text:
\section{Introduction and main results}
This paper is concerned about the chaos problem in mean-field spin glasses. It arose from the discovery that in some models, a small perturbation to the external parameters will result in a dramatic change to the overall energy landscape and the organization of the pure states of the Gibbs measure. Over the past decades, physicists have intensively studied chaos phenomenon at the free energy level utilizing the replica method, where most related works were discussed in models with Ising spin. We refer readers to the survey of Rizzo \cite{rizzo07} and the references therein along this direction. Recently, mathematical results also have been obtained in the Ising-spin mixed even-spin model. Chaos in disorder without external field was considered in Chatterjee \cite{chatterjee2009disorder} and a more general situation with external field was handled in Chen \cite{chen2013disorder}. Some special cases of temperature chaos were obtained in Chen and Panchenko \cite{chen2014chaos} and Chen \cite{chen2013approach}.

The aim of this work is to investigate the problem of disorder chaos in the spherical mean-field model. Our approach is based on Guerra's replica symmetry breaking bound for the coupled free energy with overlap constraint. This methodology was adapted in Chen \cite{chen2013disorder} to establish chaos in disorder for Ising-spin mixed even-spin model with external field, where many estimates were highly involved due to the nature of the Ising spin. In this paper, we first want to illustrate how the same method may as well be applied to the spherical model and clarify several ideas behind the proof sketch of Research Problem 15.7.14. about disorder chaos problem in Talagrand \cite{talagrand2011meanII} and Chen \cite{chen2013disorder} with more explicit and simpler computations. Our results cover both situations when the external field is present or absent. On the technical ground, we intend to understand to what extent the current approach can reach. In Panchenko and Talagrand \cite{panchenko2007overlap}, the same approach as the present paper was formerly used to study the conjectures of ultrametricity and chaos in temperature for spherical pure even-spin model, where it has been pointed out that these problems can not be achieved at the level of the free energy. We show that chaos in disorder is indeed a much stronger effect and can still be established at the free energy level even in the mixed even-spin model.

We now state our main results. For each $N\in\mathbb{N}$, let $X_N$ be a centered Gaussian process indexed by the configuration space$$S_{N}=\Bigl\{\boldsymbol{\sigma}=(\sigma_{1}, \dots, \sigma_{N})\in\mathbb{R}^{N}: \sum_{i\leq N}\sigma_{i}^{2}=N\Bigr\}$$
and equipped with the covariance structure
\begin{align*}
\e X_N(\s^1)X_N(\s^2)=N\xi(R_{1,2}),
\end{align*}
where $R_{1, 2}=N^{-1}\boldsymbol{\sigma}^{1}\cdot\boldsymbol{\sigma}^{2}$ is called the overlap between two configurations $\boldsymbol{\sigma}^{1},\boldsymbol{\sigma}^{2}\in S_N$ and $\xi:[0,1]\rightarrow \mathbb{R}$ is an even convex function with $\xi''(x)>0$ for $x>0$ and $\xi'''(x)\geq 0$ for $x\geq 0.$ The spherical model is defined on $S_N$ and its Hamiltonian takes the form,
\begin{align*}
-H_N(\s)=X_N(\s)+h\sum_{i=1}^N\sigma_i.
\end{align*}
Set the corresponding Gibbs measure,
\begin{align*}
dG_N(\s)=\frac{1}{Z_N}\exp\Bigl(-H_N(\s)\Bigr)d\lambda_N(\s),
\end{align*}
where $d\lambda_N$ is the uniform probability measure on $S_N$ and the normalizing factor $Z_N$ is called the partition function. An important example of $\xi$ is the mixed even-spin model, $\xi(x)=\sum_{p\geq 1}\beta_{p}^2x^{2p}$ for some sequence of real numbers $(\beta_{p})_{p\geq 1}$ with $\sum_{p\geq 1}2^p\beta_p^2<\infty.$ Denote by $p_N=N^{-1}\e \log Z_N$ the limiting free energy.  Probably the most important fact about the spherical model is the Crisanti-Sommers formula \cite{crisanti1993sphericalp} for the limiting free energy,
\begin{align}\label{pf}
\lim_{N\rightarrow\infty}p_N=\inf_{x,b}\mathcal{P}(x,b).
\end{align}
Here for any distribution function $x$ on $[0,1]$ and $b>\max\bigl\{1,\int_0^1\xi''(s)x(s)ds\bigr\}$,
\begin{align}\label{parisifunc}
 \mathcal P(x,b):= \frac{1}{2} \left( \frac{h^2}{b-d(0)} + \int_0^1 \frac{\xi''(q)}{b-d(q)} dq +b-1- \log b -\int_0^1 \xi''(q)x(q)dq \right),
\end{align}
where $d(q):= \int_q^1 \xi''(s) x(s) ds$. The formula \eqref{pf} was firstly verified by Talagrand \cite{talagrand2006free} and later generalized to the spherical mixed $p$-spin model including odd $p$ in Chen \cite{Chen12}. A key fact of the variational formula \eqref{pf} is the existence and uniqueness of the optimizer or the functional order parameter, which is guaranteed by Talagrand \cite[Theorem 1.2]{talagrand2006free}.

In the problem of disorder chaos, we are interested in understanding how the system would behave when the disorder is perturbed. To this end, we shall consider two copies $X_N^1$ and $X_N^2$ of $X_N$ with covariance
\begin{align*}
\mathbb{E}X_{N}^1(\boldsymbol{\sigma}^{1})X_{N}^2(\boldsymbol{\sigma}^{2})&=tN\xi(R_{1,2})
\end{align*}
for some $t\in [0,1].$ In the same manner as $H_N$, $G_N$ and $Z_N$, we denote by $H_N^1,H_N^2$ the Hamiltonians, $G_N^1,G_N^2$ the Gibbs measures and $Z_N^1,Z_N^2$ the partition functions corresponding to $(X_N^1,h)$ and $(X_N^2,h)$, respectively.
Let $\left<\cdot\right>$ denote the Gibbs expectation with respect to the product measure $dG_N^1(\boldsymbol{\sigma}^1)\times dG_N^2(\boldsymbol{\sigma}^2).$ If $t=1,$ these two systems are identically the same in which case the limiting distribution of the overlap $R_{1,2}$ under the measure $\mathbb{E}\left<\cdot\right>$ is typically non-trivial in the replica symmetry breaking region. Contrary to the situation $t=1$, our main results on disorder chaos stated in the following theorems say that the system will change dramatically at the level of the free energy and the Gibbs measure if the two systems are decoupled $0<t<1.$

\begin{Theorem}\label{thm0}
For $u\in [-1,1]$ and $\alpha>0,$ define the coupled partition function,
$$
Z_{N,u,\alpha}=\int_{|R_{1,2}-u|<\alpha}\exp\bigl(-H_N^1(\s^1)-H_N^2(\s^2)\bigr)d\lambda_N(\s^1)d\lambda_N(\s^2).
$$
and set the coupled free energy,
\begin{align}\label{thm0:eq2}
p_{N,u,\alpha}=\frac{1}{N}\e\log Z_{N,u,\alpha}.
\end{align}
 If $0<t<1$, there exists some $u^*\in [0,1)$ such that for all $u\neq u^*$,
\begin{align} \label{thm0:eq1}
\limsup_{\alpha\downarrow 0}\limsup_{N\rightarrow\infty}p_{N,u,\alpha}<2\inf_{x,b}\mathcal{P}(x,b).
\end{align}
\end{Theorem}

In other words, there is free energy cost if $u\neq u^*$ for $0<t<1$. Here the determination of $u^*$ is a technical issue, which is described through an equation related to the Crisanti-Sommers formula as well as the associated optimizer. We shall leave the details to Section $3$. Roughly speaking, $u^*$ is equal to zero if $h=0$ and it stays positive if $h\neq 0$. As an immediate application of the Gaussian concentration of measure, Theorem \ref{thm0} yields the concentration of the overlap near the constant $u^*$ in the following theorem.

\begin{Theorem}\label{thm01}
If $0<t<1$, then there exists some $u^*\in [0,1)$ such that for any $\varepsilon>0,$
\begin{align} \label{expoinq}
\mathbb{E} \langle \mathbf{1}_{  \{ |R_{1,2}-u^* |> \varepsilon \} } \rangle \leq K \exp \left(   -\frac{N}{K}\right)
\end{align}
for all $N\geq 1,$ where $K$ is a constant independent of $N$.
\end{Theorem}

This paper is organized as follows. Our approach is based on a two-dimensional extension of the Guerra replica symmetry breaking bound for \eqref{thm0:eq2} and a sketch of the proof for disorder chaos in the Ising-spin mixed even-spin model as was outlined in Talagrand \cite[Section 15.7]{talagrand2011meanII} and later implemented in Chen \cite{chen2013disorder}. In Section 2, using Guerra's bound, we will compute explicitly manageable upper bounds for the coupled free energy \eqref{thm0:eq2}. These results will be used in Section 3. We first describe how to determine the constant $u^*$ and then conclude Theorem \ref{thm0}. Finally, we carry out the proof of Theorem \ref{thm01}.

\section{Guerra's interpolation}

The main goal of this section is to derive the following upper bound for the coupled free energy \eqref{thm0:eq2}, which is an extended version of Proposition 7.8 in \cite{talagrand2006free}.

\begin{Proposition}\label{prop04}
For any distribution function $x$ on $[0,1]$, $\lambda \in \mathbb{R}$ and $b>\int_0^1\xi''(s)x(s)ds+|\lambda |$, we have that for any $u\in [-1,1],$
\begin{align} \label{upositive}
\limsup_{\alpha \downarrow 0} \limsup_{N \rightarrow \infty} p_{N,u,\alpha} &\leq  \mathcal{P}_u(x,b,\lambda),
\end{align}
where the functional $\mathcal{P}_u(x,b,\lambda)$ is defined as follows. Set $d(q)=\int_q^1 \xi''(s)x(s)ds$ and $$\phi_u(q)=d(u)+\frac{1-t}{1+t}(d(q)-d(u)).$$ Define
\begin{align*}
\mathcal{P}_u(x,b,\lambda) &:=\left\{
\begin{array}{ll}
T_u(x,b,\lambda)+\frac{h^2}{b-\lambda- d(0)},&\mbox{if $u\in[0,1]$},\\
T_u(x,b,\lambda)+\frac{h^2}{b-\lambda-\phi_{|u|}(0)},&\mbox{if $u\in[-1,0])$},
\end{array}\right.
\end{align*}
where
\begin{align}
\begin{split}\label{eq12}
T_u(x,b,\lambda)&=\log \sqrt{\frac{b^2}{b^2-\lambda^2}}+\frac{1+t}{2}  \int_0^{|u|} \frac{\xi''(s)}{b-\eta\lambda-d(s)} ds+ \frac{1-t}{2}  \int_0^{|u|} \frac{\xi''(s)}{b+\eta\lambda-\phi_{|u|}(s)} ds\\
&\quad +\frac{1}{2} \int_{|u|}^1 \frac{\xi''(s)}{b-\lambda-d(s)} ds + \frac{1}{2} \int_{|u|}^1 \frac{\xi''(s)}{b+\lambda-d(s)} ds \\
 &\quad-\lambda u +b-1- \log b - \int_0^1 \xi''(q) x(q)dq.
 \end{split}
\end{align}

