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

Due to the increase in marine anthropogenic activities, it was found that megafauna are threatened by high acoustic intensities with both physical and behavioral impacts \cite{nelms2016seismic}.
While marine mammals and pelagic fish can quickly escape high-intensity acoustic sources, this is not the case for sea turtles.
Hence, there is a need for a detection solution that can serve as a warning system, to alert the presence of sea turtles to stop or mitigate disturbance or detriment during marine operations.
This type of system can be applied over vessels performing seismic surveys that may lead to the interruption of marine turtles' normal behaviors \cite{nelms2016seismic}; within areas of sea water intake to desalination factories that can injure turtles \cite{levy2015small}; within the proximity of areas containing hot water from power plants where turtles aggregate \cite{macdonald2012home}; as well within ports and ship channels and dredging zones where turtles are abundant \cite{bolten1994seasonal}.
Identification of sea turtles' presence in their natural habitat can also be an important tool for population monitoring and conservation.
This paper takes a first step towards such a goal, and offers a pattern recognition approach for detecting sea turtles by active acoustics.

Active acoustic detection of sea turtles was studied for commercial echosounders, where target strength (TS) measurements are conducted at a frequency of 200kHz in a tank and in the open-sea \cite{mahfurdz2018green} \cite{perez2013ts}.
Other related studies \cite{jones2017broadband} use active acoustics to detect fish, based on the resonance of their swimming bladder.
However, when operating at frequencies that differ from the resonance or for species without a swimming bladder, acoustic reflection is expected to be less intense.
Detection methods to identify reflected sonar echoes for very low observable (VLO) targets are studied extensively and include methods to reduce the false alarm rate by utilizing information on reverberation and noise power \cite{abraham2002active},  classification of sonar contacts to target or clutter \cite{berg2018classification} \cite{hjelmervik2017sonar}, tracking based on a motion model \cite{davey2007comparison}, or by probabilistic analysis to identify sequences of reflections based on dynamic programming \cite{diamant2019active}.
However, to the best of our knowledge, no consideration has been given to date, to the time varying characteristics of reflections from targets like sea turtles.
In particular, a main challenge of the active sonar detection of sea turtles is to identify reflections originating from a turtle within a point cloud of clutter reflections.
The problem becomes further compounded when detection is omnidirectional and the SCR is low \cite{de2019automatic}.
On top of this, for a swimming sea turtle that changes its orientation and depth with respect to the receiver, the intensity of the acoustic reflections varies over time.
Thus, rather than a continuous reflection pattern, we expect the reflection pattern from the turtle to form clusters, or 'blobs', within the point cloud of received sonar echoes.

In this work, we introduce a novel pattern recognition-based solution for sea turtle presence detection. Our solution considers the expected time-variation of the reflections from sea turtles to reduce the false alarm rate through point cloud clustering and classification.
We start by accumulating a sequence of reflections from the active sonar signals, arranged as a point cloud such that each point is identified by its ping number and estimated range.
Then, spectral characteristics and geometrical relations between the reflection's temporal and spatial patterns are tested against limitations on the animal's speed and size.
This results in the identification of blobs associated with potential targets.
The identified blobs are then classified as either a target or clutter by examining features derived from the statistics of the cluster's members and from the reflections' spectral diversity.
The latter is based on our key assumption that, due to distortions within the turtle's body, the spectral response of reflections originating from a sea turtle is significantly more diverse than that of the clutter.
Based on this assumption, we use the entropy of the reflections' spectral response as a detection metric.
Furthermore, since we expect clutter reflections to be independent while that of a valid blob to show statistical relations, we validate a blob to be related to a target by the stability of its members.

Our contribution is three-fold:
\begin{enumerate}
	\item Design of a graph-based clustering solution that accounts for time variations within a point cloud of sonar's reflections.
	\item Utilization of the statistical dependency between the target's reflections as a measure for pattern recognition.
	\item Design of a detection metric that is based on the expected spectral diversity of acoustic reflections originating from a sea turtle.
\end{enumerate}
We explore our method's performance in both simulations and a designated sea trial.
The simulations are based on a physical model for reflections from a sea turtle and involve real clutter collected during multiple sea trials.
The sea trial involved the detection of two sea turtles we released after rehabilitation.
Results show a favorable trade-off between the false alarm and the detection rates, and resilience to low and time-varying SCR.

The structure of this paper is as follows.
Section \ref{sec: Related work} surveys the related work in the fields of active sonar detection, classification of sonar reflections, and track-before-detect (TkBD) approaches for VLO targets.
Section \ref{sec: System model} describes the system's model and assumptions, as well as a model for acoustic reflections from sea turtles.
Section \ref{sec: Methodology} details our algorithm, starting from the clustering solution, and followed by the classification of clusters.
Section \ref{sec: Performance analysis} reports the simulation and sea trial results, while conclusions are drawn in Section \ref{sec: Conclusion}.

Throughout the paper, we use the following notations: a small letter indicates a scalar; while vectors and matrices are indicated by bold small and uppercase letters, respectively. The entries of a vector or a matrix are indicated by subscript indices.

\section{Related work} \label{sec: Related work}
The common approach for detecting reflection of active sonar in Gaussian noise is by a matched filter (MF) \cite{robey1992cfar}, which is used widely for active sonar applications \cite{seo2019underwater}\cite{berg2018classification}\cite{hjelmervik2017sonar}.
However, since sound propagation in shallow water is considerably affected by reverberations, the MF's performance deviates from its optimum processing gain \cite{abraham2002active}.
A method to detect sonar echoes in a reverberant environment is proposed in \cite{abraham2002active}, where the Page test is applied on the MF output to identify the start and end of a signal.
Alternatively, for the specific case of linear frequency modulation (LFM) signals, emitted for object detection, a fractional Fourier transform (FrFT) can be applied to separate signals overlapping in time \cite{cowell2010separation}.
An application of FrFT for sonar signal processing is given in \cite{jacob2009applications} for the parameter estimation of chirp signals.
Detection based on simulations and experimental data is illustrated in \cite{yu2017fractional}, and a better accuracy than that of the MF is observed in terms of the delay estimation.
While the above detection methods aim to identify echoes in low SCR and in conditions of high interference; in practice, due to noise fluctuations, high false alarm rates \cite{hjelmervik2017sonar} are reported in real sea environments.

One way to reduce false detections is by classifying the acoustic reflections to separate between a target and clutter.
In \cite{hjelmervik2017sonar}, a machine-learning approach was demonstrated to reduce the false alarm rate (FAR) of active sonar reflections by using the backscatter intensity as a classification feature.
Similarly, the range-bearing neighborhood of MF sample outputs that passed a detection threshold are used in \cite{seo2019underwater} to extract features for classification by support vector machine (SVM).
In \cite{berg2018classification}, a similar feature set is offered as the input of a neural network to classify the sonar data after MF operation.
Alternatively, \cite{de2019automatic} implemented a convolutional neural network (CNN) to classify a target or clutter by the sonar's spectrogram images.
The drawback is the need for training data, which is often hard to obtain due to the spatial and temporal diversity of the underwater acoustic channel.
Unsupervised anomaly detection \cite{stinco2021automatic} is used to overcome this limitation, making it more practical for real world applications.
However, the classification is limited to individual detected instances, and does not exploit the information of the reflection pattern.

Temporal information of the reflection pattern is obtained when emitting a train of sonar pings whose reflections, after being synchronized, are stacked in a reflection matrix. Analyzing such a matrix can dramatically increase detection performance by using the track-before detect (TkBD) framework.
Common approaches to TkBD include dynamic programming, particle filter (PF), probabilistic multi-hypothesis tracking (PMHT), and probabilistic data association (PDA).
Dynamic programming performs tracking over a discrete grid, assuming the target's dynamics can be modeled as a Markov process with
some limitations on its velocity \cite{barniv1985dynamic}.
Although straightforward, it has the drawback of having a very large computational cost. Application for weak target detection by active sonar can be found in \cite{wei2018novel} on simulated data.
Viterbi-algorithm (VA)-based TkBD for underwater targets is presented in \cite{diamant2019active}, where detection decision are based on the calculated likelihood of optional target paths.
For lower complexity, PF samples the state-space to estimate the probability density function for target reflections \cite{davey2007comparison}.
\newline
Tracking of an underwater moving source by PF is demonstrated in \cite{jing2016detection}, while \cite{northardt2018track} demonstrated a PF-based TkBD algorithm on a multi-target passive sonar scenario.
In turn, the PMHT approach \cite{streit1994maximum} models a combination of target and noise using the expectation maximization (EM) algorithm, and estimates the target's path by a Kalman smoother.
Extensions include the histogram probabilistic multi-hypothesis tracking (H-PMHT) \cite{streit2002multitarget}\cite{vu2013track}, and the Poisson-H-PMHT \cite{gaetjens2017histogram}.
Finally, the PDA approach considers the overall probability of the set of measurements to infer the existence of a target \cite{jauffret1990track}.
Applications of ML-PDA for real bistatic and multistatic sonar data are demonstrated in \cite{willett2005application} and \cite{blanding2007sequential}, respectively.
A comparison of ML-PDA vs. PMHT on synthetic multistatic active-sonar scenarios is presented in \cite{schoenecker2013ml}.
An underlying assumption for these tracking-based methods is that a target exists, and that its probability of detection is roughly constant within the observation time (i.e., the series of pings).
While such an assumption may be valid for large targets such as submarines, this is not the case for small targets as considered here, i.e., a sea-turtle.
This is because of the high impact of orientation changes, caused by the animal's motion, on the intensity of the acoustic reflections.

