prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What happens to Ngotho after he attacks Jacobo at a workers' strike?

Read the following text and answer briefly.

Context 1: Weep Not, Child is a 1964 novel by Kenyan author Ngũgĩ wa Thiong'o  It was his first novel, published in 1964 under the name James Ngugi  It was among the African Writers Series  It was the first English language|English novel to be published by an East African  Thiong'o's works deal with the relationship between Africans and white settlers in colonial Kenya, and are heavily critical of colonial rule  Specifically, Weep Not, Child deals with the Mau Mau Uprising, and "the bewildering dispossession of an entire people from their ancestral land " Ngũgĩ wrote the novel while he was a student at Makerere University 

The book is divided into two parts and eighteen chapters  Part one deals mostly with the education of Njoroge, while part two deals with the rising Mau Mau movement 

Plot summary

Njoroge, a little boy, is urged to attend school by his mother  He is the first one of his family able to go to school  His family lives on the land of Jacobo, an African made rich by his dealings with white settlers, namely Mr  Howlands, the most powerful land owner in the area  Njoroge's brother Kamau works as an apprentice to a carpenter, while Boro, the eldest living son, is troubled by his experiences while in forced service during World War II, including witnessing the death of his elder brother  Ngotho, Njoroge's father and a respected man in the surrounding area, tends Mr  Howlands' crops, but is motivated by his passion to preserve his ancestral land, rather than for any compensation or loyalty 

One day, black workers call for a strike to obtain higher wages  Ngotho is ambivalent about participating in the strike because he fears he will lose his job  However, he decides to go to the gathering, even though his two wives do not agree  At the demonstration, there are calls for higher wages  Suddenly, the white police inspector brings Jacobo to the gathering to pacify the native people  Jacobo tries to put an end to the strike  Ngotho attacks Jacobo, and the result is a riot where two people are killed  Jacobo survives and swears revenge  Ngotho loses his job and Njoroge’s family is forced to move  Njoroge’s brothers fund his education and seem to lose respect for their father 

Mwihaki, Jacobo's daughter and Njoroge's best friend, enters a girls' only boarding school, leaving Njoroge relatively alone  He reflects upon her leaving, and realizes that he was embarrassed by his father's actions towards Jacobo  For this reason, Njoroge is not upset by her exit and their separation  Njoroge switches to another school 

For a time, everyone's attention is focused on the upcoming trial of Jomo Kenyatta – a revered leader of the movement  Many blacks think that he is going to bring forth Kenya’s independence  But Jomo loses the trial and is imprisoned  This results in further protests and greater suppression of the black population 

Jacobo and a white landowner, Mr  Howlands, fight against the rising activities of the Mau Mau, an organization striving for Kenyan economic, political, and cultural independence  Jacobo accuses Ngotho of being the leader of the Mau Mau and tries to imprison the whole family  Meanwhile, the situation in the country is deteriorating  Six black men are taken out of their houses and executed in the woods 

One day Njoroge meets Mwihaki again, who has returned from boarding school  Although Njoroge had planned to avoid her due to the conflict between their fathers, their friendship is unaffected  Njoroge passes an important exam that allows him to advance to High School  His village is proud of him, and collects money to pay Njoroge's High School tuition 

Several months later, Jacobo is murdered in his office by a member of the Mau Mau  Mr  Howlands has Njoroge removed from school for questioning  Both father and son are brutally beaten before release and Ngotho is left barely alive  Although there doesn't seem to be a connection between Njoroge's family and the murder, it is eventually revealed that Njoroge's brothers are behind the assassination, and that Boro is the real leader of the Mau Mau  Ngotho soon dies from his injuries and Njoroge finds out that his father was protecting his brothers  Kamau has been imprisoned for life  Only Njoroge and his two mothers remain free, and Njoroge is left as the sole provider of his two mothers  Njoroge fears that he cannot make ends meet; he gives up hope of continuing in school and loses faith in God 

Njoroge asks Mwihaki's for support, but she is angry because of her father’s death  When he finally pledges his love to her, she refuses to leave with him, realizing her obligation to Kenya and her mother  Njoroge decides to leave town and makes an attempt at suicide; however, he fails when his mothers find him before he is able to hang himself  The novel closes with Njoroge feeling hopeless, and ashamed of cowardice 

Characters in Weep Not, Child
 Njoroge: the main character of the book whose main goal throughout the book is to become as educated as possible 
 Ngotho: Njoroge's father  He works for Mr Howlands and is respected by him until he attacks Jacobo at a workers strike  He is fired and the family is forced to move to another section of the country  Over the course of the book his position as the central power of the family weakened, to the point where his self-realization that he has spent his whole life waiting for the prophecy (that proclaims the blacks will be returned their land) to come true rather than fighting for Kenyan independence, leads to his depression 
 Nyokabi and Njeri: the two wives of Ngotho  Njeri is Ngotho's first wife, and mother of Boro, Kamau, and Kori  Nyokabi is his second wife, and the mother of Njoroge and Mwangi 
 Njoroge has four brothers: Boro, Kamau, Kori and Mwangi (who is Njoroge's only full brother, who died in World War II) 
 Boro: Son of Njeri who fights for the Allies in World War II  Upon returning his anger against the colonial government is compounded by their confiscation of the his land  Boro's anger and position as eldest son leads him to question and ridicule Ngotho, which eventually defeats their father's will (upon realizing his life was wasted waiting and not acting)  It is eventually revealed that Boro is the leader of the Mau Mau (earlier alluded to as "entering politics") and murders Mr Howlands  He is caught by police immediately after and is scheduled to be executed by the book's end  It is highly likely that it is also Boro who kills Jacobo 
 Mwihaki: Njoroge's best friend (and later develops into his love interest)  Daughter of Jacobo  When it is revealed that his family killed Jacobo (most likely Boro), Mwihaki distances herself from Njoroge, asking for time to mourn her father and care for her mother 
 Jacobo: Mwihaki's father and an important landowner  Chief of the village 
 Mr  Howlands: A white settler who emigrated to colonial Kenya and now owns a farm made up of land that originally belonged to Ngotho's ancestors  Has three children: Peter who died in World War II before the book's beginning, a daughter who becomes a missionary, and Stephen who met Njoroge while the two were in high school 

Themes and motifs
Weep Not, Child integrates Gikuyu mythology and the ideology of nationalism that serves as catalyst for much of the novel's action  The novel explores the negative aspects of colonial rule over Kenya  Njoroge's aspiration to attend university is frustrated by both the violence of the Mau Mau rebels and the violent response of the colonial government  This disappointment leads to his alienation from his family and ultimately his suicide attempt 

The novel also ponders the role of saviours and salvation  The author notes in his The River Between: "Salvation shall come from the hills  From the blood that flows in me, I say from the same tree, a son shall rise  And his duty shall be to lead and save the people " Jomo Kenyatta, the first prime minister of Kenya, is immortalised in Weep Not, Child  The author says, "Jomo had been his (Ngotho's) hope  Ngotho had come to think that it was Jomo who would drive away the white man  To him, Jomo stood for custom and traditions purified by grace of learning and much travel " Njoroge comes to view Jomo as a messiah who will win the struggle against the colonial government 

See also

Things Fall Apart
Death and the King's Horseman

References

External links
Official homepage of Ngũgĩ wa Thiong'o
BBC profile of Ngũgĩ wa Thiong'o
Weep Not, Child at Google Books

British Empire in fiction
Novels set in colonial Africa
Historical novels
Kenyan English-language novels
Novels by Ngũgĩ wa Thiong'o
Novels set in Kenya
1964 novels
Heinemann (publisher) books
Postcolonial novels
African Writers Series
1964 debut novels



ground_truth: After attacking Jacobo at a workers' strike, Ngotho loses his job and Njoroge's family is forced to move.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the proposed approach in this research paper?

Read the following text and answer briefly.

Context 2: \section{Introduction}
\label{sec:introduction}

Probabilistic models have proven to be very useful in a lot of applications in signal processing where signal estimation is needed \cite{rabiner1989tutorial,arulampalam2002tutorial,ji2008bayesian}  Some of their advantages are that 1) they force the designer to specify all the assumptions of the model, 2) they provide a clear separation between the model and the algorithm used to solve it, and 3) they usually provide some measure of uncertainty about the estimation 

On the other hand, adaptive filtering is a standard approach in estimation problems when the input is received as a stream of data that is potentially non-stationary  This approach is widely understood and applied to several problems such as echo cancellation \cite{gilloire1992adaptive}, noise cancellation \cite{nelson1991active}, and channel equalization \cite{falconer2002frequency} 

Although these two approaches share some underlying relations, there are very few connections in the literature  The first important attempt in the signal processing community to relate these two fields was the connection between a linear Gaussian state-space model (i e  Kalman filter) and the RLS filter, by Sayed and Kailath \cite{sayed1994state} and then by Haykin \emph{et al } \cite{haykin1997adaptive}  The RLS adaptive filtering algorithm emerges naturally when one defines a particular state-space model (SSM) and then performs exact inference in that model  This approach was later exploited in \cite{van2012kernel} to design a kernel RLS algorithm based on Gaussian processes 

A first attempt to approximate the LMS filter from a probabilistic perspective was presented in \cite{park2014probabilistic}, focusing on a kernel-based implementation  The algorithm of \cite{park2014probabilistic} makes use of a Maximum a Posteriori (MAP) estimate as an approximation for the predictive step  However, this approximation does not preserve the estimate of the uncertainty in each step, therefore degrading the performance of the algorithm 

In this work, we provide a similar connection between state-space models and least-mean-squares (LMS)  Our approach is based on approximating the posterior distribution with an isotropic Gaussian distribution  We show how the computation of this approximated posterior leads to a linear-complexity algorithm, comparable to the standard LMS  Similar approaches have already been developed for a variety of problems such as channel equalization using recurrent RBF neural networks \cite{cid1994recurrent}, or Bayesian forecasting \cite{harrison1999bayesian}  Here, we show the usefulness of this probabilistic approach for adaptive filtering 

The probabilistic perspective we adopt throughout this work presents two main advantages  Firstly, a novel LMS algorithm with adaptable step size emerges naturally with this approach, making it suitable for both stationary and non-stationary environments  The proposed algorithm has less free parameters than previous LMS algorithms with variable step size \cite{kwong1992variable,aboulnasr1997robust,shin2004variable}, and its parameters are easier to be tuned w r t  these algorithms and standard LMS  Secondly, the use of a probabilistic model provides us with an estimate of the error variance, which is useful in many applications 

Experiments with simulated and real data show the advantages of the presented approach with respect to previous works  However, we remark that the main contribution of this paper is that it opens the door to introduce more Bayesian machine learning techniques, such as variational inference and Monte Carlo sampling methods \cite{barber2012bayesian}, to adaptive filtering \\


\section{Probabilistic Model}

Throughout this work, we assume the observation model to be linear-Gaussian with the following distribution,

\begin{equation}
p(y_k|{\bf w}_k) = \mathcal{N}(y_k;{\bf x}_k^T {\bf w}_k , \sigma_n^2),
\label{eq:mess_eq}
\end{equation}
where  $\sigma_n^2$ is the variance of the observation noise, ${\bf x}_k$ is the regression vector and ${\bf w}_k$ is the parameter vector to be sequentially estimated, both $M$-dimensional column vectors 