\end{Proposition}

We mainly follow the procedure of the proof of Theorem 5.3 in \cite{talagrand2006free} to prove Proposition \ref{prop04}. Fix $u \in [-1,1]$ and $\eta \in \{ 1,-1\}$ with $u = \eta |u|$. It suffices to prove \eqref{upositive} only for discrete $x.$ For $k\geq 0$, consider two sequences of real numbers $\mathbf{m}=(m_\ell)_{0\leq \ell\leq k}$ and $\mathbf{q}=(q_{\ell})_{0\leq \ell\leq k+1}$ that satisfy
\begin{align}
\begin{split}\label{eq_kmq}
&0=m_0\leq m_1\leq \cdots\leq m_k\leq m_{k}=1,\\
&0=q_0\leq q_1\leq \cdots\leq q_{k+1}\leq q_{k+1}=1.
\end{split}
\end{align}
Let $x$ be a distribution function on $[0,1]$ associated to this triplet $(k,\mathbf{m},\mathbf{q})$, that is, $x(q)=m_\ell$ for $q\in[q_\ell,q_{\ell+1})$ and $0\leq \ell\leq k$ and $x(1)=1.$ Without loss of generality, we may assume that $q_\tau=|u|$ for some $0\leq \tau\leq k+1$. Define the sequence $\boldsymbol{n}=(n_p)_{0\leq p\leq k}$ by
\begin{align}
\begin{split}\label{eq1}
&0=n_0,n_1=\frac{m_1}{1+t},\ldots,n_{\tau-1}=\frac{m_{\tau-1}}{1+t},n_{\tau}=m_{\tau},\ldots,n_{k}=m_k.
\end{split}
\end{align}
We consider further independent pairs of centered Gaussian random vectors $(y_p^1,y_p^2)_{0\leq p \leq k}$ that possess covariance
\begin{align}
\begin{split}
\label{eq3}
&\mathbb{E}(y_p^j)^2 = \xi'(q_{p+1})-\xi'(q_p), \ \ 0\leq p \leq k, \ j=1,2, \\
&\mathbb{E}y_p^1 y_p^2 = \eta t\xi'((q_{p+1})-\xi'(q_p)), \ \ 0\leq p <\tau, \\
&y_p^1, y_p^2 \ \textrm{are independent}, \ \  \tau\leq p \leq k.
\end{split}
\end{align}
Let $(y_{i,p}^1,y_{i,p}^2)_{0 \leq p \leq k}$ be independent copies of $(y_p^1,y_p^2)_{0 \leq p \leq k}$ for $1 \leq i\leq N$ and be independent of $X_N^1,X_N^2$. Following Guerra's scheme, we define the interpolated Hamiltonian $H_{N,a}(\s^1,\s^2)$ for $a\in [0,1]$,
$$
-H_{N,a}(\s^1,\s^2)=\sqrt{a}(X_N^1(\s^1)+X_N^2(\s^2))+\sum_{j=1}^2\sum_{i=1}^N\Bigl(\sqrt{1-a}\sum_{0\leq p\leq k}y_{i,p}^j+h\Bigr)\sigma_i^j.
$$
Define
\begin{align*}
F_{k+1}(a) = \log \int_{|R_{1,2}-u|< \alpha} \exp \bigl(-H_{N,t}(\s^1,\s^2)\bigr)  d \lambda_N (\boldsymbol{\sigma}^1) d \lambda_N (\boldsymbol{\sigma}^2).
\end{align*}
Denote by $\mathbb{E}_{p}$ the expectation in the random variables $(y_{i,p}^1,y_{i,p}^2),\ldots,(y_{i,k}^1,y_{i,k}^2)$ and define recursively for $0\leq p \leq k$,
\begin{align*}
F_{p}(a) = \left\{
\begin{array}{ll}
   \frac{1}{n_{p}} \log \mathbb{E}_{p} \exp n_{p} F_{p+1}(a),         & \textrm{if} \ n_{p} \neq 0, \\
   \\
    \mathbb{E}_{p} F_{p+1}(a),         & \textrm{if} \ n_{p}=0.
\end{array} \right.
\end{align*}
Finally set $\phi(a)=N^{-1}\e F_0(a)$ and denote $F_0=\phi(0).$ Following essentially the same proof as either Theorem 5 in \cite{panchenko2007overlap} or Theorem 7.1 in \cite{talagrand2006free}, one can prove that the interpolated free energy $\phi$ yields

\begin{Proposition}\label{RSB}
For any $\alpha>0$ and $x$ corresponding to $(k,\mathbf{m},\mathbf{q})$, we have that
\begin{align}\label{RSB:eq1}
p_{N,u,\alpha}&\leq F_0-(1+t)\sum_{0\leq p \leq \tau} n_p(\theta(\rho_{p+1})-\theta(\rho_p))- \sum_{\tau <p \leq k} n_p(\theta(\rho_{p+1})-\theta(\rho_p) ) + \mathcal{R}
\end{align}
where $\theta(q)=q\xi'(q)-\xi(q)$ and $\limsup_{N\rightarrow\infty}|\mathcal{R}|=0.$
\end{Proposition}

Substituting \eqref{eq1} into the right-hand side of \eqref{RSB:eq1}, a direct computation gives
\begin{align}\label{eq7}
&(1+t)\sum_{0\leq p < \tau} n_p(\theta(q_{p+1})-\theta(q_p))+\sum_{\tau \leq p \leq k+1} n_p(\theta(q_{p+1})-\theta(q_p) )\notag\\
&=\sum_{0\leq p\leq k}m_p(\theta(q_{p+1})-\theta(q_p))\notag\\
&=\int_0^1 \xi''(q)x(q)dq.
\end{align}
We now turn to the control of the quantity $F_0.$ For $b>1$, we denote by $\nu_N^b$ the probability measure of $N$ i.i.d. Gaussian random variables with mean zero and variance $b^{-1}$, that is,
\begin{align*}
d\nu_N^b(\boldsymbol{y})=\left( \frac{b}{2 \pi} \right)^{\frac{N}{2}} \exp \left( -\frac{b}{2} \| \boldsymbol{y} \|^2 \right)d\boldsymbol{y}.
\end{align*}
Let $\tau_N^b = -N^{-1} \log \nu_N^b (\{\boldsymbol{\sigma}: \| \boldsymbol{\sigma} \|^2 \geq N  \})$. Without ambiguity, we simply write $\nu^b$ for $\nu_1^b$. Given a number $\lambda$, we define the function
\begin{align*}
B_{k+1}(\boldsymbol{x}^1,\boldsymbol{x}^2,\lambda) = \log \int \exp(\boldsymbol{x}^1 \cdot \boldsymbol{\sigma}^1 + \boldsymbol{x}^2 \cdot \boldsymbol{\sigma}^2 + \lambda \boldsymbol{\sigma}^1 \cdot \boldsymbol{\sigma}^2) d \nu_N^b (\boldsymbol{\sigma}^1) d \nu_N^b (\boldsymbol{\sigma}^2)
\end{align*}
for $\boldsymbol{x}^1,\boldsymbol{x}^2\in\mathbb{R}^N$ and recursively, for $1 \leq p\leq k$,
\begin{align*}
B_{p}(\boldsymbol{x}^1,\boldsymbol{x}^2,\lambda) = \left\{
\begin{array}{ll}
 \frac{1}{n_{p}} \log \mathbb{E} \exp n_{p}B_{p+1} (\boldsymbol{x}^1+\boldsymbol{y}_{p}^1,\boldsymbol{x}^2+\boldsymbol{y}_{p}^2, \lambda), &
\textrm{if} \ n_{p} \neq 0, \\
\\
\mathbb{E} B_{p+1} (\boldsymbol{x}^1+\boldsymbol{y}_{p}^1,\boldsymbol{x}^2+\boldsymbol{y}_{p}^2, \lambda), & \textrm{if} \ n_{p}=0,
\end{array} \right.
\end{align*}
where $\boldsymbol{y}_p^j = (y_{i,p}^j)_{1 \leq i \leq N}$ for $j=1,2$ and $0\leq p \leq k$. Let $\boldsymbol{h}=(h,\ldots,h).$ Following the same argument as in the proof of Lemma 7.1 \cite{talagrand2006free}, we obtain

\begin{Lemma}\label{lem1} Let $u\in[-1,1]$, $\alpha>0$ and $\lambda\in\mathbb{R}.$ If $b>\int_0^1\xi''(s)x(s)ds+|\lambda|,$ then
\begin{align}\label{lem1:eq1}
F_0&\leq -\lambda u+|\lambda|\alpha+2\tau_N^b+\frac{1}{N}\e B_1(\boldsymbol{h}+\boldsymbol{y}_0^1,\boldsymbol{h}+\boldsymbol{y}_0^2,\lambda).
\end{align}
\end{Lemma}

To compute the term $N^{-1}\e B_1(\boldsymbol{h}+\boldsymbol{y}_0^1,\boldsymbol{h}+\boldsymbol{y}_0^2,\lambda)$, we will need a technical lemma.

\begin{Lemma}\label{prop05}
For $x^1$, $x^2 \in \mathbb{R}$, we define
\begin{align}
\begin{split}\label{prop05:eq1}
 J^1_{k+1}(x^1,x^2,\lambda)&= \log \int \exp \rho^1 \left( \frac{x^1+x^2}{\sqrt{2}} \right)  d \nu_1^{b-\lambda} (\rho^1) = \frac{(\frac{x^1+x^2}{\sqrt{2}})^2}{2(b-\lambda)}, \\
 J^2_{k+1}(x^1,x^2,\lambda)&=\log \int \exp \rho^2 \left( \frac{x^1-x^2}{\sqrt{2}} \right)  d \nu_1^{b+\lambda} (\rho^2) =  \frac{(\frac{x^1-x^2}{\sqrt{2}})^2}{2(b+\lambda)},
 \end{split}
\end{align}
and recursively for $1\leq p\leq k$ and $j=1,2$,
\begin{align*}
&J^j_{p}(x^1,x^2,\lambda)= \left\{
\begin{array}{ll}
\frac{1}{n_{p}} \log \mathbb{E} \exp n_{p}J^j_{p+1}(x^1+y_{p}^1,x^2+y_{p}^2,\lambda),   & \textrm{if} \ n_{p} \neq 0, \\
\\
\mathbb{E} J^j_{p+1}(x^1+y_{p}^1,x^2+y_{p}^2,\lambda),     & \textrm{if} \ n_{p} = 0,
\end{array} \right.
\end{align*}
then
\begin{align}
\begin{split}\label{Bequa}
&\frac{1}{N}\mathbb{E}B_1(\boldsymbol{h}+\boldsymbol{y}_0^1,\boldsymbol{h}+\boldsymbol{y}_0^2,\lambda)\\
& = \log \sqrt{\frac{b^2}{b^2-\lambda^2}}+\mathbb{E} J_{1}^1(h+y_0^1,h+y_0^2,\lambda)+ \mathbb{E} J_{1}^2(h+y_0^1,h+y_0^2,\lambda).
\end{split}
\end{align}
\end{Lemma}

