text:
\section{Analysis of Prior Approaches}
\label{sec:methods}

A number of
prior approaches
have considered uncertainty in the values of propositions, though mainly for tabular MDPs. Unfortunately, their effectiveness remains unclear when applied to complex deep RL settings where the number of states is infinite, high-level events are challenging to perfectly model, or where the environment is only partially observable.

One type of approach models the true labelling function $\mathcal{L}$ with an approximate labelling function, $\hat{\mathcal{L}}: S\times A\times S \times \mathcal{AP} \rightarrow [0,1]$ in URM-MDPs, and $\hat{\mathcal{L}}: H\times A\times \Omega \times \mathcal{AP} \rightarrow [0,1]$ in URM-POMDPs,
 that assigns probabilities to each proposition. Such an approximate labelling function might be obtained from external sensors, handcrafted heuristics, offline data, or be trained online together with the policy. Then, the predicted propositions are used to generate an estimate (or a belief) of the current RM state using one of the following methods. One appeal of this technique is that the approximate labelling functions can in principle be transferred to new environments and RMs, so long as the high-level propositions remain the same.

\textbf{\ttt{Thresholding:}} {Inspired by, e.g., \cite{da2019active, ghasemi2020task}, and \cite{tuli2022learning},
this method discretizes every proposition $p_i$ at each timestep $t$ to its most likely value under $\hat{\mathcal{L}}$. In URM-MDPs, $\hat{p}_{i,t} = \mathbbm{1}[\hat{\mathcal{L}}(s_t,a_t,s_{t+1}, p_i) \ge 0.5]$ and the $\hat{p}_{i,t}$ values are then used to produce a discrete prediction of an RM state $\hat{u}_t$. The learned policy takes the form $\pi(a_t | s_t, \hat{u}_t)$. In URM-POMDPs, we simply change the approximate labelling function to the correct form $\hat{\mathcal{L}}: H\times A\times \Omega \times \mathcal{AP} \rightarrow [0,1]$ and change the policy to condition on histories $h_t$ rather than states $s_t$.

\textbf{\ttt{Independent Belief Updating:}} Inspired by, e.g., \cite{ding2011ltl} and \cite{verginis2022joint}, this approach maintains a probabilistic belief $\tilde{u}_t$ over the current RM state under the simplifying assumption that predictions of propositions $p_{i,t}$ are independent of one another and across all timesteps. In URM-MDPs,
$\tilde{u}_t$ is updated
each timestep for all $u \in U$, given an experience $(s_t, a_t, s_{t+1})$, via
\[
\tilde{u}_{t+1}(u) = \sum_{\sigma_t \in 2^{\mathcal{AP}}, u_t \in U}{\pr(\sigma_t | s_t, a_t, s_{t+1})\tilde{u}_t(u_t) \mathbbm{1}[\delta_u(u_t, \sigma_t) = u]} \]
where $\pr(\sigma_t | s_t, a_t, s_{t+1})$ is the probability of a particular propositional assignment $\sigma_t$ under $\hat{\mathcal{L}}$. The learned policy then takes the form $\pi(a_t | s_t, \tilde{u}_t)$. In URM-POMDPs, we change $\hat{\mathcal{L}}$ to the correct form and change the policy to condition on histories $h_t$ rather than states $s_t$.

\textbf{\ttt{Recurrent Policy:}} Following \cite{kuo2020encoding}, we also consider a third approach that directly solves the URM-MDP or URM-POMDP as a general partially observable RL task
by learning
a recurrent policy of the form $\pi(a_t | s_0, a_0, ..., s_{t-1}, a_{t-1}, s_t)$ in URM-MDPs and $\pi(a_t | o_0, a_0, ..., o_{t-1}, a_{t-1}, o_t)$ in URM-POMDPs. Notice that the policy does not condition on the RM state (or an estimate of it); the non-Markovian task structure is instead handled by conditioning on the entire history. Thus, propositional values (either ground-truth, or estimated) are not required for this approach.

\subsection{Pitfalls in URM-MDPs}
\label{sec:remarks-urm-mdp}
In URM-MDPs, an approximate labelling function $\hat{\mathcal{L}}: S \times A\times S\times  \mathcal{AP} \rightarrow [0,1]$ can in principle perfectly model the ground-truth labelling function $\mathcal{L}$. In this ideal case, both \ttt{Thresholding} and \ttt{Independent Belief Updating} correctly estimate the true RM state, inheriting any optimality guarantees of the RL algorithm used to train the policy \citep{icarte2022reward}.

\input{figs/po_envs}

Unfortunately, perfectly modelling the labelling function can be impractical in complex, real-world settings.
\ttt{Thresholding} is resistant to small errors in $\hat{\mathcal{L}}$, but only estimates a single, discrete RM state and cannot represent the uncertainty in its prediction.
\ttt{Independent Belief Updating} aims to address this by estimating a belief over RM states, but the independence assumption often fails to hold
for noisy predictions under $\hat{\mathcal{L}}$. In the \emph{Mining} example, repeatedly digging in a square that is erroneously believed to contain gold will increase the perceived probability of having gold under \ttt{Independent Belief Updating}. However, digging more than once in any one square is pointless since either all digs will produce gold, or none will.

\ttt{Recurrent Policy} treats URM-MDPs as general POMDPs and avoids approximating the labelling function altogether. While it retains any convergence guarantees afforded by partially observable RL algorithms, history-based policies are notoriously hard and sample-inefficient to train in practice.

\subsection{Pitfalls in URM-POMDPs}
\label{sec:remarks-urm-pomdp}

Significant issues arise with \ttt{Thresholding} and \ttt{Independent Belief Updating} when the underlying environment is partially observable. First, even the Bayes-optimal approximate labelling function $\hat{\mathcal{L}^*}(h_t, a_t, o_t, p_i)$ is not necessarily identical to the ground-truth labelling function $\mathcal{L}$, since the propositions depend on unobservable states $s_t$. Second, the current RM state $u_t$ generally cannot be determined with certainty given the history $h_t$ due to the previous remark. Thus, \ttt{Thresholding} may predict an incorrect RM state, even with this ideal approximate labelling function $\hat{\mathcal{L}^*}$.

The \emph{Traffic Light} example in Figure~\ref{fig:po_envs} highlights how a policy might abuse this, leading to unsafe behaviour. The agent must safely drive through an intersection with a traffic light, but cannot observe the light colour when traversing the intersection \emph{in reverse}. If the light tends to be green more often than red, \ttt{Thresholding} would predict that the agent did \emph{not} pass a red light. Hence, the agent would be incentivized to drive backwards through the intersection while ignoring the light colour, rather than waiting for a green light.

\ttt{Independent Belief Updating} may similarly fail to model a correct belief over RM states, even with the ideal $\hat{\mathcal{L}^*}$. We demonstrate this in the \emph{Kitchen} example in Figure~\ref{fig:po_envs}, where a cleaning agent cannot initially observe which chores require its attention from outside the kitchen. The Bayes-optimal $\hat{\mathcal{L}^*}$ assigns $1/3$ probability that each chore is done on each timestep while outside the kitchen. If the agent wanders outside the kitchen for $t$ timesteps, \ttt{Independent Belief Updating} would predict that the dishes were washed at some point with probability $1 - (2/3)^t$. The correct probability is $1/3$, since the propositions are linked over time -- if the dishes are unwashed now, they will remain unwashed on the next step unless the agent washes them. \ttt{Independent Belief Updating} ignores this dependence and eventually predicts that all chores are done with probability close to 1, despite the agent never entering the kitchen. Unfortunately, modelling the correct temporal dependencies between propositions is hard -- in general, one may need to model the full joint distribution over all propositions up to time $t$, i.e. $\{ p_{i, t'}: 1 \le i \le |\mathcal{AP}|, 0 \le t' \le t\}$, given the history $h_t$.

