text:
\section{Introduction}\label{sec:intro}
\input{Introduction}

\section{Model}\label{sec:model}

\input{model}

\section{The Dynamic Information Design Problem} \label{sec:problem}

\input{info-structure}

\section{An Optimal Sequential Information Disclosure Mechanism}\label{sec:solution}

\input{solution}

\section{Results and Discussion} \label{sec:numerical}

\input{numerical-results}

\section{Conclusion} \label{sec:conclusion}

We studied a dynamic Bayesian persuasion problem whereby a strategic principal observes the evolution of a Markov chain and designs a recommendation policy that generates a recommendation to a strategic detector at each time. The goals of the principal and the detector are different, therefore, the long-term-optimizing detector does not have to obey the principal's recommendations unless she is convinced to do so. We presented a sequential recommendation policy that maximizes the principal's utility, and ensures the detector's obedience. We proved that the optimal policy is a threshold type, with two thresholds that can be explicitly computed. As time goes by, the optimal recommendation strategy first shifts from a no-information type to a randomized type and then switches to a full-information type.

\subsection{Problem Formulation} \label{sec:problem-formula}

A dynamic information disclosure mechanism specifies the set of messages $\mathcal{M}_t$ that the principal sends to the detector at each instant of time $t\in \mathcal{T}$, along with a distribution over $\mathcal{M}_t$ given all the information available to the principal at time $t$. The principal's information at time $t$ consists of 1) the history of evolution of the state (which the principal observes perfectly) up to time $t$, i.e. $s_{1:t}$, 2) the history of his past messages to the detector, i.e. $m_{1:t-1}$, and 3) the history of the detector's past actions, i.e. $a_{1:t-1}$. The set of dynamic information disclosure mechanisms is completely general, it includes the extremes of full information, no information, and all conceivable intermediate mechanisms. The full information mechanism is the rule that reveals perfectly the current state $s_t$ : i.e., $\mathcal{M}_t=\{g,b\}$ and $\mathbb{P} (m_t=s_t)=1$. A no information mechanism is obtained when the set of messages $\mathcal{M}_t$ has only one element and the principle sends that single message irrespective of the system state.

As it is clear from the above examples, a dynamic information disclosure mechanism could be very complicated since there is no restriction on the set of messages $\mathcal{M}_t$ or the probability distribution on $\mathcal{M}_t$, $t \in \mathcal{T}$. However, it is shown in \cite{Bayesian-persuasion} that there is no loss of generality in restricting attention to \emph{direct} dynamic information disclosure mechanisms that are \emph{obedient}. Thus, we concentrate on direct dynamic information disclosure mechanisms that are obedient.

In a direct information disclosure mechanism, at each instant of time, the principal directly recommends to the detector the action she should take. In our problem, the detector's possible actions at each time $t$ are to either keep silent ($a_t=k$) or declare the jump ($a_t=d$). Therefore, the set of messages used by the principal at each time $t$ is $\mathcal{M}_t=\mathcal{M}=\{k,d\}$, where $k$ is a recommendation to keep silent, and $d$ is a recommendation to declare a jump. As a result, the principal's behavior in a direct information disclosure mechanism can be described by a recommendation policy $\boldsymbol{\rho}=(\rho_{t}^{s_{1:t},m_{1:t-1},a_{1:t-1}}, t \in \mathcal{T})$, where $\rho_{t}^{s_{1:t},m_{1:t-1},a_{1:t-1}}$ is the probability according to which the principal sends message $k$ to the detector (i.e. recommends her to keep silent), when the sequence of the states he has observed up to time $t$ is $s_{1:t}=(s_1,\ldots,s_t)$, the history of the past messages he has sent is $m_{1:t-1}=(m_1,\ldots,m_{t-1})$, and the history of the detector's past actions is $a_{1:t-1}=(a_1,\ldots,a_{t-1})$. For each $t \in \mathcal{T}$, $s_{1:t} \in \{g,b\}^{t}$, and $m_{1:t-1}, a_{1:t-1} \in \{k,d\}^{t-1}$, the principal sends message $d$ to the detector with probability $1-\rho_{t}^{s_{1:t},m_{1:t-1},a_{1:t-1}}$. There are two features in our problem that help us to simplify the principal's information.

1) At each instant of time, the detector has two actions one of which (i.e. declaring the jump) terminates the whole process. Therefore, making a recommendation at time $t$ is meaningful for the principal only if the detector kept silent at all the previous times, i.e. $a_{1:t-1}=(k)^{t-1}$. Thus, $a_{1:t-1}$ can be omitted from the principal's information.

2) The bad state of our Markov chain is an absorbing state. Therefore, the state evolution of the Markov chain until time $t$ is of the form $s_{1:t}=((g)^{\theta_t-1},(b)^{t-\theta_t+1})$, where $\theta_t$ could take any integer value between $1$ and $t+1$. We define $\theta_t$ as the earliest possible time for the jump based on the principal's information at time $t$; i.e. $\theta_t=\min{(\theta,t+1)}$.
The parameter $\theta_t$ is equal to $\theta$ if the jump has occurred up to time $t$, however it takes value $t+1$ when the principal finds the Markov chain in the good state at time $t$. Because of this feature, we can represent the recommendation policy $\rho_{t}^{s_{1:t},m_{1:t-1}}$ of each time $t$ by $\rho_{t}^{\theta_t,m_{1:t-1}}$, where $\theta_t \in  \{1, \ldots, t+1 \}$.

When the principal designs an information disclosure mechanism, he announces the corresponding recommendation policy $\boldsymbol{\rho}$ to the detector and commits to it.

The detector is strategic; she utilizes the information she receives from the principal to her own advantage and does not necessarily follow
the actions recommended by the principal. Therefore, to achieve his goal, the principal must design an information disclosure mechanism that possesses the obedience property, that is, it provides the detector with strong enough incentives to follow his recommendations.

At each time $t \in \mathcal{T}$, the long-term-optimizing detector obeys the principal if the recommended action $m_t$ minimizes her conditional expected continuation cost, i.e.,
\begin{align}\label{eq:obedience-constraint}
m_t=\argmin_{a_t}{\left[\min_{\gamma_{t+1:T}}{\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}\}}\right]}, \hspace{0.1cm} \forall t, m_{1:t},
\end{align}
where $\gamma_{t+1:T}$ denotes her decision strategy profile from time $t+1$ up to $T$, and $\min_{\gamma_{t+1:T}}{\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}\}}$ is her minimum expected continuation cost
conditional on her information $m_{1:t}$ when the principal commits to the information disclosure strategy/mechanism $\boldsymbol{\rho}$. Therefore, to check the obedience property of a direct information disclosure mechanism at any time $t$, $t=1,2,\ldots,T$, we need to solve the series/sequence of optimization problems
\begin{align}\label{eq:obedience-constraintt}
\min_{a_t}{\left[\min_{\gamma_{t+1:T}}{\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}\}}\right]},
\end{align}
for all $m_{1:t}$. Solving these optimization problems is a challenging and time-consuming task. However, the one-shot deviation principle allows us to derive the obedience constraints by assuming that the detector sticks to the obedient strategy in the future. Specifically, considering a fixed direct information disclosure mechanism, the whole process can be seen as a finite extensive-form game between the detector and nature (principal), where at each stage $t$ nature sends a signal $m_t$ to the detector according to $\rho_t$ and then the detector takes an action $a_t$. With this interpretation, the set of obedience constraints (\ref{eq:obedience-constraint}) is a necessary and sufficient set of conditions for the strategy profile $a_t=m_t$, for $t \in \mathcal{T}$, to be a subgame-perfect Nash equilibrium (SPNE) \cite{Myerson1991}. According to the one-shot deviation principle a strategy profile $\gamma$ is a SPNE if and only if no player can increase their payoffs by deviating from $\gamma$ for one period and then reverting to the strategy \cite{fudenberg1991}. Therefore, a simpler version of the obedience constraints is as follows:
\begin{align}\label{eq:obedience-constraint2}
m_t\hspace{-0.06cm}=\hspace{-0.06cm}\argmin_{a_t}{\hspace{-0.06cm}\left[\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}, a_{t+1:T}\hspace{-0.06cm}=\hspace{-0.06cm}m^{\boldsymbol{\rho}}_{t+1:T}\}\right]},
\end{align}
for all $t$ and $m_{1:t}$, where the condition $a_{t+1:T}=m^{\boldsymbol{\rho}}_{t+1:T}$ of the expectation reflects the fact that the detector obeys the recommendations from time $t+1$ onward, and the notation $m^{\boldsymbol{\rho}}_{t+1:T}$ indicates that the messages $m_{t+1:T}$ are generated according to the policy $\boldsymbol{\rho}$.