\begin{proof} For $x^1$, $x^2 \in \mathbb{R}$ and $1 \leq p\leq k+1$, we define the following functions
\begin{align*}
\Gamma_{k+1}(x^1,x^2,\lambda)& = \log \int \exp \left(x^1 \sigma^1+ x^2 \sigma^2 +\lambda \sigma^1 \sigma^2  \right)
 d \nu^b (\sigma^1) d \nu^b(\sigma^2), \\
 \Gamma_{p}(x^1,x^2,\lambda)& =\frac{1}{n_{p}} \log \mathbb{E} \exp n_{p} \Gamma_{p+1}(x^1+y_{p}^1,x^2+y_{p}^2,\lambda),  \ 1 \leq p\leq k.
\end{align*}
Since $(\si_1^1,\si_1^2),\ldots,(\si_N^1,\si_N^2)$ are independent under the measure $\nu_N^b\times \nu_N^b$, we see recursively that
$B_{p}(\boldsymbol{x}^1, \boldsymbol{x}^2,\lambda) = \sum_{i \leq N} \Gamma_{p}(x^1_i,x^2_i,\lambda),$ where $\boldsymbol{x}^j=(x_i^j)_{i\leq N}$ for $j=1,2$. Consequently,
\begin{align*}
&\frac{1}{N} \mathbb{E}B_1(\boldsymbol{h}+\boldsymbol{y}_0^1,\boldsymbol{h}+\boldsymbol{y}_0^2,\lambda) = \mathbb{E} \Gamma_1(h+y_0^1,h+y_0^2,\lambda).
\end{align*}
Now making change of variables
\begin{align*}
\sigma^1 = \frac{\rho^1+\rho^2}{\sqrt{2}}, \ \sigma^2 = \frac{\rho^1-\rho^2}{\sqrt{2}}
\end{align*}
and noting that $\rho^1,\rho^2$ are i.i.d. Gaussian with mean zero and variance $b^{-1}$, we obtain
\begin{align*}
&\Gamma_{k+1}(x^1,x^2,\lambda) \\
&= \log \int \exp \left(\frac{x^1+x^2}{\sqrt{2}} \rho^1 + \frac{x^1-x^2}{\sqrt{2}} \rho^2 + \lambda \frac{(\rho^1)^2}{2} -  \lambda \frac{(\rho^2)^2}{2} \right) d \nu^b(\rho^1)d \nu^b(\rho^2) \\
&= \log \int \exp \left(\frac{x^1+x^2}{\sqrt{2}} \rho^1 + \lambda \frac{(\rho^1)^2}{2} \right) d \nu^b(\rho^1) +\log \int \exp \left(  \frac{x^1-x^2}{\sqrt{2}} \rho^2  -  \lambda \frac{(\rho^2)^2}{2} \right) d  \nu^b(\rho^2) \\
&= \log \sqrt{\frac{b^2}{b^2-\lambda^2}} + J^1_{k+1}(x^1,x^2,\lambda) + J^2_{k+1}(x^1,x^2,\lambda).
\end{align*}
Since $y^1_{p}+y^2_{p}$ and $y^1_{p}-y^2_{p}$ are independent, starting with \eqref{prop05:eq1}, an iterative argument implies that $J^1_{p+1}(x^1+y_{p}^1,x^2+y_p^2)$ and $J^2_{p+1}(x^1+y_{p}^1,x^2+y_p^2)$ are independent of each other, which yields
\begin{align*}
 \Gamma_{p}(x^1,x^2,\lambda)=\log \sqrt{\frac{b^2}{b^2-\lambda^2}} + J_{p}^1(x^1,x^2,\lambda)+J_{p}^2(x^1,x^2,\lambda)
\end{align*}
for $1\leq p\leq k+1$ and hence \eqref{Bequa}.
\end{proof}

\begin{proof}[Proof of Proposition \ref{prop04}] The proof is essentially based on an explicit calculation of the right hand-side of \eqref{Bequa}. To lighten notations, we set
\begin{align*}
v_p&=\xi'(q_{p+1})-\xi'(q_p)\,\,\mbox{if $0\leq p\leq k$,}\\
d_p'&=\sum_{p\leq \ell \leq \tau-1}n_\ell v_\ell=\frac{1}{1+t}\int_{q_p}^{q_\tau}\xi''(s)x(s)ds\,\,\mbox{if $0\leq p\leq \tau-1$},\,\,d_{\tau}'=0,\\
d_p&= \sum_{p\leq \ell \leq k}n_\ell v_\ell=\int_{q_p}^1\xi''(s)x(s)ds\,\,\mbox{if $\tau\leq p\leq k$},\,\,d_{k+1}=0.
\end{align*}
Recall \eqref{eq3}. It is straightforward to obtain that for $\tau\leq p\leq k$
\begin{align*}
&\mathbb{E} \left( \frac{y_p^1+y_p^2}{\sqrt{2}} \right)^2 =\mathbb{E} \left( \frac{y_p^1-y_p^2}{\sqrt{2}} \right)^2 = v_p
\end{align*}
 and for $0\leq p<\tau,$
\begin{align*}
&\mathbb{E} \left( \frac{y_p^1+y_p^2}{\sqrt{2}} \right)^2 = (1+\eta t)v_p, \,\,\mathbb{E} \left( \frac{y_p^1-y_p^2}{\sqrt{2}} \right)^2 = (1-\eta t)v_p.
\end{align*}
Combining these with the formula that for a standard Gaussian random variable $z$, $nv<L$ and $y\in\mathbb{R}$,
\begin{align*}
&\frac{1}{n}\log\e\exp \frac{n}{2L}(y+\sqrt{v}z)^2=\left\{\begin{array}{ll}
\frac{y^2}{2(L-nv)}+\frac{1}{2n}\log\frac{L}{L-nv},&\mbox{if $n>0$},\\
\frac{y^2}{2L}+\frac{v}{2L},&\mbox{if $n=0$,}
\end{array}
\right.
\end{align*}
an iterative procedure leads to
\begin{align}
\begin{split}\label{J1g}
\mathbb{E} J_1^1(h+y_0^1,h+y_0^2,\lambda)
&=\frac{2h^2}{2(b-\lambda-(d_{\tau}+(1+\eta t)d_0'))}\\
&+\frac{1}{2}\sum_{p=0}^{\tau-1}\frac{1}{n_p}\log\frac{b-\lambda-(d_{\tau}+(1+\eta t)d_{p+1}')}{b-\lambda-(d_{\tau}+(1+\eta t)d_p')}\\
&+\frac{1}{2}\sum_{p=\tau}^{k}\frac{1}{n_p}\log\frac{b-\lambda-d_{p+1}}{b-\lambda-d_p}
  \end{split}
\end{align}
and
\begin{align}
\begin{split} \label{J2g}
\mathbb{E} J_1^2(h+y_0^1,h+y_0^2,\lambda)
&=\frac{1}{2}\sum_{p=0}^{\tau-1}\frac{1}{n_p}\log\frac{b+\lambda-(d_{\tau}+(1-\eta t)d_{p+1}')}{b+\lambda-(d_{\tau}+(1-\eta t)d_p')}\\
&+\frac{1}{2}\sum_{p=\tau}^{k}\frac{1}{n_p}\log\frac{b+\lambda-d_{p+1}}{b+\lambda-d_p}.
\end{split}
\end{align}
Now recall from the statement of Proposition \ref{prop04}, $d(q)=\int_q^1\xi''(s)x(s)ds$ and $$\phi_u(q)=d(q_{\tau})+\frac{1-t}{1+t}(d(q)-d(q_{\tau})).$$
Since $d_{p}'=d(q_p)-d(q_{\tau})$ and
\begin{align*}
d_\tau+(1\pm\eta t)d_p'&=d(q_\tau)+\frac{1\pm \eta t}{1+t}(d(q_p)-d(q_\tau))=\left\{
\begin{array}{ll}
d(q_p),&\mbox{if $u\geq 0$},\\
\phi_u(q_p),&\mbox{if $u<0$,}
\end{array}
\right.
\end{align*}
we have
\begin{align}\label{eq4}
\frac{2h^2}{2(b\mp\lambda-(d_{\tau}+(1\pm\eta t)d_0'))}&=\left\{
\begin{array}{ll}
\frac{2h^2}{2(b\mp\lambda-d(0))},&\mbox{if $u\geq 0$},\\
\frac{2h^2}{2(b\mp\lambda-\phi_u(0))},&\mbox{if $u<0$.}
\end{array}
\right.
\end{align}
Using the fundamental theorem of calculus and the fact that $x(s)=m_p$ for $s\in [q_p,q_{p+1})$,
\begin{align}\label{eq5}
&\sum_{p=0}^{\tau-1}\frac{1}{n_p}\log\frac{b\mp\lambda-(d_\tau+(1\pm\eta t)d_{p+1}')}{b\mp\lambda-(d_\tau+(1\pm\eta t)d_p')}\notag\\
&=\sum_{p=0}^{\tau-1}\frac{1}{n_p}\left(\log(b\mp\lambda-(d_\tau+(1\pm\eta t)d_{p+1}'))-\log(b\mp\lambda-(d_\tau+(1\pm\eta t)d_p'))\right)\notag\\
&=\sum_{p=0}^{\tau-1}\frac{(1+t)}{m_p}\frac{(1\pm \eta t)}{1+t}\int_{q_p}^{q_{p+1}}\frac{\xi''(s)x(s)}{b\mp\lambda-(d_\tau+(1\pm\eta t)d_p')}ds\notag\\
&=\left\{
\begin{array}{ll}
(1\pm t)\int_{0}^{q_\tau}\frac{\xi''(s)}{b\mp\lambda-d(s)}ds,&\mbox{if $u\geq 0$},\\
(1\mp t)\int_{0}^{q_\tau}\frac{\xi''(s)}{b\mp\lambda-\phi_u(s)}ds,&\mbox{if $u<0$},
\end{array}
\right.
\end{align}
and
\begin{align}\label{eq6}
\sum_{p=\tau}^{k}\frac{1}{n_p}\log\frac{b\mp\lambda-d_{p+1}}{b\mp\lambda-d_{p}}&=\sum_{p=\tau}^{k}\frac{1}{n_p}\bigl(\log (b\mp\lambda-d(q_{p+1}))-\log(b\mp\lambda -d(q_{p}))\bigr)\notag\\
&=\sum_{p=\tau}^{k}\frac{1}{m_{p}}\int_{q_{p}}^{q_{p+1}}\frac{\xi''(s)x(s)}{b\mp\lambda-d(s)}ds\notag\\
&=\int_{q_{\tau}}^1\frac{\xi''(s)}{b\mp\lambda-d(s)}ds.
\end{align}
Plugging \eqref{eq4}, \eqref{eq5} and \eqref{eq6} into \eqref{J1g} and \eqref{J2g}, the equation \eqref{prop05}, Lemmas \ref{lem1}, \ref{prop05} and Proposition \ref{RSB} together complete our proof by taking $N\rightarrow\infty$ and $\alpha\downarrow 0$ in \eqref{lem1:eq1} and noting the usual large deviation principle $\lim_{N\rightarrow\infty}\tau_N^b=2^{-1}(b-1-\log b).$