\section{System model} \label{sec: System model}
Our setup includes an omnidirectional monostatic sonar, composed of a projector and hydrophone pair.
A number, $N_\mathrm{p}$, of linear frequency modulation chirp signals are emitted at a constant ping rate interval (PRI), $T_\mathrm{PRI}$, such that reflected echoes allow nearly-uniform temporal sampling of the surrounding.
In this work, we set $N_\mathrm{p} = 20$ for simulations, and $N_\mathrm{p} = 37$ for the experiment.
For each emission, we record the reflected signal, such that the analysis is performed in blocks of time-windows equal to $N_\mathrm{p}\cdot T_\mathrm{PRI}$.
In order to utilize the reflections' expected time-variations, we arrange the $N_\mathrm{p}$ reflections as a set of signals $\{ {\bf y}^{(p)} \}_{p=1}^{N_\mathrm{p}}$, attributed by their pulse index $p$.
Our goal is to find target reflection patterns within these signals.

\subsection{Main assumptions}
Our model assumes that, due to the dynamics of the sea turtle, the intensity of the acoustic reflections form 'blobs' along the target's path at the MF output.
We also assume that, due to the complex structure of the sea turtle's body, the acoustic intensity of these blobs' members is frequency dependent.
Under this model, our detector combines classification with tracking.

We assume that a valid reflection which originates from a sea turtle follows three conditions. First, the detected path should follow boundaries in terms of the turtle's maximum speed.
Specifically, the range associated with a valid reflection must be distanced up to $v_{\mathrm{max}}\cdot T_{\mathrm{PRI}}$~[m] from its previous or following valid reflection.
Second, a valid reflection must show spectral diversity which differs from that of the clutter.
Last, we expect the samples along a valid target's path at the MF output to be statistically dependent. That is, the joint
probability of the acoustic intensity of a pair of valid reflections should be greater than the multiplication of their separate
probabilities.
In terms of the channel model, we focus on the practical case in which 1) the reflections are received at low SCR, such that energy-based detection is not possible, and that 2) there is non-negligible ambient noise; therefore, statistical analysis over a number of emissions is required.

\subsection{A Model for Acoustic Reflections from Sea Turtles}
Studies on the distribution of acoustic reflections from sea turtles focus on a commercial ecosounder at a carrier frequency of 200kHz \cite{perez2013ts} \cite{mahfurdz2018green}.
Especially for omni-directional detection, this frequency greatly limits the detection range, as the acoustic attenuation above the
100~kHz becomes a dominant factor in the attenuation loss.
Instead, our transmissions are performed at lower frequencies of 7~kHz to 17~kHz and between 48~kHz to 78~kHz, where the acoustic wavelength is on the same order as the dimensions of the target sea turtle.
For this frequency range, the turtle's reflections are characterized as frequency dependent.
Frequency dependence of acoustic reflections is mostly studied for fish \cite{korneliussen2003synthetic} \cite{stanton2010new} \cite{pailhas2010analysis}.
Here, the acoustic reflections primarily originate from the fish's swim bladder, which, arguably, resemble the reflections from a sea turtle's lungs.
The general model for the spectral diversity of acoustic reflections we refer to is described in \cite{love1971measurements}.
For completeness, we now outline this model in detail below.

The frequency dependence of reflections from a finite-sized object can be divided into three regions, depending on the size of the reflecting object relative to the wavelength.
When the acoustic wavelength $\lambda$ is shorter than the object's size, $l$, the reflection is modeled as Rayleigh scattering, in which the TS rapidly increases with the frequency.
Geometric reflection, which is not frequency dependent, occurs at the optical limit when the wavelength is much smaller than the object's size.
Between these two extremes, there is an interference region in which multiple reflections from the object's boundaries interfere, thus creating a diverse frequency selective pattern.
For a well-defined object there is a clear division between the above regions.
For example, for a sphere with a radius of $a$, the interference region is in the range of $1 \leq \frac{2 \pi a}{\lambda} \leq 10$.
However, for complex shapes like a marine animal this division is not clear, and the animal's internal organs are expected to create a diverse interference pattern.
Empirical results \cite{love1971measurements} identify the interference region for fish as $0.7 \leq \frac{l}{\lambda} \leq 200$, where the lower limit may be even smaller.
For our first transmission range, 7-17~kHz, the size of an object that is within the interference region is between,
\begin{gather}\label{eq: interference region}
	l_{min} f_{min} \geq 0.7c \rightarrow l_{min} \geq \frac{0.7c}{f_{min}} = \frac{0.7 \cdot 1500}{7000} = 0.15 \text{m} \\
	l_{max} f_{max} \leq 200c \rightarrow l_{max} \leq \frac{200c}{f_{max}} = \frac{200 \cdot 1500}{17000} = 17.647 \text{m} \;,
\end{gather}
Similarly, for the frequency range of 48~kHz to 78~kHz, the interference region fits a target size between 2~cm and 3.8~m.
We therefore conclude that the acoustic reflections expected from the sea turtle are within the interference region, and a high diversity in the frequency domain is expected.
In contrast, for clutter composed of smaller elements, acoustic reflection is within the Rayleigh scattering region.
Thus, the clutter's frequency response is not expected to exhibit frequency diversity.
Our approach utilizes this difference in the frequency diversity characteristics of the two signals to separate the turtle's reflections from those of the clutter.

\begin{figure}[h]
	\centering
	\includegraphics[width=0.48\textwidth]{block_diagram.eps}
	\caption{ \label{fig: block diagram1} Block diagram of the processing chain.}
\end{figure}

\section{Methodology}\label{sec: Methodology}

\subsection{Key idea}\label{sec: Key idea}
Our processing chain flow is shown in Fig.~\ref{fig: block diagram1}.
Our solution utilizes our assumption that the acoustic reflections from sea turtles tend to appear as occasional blobs along the turtle's path.
This is due to expected temporal changes in the turtle's orientation and in the volume of its lungs.
The input for our classifier is the set $\{ (r_i, p_i) \}_{i=1}^N$, which is the point cloud after MF thresholding.
Here, $r_i$ represents the range of the point from the sonar, and $p_i$ is the time of acquisition, as illustrated in Fig.~\ref{fig: processing stages}a,b.

Referring to Fig.~\ref{fig: block diagram1}, ours is a two-stage process.
First, we segment target indications into clusters of potential targets.
To this end, we identify reflections that are close in range and time, and thus are more-likely to be from the same object.
As part of the clustering solution, we rank the connectivity between data-points by their mutual information.
Instead of pre-setting the number of clusters, which in our case is not possible, we determine it by minimizing a utility function for the 'cost' of the clustering solution.
Once clusters are formed in the shape of 'blobs', we move to the second phase where we analyze the blob's members to draw features about their statistics, and to determine whether the blob is an indication of a sea turtle-like target.
These features comprise, on the one hand, the spatial, temporal, and statistical connectivity of the acoustic reflections along the blob and, on the other hand, the spectral diversity that is expected for the reflections from a sea turtle.
The former is calculated by summing all the connections within a cluster, while the latter by the entropy of the acoustic reflections at different frequencies.
In doing so, we achieve a processing gain by analyzing groups of reflections.

We note that our solution can manage two cases: one when an exact spectral diversity model is available, and one when no model is available, but spectral diversity is expected.
The first calls for ranking the alignment between the measured diversity and a given template, while the second compares the spectral diversity of the blob to that of the clutter.
In turn, clutter is identified by clusters whose members' connectivity is low, or whose members' entropy is high.
An important notification is that, while we demonstrate our solution for the detection of sea turtles, our solution may also be applied to a variety of targets - ranging from pelagic fish to top predators.
In each case, the user should provide a mobility model (limitation on the speed and movement pattern) and spectral model, if any.