Equation (\ref{eq:obedience-constraint2}) includes $\sum_{t=1}^T{2^t}=2(2^T-1)$ constraints. These constraints force the detector to obey the recommendations after each message history $m_{1:t}$. However, due to the nature of our problem, the first time the detector is recommended to declare a jump in an obedient mechanism, she will do so and the process will terminate. Therefore, the message histories with at least one $d$ in the past are not going to occur and need not be checked. This feature reduces the obedience constraints need to be considered to the following:
\begin{align}\label{eq:obedience-constraint-k}
\begin{split}
&\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}=(k)^t, a_t=k, a_{t+1:T}=m^{\boldsymbol{\rho}}_{t+1:T}\} \\
&\leq \mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}=(k)^t, a_t=d\}, \forall t \in \mathcal{T},
\end{split}
\end{align}
\begin{align}\label{eq:obedience-constraint-d}
\begin{split}
&\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}\hspace{-0.06cm}=\hspace{-0.06cm}((k)^{t-1},d), a_t\hspace{-0.06cm}=\hspace{-0.06cm}k, a_{t+1:T}\hspace{-0.06cm}=\hspace{-0.07cm}m^{\boldsymbol{\rho}}_{t+1:T}\} \\
&\geq \mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}\hspace{-0.07cm}=\hspace{-0.07cm}((k)^{t-1},d), a_t\hspace{-0.07cm}=\hspace{-0.07cm}d\}, \forall t \hspace{-0.07cm} \in \hspace{-0.07cm} \mathcal{T},
\end{split}
\end{align}
($2T$ constraints).

Now that we derived the obedience constraints, we go through calculating the principal's utility. When the detector follows the recommendation policy $\boldsymbol{\rho}$, the expected utility the principal gets is
\begin{align}\label{eq:principal-utility}
\begin{split}
&\mathbb{E}^{\boldsymbol{\rho}} \{U^P(\tau)\}=\mathbb{E}^{\boldsymbol{\rho}} \{\tau-1\}=\mathbb{E}^{\boldsymbol{\rho}}\{\sum_{t=1}^T{1_{\{a_{1:t} = (k)^t\}}}\} \\
&=\sum_{t=1}^T{\mathbb{P}(a_{1:t} = (k)^t| \boldsymbol{\rho})}=\sum_{t=1}^T{\mathbb{P}(m^{\boldsymbol{\rho}}_{1:t} = (k)^t)}\\
&=\sum_{t=1}^T{\sum_{\theta'=1}^{T+1}{\mathbb{P}(\theta=\theta') \prod_{t'=1}^t{\rho_{t'}^{\min{(\theta',t'+1)},(k)^{t'-1}}}}}.
\end{split}
\end{align}
Therefore, we can formulate the information design problem (Problem \ref{eq:info-design-problem}) for the principal as follows:
\begin{align} \tag{\textbf{P}} \label{eq:info-design-problem}
&\max_{\boldsymbol{\rho}}{\mathbb{E}^{\boldsymbol{\rho}} \{U^P(\tau)\}},\nonumber\\
\textit{subject to}  & \textit{ the obedience constraints (\ref{eq:obedience-constraint-k})-(\ref{eq:obedience-constraint-d}),} \nonumber\\
& 0 \leq \rho_{t}^{\theta_t,m_{1:t-1}} \leq 1, \hspace{0.1cm} \forall t, \theta_t, m_{1:t-1}. \nonumber
\end{align}
That is, the principal wants to choose a feasible dynamic information disclosure mechanism $\boldsymbol{\rho}$ that satisfies the obedience constraints (\ref{eq:obedience-constraint-k})-(\ref{eq:obedience-constraint-d}) and maximizes his expected utility given by (\ref{eq:principal-utility}).

\subsection{Features of The Problem} \label{sec:problem-features}

Solving the optimization problem (\ref{eq:info-design-problem}) is a formidable task as the optimization variables are strongly coupled with many non-convex constraints. This strong coupling can be seen by taking a closer look at the expectations appearing in the obedience constraints (\ref{eq:obedience-constraint-k})-(\ref{eq:obedience-constraint-d}). According to (\ref{eq:cost-detector}), the detector's expected continuation cost from time $t$ onward when she has received messages $m_{1:t}$ and decides to declare the jump at time $t$ is
\begin{align}\label{eq:cost-declare}
\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}, a_t=d\}= \mathbb{P} (s_t=g | m_{1:t}),
\end{align}
i.e., the probability of false alarm at $t$. If the detector decides to keep silent at time $t$ and sticks to the obedient strategy at the future, her expected continuation cost is
\begin{align}\label{eq:cost-silence}
&\mathbb{E}^{\boldsymbol{\rho}}_{t:T} \{J^D(\tau,\theta) | m_{1:t}, a_t=k, a_{t+1:T}=m^{\boldsymbol{\rho}}_{t+1:T}\}= \nonumber\\
& c (1\hspace{-0.07cm}-\hspace{-0.07cm}\mathbb{P} (s_t\hspace{-0.07cm}=\hspace{-0.07cm}g | m_{1:t})) + \nonumber\\
&\mathbb{E}^{\boldsymbol{\rho}}_{t+1:T} \{J^D(\tau,\theta) | m_{1:t}, a_t\hspace{-0.07cm}=\hspace{-0.07cm}k, a_{t+1:T}\hspace{-0.07cm}=\hspace{-0.07cm}m^{\boldsymbol{\rho}}_{t+1:T}\},
\end{align}
where the first term on the right hand side is the expected delay cost at time $t$, and the second term denotes the expected value of all the future costs from time $t+1$ onward. Substituting (\ref{eq:cost-declare})-(\ref{eq:cost-silence}) in (\ref{eq:obedience-constraint-k})-(\ref{eq:obedience-constraint-d}) shows that at each time $t$, the detector's decision to obey or disobey the principal's recommendation depends on two factors:

(i) the belief the detector has about the good state of the Markov chain, i.e. $\mathbb{P} (s_t=g| m_{1:t})$; this belief is constructed according to Bayes' rule from the past messages $m_{1:t}$ she received, hence the past recommendation rules $\rho_{t'}^{\theta_{t'},m_{1:t'-1}}$ ($t' \leq t$) that generate these messages, as follows:
\small
\begin{align}\label{eq:current-belief}
&\mathbb{P} (s_t=g | m_{1:t})=\frac{\mathbb{P}(s_t=g,m_{1:t})}{\mathbb{P} (m_{1:t})}=\frac{\mathbb{P}(s_t=g) \mathbb{P} (m_{1:t} | s_t=g)}{\sum_{\theta'=1}^{T+1}{\mathbb{P} (\theta=\theta')\mathbb{P} (m_{1:t} | \theta=\theta')}}=\nonumber\\
&\frac{\mathbb{P}(\theta \hspace{-0.07cm}>\hspace{-0.07cm} t) \prod_{t'\hspace{-0.03cm}=\hspace{-0.03cm}1}^t{[\rho_{t'}^{t'\hspace{-0.04cm}+\hspace{-0.04cm}1,m_{1:t'\hspace{-0.04cm}-\hspace{-0.04cm}1}}1_{\{m_{t'} = k\}}+(1-\rho_{t'}^{t'+1,m_{1:t'-1}})1_{\{m_{t'} = d\}}]}}{\sum_{\theta'\hspace{-0.03cm}=\hspace{-0.03cm}1}^{T\hspace{-0.03cm}+\hspace{-0.03cm}1}{\mathbb{P} (\theta\hspace{-0.05cm}=\hspace{-0.05cm}\theta')\prod_{t'\hspace{-0.05cm}=\hspace{-0.05cm}1}^{t}{[\rho_{t'}^{\min{(\theta',t'+1)},m_{1:t'\hspace{-0.05cm}-\hspace{-0.05cm}1}}1_{\{m_{t'} = k\}}\hspace{-0.07cm}+\hspace{-0.07cm}(1\hspace{-0.07cm}-\hspace{-0.07cm}\rho_{t'}^{\min{(\theta',t'+1)},m_{1:t'\hspace{-0.05cm}-\hspace{-0.05cm}1}})1_{\{m_{t'} = d\}}]}}}.
\end{align}
 \normalsize
(ii) the cost the detector expects to incur in the future if she remains silent at time $t$ and follows the recommendations afterwards, i.e. $\mathbb{E}^{\boldsymbol{\rho}}_{t+1:T} \{J^D(\tau,\theta) | m_{1:t},\allowbreak a_t=k, a_{t+1:T}=m^{\boldsymbol{\rho}}_{t+1:T}\}$. This expected cost depends on the messages the detector expects to receive in the future. These messages depend on the future recommendation rules to which the principal commits, i.e. $\rho_{t'}^{\theta_{t'},m_{1:t'-1}}$, $t' > t$, $\forall \theta$.