In a non-stationary scenario, ${\bf w}_k$ follows a dynamic process  In particular, we consider a diffusion process (random-walk model) with variance $\sigma_d^2$ for this parameter vector:


\begin{equation}
p({\bf w}_k|{\bf w}_{k-1})= \mathcal{N}({\bf w}_k;{\bf w}_{k-1}, \sigma_d^2 {\bf I}),
\label{eq:trans_eq}
\end{equation}
where $\bf I$ denotes the identity matrix  In order to initiate the recursion, we assume the following prior distribution on ${\bf w}_k$

\begin{equation}
p({\bf w}_0)= \mathcal{N}({\bf w}_0;0, \sigma_d^2{\bf I}) \nonumber
\end{equation}

\section{Exact inference in this model: Revisiting the RLS filter}

Given the described probabilistic SSM, we would like to infer the posterior probability distribution $p({\bf w}_k|y_{1:k})$ 
Since all involved distributions are Gaussian, one can perform exact inference, leveraging the probability rules in a straightforward manner  The resulting probability distribution is
\begin{equation}
p({\bf w}_k|y_{1:k}) =  \mathcal{N}({\bf w}_k;{\bf\boldsymbol\mu}_{k}, \boldsymbol\Sigma_{k}), \nonumber
\end{equation}
in which the mean vector ${\bf\boldsymbol\mu}_{k}$ is given by
\begin{equation}
{\bf\boldsymbol\mu}_k = {\bf\boldsymbol\mu}_{k-1} + {\bf K}_k (y_k - {\bf x}_k^T {\bf\boldsymbol\mu}_{k-1}){\bf x}_k, \nonumber
\end{equation}
where we have introduced the auxiliary variable
\begin{equation}
{\bf K}_k = \frac{ \left(\boldsymbol\Sigma_{k-1} + \sigma_d^2 {\bf I}\right)}{{\bf x}_k^T  \left(\boldsymbol\Sigma_{k-1} + \sigma_d^2 {\bf I}\right)  {\bf x}_k + \sigma_n^2}, \nonumber
\end{equation}
and the covariance matrix $\boldsymbol\Sigma_k$ is obtained as
\begin{equation}
\boldsymbol\Sigma_k = \left( {\bf I} -  {\bf K}_k{\bf x}_k {\bf x}_k^T \right) ( \boldsymbol\Sigma_{k-1} +\sigma_d^2), \nonumber
\end{equation}
Note that the mode of $p({\bf w}_k|y_{1:k})$, i e  the maximum-a-posteriori estimate (MAP), coincides with the RLS adaptive rule
\begin{equation}
{{\bf w}}_k^{(RLS)} = {{\bf w}}_{k-1}^{(RLS)} + {\bf K}_k (y_k - {\bf x}_k^T {{\bf w}}_{k-1}^{(RLS)}){\bf x}_k  
\label{eq:prob_rls}
\end{equation}
This rule is similar to the one introduced in \cite{haykin1997adaptive} 

Finally, note that the covariance matrix $\boldsymbol\Sigma_k$ is a measure of the uncertainty of the estimate ${\bf w}_k$ conditioned on the observed data $y_{1:k}$  Nevertheless, for many applications a single scalar summarizing the variance of the estimate could prove to be sufficiently useful  In the next section, we show how such a scalar is obtained naturally when $p({\bf w}_k|y_{1:k})$ is approximated with an isotropic Gaussian distribution  We also show that this approximation leads to an LMS-like estimation 
 


\section{Approximating the posterior distribution: LMS filter }

The proposed approach consists in approximating the posterior distribution $p({\bf w}_k|y_{1:k})$, in general a multivariate Gaussian distribution with a full covariance matrix, by an isotropic spherical Gaussian distribution 

\begin{equation}
\label{eq:aprox_post}
\hat{p}({\bf w}_{k}|y_{1:k})=\mathcal{N}({\bf w}_{k};{\bf \hat{\boldsymbol\mu}}_{k}, \hat{\sigma}_{k}^2 {\bf I} ) 
\end{equation}

In order to estimate the mean and covariance of the approximate distribution $\hat{p}({\bf w}_{k}|y_{1:k})$, we propose to select those that minimize the Kullback-Leibler divergence with respect to the original distribution, i e , 

\begin{equation}
\{\hat{\boldsymbol\mu}_k,\hat{\sigma}_k\}=\arg \displaystyle{  \min_{\hat{\boldsymbol\mu}_k,\hat{\sigma}_k}} \{ D_{KL}\left(p({\bf w}_{k}|y_{1:k}))\| \hat{p}({\bf w}_{k}|y_{1:k})\right) \}  \nonumber
\end{equation}

The derivation of the corresponding minimization problem can be found in Appendix A  In particular, the optimal mean and the covariance are found as
\begin{equation}
{\hat{\boldsymbol\mu}}_{k} = {\boldsymbol\mu}_{k};~~~~~~ \hat{\sigma}_{k}^2 = \frac{{\sf Tr}\{ \boldsymbol\Sigma_k\} }{M} 
\label{eq:sigma_hat}
\end{equation}


We now show that by using \eqref{eq:aprox_post} in the recursive predictive and filtering expressions we obtain an LMS-like adaptive rule  First, let us assume that we have an approximate posterior distribution at $k-1$, $\hat{p}({\bf w}_{k-1}|y_{1:k-1}) =  \mathcal{N}({\bf w}_{k-1};\hat{\bf\boldsymbol\mu}_{k-1}, \hat{\sigma}_{k-1}^2 {\bf I} )$  Since all involved distributions are Gaussian, the predictive distribution
is obtained as %
\begin{eqnarray}
\hat{p}({\bf w}_k|y_{1:k-1}) &=& \int p({\bf w}_k|{\bf w}_{k-1}) \hat{p}({\bf w}_{k-1}|y_{1:k-1}) d{\bf w}_{k-1} \nonumber\\
&=& \mathcal{N}({\bf w}_k;{\bf\boldsymbol\mu}_{k|k-1}, \boldsymbol\Sigma_{k|k-1}), 
\label{eq:approx_pred}
\end{eqnarray}
where the mean vector and covariance matrix are given by
\begin{eqnarray}
\hat{\bf\boldsymbol\mu}_{k|k-1} &=& \hat{\bf\boldsymbol\mu}_{k-1} \nonumber \\
\hat{\boldsymbol\Sigma}_{k|k-1} &=& (\hat{\sigma}_{k-1}^2 + \sigma_d^2 ){\bf I}\nonumber 
\end{eqnarray}

From \eqref{eq:approx_pred}, the posterior distribution at time $k$ can be computed using Bayes' Theorem and standard Gaussian manipulations (see for instance \cite[Ch  4]{murphy2012machine})  Then, we approximate the posterior $p({\bf w}_k|y_{1:k})$ with an isotropic Gaussian,
\begin{equation}
\hat{p}({\bf w}_k|y_{1:k}) =  \mathcal{N}({\bf w}_k ; {\hat{\boldsymbol\mu}}_{k}, \hat{\sigma}_k^2 {\bf I} ),\nonumber
\end{equation}
where 
\begin{eqnarray}
{\hat{\boldsymbol\mu}}_{k} &= & {\hat{\boldsymbol\mu}}_{k-1}+ \frac{ (\hat{\sigma}_{k-1}^2+ \sigma_d^2)  }{(\hat{\sigma}_{k-1}^2+ \sigma_d^2)  \|{\bf x}_k\|^2 + \sigma_n^2} (y_k - {\bf x}_k^T {\hat{\boldsymbol\mu}}_{k-1}){\bf x}_k  \nonumber  \\
&=& {\hat{\boldsymbol\mu}}_{k-1}+ \eta_k (y_k - {\bf x}_k^T {\hat{\boldsymbol\mu}}_{k-1}){\bf x}_k   
\label{eq:prob_lms}
\end{eqnarray}
Note that, instead of a gain matrix ${\bf K}_k$ as in Eq ~\eqref{eq:prob_rls}, we now have a scalar gain $\eta_k$ that operates as a variable step size 


Finally, to obtain the posterior variance, which is our measure of uncertainty, we apply \eqref{eq:sigma_hat} and the trick ${\sf Tr}\{{\bf x}_k{\bf x}_k^T\}= {\bf x}_k^T{\bf x}_k= \|{\bf x}_k \|^2$,

\begin{eqnarray}
\hat{\sigma}_k^2 &=& \frac{{\sf Tr}(\boldsymbol\Sigma_k)}{M} \\
&=& \frac{1}{M}{\sf Tr}\left\{ \left( {\bf I} -  \eta_k {\bf x}_k {\bf x}_k^T \right) (\hat{\sigma}_{k-1}^2 +\sigma_d^2)\right\} \\
&=& \left(1 - \frac{\eta_k \|{\bf x}_k\|^2}{M}\right)(\hat{\sigma}_{k-1}^2 +\sigma_d^2) 
\label{eq:sig_k}
\end{eqnarray}
If MAP estimation is performed, we obtain  an adaptable step-size LMS estimation

\begin{equation}
{\bf w}_{k}^{(LMS)} = {\bf w}_{k-1}^{(LMS)} + \eta_k (y_k - {\bf x}_k^T {\bf w}_{k-1}^{(LMS)}){\bf x}_k, 	
\label{eq:lms}
\end{equation}
with
\begin{equation}
\eta_k = \frac{ (\hat{\sigma}_{k-1}^2+ \sigma_d^2)  }{(\hat{\sigma}_{k-1}^2+ \sigma_d^2)  \|{\bf x}_k\|^2 + \sigma_n^2} \nonumber
\end{equation}
At this point, several interesting remarks can be made:

\begin{itemize}

\item The adaptive rule \eqref{eq:lms} has linear complexity since it does not require us to compute the full matrix $\boldsymbol\Sigma_k$ 

\item For a stationary model, we have $\sigma_d^2=0$ in \eqref{eq:prob_lms} and \eqref{eq:sig_k}  In this case, the algorithm remains valid and both the step size and the error variance, $\hat{\sigma}_{k}$, vanish over time $k$  

\item Finally, the proposed adaptable step-size LMS has only two parameters, $\sigma_d^2$ and $\sigma_n^2$, (and only one, $\sigma_n^2$, in stationary scenarios) in contrast to other variable step-size algorithms \cite{kwong1992variable,aboulnasr1997robust,shin2004variable}  More interestingly, both $\sigma_d^2$ and $\sigma_n^2$ have a clear underlying physical meaning, and they can be estimated in many cases  We will comment more about this in the next section  
\end{itemize}



\section{Experiments}
\label{sec:experiments}

We evaluate the performance of the proposed algorithm in both stationary and tracking experiments  In the first experiment, we estimate a fixed vector ${\bf w}^{o}$ of dimension $M=50$  The entries of the vector are independently and uniformly chosen in the range $[-1,1]$  Then, the vector is normalized so that $\|{\bf w}^o\|=1$  Regressors $\boldsymbol{x}_{k}$ are zero-mean Gaussian vectors with identity covariance matrix  The additive noise variance is such that the SNR is $20$ dB  We compare our algorithm with standard RLS and three other LMS-based algorithms: LMS, NLMS \cite{sayed2008adaptive}, VSS-LMS \cite{shin2004variable} \footnote{The used parameters for each algorithm are: for RLS $\lambda=1$, $\epsilon^{-1}=0 01$; for LMS $\mu=0 01$; for NLMS $\mu=0 5$; and for VSS-LMS $\mu_{max}=1$, $\alpha=0 95$, $C=1e-4$ } The probabilistic LMS algorithm in \cite{park2014probabilistic} is not simulated because it is not suitable for stationary environments 