Finally, we note that \ttt{Recurrent Policy} does not significantly distinguish between URM-POMDPs and URM-MDPs; a history-based policy is learned in each case. Thus, our remarks from the URM-MDP setting carry over to URM-POMDPs as well.

\section{Proposed Approach}
\label{sec:approach}
We propose a new approach, \emph{Reward Machine State Modelling} (\textbf{\ttt{RMSM}}) to address the shortcomings of prior approaches in URM-(PO)MDPs. Our key observation is
that the utility of modelling the labelling function is to accurately predict the RM state.
Thus, we propose to directly learn the belief over RM states, given the history, using a recurrent neural network (RNN) $g_\phi$ trained via supervised learning. The policy $\pi_\theta$ then conditions on this predicted belief in place of the ground-truth RM state.

We describe \ttt{RMSM} in detail for URM-MDPs in Algorithm~\ref{algo:rmsm}. In this setting, the network inputs are $g_\phi(u_t | s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t)$ for the RM belief RNN and $\pi_\theta(a_t | s_t, \tilde{u}_t)$ for the policy, where $\tilde{u}_t = g_\phi(\cdot | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)$ is the predicted belief over RM states. Note that $\tilde{u}_t$ can be compactly represented with a vector of $|U|$ probabilities. In URM-POMDPs, the policy $\pi_\theta$ instead conditions on $(h_t, \tilde{u}_t)$, and the RM belief $g_\phi$ conditions on the observation-action history.
\ttt{RMSM} then concurrently optimizes two independent objectives: prediction of a belief over RM states by minimizing a negative-log-likelihood loss $L_\phi$ and maximization of the policy's expected return $J_\theta$.

\input{figs/algo}

\begin{subsection}{Theoretical Advantages}
\ttt{RMSM} offers a number of intuitive benefits over prior approaches. First, when the objective $\mathcal{L}_\phi$ is minimized with respect to $\phi$, $g_\phi$ returns the Bayes-optimal belief over RM states given the history $\pr(u_t | s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t)$ for histories with positive probability under $\pi_\theta$. In contrast, recall that \ttt{Thresholding} and \ttt{Independent Belief Updating} may fail to predict the correct RM state belief in URM-POMDPs, even with the Bayes-optimal approximate labelling function $\hat{\mathcal{L^*}}$. Theorem~\ref{theorem:rmsm} in the Appendix further adds that under some assumptions, when both \ttt{RMSM} objectives are simultaneously optimized, the resultant policy is optimal in the URM-(PO)MDP.

\ttt{Recurrent Policy}, like \ttt{RMSM}, also optimizes an objective aligned with solving the URM-(PO)MDP. However, \ttt{RMSM} exploits the task structure to reduce the complexity of the RL problem, while \ttt{Recurrent Policy} treats the problem as a general POMDP. This is evident in the URM-MDP case, where \ttt{Recurrent Policy} trains a policy conditioned on the entire state-action history, while the \ttt{RMSM} policy only conditions on the current state $s_t$ and a compact RM state belief representation. In URM-POMDPs, both \ttt{RMSM} and \ttt{Recurrent Policy} must train policies conditioned on entire histories, but nonetheless, exposing the predicted RM belief to the policy may facilitate learning.

\end{subsection}

\section{Additional Definitions}

\section{Experimental Details}

\begin{subsection}{Toy Experiments}

\end{subsection}
In the toy \emph{Mining} experiments, all baselines were trained using tabular Q-learning. \ttt{Independent Belief Updating} and \ttt{Belief Updating+} also used a linear approximation to condition on continuous beliefs over RM states, where the probability of each RM state was a feature. All methods were trained for 1 million frames using learning rate $0.01$, discount factor $\gamma = 0.97$, and random-action probability $\epsilon = 0.2$.

\begin{subsection}{Deep RL Experiments}

\begin{figure}[b]
    \centering
    \includegraphics[align=c,width=0.44\textwidth]{figs/traffic.png}
    \qquad
    \includegraphics[align=c,width=0.36\textwidth]{figs/kitchen.png}

    \caption{The \emph{Traffic Light} (left) and \emph{Kitchen} (right) tasks implemented in MiniGrid.}
    \label{fig:minigrid}
\end{figure}

\textbf{Task Descriptions:} \hspace{1mm} We encode the \emph{Traffic Light} and \emph{Kitchen}  tasks as MiniGrid environments, as shown in Figure~\ref{fig:minigrid}. In the \emph{Traffic Light} domain, the goal is to collect a package at the end of the road (represented by a blue square), and then return home (represented by the green square) without crossing a red light. The light colour stays green for a random duration, becomes yellow for one timestep, and then stays red for a random duration before returning to green. The agent can only observe squares ahead of itself, so the only safe way to cross the intersection is to check that the light is green before proceeding (at worst, the light becomes yellow while in the intersection, which is considered safe).

We introduce propositions to determine if the agent is at the package, if the agent is at home, and if the agent is in the intersection during a red light. The RM state captures two pieces of information: whether the agent has crossed a red light at any time, and whether the agent has picked up the package. Reaching the package for the first time always yields a reward of 1. Returning home with the package ends the episode and yields another reward of 1. However, if the agent has crossed a red light, it instead receives a traffic ticket in the mail (and a -1 reward).

In the \emph{Kitchen} domain, the agent must enter the kitchen, perform a set of chores (represented by the coloured squares in the right room, which turn gray when finished) by visiting them, before returning to the charging port at the top left. At the start, some chores may not need the agent's attention (e.g., if there are no dirty dishes) and that dish is considered done from the start. This occurs with a 1/3 probability for each chore, but the agent initially cannot observe which chores are done while outside the kitchen.

Propositions for each chore determine on each timestep whether that chore is currently considered done, and an additional proposition determines if the agent is at the charging port. The RM for this task captures the subset of chores completed, resulting in $9$ possible RM states (including an additional terminal state for returning to the charging port). Returning to the charging port ends the episode, giving a reward of 1 if all chores are complete and 0 otherwise. We also introduce an energy cost of -0.05 for opening the kitchen door and performing each chore (including if it's already done, e.g. if the agent rewashes clean dishes) so that the agent must make careful decisions.

\medskip
\textbf{Policy Architectures:} \hspace{1mm} \ttt{Perfect RM}, \ttt{Independent Belief Updating}, \ttt{Thresholding}, and \ttt{RMSM} each learned a policy conditioned on the current observation $o_t$ and a belief estimate of the RM state $\tilde{u}_t$ (or the ground-truth RM state, in the case of \ttt{Perfect RM}). We chose to condition policies on $o_t$ rather than the full history $o_0, a_0, \ldots, o_{t-1}, a_{t-1}, o_t$ to ensure that policies depended on the estimate $\tilde{u}_t$ to capture any relevant information from previous states.

Each policy consisted of the following components. Observations $o_t$ were encoded by a 16-channel convolutional layer, a max pooling layer, a 32-channel convolutional layer, and a 64-channel convolutional layer, in that order, each with kernel size $2 \times 2$ and stride $1$. Encoded observations and the belief over RM states $\tilde{u}_t$ were passed into an actor head with 3 hidden layers of $64$ units and ReLU activations, and a critic head with 2 hidden layers of 64 units and tanh activations.

\ttt{Recurrent PPO} used a similar architecture, except the history of observations were passed through an LSTM with hidden size 64.

\textbf{RM State Belief Prediction Architectures:} \hspace{1mm} \ttt{Independent Belief Updating} and \ttt{Thresholding} each learned an approximation of the labelling function $\hat{\mathcal{L}}$ by predicting $|\mathcal{AP}|$ logits (representing the probabilities of each binary proposition) conditioned on the history of observations. Observations were encoded by a similar architecture as in the policy, except the final output channel was 16. The sequence of observation encodings were passed into an LSTM with hidden size 16. Final predictions were decoded from the LSTM embedding using a single hidden layer of size 16. The predicted probabilities of propositions were used to derive estimates or beliefs over RM states, as outlined in Section~\ref{sec:methods}.