Therefore, the detector's decision at each time $t$ depends not only on the recommendation policy for time $t$, but also on the recommendation policies for all times before and after $t$. The dependence of the detector's decision at each time $t$ on the recommendation policy for the entire horizon makes the discovery of an optimal information disclosure mechanism that satisfies the obedience property very challenging. This is mainly because any change in the principal's recommendation policy at any time $t$ affects the detector's decisions at all times. Therefore, the principal cannot optimize the recommendation policies of different time slots separately just by considering the obedience constraints at that time, instead he needs to optimize the recommendation policies of the whole horizon simultaneously.

\subsection{Review of Related Works} \label{sec:literature}

Information disclosure mechanisms can be seen as a communication protocol between an information transmitter (he) and one or multiple receivers. A significant part of the existing works in this area have studied the nonstrategic case, where the information transmitter and receivers are cooperative and jointly wish to maximize the global utility \cite{Witsenhausen79,Pravin83, Aditiya2009,Ashutosh1,Demos2006}.

The strategic case of information disclosure mechanisms (Bayesian Persuasion), where the transmitter (principal) and receiver have misaligned objectives, is in tradition of cheap talk \cite{Crawford-Sobel, Battaglini2002, Yuksel2015, Multi-sender2008, Dynamic-cheap-talk2015,Ivanov2016}, and signaling games \cite{Spence,Signaling2017}. In signaling games, the transmitter's utility depends not only on the receiver's actions, but also on his type (private information). However, in information design problems neither the principal's type nor his actions enter his utility directly; they only influence his utility through the effect they have on the receivers' actions. This feature of the model enables us to investigate/analyze the pure effect of principal's private information on the receivers' behaviors.

The main difference between cheap talk and information design is the level of commitment power they give to the principal. In the cheap talk literature, the principal has \emph{no commitment power}; he decides on the information message to be sent after seeing the realization of his private information. The cheap talk model induces a simultaneous game between the principal and the agents. Thus, the main goal of this strand of works is to characterize the (Nash) equilibria of the induced game. Most of the existing work has focused on the static setting \cite{Crawford-Sobel, Battaglini2002, Yuksel2015, Multi-sender2008}. The work of \cite{Crawford-Sobel} shows that when the state of the system (principal's private information) is one-dimensional and both the principal's and the agent's utilities are quadratic, the principal's equilibrium strategy employs quantization. More general models of cheap talk, such as multidimensional sources \cite{Battaglini2002}, noisy communication \cite{Yuksel2015} and multiple principals with misaligned objectives \cite{Multi-sender2008}, have been studied in the literature for static settings. There are a few works that study the dynamic version of the cheap talk communication \cite{Dynamic-cheap-talk2015,Ivanov2016}. These works show that allowing for dynamic information transmission improves the informativeness of communication.

In information design problems the transmitter is endowed with \emph{full commitment power}. In this model, the transmitter is allowed to send any distribution of messages as a function of the system state, but he should choose and announce his information disclosure policy before observing the system state and then stay committed to it forever. By committing to an information disclosure policy at the very beginning of the system's operation, the transmitter can persuade all other agents to employ strategies that achieve his objective. The fact that a player in a game can improve his outcome through commitment was first established in \cite{Stackelberg1934,Schelling1956,schelling1980} (see also \cite{KALAI2010}). The full commitment assumption holds in many economic (\cite{Goldstein2018,Inostroza2018,price-discrimination2015}) and engineering (\cite{Kamenica2017,Hamid-Allerton}) multi-agent systems.

The literature on information design is generally divided into two main categories: \emph{static} and \emph{dynamic} information design problems.

\textbf{Static information design problems}. The static version of the problem, where the state of the system is fixed and no time is involved, has been studied extensively in the literature. The authors of \cite{Cedric2017} consider a problem of static information disclosure where the state of the system is Gaussian and the utilities are quadratic, and show that there exists a linear policy for the principal that leads to a Stackelberg equilibrium. In \cite{Bayesian-persuasion, Unified-approach} the authors propose a concavification method for deriving an optimal information provision mechanism in static settings. The concavification approach was first developed by a group of U.S. economists and game theorists, led by R. Aumann and M. Maschler, with the context of the negotiations for the Strategic Arms Limitation Treaty (SALT) between the U.S. and U.S.S.R. (see \cite{Aumann1995}). The approach was developed for problems that can be modeled as repeated games of incomplete information. For over half a century, this idea played an important role in the analysis of repeated games (see \cite{ZAMIR1992,FORGES1992} and references therein) but has not been applied to information design problems until 2011 \cite{Bayesian-persuasion}.

Following \cite{Bayesian-persuasion}, information design problem has been studied for more general settings, such as costly communication \cite{costly2015}, multi-dimensional state \cite{Tamura2012}, multiple principals \cite{multiple-senders2017,multiple-senders2018}, multiple receivers \cite{Bergemann-multiagent,Bergemann2016}, and receivers with different prior beliefs \cite{heterogeneous-priors2016}. A case of information design problem with transfers where the principal can provide both information and monetary incentives to the receiver is also studied in \cite{with-transfer2017}. There is a group of works in static information disclosure which are more applied and aim to understand or improve real-world institutions via information design. Research in this strand includes applications to grading in schools \cite{Grading2015}, research procurement \cite{research-procurement2019}, medical testing \cite{medical-testing2018}, price discrimination \cite{price-discrimination2015}, insurance \cite{insurance2018}, and routing software \cite{Routing2014,Kamenica2017,Hamid-Allerton,Bayesian-Persuasion-routing-game,Saurabh2019}. A through discussion of the literature on information design up until 2018 appears in \cite{Kamenica-survey}.

\textbf{Dynamic information design problems}. The dynamic version of the information design problem, where the informed-player/principal can disclose his superior information sequentially over time, has recently been attracting rapidly growing interest. In dynamic environments, agents' decisions at each instant of time affect their opponents' decisions, not only at present but also in the future. The problem becomes more tangled if the information transmitter has commitment power. In this case, the information disclosure policy that the principal commits to for the future, has a direct effect on the receivers' estimation of what they can gain in the future, and hence on their current decisions. The interdependency among the agents' decision making processes over time makes the dynamic information design problems very complex and challenging.

Most of the available works avoid this challenge by assuming that the agents are myopic, that is they only look at each instant at the immediate consequence of their actions, ignoring the subsequent (future) effects. In \cite{Farokhi2017} and \cite{Basar2016-tracking} both the information transmitter and receivers are assumed to be myopic. Under this simplifying assumption, \cite{Basar2016-tracking} shows that the principal's optimal information disclosure policy is a set of linear functions of the current state.