In stationary environments, the proposed algorithm has only one parameter, $\sigma^2_n$  We simulate both the scenario where we have perfectly knowledge of the amount of noise (probLMS1) and the case where the value $\sigma^2_n$ is $100$ times smaller than the actual value (probLMS2)  The Mean-Square Deviation (${\sf MSD} = {\mathbb E} \| {\bf w}_0 - {\bf w}_k \|^2$), averaged out over $50$ independent simulations, is presented in Fig  \ref{fig:msd_statationary} 



\begin{figure}[htb]
\centering
\begin{minipage}[b]{\linewidth}
  \centering
  \centerline{\includegraphics[width=\textwidth]{results_stationary_MSD}}
\end{minipage}
\caption{Performance in terms of MSD of probabilistic LMS with both optimal (probLMS1) and suboptimal (probLMS2) compared to LMS, NLMS, VS-LMS, and RLS }
\label{fig:msd_statationary}
\end{figure}

The performance of probabilistic LMS is close to RLS (obviously at a much lower computational cost) and largely outperforms previous variable step-size LMS algorithms proposed in the literature  Note that, when the model is stationary, i e  $\sigma^2_d=0$ in \eqref{eq:trans_eq},  both the uncertainty $\hat{\sigma}^2_k$, and the adaptive step size $\eta_k$, vanish over time  This implies that the error tends to zero when $k$ goes to infinity  Fig  \ref{fig:msd_statationary} also shows that the proposed approach is not very sensitive to a bad choice of its only parameter, as demonstrated by the good results of probLMS2, which uses a $\sigma^2_n$ that is $100$ times smaller than the optimal value  


\begin{figure}[htb]
\centering
\begin{minipage}[b]{\linewidth}
  \centering
  \centerline{\includegraphics[width=\textwidth]{fig2_final}}
\end{minipage}
\caption{Real part of one coefficient of the measured and estimated channel in experiment two  The shaded area represents two standard deviations from the prediction {(the mean of the posterior distribution)} }
\label{fig_2}
\end{figure}


\begin{table}[ht]
\begin{footnotesize}
\setlength{\tabcolsep}{2pt}
\def1 5mm{1 5mm}
\begin{center}
\begin{tabular}{|l@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|c@{\hspace{1 5mm}}|}
\hline
Method &  LMS &  NLMS & LMS-2013 & VSSNLMS & probLMS & RLS \\
\hline
\hline
MSD (dB) &-28 45 &-21 07 &-14 36 &-26 90 &-28 36 &-25 97\\
\hline                                                                     
\end{tabular}
\end{center}
\caption{Steady-state MSD of the different algorithms for the tracking of a real MISO channel }
\label{tab:table_MSD}
\end{footnotesize}

\end{table}
\newpage
In a second experiment, we test the tracking capabilities of the proposed algorithm with {real} data of a wireless MISO channel acquired in a realistic indoor scenario  More details on the setup can be found in \cite{gutierrez2011frequency}  Fig  \ref{fig_2} shows the real part of one of the channels, and the estimate of the proposed algorithm  The shaded area represents the estimated uncertainty for each prediction, i e  $\hat{\mu}_k\pm2\hat{\sigma}_k$  Since the experimental setup does not allow us to obtain the optimal values for the parameters, we fix these parameters to their values that optimize the steady-state mean square deviation (MSD)  \hbox{Table \ref{tab:table_MSD}} shows this steady-state MSD of the estimate of the MISO channel with different methods  As can be seen, the best tracking performance is obtained by standard LMS and the proposed method  





\section{Conclusions and Opened Extensions}
\label{sec:conclusions}

{We have presented a probabilistic interpretation of the least-mean-square filter  The resulting algorithm is an adaptable step-size LMS that performs well both in stationary and tracking scenarios  Moreover, it has fewer free parameters than previous approaches and these parameters have a clear physical meaning  Finally, as stated in the introduction, one of the advantages of having a probabilistic model is that it is easily extensible:}

\begin{itemize}
\item If, instead of using an isotropic Gaussian distribution in the approximation, we used a Gaussian with diagonal covariance matrix, we would obtain a similar algorithm with different step sizes and measures of uncertainty, for each component of ${\bf w}_k$  Although this model can be more descriptive, it needs more parameters to be tuned, and the parallelism with LMS vanishes 
\item Similarly, if we substitute the transition model of \eqref{eq:trans_eq} by an Ornstein-Uhlenbeck process, 

\begin{equation}
p({\bf w}_k|{\bf w}_{k-1})= \mathcal{N}({\bf w}_k;\lambda {\bf w}_{k-1}, \sigma_d^2), \nonumber
\label{eq:trans_eq_lambda}
\end{equation}
a similar algorithm is obtained but with a forgetting factor $\lambda$ multiplying ${\bf w}_{k-1}^{(LMS)}$ in \eqref{eq:lms}  This algorithm may have improved performance under such a kind of autoregresive dynamics of ${\bf w}_{k}$, though, again, the connection with standard LMS becomes dimmer 

\item As in \cite{park2014probabilistic}, the measurement model \eqref{eq:mess_eq} can be changed to obtain similar adaptive algorithms for classification, ordinal regression, and Dirichlet regression for compositional data  

\item A similar approximation technique could be applied to more complex dynamical models, i e  switching dynamical models \cite{barber2010graphical}  The derivation of efficient adaptive algorithms that explicitly take into account a switch in the dynamics of the parameters of interest is a non-trivial and open problem, though the proposed approach could be useful 

\item Finally, like standard LMS, this algorithm can be kernelized for its application in estimation under non-linear scenarios 

\end{itemize}


\begin{appendices}

\section{KL divergence between a general gaussian distribution and an isotropic gaussian}
\label{sec:kl}

 We want to approximate  $p_{{\bf x}_1}(x) = \mathcal{N}({\bf x}; \boldsymbol\mu_1,\boldsymbol\Sigma_1)$ by $p_{{\bf x}_2}({\bf x}) = \mathcal{N}({\bf x}; \boldsymbol\mu_2,\sigma_2^2 {\bf I})$  In order to do so, we have to compute the parameters of $p_{{\bf x}_2}({\bf x})$, $\boldsymbol\mu_2$ and $\sigma_2^2$, that minimize the following Kullback-Leibler divergence,

\begin{eqnarray}
D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) &=&\int_{-\infty}^{\infty} p_{{\bf x}_1}({\bf x}) \ln{\frac{p_{{\bf x}_1}({\bf x})}{p_{{\bf x}_2}({\bf x})}}d{\bf x} \nonumber  \\
&= &  \frac{1}{2} \{ -M + {\sf Tr}(\sigma_2^{-2} {\bf I}\cdot \boldsymbol\Sigma_1^{-1})  \nonumber \\
  & &  + (\boldsymbol\mu_2 - \boldsymbol\mu_1 )^T \sigma^{-2}_2{\bf I} (\boldsymbol\mu_2 - \boldsymbol\mu_1 )  \nonumber \\
 & &   +  \ln \frac{{\sigma_2^2}^M}{\det\boldsymbol\Sigma_1} \}   
\label{eq:divergence}
\end{eqnarray}
Using symmetry arguments, we obtain 
\begin{equation}
\boldsymbol\mu_2^{*} =\arg \displaystyle{  \min_{\boldsymbol\mu_2}} \{ D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) \} = \boldsymbol\mu_1 
\end{equation}
Then, \eqref{eq:divergence} gets simplified into 

\begin{eqnarray}
D_{KL}(p_{{\bf x}_1}\| p_{{\bf x}_2}) = \frac{1}{2}\lbrace { -M + {\sf Tr}(\frac{\boldsymbol\Sigma_1}{\sigma_2^{2}}) + \ln \frac{\sigma_2^{2M}}{\det\boldsymbol\Sigma_1}}\rbrace 
\end{eqnarray}
The variance $\sigma_2^2$ is computed in order to minimize this Kullback-Leibler divergence as

\begin{eqnarray}
\sigma_2^{2*} &=& \arg\min_{\sigma_2^2} D_{KL}(P_{x_1}\| P_{x_2}) \nonumber \\
 &=& \arg\min_{\sigma_2^2}\{ \sigma_2^{-2}{\sf Tr}\{\boldsymbol\Sigma_1\} + M\ln \sigma_2^{2} \}  
\end{eqnarray}
Deriving and making it equal zero leads to

\begin{equation}
\frac{\partial}{\partial \sigma_2^2} \left[ \frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{\sigma_2^{2}} + M \ln \sigma_2^{2} \right] = \left  {\frac{M}{\sigma_2^{2}}-\frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{(\sigma_2^{2})^2}}\right|_{\sigma_2^{2}=\sigma_2^{2*}}\left  =0 \right   
\nonumber
\end{equation}
Finally, since the divergence has a single extremum in $R_+$,
\begin{equation}
\sigma_2^{2*} = \frac{{\sf Tr}\{\boldsymbol\Sigma_1\}}{M} 
\end{equation}