\end{proof}

\section{Proofs of main results}

Now we are ready to prove our main results. Throughout this section, $({x},{b})$ stands for the optimizer in \eqref{pf}. Denote $ {d}(q) = \int_q^1\xi''(s)  {x}(s)ds$ and $$ {\phi}_u(q)= {d}(u)+\frac{1-t}{1+t}( {d}(q)- {d}(u)).
$$
First of all, we start with a proposition that is used to determine the value $u^*$ stated in Theorems \ref{thm0} and \ref{thm01}.
Let $u_{ {x}}$ be the smallest value of the support of $ {x}.$ A crucial fact about $u_{ {x}}$ is that it must satisfy the following equation,
\begin{align}\label{eq8}
\frac{h^2+\xi'(u_{ {x}})}{( {b}- {d}(0))^2}=u_{ {x}}.
\end{align}
This can be seen from the proof of Theorem 7.2 in \cite{talagrand2006free}. In particular, \eqref{eq8} implies $u_{ {x}}>0$ if $h\neq 0.$

\begin{Proposition}\label{prop01}
For $t\in(0,1)$, define the function
\begin{align} \label{fixedpoint}
f(u)=\frac{h^2+t\xi'(u)}{( {b}- {d}(0))^2}-u
\end{align}
for $u\in [-u_{ {x}},u_{ {x}}].$ Then $f(u)=0$ has a unique solution $u^*$. Moreover, $u^*=0$ when $h =0$ and $u^* \in (0,u_{ {x}})$ when $h\neq 0$.
\end{Proposition}

\begin{proof} Note that $\xi'''$ is an odd function. This implies that $f$ is convex on $[0,u_{ {x}}]$ and is concave on $[-u_{ {x}},0]$. Assume that $h\neq 0.$ In this case, since $f(0)>0$ and $f(u_{ {x}})<0$ by \eqref{eq8}, the intermediate value theorem and the convexity of $f$ on $[0,u_{ {x}}]$ conclude that $f(u)=0$ has a unique solution $u^*$ on $[0,u_{ {x}}]$ and it satisfies $u^*\in(0,u_{ {x}}).$ In addition, since from \eqref{eq8},
$$
f(-u_{ {x}})=-\frac{-h^2+t\xi'(u_{ {x}})}{( {b}- {d}(0))^2}+u_{ {x}}>-\frac{h^2+\xi'(u_{ {x}})}{( {b}- {d}(0))^2}+u_{ {x}}=0,
$$
the concavity of $f$ on $[-u_{ {x}},0]$ and $f(0)>0$ imply that $f(u)=0$ has no solution on $[-u_{ {x}},0].$ This finishes the proof for the case $h\neq 0.$ The situation for $h=0$ is essentially identical. If $u_{ {x}}=0$, obviously $u^*=0.$ If $u_{ {x}}\neq 0,$ we still have $f(-u_{ {x}})>0>f(u_{ {x}})$, but now $f(0)=0.$ The convexity and concavity of $f$ on $[0,u_{ {x}}]$ and $[-u_{ {x}},0]$ respectively conclude that $0$ is the unique solution to $f(u)=0$ on $[-u_{ {x}},u_{ {x}}].$
\end{proof}

\begin{proof}[Proof of Theorem \ref{thm0}] Note that
\begin{align}
\begin{split}\label{eq10}
\mathcal{P}_u( {x}, {b},0)&=\left\{
\begin{array}{ll}
T_u(x,b,0)+\frac{h^2}{ {b}- {d}(0)},&\mbox{if $u\in[0,1]$},\\
T_u(x,b,0)+\frac{h^2}{ {b}- {\phi}_{|u|}(0)},&\mbox{if $u\in[-1,0)$},
\end{array}\right.
\end{split}
\end{align}
where from \eqref{eq12},
\begin{align}
\begin{split}\label{eq9}
T_u(x,b,0)&:=\frac{1+t}{2}  \int_0^{|u|} \frac{\xi''(s)}{ {b}- {d}(s)} ds+ \frac{1-t}{2}  \int_0^{|u|} \frac{\xi''(s)}{ {b}- {\phi}_{|u|}(s)} ds\\
&\quad+\int_{|u|}^1 \frac{\xi''(s)}{ {b}- {d}(s)} ds+ {b}-1- \log  {b} - \int_0^1 \xi''(q)  {x}(q)dq.
\end{split}
\end{align}
 Consider first that $|u|>u_{ {x}}.$ Since $ {x}(q)>0$ for $q\in(u_{ {x}},|u|)$, we have that for all $s\in[0,|u|),$
\begin{align}\label{dsphi}
 {d}(s)- {\phi}_{|u|}(s) = \frac{2t}{1+t}( {d}(s)- {d}(|u|))=\int_s^{|u|} \xi''(q) {x}(q) dq >0
\end{align}
and from \eqref{eq10},
$$
\mathcal{P}_u( {x}, {b},0)\leq T_u(x,b,0)+\frac{h^2}{ {b}- {d}(0)}
$$
for any $u\in[-1,1]$. In addition, from \eqref{dsphi}, the first line of \eqref{eq9} is strictly bounded above by
\begin{align*}
\frac{1+t}{2} \int_0^{|u|} \frac{\xi''(s)}{ {b}- {d}(s)} ds+ \frac{1-t}{2}  \int_0^{|u|} \frac{\xi''(s)}{ {b}- {d}(s)} ds=\int_{0}^{|u|}\frac{\xi''(s)}{ {b}- {d}(s)} ds
\end{align*}
and as a result, these inequalities together with the equation \eqref{parisifunc} lead to $\mathcal{P}_u( {x}, {b},0)<2\mathcal{P}( {x}, {b})$. This completes the proof for \eqref{thm0:eq1} with $|u|>u_{ {x}}$ by using Proposition \ref{prop04}. As for the case $|u|\leq u_{ {x}},$ since $x(q)=0$ for $q\in[0,|u|),$ we have that for all $s\in[0,|u|],$
\begin{align*}
d(s)&=\int_{u_{ {x}}}^1\xi''(q) {x}(q)dq= {\phi}_{|u|}(s).
\end{align*}
This allows us to write
\begin{align*}
\mathcal{P}_u( {x}, {b},\lambda)&=\log \sqrt{\frac{b^2}{b^2-\lambda^2}}+\frac{h^2}{b-\lambda- d(0)}\\
&\quad+  \frac{1+t}{2}  \int_0^{|u|} \frac{\xi''(s)}{b-\eta\lambda-d(s)} ds+ \frac{1-t}{2}  \int_0^{|u|} \frac{\xi''(s)}{b+\eta\lambda-d(s)} ds\\
&\quad +\frac{1}{2} \int_{|u|}^1 \frac{\xi''(s)}{b-\lambda-d(s)} ds + \frac{1}{2} \int_{|u|}^1 \frac{\xi''(s)}{b+\lambda-d(s)} ds \\
 &\quad-\lambda u +b-1- \log b - \int_0^1 \xi''(q) x(q)dq
\end{align*}
for all $u\in [-u_{ {x}},u_{ {x}}].$ A direct computation gives that
\begin{align*}
\mathcal{P}_u( {x}, {b},0)&=2\mathcal{P}( {x}, {b}),\,\,\partial_\lambda\mathcal{P}_u( {x}, {b},0)=f(u)
\end{align*}
and moreover, for $\lambda$ in a small open neighborhood of $0$,
\begin{align*}
|\partial_{\lambda\lambda}\mathcal{P}_u( {x}, {b},\lambda)|&\leq L,
\end{align*}
where $L$ is a positive constant independent of $\lambda.$
Consequently, applying the Taylor theorem and taking $\lambda =-\delta f(u)/L$ for sufficiently small $\delta>0$, if $u\in[-u_{ {x}},u_{ {x}}]$ and $u\neq u^*,$ then Proposition \ref{prop01} yields
\begin{align*}
\limsup_{\alpha\downarrow 0}\limsup_{N\rightarrow\infty}p_{N,u,\alpha}
&\leq\mathcal{P}_u( {x}, {b},0)+\partial_\lambda\mathcal{P}_u( {x}, {b},0) \lambda+\frac{L}{2}\lambda^2\\
&=2\mathcal{P}( {x}, {b})-\frac{\delta f(u)^2}{L}\Bigl(1-\frac{\delta}{2}\Bigr)\\
&<2\mathcal{P}( {x}, {b}).
\end{align*}
This proves \eqref{thm0:eq1} for $|u|\leq u_{ {x}}$ with $u\neq u^*.$
\end{proof}

At the end of this section, we prove Theorem \ref{thm01}. It will need an inequality of Gaussian concentration of measure from the appendix of \cite{panchenko2007note} stated below.

\begin{Lemma}\label{lem03}
Let $\nu$ be a finite measure on $\mathbb{R}^N$ and $g(z)$ be a centered Gaussian process indexed on $\mathbb{R}^N$ such that
$\mathbb{E} g(z)^2 \leq a$ for $z$ in the support of the measure $\nu$. If
\begin{align*}
X = \log \int_{\mathbb{R}^N} \exp g(z) d \nu (z),
\end{align*}
then for all $s>0$,
\begin{align*}
\mathbb{P} (|X-\mathbb{E}X| \geq s) \leq 2 \exp \left( -\frac{s^2}{4a} \right).
\end{align*}
\end{Lemma}

\begin{proof}[Proof of Theorem \ref{thm01}] Let $\varepsilon>0$ and set $S_\varepsilon=[-1,1]\setminus (u^*-\varepsilon,u^*+\varepsilon).$ Using \eqref{pf} and \eqref{thm0:eq1}, for any $u\in S_\varepsilon$, there exist $\alpha_u>0$ and $N_u\in\mathbb{N}$ such that
$
p_{N,u,\alpha_u}<2p_N-\varepsilon
$
for all $N\geq N_u$. Set $I_u=(u-\alpha_u,u+\alpha_u)$. Since $\{I_u:u\in S_\varepsilon\}$ forms an open covering of $S_\varepsilon$, the compactness of $S_\varepsilon$ implies that there exist $u_1,\ldots,u_n$ such that $\cup_{i=1}^nI_{u_i}$ covers $S_{\varepsilon}.$ Letting $N_0=\max\{N_{u_i}:1\leq i\leq n\}$, we obtain that
\begin{align}
\label{eq11}
p_{N,u_i,\alpha_{u_i}}<2p_N-\varepsilon
\end{align}
for all $1\leq i\leq n$ and $N\geq N_0.$ Next, applying Lemma \ref{lem03}, the event $A_N$ such that
\begin{align*}
\min\left\{\frac{1}{N}\log Z_N^1,\frac{1}{N}\log Z_N^2\right\}\geq p_N-\frac{\varepsilon}{8}
\end{align*}
and
\begin{align*}
\max\left\{\frac{1}{N}\log Z_{N,u_i,\alpha_{u_i}}:i=1,\ldots,n\right\}\leq p_{N,u,\alpha}+\frac{\varepsilon}{8}
\end{align*}
has probability at least $1-K\exp(-N/K)$, where $K>0$ is independent of $N.$ On $A_N$, these inequalities and \eqref{eq11} lead to
\begin{align*}
\la 1_{\left\{R_{1,2}\in S_\varepsilon\right\}}\ra&\leq \sum_{i=1}^n\bigl\la 1_{\{R_{1,2}\in I_{u_i}\}}\bigr\ra\\
&\leq \sum_{i=1}^n\exp\bigl(\log Z_{N,u_i,\alpha_{u_i}}-\log Z_{N}^1-\log Z_N^2\bigr)\\
&\leq \sum_{i=1}^n\exp\Bigl(-N\Bigl(p_{N,u_i,\alpha_{u_i}}-2p_N+\frac{\varepsilon}{4}\Bigr)\Bigr)\\
&\leq n\exp\Bigl(-\frac{3\varepsilon N}{4}\Bigr).
\end{align*}
Therefore,
\begin{align*}
\e\la 1_{\left\{R_{1,2}\in S_\varepsilon\right\}}\ra&\leq n\exp\Bigl(-\frac{3\varepsilon N}{4}\Bigr)\p(A_N)+\p(A_N^c)\\
&\leq n\exp\Bigl(-\frac{3\varepsilon N}{4}\Bigr)+K\exp\Bigl(-\frac{N}{K}\Bigr),
\end{align*}
which completes our proof.
\end{proof}

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Panchenko, D. (2007) A note on Talagrand's positivity principle. {\it Electron. Comm. Probab.}, {\bf 12}, 401--410.

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Panchenko, D. and Talagrand, M. (2007) On the overlap in the multiple spherical SK models. {\it Ann. Probab.}, {\bf 35}, no. 6, 2321--2355.

