findings for these two omissions were likewise supported by substantial evidence.
It is not clear and convincing evidence of deceptive intent that the applicant did not inform the examiner of the examiner's grant of a related case of common parentage a few months earlier, a case that was examined by the same examiner and whose existence has previously been explicitly pointed out by the same applicant. Nor is it clear and convincing evidence of deceptive intent that the applicant did not cite a reference that the applicant had cited in the same related case, and that had been explicitly discussed with the same examiner in the related case.
procedures of patent prosecution, precedent firmly requires that the intent element of inequitable conduct must be established by clear and convincing evidence of deceptive intent -- not of mistake, if there were such, but of culpable intent.
Time will tell whether Judge Newman's concerns about inequitable conduct allegations are well-founded.
To read the full decision in McKesson Info. Solutions, Inc. v. Bridge Med., Inc., click here.


text:
import React from 'react';
import ReactDOM from 'react-dom';
import {
  renderIntoDocument,
  scryRenderedDOMComponentsWithClass,
  Simulate
} from 'react-addons-test-utils';
import {List, Map} from 'immutable';
import {Results} from '../../src/components/Results';
import {expect} from 'chai';

describe('Results', () => {

  it('renders entries with vote counts or zero', () => {
    const pair = List.of('Trainspotting', '28 Days Later');
    const tally = Map({'Trainspotting': 5});
    const component = renderIntoDocument(
      <Results pair={pair} tally={tally} />
    );
    const entries = scryRenderedDOMComponentsWithClass(component, 'entry');
    const [train, days] = entries.map(e => e.textContent);

    expect(entries.length).to.equal(2);
    expect(train).to.contain('Trainspotting');
    expect(train).to.contain('5');
    expect(days).to.contain('28 Days Later');
    expect(days).to.contain('0');
  });

  it('invokes action callback when next button is clicked', () => {
    let nextInvoked = false;
    function next() { nextInvoked = true; }

    const pair = List.of('Trainspotting', '28 Days Later');
    const component = renderIntoDocument(
      <Results pair={pair}
               tally={Map()}
               next={next}/>
    );
    Simulate.click(ReactDOM.findDOMNode(component.refs.next));

    expect(nextInvoked).to.equal(true);
  });

  it('invokes action callback when restart button is clicked', () => {
    let restartInvoked = false;
    const pair = List.of('Trainspotting', '28 Days Later');
    const component = renderIntoDocument(
      <Results pair={pair}
               tally={Map()}
               restart={() => restartInvoked = true}/>
    );
    Simulate.click(ReactDOM.findDOMNode(component.refs.restart));

    expect(restartInvoked).to.equal(true);
  });

  it('renders the winner when there is one', () => {
    const component = renderIntoDocument(
      <Results winner="Trainspotting"
               pair={["Trainspotting", "28 Days Later"]}
               tally={Map()} />
    );
    const winner = ReactDOM.findDOMNode(component.refs.winner);
    expect(winner).to.be.ok;
    expect(winner.textContent).to.contain('Trainspotting');
  });

});