\subsection{Clustering}\label{sec: Clustering}

The goal of the clustering phase is to segment the thresholded data-points in blobs of possible targets.
These blobs should contain data-points that are close in range and time, and have similar reflection spectrums.
To measure this similarity, we use the normalized information distance (NID) \cite{vinh2010information}, which is calculated for the spectral entropy of the signals associated with reflections from each pair of data-points.
Denote the time domain signal corresponding to the $i$th data-point by ${\bf y}^{(i)}$, and its normalized power spectrum by $\hat {\bf z}^{(i)}_{M \times 1}$.
We calculate the spectral entropy for the $i$th data-point by \cite{misra2004spectral}
\begin{equation}\label{eq: spectral entropy}
	H_i = - \sum_{m=1}^M \hat z^{(i)}_m \mathrm{log_2} \hat z^{(i)}_m,
\end{equation}
where $m$ attributes the frequency bins in which the power spectrum is calculated, and $\hat {\bf z}$ is normalized such that $\bf{\hat z} ^\mathrm T \bf{\hat z} = 1$.
The NID used to quantify spectral similarity between data-points $i$ and $j$ is calculated by
\begin{equation}\label{eq: NID}
	\mathrm{NID}_{ij}( \hat {\bf z}^{(i)}; \hat {\bf z}^{(j)}) = 1 - \frac{ I_{ij}( \hat {\bf z}^{(i)}; \hat {\bf z}^{(j)}) }{ \mathrm{max} [H_i(\hat {\bf z}^{(i)}), H_j(\hat {\bf z}^{(j)})] },
\end{equation}
where $I_{ij}$ is the mutual information between $\hat {\bf z}^{(i)}$ and $\hat {\bf z}^{(j)}$ obtained by
\begin{equation}\label{eq: mutual information}
	I_{ij}( \hat {\bf z}^{(i)}; \hat {\bf z}^{(j)}) = H_i(\hat {\bf z}^{(i)}) + H_j(\hat {\bf z}^{(j)}) - H_{ij}(\hat {\bf z}^{(i)}, \hat {\bf z}^{(j)}) \;,
\end{equation}
and the term $H_{ij}(\hat {\bf z}^{(i)}, \hat {\bf z}^{(j)})$ is the joint entropy of $\hat {\bf z}^{(i)}$ and $\hat {\bf z}^{(j)}$.
The reason we use the NID measure is because it relates to the mutual information of the reflection spectrum of each pair of data-points \cite{vinh2010information}.
Specifically, a value of NID close to 0 indicates a high level of mutual information, while an NID close to 1 is a case where $\hat {\bf z}^{(i)}, \hat {\bf z}^{(j)}$ are independent.
The range difference of two data-points is denoted by $\Delta r_{ij} = |r_i - r_j|$, and their time-difference by $\Delta t_{ij} = |p_i - p_j |T_\mathrm{PRI}$.
We define the distance of two data-points $i$ and $j$ by
\begin{equation} \label{eq: Delta_ij}
	\Delta_{ij} = \alpha \mathrm{NID}_{ij} + \beta \Delta r_{ij} \mathrm{u}( \Delta r_{ij} - l) +  \tau \Delta t_{ij},
\end{equation}
where $\mathrm{u(.)}$ is the Heaviside step function.
The parameters $\alpha$, $\beta$ and $\tau$ tune the relative importance of the frequency diversity, range difference, and ping difference, respectively.

Our clustering solution is based on the method proposed in \cite{ng2002spectral}, which performs spectral clustering to a pre-defined number of clusters. Here, we perform an additional search to find the most appropriate number of clusters.
This spectral clustering method was selected because it enables the formation of non-convex clusters as expected in our application (i.e., the maneuvering sea turtle does not move in straight lines).
In this method, the data is encoded as a weighted graph, where data-points are the nodes and their edges are weighted according to distances $\Delta_{ij}$ defined in \eqref{eq: Delta_ij}.
We define the weight of the edge between the $i$th and $j$th data-point by
\begin{equation}\label{eq: w_ij}
	w_{ij} = e^{-\Delta_{ij}} \mathrm{u}( v_\mathrm{max} - \frac{2 \Delta r_{ij}}{\Delta t_{ij}} ),
\end{equation}
where the step-function constrains the maximal velocity allowed by the model $v_\mathrm{max}$, and factor 2 is present because the range is two-way.
This processing stage is illustrated in Fig.~\ref{fig: processing stages}c, where the graph edges are marked as dashed lines.
Following \cite{ng2002spectral}, we define a matrix $\bf A$ of entries
\begin{equation} \label{eq: A_ij}
	a_{ij} =
	\begin{dcases}
		w_{ij}, ~& i \neq j \\
		0, ~& i=j,
	\end{dcases}
\end{equation}
and a diagonal matrix $\bf D$ with entries
\begin{equation} \label{eq: D_i}
	d_{i} = \sum_{j=1}^N A_{ij}.
\end{equation}
We then calculate the symmetric graph-Laplacian by
\begin{equation} \label{eq: graph-Laplacian}
	{\bf L} = {\bf D}^{-1/2} ({\bf D - A}) {\bf D}^{-1/2}\;.
\end{equation}
The spectral clustering algorithm \cite{ng2002spectral} identifies clusters' centers in the space of the graph-Laplacian's eigenvectors, as detailed in the Appendix.
However, the number of clusters should be provided, as the final stage of \cite{ng2002spectral} relies on k-means clustering.

We estimate the appropriate number of clusters by considering the total 'cost' of the clustering solution.
We note that the term $ {\bf D}^{-1/2} {\bf A} {\bf D}^{-1/2}$ in \eqref{eq: graph-Laplacian} is the ratio of the inner to outer connectivity of each pair of nodes, $0 \leq a_{ij} / \sqrt{d_i d_j} \leq 1$.
Denote the $k$th cluster by an $N \times 1$ binary vector ${\bf b}_k$, whose entries is a binary indicator that is set to 1 if the corresponding data-point belongs to the cluster.
We relate to ${\bf b}_k^\mathrm{T} {\bf L} {\bf b}_k$ as a cost function for forming nodes $i$ and $j$ in the same $k$th cluster.
The appropriate number of clusters, $\hat K$, is determined by minimizing the mean partition cost,
\begin{equation} \label{eq: cost}
	\begin{split}
		& \hat K = \argmin_K \frac{1}{K}\sum_{k=1}^K {\bf b}_k^\mathrm{T} {\bf L} {\bf b}_k + \epsilon K \\
		& \text{s.t. } 	b_i \in [0,1], ~ {\bf b}_k ^\mathrm{T} {\bf b}_l = 0 \quad \forall k \neq l
	\end{split}
\end{equation}
where $\epsilon K$ is a penalty for forming 'too many' clusters.
This model-order selection process is illustrated in Fig.~\ref{fig: processing stages}d, while the formed clusters are shown in Fig.~\ref{fig: processing stages}e.

\subsection{Classify clusters}\label{sec: Classify Clusters}
Classification of the formed clusters to targets of interest, illustrated in Fig.~\ref{fig: processing stages}f, is based on the statistics of the data-points within the identified cluster.
The selection of features for classification is application dependent, and should reflect the difference between the desired target and clutter.
Recall that for the task of distinguishing between reflections from turtles and from clutter, we expect that:
\begin{enumerate}
	\item Reflections from a sea turtle will form clusters with relatively high connectivity, while clutter-related data-points will form clusters that are less connected.
	\item Reflections from a sea turtle will exhibit a diverse frequency spectrum, due to interference from the turtle's internal organs, while clutter-related reflections will have a more uniform frequency spectrum.
\end{enumerate}
To quantify how well a cluster is connected, we define the \textit{connectivity} of a cluster as the sum of all connections \eqref{eq: w_ij} within the cluster.
For the $k$th cluster, the connectivity is calculated by
\begin{equation} \label{eq: c_k}
	c_k = \sum_{i,j \in \mathrm{cluster}~k} w_{ij},
\end{equation}
or, in a matrix form,
\begin{equation} \label{eq: c_k matrix form}
	c_k =  {\bf b}_k^\mathrm{T} {\bf W} {\bf b}_k \;,
\end{equation}
where $\bf W$ holds the weights $w_{ij}$ from \eqref{eq: w_ij}.
To characterize the cluster's frequency diversity, we rank the spectral entropy of the cluster's members.
Here, a low entropy reflects high frequency diversity.
This information is obtained by performing the median,
\begin{equation}
	\bar H_k = \mathrm{median}[\{ H_i (\hat {\bf z}^{(i)}) \}_{i \in \mathrm{cluster}~k}]\;.
\end{equation}

For our application, since stability and spectral diversity are not necessarily related, we combine the two above features by
\begin{equation}
	\mathrm{class}({\bf b}_k) =
	\begin{dcases}
		\text{target}  & (c_k > \eta_c)  \land (\bar H_k < \eta_h) \\
		\text{clutter} & ~~~~~\text{otherwise}
	\end{dcases},\;
\end{equation}
where thresholds $\eta_c$ and $\eta_h$ are user defined.
A suggested approach to calculate these thresholds is by the distribution of features of the clutter-related data-points.
When the SCR is low, and most data-points are clutter-related, we expect the target's features to be anomalous relative to the clutter.
Since both connectivity and entropy are pre-calculated for all data-points, we can determine the thresholds based on, e.g., the empirical cumulative distribution functions of these features.
Alternatively, when the SCR is high, a large fraction of the data-points is target-related, and we cannot rely on anomaly detection.
In such cases, the clutter's entropy distribution can be estimated from a sample of the MF outputs that did not pass the threshold.
Still, to calculate connectivity, we need to apply the clustering algorithm. Consequently, we recommend learning the connectivity of the clutter offline, by using recordings from diverse sea experiments.

\begin{figure*}[h]
\centering
\subfloat{\includegraphics[width=0.4\textwidth]{stage_a.eps}%
\label{fig_a}}
\subfloat{\includegraphics[width=0.4\textwidth]{stage_b.eps}%
\label{fig_b}}
\hfill
\subfloat{\includegraphics[width=0.4\textwidth]{stage_c.eps}%
\label{fig_c}}
\subfloat{\includegraphics[width=0.4\textwidth]{stage_d.eps}%
\label{fig_d}}
\hfill
\subfloat{\includegraphics[width=0.4\textwidth]{stage_e.eps}%
\label{fig_e}}
\subfloat{\includegraphics[width=0.4\textwidth]{stage_f.eps}%
\label{fig_f}}
\caption{\label{fig: processing stages} Processing stages: (a) reflection matrix after MF; (b) the reflection matrix after preliminary detection; (c) graph formation; (d) choosing model order $(\epsilon=1)$; (e) clusters (color coded); (f) classification.}
\label{fig_sim}
\end{figure*}

\subsection{Discussion}
The parameters of our above algorithm are $\alpha$, $\beta$ and $\tau$, which control the relative importance of the frequency diversity, range difference, and ping difference, respectively.
The role of these parameters is to penalize the weights of the graph's edges when pairs of data-points do not fit the model of a maneuvering target.
Setting the value too low may give low impact to the model assumptions during the clustering, while setting a value that is too high may decrease the weights, rendering the clustering ineffective.
We advise setting the above values such that $\alpha, \beta \| \Delta r_{ij} \|_{\infty}$ and $\tau \| \Delta t_{ij} \|_{\infty}$ are close to 1, and then doing some fine-tuning according to the experimental setup, e.g., by clustering together reflections from large objects, such as a ship hull or the sea floor.