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Navigation: Home » Blog » Why this Harvard lawyer left the Boston Consulting Group to start an online language learning company
Why this Harvard lawyer left the Boston Consulting Group to start an online language learning company
This interview is with Alan Park, founder of FluentFlix, a startup that helps people learn Chinese through movies and TV. (Download the audio recording of this interview.)
Career path:
Duke undergrad
Founded FluentFlix
Q. Tell us about your background.
A. I'm 30 years old. I graduated from Duke University with a degree in Political Science, and after that I went to Harvard Law School.
After law school, I went to work at the Boston Consulting Group in Hong Kong. I left BCG to work on my own startup called FluentFlix, which helps people learn Chinese.
Q. Tell us how your career path has unfolded.
A. It's been a pretty roundabout path.
One key decision for me was to go to law school after undergrad. At that point, I was thinking that I would be interested in a career in academia. But once I got to law school, I realized I wanted to explore the world more, and working in law might not be as interesting as I thought.
So I went into management consulting. When I was in consulting, which I did for two years, I came to a turning point, where a lot of people have to decide whether to stay in management consulting, go to corporate, or do a startup.
For me, doing a startup was something I'd always wanted to do. At the same time, my last project in consulting made me realize that corporate might not be the right path for me, either. I also thought the startup idea I had needed to be done and it was a good time for me to try it out. So I took the plunge.
Q. You moved from law to consulting, and then from consulting to starting your own company. What specific steps did you take to make each transition?
A. Sure. For the transition from law to consulting, it helped that I started thinking about it really early on while I was in law school.
After my first year of law school, I got a pretty good sense that I wasn't as interested in law as I wanted to be. The summer after my first year, I interned at a law firm, and right after that I started pivoting really hard, and I met as many business school people as I could. I started applying to consulting firms and preparing really hard for those interviews.
Then the summer after my second year, I interned at both a law firm and a consulting firm, and after those experiences, it was clear to me that consulting would be a better fit.
For the transition from consulting to entrepreneurship, I didn't spend as much time preparing for that. For a long time, over several years, I thought about entrepreneurship, so I jumped into it when it felt right.
Q. What were the thought processes you wrestled with that helped you make the leap?
A. Right. I thought about a future career in consulting, which seemed like it would be a good career. But I knew something would be missing there.
In consulting, you don't own the actual output. You create a strategy, you make a presentation, but the results are in the hands of your client. That made me think consulting wasn't the long-term thing for me.
Then for my last consulting project, I worked with a big corporation. I basically worked in a project management function, sitting with the client — in some sense, I became the client. And that made me question whether corporate was for me as well.
Meanwhile, entrepreneurship was something I'd always wanted to do. And I knew it was probably the best time to do it. Once you start getting older, you get married, and you have other obligations, then it becomes a lot trickier.
So I just did a very basic assessment. I thought the upside for entrepreneurship could be great; if it didn't work out, I could always go back to consulting or a corporation.
So I thought I'd give it a shot. I think for some things, there's really only one way to figure it out, and that's by really doing it.
Q. What is it like building your startup and what do you do day-to-day?
A. FluentFlix helps people learn Chinese through authentic video content, things like music videos, commercials, news, and inspiring talks.
We take that content, and we convert it into a form that people can learn from. Building the product involves creating content. We put on a layer of language learning content that enables people to understand these videos.
It also involves a lot of software development, so we have developers building the underlying site. And then it involves marketing and reaching out to customers and other potential partners.
So basically my days revolve around doing those things.
Q. What do you spend the bulk of your time doing these days?
A. I've started handling a lot of the user experience elements. I basically designed the FluentFlix product. So I'm drawing mock ups, and I'm talking to users with those mock ups.
The point of that is, if we can perfect as much as we can before developers actually code anything, we actually end up saving a lot of time and money.
I also spend a lot of time talking with users about potential features, as well as managing our content people and developers.
Q. What do you find most exciting about your current role?
A. The number one thing is that entrepreneurship is an act of creativity. There's something that didn't exist in the world before you started, and through your efforts, it comes into being. The world is a different place because you started on that path. That's the most exciting thing.
You also build a team, and you try to create an environment where everyone can perform at their best. That's been very rewarding. And creating something that customers like, that improves their lives, has been fantastic.
Q. You work with a remote team. What are best practices you've learned around how to do that successfully?
A. My team is in Shanghai and Taiwan. I've met one of my employees a few times and the others I've never met.
It works, firstly, because they are good, responsible people who are passionate about the product. That makes up for a lot of other difficulties that could arise.
You can also do certain things to structure things better and facilitate communication. For example, having standard work hours when you know when each of the people are going to be online. So, I wake up at 5:30 a.m., and they get off work around 6 p.m., so we can touch base then. And right before I go to sleep around 9 or 10-ish, we touch base again. So things like that help.
Using online tools like this project management software called "Flow" also lets you stay on top of what's going on in each other's calendars. So using productivity tools like that is also key.
Q. Where do you see yourself in the future, and how will what you're doing today help you toward that goal?
A. I'd like for us to become a company that's well known for providing technology solutions to help with learning foreign languages. In particular, I'd like for us to be known for bringing immersive experiences to language learning, because I think language learning right now tends to be very textbook-based, very boring, very cookie cutter, and not customized at all. So we'd like to bring things like video and personalization to make language learning exciting and addicting for everyone. I'm having a blast with that, and I'd like for us to keep having fun.
Q. What advice do you have for people who are potentially interested in exploring some of the roles you've had?
A. For people who are interested in entrepreneurship, I think the most helpful thing is to have habits that make you think a lot about entrepreneurship, and to feed your brain with useful advice. You can do that with sites like CareerHoot, or Mixergy, or Lifestyle Business Podcasts. I think trying to absorb as much useful information like this as you can will help point you in the right direction.
A lot of people who have gone to good schools and have had a lot of success based on conventional paths, I think, try to optimize and be better than everybody else according to those conventional paths. But there's no jury out there or crowd you have to please — that's all in your head. And I think the sooner you can discover and pursue your actual passions and make a unique contribution to the world, that's success for yourself and will be in the eyes of people around you.
My advice would be to find your passion, pursue it early, and don't be distracted by the noise of people around you who may be optimizing for general success.
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I started Hack Your Wealth in 2015 because I was frustrated by the quality of "financial independence, retire early" (FIRE) content on the web. I found much of it to be generic personal debt journeys, but that didn't help me because I already routinely saved over half my income. What I wanted instead was deep, analytical, step-by-step insights – and hardcore spreadsheet tools to match! – on how to rapidly grow wealth and manage it strategically and tax-efficiently to get to financial independence…all while raising a family. So as I became increasingly expert in wealth management, tax-planning, and estate planning, I started documenting the biggest strategies I was thinking long and hard about. That content became HYW.
What are my bona fides? I cut my teeth at McKinsey and HGGC private equity (Bain Capital spinout), picking up a CFA along the way, before going into product at LinkedIn, Redfin, Pinterest, and Google. BA from UT-Austin, JD from Harvard Law School. Licensed to practice law in NY, CA, and HI.
These days, I get a kick out of interviewing guests on the HYW podcast about wealth management, tax-planning strategies, and life hacks; getting the occasional dopamine rush after scoring a juicy travel hack award; and showing my hilarious and silly(!) daughter all the tricks she needs to know to have an epic childhood. Read more about my story.


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Employers set to provide Job Shadows for 925 area students
Photo Credit: Rio Grande High School students at UWCNM 2018 job shadow day.
ALBUQUERQUE, NM, Feb. 3, 2019: About 925 students from five area school districts will visit 30 different work sites during Groundhog Job Shadow Week (GJSW) Feb. 3-7, 2020. Visits during the week provide students with opportunities to learn about the company they visit, understand education and job requirements, and practice interviewing.
Students represent charter and traditional public high schools from around the city, and Sandoval and Valencia Counties. In 2018, 325 students participated in GJSW with 15 employers. In 2019, that number doubled to 650 students and 30 employers.
"We have to give students an opportunity to learn about the different types of careers that exist in their community to help them identify their interests and make smart choices about their future," explains Jessica Nojek, United Way of Central New Mexico's Mission: Graduate executive director. "This could be the motivator that reengages the student and encourages them to stay in school to get the education they need to get the job they want."
Following a Junior Achievement curriculum, employers customize a set of discussions and experiences for students to learn about the different jobs within each company. Activities include touring a facility, networking, participating in mock interviews, and learning about the culture, policies, and ethics of the organization.
"We are grateful to our participating central New Mexico employers and educators who have joined together for Groundhog Job Shadow Week 2020," says Erin Hagenow, Junior Achievement president. "Students and our economy thrive when the community unites to offer crucial work readiness skills and meaningful career exploration opportunities to New Mexico's young people.
Participating employers include: AT&T, AUI Inc, Adelante, Albuquerque Public Schools, Bernalillo County, Bradbury Stamm Construction, Chavez-Grieves Consulting Engineers, City of Albuquerque, Comcast, Delta Dental, Dekker/Perich/Sabatini, Explora, Enterprise Holdings, Fidelity Investments, French Funerals & Cremations, Jabil, Kirtland Air Force Base, Lovelace Health Systems, Presbyterian Healthcare Services, PNM, Rio Grande Jewelry Supply, Rural Sourcing, Sandia National Laboratories, Southwest Labs, T-Mobile, TLC Plumbing & Utility, US Eagle Federal Credit Union, United Way of Central New Mexico, Visit ABQ, and Wells Fargo
GJSW is a partnership between United Way of Central New Mexico's Mission: Graduate and Junior Achievement of New Mexico. Shadow experiences are made possible through sponsorship by State Farm, PNM, Sandia National Laboratories, Lovelace Health Systems, and AT&T.
Mission: Graduate is the education initiative of United Way of Central New Mexico. UWCNM was founded in 1934 and serves a four-county region. Its mission is to bring people and resources together to measurably improve lives and strengthen our communities. To learn more, visit www.uwcnm.org or call 505-247-3671.
Junior Achievement of New Mexico, Inc. is the state's largest economic education organization for young people. Junior Achievement uses hands-on experiences to help young people understand the economics of life. In partnership with business and educators, Junior Achievement brings the real world to students, opening their minds to their potential.


Online club entries for the 2019 Virgin Money London Marathon are now closed. Officials managing their club places were given until 17:00 on Monday 3 December to submit an application.
An email was sent to successful clubs confirming the number of entries allocated to the club, together with instructions for logging on to the entry console and entering runners. The deadline for runners to complete and pay for their entries was 17:00 on Friday 25 January 2019. There will be no extension to this deadline under any circumstances. It is the club official's responsibility to ensure the entries are completed by the closing date.
Athletics clubs associated with British Athletics were able to apply for club entries into the 2019 Virgin Money London Marathon. The number of entries given to each club is based on the number of first claim-registered members over the age of 18 who are registered with British Athletics.
Clubs with fewer than 10 first claim-registered members will be placed in a ballot. After the application deadline, 20 clubs will be drawn at random and allocated one place each.
Please note that we will only accept the number of first claim members registered for a club as at 5 November 2018.


For use with a glass or titanium nail, this Weed Star cylinder is made of high quality borosilicate glass. Used together with a nail, this buck helps capture the vapour when using concentrates or oil. Heat the nail up first then cover with the glass buck before dabbing with your tool of choice.
Designed with a 18.8mm connection, this bowl will slide on your favourite glass bong in seconds.


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Through the ups and downs, the team gave it all they had both on and off the pitch, and played as a solid team. Incoming Freshman Macey O'Field who played in the Glendale Youth Program for years made an indelible impression on the team with her hard hits as well as words of encouragement to her teammates.
Scrum half and Co-Captain Sammy Barger, Senior, proved to be one of the most consistent and solid players throughout the season. "Not only has her leadership on and off the field helped the team make it to site, but also her athleticism and ability to always be where the ball is on the field has helped make many tries happen," stated Roberts.
Additional big impacts this season include Juliane Wera, whose speed and accuracy put a majority of the points on the board, and Lena Luciano, who added her fair share of tries and conversion kicks and proved to be a solid force to be reckoned with this season.
The Glendale Varsity High School team will take the pitch this Saturday, November 10th at Garry Berry Stadium in Colorado Springs to compete in the State playoffs. The first game will kick-off at 11:40am.