text:
Report: Charities See Only 35 Cents For Each Dollar Raised
Filed Under:Charities, charity, donations, fundraising, Michigan Attorney General, solicitation
LANSING (WWJ) – A new report from the State Attorney General's Office says the middleman that charities use to solicit donations is actually getting more money than the charities themselves.
The state's first annual Professional Fundraising Charitable Solicitation Report found that charities collect an average of only thirty-five cents for every dollar raised by professional fundraisers soliciting donations in Michigan.
"What happens is a charity hires a professional fundraiser, and the fundraiser raises them $100. The fee for that service is, on average, 65 of those dollars go back to the fundraiser and only $35 goes to the charity," said Attorney General spokeswoman Joy Yearout.
Under Michigan law, a professional fundraiser is defined as a person or organization that solicits contributions on behalf of a charity in exchange for compensation. This is different from a charity that hires its own staff member for development and other fundraising activities.
Michigan law requires professional fundraisers to submit the results of their campaigns to the Attorney General. The data includes the type of appeal conducted (mail, telephone, etc.), gross receipts raised, the amount paid to the fundraiser, and the final amount and percentage that went to the charity.
Any charity fundraising in Michigan is required to report these results, so the Professional Fundraising Charitable Solicitation Report includes data from charities across the country. The report includes the results of fundraising campaigns reported to the Attorney General during the 2012 calendar year.
Although hiring professional fundraisers and fundraising council may benefit certain charities, some professional fundraisers leave little of the donations for the intended charity.
"Michigan citizens have generous hearts and deserve to know how much of their donation actually makes it to their intended charity, especially in these times when every dollar makes a difference," Attorney General Bill Schuette said in a statement.
According to the Better Business Bureau's Standards for Charity Accountability, charities should "spend no more than 35 percent of related contributions on fundraising. Related contributions include donations, legacies, and other gifts received as a result of fundraising efforts."
Schuette noted that states are limited in their ability to pass laws to regulate professional fundraisers' solicited contributions. States are also limited to passing laws that prohibit fraudulent fundraising practices and require reporting from charities and their professional fundraisers. Michigan law addresses both aspects.
Schuette added that examples of fraudulent fundraising practices prohibited by Michigan law include: (1) falsely telling a donor that he or she gave six months ago and it's time to give again, or (2) falsely telling a donors that 90 percent of their donations go to the charity, when that is in fact not true.
Yearout said before Michigan residents donate to a charity, they should do some research first.
"You can also avoid this by donating directly to the charity instead of responding to an unsolicited phone call or a mailer. If you contact the charity directly and find out how to donate to them without using a middleman, it's more likely that 100 percent of your donation will go toward the charitable cause," she said.
For more on which charities are being hurt most by this practice, visit www.michigan.gov/AGCharitySearch.


insert forecast sheet for MAC and waterfall charts for MAC – Welcome to Excel's Suggestion Box!
Since this request was about 2 different features, and the Waterfall chart is complete, I'm marking this suggestion as completed. If you were requesting the Forecast Sheet feature, please feel free to create a new suggestion and specify just that particular item so that we can get an accurate picture of the support for it.
Waterfall charts are available in version 16 of Excel for Mac. We will continue to monitor for votes regarding the forecast sheet.
In the absence of the forecast sheet, you are able to use the FORECAST.ETS functions to create the same forecast, but there is no wizard to lead you through the process. Please visit Office.com for help regarding these functions.
Need Waterfall charts for the MAC office version, thanks!
Why do we pay same for Mac subscription but don't get the same functionality - waterfall chart asap please!
Please add the waterfall chart to the standard excel 2016 for mac functionality, or tell everyone it is currently not in here!


text:
Q: MPEG-4 format to mp4v I have two mp4 files, one is in MPEG-4, other is in mp4v.
I was able to convert mp4v to MPEG-4, but is it possible to convert mpv4 to MPEG-4 ?
Why is it that whatsapp takes one MPEG-4 as video and mp4v as gif ?
Info about files

redpajama_set_name: RedPajamaStackExchange


text:
SIGNING: Klok Signs Short-Term Deal
Manager Steve Robinson has signed midfielder Marc Klok on an initial six-month contract, subject to international clearance.
The Dutchman, who operates as a defensive midfielder, started his career with FC Ultrecht where he scored twice in 17 games for the B team.
He made the trip to Scotland in 2013, joining Scottish Premier League side Ross County.
After one season with them, he joined Bulgarian side Cherno More where he played 37 times in a two year spell.
Welcome to the club, Marc!


text:
A year of wine and chocolates
Home/Cruise News/A year of wine and chocolates
A YEAR ago this week, the Queen toured the Cunard ship that bears her name, shortly before smashing a bottle of wine against the hull to christen the vessel.
Since then, the new Queen Elizabeth – the ship, that is, not the monarch – has visited 107 ports around the world in a journey totalling 124,375 nautical miles and including transits of both the Suez and Panama canals.
Her Majesty has not, however, been among the 52,600 passengers.
Since the decommissioning of the Royal Yacht Britannia – an act former Prime Minister Tony Blair apparently now regrets – her days at sea are limited to occasional charters of the Hebridean Princess, a luxurious converted car ferry that carries 50 passengers compared with the Cunard ship's 2,000-plus.
Meanwhile, wine, chocolate and cruising – is there a more mouth-watering combination?
Passengers on Thomson Dream travelling to the Caribbean in December can take part in an art of chocolate-making course over eight sessions during a Transatlantic crossing from Tenerife to Barbados.
The 16-night voyage departs December 2, with fares from £999 (including flights). Other ports of call on the journey include Antigua, St Maarten, Tortola, St Kitts, St Lucia and St Vincent.
Next autumn, passengers on Celebrity Constellation sailing from Southampton will visit top wine-making regions in France, Spain and Portugal, with excursions to vineyards in Bordeaux and Rioja and cellars in Oporto.
On the seven, 12-night sailings between September and November, passengers will also be offered tasting sessions in the ship's Cellar Master's wine bar. Fares from £899.
By John Honeywell| 2011-10-15T09:54:13+00:00 15 October 2011|Cruise News|0 Comments