\ttt{RMSM} used the same architecture as the approximate labelling function above, except the predicted outputs were $|U|$ logits, representing a Categorical distribution over $|U|$ reward machine states.

\textbf{Hyperparameters:} \hspace{1mm} All policies were trained using PPO (\cite{schulman2017proximal}) for a total of 25 million frames in \emph{Traffic Light} and 10 million frames in \emph{Kitchen}. Hyperparameters are reported in Table~\ref{table:hyperparams}. For \ttt{Recurrent PPO}, the number of LSTM backpropagation steps was 4.

\input{figs/hyperparams}

\textbf{Handcrafted RM State Belief:} \hspace{1mm} In Section~\ref{sec:minigrid_exps}, we compared the RM state beliefs of \ttt{RMSM}, \ttt{Independent Belief Updating}, and \ttt{Thresholding} against a handcrafted approximation of the true RM state belief. Note that the ground-truth RM state belief can be difficult to determine exactly.

Our approximation in \emph{Traffic Light} works as follows. Propositions for collecting the package and returning home can always be determined with certainty. When crossing the intersection, we sometimes know the light colour with certainty (e.g. if the agent observed the light was green on the previous timestep, it cannot be red this timestep). We consider all other crossings of the intersection "dangerous", where the light colour is uncertain. We approximate all "dangerous" crossings to have a $0.36$ probability of occurring during a red light, the steady-state probability of the light being red after sufficient time, absent any other knowledge. Using this model of the propositions, we determine an approximate belief of the current RM state given a history.

For \emph{Kitchen}, the agent has no information regarding whether each chore is initially complete while outside the kitchen. The belief over RM states during this period is easily determined using the known prior probabilities of each chore being complete. Once the agent enters the kitchen, we assume the RM state is known with certainty. Note that while this is often the case, the agent may sometimes enter the kitchen without looking at the state of all chores.
We again use this model of the propositions to derive an approximate belief of the current RM state given a history.

\begin{figure}[tb]
    \centering
    \begin{tikzpicture}
    \large
    \draw (-4.5,0) node[rotate=90] {Total variation distance};
    \node at (0, 0){\includegraphics[align=c,width=0.6\textwidth]{figs/bars.pdf}};
    \end{tikzpicture}

    \caption{The accuracy of RM state beliefs learned by \ttt{RMSM}, \ttt{Thresholding}, and \ttt{Independent Belief Updating} compared against a handcrafted approximation of the ground-truth RM state belief. Beliefs are conditioned on a history generated by a random policy. We report the Total Variation Distance between the predicted and (approximate) ground-truth beliefs, averaged over 8 seeds, 5 episodes per seed, and all possible histories in that episode. Error bars report standard error.}
    \label{fig:bars}
\end{figure}

\end{subsection}

\section{Additional Definitions, Theorems, and Proofs}

\begin{definition}[\emph{Cross Product Belief MDP}]
\label{def:cross_product_belief_mdp}
Given a URM-MDP $\mathcal{K}$ associated with RM-MDP \revisit{$\langle S, T, A, P, \gamma, \mu, U, u_0, F, \mathcal{AP}, \delta_t, \delta_r, \mathcal{L} \rangle$}, we define a cross product belief MDP as an MDP $\mathcal{K}_U$ with state space $S' = S \times \tilde{U}$ (where $\tilde{U}$ are the set of beliefs over $U$, i.e. $|U|$-dimensional probability vectors), action space $A' = A$, and discount factor $\gamma'=\gamma$.

Now we define the transition probabilities, initial state distribution, and reward function for the cross product belief MDP. To simplify notation, define $b_u: (S \times A)^* \times S \rightarrow \tilde{U}$, $b_u(s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t) = \pr(\cdot | s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t)$ to be the Bayesian belief of the unknown RM state $u_t$ given the state-action history.

Then, the transition probabilities are $P'(s_{t+1}, \tilde{u}_{t+1} | s_t, \tilde{u}_t, a_t) = P(s_{t+1} | s_t, a_t) \cdot \mathbb{I}[\tilde{u}_{t+1} = b_u(s_0, a_0, \ldots, s_t, a_t, s_{t+1})]$, the initial state distribution is $\mu'(s_0, \tilde{u}_0) = \mu(s_0) \mathbb{I}[\tilde{u}_0 = b_u(s_0)]$, and the (stochastic) reward function is given by $R'(r_t | s_t, \tilde{u}_t, a_t, s_{t+1}, \tilde{u}_{t+1}) = \sum_{u_t \in U} {p(u_t | \tilde{u}_t) \delta_r(u_t, \mathcal{L}(s_t, a_t, s_{t+1}))}$.

\end{definition}

\bigskip
\begin{theorem}[Optimal Policy in a URM-MDP]
\label{theorem:rm_belief}
Given a URM-MDP $\mathcal{K}$ associated with RM-MDP \revisit{$\langle S, T, A, P, \gamma, \mu, U, u_0, F, \mathcal{AP}, \delta_t, \delta_r, \mathcal{L} \rangle$}, there exists an optimal policy of the form $\pi(a | s, \tilde{u})$, where $a \in A, s \in S$ and $\tilde{u}$ is the belief distribution over reward machines states $U$ given the history of states and actions, i.e. $\tilde{u}(u) = \pr(u_t = u | s_0,a_0, \ldots, s_{t-1}, a_{t-1}, s_t)$.

\medskip
\emph{Proof.} It is well known that any POMDP can be formulated as an equivalent \emph{belief MDP} whose states are beliefs over the original states of the POMDP (\cite{aastrom1965optimal}). In the case of a URM-MDP $\mathcal{K}$, the corresponding belief MDP $\mathcal{K}_{S \times U}$ (whose states are beliefs over $S \times U$) is equivalent to the cross product belief MDP $K_{U}$, in the following sense. A state at time $t$ in the belief MDP $K_{S \times U}$ is a distribution $b_t$ over $S \times U$. However, in a URM-MDP, $s_t \in S$ is known and observable at time $t$, thus the distribution $b_t$ must only assign positive probability to states $(s,u) \in S \times U$ where $s = s_t$. $b_t$ can equivalently be represented as $(s_t, \tilde{u})$, where $\tilde{u}$ is the belief distribution over $U$. The transitions in the cross product MDP $K_{U}$ precisely mimic those in the belief MDP $K_{S \times U}$, bar this change in representation.

Hence, solving a URM-MDP is equivalent to solving the corresponding cross product belief MDP, which has an optimal solution of the form $\pi^*(a_t | s_t, \tilde{u}_t)$, where $\tilde{u}_t$ is the Bayesian belief over $u_t$, given $s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s$.
\qed
\end{theorem}