To make the problem closer to reality, the authors of \cite{Lingenbrink,Ely-Beep,RENAULT-dynamic,Best1,Best2} consider the myopic assumption only for the information receivers. This set of works studies the interactions between a long-term-optimizing principal and either a myopic receiver or a sequence of short-lived receivers. In the latter case, at each instant of time a new receiver enters the system, forms her belief about the sender's strategy by observing the history of the past messages, takes her action, and then exits the system. In such a case, since the receivers leave the system after taking only one action, they are not concerned about the subsequent effects of their decisions. Therefore, considering a sequence of short-lived receivers is exactly equivalent to assuming that the receiver is myopic. Under this assumption, \cite{Ely-Beep} proposes a generalization of the concavification method for dynamic information design problems. The authors of \cite{RENAULT-dynamic} show that when the receiver is myopic, the greedy disclosure policy where the principal minimizes the amount of information being disclosed in each stage, under the constraint that it maximizes his current payoff, is optimal in many cases, but not always.

There are only a few papers which study the dynamic information design problem with both long-term-optimizing principal and long-term-optimizing receivers \cite{HONRYO-dynamic,Skrzypacz-dynamic,Skrzypacz-selling-info,Ely-goalpost,Ely-sequential-info-design,Basu2017Dynamic,Hung-dynamic,Farhadi2018,Hamid-Allerton,Asu2020}. In \cite{HONRYO-dynamic,Skrzypacz-dynamic,Skrzypacz-selling-info} principal is assumed to have no commitment power. This assumption simplifies the problem as in this case, the principal's policy at each time instant affects the receiver's decisions only at the future and not at the past. Although in some of these works communication is costly, they could be seen, due to lack of commitments, as dynamic versions of cheap-talk problem. The authors in \cite{Ely-goalpost,Ely-sequential-info-design,Basu2017Dynamic,Hung-dynamic,Farhadi2018,Hamid-Allerton,Asu2020} study the dynamic interactions between a long-term-optimizing principal who has full commitment power and a long-term optimizing receiver. In \cite{Ely-goalpost,Ely-sequential-info-design,Basu2017Dynamic,Hung-dynamic} the private information of the principal is considered to be constant and not varying with time. The problem with time-varying private information for the principal is discussed in \cite{Farhadi2018,Hamid-Allerton, Asu2020} for dynamic two-stage settings. The authors of \cite{Asu2020} also tackle the information design problem in an \emph{infinite-horizon} setting. In this setting, they first simplify the problem by restricting attention to a special class of information disclosure mechanisms and then characterize a mechanism that improves the principal's utility, but is not always optimal.

To the best of our knowledge, this paper is the first work that provides an optimal information disclosure mechanism in a dynamic setting with an arbitrary horizon length and long-term-optimizing principal and receiver, when the principal has full commitment power and his private information evolves over time.

There are a few works in the literature of information design that combine mechanism design and information design to obtain the benefits of both approaches \cite{Skrzypacz-selling-info,Ely-sequential-info-design}. In these papers, the principal changes both the game-form and the information structure of the play so as to persuade the receiver to take his desirable actions. This approach is not relevant to this paper, as we want to study the effect of the transmitter's information superiority in controlling receivers' behaviors.

\subsection{Contribution} \label{sec:contribution}
We formulate a dynamic information design problem over finite time horizon, where the information transmitter (principal) and the information receiver are long-term optimizing strategic agents. In this problem, the principal wants to use his superior information about system state, which evolves over time, to encourage the receiver to behave such that the interests of principal could be maximized. For this setting, we determine the optimal strategies of both the principal and the receiver. We prove that it is optimal for the principal to give no information to the receiver before a time threshold, run a mixed strategy to confuse the receiver at the threshold time, and reveal the true state afterwards. The principal should announce this information disclosure policy before observing the system state and then stay committed to it forever.

To the best of our knowledge, this is the first instance of a dynamical information design problem with long-term optimizing agents where an explicit solution for the optimal strategies of the agents is determined.

\subsection{Organization of the Paper} \label{sec:outline}
The rest of the paper is organized as follows. We present our
dynamic information design problem with strategic and long-term-optimizing agents in
Section \ref{sec:model}. In Section \ref{sec:problem}, we formulate the principal's
problem as a dynamic information design problem and discuss its main features. We describe the optimal sequential information disclosure mechanism we propose for the solution to this problem
in Section \ref{sec:solution}. In Section \ref{sec:numerical}, we show the superiority of our proposed mechanism by comparing it to non-strategic mechanisms that are used in real-world applications. We
conclude our paper in Section \ref{sec:conclusion}. The proofs of all the technical results appear in Appendices 1-9.

redpajama_set_name: RedPajamaArXiv


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Punjab Teachers Union (PTU) District Khushab President Malik Aman Ullah Joyia and local leader Ehsan Leghari have demanded that salaries of provincial government employees should be raised in the next budget commensurate with the price-hike. In a statement issued here on Monday, they said the govt should provide relief to the employees by including allowances into the basic pay and increase the salaries in accordance with the price-hike. They also demanded that in service promotion package issue of teachers of Khushab district should also be resolved immediately. They further said the up-gradation of PSTs had also been pending for long and the district government Khushab should approve all such cases immediately.


Smashwords – Books Tagged "biological mother"
These results show books which have been specifically tagged with this keyword. You can also try doing a general search for the term "biological mother" .
Jo finds herself pregnant in the early 1960's with limited options. Derailed by betrayal, she must make an impossible decision. Ellen lives with the challenges of being an adoptee. She is compelled to unearth her past in order to definitively prove her Jewish heritage. A Question of Heritage resonates with the angst of those in the adoption triad, leaving the reader with insight and hope.
Edward, a young English professor, was obsessed with the violin he had inherited from his Aunt Susan. When he faces Susan's portrait and plays the music she left him, her secret romance and other family secrets play out before him. His girlfriend, Cynthia, dislikes Edward's attention to Susan's violin, and coaxes him into the bedroom at every opportunity.