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Gerresheimer optimizes cold-end operations at pharma glass production plants with state-of-the-art packing robots
2017-01-31 Manufacturing technology
Every year Gerresheimer's customers order several hundreds of millions of glass pharmaceutical packaging products manufactured at the company's plants in Essen and Lohr.
Packing robots were recently introduced to improve the efficiency and reliability of packing operations before the pharmaceutical glass products are delivered to customers.
"Innovative automated processes are safeguarding the future of our plants and improving the quality of our products," commented Dr. Jürgen Unruh, General Manager at Gerresheimer Essen. He added that the installation of packing robots at the Essen facility serves as an example for the other production plants in the Gerresheimer Group.
Pharmaceutical packaging products, such as the glass bottles manufactured by Gerresheimer, have to satisfy stringent requirements and be low in germs and particles. The extremely high temperatures in the glass moulding process initially kill all the germs. To prevent re-contamination, the bottles go straight from the annealing oven to the clean room, where various mechanical and optical inspection systems are used to identify and sort out defective bottles. After the final inspection, the bottles in the clean room are shrink wrapped in the required pack size with safe pack technology to ensure that they are hermetically sealed in a germ-free environment.
The shrink wrapped packs then have to be packaged and palletized to prevent transportation damage. In the past, production plant personnel working in shifts loaded the transport pallets. This kind of work involves a great deal of effort and concentration because it takes place at high speeds. Gerresheimer decided to auto...
The shrink wrapped packs then have to be packaged and palletized to prevent transportation damage. In the past, production plant personnel working in shifts loaded the transport pallets. This kind of work involves a great deal of effort and concentration because it takes place at high speeds. Gerresheimer decided to automate the process in order to eliminate the resulting pallet packing errors.
All the necessary information for the palletization process is contained in the order number. The products are shrink wrapped with safe pack technology in a clean room environment according to the customer's specifications on packing format. There are currently around 1500 different packing formats, 1000 of which can be implemented by the safe pack machine. In the future, a 100% reliable camera system will perform continuous visual inspections to ensure that the packing formats, stability and quality are correct.
The shrink wrapped packs are transported by conveyor belt from the clean room to the packing robots. At the removal station a robot takes a pack off the conveyor belt and places it on the pallet as per the packing instruction. An operator can use a touch screen to adjust the position of the packs. When one pallet layer is finished, and before the next layer is placed on top, the packing robot adds a protective interim layer. When the pallet is ready it is taken to the holding area in front of the turntable, and the next pallet is loaded. The pallet labels are affixed manually by an operator, who also releases the pallets for delivery. The final stage of the process is the shrink wrapping of the pallets.
glass packaging
pharmaceutical glass
pharma glass
glass bottle packaging
glass packing robots
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NEW YORK, September 10, 2015 – Getty Images, the global leader in visual communication, in collaboration with Instagram, today announced the recipients of the Getty Images Instagram Grant, an inaugural grant program founded to reward photographers documenting stories from underrepresented communities around the world using Instagram.
– Ismail Ferdous (@afterranaplaza), a Bangladeshi documentary photographer using Instagram to cover social humanitarian issues, receives a grant for his project titled After Rana Plaza, which centers around the surviving relatives of those killed in the 2013 collapse of the Rana Plaza garment factory.
– Adriana Zehbrauskas (@adrianazehbrauskas), a Brazilian-born photographer currently residing in Mexico City, has been awarded for her Instagram portfolio of work which covers topics such as climate change and the documentation of the everyday lives of Latin Americans. Adriana intends to use the grant to fund her project "Next of Kin: Family Matters", shooting portraits of the families of 43 missing students who went missing from the Ayotzinapa Rural Teachers School last year. Adriana is also a contributor to the Instagram collective @everydayclimatechange.
Each recipient will receive a grant of US $10,000 and mentorship from one of Getty Images' award-winning photojournalists, who include: John Moore Chris McGrath and Andrew Burton. In addition, recipients' work will be exhibited at Photoville, the largest annual photographic event in New York City, which opens today and runs through to September 20, 2015. The three winners will attend Photoville and are available for press interviews.
In addition to the three grant recipients, the judges have elected to recognize the work of an additional five deserving photographers: Tasneem Asultan (@tasneemalsultan) of Dubai, UAE; Kevin Cook (@kevincookphoto) of Philadelphia, USA; Igor Pisuk (@igorpisuk) of Stockholm, Sweden; Cassandra Giraldo (@afterschoolproject) of New York, USA and Ako Salemi (@f64s125) of Tehran, Iran. These photographers will receive a personal mentorship from a member of the Getty Instagram Grant judging panel.
For more information about the Getty Images Instagram Grant program and to view the awarded portfolios, visit http://gettyimages.com/InstagramGrant.
Born in Dhaka, Bangladesh in 1989, Ismail Ferdous has always been fascinated by the stories of people living in underrepresented communities. As a documentary photographer, Ismail covers social and humanitarian issues. His most recent project "The Cost of Fashion" is a photo and video advocacy project that began after he documented the Rana Plaza factory collapse, which led to his follow-up project two years later "After Rana Plaza." The project continues to spread awareness about the fashion industry and its negative effects on workers in Bangladesh.
Since 2011, Ismail has also documented the effects of global warming and HIV/AIDS on local communities. Additionally, he has documented violence against women in Guatemala, refugees along the border of Turkey and Syria, human trafficking in South-East Asia and, most recently, the earthquake in Nepal.
Ismail has worked for many NGOs, agencies and news organizations including MSNBC, Al Jazeera, Associated Press, Showtime, the World Bank, SIDA-Global Reporting and Ocean Conservancy. He has won numerous awards including NPPA's Best of Photojournalism award (2014 and 2015), Days Japan Photojournalism Award, Alexia Foundation Award of Excellence in 2012, Dart Foundation Asia Pacific Fellowship, Eddie Adams Workshop and World Bank Young Artist.
Getty Images is the world's leader in visual communication; with over 190 million assets available through its premium content site www.gettyimages.com and its leading stock content site www.istock.com. With its advanced search and image recognition technology, Getty Images serves business customers in more than 100 countries and is the first place creative and media professionals turn to discover, purchase and manage images and other digital content. Its award-winning photographers and content creators help customers produce inspiring work which appears every day in the world's most influential newspapers, magazines, advertising campaigns, films, television programs, books and online media. Visit Getty Images at www.gettyimages.com to learn more about how the company is advancing the unique role of digital media in communications and business, and enabling creative ideas to come to life. For company news and announcements, visit press.gettyimages.com, and for the stories, innovation and inspiration behind our content, visit Stories & Trends http://stories.gettyimages.com. Find us on Instagram at https://instagram.com/gettyimages/, Facebook at www.facebook.com/gettyimages, Twitter at https://twitter.com/GettyImages, or download Stream, our free consumer app, to view and share the world's best imagery.