\end{appendices}

\vfill
\clearpage

\bibliographystyle{IEEEbib}

Context 3: Outdoors	February 19, 2017
You are here: Home / Archives for Departments / OutdoorsActor Sam Waterson Hosts PBS Documentary on Lyme Land Trust January 14, 2017 by admin Leave a Comment Jack Tiffany, owner of Tiffany Farms on Rte  156 and an earlier pioneer in Lyme land preservation, is interviewed by PBS “Visionaries” documentary producers 
Filed Under: Lyme, Outdoors Application Deadline for Environmental Leadership Scholarship is Feb  1 January 8, 2017 by admin Leave a Comment Applications are now being accepted for the Virginia R  Rollefson Environmental Leadership Scholarship, a $1,000 award to recognize a high school student who has demonstrated leadership and initiative in promoting conservation, preservation, restoration, or environmental education 
Filed Under: Lyme, News, Old Lyme, Outdoors, Top Story Preserves in Lyme Now Closed for Hunting During Weekdays November 17, 2016 by admin Leave a Comment Starting yesterday, Wednesday, Nov  16, the following Preserves in Lyme will be closed Monday through Friday until Tuesday, Dec  20, 2016, except to licensed hunters with valid consent forms from the Town of Lyme Open Space Coordinator:
Banningwood Preserve
Beebe Preserve
Chestnut Hill Preserve
Eno Preserve
Hand Smith
Honey Hill Preserve
Jewett Preserve
Mount Archer Woods
Pickwick’s Preserve
Plimpton Preserve
Slawson Preserve
These preserves, owned by the Town of Lyme or the Lyme Land Conservation Trust, will be open on Saturdays and Sundays during this hunting period as no hunting is allowed on weekends 
The hunting program is fully subscribed 
For more information on the hunting program in Lyme, visit http://www lymelandtrust org/stewardship/hunting-program/
Filed Under: Lyme, Outdoors, Top Story Town of Old Lyme Offers Part-time Land Steward Opportunity October 11, 2016 by admin Leave a Comment The Town of Old Lyme is seeking a part-time individual to maintain and manage the trail systems on its major preserves  Keeping trails cleared, maintaining markers, kiosks, entrances, parking areas, and managing for wildlife and other natural resources are the priorities 
For more information, visit the job posting on the home page of the Town’s web page at http://www oldlyme-ct gov/Pages/index 
To learn about the Open Space Commission and the properties it manages, visit http://www oldlyme-ct gov/Pages/OldLymeCT_Bcomm/open_space
Filed Under: Old Lyme, Outdoors, Top Story CT Fund for the Environment Annual Meeting to be Held Sunday in Hartford September 22, 2016 by admin Leave a Comment Engaging and educating communities for preservation of the Long Island Sound tidal estuary
Save the Sound is celebrating National Estuaries Week Sept  17 – 24 with a series of interactive and educational events throughout the Long Island Sound region  This annual celebration of estuaries—the vital coastal zones where freshwater rivers meet salty seas—is sponsored by Restore America’s Estuaries and its member organizations including Save the Sound  This year’s events call attention to the many benefits of thriving coastal ecosystems, including how estuary conservation efforts support our quality of life and economic well-being 
“The Long Island Sound estuary is not only where freshwater rivers meet the saltwater Atlantic, but where wildlife habitat meets beaches and boating, and where modern industry meets traditional oystering,” said Curt Johnson, executive director of Save the Sound, which is a bi-state program of Connecticut Fund for the Environment (CFE) 
Johnson continued, “All over the country, estuaries are the lifeblood of coastal economies  From serving as natural buffers to protect our coastlines from storms to providing unique habitat for countless birds, fish, and wildlife, estuaries deserve our protection and our thanks ”
Save the Sound is celebrating estuaries with a number of events this week, including the release of a new video, a presentation on Plum Island at the Old Lyme-Phoebe Griffin Noyes Library and the CFE/Save the Sound annual meeting:
Aerial view of Plum Island lighthouse  (From Preserve Plum Island website)
Chris Cryder, Special Projects Coordinator for Save the Sound and Outreach Coordinator for the Preserve Plum Island Coalition, will host Preserving Plum Island for Future Generations, a special presentation on the importance of conserving the wildlife habitats and historic buildings of Plum Island, New York 
Plum Island flanks Plum Gut in the Long Island Sound estuary’s eastern end, where fast-moving tides create highly productive fishing grounds  The talk is part of a multi-week series featuring photographs and paintings of Plum Island, and lectures on its ecology, geology, and history 
Old Lyme-Phoebe Griffin Noyes Library, 2 Library Lane, Old Lyme, Connecticut
Register by calling the library at 860-434-1684 
The Annual Meeting of Connecticut Fund for the Environment and its bi-state program Save the Sound will take place in the Planet Earth exhibit at the Connecticut Science Center  The event is open to the public with registration, and will feature a keynote address from Curt Spalding, administrator of EPA’s New England Region  Spalding is a leader in combatting nitrogen pollution and in climate change resilience planning efforts for New England 
Connecticut Science Center, 250 Columbus Blvd, Hartford, Connecticut
4 – 7 p m
RSVP to mlemere@ctenvironment org
To celebrate the contributions of volunteers to restoring the Long Island Sound estuary, Save the Sound has released a new video of a habitat restoration planting at Hyde Pond in Mystic  Following removal of the old Hyde Pond dam and opening 4 1 miles of stream habitat for migratory fish last winter (see time lapse video here), in May about 30 volunteers planted native vegetation along the Whitford Brook stream bank, under the direction of U S  Fish and Wildlife Service, CT DEEP’s Fisheries division, and Save the Sound staff 
Find more information on the project’s benefits and funders here 
Look for the planting video on Save the Sound’s website, YouTube, Facebook, and Twitter accounts 
Filed Under: Old Lyme, Outdoors 750+ Volunteers Clean Beaches from Norwalk to New London Including Griswold Point in Old Lyme September 17, 2016 by admin Leave a Comment Kendall Perkins displays a skull she found during Save The Sound‘s Coastal Clean-up Day held yesterday at White Sand Beach 
Save the Sound, a bi-state program of Connecticut Fund for the environment, organized 31 cleanups across Connecticut’s shoreline this weekend  The efforts are part of International Coastal Cleanup, which brings together hundreds of thousands of people each year to remove plastic bags, broken glass, cigarette butts, and other trash from the world’s shores and waterways  One of the areas included in the cleanup effort was from White Sand Beach to the tip of Griswold Point in Old Lyme 
The event was founded by Ocean Conservancy in 1985, and Save the Sound has served as the official Connecticut coordinator for the last 14 years 
“We didn’t plan it this way, but I can’t imagine a better way to celebrate the 31st anniversary of International Coastal Cleanup Day than with 31 cleanups!” said Chris Cryder, special projects coordinator for Save the Sound  “The cleanup just keeps growing, in Connecticut and worldwide  We have some terrific new and returning partners this year, including the SECONN Divers, folks from the U S  District Court, multiple National Charity League chapters, and many more ”
Cryder continued, “The diversity of the groups involved really reflects the truth that ocean health affects all of us  Clean beaches and oceans are safer for beachgoers and boaters, they’re healthier for wildlife that aren’t eating plastic or getting tangled up in trash, and they’re economic powerhouses for the fishing and tourism industries ”
The cleanups are co-hosted by a wide array of local partners including high schools, youth groups, and scout troops; churches; boaters and divers; watershed associations, park stewards, and land trusts  Twenty-eight cleanups will be held Saturday, with three more on Sunday and others through mid-October, for a total of 70 cleanups statewide 
Based on the estimates of cleanup captains, between 750 and 900 volunteers were expected to pitch in on Saturday alone  Last year, a total of 1,512 volunteers participated in Save the Sound cleanups throughout the fall  They collected more than three tons of litter and debris from 58 sites on Connecticut beaches, marshes, and riverbanks 
Over the event’s three-decade history, 11 5 million volunteers have collected 210 million pounds of trash worldwide  Every piece of trash volunteers find is tracked, reported to Save the Sound, and included in Ocean Conservancy’s annual index of global marine debris  The data is used to track trends in litter and devise policies to stop it at its source 
Filed Under: Old Lyme, Outdoors, Top Story Stonewell Farm Hosts Two-Day Workshop on Dry Stone Wall Building, Sept  24, 25 September 13, 2016 by admin Leave a Comment Andrew Pighill’s work includes outdoor kitchens, wine cellars, fire-pits, fireplaces and garden features that include follies and other whimsical structures in stone 
KILLINGWORTH — On Sept  24 and 25, from 9 a m  to 4 p m  daily, Andrew Pighills, master stone mason, will teach a two-day, weekend long workshop on the art of dry stone wall building at Stonewell Farm in Killingworth, CT 
Participants will learn the basic principles of wall building, from establishing foundations, to the methods of dry laid (sometimes called dry-stacked) construction and ‘hearting’ the wall  This hands-on workshop will address not only the structure and principles behind wall building but also the aesthetic considerations of balance and proportion 
This workshop expresses Pighill’s commitment to preserve New England’s heritage and promote and cultivate the dry stone wall building skills that will ensure the preservation of our vernacular landscape 
This workshop is open to participants, 18 years of age or older, of all levels of experience  Note the workshop is limited to 16 participants, and spaces fill up quickly 
You must pre-register to attend the workshop  The price for the workshop is $350 per person  Stonewell Farm is located at 39 Beckwith Rd , Killingworth CT 06419
If you have any questions or to register for the workshop, contact the Workshop Administrator Michelle Becker at 860-322-0060 or mb@mbeckerco com
At the end of the day on Saturday you’ll be hungry, tired and ready for some rest and relaxation, so the wood-fired Stone pizza oven will be fired up and beer, wine and Pizza Rustica will be served 
About the instructor: Born in Yorkshire, England, Andrew Pighills is an accomplished stone artisan, gardener and horticulturist  He received his formal horticulture training with The Royal Horticultural Society and has spent 40+ years creating gardens and building dry stone walls in his native England in and around the spectacular Yorkshire Dales and the English Lake District  Today, Pighills is one of a small, but dedicated group of US-based, certified, professional members of The Dry Stone Walling Association (DSWA) of Great Britain  Having moved to the United States more than 10 years ago, he now continues this venerable craft here in the US, building dry stone walls, stone structures and creating gardens throughout New England and beyond 
His particular technique of building walls adheres to the ancient methods of generations of dry stone wallers in his native Yorkshire Dales  Pighills’ commitment to preserving the integrity and endurance of this traditional building art has earned him a devoted list of private and public clients here and abroad including the English National Trust, the English National Parks, and the Duke of Devonshire estates  His stone work has been featured on British and American television, in Charles McCraven’s book The Stone Primer, and Jeffrey Matz’s Midcentury Houses Today, A study of residential modernism in New Canaan Connecticut  He has featured in the N Y Times, on Martha Stewart Living radio, and in the Graham Deneen film short “Dry Stone”, as well as various media outlets both here and in the UK, including an article in the Jan/Feb 2015 issue of Yankee Magazine 
Pighills is a DSWA fully qualified dry stone walling instructor  In addition to building in stone and creating gardens, Pighills teaches dry stone wall building workshops in and around New England  He is a frequent lecturer on the art of dry stone walling, and how traditional UK walling styles compare to those found in New England  His blog, Heave and Hoe; A Day in the Life of a Dry Stone Waller and Gardener, provides more information about Pighills 
For more information, visit www englishgardensandlandscaping com
Filed Under: Outdoors CT Port Authority Chair Tells Lower CT River Local Officials, “We’re All on One Team” August 27, 2016 by Olwen Logan 2 Comments Enjoying a boat ride on the Connecticut River, but still finding time for discussions, are (from left to right) Chester First Selectwoman Lauren Gister, Old Lyme First Selectwoman and Connecticut Port Authority (CPA) board member Bonnie Reemsnyder, Essex First Selectman Norm Needleman, CPA Chairman Scott Bates and Deep River First Selectman Angus McDonald, Jr 
Filed Under: Chester, Deep River, Essex, News, Old Lyme, Outdoors, Politics, Top Story House Approves Courtney-Sponsored Amendment Restricting Sale of Plum Island July 10, 2016 by admin 2 Comments Representative Joe Courtney
Local Congressional Representative Joe Courtney (CT-02) announced Thursday (July 7) that a bipartisan amendment he had led, along with Representatives Rosa DeLauro (CT-03), Lee Zeldin (R-NY) and Peter King (R-NY), to prohibit the sale of Plum Island was passed by the House of Representatives 
The amendment, which will prohibit the General Services Administration (GSA) from using any of its operational funding to process or complete a sale of Plum Island, was made to the Financial Services and General Government Appropriations Act of 2017  