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by Eric Dombach | Apr 1, 2022 | How to Become a Business Coach
There's a need out there, folks. A need for your skillset, compassion, and mentorship. A need for someone to help struggling business owners find more freedom in their businesses and lives. A need for more business coaches.
I'm here to make the case today that you should become a business coach.
In the United States alone, there are over 7.2 million businesses that have enough substance and enough growth to have payrolled employees. And 98% of these businesses have fewer than 100 full-time employees.
This means that in the United States and North America, the vast majority of entrepreneurs have these businesses, slugging it out every day, doing their best, making a living, and helping their employees make a living. It's literally the backbone of what we used to call "the American dream."
But we know, from a lot of research that's been done, that out of every 100 independently owned small businesses, about 90% of them will fail within 10 years. Sad, but true.
So why does this happen?
Mapping the Trends
The Service Corps of Retired Executives (SCORE) has looked into the question of why 90% of small businesses fail in 10 years. Their results?
78% lack a solid business plan
73% are overly optimistic about their ability to get sales
77% don't price their products or services properly
70% don't recognize where they're vulnerable or seek help when they need it
But this just opens the door to opportunity for entrepreneurs like you–because business coaches can reverse this trend! As a business coach, you help struggling business owners correct the problems SCORE outlined above…and in the process, build a thriving business yourself!
As a business coach, you help struggling business owners correct the problems SCORE outlined above...and in the process, build a thriving business yourself!
And, by the way, with the way business coaches now operate in our virtual, internet-based world, business coaching has become a hyper-profitable business you can run from anywhere.
How Much Do Business Coaches Earn?
I chose the words "hyper-profitable" for a reason. Many of the coaches we've trained are able to build businesses that look a lot like this (EBR in the chart stands for "Effective Billable Rate"):
Of course, you don't just waltz into this kind of revenue. You need to start smart, have an effective sales and marketing plan, and some basic characteristics that translate to being a good coach.
But it's not true that you need a university degree, certification, or 20+ years of experience in business to be successful. What you really need to do is decide, commit, and act.
First things first, I suggest reading our FREE ebook, How to Become a Business Coach. It walks you through everything you need to know and do to get started on the right foot. I might also suggest checking out Do You Have What it Takes to Be a Successful Business Coach, which outlines the eight behavioral attributes that have been proven to correlate to success as a business coach with 95% certainty.
There is a world of opportunity out there…and literally millions of business owners who need a coach to guide them to higher levels of success. If you're considering becoming a business coach, don't wait: NOW is the time to explore further. You'll be glad you did!
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SPOKANE, Wash. – Gonzaga University baseball moves into its second weekend of play Thursday as the club heads to Nelson Wolff Stadium (San Antonio, Texas), for the University of Notre Dame hosted Irish Baseball Classic.
Gonzaga opens the tournament with University of the Incarnate Word Thursday at 1 p.m. followed by Notre Dame (Friday at 10:30 a.m.), Santa Clara University (Saturday at 10:30 a.m.) and one of those three teams Sunday. After round-robin play, the best two records will play and the worst two records will play on Sunday.
GU will look to rebound as it opened the season 1-3 last weekend in Arizona.
SAN ANTONIO, Texas – Gonzaga University baseball head coach Mark Machtolf reached the 300th career win milestone Thursday when the Bulldogs defeated University of the Incarnate Word, 6-1, in the opening game of the Irish Baseball Classic in Nelson Wolff Stadium.
Gonzaga improves to 2-3 on the year while Incarnate Word falls to 1-3.
Junior Payden Cawley Lamb went 1-for-3 with a pair of RBIs and Sam Brown had a game-high three hits to pace the Bulldogs. As a team, GU out-hit the Cardinals 8-6.
Incarnate Word was the first team to get on the board in the top of the opening inning. Sophomore Taylor Jones (1-0), making his first career start, gave up an RBI double to Jesse Hoover to give the Cardinals their lone lead of the day.
However GU got on the Cardinal starter Dylan Boss in the bottom of the frame. Boss walked junior Cory LeBrun to load the bases and then proceeded to hit Lamb to tie the game. Beau Bozett would then walk to bring in the go ahead run. Cabe Reiten flied out to right field to end the inning but GU took a 2-1 lead it would not relinquish.
Boss was pulled after the first in favor of Alex Shaffer. In total, Incarnate Word would use five pitchers in the game.
GU added a pair of insurance runs in the bottom of the fifth. Lamb singled through the right side with runners on the corners for a run. The next run came on a Reiten fielder's choice to the second baseman.
Zag starter Jones pitched into the sixth inning before being pulled for senior Karl Myers. The Cardinals threatened by getting two runners on with one out when Myers entered. Incarnate Word would load the bases with two outs but Myers struck out Jonathan Armijo to end the inning.
Myers was credited with the save after working 3.2 scoreless innings in relief.
The Bulldogs final run came in the bottom half of the sixth. LeBrun singled to left field bringing home Mitchell Gunsolus giving GU the 6-1 cushion.
Next for the Zags in the Irish Classic is a contest with tournament host University Notre Dame. The two will face Friday at 10:30 a.m. (PT) at Nelson Wolff Stadium.
Terp, what do you know about the team they beat?
in San Antonio, Texas originally founded by the Sisters of Charity.
that he was telling the truth.
names was just awful. When I first listened in I had no idea who was leading and what inning it was.
This young man would make Greg Heister seem like Vin Scully!
SAN ANTONIO, Texas – Irish Baseball Classic host University of Notre Dame got the best of the Gonzaga University baseball team 3-2 Friday, despite the dramatic ninth inning comeback by the Bulldogs at Nelson Wolff Stadium.
Trailing 3-0 entering the final frame, the Zags attempted a late two-out rally to shock the Irish.
On a full count, Caleb Wood singled to center to score Jeffrey Bohling (who reached on a walk) to keep the Gonzaga hopes alive. Mitchell Gunsolus followed with a single to left field to bring home Wood. However Notre Dame reliever Cristian Torres got Cory LeBrun to ground out to the shortstop to end the game.
The defeat moves the Bulldogs to 2-4 on the year. Notre Dame improves to 2-3.
Freshman right-handed pitcher Brandon Bailey (0-1) delivered another phenomenal performance to keep the Bulldogs in the game. Going the distance for Gonzaga, the Broomfield, Colo., native allowed three runs (two earned) on six hits while striking out five and walking four.
The Zags did have its chances in the game. The Bulldogs out-hit Notre Dame 10-6 but three Irish double plays stalled the Gonzaga offense. In total, Gonzaga would strand 11 on base.
GU had a great opportunity to score in its first at bat. Notre Dame's starter Robert Youngdahl (1-0) walked three Bulldogs to load the bases. However Youngdahl got freshman Nick Brooks to hit into an inning ending double play to shut down the GU threat.
The top of the Bulldogs lineup gave Youngdahl another stressful inning in the third. Much like the first inning, Brooks stepped up to the plate with one out and the bases loaded. Unfortunately, also like the first inning, Brooks hit into the inning ending double play on a 0-2 count.
Youngdahl's day ended in the top of the sixth inning after giving up a one out single to Payden Cawley Lamb.
The Gonzaga woes continued in the top of the seventh inning where GU left its ninth and 10th runners on base. With two outs, Irish reliever Ryan Smoyer gave up back-to-back base hits to Wood and Gunsolus. Notre Dame then went to its bullpen and brought in Michael Hearne who was able to get LeBrun to fly out to center field for the final out of the frame.
The Irish extended its lead to 3-0 after scoring a pair in the bottom of the eighth. The Irish had runners on the corners with two outs when Kyle Richardson singled to right field to drive in one. The other came home on a Joey Harris throwing error to first base.
The Irish Baseball Classic continues Saturday when Gonzaga faces WCC foe Santa Clara University in a 10:30 a.m. tilt.
Thanks Terp. Too lazy to look it up, was just wondering if they were even D-1?
In August 2012, UIW accepted an invitation to move up to Division I as a member of the Southland Conference. UIW entered the NCAA Division I Southland Conference on July 1, 2013. The football team is a Division I FCS independent in 2013, beginning conference play in 2014 due to schedule commitments. UIW will be fully eligible for Division I championships starting in the 2017-18 season. Prior to moving up to Division I, UIW was a member of Division II's Lone Star Conference.
SPOKANE, Wash. – Gonzaga University baseball had its nine-game winning streak against West Coast Conference foe Santa Clara University snapped Saturday, as the Zags fell 3-2 at Nelson Wolff Stadium in the Irish Baseball Classic.
Gonzaga drops to 2-5 overall while the Broncos improve to an even 4-4.
Santa Clara took the late lead by loading the bases in the bottom of the eighth inning off reliever Kenny Smith (0-2). The go ahead run scored on a Casey Munoz pinch-hit single to left field. Even with the bases jammed, Smith limited the damage in the inning and recorded the final three outs to leave three Broncos on base.
GU gave one last push in the top of the ninth by getting the tying run on second with one out. However Bronco reliever Reece Karalus closed the game on a ground out and a Caleb Wood fly out.
Reigning WCC Rawling Pitcher of the Week Andrew Sopko (1-0) made the start for GU and left with a no decision. The right-hander allowed two runs on eight hits and struck out four in six innings.
Santa Clara scored the first run of the game in the opening at bat. Greg Harisis led off with a double to left field and advanced to third on a Sopko balk. Harisis scored on a Czaplak groundout to shortstop Mitchell Gunsolus.
Gonzaga tied the game in the fourth inning. With two outs, Payden Cawley Lamb had an RBI single to left field to knot the game at one.
An inning later, GU took its only lead of the game. Brock Slavin (walked) and Joey Harris (error) reached to open the frame. Sam Brown grounded out to first to bring home Slavin for the 2-1 edge. The Zags would load the bases with two outs but SCU starter Steven Wilson escaped on a Cory LeBrun ground out.
Wood nearly drove in an insurance run in the top of the seventh. With Jeffrey Bohling on second with two outs, Wood singled to right field but unfortunately Bohling was thrown out at home by C.J. Jacobe.
Sopko left in the seventh inning for Smith after allowing a leadoff single. Two batters later, Harisis doubled to right field to bring in the tying run. Later in the inning Santa Clara loaded the bases with two outs but Smith stopped the bleeding by forcing Rory Graf-Brennen to ground out.
The Zags had another opportunity to take the lead in the eighth. With two outs and two on, Beau Bozett pinch hit for Slavin against SCU reliever Chris Heckert. A back-and-forth at bat went Heckert's way as Bozett grounded out to end the threat.
GU closes out the weekend Sunday. The Zags will face the winner of University of Notre Dame and University of the Incarnate Word game which will be played Saturday afternoon. The game with be played at 9:30 a.m. (PT).
NOTE: Even though Gonzaga was facing a fellow West Coast Conference school, this game will not count towards GU's conference record since the contest was part of the Irish Baseball Classic. The schools will meet for a three-game WCC series in Spokane in April.
SAN ANTONIO, Texas – Gonzaga University baseball dropped its third consecutive game Sunday as the Zags fell 11-8 to University of the Incarnate Word in the Irish Baseball Classic.
GU finishes the tournament 1-3 and sits at 2-6 overall.
The Bulldogs held a five run advantage, 8-3, heading into the sixth inning but Incarnate Word stormed back to take a three run lead.
The eight-run inning was manufactured with two outs. Bryce Shepherd and Mark Whitehead each connected for a two RBI base hit which chased Gonzaga starter Derek Callahan (0-2) from the game.
The troublesome inning continued for Zag reliever David Bigelow. The right-hander was touched for four runs (two charged to Callahan) on a hit batter and a bases clearing double to Slade Brown. The frustrating inning ended when Bigelow induced a fielder's choice groundout to third base.
Prior to the inning Callahan was in firm control. Unfortunately the lefty was responsible for nine earned runs on six hits in 5.2 innings.
GU had a nice start to the game as it was the first team to score.
Cardinal start Jacob Potts recorded the first two outs in the top of the first inning but then allowed three consecutive hits to Mitchell Gunsolus, Cory LeBrun and Payden Cawley Lamb. The RBI was a team-high sixth for Lamb.
Gonzaga extended its early lead to 5-0 in the top of the third. The first three runners reached for the Bulldogs followed by a LeBrun bases clearing double. Beau Bozett brought LeBrun home later in the frame with an RBI through the left side.
Incarnate Word pushed across its first runs of the game in the third on one swing of the bat. Jesse Hoover connected for a three-run homer cutting the Gonzaga lead 5-3.
The Zags appeared to add three insurance runs in the fifth inning. Nick Brooks, Sam Brown and Gunsolus all recorded an RBI. The 8-3 lead was short lived however as the Cardinals had its eight run rally an inning later.
Gonzaga out-hit the Cardinals 13-7 in the game. Gunsolus paced the club with four hits while Bozett, Brown and LeBrun each had two hits. Freshman Wyatt Mills made his second appearance of the year by reliving Bigelow for two outs in the eighth.
Gonzaga is back on the diamond Feb. 27 in Surprise, Ariz. The Bulldogs will play in the Spring Training Classic hosted by Arizona State University and open the weekend with Oklahoma State University Thursday at 3 p.m.