Considering features for cluster classification, we note that, while the features we use are suitable for our application, one may consider additional features, such as the cluster's size and spatial extent.
Filtering out seemingly non-related data points from clusters is also possible.
However, a main source of complexity is the computation of the mutual information, which involves calculating the joint entropy of all pairs of data-points.
A suggestion to reduce this bottleneck is to split the computation of \eqref{eq: Delta_ij}, such that \eqref{eq: mutual information} will not be calculated for $\alpha << \beta \Delta r_{ij} \mathrm{u}(\Delta r_{ij}-l) + \tau \Delta t_{ij}$, where it has a negligible contribution.
Finally, we note that our solution allows for using an alternative preliminary detection method than the MF method which we presented. Examples are given in \cite{abraham2002active, yu2017fractional, berg2018classification, de2019automatic, seo2019underwater, stinco2021automatic}.

\section{Performance Analysis} \label{sec: Performance analysis}
The task we explore can be considered a mixture of detection and classification.
\textit{Detection} is considered when we wish to identify the existence/absence of a target.
We measure detection per-scenario by the trade-off between the probability of detection, $P_{\mathrm{D}}$, and the probability of false alarm, $P_{\mathrm{FA}}$.
\textit{Classification} of individual data-points to either clutter or a target is considered a generalization of detection to account for a soft threshold to the indicated existence/absence of a target.
We measure the performance of our classifier per-data-point, and evaluate it by the precision and recall trade-off.
As a benchmark, we use the Viterbi-algorithm (VA)-based detection method \cite{diamant2019active}, which performs track-before-detect to find a target's path within a clutter by probabilistic analysis.
\newline
We define a \textit{true detection} as at least one cluster per the emission of $N_p$ pings that is correctly classified as a target.
Similarly, we define a \textit{false alarm} as at least one cluster per the emission of $N_p$ pings that is falsely classified as a target.
Formally, $P_\mathrm{D}$ and $P_\mathrm{FA}$ are calculated by
\begin{subequations}\label{eq: PD and PFA}
	\begin{align}
		&  P_\mathrm{D} = \frac{
		\begin{matrix}
	        \text{number of scenarios with} \\
	        \text{targets that are detected}
	    \end{matrix}
		}{
		\begin{matrix}
	        \text{total number of simulated} \\
	        \text{scenarios without target}
	    \end{matrix}
		} \\
		& P_\mathrm{FA} = \frac{
	    \begin{matrix}
	        \text{number of scenarios without target,} \\
	        \text{but detection is determined}
	    \end{matrix}
	    }
	    {
	    \begin{matrix}
	        \text{total number of simulated} \\
	        \text{scenarios without target}
	    \end{matrix}
		}
	\end{align}
\end{subequations}
To evaluate classification, we define \textit{precision} by
\begin{equation}
	\text{precision} = \frac{ n_\mathrm{TP} }{ n_\mathrm{TP} + n_\mathrm{FP} },
\end{equation}
where $n_\mathrm{TP}$ is the number of data-points correctly classified as a target, and $n_\mathrm{FP}$ is the number of data-points falsely classified as a target.
The recall is defined by
\begin{equation}
	\text{recall} = \frac{ n_\mathrm{TP}}{ n_\mathrm{TP} + n_\mathrm{FN}},
\end{equation}
where $n_\mathrm{FN}$ is the number of data-points that are indeed a target, but are falsely classified as a non-target.
The ground truth for classification is obtained according to the distance of a determined valid data-point to the simulated path of the target, such that
\begin{equation}
	\text{ground truth class for }(r_i, p_i) =
	\begin{dcases}
		\text{target}  & |r_i - \rho(p_i)| < \rho_0 \\
		\text{clutter} & |r_i - \rho(p_i)| \geq \rho_0
	\end{dcases}
\end{equation}
where $\rho(p_i)$ is the simulated target's path at ping $p_i$, and $\rho_0=0.5$~m.

\subsection{Numerical Simulations}

\subsubsection{Simulation Setup}
The simulation facilitates acoustic reflections from a maneuvering target.
We use a chirp signal, $s(t)$, of a $T_\mathrm{s}=10$~ms duration and a frequency band of 7-17~kHz.
A single simulation scenario is determined as a set for $N_\mathrm{p}=20$ pings.
The time segment duration of data for each ping is 90~ms, corresponding to a two-way range of $\sim$70~m.
For each scenario, the target's path is simulated by a random process, $\rho_{m+1} = \rho_m + n_m$, where $n_m \sim \mathrm{N}(0, \sigma_\mathrm{n}=2~\text{m}), m=1,...N_\mathrm{p}$.
We simulate the acoustic signal associated with ping $m$, $y^{(m)}_\mathrm{sim}(t)$, by
\begin{equation}
	y^{(m)}_\mathrm{sim}(t) = \\
	\begin{dcases}
		s(t-T_m) * h(t - T_m), & T_m \leq t \leq T_m+T_\mathrm{s} \\
		y_\mathrm{clutter}(t),                                               & \text{otherwise}
	\end{dcases}
\end{equation}
where $T_m=\frac{2 \rho_m}{c}$, $y_\mathrm{clutter}(t)$ are clutter samples and $h(t)$ is the simulated target's impulse response.
We consider the case where the turtle's impulse response distorts the transmitted signal $s(t)$ in a manner which we cannot predict. We therefore simulate $h(t)$ by a multivariate random variable, ${\bf h}_{100 \times 1}$, that is uniformly distributed in [-1  1], and then normalized such that ${\bf h}^\mathrm T {\bf h} = 1$.
The same impulse response is used for all pings within a single simulation scenario.
To explore performance over a realistic scenario, clutter samples $y_\mathrm{clutter}(t)$ are taken from sea experiments. In these experiments, we deployed our sonar to a depth of roughly 20~m, and transmitted the same chirp signals used in the simulation.
The bottom depth was 125~m, and a manual inspection ensured that the reflection pattern contained only clutter.
The overall duration of obtained clutter samples is 257~s, from which we randomly uniformly choose in each simulation run.
The desired SCR is achieved by controlling the amplitude of the simulated target's echo.
No ambient noise is added.
We run $300$ simulation scenarios per SCR value including target, and $1000$ scenarios to explore false alarms.

\subsubsection{Simulation Results}
We start by exploring the sensitivity of our algorithm for parameters $\alpha, \beta$ and $\tau$.
The classification sensitivity for $\alpha$ is presented in Fig.~\ref{fig: parameters_sensitivity}a, while setting $(\beta, \tau) = 0$, and changing the threshold $\eta_\mathrm{c}$.
The observable maxima in the precision-recall curve indicates that there is a connectivity threshold $\eta_\mathrm{c}$ under which detection degrades drastically.
From this figure, it is evident that the frequency diversity alone, without using the spatial and temporal information, contains sufficient information.
We also observe that classification performance is sensitive to $\alpha$.
This is because the exponent in \eqref{eq: w_ij} is multiplied by $\alpha$ and thus any change in $\alpha$ has an impact on weights $w_{ij}$.
A similar trend is observed in Fig.~\ref{fig: parameters_sensitivity}b, which shows the classification results when only $\beta$ varies, i.e., exploring the impact of the spatial feature in the reflections on classification. Here, we set $\alpha=0$, but $\tau=1$, since we need the temporal connection to form clusters that are geometrically valid.
We observe that both precision and recall improve with $\beta$, but converge for $\beta>5$.
Next, the sensitivity for the temporal feature in the reflections is explored by changing parameter $\tau$, keeping $\beta=1$ and $\alpha=0$.
The results in Fig.~\ref{fig: parameters_sensitivity}c show a trade-off: a lower $\tau$ increases the recall at the cost of precision, i.e., the algorithm tends to classify too many instances as a 'target'.
On the other hand, a higher $\tau$ reduces both false-positives and true-positives.
It seems that a favorable trade-off is $\tau=1$.
In the following, we pick the values $\alpha=0.1$, $\beta=1$, and $\tau=1$.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.4\textwidth]{alpha_sensitivity.eps}
	\includegraphics[width=0.4\textwidth]{beta_sensitivity.eps}
	\includegraphics[width=0.4\textwidth]{tau_sensitivity.eps}
	\caption{ \label{fig: parameters_sensitivity} Precision-recall curves for exploring sensitivity to parameters, while changing the connectivity threshold. SCR = -9dB. (a) sensitivity to $\alpha$, (b) sensitivity to $\beta$, (c) sensitivity to $\tau$.}
\end{figure}