Seven Energy, the leading integrated gas company in south-east Nigeria, with oil and gas interests in the region has won "The Sustainability and Responsibility Award" at the 2016 African Assembly of the Oil and Gas Council held in London on 20 and 21 June.
The African Assembly is one of the most influential corporate development, strategy, finance and investment gatherings for Africa outside of Africa.
The Award recognizes deserving organizations in the energy sector that have demonstrated impact investments in corporate social responsibility (CSR), local content, health and safety, training and education, environmental stewardship, regulatory and ethical compliance and community engagement.
Chief Executive Officer, Seven Energy, Phillip Ihenacho stated: "We sincerely appreciate this award from the Oil and Gas Council. We are pleased that our contribution towards delivering improved standards of living to Nigerians through our commitment and investment in positive stakeholder relations is being recognized. In a demanding and cost focused business environment, we have ensured that our vision of developing and providing gas to light up Nigeria is sustainable. This award will further encourage us in the pursuit of social programs that positively impact Nigerian communities while delivering value to our stakeholders".
The Oil & Gas Council cited a number of reasons for honoring Seven Energy with this award. In particular was Seven Energy's Green Team Initiative, a pioneering engagement initiative serving as an example of what is possible through corporate-community partnership, which was launched in June 2015 in a bid to ensure that its gas pipelines and associated Rights of Way ("ROW") are kept safe, accessible, clear and clean. Through this initiative over 200 youths across Akwa Ibom and Cross River states have been engaged.
In addition, in October 2015 Seven Energy commenced a weekly community radio programme entitled, 'Safety and You' across Akwa Ibom, Cross River and surrounding states. The programme was delivered by Seven Energy staff and provided guidance on a range of safety related subjects such as natural gas pipeline safety, fire safety, electrical safety, pedestrian safety, kerosene and petrol safety amongst others.
Seven Energy is currently delivering total gas volumes in excess of 100 million standard cubic feet per day ("MMcfpd") to three power stations and a cement factory. As the power stations – Alaoji, Calabar and Ibom – complete their commissioning work and electricity transmission infrastructure, the Group forecasts gas deliveries in excess of 200 MMscfpd over the coming year.
This award is coming on the heels of the "Impactful Investment in Gas to Power and Industry" award conferred on Seven Energy by the Lagos Chamber of Commerce & Industry.


text:
Q: I'm reading Python Crash Course, and It says to create a copy and not to edit the real group, but I've tried it both ways and both seem to work fine Here is how the book tells you to write the code:
        for bullet in self.bullets.copy():
            if bullet.rect.bottom <= 0:
                self.bullets.remove(bullet)
        print(len(self.bullets))
        self._update_screen()

However doing this works just fine:
        for bullet in self.bullets.sprites():
            if bullet.rect.bottom <= 0:
                self.bullets.remove(bullet)
        print(len(self.bullets))
        self._update_screen()

So is there one that is internally better?

A: Probably the main reason the tutorial tells you to make a shallow copy is because of the sometimes unexpected behavior of deleting an object in a for loop (for example you could get an out of bounds error depending on the exact implementation).
You should probably stick to the original version or look up other ways to remove elements from an array in a loop.
Example #1 - works
For example, this example removes all even numbers from a list:
arr = [i for i in range(10)]
print(arr) #prints: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

for x in arr:
    if x%2==0:
        arr.remove(x)

print(arr)#prints: [1, 3, 5, 7, 9]

Example #2 - IndexError
This attempts to do the same thing but throws an index error:
arr = [i for i in range(10)]
for x in range(len(arr)):
    if arr[x]%2==0:
        arr.remove(arr[x])

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-3-2b0b17a4b250> in <module>
     10 arr = [i for i in range(10)]
     11 for x in range(len(arr)):
---> 12     if arr[x]%2==0:
     13         arr.remove(arr[x])

IndexError: list index out of range

But you can get it to work by operating on a shallow copy:
import copy
arr = [i for i in range(10)]
c = copy.copy(arr) #create a shallow coppy
for x in range(len(arr)):
    if c[x]%2==0:# make accesses only to the copy
        arr.remove(c[x])#delete only by value (and not by index)

print(arr)#prints: [1, 3, 5, 7, 9]

A: This is a bit of a stab in the dark, but I'll say, assuming:

*

*This is pygame.

*bullets isn't a custom subclass with a custom definition of sprites
Your way is fine (for now *).

They are likely using copy because you should not remove from a list (or any iterable) while iterating over an iterator of it. By making a copy, you're iterating over the copy while removing from the original, which is safe.
The question is then does sprites make a copy? I don't use pygame, but after searching through the source, it appears as though it does. Every definition I can find for it looks essentially like:
def sprites(self):
    return list(self.spritedict)

And list returns a shallow copy of the iterable given to it.

* That being said, this is also the docstring for sprites:

Returns an object that can be looped over with a 'for' loop. (For now,
it is always a list, but this could change in a future version of
pygame.)

Which suggests that they may change the implementation in the future. If they change the implementation to no longer produce a shallow copy, your code may break when you update the library later.
For the sake of being clear and preventing accidental breakage later, I'd go with the book's suggestion to use .copy.

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text:
Nadia Tagrine (1917-2003), une pianiste franco-russe ;
 Nathalie Béra-Tagrine (1960-), une pianiste française d'origine russe.

Voir aussi
 Rue Michel-Tagrine, une voie du 19e arrondissement de Paris, en France

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text:
Neurologic catastrophes in the emergency department.
Susan M Robinson
Accident and Emergency Department, Addenbrooke's Hospital, Cambridge
http://dx.doi.org/10.1136/emj.18.4.322-b
By E F M Wijdicks (Pp 266; £42.50). Butterworths Heinemann, 2000. ISBN 0-7506-7055-X.
Neurology is not generally perceived as one of the more glamorous medical specialties. This textbook has an upbeat approach. In the preface, the author borrows the now ubiquitous "golden hour" concept for acute neurology.
The text is said to be "brief to facilitate reading" and "is intended to reflect the train of thought and action in the emergency department". Compared with the average neurological textbook it may be brief but it would not be recognised as such by most emergency physicians.
The book is divided into two sections. The first covers conditions affecting the neuroaxis and the second, neurological disorders attributable to specific causes. Detailed descriptions of a number of neurological conditions and their aetiology are provided. The usual neurological emergencies are included, for example, status epilepticus and aneurysmal subarachnoid haemorrhage. In addition rather less obvious emergencies such as acute obstructive hydrocephalus and acute white matter disease are also discussed. The chapter on altered arousal and coma contains an exhaustive list of the major causes of coma, some of these conditions are unlikely to form part of a differential diagnosis formulated in the emergency department. However, the detail contained within the sections on examination of the patient in coma and the assessment of patients with acute unilateral masses reminded me of a number of long forgotten clinical signs. In many chapters there is a brief but detailed and informative review of anatomy and pathophysiology.
Many of the investigations, for example, EEG, SPECT suggested in other chapters might be problematic to arrange in the average emergency department. "I want a SPECT stat".
In parts the clinical practice described does not follow current UK practice (or even standard clinical practice of 10 years ago). For example, it is implied that the administration of antibiotics in bacterial meningitis be delayed until CT/MRI and lumbar puncture have been performed.
The book is unlikely to be used "acutely" on a daily or weekly basis. I suspect this book is akin to an interview suit, something to be dragged out on rare, special and stressful occasions. It will prove a useful reference book for those reviewing cases, those on a neurosciences secondment or doctors preparing for examination. What were those five causes of upgoing plantars and absent ankle jerks again?


text:
Keywords: Anatomy, IFAA, International, Nomenclature, Standardization, Terminology
R. Shane Tubbs
Professor of Neurosurgery, Neurology, Surgery, Otolaryngology, and Structural and Cellular Biology. Tulane University School of Medicine, New Orleans, Louisiana, USA
The Federative International Programme of Anatomical Terminology (FIPAT) is one of many committees/programs of the International Federation of Associations of Anatomists (IFAA), which was founded in 1903. Other committees include those related to education, scientific publications, anatomical research, equality and diversity, and ethics and medical humanities. These various groups are overseen by the IFAA Executive Committee composed of a president, past president, secretaries, treasurer, and the chairs of the other committees and Programs.
FIPAT is composed of a chair, secretary, working groups and their leaders. The working groups are made up of approximately 50 members from anatomists from around the world. Drafts of the Terminologies arise in the specific working groups and are reviewed by the group, leaders of the other FIPAT committees, the IFAA Executive, and finally, approved by Member Societies with final approval given by the General Assembly of the IFAA. The Terminologies serve as the internationally agreed upon official anatomical nomenclature.
As all anatomists will undoubtedly agree, it is very important to have a standardized reference for terminology in the anatomical sciences. As anatomical terms can vary from country to country, a dedicated go-to source for official terminology is important when communicating with a global audience e.g., peer review publications. Additionally, often, the anatomical terminology used by clinicians can vary and often uses non-standard terminology e.g., eponyms. Therefore, without a standardization of anatomy terms, the potential for a tower of Babel might occur. As unequivocal communication is so essential in the descriptive nature of the anatomical sciences, standardization is of paramount importance.
For the IFAA terminologies, Latin is the official language. There are many reasons for this, and in some countries Latin terms are used for teaching and communication in the anatomical sciences e.g., textbooks. For the Terminologies, which are readily found online (https://fipat.library.dal.ca/TA2/), one can find a seven-column system (Fig. 1). The first column is used to provide a unique identification number to the anatomical term. The second column lists the official Latin term for the anatomical structure. Following this, in a third column, when a Latin synonym exists, it is listed. Columns four and five list the British and US English spellings of the term, respectively. Finally, in the seventh column, an English synonym, when appropriate, is listed and includes any common eponyms.
An initial move forward in regard to standardization of anatomical terminology came by way of the Basel Nomina Anatomica, which was approved in 1895 by the Congress of the Anatomische Gesellschaft. This would be followed by revisions in 1933 and 1935 in Birmingham and Jena, respectively. Later, in 1950, the International Anatomical Nomenclature Committee (IANC) was established by the IFAA. Then, in 1955, Nomina Anatomica was approved in Paris at the sixth Congress meeting. Nomina Anatomica would go through several editions in the 1960s, 1970s, and 1980s, with the latter including Nomina Histologica and Nomina Embryologica. In the late 1980s, a dispute between the IFAA and IANC resulted in a sixth edition of Nomina Anatomica being published, but without IFAA approval. Derived from this dispute, in 1998, Terminologia Anatomica was produced by the Federative Committee on Anatomical Terminology (FCAT), a committee of the IFAA. In 1999, FCAT was changed to Federative International Committee on Anatomical Terminology (FICAT), which is now, since 2009, known as FIPAT. FIPAT has produced Terminologia Embryologica, first and second editions, Terminologia Neuroanatomica, and in 2019, TA2. TNA, TE2 and TA2 are all available online. Currently, a second edition of Terminologia Histologica is underway in addition to several newer terminologies including Termionologia Oroanatomica and Terminologia Anatomica Anthropologica.
Unlike in the past, where a print copy of the book was necessary and the required index searching, which was inconvenient, the online archive for the Terminologies allows them to be 'living documents', includes errata sections, and includes a TA2 Viewer. To increase the use and ease of accessing TA, the TA2 Viewer is now available (https://ta2viewer.openanatomy.org). This is a searchable, dynamic web application of TA2, and is a collaboration between the IFAA and the Open Anatomy Project at the Brigham and Women's Hospital (Boston, USA). The Viewer is a powerful tool not only for searching TA2; it also includes links to the use of the term on various search engines e.g., Google. Additionally, links to Medical Subject Headings (MeSH) terms, important online resources such as Gray's Anatomy (20thedition) published in Philadelphia in 1918, and informatics sites such as the Foundational Model of Anatomy (FMA) from the Structural Informatics Group are included. The reader is encouraged to take advantage of this resource.
Anatomical terminology must avoid ambiguity. To this end, the standardized and internationally agreed upon nomenclature provided by the IFAA's Terminologies is important not only to the anatomist but also practitioners of medicine and the lay public. Although a single collection of tens of thousands of terms will never be perfect (Chmielewski and Domagała, 2020), constantly revising and reevaluating the IFAA's Terminologies will help to keep these terms relevant now and into the future (Neumann et al., 2017a; Neumann et al., 2017b; Neumann et al., 2020).
Shane Tubbs
Chair, FIPAT
Eur. J. Anat.
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Considerations for the containment of COVID-19 in cadavers: ensuring the continuance of human dissection for the education of healthcare professionals
Chmielewski PP, Domagała ZA (2020) Terminologia Anatomica and its practical usage: pitfalls and how to avoid them. Folia Morphol (Warsz), 79(2): 198-204.
Neumann PE, Baud R, Sprumont P (2017a) Ordering by the numbers in anatomy and by letters Too. Clin Anat, 30(6): 700-702.
Neumann PE, Baud R, Sprumont P (2017b) Human anatomy nomenclature rules for the computer age. Clin Anat, 30(3): 300-302.
Neumann PE, Gest TR, Tubbs RS (2020) The principles of anatomical nomenclature revision: They're more like guidelines anyway. Clin Anat, 33(3):327-331.
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Remember at the beginning of the description of the ibadurrahman, Allah says when they meet the ignorant, they bear them with a patient shrug and say words of peace?
The following is a discussion of the positive outcomes that are due to the patient one according to science.
In a 2007 study, Sarah A. Schnitker and Robert Emmons demonstrated that patient individuals had better mental health because they felt more abundance, experienced less depression, had fewer negative emotions and were more mindful and more connected to mankind.
Professor Terrie E. Moffitt, a psychological scientist at the Duke University believes that the developed world needs patience now as they needed education at the dawn of the 20th Century. She said this during her keynote speech at the inaugural International Convention of Psychological Science in Amsterdam.
The second kind of patience is the strength to bear daily hassles – such as a traffic gridlock – without losing your head.
Yet, from the Islamic perspective, it is not now that self-control has come to mean so much. Everywhere you turn in the Qur'an Allah commands His servants to be patient so that they will be successful.
For example, the Qur'an clearly shows us how Allah prepared Prophet Muhammad (SAW) for the message in chapter 73.