\bigskip
\begin{definition}[\emph{Uncertain-Proposition Reward Machine POMDP} \textbf{(URM-POMDP)}]
\label{urmpomdp}
Given a POMDP (without reward function) $\mathcal{M} = \langle {S},\Omega, {T},{A},{P}, {O}, \gamma, \mu \rangle$, a finite set of atomic propositions $\mathcal{AP}$, a (ground-truth) labelling function $\mathcal{L}: S\times A \times S \rightarrow 2^{\mathcal{AP}}$, and a reward machine $\mathcal{R} = \langle U, u_0, F, \delta_u, \delta_r \rangle$, a {URM-POMDP} is a POMDP $\mathcal{K} = \langle S_\mathcal{K}, \Omega_\mathcal{K}, T_\mathcal{K}, A_\mathcal{K}, P_\mathcal{K}, O_\mathcal{K}, R_\mathcal{K}, \gamma_\mathcal{K}, \mu_\mathcal{K} \rangle $ with state space $S_\mathcal{K} = S \times U$, observation space $\Omega_\mathcal{K} = \Omega$, terminal states $T_\mathcal{K} = (T\times U)\cup (S\times F)$, action space $A_\mathcal{K} = A$, transition probabilities $P_\mathcal{K}((s_{t+1}, u_{t+1}) | (s_t,u_t),a_t) = P(s_{t+1}|s_t,a_t) \cdot \mathbbm{1}[\delta_u(u_t, \mathcal{L}(s_t, a_t, s_{t+1})) = u_{t+1}]$, observation probabilities $O_\mathcal{K}(o_t|(s_t,u_t), a_t) = O(o_t|s_t,a_t)$, reward function $R_\mathcal{K}((s_t,u_t),a_t,(s_{t+1},u_{t+1})) = \delta_r(u_t, \mathcal{L}(s_t, a_t, s_{t+1}))$, discount factor $\gamma_\mathcal{K}=\gamma$ and initial state distribution $\mu_\mathcal{K}(s,u) = \mu(s)\mathbbm{1}[u = u_0]$.
\end{definition}

\bigskip
\begin{theorem}[Optimality of \ttt{RMSM}]
\label{theorem:rmsm}
Let $\mathcal{K}$ be a URM-MDP or URM-POMDP, $\pi_\theta$ a policy, and $g_\phi$ an RM state belief predictor as defined in the \ttt{RMSM} algorithm. Assume that every feasible trajectory in $\mathcal{K}$ occurs with non-zero probability under $\pi_\theta$. If $g_\phi$ minimizes $L_\phi$ with respect to $\phi$ and $\pi_\theta$ maximizes $J_\theta$ with respect to $\theta$, then $\pi_\theta$ is an optimal policy in $\mathcal{K}$ and $g_\phi$ matches the ground-truth belief over RM states given the history.

\medskip
\emph{Proof.} First, consider when $\mathcal{K}$ is a URM-MDP. For any particular history $s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t$ under $\pi_\theta$,
$- \log {g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)}$ is minimized when $g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t) = \pr(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)$ from a well-known result about information entropy. Minimizing $L_\phi = \mathbb{E}_{\pi_\theta}[- \log {g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)}]$ (with respect to $\phi$) requires that $g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t) = \pr(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)$ for all feasible histories $s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t$, since all feasible histories have positive probability under $\pi_\theta$. In other words, $g_\phi$ matches the ground-truth belief over RM states given the history.

\medskip
Now consider $\pi_\theta(a_t | s_t, \tilde{u}_t)$, where $\tilde{u}_t = g_\phi(\cdot | s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t) = b_u(s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t)$, and $b_u$ returns the ground-truth belief over RM states given the history. The inputs $s_t, \tilde{u}_t$ to the policy are precisely the states of the corresponding Cross Product Belief MDP $\mathcal{K}_U$ of $\mathcal{K}$, thus $\pi_\theta$ maximizes the expected discounted return in $\mathcal{K}_U$. This implies $\pi_\theta$ is also an optimal policy in the original URM-MDP $\mathcal{K}$.

\medskip
When $\mathcal{K}$ is a URM-POMDP, the proof that $g_\phi$ matches the ground-truth belief over RM states given the history remains virtually unchanged. On the policy side, the \ttt{RMSM} policy is of the form $\pi_\theta(a_t | h_t, \tilde{u}_t)$. Note, however, that there even exists an optimal policy in the URM-POMDP of the form $\pi^*(a_t | h_t)$. Regardless of $g_\phi$, maximizing $J_\theta$ (with respect to $\theta$) can always recover an optimal policy in $\mathcal{M}$ by ignoring $\tilde{u}_t$.
\qed

\end{theorem}

\section{Additional Definitions, Theorems, and Proofs}

\begin{definition}[\emph{Uncertain-Proposition Reward Machine POMDP} \textbf{(URM-POMDP)}]
\label{urmpomdp}
Given a POMDP (without reward function) $\mathcal{M} = \langle {S},\Omega, {T},{A},{P}, {O}, \gamma, \mu \rangle$, a finite set of atomic propositions $\mathcal{AP}$, a (ground-truth) labelling function $\mathcal{L}: S\times A \times S \rightarrow 2^{\mathcal{AP}}$, and a reward machine $\mathcal{R} = \langle U, u_0, F, \delta_u, \delta_r \rangle$, a {URM-POMDP} is a POMDP $\langle S', \Omega, T', A, P', O', R', \gamma, \mu' \rangle $ with state space $S' = S \times U$, observation space $\Omega$, terminal states $T' = (T\times U)\cup (S\times F)$, action space $A$, transition probabilities $P'((s_{t+1}, u_{t+1}) | (s_t,u_t),a_t) = P(s_{t+1}|s_t,a_t) \cdot \mathbbm{1}[\delta_u(u_t, \mathcal{L}(s_t, a_t, s_{t+1})) = u_{t+1}]$, observation probabilities $O'(o_t|(s_t,u_t), a_t) = O(o_t|s_t,a_t)$, reward function $R'((s_t,u_t),a_t,(s_{t+1},u_{t+1})) = \delta_r(u_t, \mathcal{L}(s_t, a_t, s_{t+1}))$, discount factor $\gamma$, and initial state distribution $\mu'(s,u) = \mu(s)\mathbbm{1}[u = u_0]$.
\end{definition}

\bigskip

\begin{theorem}[Optimality of \ttt{RMSM}]
\label{theorem:rmsm}
Let $\mathcal{K}$ be an URM-MDP or URM-POMDP, $\pi_\theta$ a policy, and $g_\phi$ an RM state belief predictor as defined in the \ttt{RMSM} algorithm. Assume that every feasible trajectory in $\mathcal{K}$ occurs with non-zero probability under $\pi_\theta$. For neural networks $g_\phi, \pi_\theta$ of sufficient capacity, assume that $g_\phi$ is a global minimum of $L_\phi$ and $\pi_\theta$ is a global maximum of $J_\theta$.
Then $\pi_\theta, g_\phi$ together form an optimal policy in $\mathcal{K}$, and $g_\phi$ predicts the ground-truth belief over $u_t$, given the history.

\medskip
\emph{Proof.} First, consider when $\mathcal{M}$ is a URM-MDP. For any particular history $s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t$ under $\pi_\theta$,
$\mathbb{E}_{u_t \sim \pr(\cdot | s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t)} [- \log {g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)}]$ is minimized when $g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t) = \pr(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)$ for all $u_t \in U$  by Gibbs' inequality. For $g_\phi$ with sufficient model capacity, minimizing $L_\phi = \mathbb{E}_{\pi_\theta}[- \log {g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)}]$ (with respect to $\phi$) requires that $g_\phi(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t) = \pr(u_t | s_0, a_0, \ldots, s_{t-1},a_{t-1},s_t)$ for all feasible histories $s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t$, since all feasible histories have positive probability under $\pi_\theta$. In other words, $g_\phi$ matches the ground-truth belief over RM states given the history. Note that for URM-MDP's, the ground-truth belief over RM states assigns all probability mass to the true RM state at time $t$.

\medskip
Now consider $\pi_\theta(a_t | s_t, \tilde{u}_t)$, where $\tilde{u}_t = g_\phi(\cdot | s_0, a_0, \ldots, s_{t-1}, a_{t-1}, s_t)$. As articulated above, $g_\phi$ assigns all probability mass to the ground-truth RM state $u_t^*$ at time $t$ and so the inputs to $\pi_\theta$ precisely mimic the transitions in the corresponding RM-MDP (where the true RM state is observable) to $\mathcal{K}$. Since $\pi_\theta$ is an optimal solution to $J_\theta$, it is an optimal policy in this RM-MDP, and hence must be optimal in $\mathcal{K}$ as well.