The effect of the entropy threshold is explored in Fig.~\ref{fig: entropy_ROC}, where $\eta_\mathrm{h}$ is used as a parameter, with $2 \leq \eta_\mathrm{h} \leq5$, while three values for $\eta_\mathrm{c}$ are tested.
Here, the SCR is -9~dB.
Fig.~\ref{fig: entropy_ROC}a shows results for the case where the reflections of each of the $N_\mathrm{p}=20$ emissions include a valid target in addition to clutter.
In contrast, Fig.~\ref{fig: entropy_ROC}b shows the case where only 70\% of the 20 emissions include a valid reflection, such that the target appears as 'blobs' of sporadic detections.
We observe that the performance of our algorithm degrades in this latter case, since fewer emissions are available for detection.
In both cases, it is evident that higher $\eta_\mathrm{c}$ produces better ROCs, but the maximal $P_\mathrm{D}$ that is reached is limited.
This is because target-related clusters with lower connectivity are misclassified as clutter.
The circles markers on the plots are for $\eta_\mathrm{h}=4.5$, which we identify as a reasonable trade-off that keeps $P_\mathrm{D}$ relatively constant for a large range of $\eta_\mathrm{c}$ values.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.4\textwidth]{entropy_ROC_pings100.eps}
	\includegraphics[width=0.4\textwidth]{entropy_ROC_pings70.eps}
	\caption{ \label{fig: entropy_ROC} ROC where $\eta_\mathrm{h}$ is parameter, and $(\alpha, \beta, \tau) = (0.1, 1, 1)$. Percentage of valid pings is (a) 100\%, (b) 70\%. SCR = -9dB.}
\end{figure}

Fig.~\ref{fig: ROC_connectivity} shows the impact of the SCR level on the detection performance, and the two cases of 100\% and 70\% valid targets in the 20 emissions are presented in Figs.~\ref{fig: ROC_connectivity}a,b, respectively.
Here, we set the entropy threshold to be $\eta_\mathrm{h}=4.5$.
Additional fixed parameters are $\eta_\mathrm{MF}=5 \cdot 10^{-6}$, $(\alpha, \beta, \tau) = (0.1, 1, 1)$.
The track-before-detect VA benchmark is marked by a dashed line.
As expected, both algorithms perform well for high SCR=-6~dB, while performance degrades rapidly as the SCR decreases.
It is evident that, for low SCR, our algorithm outperforms the benchmark.
Additionally, in the case of 70\% valid pings, the performance of the VA-based approach highly degrades, while our method, although affected, is more robust.
This is because our method is designed to look for 'blobs' of detection, while the VA-based method assumes that the reflections form a path.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.35\textwidth]{ROC_pings100_beta1.eps}
	\includegraphics[width=0.35\textwidth]{ROC_pings70_beta1.eps}
	\caption{ \label{fig: ROC_connectivity} ROC results when: (a) all emissions include a valid reflection, (b) $70\%$ of the emissions are valid. $(\alpha, \beta, \tau) = (0.1, 1, 1)$.}
\end{figure}

\subsection{Field Experiments}
The above simulation results explored the performance statistically, but lack a reliable model for the acoustic reflections from the sea turtle.
To this end, we conducted a designated sea experiment that involved the release of two rehabilitated sea turtles, and measured their acoustic reflections.
The experiment was carried out roughly 3~km off the coast of Haifa, Israel, in 30~m of water.
The sea turtles' released weight was roughly 40~kg, and their size was roughly 60~cm in diameter.
These were mature turtles that had suffered a shock wave and were rehabilitated in the Israeli Rescue Center for Sea Turtles. The release was performed by the center's personnel, under the approval of the Israeli Nature and Park Authority (NPA).
An image of the release of one of the turtles is shown in Fig.~\ref{fig: turtles}.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.4\textwidth]{turtles_on_boat.jpeg}
	\includegraphics[width=0.4\textwidth]{turtle_release.jpeg}
	\caption{ \label{fig: turtles} The sea turtles that were released, and one of the release activities.}
\end{figure}

\subsection{Experimental Setup}
The experimental setup is illustrated in Fig.~\ref{fig: experimental setup}.
To transmit the chirp signals, we used the Evologics S2CR~7/17 and S2C~M~48/78 software-defined acoustic modems to emit trains of chirp signals of 10~ms duration at a PRI of 0.7~s and at frequency ranges of 7-17~kHz and 48-78~kHz, respectively. The emission power was 170~dB re. $1 \mu$P@1m.
The modems were deployed from the boat to a depth of 3~m.
Two omni-directional self-made receivers were deployed from the boat to a depth of 20~m.
Continuous recording took place at 192k samples per second with 3 Byte resolution per sample.
The modems started emitting the signals prior to the release of the sea turtles.
During these events, the turtles mostly swam on the surface, but also submerged from time to time. We visually observed their behavior from the vessel, and documented the rise and submerge times.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.48\textwidth]{Experimental_setup.eps}
	\caption{\label{fig: experimental setup}The sea experiment setup.}
\end{figure}

\subsection{Experimental Results}

\subsubsection{Detection of a sea turtle}
For analysis, we considered the parameter set $(\alpha, \beta, \tau) = (0.1, 1, 1)$.
We applied our algorithm on patches of 37 pings with a duration of 60~ms each.
Fig.~\ref{fig: turtle 7-17kHz results} shows results for the frequency range of 7-17~kHz.
In this experiment, there was a plastic buoy in the water with a GPS receiver at a range of no more than 20~m from the sea turtle.
The path of this GPS is marked by a dashed line.
Panel (a) shows the data-sample matrix after the MF processing, but before the thresholding operation.
Here, we merge the reflections from all the emissions.
We observe that the main reflection comes from the bottom at roughly 35~ms.
The detection indications after thresholding are shown in Panel (b), and detections that are classified as targets are marked in red.
The path detected by the VA benchmark is plotted in cyan, using a threshold value of 94.
Panels (c) and (d) show the connectivity and the median entropy of the clusters, respectively; and clusters classified as targets are marked by rectangles.
We observe two target indications along the path of the GPS: one at emission 191 that is $\sim$ 7~m from the path, and the other at emission 304 that is right on the path.
The range to these targets, measured on the surface, is $28.7 \pm 2$~m and $60.2 \pm 4.8$~m, respectively.
In addition, there are two clusters that were falsely classified as targets on emissions 5 and 44 at ranges of $47.1 \pm 4.2$~m and $61.5 \pm 1.5$~m, respectively.
We see that the benchmark VA detects intense reflections at the leftmost part of the data-sample matrix, and follows them instead of the assumed turtle.
This is because the VA uses only intensities as an input, and is not able to detect more than a single target per-patch.
Instead, our method has the following advantages: it uses spectral information, and multiple targets can be detected.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.48\textwidth]{file_2190_WF_alpha0.1.eps}
	\includegraphics[width=0.48\textwidth]{file_2190_entropy_alpha0.1.eps}
	\caption{ \label{fig: turtle 7-17kHz results} Results for transmission signals in the range 7-17kHz. (a) Intensity  image of the MF's output. (b) Detections after threshold (our target indications are in red, VA detected path in cyan). (c) Connectivity of clusters. (d) Median entropy of clusters. Target indications are marked by rectangles in (c) and (d).}
\end{figure}

Results obtained for the 48-78~kHz frequency range are shown in Fig.~\ref{fig: turtle 48-78kHz results}.
In this experiment, there was no GPS buoy, and we rely on the experiment's log to identify the events.
The sea turtle was released around ping 108, and was swimming on the surface, thus making its detection very challenging.
Approximately 90 seconds after its release, at emission ping 236, the turtle was observed taking air, indicating that it was about to dive.
This arguable dive enabled its detection, and indeed, we observed a detection that matches a low-entropy cluster around emission 264 with a time delay of $\sim 74$~ms, corresponding to a range of $61.9 \pm 2.1$~m.
In this case, no false alarms were observed.
Moreover, in this case, the VA benchmark, applied with a threshold of 147, is blinded by high-intensity reflections, and cannot detect the turtle.
\begin{figure}[h]
	\centering
	\includegraphics[width=0.48\textwidth]{file_2197_WF_alpha0.1.eps}
	\includegraphics[width=0.48\textwidth]{file_2197_entropy_alpha0.1.eps}
	\caption{ \label{fig: turtle 48-78kHz results} Results for transmission signals in the range 48-78kHz.  (a) Intensity  image of the MF's output. (b) Detections after threshold (our target indications are in red, VA detected path in cyan). (c) Connectivity of clusters. (d) Median entropy of clusters. Target indications are marked by rectangles in (c) and (d).}
\end{figure}