text:
Top NPR Executive Resigns After Sexual Harassment Allegations
Published November 2, 2017 at 5:04 AM EDT
And let's follow up now on allegations against an executive here at NPR that have led to increasing tensions within our newsroom. Our company's chief editor, Michael Oreskes, resigned yesterday after being accused of sexual harassment. And let's just remember how this all developed.
The Washington Post reported Tuesday that two women recently accused Oreskes of abruptly kissing them after they approached him to talk about job opportunities. These incidents happened in the late 1990s when Oreskes worked for The New York Times. But Oreskes is also facing more recent complaints, including from within the NPR newsroom.
NPR media correspondent David Folkenflik is on the line. And, David, it sounds like you are hearing from more women now coming forward to talk about Oreskes' conduct.
DAVID FOLKENFLIK, BYLINE: Yes. Let's separate what we know from what's new. There are the two women who came forward to NPR - one in 2016, one just last month to tell them about these incidents from nearly two decades ago. That was reported, as you said, in The Post. There was another I reported on - incident from 2015 involving one of our younger colleagues that I reported on Tuesday night and yesterday. And then there are five women I've spoken to in the last 24 hours.
The women range from a reporter in her 20s to a producer in her 50s. Two are still at NPR. The others were seeking career advice as long ago as a decade and as recently as this past summer. One told me - the producer told me that Oreskes put his palm on her stomach as he passed her in the office and what she called a strong and lingering and definitely unwanted physical caress.
Several others said he sought to convert professional conversations about career paths into very highly personal sessions over wine and dinner. A couple of them said there was the clear implication of romantic involvement, particularly if they had wanted to pursue jobs here at NPR - nothing explicit but very clear to them. They said this was deeply troubling. Two women said they didn't apply to NPR for jobs as a result.
GREENE: OK. Incredibly serious allegations - a growing number of them, it sounds like. And we heard later - late yesterday from our CEO - NPR CEO Jarl Mohn. Go through how he responded to all this.
FOLKENFLIK: Well, there was a surreal moment. He was interviewed yesterday by our colleague, Mary Louise Kelly, for All Things Considered. Dozens of colleagues gathered in the NPR newsroom to look on at this - you know, the windowed studio. They're in our headquarters in D.C. Jarl Mohn, our CEO, stated that, you know, as I said, one of the women first contacted NPR in 2016 about her allegations about what Oreskes has done at the time. And we have a clip of that here.
JARL MOHN: The important distinction here is, first, that did not happen at NPR. It was not an NPR employee. It was at The New York Times, and it occurred 20 years ago. Had that happened at NPR, we would have had a very different reaction to it.
FOLKENFLIK: You know, the incident in 2015 that I had reported on earlier this week did not involve such physical contact. Mohn said, to his knowledge, nothing of the same severity had happened at NPR. And he said that, you know, there was concern about rumors roiling the NPR headquarters and newsrooms, but they couldn't act on rumors.
Last month, he even sent out an email seeking additional - in a generic sense, anyone who'd report anything that they had heard about sexual harassment that was troubling in light of sort of the age of Harvey Weinstein and Roger Ailes and all of these allegations we've heard of against media executives. He said no employee came forward at that time.
GREENE: We should say that Jarl Mohn has not been directly asked yet about some of the details that you were giving us about these other women who are coming forward. Is that right?
FOLKENFLIK: That's right. And let's also be clear, Michael Oreskes has not commented on any specifics. He's just simply said he's deeply sorry that his behavior was wrong and inexcusable and he accepted responsibility. But I think there are a lot of people in our newsroom, not just women, who are deeply upset. They feel that NPR knew about troubling indicators early on - should have acted more quickly to protect their colleagues.
GREENE: OK, NPR media correspondent David Folkenflik. David, thanks for your reporting.


One of the best things to work on is self-development. Don't you agree? By enhancing the quality of your life, you not only achieve more but also become a better person. We often look outside for happiness, but the fact is that happiness comes from within. When you work towards pursuing happiness, you realize that you'll be able to achieve more by adapting to situations. Maybe the previous year did not do much great to any of us, but the coming year can be a turnover. Here are a few personal development goals you should set for yourself to expect the best out of the New Year.
Don't you think it's about time to start getting up early? Well, by waking up early, you can transform your entire day. You will be able to spend time in meditation, eat a healthy breakfast, and even watch the sunrise. It will surprisingly keep you more active, bright, and cheerful throughout the day as compared to when you oversleep. Crankiness comes with oversleeping or lack of sleep. To be happy, your body needs to be well rested. Try to wrap up work earlier at night so that you can get a good 6-8 hours of sleep.
Your self-confidence is basically how you think of yourself. To boost your self-esteem, you must start by considering yourself worthy of success and happiness. In a way, your confidence can determine your success. When you jot down your self-development goals, ensure that becoming more confident is on top of the list. It plays an important role in both personal and professional lives as how you see yourself can influence how other people will look at you.
Being mindful can help you make better decisions in life. Recognize the good and abundance of luck in your life and use it wisely. Instead of thinking about what could not happen, think about what could. Be more present at the moment. By being more mindful, you can take charge of your duties and responsibilities and look forward to the future. Do not allow your mind to wander, and replace those thoughts with positive beliefs. This will allow you to achieve exactly what you want from life. Mindfulness will boost your willpower, which is essential to accomplish anything worthwhile.
You can be truly happy only if you let go of the past. You can't live in the past or in those resentful moments. What has happened is already over, and you cannot change it. Most of us are haunted by our pasts, so much so that we let go of good opportunities. Releasing the past will help you think and see more clearly. And by the end of it, you will see happiness. It may be difficult, but it's important to acknowledge that what's done is done, and you can't let that keep you from being free and happy. So make releasing your past one of your goals, and you will see the difference it makes.
People who are proactive see themselves as creators, and often, they are the go-getters. They take charge of what they want in life and work towards it. This should be a mandatory goal we need to set for ourselves if we want a life of our own. It means moving ahead, looking forward to the future, and making things happen. Being actively charged and engaged is what you need to succeed. Take charge of your duties and responsibilities – instead of being a passive observer, be the doer.
Life has so much to offer if you make the most out of it. By setting these personal development goals, you can become a better person. Your attitude is your state of mind. Instead of limiting your capabilities, push yourself, and you will see that you can do so much more. You will be able to try new things and take risks. How you see, life will determine your future and the quality of life. So, let the new year be the turning point for you. You will be the master of the world.
Nisha has a great passion towards writing and loves the idea of sharing. She has written many articles on yoga, fitness, wellness, remedies and beauty. She keeps reading articles on different blogs that gives a kick to her passion and provides her with different ideas. She is growing day by day and mastering herself in writing appealing articles. She is a regular contributor to StyleCraze.com & Other few websites too.
Solitude: Why We Need It.


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NC teacher screening bill passes Senate
Tonya Maxwell
tmaxwell@citizen-times.com
State legislation that expands protections for North Carolina's public school students is expected to move to the House after passing the Senate unopposed Wednesday.
Under the bill, the State Board of Education would require that prospective public school teachers undergo a fingerprint criminal history check against state and federal databases.
Currently, criminal history checks are left to the state's 115 school districts and searches that rely on fingerprints are not required, creating a disparate screening system without an overarching standard.
"Requiring criminal background checks for teachers and school personnel is a commonsense step that will not only provide a safer place for our students to learn, but also a safer place for teachers to work and educate our children," said bill sponsor Sen. Chad Barefoot, a Republican representing Franklin and portions of Wake counties, in a statement.
The issue began drawing attention of state policymakers in February, after the Citizen-Times examined problems with teacher screening, while a nationwide look by USA Today handed North Carolina a failing grade for its lackluster efforts in screening out problematic teachers.
"The recent USA Today article giving North Carolina an 'F' for its public school background screening system highlights the need for the state to ensure that our students and teachers are in the company of good actors," Sen. Trudy Wade, also a sponsor and Guilford County Republican, said in a press release.
Under the legislation, the cost of background checks – expected to be about $50 – would be paid by teacher applicants. Those costs are borne now by local school districts.
In 2015, state education officials received 12,000 applications for initial licenses and 31,000 applications for renewals, typically required every five years.
A legislative fiscal note does not offer an estimate of the legislation, but does indicate that expanding checks to licensed teachers at renewal would cost about $2.2 million.
The Department of Public Education has also estimated that processing the background checks would require a new attorney and paralegal position at an approximate annual cost of $140,000.
The licensure system is now staffed by two people who examine criminal background issues at the state level: an attorney and paralegal who each have additional duties.