OG Kush is considered one of the ultimate Kush varieties and is famous all over the world because of its strong and complex effects and intense flavor. Many Hollywood celebrities, rappers, medicinal users and die-hard blowers have indicated that this is their favorite type when it comes to power. The meaning of 'OG' in the name is much discussed, but they never doubt the strength.
The true genetics are unknown. Some say OG Kush is a mix of ChemDawg with a Lemon Thai and Pakistani Kush. Others say it's just a special cutting of the ChemDawg is from the early nineties. Even on the meaning of the name OG is discussed; some argue that it means Original Gangster. The most people would agree that, because of its origin, means Ocean Grown.
Kush is a Hindu boy's name. It means `son of Hindu God`. Kush is a type of the indica variety. There are many forms like Bubba Kush and OG kush. Kush cannabis originates from plants from Afghanistan, Iran, Pakistan and the north side from India. The name refers to the Hindu Kush mountains.
OG Kush is known that they will stretch slightly during growth, but quickly fills up during flowering. Generally it is 90 to 160 cm high. The buds are large and thick; lime green clusters covered with a thick layer of resin. There are many good reasons why OG Kush has become so popular. Now available as a feminized varieties & quality of the Kera Classic line, so you can try out this amazing strain yourself. The effect is as strong and complex as the flavor. OG Kush grows eight weeks and the average yield is 65 grams per plant.
The effect of OG Kush is as strong physically and mentally. OG Kush is predominantly governed by Indica genes, but the ultimate thrill that you feel is absolutely the Sativa and is quickly followed by a body relaxing and numb sensation.