\section{Conclusion} \label{sec: Conclusion}
In this work, we proposed an unsupervised remote sensing algorithm to identify a sea turtle within a point cloud of sonar's reflections under low SCR conditions.
We designed a clustering algorithm, which is based on the geometrical relations between a sample within the point cloud that relates to the target's reflections, as well as on the expected spectral diversity of the turtle's reflections.
We also utilized the expected stability of target-related reflections as another means of detection verification.
We explored the performance of our algorithm in both simulations and in a designated sea experiment, where we released two rehabilitated sea turtles and tracked their trajectory acoustically.
Compared to a track-before-detect benchmark, our results show an improved robustness to fluctuating intensity, and a better trade-off between the false alarm and detection rates.
Future research may improve classification by adding more features and exploring a multivariate feature combination.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


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text:
AB De Villiers Workout And Diet Routine
South African captain, and batsman, AB De Villiers is quite fit for his age. At just 33 years of age, he has set marvelous amount of milestones. He is certainly counted amongst the best batsmen all over the world. The star plays for South Africa as the captain and in the Indian Premier League as a player of Royal Challengers Bangalore.
He is sometimes called one of the most destructive batsmen in the world of cricket and has an average more than 50 in both ODIs as well as Tests. He has proved himself in both short and long format of the game. In his cricket career, Ab de Villiers has made over 18500 runs, 9000 of which have had a striking rate of 54.28 and he also holds the record for making the fastest 50, century and 150.
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Workout Routine
Running is a crucial part of a cricketer's work out. One has to be quick to make runs and catch out balls and stop the other team from making more runs. It is great for AB that his upbringing has included long distance running. His parents have always run Comrades Marathon as so as De Villiers. It is quite challenging.
Although AB's dad is a doctor, he is also kind of a sports enthusiast who loves to play Rugby. He has also encouraged De Villiers to get into sports from a very tender age, and that is how he chose cricket as his career option. He shared, "I grew up loving sports and will always love sports, but I do realize there is more to life. It is all about finding the right balance." Indulging yourself in various sports is the most effective and interesting form of exercise.
AB De Villiers' core gym exercises include:
He likes to stay hydrated before his work out and often takes the protein shake. Watch the video to know more about his fitness secrets:
As he seems to travel a lot, mostly for matches, it becomes difficult to keep a healthy diet. But despite these hurdles, De Villiers does manage to eat healthy most of the time.
He likes to eat salmon, chicken, and tuna as a healthy source of protein.
More sources would be milk, eggs and cereal and some protein shake.
He does have a couple of cheat days but only once in a while.
He loves red wine, seafood and Italian as his cheat meals.
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redpajama_set_name: RedPajamaCommonCrawl


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Half of the week is almost gone and we're back with some more app sales. Today's list is rather short, so be sure to go back and look at Monday's post if you haven't already. We also have the partner to the 0.10 app that appeared at the beginning of this week.
Half of the week is gone (or mostly), which means it's time for yet another round of app sales. The list is much smaller today than it was Monday, and some of the apps from that post are still free or discounted so be sure to check it out.
Besides a dogfood version of Play Games, update Wednesday brought us a new version of Play Books - 3.4.5. The changes in this update aren't major (or even immediately apparent), but they are worth taking a quick look at.
First up, there's a brand new translation interface. Rather than a toolbar and sheet overlay, the new translate interface lives on a card, just like the existing notes and dictionary interfaces. Here's a quick before and after.
Next up, new changes to notes. The ability to take notes in a book was present in 3.3, but users could not do that in a free sample of a book.
Cross one more item off your list of Google apps in need of material facelifts! Next on this bountiful Update Wednesday, Google Keep is receiving a bump to version 3.0 with some new material-inspired touches, the most obvious one being its launcher icon. Instead of a realistic stack of sticky notes, we now have a single dog-eared sheet of paper with a lightbulb cutout sitting on top.
Once you're inside the app, there's plenty to look at. There's a new search interface that (like Keep's web update) allows users to search by type of note (list, voice, image, or reminder), or by color.
It's been a long, hard road, but the Notion Ink Adam has finally been approved by the FCC and is going to start shipping "around Wednesday" to those who pre-ordered.
Although the product isn't yet available in the FCC's database, Notion Ink CEO Rohan Shravan has let us all in on the good news via the NI blog. He claims that the tablet's product code will be NI3421A01, where "NI" stands for "Notion Ink," "A01" means "Adam 1 Series," and "3421" is a string of consecutive digits in the Fibonacci series.
Rohan also informs us that pre-orders will commence within a few days (initially, pre-orders sold out shortly after they begun).


text:
Octomeria hatschbachii är en orkidéart som beskrevs av Rudolf Schlechter. Octomeria hatschbachii ingår i släktet Octomeria och familjen orkidéer. Inga underarter finns listade i Catalogue of Life.

Källor

Orkidéer
hatschbachii

redpajama_set_name: RedPajamaWikipedia


text:
require 'spec_helper'
require 'recap/tasks/deploy'

describe Recap::Tasks::Deploy do
  let :config do
    Capistrano::Configuration.new
  end

  let :namespace do
    config.deploy
  end

  let :commands do
    sequence('commands')
  end

  before do
    Recap::Tasks::Deploy.load_into(config)
  end

  it 'configures capistrano to use ssh key forwarding' do
    config.ssh_options[:forward_agent].should be_true
  end

  it 'configures capistrano to use a pty session when running commands' do
    config.default_run_options[:pty].should be_true
  end

  describe 'Settings' do
    describe '#application' do
      it 'exits if accessed before being set' do
        namespace.expects(:abort).with(regexp_matches(/You must set the name of your application in your Capfile/))
        config.application
      end
    end

    describe '#repository' do
      it 'exits if accessed before being set' do
        namespace.expects(:abort).with(regexp_matches(/You must set the git respository location in your Capfile/))
        config.repository
      end
    end

    describe '#application_user' do
      it 'defaults to the name of the application' do
        config.set :application, 'rabbitfoot'
        config.application_user.should eql('rabbitfoot')
      end
    end

    describe '#application_group' do
      it 'defaults to the name of the application user' do
        config.set :application_user, 'rabbitfoot'
        config.application_group.should eql('rabbitfoot')
      end
    end

    describe '#branch' do
      it 'defaults to master' do
        config.branch.should eql('master')
      end

      it 'honours value in pre-set variable' do
        config.set(:branch, 'branch-from-command-line')
        Recap::Tasks::Deploy.load_into(config)
        config.branch.should eql('branch-from-command-line')
      end
    end

    describe '#deploy_to' do
      it 'defaults to an `app` folder within the application user home directory' do
        config.set :application, 'hare'
        config.set :application_user, 'rabbitfoot'
        config.deploy_to.should eql('/home/rabbitfoot/app')
      end
    end

    describe '#release_tag' do
      it 'defaults to the current timestamp' do
        now = Time.now
        Time.stubs(:now).returns(now)
        config.release_tag.should eql(Time.now.utc.strftime("%Y%m%d%H%M%S"))
      end
    end

    describe '#release_matcher' do
      it 'defaults to a matcher matching timestamps' do
        ("20130908123422" =~ config.release_matcher).should be_true
      end

      it 'does not match timestamp-like numbers with too many digits' do
        ("201309081234221" =~ config.release_matcher).should be_false
      end

      it 'does not match timestamp-like numbers with too few digits' do
        ("2013090812342" =~ config.release_matcher).should be_false
      end

      it 'does not match strings with non-numeric characters' do
        ("2013090a123421" =~ config.release_matcher).should be_false
      end
    end

    describe '#latest_tag' do
      it 'memoizes call to latest_tag_from_repository' do
        namespace.stubs(:latest_tag_from_repository).returns('abc123').then.returns('something-else')
        config.latest_tag.should eql('abc123')
        config.latest_tag.should eql('abc123')
      end
    end
  end

  describe 'Tasks' do
    let :application do
      'romulus'
    end

    let :repository do
      'git@github.com/example/romulus.git'
    end

    let :deploy_to do
      '/path/to/deploy/romulus/into'
    end

    before do
      config.set :application, application
      config.set :repository, repository
      config.set :deploy_to, deploy_to
    end

    describe 'deploy:setup' do
      it 'runs env:set and deploy:clone_code tasks' do
        env = stub('env')
        config.stubs(:env).returns(env)
        env.expects('set')
        namespace.expects(:clone_code)
        config.find_and_execute_task('deploy:setup')
      end

      it 'calls deploy:clone_code task within a transaction' do
        namespace.stubs(:transaction)
        namespace.expects(:clone_code).never
        config.find_and_execute_task('deploy:setup')
      end

      it 'removes the deploy_to dir if a rollback is triggered' do
        config.stubs(:env).returns(stub_everything('env'))
        namespace.stubs(:as_app)
        namespace.expects(:as_app).with('rm -fr ' + deploy_to)
        namespace.stubs(:git).raises(RuntimeError)
        config.find_and_execute_task('deploy:setup') rescue RuntimeError
      end
    end

    describe 'deploy:clone_code' do
      it 'creates deploy_to dir, ensures it\'s group writable, then clones the repository into it' do
        config.set :branch, 'given-branch'