\medskip
When $\mathcal{M}$ is a URM-POMDP, the proof that $g_\phi$ matches the ground-truth belief over RM states given the history remains virtually unchanged. On the policy side, the \ttt{RMSM} policy is of the form $\pi_\theta(a_t | h_t, \tilde{u}_t)$. Note, however, that there even exists an optimal policy in the URM-POMDP of the form $\pi^*(a_t | h_t)$. Regardless of $g_\phi$, maximizing $J_\theta$ (with respect to $\theta$) can always recover an optimal policy in $\mathcal{M}$ by ignoring $\tilde{u}_t$.
\qed

\end{theorem}

\section*{Acknowledgements}
We gratefully acknowledge funding from the Natural Sciences and
Engineering Research Council of Canada (NSERC), the Canada CIFAR AI Chairs Program, and Microsoft Research. Resources used in preparing this research were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR, and companies sponsoring the Vector Institute for Artificial Intelligence (\url{https://vectorinstitute.ai/partners}). Finally, we thank the Schwartz Reisman Institute for Technology and Society for providing a rich multi-disciplinary research environment.

redpajama_set_name: RedPajamaArXiv


Excellent job again!! Love coming home to a beautifully cleaned home ! Thx again Jackie!
The White Tornado has struck again. Thanks so much.
Jackie was awesome! She took care of months' worth of dust, cat hair, and who knows what else. She was super friendly and thorough. Highly recommend.
This woman is the White Tornado.
This woman is amazing. There's no nock left unturned. She is the best we've ever had. Thank you for sending her to me.
Jackie is great! She's professional, hard working and reliable. Thx, Jackie. I really appreciate you!
Jackie was the most through cleaner we've had yet. Excellent repore, and very miticulas. Thank you for recommendING her.
Thank you, cleaning was awesome. Sorry i dont often open the app so hope you got tip, even a few weeks late!


NEW YORK - Hyman Golden, a businessman who was a cofounder of the Snapple Beverage Corp. and served as its chairman as Snapple's flavored teas and juices became a national phenomenon, died Sept. 14 in Great Neck, N.Y. He was 85.
The cause was complications from a stroke, said his daughter, Sharon Golden Brenner.
With a small investment in 1972, Mr. Golden and two partners started a business that would eventually produce one of the nation's leading flavored beverages and compete with such industry stalwarts as Coca-Cola and PepsiCo.
By the time the company was purchased by Quaker Oats Co. for about $1.7 billion in 1994, it had annual sales of $700 million, and its bottles of juices, with their familiar blue-and-white logos, could be found in delis, supermarkets, vending machines, and homes nationwide.
Mr. Golden, who had little formal education, had a humble upbringing in Queens County, working first as a window washer for his father, a Romanian immigrant. He later worked as a business broker and founded a maintenance company with his brother-in-law, Leonard Marsh.
In 1972, Marsh introduced Mr. Golden to Arnold Greenberg, a childhood friend who ran a health food store in the East Village neighborhood of Manhattan. The three decided to join forces and founded a company - called Unadulterated Food Products - selling juices to health food stores.
In 1980, the company introduced a line of all-natural juices with the Snapple name, which came from one of its first products, a carbonated apple juice that had a "snappy apple taste."
"When it first came out," Greenberg told The New York Times in July 1994, "we sold 500 cases. The next month we sold 500 more cases and got some calls from distributors. 'You've changed your formula,' they said. 'This Snapple's tasting better and better.' Then one day in our warehouse the tops of the bottles started shooting off. Bang! Pop! We found out it was fermenting. We'd made champagne."
The company enjoyed modest success with its natural sodas in the early 1980s; when it introduced its iced tea in 1987 sales soared. Amid a nationwide rise in health consciousness, Snapple became perhaps the only ready-to-drink iced tea promoted as having natural ingredients and being made from real brewed tea. Consumers increasingly chose it over its carbonated competitors.
Besides winning appeal through its 52 fruity flavors, Snapple quickly endeared itself to Americans with an aggressive marketing campaign. Its unconventional television ads featured a wildly popular spokeswoman from Long Island, Wendy Kaufman, or Wendy the Snapple Lady, who would read letters from devoted Snapple drinkers in her distinct "New Yawk" accent while promoting the beverage as "Made from the best stuff on Earth." Snapple is now sold in 80 countries.
The company, founded in Brooklyn, eventually moved to Long Island, where Mr. Golden and his two business partners lived. The three friends cherished their product, having a level of fun with it that was reflected in its quirky flavors and reputation.
"They used to sit in their office with chemists, and they would have concentrates all over the table as they did taste tests," said Mr. Golden's daughter, Sharon. "It wasn't even work to them. It was total enjoyment and they just loved what they were doing. They had a ball with it."
Hyman Golden was born in Passaic, N.J., and grew up in Queens. He served in the Air Force, and in 1948 met his wife, Mitzi, whom he married the next year.
In the early 1990s, as Snapple was exploding in popularity, Mr. Golden served as its chairman. The company was sold several times - eventually ending up with Cadbury Schweppes, now known as the Dr Pepper Snapple Group - making the men a fortune. But Mr. Golden, who retired in 1995, always remained thankful, his daughter said.
"He accomplished the American dream," she said. "When he and his partners would get together for events and celebrations, their favorite song to sing was 'God Bless America,' because they were so appreciative."
"In their wildest dreams," she added, "they never thought that this would be the end result."


Ambrane launches Smartwatch ASW-11 with fitness tracking capabilities - AndroGuider | One Stop For The Techy You!
Ambrane earlier this year set foot into the Indian wearable market with a fitness tracker called Flexi Fit. Now the popular accessories maker is launching its first smartwatch called Smartwatch ASW-11. The wearable also functions as fitness tracker, and is able to track activities like steps taken, distance traveled, calories burned and sleep monitoring.
The Ambrane Smartwatch ASW-11 is said to be a "multi-functional' watch with built-in speaker and microphone, and lets users to accept/reject calls, play music, snooze an alarm and set call or message reminder. The smartwatch also has a stopwatch, a calendar, and lets you create short reminders and manage to-do lists.
The watch has 1.44-inch touch screen display, comes with rubber strap and weighs just 50g. It is fueled by 200mAh battery, which promises two days of run time. It is compatible with Android and iOS devices.
The Smartwatch AQ-11 is priced at Rs. 899, and is available on Flipkart in Black color.


Did you know how important of a role gutters play in the protection of your home? Poor gutter systems can be a constant hassle for homeowners who experience a high volume of leaves throughout the year. Leaving them with unnecessary expenses and constant maintenance to keep clean. When gutters and downspouts clog it doesn't allow for proper drainage, that can quickly result in flooding. Water flow from over the gutters often collects at the foundation of your home, rather than away from it, often resulting in basement or first floor flooding and even foundation damage.
Griffith Exteriors' mission is to not only improve the appearance of your homes exterior, but also its functionality. Our seamless gutter systems help to keep your home safe from water damage! Griffith Exteriors offers modern traditional aluminum gutters as well as copper gutters that are a beautiful accent to any home. When properly installed they create a very efficient drainage system. Put an end to outdated, high maintenance gutters and let us help you choose the best gutter system to improve the functionality of your home.
Are you fed up with having to constantly clean your gutters? Griffith Exteriors offers additional Leaf Guard Systems that puts an end to clogged gutters! Leaf Relief systems are designed with guards that allow water to reach the gutters while keeping leaves and debris out! Other gutter guard systems can still become clogged and become keep clean and clear because of the guard in place. Let our knowledgeable staff help you decide if this option is right for you!