In a joint statement, the Representatives said, “Our amendment passed today is a big step toward permanently protecting Plum Island as a natural area  Plum Island is a scenic and biological treasure located right in the middle of Long Island Sound  It is home to a rich assortment of rare plant and animal species that need to be walled off from human interference ”
The statement continued, “Nearly everyone involved in this issue agrees that it should be preserved as a natural sanctuary – not sold off to the highest bidder for development ” Presumptive Republican Presidential nominee Donald Trump had shown interest in the property at one time 
In 2008, the federal government announced plans to close the research facility on Plum Island and relocate to Manhattan, Kansas  Current law states that Plum Island must be sold publicly to help finance the new research facility 
Aerial view of Plum Island 
The lawmakers joint statement explained, “The amendment will prevent the federal agency in charge of the island from moving forward with a sale by prohibiting it from using any of its operational funding provided by Congress for that purpose,” concluding, ” This will not be the end of the fight to preserve Plum Island, but this will provide us with more time to find a permanent solution for protecting the Island for generations to come ”
For several years, members from both sides of Long Island Sound have been working in a bipartisan manner to delay and, ultimately, repeal the mandated sale of this ecological treasure  Earlier this year, the representatives, along with the whole Connecticut delegation, cosponsored legislation that passed the House unanimously to delay the sale of Plum Island 
Filed Under: Outdoors July 1 Update: Aquatic Treatment Planned for Rogers Lake, July 5 July 1, 2016 by admin Leave a Comment We received this updated information from the Old Lyme Selectman’s office at 11:05 a m  this morning:
Filed Under: Lyme, Old Lyme, Outdoors, Town Hall They’re Everywhere! All About Gypsy Moth Caterpillars — Advice from CT Agricultural Experiment Station June 2, 2016 by Adina Ripin Leave a Comment Gypsy moth caterpillars – photo by Peter Trenchard, CAES 
The potential for gypsy moth outbreak exists every year in our community 
Dr  Kirby Stafford III, head of the Department of Entomology at the Connecticut Agricultural Experiment Station, has written a fact sheet on the gypsy moth available on the CAES website  The following information is from this fact sheet 
The gypsy moth, Lymantria dispar, was introduced into the US (Massachusetts) by Etienne Leopold Trouvelot in about 1860  The escaped larvae led to small outbreaks in the area in 1882, increasing rapidly  It was first detected in Connecticut in 1905  By 1952, it had spread to 169 towns  In 1981, 1 5 million acres were defoliated in Connecticut  During the outbreak of 1989, CAES scientists discovered that an entomopathogenic fungus, Entomophaga maimaiga, was killing the caterpillars  Since then the fungus has been the most important agent suppressing gypsy moth activity 
The fungus, however, cannot prevent all outbreaks and hotspots have been reported in some areas, in 2005-06 and again in 2015 
The life cycle of the gypsy moth is one generation a year  Caterpillars hatch from buff-colored egg masses in late April to early May  An egg mass may contain 100 to more than 1000 eggs and are laid in several layers  The caterpillars (larvae) hatch a few days later and ascend the host trees and begin to feed on new leaves  The young caterpillars, buff to black-colored, lay down silk safety lines as they crawl and, as they drop from branches on these threads, they may be picked up on the wind and spread 
There are four or five larval stages (instars) each lasting 4-10 days  Instars 1-3 remain in the trees  The fourth instar caterpillars, with distinctive double rows of blue and red spots, crawl up and down the tree trunks feeding mainly at night  They seek cool, shaded protective sites during the day, often on the ground  If the outbreak is dense, caterpillars may feed continuously and crawl at any time 
With the feeding completed late June to early July, caterpillars seek a protected place to pupate and transform into a moth in about 10-14 days  Male moths are brown and fly  Female moths are white and cannot fly despite having wings  They do not feed and live for only 6-10 days  After mating, the female will lay a single egg mass and die  The egg masses can be laid anywhere: trees, fence posts, brick/rock walls, outdoor furniture, cars, recreational vehicles, firewood  The egg masses are hard  The eggs will survive the winter and larvae hatch the following spring during late April through early May 
The impact of the gypsy moth can be extensive since the caterpillar will feed on a wide diversity of trees and shrubs  Oak trees are their preferred food  Other favored tree species include apple, birch, poplar and willow  If the infestation is heavy, they will also attack certain conifers and other less favored species  The feeding causes extensive defoliation 
Healthy trees can generally withstand one or two partial to one complete defoliation  Trees will regrow leaves before the end of the summer  Nonetheless, there can be die-back of branches  Older trees may become more vulnerable to stress after defoliation  Weakened trees can also be attacked by other organisms or lack energy reserves for winter dormancy and growth during the following spring  Three years of heavy defoliation may result in high oak mortality 
The gypsy moth caterpillars drop leaf fragments and frass (droppings) while feeding creating a mess for decks, patios, outdoor furniture, cars and driveways  Crawling caterpillars can be a nuisance and their hairs irritating  The egg masses can be transported by vehicles to areas where the moth is not yet established  Under state quarantine laws, the CAES inspects certain plant shipments destined to areas free of the gypsy moth, particularly for egg masses 
There are several ways to manage the gypsy moth: biological, physical and chemical 
Biologically, the major gypsy moth control agent has been the fungus E  maimaiga  This fungus can provide complete control of the gypsy moth but is dependent on early season moisture from rains in May and June to achieve effective infection rates and propagation of the fungus to other caterpillars  The dry spring of 2015 resulted in little or no apparent fungal inoculation or spread until it killed late-stage caterpillars in some areas of the state, after most defoliation 
Infected caterpillars hang vertically from the tree trunk, head down  Some die in an upside down “V” position, a characteristic of caterpillars killed by the less common gypsy moth nucleopolyhedrosis virus (NPV)  This was not detected in caterpillars examined in 2015 
Physical controls include removing and destroying egg masses, which can be drowned in a soapy water and disposed of  Another method is to use burlap refuge/barrier bands wrapped around tree trunks so that migrating caterpillars will crawl into or under the folded burlap or be trapped by the sticky band 
There are a number of crop protection chemicals labeled for the control of gypsy moth on ornamental trees and shrubs  There are treatments for egg masses, larvae and adult moths  Detailed information about these chemical treatments is available in the CAES factsheet 
For complete information about the gypsy moth and its management, visit the CAES website and look for the fact sheet on gypsy moth 
Filed Under: News, Outdoors East Lyme Public Trust Invites Community to Celebrate Boardwalk Re-dedication May 25, 2016 by admin Leave a Comment On Saturday, May 28, at 11 a m , the East Lyme Public Trust Foundation, in co-operation with East Lyme Parks and Recreation Department, will sponsor A Dream Fulfilled, the official re-dedication of the East Lyme Boardwalk  The re-dedication ceremony, which will be held on the Boardwalk, will feature keynote speaker, Sen  Paul Formica, former First Selectman of East Lyme 
Other speakers will include East Lyme First Selectman Mark Nickerson, Public Trust President Joe Legg, Public Trust Past-President Bob DeSanto, Public Trust Vice-President John Hoye, and Parks and Recreation Director Dave Putnam; all the speakers will recognize the many people who have helped made this dream a reality 
The East Lyme Public Trust Foundation would like to invite the general public to witness this historic occasion  In addition, the members would especially like to encourage the participation of the 200 people who dedicated benches and the innumerable people who sponsored plaques  They would also love to welcome all members of the Trust – past and present – and all those who originally helped make the Boardwalk a reality 
Participants should enter the Boardwalk at Hole-in-the Wall on Baptist Lane, Niantic  Then, there will be a short walk to the area of the monument where the ceremony will take place  At the entrance to Hole-in-the Wall, the Public Trust will have a display of historical information and memorabilia related to the construction and re-construction of the Boardwalk  Public Trust members, Pat and Jack Lewis will be on hand to host the exhibit titled Before and After and to welcome participants  After the ceremony, participants will have the opportunity to visit “their bench” and re-visit “their plaque ” During and after the dedication, music will be provided by Trust member, Bill Rinoski, who is a “D J  for all occasions ” Rinoski will feature “Boardwalk-related” music and Oldies plus Top 40 selections  This historic occasion will be videotaped as a public service by Mike Rydene of Media Potions of East Lyme  High school volunteers will be on hand to greet participants and help with directions 
The organizing committee is chaired by Michelle Maitland  Her committee consists of Joe Legg, President of the East Lyme Public Trust, Carol Marelli, Bob and Polly DeSanto, June Hoye, and Kathie Cassidy 
Visit Facebook – East Lyme Public Trust Foundation – for more information on the re-dedication ceremony  For more information on the Boardwalk, explore this website 
Filed Under: Outdoors Lyme Land Trust Seeks to Preserve Whalebone Cove Headwaters May 8, 2016 by admin Leave a Comment Lyme Land Trust Preservation Vice President Don Gerber stands with Chairman Anthony Irving (kneeling) next to Whalebone Creek in the proposed Hawthorne Preserve in Hadlyme 
The Lyme Land Conservation Trust has announced a fund raising drive to protect 82 acres of ecologically strategic upland forest and swamp wildlife habitat in Hadlyme on the headwaters of Whalebone Cove, one of the freshwater tidal wetlands that comprises the internationally celebrated Connecticut River estuary complex 
The new proposed preserve is part of a forested landscape just south of Hadlyme Four Corners and Ferry Road (Rt  148), and forms a large part of the watershed for Whalebone Creek, a key tributary feeding Whalebone Cove, most of which is a national wildlife refuge under the management of the US Fish & Wildlife Service 
The Land Trust said it hopes to name the new nature refuge in honor of William Hawthorne of Hadlyme, whose family has owned the property for several generations and who has agreed to sell the property to the Land Trust at a discount from its market value if the rest of the money necessary for the purchase can be raised by the Land Trust 
“This new wildlife preserve will represent a triple play for habitat conservation,” said Anthony Irving, chairman of the Land Trust’s Preservation Committee 
“First, it helps to protect the watershed feeding the fragile Whalebone Cove eco-system, which is listed as one of North America’s important freshwater tidal marshes in international treaties that cite the Connecticut River estuary as a wetland complex of global importance  Whalebone Creek, one of the primary streams feeding Whalebone Cove, originates from vernal pools and upland swamps just south of the Hawthorne tract on the Land Trust’s Ravine Trail Preserve and adjacent conservation easements and flows through the proposed preserve  Virtually all of the Hawthorne property comprises much of the watershed for Whalebone Creek 
“Second, the 82 acres we are hoping to acquire with this fund raising effort represents a large block of wetlands and forested wildlife habitat between Brush Hill and Joshuatown roads, which in itself is home to a kaleidoscope of animals from amphibians and reptiles that thrive in several vernal pools and swamp land, to turkey, coyote, bobcat and fisher  It also serves as seasonal nesting and migratory stops for several species of deep woods birds, which are losing habitat all over Connecticut due to forest fragmentation 
“Third, this particular preserve will also conserve a key link in the wildlife corridors that connects more than 1,000 acres of protected woodland and swamp habitat in the Hadlyme area ” Irving explained that the preserve is at the center of a landscape-scale wildlife habitat greenway that includes Selden Island State Park, property of the US Fish & Wild Life’s Silvio O Conte Wildlife Refuge, The Nature Conservancy’s Selden Preserve, and several other properties protected by the Lyme Land Conservation Trust 
“Because of its central location as a hub between these protected habitat refuges,” said Irving, “this preserve will protect forever the uninterrupted access that wildlife throughout the Hadlyme landscape now has for migration and breeding between otherwise isolated communities and families of many terrestrial species that are important to the continued robust bio-diversity of southeastern Connecticut and the Connecticut River estuary ”
Irving noted that the Hawthorne property is the largest parcel targeted for conservation in the Whalebone Cove watershed by the recently developed US Fish & Wildlife Service Silvio O Conte Wildlife Refuge Comprehensive Conservation Plan  Irving said the Land Trust hopes to create a network of hiking trails on the property with access from both Brush Hill Road on the east and Joshuatown Road on the west and connection to the Land Trust’s Ravine Trail to the south and the network of trails on the Nature Conservancy’s Selden Preserve 