Incorporates ED glass element for brightness and contrast.
A remarkably useful addition to any eyepiece collection!
Obviously being a 2" barlow this is going to be larger than your average. It has produced good clear images for me so far when observing the moon, planets and even tight doubles. It's not the easiest bit of kit to use with my Skywatcher 200p however, the barrel is so long it will not fully sit in the focuser when not using the telescopes supplied 2" focuser lengthener. Also depending on your target you will sometimes need to use the focus lengthener adaptor and sometimes you wont, but either way you will not be able to achieve focus with the barlow slotted in as far as it will go, you have to instead focus with the barlow by sliding it up/down the focuser (obviously with your focuser at it's max length) before screwing it down in your focuser tube. Once you're comfortable working around this Barlow's quirks you should find it more than adequate for the job, but i would say unless you absolutely NEED a 2" barlow (I bought as i was unsure about 1.25" and 2" EP's at the time, so bought this as it can fit both) you're probably better off looking for a smaller and lighter 1.25" equivalent.
I bought this as I needed a lower power Barlow for Lunar imaging when seeing conditions are below optimal, my original 2.5x Barlow was too much.
Well build and solid with good optics as proven by a session shortly after I bought it.
Works well with my 12" Meade ACF and I like having the 2" mount. On the viewing end it will accpet both 2" and 1.25" ep's.