text:
Capita People Solutions
Human to Hybrid
Home » Blogs » Escaping the L&D Echo Chamber
Escaping the L&D Echo Chamber
L&D has been talking about the need for change for what seems like a very long time.
We know the narrative off by heart. Digital transformation, new patterns of working, new organisational structures and a constantly changing skills landscape, have combined to leave the role of L&D in question, never mind the impact (if any) it is delivering for the business.
Alongside this is the talk of an L&D department that is acutely aware of the need to evolve; to take on a more strategic, commercially-focused role; and to deliver competitive advantage in a skills-driven future economy.
L&D knows what's needed and we're hell bent on delivering it.
That's how the story goes… at least in the L&D industry.
Step outside the L&D echo chamber and you might be surprised to learn that there is a whole other perspective on L&D's place in the world, both now and in the future.
Another side to the L&D story
We recently carried out research exploring L&D's role within organisations today, the internal and external factors that are impacting upon it, and how best it should re-invent itself over the coming years. You can read the full white paper, How to solve a problem like L&D, here.
Significantly, we didn't just ask L&D professionals for their opinions, as valuable though they are. We also spoke to business managers, the people responsible for assembling, managing and retaining teams, and whose success comes down to the skills and competencies of their talent.
It may seem blindingly obvious, but it's a point on which the L&D industry should reflect. Our research actually found that 44% of line managers are frustrated by L&D's lack of collaboration and alignment with the business. Too many L&D departments are still operating in a silo and clearly that's a problem.
The word from the business
By talking to the wider business, we've confirmed some things that we already knew or at least suspected. Business managers want L&D to become more proactive, to get better at predicting future skills and to align measurement to tangible business metrics such as productivity and performance.
But we've also uncovered some really interesting and surprising insights, three of which I will touch on here, and are worth consideration for any L&D professional. (There are lots more in the white paper, which you can find here).
Firstly, line managers are significantly more positive about L&D's current value than L&D professionals themselves and, far from wanting the L&D department to be put out to pasture, they are actually demanding a more influential, strategic and empowered L&D function at the heart of the organisation. The situation isn't as bleak as we sometimes make out.
Secondly, there is a stark disconnect between L&D and business managers about who should take responsibility for day-to-day training requirements across the business. Line managers are adamant that L&D must hand over responsibility to them, whereas L&D professionals remain reluctant to do so, even though they acknowledge the need to focus their efforts on more strategic activities.
It's possible that this refusal to 'let go' is the single biggest reason why L&D has struggled to evolve in line with business needs over the last couple of years.
Finally, despite differing opinions on where L&D should be focusing its attention over the next two years and how it should approach its own transformation, business managers and L&D professionals do share a common vision of how L&D can best serve the needs of the organisation in the future. That's an L&D function that connects people, processes and skills, enables organisational change and drives transformation.
It's time for L&D to stop worrying about the future and to start listening to our colleagues around the business. We need to recognise line managers as valuable partners in delivering skills and instilling positive learning cultures across our organisations.
There's an exciting future out there for L&D – we just need to listen a bit more.
The CSuite Must Wake Up to L&D
Thousands of new graduates have just entered the workforce at this time of year, and the skills gap remains...
The Great Productivity Conundrum
What's keeping UK business leaders awake at night? Productivity. Or more accurately, a lack of productivity.
Unlocking people's potential: attracting, developing and engaging the workforce of the future
More than 150 HR and business leaders gathered at Landing Forty Two in October to attend the launch of our latest Human to Hybrid research, focusing on the role people will play in the future of work.
The difference between success and failure in the hybrid workforce
People's roles and the type of work they do will change extensively over the coming years, and so will the skills they'll need to do those jobs...
Creating a diverse and inclusive workforce in the future of work
To be successful in the new hybrid world of work, organisations will need to find the necessary skills and ability from all areas of talent. So how do you start to facilitate D&I in your culture?
The transformational power of data within L&D
Ray Brown, Sales Director – Learning and Development at Capita People Solutions, looks at the challenges and benefits of using learning data to drive business performance – now and in the future.
AI in recruitment: The problem of bias
As technologies such as Artificial Intelligence (AI) and Machine Learning (ML) play a bigger role in recruitment to remove human error and bias, are they really any better than we are?
Looking forward to a comfortable retirement
What is the reality of retirement? Read the actual Capita Employee Solutions perspective on pensions and retirement.
Giving the data story a happy ending
Organisations need to take a 'data-first' approach to operations, marketing and communications, and to building a genuine 'organisational personality' that can win hearts and minds.
The Insight Edge in Employee Benefits: the Capita People Solutions perspective
Dr Tirath Virdee, Director of Artificial Intelligence, Capita People Solutions, shares his views on how data is set to transform employee benefits.
Future Face of Retirement: the Capita Employee Solutions perspective
Fraser Stewart, Business Development Manager, Capita Employee Solutions shares his views on the storm brewing in the UK pensions industry.
Can data and insight tackle the skills crisis?
This month our attention turns to data, and the extent to which HR and recruitment see it as the lever to tackling the skills crisis in our latest research, 'The insight edge to talent acquisition'
The Power of Data in a Hybrid Workforce
Over a hundred HR leaders gathered in London on 26th June 2019 to attend the exclusive launch of the next phase in the Human to Hybrid programme.
Gut instinct or data-led recruitment? It depends if you want the skills to succeed
How can recruitment create a flexible talent pipeline, especially since the skills required for the future relate to jobs that haven't even been created yet? The answer is through data.
The Digital Opportunity: Re-imagining the employee experience in benefits
There is no doubt that digital has a massive role to play if benefits is to become a more strategic lever for organisations to drive improved talent acquisition and retention.
Online benefits: what's gone wrong and how you can turn it around
Over the next decade, the workforce will undergo enormous changes, driven primarily by the emergence of new technologies such as AI, RPA and Machine Learning.
Mind the gap: using data and digital to tackle skills shortages
As technology drives us towards the next industrial revolution, the skills needed in the transport sector will also take a new direction. So how can we mind the skills gap?
the prospect of technology making the recruitment process more objective, less discriminatory and more supporting of diversity is one many are striving for. But can AI be just as bias as we are?
Diversity and inclusion will be an even bigger enabler of value in a future workplace. To be successful in this hybrid world, organisations will need to find the skills in all sections of society.
People and robots: The future of workplace culture and collaboration
Getting culture right is hard enough with a conventional workforce – the dangers of siloes, poor communication or a reluctance to collaborate.
Building a vision and strategy for the future of HR – the three things you need to do now
The world of work isn't transforming, it has already transformed. Technological innovation has been integrated and traditional roles are being reshaped into new career paths.
Back to Insights & Events
© 2019 Capita PLC

redpajama_set_name: RedPajamaCommonCrawl


90 Day Fiancé Star Darcey Silva Transformation: See the Before and After Photos!
Talk about a transformation! 90 Day Fiancé star Darcey Silva recently took to Instagram to post a side-by-side photo of herself, and she looks seriously stunning! The 43-year-old mama once had darker hair and a fuller face, and TBH, she looks like a totally different person now. Watch the video below to see for yourself!
Last month, fans were wondering whether or not Darcey and her 24-year-old boyfriend Jesse Meester — who hails from Amsterdam — were still together and all social media posts point to yes! Jesse flew to New York City and was photographed with Darcey and her daughters on Sept. 24 to celebrate her birthday. The photo of the happy family was posted by Darcey on her Snapchat and shows all four enjoying a visit to the Sugar Factory.
Yikes. Well, one thing's for sure. If they're no longer together, we bet Jesse is pretty bummed he let her go!