Irving said there is strong support for the Land Trust’s proposal to preserve the property both within the Hadlyme and Lyme communities and among regional and state conservation groups  He noted letters of support have come from the Hadlyme Garden Club, the Hadlyme Public Hall Association, the Lyme Inland Wetlands & Watercourses Agency, the Lyme Planning and Zoning Commission, the Lyme Open Space Committee, the Lower Connecticut River Valley Council of Governments, the Lyme Garden Club, the Lyme Public Hall, The Nature Conservancy, The Silvio O Conte Refuge, the Connecticut River Watershed Council, and the Friends of Whalebone Cove, Inc 
He reported that between Hawthorne’s gift and several other pledges the Land Trust has already received commitments of 25 percent of the cost of the property 
Filed Under: Lyme, Outdoors, Top Story, vnn Old Lyme Tree Commission Celebrates Arbor Day April 29, 2016 by admin Leave a Comment Members of the three groups gather around the new oak tree  From left to right are Kathy Burton, Joanne DiCamillo, Joan Flynn  Anne Bing, Emily Griswold and Barbara Rayel 
Filed Under: Old Lyme, Outdoors, Top Story, Town Hall Enjoy a Tour of Private Gardens in Essex, June 4 April 28, 2016 by Adina Ripin Leave a Comment See this beautiful private garden in Essex on June 4 
ESSEX – On Saturday, June 4, from 10 a m  to 3 p m , plan to stroll through eight of the loveliest and most unusual private gardens in Essex  Some are in the heart of Essex Village while others are hidden along lanes most visitors never see  While exploring, you will find both formal and informal settings, lovely sweeping lawns and panoramic views of the Connecticut River or its coves  One garden you will visit is considered to be a ‘laboratory’ for cultivation of native plants  Master Gardeners will be available to point out specific features, offer gardening tips, and answer questions 
The garden tour is sponsored by the Friends of the Essex Library  Tickets are $25 in advance and $30 at the Essex Library the day of the event  Cash, checks, Visa or Master Card will be accepted  Tickets can be reserved by visiting the library or by completing the form included in flyers available at the library and throughout Essex beginning May 2  Completed forms can be mailed to the library  Confirmations will be sent to the email addresses on the completed forms 
Your ticket will be a booklet containing a brief description of each garden along with a map of the tour and designated parking  Tickets must be picked up at the library beginning at 9:45 a m  the day of the event 
Richard Conroy, library director, has said, “The Essex Library receives only about half of its operating revenue from the Town  The financial assistance we receive each year from the Friends is critical  It enables us to provide important resources such as Ancestry com and museum passes, as well as practical improvements like the automatic front doors that were recently installed  I urge you to help your Library by helping our Friends make this event a success! Thank you for your support ”
The tour will take place rain or shine  For more information, call 860-767-1560  All proceeds will benefit Friends of the Essex Library 
Filed Under: Outdoors Potapaug Presents Plum Island Program April 7, 2016 by admin Leave a Comment Potapaug Audubon presents “Preserving Plum Island” on Thursday, April 7, at 7 p m  at Old Lyme Town Hall, 52 Lyme St , Old Lyme, with guest speaker Chris Cryder, from the Preserve Plum Island Coalition 
Cryder will discuss the efforts to protect the island, which provides vital habitat for threatened and endangered birds 
This is a free program and all are welcome 
Filed Under: Old Lyme, Outdoors CT Legislators Support Study to Preserve Plum Island From Commercial Development March 28, 2016 by Jerome Wilson 1 Comment Aerial view of Plum Island lighthouse  (From Preserve Plum Island website)
Last Thursday, March 24, at a press conference in Old Saybrook, a triumvirate of Congressional legislators from Connecticut, State Senator Richard Blumenthal and US Representatives Joe Courtney (D-2nd District) and Rosa DeLauro (D-3rd District) confirmed their support for a study to determine the future of Plum Island located in Long Island Sound 
Members of the Plum Island Coalition — which has some 65 member organizations all dedicated to preserving the island — were in attendance to hear the good news 
The island still houses a high-security, federal animal disease research facility, but the decision has already been taken to move the facility to a new location in Kansas with an opening slated for 2022  The current facility takes up only a small percentage of the land on the island and significantly for environmentalists, the remainder of the island has for years been left to nature in the wild 
In supporting a federal study on the future of Plum Island, Sen  Blumenthal said, “This study is a step towards saving a precious, irreplaceable national treasure from developers and polluters  It will provide the science and fact-based evidence to make our case for stopping the current Congressional plan to sell Plum Island to the highest bidder ” He continued, “The stark truth is the sale of Plum Island is no longer necessary to build a new bioresearch facility because Congress has fully appropriated the funds  There is no need for this sale – and in fact, Congress needs to rescind the sale ” Congress, however, still has a law on the books that authorizes the sale of Plum Island land to the highest bidder  Therefore, opponents of the sale will have the burden of convincing Congress to change a law that is currently in place 
Filed Under: Old Lyme, Outdoors, Top Story, vnn Land Trusts’ Photo Contest Winners Announced March 24, 2016 by admin Leave a Comment Winner of the top prize, the John G  Mitchell Environmental Conservation Award – Hank Golet
The 10th Annual Land Trust’s Photo Contest winners were announced at a March 11 reception highlighting the winning photos and displaying all entered photos  Land trusts in Lyme, Old Lyme, Salem, Essex and East Haddam jointly sponsor the annual amateur photo contest to celebrate the scenic countryside and diverse wildlife and plants in these towns  The ages of the photographers ranged from children to senior citizens 
Hank Golet won the top prize, the John G  Mitchell Environmental Conservation Award, with his beautiful photograph of a juvenile yellow crowned night heron in the Black Hall River in Old Lyme  Alison Mitchell personally presented the award, created in memory of her late husband John G  Mitchell, an editor at National Geographic, who championed the cause of the environment 
William Burt, a naturalist and acclaimed wildlife photographer, who has been a contest judge for ten years, received a special mention  Judges Burt; Amy Kurtz Lansing, an accomplished art historian and curator at the Florence Griswold Museum; and Skip Broom, a respected, award-winning local photographer and antique house restoration housewright, chose the winning photographs from 219 entries 
The sponsoring land trusts – Lyme Land Conservation Trust, Essex Land Trust, the Old Lyme Land Trust, Salem Land Trust, and East Haddam Land Trust – thank the judges as well as generous supporters RiverQuest/ CT River Expeditions, Lorensen Auto Group, the Oakley Wing Group at Morgan Stanley, Evan Griswold at Coldwell Banker, Ballek’s Garden Center, Essex Savings Bank, Chelsea Groton Bank, and Alison Mitchell in honor of her late husband John G  Mitchell  Big Y and Fromage Fine Foods & Coffee provided support for the reception 
The winning photographers are:
John G  Mitchell Environmental Award, Hank Golet, Old Lyme
1st: Patrick Burns, East Haddam
2nd: Judah Waldo, Old Lyme
3rd: James Beckman, Ivoryton
Honorable Mention Gabriel Waldo, Old Lyme
Honorable Mention Sarah Gada, East Haddam
Honorable Mention Shawn Parent, East Haddam
Cultural/Historic
1st: Marcus Maronne, Mystic
2nd: Normand L  Charlette, Manchester
3rd: Tammy Marseli, Rocky Hill
Honorable Mention Jud Perkins, Salem
Honorable Mention Pat Duncan, Norwalk
Honorable Mention John Kolb, Essex
Landscapes/Waterscapes
1st: Cheryl Philopena, Salem
2nd: Marian Morrissette, New London
3rd: Harcourt Davis, Old Lyme
Honorable Mention Cynthia Kovak, Old Lyme
Honorable Mention Bopha Smith, Salem
1st: Mary Waldron, Old Lyme
2nd: Courtney Briggs, Old Saybrook
3rd: Linda Waters, Salem
Honorable Mention Pete Govert, East Haddam
Honorable Mention Marcus Maronne, Mystic
Honorable Mention Marian Morrissette, New London
First place winner of the Wildlife category – Chris Pimley
1st: Chris Pimley, Essex
2nd: Harcourt Davis, Old Lyme
Honorable Mention Thomas Nemeth, Salem
Honorable Mention Jeri Duefrene, Niantic
Honorable Mention Elizabeth Gentile, Old Lyme
The winning photos will be on display at the Lymes’ Senior Center for the month of March and Lyme Public Library in April  For more information go to lymelandtrust org 
Filed Under: Outdoors Old Lyme’s Open Space Commission Hosts Talk on Sea Level Rise, Salt Marsh Advance March 11, 2016 by admin 1 Comment The Town of Old Lyme’s Open Space Commission invites all interested parties to a workshop by Adam Whelchel, PhD, Director of Science at The Nature Conservancy’s Connecticut Chapter  The workshop will be held on Friday, March 11, at 9 a m  in the Old Lyme Town Hall 
Filed Under: Outdoors, Town Hall Inaugural Meeting of ‘Friends of Whalebone Cove’ Held, Group Plans to Protect Famous Tidal Wetland March 7, 2016 by admin Leave a Comment The newly formed ‘Friends of Whalebone Cove’ are working to preserve and protect the Cove’s fragile ecosystem 
A new community conservation group to protect Whalebone Cove, a freshwater tidal marsh along the Connecticut river in Hadlyme recognized internationally for its wildlife habitat, will hold its first organizational meeting this coming Sunday, March 6, at 4 p m 
Calling the group “Friends of Whalebone Cove” (FOWC), the organizers say their purpose is to “create a proactive, community-based constituency whose mission is to preserve and protect the habitat and fragile eco-systems of Whalebone Cove ”
Much of Whalebone Cove is a nature preserve that is part of the Silvio O  Conte National Wildlife Refuge (www fws gov/refuge/silvio_o_conte) under the jurisdiction of the U S  Fish & Wildlife Service (USFW)  The Refuge owns and manages 116 acres of marshland in Whalebone Cove and upland along its shores 
Prior to being taken over by USFW, the Whalebone Cove preserve was under the protection of The Nature Conservancy 
As part of the Connecticut River estuary, the Cove is listed in the Ramsar Convention on International Wetlands (www ramsar org) as tidal marshlands on the Connecticut River that constitute a “wetlands complex of international importance ”
The Ramsar citation specifically notes that Whalebone Cove has one of the largest stands of wild rice in the state  Except at high tide, most of the Cove is open marshland covered by wild rice stands with relatively narrow channels where Whalebone Creek winds its way through the Cove to the main stem of the Connecticut River 
Brian Slater, one of the group’s leaders who is filing the incorporation documents creating FOWC, said the creation of the organization was conceived by many of those living around the Cove and others in the Hadlyme area because of increased speeding motor boat and jet ski traffic in the Cove in recent years, damaging wetland plants and disrupting birds and other wildlife that make the Cove their home 
Slater said “Our goal is to develop a master plan for protection of the Cove through a collaborative effort involving all those who have a stake in Whalebone Cove – homeowners along its shores and those living nearby, the Silvio O  Conte Refuge, the Connecticut Department of Energy & Environmental Protection (DEEP), hunters, fishing enthusiasts, canoeing and kayaking groups, Audubon groups, the Towns of Lyme and East Haddam, The Nature Conservancy, the Connecticut River Watershed Council, the Lyme Land Conservation Trust, the Connecticut River Gateway Commission, and others who want to protect the Cove ”
“Such a plan”, said Slater, “should carefully evaluate the habitat, plants, wildlife and eco-systems of the Cove and the surrounding uplands and watershed and propose an environmental management plan that can be both implemented and enforced by those entrusted with stewarding the Cove and its fragile ecosystems for the public trust ”
FOWC has written a letter to Connecticut DEEP Commissioner Rob Klee asking that he appoint a blue ribbon commission to conduct the research and develop the management plan  FOWC also asked that Commissioner Klee either deny or defer approval on any applications for new docks in the Cove until the management plan can be developed and implemented  Currently there are no docks in the Cove 
“We are very concerned that the installation of docks permitted for motor boat use will greatly increase the amount of motorized watercraft in the Cove,” said Slater  “There’s already too much jet ski and speeding motorboat traffic in the Cove  Those living on the Cove have even seen boats towing water skiers crisscrossing the wild rice plants at high tide  Something has to be done to protect the birds and marine life that give birth and raise their young in the Cove ”
Slater urged all those “who treasure Whalebone Cove and the many species of birds, turtles, fish, reptiles, amphibians, beaver, and rare flora and fauna that make their home in it to attend the meeting, whether they live in the Hadlyme area or beyond ”
Expected to be at the meeting will be representatives from USFW, DEEP, the Connecticut River Watershed Council, and several other conservation organizations 
The meeting will be held at Hadlyme Public Hall, 1 Day Hill Rd , in Lyme, which is at the intersection of Ferry Rd  (Rte  148), Joshuatown Rd , and Day Hill Rd  Representatives from the Silvio O  Conte Refuge will make a short presentation on the history and mission of the Conte Refuge system, which includes nature preserves throughout the Connecticut River Valley in four states 
For more information, call 860-322-4021 or email fowchadlyme@gmail com
Filed Under: Lyme, News, Outdoors Next Page »