        namespace.expects(:as_app).with('mkdir -p ' + deploy_to, '~').in_sequence(commands)
        namespace.expects(:as_app).with('chmod g+rw ' + deploy_to).in_sequence(commands)
        namespace.expects(:deployed_dir_exists?).with('.git').in_sequence(commands)
        namespace.expects(:git).with('clone ' + repository + ' .').in_sequence(commands)
        namespace.expects(:git).with('reset --hard origin/given-branch').in_sequence(commands)
        config.find_and_execute_task('deploy:clone_code')
      end
    end

    describe 'deploy' do
      it 'runs env:set, deploy:update_code, deploy:tag and then deploy:restart tasks' do
        namespace.stubs(:transaction_with_lock).yields
        env = stub('env')
        config.stubs(:env).returns(env)
        env.expects('set')
        namespace.expects(:update_code).in_sequence(commands)
        namespace.expects(:tag).in_sequence(commands)
        namespace.expects(:restart).in_sequence(commands)
        config.find_and_execute_task('deploy')
      end

      it 'calls deploy:update_code task within a locked transaction' do
        namespace.stubs(:transaction_with_lock)
        namespace.expects(:update_code).never
        config.find_and_execute_task('deploy')
      end

      it 'calls deploy:tag task within a locked transaction' do
        namespace.stubs(:transaction_with_lock)
        namespace.expects(:tag).never
        config.find_and_execute_task('deploy')
      end

      it 'calls restart outside the transaction' do
        namespace.stubs(:transaction_with_lock)
        namespace.expects(:restart)
        config.find_and_execute_task('deploy')
      end
    end

    describe 'deploy:full' do
      it 'sets force_full_deploy and calls the default deployment task' do
        namespace.expects(:default)
        config.find_and_execute_task('deploy:full')
        namespace.force_full_deploy.should be_true
      end
    end

    describe 'deploy:update_code' do
      it 'fetches latest changes, then resets to repository branch' do
        config.set :branch, 'release-branch'
        namespace.expects(:git).with('fetch').in_sequence(commands)
        namespace.expects(:git).with('reset --hard origin/release-branch').in_sequence(commands)
        namespace.find_and_execute_task('deploy:update_code')
      end
    end

    describe 'deploy:tag' do
      before do
        config.set :release_tag, '20120101012034'
        config.set :release_message, 'Released into the wild'
      end

      it 'tags code with the release tag and release message' do
        namespace.expects(:git).with('tag 20120101012034 -m \'Released into the wild\'')
        namespace.find_and_execute_task('deploy:tag')
      end

      it 'aborts if prospective release_tag does not match release_matcher' do
        config.set :release_matcher, /abcd/
        namespace.expects(:abort).with("The release_tag must be matched by the release_matcher regex, 20120101012034 doesn't match (?-mix:abcd)")
        namespace.stubs(:git)
        namespace.find_and_execute_task('deploy:tag')
      end
    end

    describe 'deploy:rollback' do
      it 'deletes latest tag, resets to previous tag and restarts' do
        config.stubs(:latest_tag).returns('release-2')
        config.stubs(:latest_tag_from_repository).returns('release-1')
        namespace.expects(:git).with('tag -d release-2').in_sequence(commands)
        namespace.expects(:git).with('reset --hard release-1').in_sequence(commands)
        namespace.expects(:restart).in_sequence(commands)
        namespace.find_and_execute_task('deploy:rollback')
      end

      it 'aborts if no tag has been deployed' do
        config.stubs(:latest_tag).returns(nil)
        namespace.rollback.expects(:abort).with('This app is not currently deployed')
        namespace.find_and_execute_task('deploy:rollback')
      end
    end

    describe 'deploy:lock' do
      it 'locks deployments with the message DEPLOY_LOCK_MESSAGE if available' do
        ENV.stubs("[]").with("DEPLOY_LOCK_MESSAGE").returns("custom-message")
        namespace.expects(:claim_lock).with("custom-message")
        namespace.find_and_execute_task('deploy:lock')
      end

      it 'locks deployments with a default message if no message provided' do
        now = Time.now
        Time.stubs(:now).returns(now)
        namespace.expects(:claim_lock).with("Manually locked at #{Time.now}")
        namespace.find_and_execute_task('deploy:lock')
      end
    end

    describe 'deploy:unlock' do
      it 'removes any existing locks' do
        namespace.expects(:release_lock)
        namespace.find_and_execute_task('deploy:unlock')
      end
    end

    describe 'deploy:restart' do
      it 'does nothing (but can be overidden by other recipes)' do
        namespace.expects(:run).never
        namespace.expects(:sudo).never
        namespace.find_and_execute_task('deploy:restart')
      end
    end

    describe 'deploy:destroy' do
      it 'removes all files from the deployment folder' do
        config.set :deploy_to, 'path/to/deploy/app'
        config.expects(:sudo).with('rm -rf path/to/deploy/app')
        config.find_and_execute_task('deploy:destroy')
      end
    end
  end
end

redpajama_set_name: RedPajamaGithub


mateocarvajal.co Page 11: handmade copper lamp shades. baby lamp shades nursery. dome lamp shades. glass lamp shades lowes. striped lamp shade. victorian lamp shades.
Published at Thursday 18th, April 2019, in Lamp Shades. By .


text:
When a girl really needs Oman
Last year, as winter dragged on, I was finding it hard to keep my spirits up. It didn't help that three months earlier I had given up a 20-a-day menthol cigarette habit and now urgently needed to get a grip on my new salted peanut and Crunchie bar addiction. What I felt I most needed was a spa with blue skies and sunshine.
In the past, when I have felt like an old car needing a service, I have flown half way around the world to find out-of-season sun, then spent a week recovering from jet lag. But with two school-age children and my own business, I have to grab short holidays - a fortnight away is just not an option.
So, after talking to friends I decided to try the Barr Al Jissah Resort and Spa in Oman – only a seven-hour flight (same as to New York) and, even better, only a four-hour time difference to recover from on my return.
I arrived in Muscat late at night and was met by Pat of Desert Adventure Tours. We hit it off immediately as she was carrying one of my handbags. From that moment she took care of my every move, at least when I was not in the spa or flat on my back by the pool.
I have never been to a country where everyone you meet is so keen to tell you how well they live and how fortunate they are. This seems to be due to the benevolence of the sultan, who is widely admired. By chance I was there for National Day, the 37th anniversary of his accession. In his father's day it was three nights in jail for smoking a cigarette. It wasn't that he disapproved of smoking – he was all for the traditional shisha pipes, but cigarettes and other modern ways he firmly rejected. There was neither electricity nor proper roads, and he wanted every Omani to live according to the sultanate's ancient traditions.
Electricity, and especially coloured light bulbs, was much in evidence for National Day – everything was festooned with lights, including the 20-odd miles of new roads between the airport and the beautiful mountains and coastal setting of the Barr Al Jissah.
En route to my hotel, my driver proudly pointed out the spectacular new mosque, the largest in Oman. Inside, the biggest chandelier in the world is made entirely from Swarovski crystals and weighs 5.8 tons. The building also boasts the world's largest hand-woven carpet – when I visited later in the week it certainly had the wow factor in spades.
Barr Al Jissah is actually three hotels. My week was to be spent in the Al Husn, the best of the trio, raised high on a bluff above the main beach.
Al Husn turned out to be the last word in discreet and sophisticated luxury, epitomised by the worldly charm of the 7ft German manager (really, seven feet tall), who seemed to be everywhere at all times, smoothing every guest's stay. Whether they needed one of the hotel's Bentleys for the airport or a golf buggy to take them to the fine CHI Spa, he was there, dapper and full of self-deprecating humour.
What makes a good hotel? I found out the next day when venturing to the beautifully designed infinity pool, where a helpful and smiling pool attendant brought me not only towels and chilled water to drink but an iced face spray. In the mornings, I stayed by the pool. In the afternoons, I hit the spa to encourage my regime and smooth my wrinkled brow (and I thoroughly recommend the treatment I had on the first day. It took four hours and took me from stressed to serene).
The resort's other two hotels are the Al Waha and the Al Bandar (guests in Al Husn have access to their facilities, but not vice versa). The Al Waha is promoted as "Oman's first dedicated leisure hotel" and is the largest. Little Turtles, the resort's children's club, is there and is ideal for guests with small children as the babysitting service allows undisturbed evenings in the restaurants and bars.
The feature I most enjoyed was the "Lazy River", which wound from one hotel pool to the next, great fun for all ages to float lazily along under bridges and through the beautiful tropical landscaping.
It would have been easy not to leave this paradise – especially now I had discovered Al Husn's enchanting private beach, which had not only a perfect cove in which to swim and snorkel, but also comfortable sun beds and umbrellas and, as by the pool, a face-spray service.
However, I did manage to drag myself away twice. Pat organised a tour around Muscat Old Town, where everything was on a very small scale. Even the museum, which records Oman's history, is small and perfectly formed.
I loved its wonderful antique jewellery, which had me chomping at the bit to get to the souk where the best jewellery and artefact shop was owned by a Mr Akhdar Al Balushi.
The thousands of coloured necklaces hung from the ceiling, and great barrels filled with rings and small objects, all around £5-£10, kept me happy for hours. The owner – fabulous in his finery – asked to have his photograph taken with me and then proudly showed me his wall of fame. He was particularly proud of a picture of himself with Kate Moss festooned in his jewellery.
The only other place I left my mountain oasis for was the Chedi, a more contemporary-looking hotel closer to Muscat, where I had an excellent dinner at the seafood Beach restaurant. The Chedi is a fabulous looking hotel – the whale vertebrae, mounted on plinths and beautifully lit at the entrance to the restaurant, were quite stunning. Its location, though, and beachfront are disappointing.
Back at the Al Husn I was not surprised to read that various publications had voted it among the world's best new hotels of 2007. The pride of everyone who worked there mirrored the pride the Omanis all seem to have in their country.
It was very refreshing after listening to everyone moaning in London – but with free schools and college education, free hospitals, no income tax and money being pumped into tourism, the local people have a lot to smile about. I shall certainly be returning next time I need to top up on sun, serenity, souks and smiles.
Cadogan Holidays (0845 615 6793; www.cadoganholidays.com) offers stays at Shangri-La's Barr Al Jissah Resort & Spa from £687 per person for a three-night break and from £876 for seven nights on a b&b basis.
Return flight from Heathrow, using the scheduled services of Etihad Airways, and private transfers are included. The company can also organise seven-day tailor-made tours of Oman, including stays at Al Husn from £1,068 or Al Bandar, from £852, excluding flights.
Oman Tourist Office (020 8877 4524; www.omantourism.gov.om).