Connor Radley is the 11-year-old son of our Controller, Erin Radley. In November of 2017 he was diagnosed with osteosarcoma, a type of bone cancer. He is undergoing treatment at Upstate Golisano Children's Hospital and is part of the Beads of Courage: Carry a Bead program.
Beads of Courage is a program sponsored by Maureen's Hope Foundation, a local non-profit organization. Their mission is to offer practical support and assistance to people facing the challenges of a cancer diagnosis or other life altering disease.
The Beads of Courage Program is designed to support and strengthen children and families coping with serious illness. Through this program, children tell their story using colorful beads as meaningful symbols of courage that commemorate milestones they have achieved along their unique treatment path. It launched at Golisano Children's Hospital in 2010 for pediatric oncology patients.
In March, Connor had the opportunity to represent Maureen's Hope Foundation and their Beads of Courage: Carry a Bead program for the Syracuse Crunch hockey team. He was able to show the team his beads, each one a visual representation of the cancer treatments he has been through.
To learn more about Beads of Courage and how you can participate in the Carry a Bead Program visit, Maureen's Hope Foundation.
Camo for Connor, a benefit for Connor Radley, will be held on June 9th from 1-5pm at Pope's Grove Golf Course. To learn more about how you can help Connor, visit Camo for Connor.


text:
Harald Kienast (* 28. September 1894; † 1986) war ein deutscher Konteradmiral der Kriegsmarine.

Leben
Harald Kienast trat im April 1913 in die Kaiserliche Marine ein. Später diente er bis August 1915 als Fähnrich zur See auf der Nymphe und kam dann bis November 1915 auf die Stralsund. Am 18. September 1915 war er zum Leutnant zur See ernannt worden. Bis Mai 1917 kam er in den Stab des Befehlshabers der Aufklärungsschiffe, war Flaggleutnant und sogenannter Funkenoffizier. Anschließend kam er bis Kriegsende auf die Hindenburg.

Nach dem Krieg wurde er in die Reichsmarine übernommen und hier erst am 7. Januar 1920 Oberleutnant zur See und dann am 1. April 1925 Kapitänleutnant. 1931 war er Erster Offizier auf der Meteor.

1936 war er als Fregattenkapitän (Beförderung am 1. Oktober 1936) Leiter der Gruppe Technisches Nachrichtenwesen (BB VI N) im Allgemeinen Marineamt.

1943 war er kurz Kommandant der Seewasserstraße Kaiser-Wilhelm-Kanal, wurde dann Höherer Kommandeur der Marinenachrichtenschulen. Später wurde er durch Ludwig Stummel ersetzt und erhielt eine andere Kommandierung.

Literatur
 Marine-Offizier-Verband (Hrsg.), Albert Stoelzel: Ehrenrangliste der Kaiserlich Deutschen Marine. 1914–18. Thormann & Goetsch, Berlin 1930, S. 434.

Einzelnachweise

Leutnant zur See (Kaiserliche Marine)
Konteradmiral, Charakter (Kriegsmarine der Wehrmacht)
Person im Ersten Weltkrieg (Deutsches Reich)
Person im Zweiten Weltkrieg (Deutsches Reich)
Deutscher
Geboren 1894
Gestorben 1986
Mann

redpajama_set_name: RedPajamaWikipedia


The MAA MathFest Grand Opening Reception will launch this year's MAA MathFest on a high note. This event is intended to draw attendees together in a spirit of camaraderie. We warmly invite you to enjoy complimentary light hors d'oeuvres while you mix and mingle in the Exhibit Hall with other registered participants and guests, sponsors, and exhibitors.
Join us for an evening of musical performances by your mathematical friends and colleagues, and along the way we will recognize and honor those members of our Association who've been members for twenty-five years or more.
Join MAA for refreshments as we celebrate eighty years of publishing with MAA Press.
Many mathematics departments offer courses specifically for preservice teachers, often designed and overseen by one or two faculty members per department. These courses can be stimulating to teach, yet also challenging because of the lack of shared wisdom in the community on what and how to teach in the courses. The organizers of this session are looking into the possibility of starting a SIGMAA to support the teaching of mathematics courses for preservice teachers. This session is an opportunity to gauge interest in such a SIGMAA, and more importantly, for faculty teaching these courses to share ideas and raise questions or concerns in a community. The organizers will facilitate discussion and conversation on what is known in the literature about the teaching and learning of mathematical knowledge for teaching at elementary and secondary levels, the perspectives represented in policy documents and commonly available textbooks, and approaches to these content courses.
Math Wrangle will pit teams of students against each other, the clock, and a slate of great math problems. The format of a Math Wrangle is designed to engage students in mathematical problem solving, promote effective teamwork, provide a venue for oral presentations, and develop critical listening skills. A Math Wrangle incorporates elements of team sports and debate, with a dose of strategy tossed in for good measure. The intention of the Math Wrangle demonstration at the Joint Math Meetings is to show how teachers, schools, circles, and clubs can get students started in this exciting combination of mathematical problem solving with careful argumentation via public speaking, strategy and rebuttal.
NSA's Women in Mathematics Society (WiMS) will host a networking session during the MathFest Conference on Thursday, July 27, 2017 from 6:00 p.m. until 8:00 p.m. Approximately 75-125 guests are expected to engage in conversations that encourage the professional development of women. Everyone is invited to attend this event. MathFest attendees are encouraged to stop by the NSA booth in the exhibit area to find out the exact location. Invitations will be available at the booth.
Join Susquehanna International Group (SIG) for a game that combines the world of trading with mathematical estimation. Working on a team, try to get better estimates for 8 numerical problems than the other teams as quickly as you can – if you fall behind, you'll lose valuable opportunities to make money*. The only way to get ahead is to trade with other teams who have worse guesses than you do. Whoever's got the best combination of math skills, strategy, and quick wits will take home the prize* -- will you be wolves or sheep?
*in-game money is fake, prize money is real!
If you're looking for a mindbending mixture of math and trivia, look no further! Jane Street Capital presents The Estimathon contest: teams will have 30 minutes to work on 13 problems, ranging from totally trivial to positively Putnamesque. Can your team beat the all-time best score?? The top teams will receive prizes!
As in past years, we will run 2 contests. Feel free to show up to either one!
4:15 pm. Welcome, overview of rules and scoring.
Besides cake and ice cream, we will recognize all students who gave talks in the MAA Student Paper Sessions. Prizes will be awarded for the best of these talks, and the AWM Student Chapter Awards will also be presented. All are invited.
Graduate students are invited for some refreshments and to meet several of the invited speakers.
Join your fellow SIGMAA TAHSM members at our annual reception and business meeting. Some SIGMAA business will be discussed, but mostly this is a time to communicate with your colleagues while enjoying some light hors d'oeuvres. We will also be recognizing the 2016 Edyth May Sliffe award winners.


text:
Psycholinguistic variables matter in odor naming
Huisman JLA., Majid A.
People from Western societies generally find it difficult to name odors. In trying to explain this, the olfactory literature has proposed several theories that focus heavily on properties of the odor itself but rarely discuss properties of the label used to describe it. However, recent studies show speakers of languages with dedicated smell lexicons can name odors with relative ease. Has the role of the lexicon been overlooked in the olfactory literature? Word production studies show properties of the label, such as word frequency and semantic context, influence naming; but this field of research focuses heavily on the visual domain. The current study combines methods from both fields to investigate word production for olfaction in two experiments. In the first experiment, participants named odors whose veridical labels were either high-frequency or low-frequency words in Dutch, and we found that odors with high-frequency labels were named correctly more often. In the second experiment, edibility was used for manipulating semantic context in search of a semantic interference effect, presenting the odors in blocks of edible and inedible odor source objects to half of the participants. While no evidence was found for a semantic interference effect, an effect of word frequency was again present. Our results demonstrate psycholinguistic variables—such as word frequency—are relevant for olfactory naming, and may, in part, explain why it is difficult to name odors in certain languages. Olfactory researchers cannot afford to ignore properties of an odor's label.
Memory and Cognition