ground_truth: This research paper proposed an approach based on approximating the posterior distribution with an isotropic Gaussian distribution.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the group's request to the Connecticut DEEP Commissioner?

Read the following text and answer briefly.

Context 4:  The magnetic field is applied in the film plane  The inset shows the temperature dependence of a sample grown at 130$^{\circ}$C and annealed at 650$^{\circ}$C for 15 minutes  After annealing, the magnetic signal mostly arises from Ge$_{3}$Mn$_{5}$ clusters  (b) ZFC-FC measurements performed on Ge$_{0 93}$Mn$_{0 07}$ samples for different growth temperatures  The in-plane applied field is 0 015 T  The ZFC peak at low temperature ($\leq$150 K) can be attributed to the superparamagnetic nanocolumns  This peak widens and shifts towards high blocking temperatures when increasing growth temperature  The second peak above 150 K in the ZFC curve which increases with increasing growth temperature is attributed to superparamagnetic Ge$_{3}$Mn$_{5}$ clusters  The increasing ZFC-FC irreversibility at $\approx$ 300 K is due to the increasing contribution from large ferromagnetic Ge$_{3}$Mn$_{5}$ clusters  The nanocolumns signal completely vanishes after annealing at 650$^{\circ}$C for 15 minutes }
\label{fig7}
\end{figure}

In Fig  7a, the saturation magnetization at 2 Tesla in $\mu_{B}$/Mn of Ge$_{1-x}$Mn$_{x}$ films with 7 \% of Mn is plotted as a function of temperature for different growth temperatures ranging from $T_{g}$=90$^{\circ}$C up to 160$^{\circ}$C  The inset shows the temperature dependence of the magnetization at 2 Tesla after annealing at 650$^{\circ}$C during 15 minutes  Figure 7b displays the corresponding Zero Field Cooled - Field Cooled (ZFC-FC) curves recorded at 0 015 Tesla  In the ZFC-FC procedure, the sample is first cooled down to 5 K in zero magnetic field and the susceptibility is subsequently recorded at 0 015 Tesla while increasing the temperature up to 400 K (ZFC curve)  Then, the susceptibility is recorded under the same magnetic field while decreasing the temperature down to 5 K (FC curve)  Three different regimes can be clearly distinguished  \\
For $T_{g}\leq$120$^{\circ}$C, the temperature dependence of the saturation magnetization remains nearly the same while increasing growth temperature  The overall magnetic signal vanishing above 200 K is attributed to the nanocolumns whereas the increasing signal below 50 K originates from diluted Mn atoms in the surrounding matrix  The Mn concentration dependence of the saturation magnetization is displayed in figure 8  For the lowest Mn concentration (4 \%), the contribution from diluted Mn atoms is very high and drops sharply for higher Mn concentrations (7 \%, 9 \% and 11 3 \%)  Therefore the fraction of Mn atoms in the diluted matrix decreases with Mn concentration probably because Mn atoms are more and more incorporated in the nanocolumns  In parallel, the Curie temperature of nanocolumns increases with the Mn concentration reaching 170 K for 11 3 \% of Mn  This behavior may be related to different Mn compositions and to the increasing diameter of nanocolumns (from 1 8 nm to 2 8 nm) as discussed in section \ref{structural} 

\begin{figure}[htb]
\center
   \includegraphics[width= 7\linewidth]{ /fig8 eps}
    \caption{Temperature dependence of the saturation magnetization (in $\mu_{B}$/Mn) of Ge$_{1-x}$Mn$_{x}$ films grown at 100$^{\circ}$C plotted for different Mn concentrations: 4 1 \%; 7 \%; 8 9 \% and 11 3 \% }
\label{fig8}
\end{figure}

ZFC-FC measurements show that the nanocolumns are superparamagnetic  The magnetic signal from the diluted Mn atoms in the matrix is too weak to be detected in susceptibility measurements at low temperature  In samples containing 4 \% of Mn, ZFC and FC curves superimpose down to low temperatures  As we do not observe hysteresis loops at low temperature, we believe that at this Mn concentration nanocolumns are  superparamagnetic in the whole temperature range and the blocking temperature cannot be measured  For higher Mn contents, the ZFC curve exhibits a very narrow peak with a maximum at the blocking temperature of 15 K whatever the Mn concentration and growth temperature (see Fig  7b)  Therefore the anisotropy barrier distribution is narrow and assuming that nanocolumns have the same magnetic anisotropy, this is a consequence of the very narrow size distribution of the nanocolumns as observed by TEM  To probe the anisotropy barrier distribution, we have performed ZFC-FC measurements but instead of warming the sample up to 400 K, we stopped at a lower temperature $T_{0}$  

\begin{figure}[htb]
\center
   \includegraphics[width= 6\linewidth]{ /fig9 eps}
\caption{Schematic drawing of the anisotropy barrier distribution n($E_{B}$) of superparamagnetic nanostructures  If magnetic anisotropy does not depend on the particle size, this distribution exactly reflects their magnetic size distribution  In this drawing the blocking temperature ($T_{B}$) corresponds to the distribution maximum  At a given temperature $T_{0}$ such that 25$k_{B}T_{0}$ falls into the anisotropy barrier distribution, the largest nanostructures with an anisotropy energy larger than 25$k_{B}T_{0}$ are blocked whereas the others are superparamagnetic }
\label{fig9}
\end{figure}

If this temperature falls into the anisotropy barrier distribution as depicted in Fig  9, the FC curve deviates from the ZFC curve  Indeed the smallest nanostructures have become superparamagnetic at $T_{0}$ and when decreasing again the temperature, their magnetization freezes along a direction close to the magnetic field and the FC susceptibility is higher than the ZFC susceptibility  Therefore any irreversibility in this procedure points at the presence of superparamagnetic nanostructures  The results are given in Fig  10a  ZFC and FC curves clearly superimpose up to $T_{0}$=250 K thus the nanocolumns are superparamagnetic up to their Curie temperature and no Ge$_{3}$Mn$_{5}$ clusters could be detected  Moreover for low $T_{0}$ values, a peak appears at low temperature in FC curves which evidences strong antiferromagnetic interactions between the nanocolumns \cite{Chan00} 

\begin{figure}[htb]
\center
    \includegraphics[width= 35\linewidth]{ /fig10a eps}
    \includegraphics[width= 63\linewidth]{ /fig10b eps}
\caption{(a) ZFC-FC measurements performed on a Ge$_{0 887}$Mn$_{0 113}$ sample grown at 115$^{\circ}$C  The in-plane applied field is 0 015 T  Magnetization was recorded up to different T$_{0}$ temperatures: 30 K, 50 K, 100 K, 150 K, 200 K and 250 K  Curves are shifted up for more clarity  (b) ZFC-FC curves for in-plane and out-of-plane applied fields (0 015 T) }
\label{fig10}
\end{figure}

In order to derive the magnetic size and anisotropy of the Mn-rich nanocolumns embedded in the Ge matrix, we have fitted the inverse normalized in-plane (resp  out-of-plane) susceptibility: $\chi_{\parallel}^{-1}$ (resp  $\chi_{\perp}^{-1}$)  The corresponding experimental ZFC-FC curves are reported in Fig  10b  Since susceptibility measurements are performed at low field (0 015 T), the matrix magnetic signal remains negligible  In order to normalize susceptibility data, we need to divide the magnetic moment by the saturated magnetic moment recorded at 5 T  However the matrix magnetic signal becomes very strong at 5 T and low temperature so that we need to subtract it from the saturated magnetic moment using a simple Curie function  From Fig  10b, we can conclude that nanocolumns are isotropic  Therefore to fit experimental data we use the following expression well suited for isotropic systems or cubic anisotropy: $\chi_{\parallel}^{-1}= \chi_{\perp}^{-1}\approx 3k_{B}T/M(T)+\mu_{0}H_{eff}(T)$  $k_{B}$ is the Boltzmann constant, $M=M_{s}v$ is the magnetic moment of a single-domain nanostructure (macrospin approximation) where $M_{s}$ is its magnetization and $v$ its volume  The in-plane magnetic field is applied along $[110]$ or $[-110]$ crystal axes  Since the nanostructures Curie temperature does not exceed 170 K, the temperature dependence of the saturation magnetization is also accounted for by writting $M(T)$  Antiferromagnetic interactions between nanostructures are also considered by adding an effective field estimated in the mean field approximation \cite{Fruc02}: $\mu_{0}H_{eff}(T)$ 
The only fitting parameters are the maximum magnetic moment (\textit{i e } at low temperature) per nanostructure: $M$ (in Bohr magnetons $\mu_{B}$) and the maximum interaction field (\textit{i e } at low temperature): $\mu_{0}H_{eff}$ 

\begin{figure}[htb]
\center
   \includegraphics[width= 7\linewidth]{ /fig11 eps}
\caption{Temperature dependence of the inverse in-plane (open circles) and out-of-plane (open squares) normalized susceptibilities of a Ge$_{0 887}$Mn$_{0 113}$ sample grown at 115$^{\circ}$C  Fits were performed assuming isotropic nanostructures or cubic anisotropy  Dashed line is for in-plane susceptibility and solid line for out-of-plane susceptibility }
\label{fig11}
\end{figure}