This is part three (and the final part) in a series of posts.
There are many reasons that I enjoyed this trip more than past trips, but the main one I want to talk about is my own personal experiences with the music. (The other main reason is that it was a much more social experience for me, and I feel I socialised with new people from my school, as well as people from other schools, but that's not very interesting for anyone other than myself.) The Beethoven symphony is my favourite piece of music of all time. Some of the pieces I wasn't playing in were great to listen to, James Bond, Viva la Vida, Smoke on the Water, Jump from Glee. But that isn't the best of it. In two of the pieces, I was the only clarinet to play. One Short Day, from the musical Wicked, was for choir and a small band. I've had experience with pieces like this before, and although they look simple at first, they're always actually quite a challenge. This was no exception, although it was great fun to play, being the only one playing at many points.
The other piece that I loved was called Look at the World. It was originally for the whole orchestra, but the conductor decided he only wanted 6 strings, 1 flute, and 1 clarinet to play. I was the best clarinet there, so he asked me to play. It was incredibly beautiful, but also very hard at points. For me, those two pieces were the highlight of the whole trip.
There's so much more I could say, but this is already 3 parts long, so I'll just finish by saying what a great experience it was, and I can't wait until next year in Beijing!
This is part two in a series of posts.
The organisation on periphery matters (things not directly relating to the music) this year was not as great as in the past. The food was in general just acceptable, although the opening dinner, and the final gala dinner were spectacular.
My second workshop was GarageBand. To be honest, it was kinda a waste of time. They basically only taught us how to create a song using loops, and nothing more than that. Although I've never actually done it before, it's incredibly easy to do, so I didn't think it was really worth my time. There was another workshop that I wish I had done, but still wouldn't have taught me anything. In the conducting workshop, they showed a video of Rowan Atkinson conducting Beethoven's 5th, which I actually showed to a friend the night before. Apparently it was only the absolute basics of conducting anyway: showing how to beat it 2, 3, and 4, and how to end a piece. I've already had some experience with conducting an actual orchestra, so although this workshop would have been fun, I wouldn't have learnt anything anyway.
Check back in three days for the next part of the series.
This is part one of a series of posts.
FOBISSEA: Federation Of British International Schools in South-East Asia.
FOBISSEA Music is a festival in which a large number of talented musicians from British International Schools in the South-East Asian region. Over the course of around 6 days, a large group of musicians meet and rehearse music for a gala concert at the end of the festival. It's a great opportunity for young musicians to expand their musical ability, while making new friends and just generally having a good time.
The selection of music this year was spectacular. Music including an a capella version of James Bond; string orchestra version of Coldplay's Viva la Vida; music from the musical Wicked, the film version of Fame, Star Wars, and glee; some well-known classical pieces such as Beethoven's 5th and Elgar's Pomp and Circumstance; and When You Believe, from Prince of Egypt.
Upon arriving in Hong Kong in the mid-afternoon, most of my friends went into Hong Kong Disneyland (we were staying at the Disneyland hotel), but I chose to stay behind and catch up on some homework — so I didn't have too much work to do when we got back. Also, it was quite late, so they only got two hours in Disneyland: I didn't think it was worth it.
Despite this, playing such challenging and fun music was definitely worth the pain.


It is the duty of the diving contractor to identify all confined spaces present at a diving project and ensure that the requirements of confined space entry stipulated in the General Safety Regulations are complied with.
The diving contractor must also take cognizance of risks associated with differential pressure situations as well as the risks associated with possible entrapment and manage these risks appropriately. (See also section 10.2).


We are passionate about our school working collaboratively with the local community and us providing educational opportunities for everyone. We currently have a group of parents and local friends called the Friends of UBHS. The purpose of this group is to further build and develop the schools links with the local community, primary schools colleges and businesses. If you would be interested in finding out more about this group and their activities in and around school then please contact Mrs J. Dent and Mrs D. Clyne.