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Alan Sanchez
Born in Detroit, Michigan in 1960, Alan began painting at a very early age enrolling in adult classes at the local YMCA at the age of 10. In his senior year of high school he began taking classes at the Detroit Institute of Art under the instruction Detroit Artist Allie McGee. It was here he ... moreBorn in Detroit, Michigan in 1960, Alan began painting at a very early age enrolling in adult classes at the local YMCA at the age of 10. In his senior year of high school he began taking classes at the Detroit Institute of Art under the instruction Detroit Artist Allie McGee. It was here he learned of contemporary art and more importantly of the local art school, the Center for Creative Studies.
After high school graduation Alan was accepted at the Center for Creative Studies, studying Graphic Design. The following year he transferred to the Fine Art department headed by New York/ Detroit artist Aris Koutroulis. By his senior year Alan was awarded a residency to the New York Studio School in Greenwich Village, N.Y.C. and began exhibiting with Provenance Gallery in Chelsea N.Y. He earned his B.F.A from the Center for Creative Studies in 1983 with a major in figure drawing and painting with a minor in anatomy.
During this time Alan participated in his first group show in 1979 at the Pontiac Art Center and his first one man show at the Peterboro Gallery in Detroit in 1983.
Alan moved permanently to New York City after graduation and continued exhibiting with Provenance Gallery until 1990. It was while he was showing here that he created numerous commission portraits for celebrities, including Farrah Fawcett. In 1988 he also expanded his reach to Paris, France where he began showing in Galerie Rec in the Marais district.
Opening his own design and fabrication company in Brooklyn in 1992, Alan created furniture and interiors for architects and designers, while continuing to exhibit with galleries in both NYC and Detroit.
In February 2004 Alan moved to the south west of France, exhibiting with Galerie 17 in Pezanas, France. Alan was selected to represent Galerie 17 at the prestigious annual International art exhibition "Art en Nime", in the city of Nimes. During the summers Alan instructed students at the Center for Creative Studies in art history and referencing, concept drawing, sculpture in clay and metal fabrication.
It was while he was exhibiting with Galerie Bex in the Montparnasse district of Paris, France, that the gallery owner Eric Bex also acted as Alan's artistic agent and procured a high-profile commission project - a 4 meter by 2 meter painting created in the headquarters lobby of the French petroleum research company Technip, in La Defense, Paris. Alan worked ten hours a day with spectators not only watching the creation but also encouraged to either write or paint on the canvas alongside the artist. Soon after, he was commissioned to create two large paintings in the presence of 300 plus spectators in the Garage showroom of Piaggio Scooters in Paris, France, two large pieces, "Apollo" and "Venus".
During this time, Alan was also teaching painting techniques including Italian renaissance at the art school Andre Malraux in Villeneuve sur Lot from 2012-2016 while continuing to exhibit throughout the southwest of France including two solo exhibitions at the 13th century church Our Lady of Pinel, in the village of Pinel. Here he showed his religious works including the ongoing series "the five apparitions of Juan Diego". These two exhibits were the realization of a dream of the artist to exhibit this series in a sacred church.
In January of 2017 Alan moved to the Phoenix area of Arizona where he now finds inspiration in the beautiful and curious landscape and history of Arizona. "I find the landscapes of the desert and mountains here to be very inspiring. I compare the landscapes here to the painting of Picasso, almost austere, with the beauty in its imposing majesty, honesty and natural force."
"My work has been a daily part of my life for over forty years. A great deal of my imagery has been inspired by stories particularly religious stories, like the "Five Apparitions of Juan Diego and Guadalupe."
Representing The Finest in Religious Art
-To do something beautiful for God
-To enrich and inspire lives
-To bring people closer to God through beauty in art
-To support and encourage artists to create fine religious art
We are here to help fill your need in religious art, whether as an inspirational piece for your home, as a large project for your church, or a gift of beauty for a loved one.
7165 E. Main Street, Scottsdale, AZ 85251 480-946-1003 ask@thesacredartgallery.com


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Author - Sally Cox
Pell Appeal
Sally Cox2020-11-27T00:00:50+11:00 The Victorian Court of Appeal has today upheld on appeal Cardinal George Pell's convictions for sexually abusing two then 13-year-old boys. Cardinal George Pell's appeal failed. On 11 December 2018, Cardinal George Pell was convicted unanimously by a jury of 12 men and women in the County Court of Victoria of five charges of sexual offending against two young choir boys in 1996 at St...
August 21, 2019By Sally CoxPersonal InjuryChild Sexual Abuse, Compensation, compensation lawyer, George Pell, Personal Injury1 CommentRead more...
Call for Witnesses – The Scots College
Sally Cox2020-11-27T00:01:23+11:00"CALL FOR WITNESSES TO COME FORWARD" The Scots College PH: 02 9283 5599 John Beckett John Beckett ("Beckett") was a long-standing and respected teacher at The Scots College. He was appointed as a mathematics teacher in 1974 and taught at the school from 1974 until 1999. During the 1970s, 80s and 90s he was involved in the many facets of school life including pastoral care and extracurricular activities....
August 14, 2019By Sally CoxPersonal Injurythe scots college0 CommentsRead more...
Call for Witnesses – Robert "Dolly" Dunn
Sally Cox2020-11-26T23:40:23+11:00"CALL FOR WITNESSES TO COME FORWARD" Robert "Dolly" Dunn and the Marist Brothers Schools PH: 02 9283 5599 Robert "Dolly" Dunn Robert "Dolly" Dunn was a former school teacher at Marist College Penshurst where he was continuously employed from 1971 to 1987. Dunn is known as a notorious paedophile and drug dealer who had a long history of abusing boys between the ages of 7 and 15 years old....
July 18, 2019By Sally CoxPersonal InjuryDolly Dunn, Marist Brothers, Robert Dunn, Robert Joseph Dolly Dunn0 CommentsRead more...
Call for Witnesses – Kostka Chute
Sally Cox2020-11-27T00:03:06+11:00"CALL FOR WITNESSES TO COME FORWARD" "Brother Kostka Chute and the Marist Brothers Schools" PH: 02 9283 5599 John William Chute, also known by his religious name as Brother Kostka, was a teacher and principal at a large number of schools operated by the Marist Brothers in Queensland, New South Wales and the Australian Capital Territory. He was a sexual predator who abused numerous young boys over...
July 11, 2019By Sally CoxPersonal Injury1 CommentRead more...
South Australian School Teacher Jailed
Sally Cox2019-05-17T22:25:30+10:00 Former South Australian School Teacher Jailed for Abusing Students Stephen John Hamra, a former primary school teacher at St Ignatius College and Christian Brothers College in South Australia has been found guilty of persistent sexual exploitation of a child and maintaining an unlawful sexual relationship with a child between 1977 and 1982. He was sentenced by Adelaide District Court Judge Paul Rice on the 4 April...
April 27, 2019By Sally CoxLitigation, Personal InjuryChild Sexual Abuse, South Australia, Stephen John Hamra0 CommentsRead more...
Pseudonyms in Historic Child Sexual Abuse
Sally Cox2019-05-06T15:24:29+10:00 The Use of Suppression Orders and Pseudonyms in Historic Child Sexual Abuse Cases A common barrier to seeking compensation for people who have suffered sexual abuse as a child in institutional settings is a sense of fear. Additionally embarrassment or shame occur at the prospect of being identified as a victim/survivor of child sexual abuse. The decision to seek redress for historic child sexual abuse...
April 27, 2019By Sally CoxLitigation, Personal InjuryCourt Orders, Court Suppression, Sexual Abuse, Suppression Order0 CommentsRead more...


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Frequency of prayer among adults with an education level of high school or less by views about same-sex marriage
Frequency of prayer among adults with an education level of high school or less by views about same-sex marriage (2014) Switch to: Views about same-sex marriage among adults with an education level of high school or less by frequency of prayer
% of adults with an education level of high school or less who pray…
Views about same-sex marriage
At least daily
Strongly favor/favor
44% 18% 7% 30% < 1% 4,520
Oppose/strongly oppose
70% 14% 4% 11% 1% 5,075
60% 16% 5% 15% 3% 989
Learn More: At least daily, Weekly, Monthly, Seldom/never


How well off is Noemi?
This did not satisfy Jeffrey, and the relationship between them became more distant.
Ragnar was sitting near two men in expensive suits.
Patricio kept splashing water in Brooke's face.
Lucifer makes an excellent martini.
Torsten listened to my opinion.
Tran didn't know that song.
"What did you think of Gypsy?" "He's got a nice voice." "Just a nice voice?" "Well, his face is nothing special, right?" "Really! I think he's pretty good looking."
Myron lived in Boston for a while.
I'd like to meet Ronald's sister.
Roxie suffocated Sehyo with a plastic bag.
I saw Radek this morning.
May I speak to Gale?
Suddenly, Takao cried out in pain.
Is that what you told Sherman?
Frances and Kikki's relationship became strained.
Guido isn't really as busy as he says he is.
Marc has been waiting for ten minutes in the car.
Ofer is bound to come here.
Danielle watched Moses pour a drink.
Keith can speak both French and English quite well.
You look just like your brother.
Samuel will never find it.
It looks like Those doesn't want to be here.
Barrio didn't notice Wolf leave.
Do you agree with Jeffery's recommendations?
Mara was able to answer all the questions.
Thuan and I went to a party last night.
Tait promised me he'd do it.


Hi, my name is Francesco and I am located near Milan.
As financial controller, I have been working for decades in international groups, supervising subsidiaries worldwide.
Among other duties and responsibilities, I have negotiated insurance policies and managed claims for years.
I found out that the insurance domain is not as covered as others, like banking, by small and medium-sized companies. Financial managers tend to rely on brokers and agents and focus very seldom on risk management and cost reduction.
Insurance is actually quite a tricky speciality if you don't have a solid background.
My passion for IT (see another project of mine) and additional research have filled the gap.
NEAT COVERAGE is an answer to an actual need of keeping track of insurance policies and related documents to make sure that risks are managed properly. The application can be used wordwide tough the language mainly derives from the US insurance industry.
The right tool and a its focused approach will make insurance and risk management much more rewarding.


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When September arrives, Denny's court date arrives with it. Denny leaves in the morning wearing a suit and returns late in the afternoon. He smiles at Enzo, and behind him is Zoë. The family spends a joyous afternoon playing, and after dinner, they have ice cream. Suddenly, Zoë asks if Denny is going back to Europe. When he says no, she's overjoyed at getting her room back. Denny explains to her that she can't come home yet because the lawyers still have to make a decision on where she'll live. Frustrated, Zoë instructs Denny to tell them that she wants to live with him. He tries to explain that he's been accused of doing something bad and he has to prove he didn't do it before she can come home.
The power of the story that Zoë was told through the letter exchange still holds, as she obviously still believes that Denny was in Europe. Zoë's explicitly stated desire to live with Denny adds to the sense of frustration at the situation. The reader, as well as the characters, know that the rape suit is bogus, but the power of that story is strong enough to maintain the status quo and keep the family apart for the time being.
After thinking for a moment, Zoë asks if it was her grandparents who accused Denny. She stares into her bowl of ice cream and says that she made Trish and Maxwell love her too much, and that she should have misbehaved so they didn't want to keep her. Denny is dismayed, but the conversation is over.
Enzo has previously commented on how perceptive Zoë is for her age, and here we see the heartbreaking result of her precociousness.
Later, the doorbell rings and Mark Fein is there to pick up Zoë. Mark reminds Denny that this is a victory and lays out the custody arrangement, where Denny gets Zoë one day after school and every other weekend. Mark calls Denny a champion, and then takes Zoë back to Trish and Maxwell.
Mark Fein, in trying to impress upon Denny how great this win is, uses driving language to connect with him. This first victory provides a sense of hope for the outcome of the impending rape trial.
Enzo finally understands that the trial that day had been only about Zoë's custody and not Denny's criminal charges, and that the trial had been put off while all the lawyers took vacations. However, having seen Zoë and Denny together again, Enzo's faith is restored. He tells the reader that now that Denny has fresh tires and a full load of fuel, he'll continue the race as a formidable foe.
Enzo also uses racing language to interpret Denny's win. He sees the restored contact with Zoë as emotional fuel for Denny as well as himself to get them through the grueling trial ahead.
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