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← On Theresa May's departure as Prime Minister, 24 July 2019
Patricia Fowles – 10 December 1931- 28 July 2019 R.I.P. →
Correlation and Causation – why Independent schools are not to blame for the success of their pupils!
Posted on August 5, 2019 by jameswilding
Over recent months, there has been a growing stridency in the voice of the Labour party and its fellow travellers about the role of Independent schools in England's Education system. Using the #AbolishEton, the group, Labour Against Private Schools, hopes to persuade the party's conference in September to commit a Labour government to their integration into the state system, whilst at the same time stripping fee-paying schools of their 'privileges'. You can read more of that in this Guardian article of 9 July. The Guardian has been carrying quite a lot of anti-independent school copy on its pages for many years, but when independent think tank studies such as this one by the Sutton Trust continue to report that Britain's top jobs are still in the hands of a private school elite, it does cause us all to take a deeper look into quite what is going on in this 'education space' of ours. And of course, last week in comes Boris Johnson, the 20th Old Etonian to serve as our new Prime Minister, and 'Quod Erat Demonstrandum' Q.E.D. it must be true.
It's certainly true that Eton has been an utterly extraordinary institution for centuries, endowed as a King's College by Henry VII, attracting the sons of the mighty alongside poor scholars, and yet, within its walls, ensuring that all were treated with great equality, so that its alumni could then ensure that Eton would 'Esto perpetua', translating as 'May it last forever'. With 300 students a year graduating to the very best universities in the world, it should come as no surprise to anyone that its alumni are to be found in positions of influence. Johnson's cabinet does have 2 other Etonians (his brother Jo and Rees-Mogg Esq.) plus a total 64% of other ministers independently educated. Take a closer look at the England Cricket or Rugby sides, and it is apparent that independent schools more broadly have been developing talent disproportionately more successfully than one might expect of their apparent 7% hold on the country's population. The BBC summarised the Sutton report in this area well, the graphic below from their report:
My school at 59 years of age, with now circa 100 boys and girls graduating a year from GCSEs/A levels, tracks the success of its former pupils with interest but not forensically, though anecdotally we can certainly see they represent well on departure the qualities of ambition, collegiality and stickability that's needed later on in life, and their track records subsequently look very encouraging and magnificently diverse. It's interesting to note that the few of our best footballers that appeared good enough to make it in that sport have had more options than just football, with other sports and higher education seeming more alluring and open as routes. Swap sport for music, drama, the arts, and it's clear our best have gone on to thrive, build commercial careers, win glittering prizes and awards. Or indeed, stay resolutely academic and reach for University, Doctorates and beyond – CC alumni are there too. In short, the block chain works well – enter Independent Education, gather the academic, social and collaborative skills needed to get on in life, and guess what, you will.
Behind every child to be found in an independent school, and you find a family deeply interested in the school being the right place for their child and getting the best out of them. Throughout my professional career, I have seen successive governments (Labour and Conservative) shift the focus of the state sector from providing a full, broadly facilitated education to one that is only required (and therefore funded) to cover academic subjects in the classroom. As I look at our plans for a new campus to be considered by the RBWM planners at the end of this month, we are clearly not just seeking to cover a narrow academic core. Apart from a rather obvious centre of excellence for regional hockey, the buildings cover all the arts, mathematics, sciences, languages, business, computing and enterprise education we could hope for. Who wouldn't want their child to have such a set of opportunities? The master blueprint though that's been allowed has not provided any silver spoons or gold taps – but what it does do is declare unequivocally that 'all of the various skills and talents that a child might have' will be nourished here.
And therein lies the heart of the reason why ambitious parents might choose independent education for their children; namely to ensure they have the opportunity to test out their mettle and find their spark. And having chosen to make such an 'investment', continuing to hold their attention on the child so that the 'sparks' are captured and nourished into the flames of a future ambition. If this is the root of why children succeed, that is, the energy and commitment of their parents and wider family to that success, why don't the Sutton Trust and others just come out and say that? I'm not blaming the Sutton Trust or others for that matter for being 'lay journalists', indeed the founder of the Trust, Sir Peter Lampl actively espouses that the state should fund thousands of place in independent schools in order to "improve educational opportunities for young people from non-privileged backgrounds and increase social mobility." The truth is that it is government's place to make the core decisions on funding, and it hasn't joined up enough over the past 10 years to make this happen. And here perhaps is why…
Last month, Professor Christopher Ferguson* wrote an excellent article on Bad Data Analysis and Psychologies Replication crisis in Quillette, an aggregating website on ideas help human societies flourish and progress. This triggered a commentary on the same site by Professor April Bleske-Rechek, headlining this Crisis in Psychology, namely the willingness of this new science to sensentationalise weak effects and to bias publications in favour of sales of the ideas in question. She writes "That illness is the conflation of correlation with causation, and the latest research suggests that scientists, and not lay people and the media, are the underlying culprits.Last month, Professor Christopher Ferguson* wrote an excellent article on Bad Data Analysis and Psychologies Replication crisis in Quillette, an aggregating website on ideas help human societies flourish and progress. This triggered a commentary on the same site by Professor April Bleske-Rechek, headlining this Crisis in Psychology, She writes "I believe a related, but perhaps less-recognized, illness plagues psychology and related disciplines (including the health sciences, family studies, sociology, and education). That illness is the conflation of correlation with causation, and the latest research suggests that scientists, and not lay people and the media, are the underlying culprits.
This morning I was listening to Alan Johnson, former Home Secretary and minister in the Blair/Brown Labour government of the noughties. Johnson expressed so clearly that the difference in life expectancy of a boy born in 1950 between North Kensington (where he grew up) and South Kensington is 16 years today. That's got nothing to do with state or private education, and everything to do with the failure of national government to invest in a joined up way in health, education, welfare and social care. You may recall he was the Minister of State for Universities, and introduced the loans-for-degrees we now have. This has been an amazingly important way of increasing the number of disadvantaged students (on free school meals) from 10% (when student grants existed) to 27% today in 2019 (from 31:00 mins). Any English qualified national can apply to University and receive the funding to attend, with the 'tax' on their funding being the requirement to pay back in adult life from the additional earnings as they receive them. Alan Johnson was absolutely clear about what needs to happen if we are to see growing social equality in our country, which is for the Prime Minister to take this requirement for society to provide greater social mobility as the core mission of their premiership and cause the great offices of state to bend to the task. Theresa May expressed this so clearly in her opening speech on entering 10 Downing Street, and was thwarted by the confusion of Brexit.
There is a clear correlation that exists between opportunity and success that follows, and a clear model already in the UK that shows how opportunity can be extended, through the generous funding for all that is needed for education to work. Of course, you could just nationalise our independent schools, cut the funding to the bone and watch our excellence whither. Alternatively, wise government would introduce vouchers that entitle any to spend to acquire the education of their choice, a situation that works for higher education, and now needs to enter lower down too. Those vouchers would inevitably not cover the full cost of the education received, but would provide to the child concerned a funded place. As universities have had to seek additional revenue streams, so have our independent schools too, and this requirement would continue into the future. Where state schools are already good enough, and there are so many that are just that, parents would not need such a voucher. But since such schools cause house prices to be so much higher, entry into an alternative independent school would provide other opportunities for parents to consider.
I'll close with a 'nod' to the chairman of the Independent Schools Association, Matthew Adshead, HM of the Old Vicarage school, Derby, who appeared on the Radio 4 Today programme a couple of weeks ago alongside the founder of the @AbolishEton campaign, Holly Rigby, a state school teacher and coordinator of the campaign. Her stance was "There is no justification for the fact that young people's opportunity to flourish and fulfil their potential is still determined by the size of their parents' bank balance." Matthew's riposte was perfect, asking her to visit his school, and meet with the parents, the postman, the shopkeeper, the hardworking artisans choosing to spend their earnings on their children as they thought best. And therein lies the rub, our parents are everything in our schools, causing the success of their children's school lives and beyond; we may be architects, designers and such like of course of the opportunities needed, but we but bask in that reflected glory which is of amazing children doing really well. Holly, Jeremy and all, please don't blame us for the success of our schools, celebrate with us. Don't let your fury at a Johnson entering Downing Street blind you to the wisdom of another Johnson, one of your own party, who even today clearly is worth celebrating for the actions he caused when in government to improve social mobility.
* Professor Christopher Ferguson has a book coming out in January 2020, entitled How Madness shaped History. His tag line suggests an interesting read – "This lively investigation demonstrates that, when conditions are ripe, one unstable individual can create the best or worst moments of a generation or even a century."
With Trump in the White House and Johnson in 10 Downing Street, who possibly has he in mind?
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Northeast Arkansas Career and Technical Center » News » Archived » Students Earn State Championships Medals
Little Rock, Hot Springs - Results are in and celebrations continue at NEA Career & Technical Center in Jonesboro.
While Health Science Technology students returned with numerous awards from state HOSA competition in Hot Springs, students in all other NEACTC programs of study continued their preparations for competing at Pro Start and Skills USA. And needless to say, it was quite a successful year as students from seven programs of study walked away with the hardware--literally.
Students earned a total of 29 state medals. Nine students won gold, seven won silver, and an additional thirteen walked away with bronze awards at state. After tallying the results, NEACTC Director Eddie Crain stated, "This has been a phenomenal year for student achievement. I am very proud of our students but none of this would be possible without the dedication of our instructional staff guiding and teaching those students."
Crain noted that it is critical that Arkansas Career Ed officials ensure competitions are held in all content areas so that secondary technical center students have a venue to showcase their skills.
"This year we have a new program of study in Industrial Maintenance created to meet the demand of NEA industry. Although there is national competition, none was held at the state level in critical areas. Students from our IT program had competed at Burdette in early February and after just four months of this course of study, students won 2nd and 3rd in regional mechatronics competition. Therefore, we have reason to believe those students could have been successful competing at the state level--IF there had been competition held in mechatronics. Nonetheless, it was an amazing year for our students and I could not be more proud of everyone involved," Crain stated.
At the Burdette and Blytheville regional competition February 2nd, an additional seven NEACTC students earned competition medals. Three NEACTC programs of study competed with each program of study earning medals. An NEACTC student earned gold in Early Childhood (hands-on), the HST team won silver in the Medical Professions Quiz Bowl, and two IT students earned medals, with one each in silver and bronze.
At Little Rock, the four-member team representing NEACTC Hospitality and Culinary Arts each earned bronze medals and a total of $48,000 in scholarship offers for their efforts.
A hearty CONGRATULATIONS to NEACTC staff and students for your 2018 efforts!
To learn more about individual winners, competition and misc. photos, visit the official NEACTC Twitter site @NEACTC1.


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GOP presidential nominee Mitt Romney went after President Barack Obama for the White House's weak response to the attacks on the U.S. Embassy in Cairo. and the U.S. consulate in Benghazi.
"I'm outraged by the attacks on American diplomatic missions in Libya and Egypt and by the death of an American consulate worker in Benghazi," said Mr. Romney in a statement.
"It's disgraceful that the Obama Administration's first response was not to condemn attacks on our diplomatic missions, but to sympathize with those who waged the attacks," he said.
The U.S. embassy in Cairo put out a statement early Tuesday that apologized for an anti-Muslim film being circulated by an Israeli-American real estate developer.
"The Embassy of the United States in Cairo condemns the continuing efforts by misguided individuals to hurt the religious feelings of Muslims – as we condemn efforts to offend believers of all religions," the embassy said in a statement published online.
Embassy Cairo also tweeted out that Islam was a "wonderful religion" while engaging in a debate with an unknown individual on Twitter on Tuesday.