In Fig  11, the best fits lead to $M\approx$1250 $\mu_{B}$ and $\mu_{0}H_{eff}\approx$102 mT for in-plane susceptibility and $M\approx$1600 $\mu_{B}$ and $\mu_{0}H_{eff}\approx$98 mT for out-of-plane susceptibility  It gives an average magnetic moment of 1425 $\mu_{B}$ per column and an effective interaction field of 100 mT  Using this magnetic moment and its temperature dependence, magnetization curves could be fitted using a Langevin function and $M(H/T)$ curves superimpose for $T<$100 K  However, from the saturated magnetic moment of the columns and their density (35000 $\rm{\mu m}^{-2}$), we find almost 6000 $\mu_{B}$ per column  Therefore, for low growth temperatures, we need to assume that nanocolumns are actually made of almost four independent elongated magnetic nanostructures  The effective field for antiferromagnetic interactions between nanostructures estimated from the susceptibility fits is at least one order of magnitude larger than what is expected from pure magnetostatic coupling  This difference may be due to either an additional antiferromagnetic coupling through the matrix which origin remains unexplained or to the mean field approximation which is no more valid in this strong coupling regime  As for magnetic anisotropy, the nanostructures behave as isotropic magnetic systems or exhibit a cubic magnetic anisotropy  First we can confirm that nanostructures are not amorphous otherwise shape anisotropy would dominate leading to out-of-plane anisotropy  We can also rule out a random distribution of magnetic easy axes since the nanostructures are clearly crystallized in the diamond structure and would exhibit at least a cubic anisotropy (except if the random distribution of Mn atoms within the nanostructures can yield random easy axes)  Since the nanostructures are in strong in-plane compression (their lattice parameter is larger than the matrix one), the cubic symmetry of the diamond structure is broken and magnetic cubic anisotropy is thus unlikely  We rather believe that out-of-plane shape anisotropy is nearly compensated by in-plane magnetoelastic anisotropy due to compression leading to a \textit{pseudo} cubic anisotropy  From the blocking temperature (15 K) and the magnetic volume of the nanostructures , we can derive their magnetic anisotropy constant using $Kv=25k_{B}T_{B}$: K$\approx$10 kJ m$^{-3}$ which is of the same order of magnitude as shape anisotropy 

\begin{figure}[htb]
\center
    \includegraphics[width= 35\linewidth]{ /fig12a eps}
    \includegraphics[width= 63\linewidth]{ /fig12b eps} 
\caption{(a) ZFC-FC measurements performed on a Ge$_{0 93}$Mn$_{0 07}$ sample grown at 122$^{\circ}$C  The in-plane applied field is 0 015 T  Magnetization was recorded up to different T$_{0}$ temperatures: 50 K, 100 K, 150 K, 200 K and 250 K  Curves are shifted up for more clarity  (b) ZFC-FC curves for in-plane and out-of-plane applied fields  (0 015 T) }
\label{fig12}
\end{figure}

For growth temperatures $T_{g}\geq$120$^{\circ}$C and Mn concentrations $\geq$ 7 \%, samples exhibit a magnetic signal above 200 K corresponding to Ge$_{3}$Mn$_{5}$ clusters (see Fig  7a)  As we can see, SQUID measurements are much more sensitive to the presence of Ge$_{3}$Mn$_{5}$ clusters, even at low concentration, than TEM and x-ray diffraction used in section \ref{structural}  We also observe a sharp transition in the ZFC curve (see Fig  7b, Fig  12a and 12b): the peak becomes very large and is shifted towards high blocking temperatures (the signal is maximum at $T=$23 K)  This can be easily understood as a magnetic percolation of the four independent nanostructures obtained at low growth temperatures into a single magnetic nanocolumn  Therefore the magnetic volume increases sharply as well as blocking temperatures  At the same time, the size distribution widens as observed in TEM  In Fig  12a, we have performed ZFC-FC measurements at different $T_{0}$ temperatures  The ZFC-FC irreversibility is observed up to the Curie temperature of $\approx$120 K meaning that a fraction of nanocolumns is ferromagnetic (\textit{i e } $T_{B}\geq T_{C}$) 
In Fig  12b, in-plane and out-of-plane ZFC curves nearly superimpose for $T\leq$150 K due to the isotropic magnetic behavior of the nanocolumns: in-plane magnetoelastic anisotropy is still compensating out-of-plane shape anisotropy  Moreover the magnetic signal above 150 K corresponding to Ge$_{3}$Mn$_{5}$ clusters that start to form in this growth temperature range is strongly anisotropic  This perpendicular anisotropy confirms the epitaxial relation: (0002) Ge$_{3}$Mn$_{5}$ $\parallel$ (002) Ge discussed in Ref \cite{Bihl06}  The magnetic easy axis of the clusters lies along the hexagonal $c$-axis which is perpendicular to the film plane 

\begin{figure}[ht]
\center
   \includegraphics[width= 35\linewidth]{ /fig13a eps}
   \includegraphics[width= 63\linewidth]{ /fig13b eps} 
\caption{(a) ZFC-FC measurements performed on a Ge$_{0 887}$Mn$_{0 113}$ sample grown at 145$^{\circ}$C  The in-plane applied field is 0 015 T  Magnetization was recorded up to different T$_{0}$ temperatures: 50 K, 100 K, 150 K, 200 K, 250 K and 300 K  Curves are shifted up for more clarity  (b) ZFC-FC curves for in-plane and out-of-plane applied fields (0 015 T) }
\label{fig13}
\end{figure}

For growth temperatures $T_{g}\geq$145$^{\circ}$C the cluster magnetic signal dominates (Fig  13b)  Superparamagnetic nanostructures are investigated performing ZFC-FC measurements at different $T_{0}$ temperatures (Fig  13a)  The first ZFC peak at low temperature \textit{i e } $\leq$ 150 K is attributed to  low-$T_{C}$ nanocolumns ($T_{C}\approx$130 K)  This peak is wider than for lower growth temperatures and its maximum is further shifted up to 30 K  These results are in agreement with TEM observations: increasing $T_{g}$ leads to larger nanocolumns (\textit{i e } higher blocking temperatures) and wider size distributions  ZFC-FC irreversibility is observed up to the Curie temperature due to the presence of ferromagnetic columns  The second peak above 180 K in the ZFC curve is attributed to Ge$_{3}$Mn$_{5}$ clusters and the corresponding ZFC-FC irreversibility persisting up to 300 K means that some clusters are ferromagnetic  We clearly evidence the out-of-plane anisotropy of Ge$_{3}$Mn$_{5}$ clusters and the isotropic magnetic behavior of nanocolumns (Fig  13b)  In this growth temperature range, we have also investigated the Mn concentration dependence of magnetic properties  

\begin{figure}[ht]
\center
    \includegraphics[width= 49\linewidth]{ /fig14a eps}
    \includegraphics[width= 49\linewidth]{ /fig14b eps} 
\caption{Temperature dependence of the saturation magnetization (in $\mu_{B}$/Mn) of Ge$_{1-x}$Mn$_{x}$ films grown at 150$^{\circ}$C plotted for different Mn concentrations: 2 3 \%; 4 \%; 7 \%; 9 \%; 11 3 \%  (b) ZFC-FC measurements performed on Ge$_{1-x}$Mn$_{x}$ films grown at 150$^{\circ}$C  The in-plane applied field is 0 025 T for 2 3 \% and 4 \% and 0 015 T for 8 \% and 11 3 \%  }
\label{fig14}
\end{figure}

In Fig  14a, for low Mn concentrations (2 3 \% and 4 \%) the contribution from diluted Mn atoms in the germanium matrix to the saturation magnetization is very high and nearly vanishes for higher Mn concentrations (7 \%, 9 \% and 13 \%) as observed for low growth temperatures  Above 7 \%, the magnetic signal mainly comes from nanocolumns and Ge$_{3}$Mn$_{5}$ clusters  We can derive more information from ZFC-FC measurements (Fig  14b)  Indeed, for 2 3 \% of Mn, ZFC and FC curves nearly superimpose down to low temperature meaning that nanocolumns are superparamagnetic in the whole temperature range  Moreover the weak irreversibility arising at 300 K  means that some Ge$_{3}$Mn$_{5}$ clusters have already formed in the samples even at very low Mn concentrations  For 4 \% of Mn, we can observe a peak with a maximum at the blocking temperature (12 K) in the ZFC curve  We can also derive the Curie temperature of nanocolumns: $\approx$45 K  The irresversibility arising at 300 K still comes from Ge$_{3}$Mn$_{5}$ clusters  Increasing the Mn concentration above 7 \% leads to: higher blocking temperatures (20 K and 30 K) due to larger nanocolumns and wider ZFC peaks due to wider size distributions in agreement with TEM observations (see Fig  3a)  Curie temperatures also increase (110 K and 130 K) as well as the contribution from Ge$_{3}$Mn$_{5}$ clusters \\
Finally when increasing $T_{g}$ above 160$^{\circ}$C, the nanocolumns magnetic signal vanishes and only Ge$_{3}$Mn$_{5}$ clusters and diluted Mn atoms coexist  The overall magnetic signal becomes comparable to the one measured on annealed samples in which only Ge$_{3}$Mn$_{5}$ clusters are observed by TEM (see Fig  7a) \\
The magnetic properties of high-$T_{C}$ nanocolumns obtained for $T_{g}$ close to 130$^{\circ}$C are discussed in detail in Ref \cite{Jame06} \\
In conclusion, at low growth temperatures ($T_{g}\leq$120$^{\circ}$C), nanocolumns are made of almost 4 independent elongated magnetic nanostructures  For $T_{g}\geq$120$^{\circ}$C, these independent nanostructures percolate into a single nanocolumn sharply leading to higher blocking temperatures  Increasing $T_{g}$ leads to larger columns with a wider size distribution as evidenced by ZFC-FC measurements and given by TEM observations  In parallel, some Ge$_{3}$Mn$_{5}$ clusters start to form and their contribution increases when increasing $T_{g}$  Results on magnetic anisotropy seems counter-intuitive  Indeed Ge$_{3}$Mn$_{5}$ clusters exhibit strong out-of-plane anisotropy whereas nanocolumns which are highly elongated magnetic structures are almost isotropic  This effect is probably due to compensating in-plane magnetoelastic coupling (due to the columns compression) and out-of-plane shape anisotropy  

\section{Conclusion}

In this paper, we have investigated the structural and magnetic properties of thin Ge$_{1-x}$Mn$_{x}$ films grown by low temperature molecular beam epitaxy  A wide range of growth temperatures and Mn concentrations have been explored  All the samples contain Mn-rich nanocolumns as a consequence of 2D-spinodal decomposition  However their size, crystalline structure and magnetic properties depend on growth temperature and Mn concentration  For low growth temperatures, nanocolumns are very small (their diameter ranges between 1 8 nm for 1 3 \% of Mn and 2 8 nm for 11 3 \% of Mn), their Curie temperature is rather low ($<$ 170 K) and they behave as almost four uncorrelated superparamagnetic nanostructures  Increasing Mn concentration leads to higher columns densities while diameters remain nearly unchanged  For higher growth temperatures, the nanocolumns mean diameter increases and their size distribution widens  Moreover the 4 independent magnetic nanostructures percolate into a single magnetic nanocolumn  Some columns are ferromagnetic even if Curie temperatures remain quite low  In this regime, increasing Mn concentration leads to larger columns while their density remains nearly the same  In parallel, Ge$_{3}$Mn$_{5}$ nanoclusters start to form in the film with their $c$-axis perpendicular to the film plane  In both temperature regimes, the Mn incorporation mechanism in the nanocolumns and/or in the matrix changes above 5 \% of Mn and nanocolumns exhibit an isotropic magnetic behaviour due to the competing effects of out-of-plane shape anisotropy and in-plane magnetoelastic coupling  Finally for a narrow range of growth temperatures around 130$^{\circ}$C, nanocolumns exhibit Curie temperatures higher than 400 K  Our goal is now to investigate the crystalline structure inside the nanocolumns, in particular the position of Mn atoms in the distorted diamond structure, which is essential to understand magnetic and future transport properties in Ge$_{1-x}$Mn$_{x}$ films 

\section{Aknowledgements}
The authors would like to thank Dr  F  Rieutord for grazing incidence x-ray diffraction measurements performed on the GMT station of BM32 beamline at the European Synchrotron Radiation Facility 





ground_truth: Appointing a blue ribbon commission to conduct the research and develop the management plan and denying or defering approval on any applications for new docks in the Cove until the management plan can be developed and implemented.