text:
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Top 15 Website You Should Never Visit. No 2 will surprise you!
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Author Topic: Top 15 Website You Should Never Visit. No 2 will surprise you! (Read 17816 times)
Timi Dapsin
Today is that tomorrow you worried about yesterday
It might sound scary right? While to some it's nothing but just an ordinary website.
Well i might leave you to decide that yourself.
There are many disturbing and creepy websites on the internet, when you visit, it scares the underworld out of you. These horrifying websites are so dreadful, that it sends shivers down your spine, no matter how strong of a horror fan you maybe. These sites will be hard to digest, once you go into the depth of these horrifying websites. Hence a strict warning, that you should never ever visit these horrifying websites, for your well being.
Many of these horrifying websites founders have fallen into legal problems over the content, which is shared.
These sites ranges from online games to serial killers blogs.
Here are Top Horrifying Websites You Should Never Visit
15. Cryptomundo
This site documents their encounters or attempts to hunt down creatures like Chupacabras, Bigfoot, and an array of lake monsters and sea serpents. A very spooky site where they describe some very believable sightings of these creatures in locations all over the world, which leaves you answerless, whether there is any truth to the conspiracy theories behind their existence.
14. Hashima Island
It is a site where you travel around the forgotten world of Hashima, a deserted, creepy and abandoned island on the coast of Japan, which has a dark history, with its peak population in 1959 with 5,259 people occupying the island. In 1974, the coal mines were closed and all the residents departed leaving the island abandoned and has since been known as "the ghost island of Japan." On the site, you will see everything from the "stairway to underworld" to the actual coal mines and all of it looks so real giving a very creepy feeling.
13. White Enamel
This is a game site, which is certainly not for the weak-hearted, where you are made to go around an abandoned insane asylum and the game's uncanny soundtrack of an old man singing will certainly startle you.This game is so terrifying that players often mistake the footage of the asylum as being real. Some even feel as if they are watching a horror movie. It can shockingly affect the weak-hearted. So, never ever play this game.
12. Plane Crash Info
A very heartbreaking site on this list, which provides access to accident stats, reports, maps, photos, and last words of plane crash victims, actual audio depicting the plane's final moments in the air, the pilot's orders, passengers' final words, and the devastating moments the plane actually crashes below. This is really heavy and an emotional crash to deal with, for a normal person, to witness something so devastating.
11. Bestgore
The founder of this site Mark Marek was thrown in jail because this site was so controversial and disturbing. This is actually a shock site whose aim is inflicting shock to its users, with the most disturbing videos of beheadings and dismemberment. These are violent real-life news, photos, and videos, which is a disturbingly real depiction of the horrors happening around the world. Better to stay away than regret.
10. Death Map
This site shows you every death occurring in the world at any given time you log on, red dots will start appearing on whichever country has just had a death. Along with this, there are green dots are also popping up to show all the births that are happening in the world. Hence, you witness the population ratio of the world balancing. With the death, a symbol pops up to present the person's religion, like a cross for a Christian. Strongly advise never ever to visit this site.
9. Death Date
This site tells someone the exact date they are going to die. If you want to know when you are gonna die, then a detail of personal information has to be submitted. A date will be provided and repeated reminders will be given on time left for death to arrive. Exact prediction of death is done or not, but it's a very unhealthy site, which engulfs a person in negative thoughts about his own death. One of the most horrifying websites never ever visit.
8. Bongcheon-Dong Ghost
It's an online comic that you should never ever Google search, especially late at night. One of the scariest webcomic on the internet, which is very disturbing. The entire text is in Korean and the illustrations are so graphic and clear that the language barrier doesn't take away any of the comic's scariness. The comic strip begins with a girl walking on a deserted street alone when she sees a strange-looking man in the distance, and from here on, things don't get any less eerie. Bongcheon was originally the title of an extremely impoverished area of Seoul, South Korea.
7. The Fifth Nail Exposed
One of the horrifying websites which are completely based on one man's life as a convicted serial killer and violent sexual predator. It contains content from the criminal himself Joseph E. Duncan III, who began his crimes in the '70s and is now still in jail, he sends handwritten content to the creepy guy running the blog. It is extremely disturbing where one can get a clear insight into the mind and actions of a dangerous serial killer. Don't visit this site alone.
6. Death Row Information
This site provides all types of death row information available from the Texas Department of Criminal Justice. It includes exact details of all death row-related, including accounts of past executions and the final words of criminals just before they were executed. You can also see people who are currently on death row, their case history and the waiting list for their execution. Basically, it's a calendar highlighted with all the upcoming executions.
5. Joy of Satan
This site is dedicated to the religion Satanism. This site was founded in 1966 by people having ideological and philosophical beliefs based on Satan. They focus mostly on teens and children rigging them with their beliefs, origins, details about Lucifer, and even how to become a Satanist and join the underworld's army. Everybody has the freedom to believe, but kids should never ever believe something so Satanic.
4. Darwin Time
One of the horrifying websites consisting a compilation of all the conspiracy theories including 9/11, Hitler, and even Woodstock. This site is extremely messy and disorganized with very gruesome images, writings all laid out haywire on top of each other, thousands of hyperlinks cluttered randomly and all seem to work. A Twitter account associated with this website had to shut down because of its weird and creepy content.
3. Skyway Bridge
This website has the tracking of all the suicides which took place from the 4th most popular bridge the Sunshine Skyway Bridge located on the West Coast of Florida, USA. This site shows you all the tragic deaths, the detail of people who leaped to their death. By clicking on this site you can see the entire history of this ill-fated bridge suicides. Strongly recommend never ever to visit this site.
2. Human Leather
Human Leather is a British sales website that sells products which have been manufactured from human skin, which resemble almost like leather. The skin comes from people who have entrusted it to the site, prior to their death. They manufacture shoe, wallets, and bags from human skin. Belts have the highest demand and sales. This is the creepiest site, which you should never ever visit if you don't wish these products to haunt you mentally, for weeks.
1. A Columbine Site
This website documented the tragic shootings that took place at Columbine High School, 20 years ago in Colorado on 20th, April 1999. It was a highly planned attack by two senior students, where 12 were d*ad and 21 left injured. This site gives actual descriptions of the mass murder, a video footage of the murderers and the exact route they took to school to perform their madness, who later committed suicide. Visit at your own risk.
Remain Safe!
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One of the more substantial ways we can make a difference in our culture is by promoting and living out the real and try relations of the Family. We as the church must assume our rightful role in advancing the truth of the bible in its statutes concerning the family. The home is the primary place for nurturing faith. Since God established the Unit to be such a vital proponent in the world, we must do whatever it takes to support and foster its original order.
ONE FLESH is the ministry designed to focus on the needs of the husband and wife. The ministry will empower the couples with the necessary tools to remain focused on Christ as he strengthens them to continue loving each other. Email Demetrius and Alexis McClendon at oneflesh@discoveronechurch.org.
OC Kids is our ministry dedicated to children! They are currently engaged in Veggie Connections based on one of the favorites of this generation, Veggie Tales! This innovative curriculum stimulates the minds and souls of our children with understanding of the love of Christ. This program will acquaint the children with Biblical text that will help them understand the decisions they are making in everyday life.
OC Student Ministry is our ministry dedicated to our oldest children (grades 6-12.) We focus on the same study focus as the adults but in a student ministry age perspective. We also focus on making and building relationships with each other, so we have lots of creative activities and events on campus and off campus throughout the year.
TEA is the perfect blend of fellowship, relationship, discipleship and community involvement. Come and enjoy Tea Time with the Ladies of ONE Church every first Friday at 7:00 p.m. For further meeting information please email Alexis McClendon tea@discoveronechurch.org.
Vision Statement: At One Church we biblically train and equip men to be balanced in their faith which influences marriage, relationships, home, health and business. We seek to encourage every man to make a positive impact from his home to his community and to the next generation. This will be accomplished through Identity Truths, Discipleship, Leadership Development, Accountability Partners, Advances (no retreats) and Special Events.
Have you experienced the loss of a loved one or close relative recently? We want to partner with you in the following ways during this time of grief and mourning.
We rejoice with you in the celebration of the birth of your newborn! We are excited to assist as you adjust to your new bundle(s) of joy!
Baby Shower – including the necessities for you and the baby.