Banania is a chocolate powder formula that naturally combines the delicious taste of good cocoa with the benefits of crispy cereal grains, plus a touch of honey and banana to give it a gourmet flair and that unique taste!
Ingrédients : Sugar, non-fat cocoa solids (19%), cereals (WHEAT flour, BARLEY flour, malted WHEAT flour) : 12%, banana flakes (0.25%), honey, vanilla flavor, salt.
Unlike the formulas traditionally used to make chocolate powder, Banania stands out for its 12% cereal content (wheat, barley, and malted wheat). This unique feature makes for an inimitable crispy taste that also allows the refined sugars to be replaced with complex carbohydrates, providing energy that's progressively usable throughout the day.


Everyone knows how to make a breaded and fried pork chop, this is nothing new to me, I make pork chops occasionally, the interesting thing about this recipe is the sauce/glaze that the fried pork chop is coated in after cooking. I found the idea on Pinterest and adjusted the glaze to suit my own tastes.
Heat a skillet on the stove with about a half inch of olive oil covering the bottom. You will want to regulate the temperature here so that the chops do not brown too quickly on the outside before they are fully cooked on the inside. I find just below medium heat works well. Fry them gently for about 4 or 5 minutes per side until golden brown and crispy. I placed mine in a warm oven on a rack (200 degrees) after frying to keep them warm and crispy.
When you are finished cooking all the chops, dip the cooked chops into the Honey Soy Sauce (recipe below).
Simmer together for 5-10 minutes, watching carefully as it simmers because it can foam up over the pot and create a huge mess.
The sauce will thicken as it cools, so make sure that you are using warm sauce to coat easily.
Serve with your favorite sides, it is sweet, salty and a bit spicy, but mostly, it is delicious!


Specialist and unique transgenic models demand a large up-front investment of time and resources. Even once they are established, the costs continue to mount as day-to-day upkeep of an established cohort requires costly facility space and animal care technicians. On-going monitoring for genotype and genetic drift will be necessary.
Moreover, in today's complex research landscape, animal models are not just a static research tool – they are a potential variable in your research. This variability becomes a significant risk to research outcomes, budgets and timelines. Whether working with immunocompromised, transgenic or immunodeficient models or even microbiota research projects, cryopreservation and outsourced contract breeding allows you to maintain a strain at a specific genetic state in time and, when needed, you can refresh the colony back to that genetic moment.
As well as safeguarding your research models – and the integrity of your research – cryopreservation can reduce the space and resources required for animal care, and allow your lab to focus instead on actively-used colonies. This eliminates potential waste from continued breeding when a study is on hold. Licensing bodies look favorably on this 'welfare mindset,' as it helps demonstrate the three R's—replacement, reduction and refinement, and responsible model use.
Cryopreservation is also helpful when working with countries where sending live models is cumbersome, lengthy and paperwork-intensive, such as Australia and Japan. Using cryopreserved material to transport a line allows you to bypass this lag time.
Cryopreservation should take place when the proper background has been established for the line, and before the genetic background has a chance to shift. Alternately, you could freeze as soon as the 'founders' or first transgenic animals are produced. Ideally, cryopreservation should also then take place at key stages of breeding multiple transgenic lines, in order to capture an expensive, complex genetic status.
Once you've decided the timeline for cryopreservation, the next decision is what technique to use: sperm or embryo? Sperm cryopreservation is the most cost effective, but only provides one copy of the genome. Typically, a minimum of two males can provide enough material to freeze a line. Embryo cryopreservation, on the other hand, generally requires twenty females and ten breeder males. While the cost of embryo cryopreservation is higher, it ensures an exact copy of the genotype. Further, depending on whether the model is bred as a heterozygote or homozygote, a high number of embryos are captured – one hundred fifty to three hundred!
With all the effort that goes into developing and maintaining a line, it's essential to ensure that cryopreservation is undertaken with the same dedication to quality control. Make sure your provider can validate and demonstrate (both before and after cryopreservation) that the material is properly preserved and can successfully reproduce live animals. Ask potential providers how they perform quality control. Many providers will offer dual storage of frozen materials, which will guarantee that at least one set remains viable in case of facility failure.
Now that you've frozen your vulnerable strain, when is the best time to revitalize it? Planning ahead is imperative. It typically takes seven to ten weeks to reconstitute a cryopreserved line: one week to set up the process, three weeks for pregnancy gestation and a minimum of three weeks for monitoring. This is quicker than the time it typically takes to recover a live, non-producing line, which can take up to 15 weeks.


Caroline Fraser is the editor of the Library of America edition of Laura Ingalls Wilder's Little House books and the author of three works of nonfiction, including 2017's Prairie Fires: The American Dreams of Laura Ingalls Wilder. One of the New York Times' Ten Best Books of the Year, Prairie Fires won the 2018 Pulitzer Prize for Biography and the National Book Critics Circle Award for Biography. Fraser holds a Ph.D. in English and American literature from Harvard University.


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Q: Adding and removing fields with conditions on click using JavaScript JavaScript rookie here..
I am trying to build a form where I have a certain field that I want people to be able to add more of up to 4 fields. I think I managed to do that part (although probably very clunky code) but I dont know how to make the remove function work. The challenge is that when somebody clicks on the minus sign, I want to delete the last field created and that last field only.
Thanks for your help!
HTML:
<form action="">

        <input type="text" name="Name" id="" placeholder="Full Legal Name">

Broker Principal(s)

        <input type="text" name="Name" id="" placeholder="Broker Principal">

</form>

JS:
var plus = document.getElementById("add");
var minus = document.querySelector(".minus");
var array = [1,2,3,4,5];
var counter = 2;
var field = document.getElementById("addField");

plus.addEventListener("click", function(){
    if(counter !== 0){
        field.insertAdjacentHTML("beforeend", '
' + '<input type="text" name="Broker Principal ' + counter + '" id="" placeholder="Broker Principal ' + counter + '">' + "
");
        minus.classList.remove("hidden");
        counter = (counter + 1) % array.length;
    }
});

CSS:
body {
font-size: 17px;
}

input {
    padding: 10px 20px;
    font-size: 17px;
}

.form-element {
    display: block;
    margin: 8px 0;
}

i {
    color: #FDB813;
    transition: all 0.3s;
    cursor: pointer;
}

i:hover {
   color: #FEC849;
}

@keyframes fadeOutIn {
  0% {opacity: 0;}
  50% {opacity: 0.4;}
  100% {opacity: 1;}
}

.fadeOutIn {
  animation-name: fadeOutIn;
  animation-duration: 400ms;
 }

 .hidden {
     display: none;
 }

A: You could do something like this
minus.addEventListener("click", function(){
    var form = document.getElementById('addField');
    form.removeChild(form.childNodes[form.childNodes.length-1]);
}

redpajama_set_name: RedPajamaStackExchange


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Evgenii Dainov
Evgenii Dainov (I958, Plovdiv) is a Bulgarian academic, author, and political commentator. He teaches Political Science at the New Bulgarian University in Sofia and publishes comments in both international and Bulgarian media.
Dainov is a founding member of the Green Movement political party in Bulgaria and has been a civic and environmental activist since the second half of the 1980s.
The Bulgarian version of his latest book Spirit of the Age: How Did We Get from Love Me Do to Donald Trump is due to be published in October 2020, while the English translation is expected in spring 2021.
He graduated in Modern History at Oxford (Corpus Christi College) where he later taught, as well. Daniov followed specialisation courses in Moscow, Paris, and Vienna. He holds a Honorary Doctor Degree from the Economic Institute Plekhanov (Tashkent, Uzbekistan).
Dainov plays guitar and composes songs for rock bands: the third album of his current band Magistri is expected by the end of 2020.


43 Summer Camps in for "Upper Black Eddy, PA"
Half and anf full day rock climbing camp. Indoor and outdoor options.
Briarwood Day Camp is one of the leading day camps in Greater Philadelphia. Located on 30 wooded acres in Bucks County, Briarwood campers go home every day happy, healthy, tired and rarin' for more.
Sharing Christ with people who are disabled. Challenging boys, men and their families with the life-changing message of Jesus Christ!
Israel-oriented traditional Jewish camp, simulates Kibbutz life, teaches community building & sharing, sports, swimming, conversational Hebrew, Kosher.
REALgirl® is a self-esteem based empowerment program dedicated to guiding and inspiring girls to discover their 'REAL' (authentic) selves.