text:
Educate & Develop
Diversity Council & ERG Education Resources
Welcome to the Education Resources section of ErgCouncil.com. Here you will find a variety of tools designed to help grow your skills and increase your diversity competence.
Education resources and tools in this learning center allow you the flexibility to work on programs and learn at your own pace and are designed to give individuals the insight and the tools to build their own and others' inclusiveness. These programs are crafted to appeal to all learning styles, giving participants the opportunity to listen, observe, practice and reflect, which is shown to develop long term behavior change.
How ERGs can provide a space for political dialogue in the Post-Truth Era
Organizations must ask the hard questions if they are purposeful in creating a safe inclusive environment that considers how politics affect their employees...
See All Hot Topics »
Leveraging ERGs in the Age of COVID-19
Featuring: Dr. Karen Francis, Director, D&I at the American Institutes for Research, Anna Ettin, D&I Thought Leader at Amazon, and Shary Tran, Director, D&I at Froedtert Health.
Watch the webinar »
Taking Your Training to the Next Level with PRISM's Leveraging Diversity and Inclusion for Engagement and Innovation™
As an Association Member you have access to view our recorded Best Practice Webinars and Inspirational Presentations. The recorded presentations are available for Playback at anytime during your active membership.
Explore the Video Library »
American Airlines Takes Flight with Honors Award Recognition
We are extremely proud to have been honored as one of the top 25 recipients of the Diversity Council Honors Award since the award's inception in 2008...
The Statistics of Black History
To commemorate and celebrate the contributions to our nation made by people of African descent, American historian Carter G. Woodson established Black History Week.
Discover more Fast Facts »
How to Get Audiences to Listen to Your ERG Presentations
Joe Santana shares his tips for capturing and keeping audience attention during your session.
Explore Articles & White Papers»
Honors Award Best Practice Report
A compilation of best practices from the 2017 ERG & Council Honors Award
48 pages of best practices encompassing the efforts and initiatives of the Top 25 Honors Award recipients for 2017. Their initiatives are divided into the four focus areas and sub-measures that comprised the Award application...
Become a member to view »
Answering Tough Questions
When it comes to inclusion, how do you foster a work environment where people with different backgrounds feel valued for their differences?
Many employers struggle to foster inclusion. A recent Deloitte study found that 71 percent of organizations said they aspire to an inclusive culture, but only 12 percent said that they've achieved this goal...
Get the answers »
© Association of ERGs & Councils


More and more, the question of herbicide residue and its potential for crop damage requires an accurate assessment of residue presence. A&L Canada, recognizing this as an important concern, offers plant bioassays to screen for the presence of crop damaging chemicals. Bioassays are recognized as a useful means for determining the presence or absence of herbicide chemicals that may inhibit normal development of sensitive plants. Bioassays use herbicide susceptible plants, which are exposed to the suspect soil and grown alongside a control sample for comparison. The degree of plant growth and its physiological characteristics are compared to the control plant to assess whether or not the soil-seed combination will produce a healthy plant stand. Bioassays can identify known residues as well as potential residues in soils with an unknown history of herbicide use.
A&L Canada has complete pesticide analysis capabilities for water and soil. More than 100 pesticides are analyzed for prevention and diagnosis of crop damage. Cropping rotations or renting land may require specific pesticide analysis to ensure the residue levels are not such that they restrict the growth of succeeding crops.


text:
Rowett's grandson visits Aberdeen for Boyd Orr lecture
John Quiller Rowett's grandson Jan Chojecki was welcomed to a special lecture as part of celebrations to mark 100 years since the establishment of the Rowett Institute.
The Boyd Orr lecture was delivered by Sir Stephen O'Rahilly MD FRS FMedSci, Professor of Clinical Biochemistry and Medicine, Director, MRC Metabolic Diseases Unit, Wellcome-MRC Institute of Metabolic Science, University of Cambridge and covered obesity and related health implications.
In 1920 John Quiller Rowett donated £20,000 (nearly £1m in today's value) which unlocked matched funding from the Government and enabled the purchase of land as well as the building of a stand-alone research institute.
In recognition of his incredibly generous gift, it was named the Rowett Research Institute and was formerly opened by Queen Mary in 1922.
This name was retained when the Rowett Institute became part of the University of Aberdeen in 2008.
Today both John Quiller Rowett and John Boyd Orr, the Institute's founding director, are represented in the reception area of the purpose-built building at Foresterhill which opened in 2016.
It was a real pleasure to welcome Jan Chojecki and Professor Sir Stephen O'Rahilly to the Rowett Institute for a very special day in its history." Director of the Rowett Institute Professor Jules Griffin
Director of the Rowett Institute Professor Jules Griffin said: "It was a real pleasure to welcome Jan Chojecki and Professor Sir Stephen O'Rahilly to the Rowett Institute for a very special day in its history.
"Jan and Stephen have both dedicated their careers to science and it was fitting that our students and staff had the opportunity to meet them and discuss the truly ground-breaking studies on diet and health which are being done here.
"The health challenges facing the country will only be addressed if sustainable nutrition is part of that solution. Boyd Orr was a passionate advocate of this and we continue this work today at the Rowett.
"On behalf of everyone at the Rowett I would like to warmly thank Jan and Stephen and all our guests for their support.
"I am proud to say with confidence that the Rowett is well-placed to tackle the challenges of today."
Select year 2023 2022 2021 2020


text:
Q: How does ground affect a battery? (Nodal Analysis) I began solving this question with nodal analysis, but I ran into 2 problems while solving the question:

*

*V_A has to be equal to zero to solve the question (and get R_1). I get 40V... I think that ground is affecting my battery?... Why is this?

*I got a negative value for R_3. Does this mean the current is in the wrong direction that I assumed?

redpajama_set_name: RedPajamaStackExchange


text:
class ChangeOnTheMindStatementsProfileAnswersCommentsTextLength < ActiveRecord::Migration
  def change
    change_column :social_networking_comments, :text, :string, limit: 1000
    change_column :social_networking_goals, :description, :string, limit: 1000
    change_column :social_networking_on_the_mind_statements, :description, :string, limit: 1000
    change_column :social_networking_profile_answers, :answer_text, :string, limit: 1000
  end
end


The Manor Bareilly Hotel is known for providing the best of comfort and hospitality. The hotel offers spacious Deluxe Rooms that are equipped with modern amenities. These rooms reflect warm colour tones in its interiors, exuding an inviting look.
The hotel provides 2 Deluxe Rooms. Book our rooms now and enjoy a comfortable stay.


Testimonials - Essence Of My Heart - Pilates & Yoga in Warwick, QLD.
I have been attending regular weekly yoga and Pilates classes with Jes for 6 years now! I love attending her classes because I find her teaching and instructional style very easy to follow… and Jes provides lots of variety so you don't get bored! A great workout in a truly relaxing and caring environment.
Had my first yoga class and thoroughly enjoyed it. Thank you very much for being patient and such a wonderful loving soul.
I just want to share how much I love the beginner yoga class. I feel like I am starting to get the breathing and can really see the benefits of yoga breathing. I have time to focus on breathing cause I'm comfortable with the poses at this level. I will never get bored with the beautiful slow flow and simple moves. You inspired me this morning to get to general yoga. I can do it…. Thank You for your inspiration and beautiful soul at every single class. I am grateful to you every day for bringing yoga into my life.
Jes, just a short note to thank you for the beautiful yoga class I did with you. Your very professional manner and clear instructions were very helpful.
I have attended classes for a couple of years with Jes, then last year, I was diagnosed with breast cancer. For many months I was unable to attend any classes, but Jes sent lovely messages of support and provided encouragement to come back.
Towards the end of chemotherapy, I was able to attend a few Restorative Yoga classes. They were amazing. The stretch to various parts of my body and the improved lung capacity was exactly what I needed. I felt a bit woozy the day after, but am convinced that the Restorative Yoga was helping to detox my system.
The poses helped to rid my body of all the chemicals in such a gentle way. Jes was very supportive. She ensured there were alternative poses for me to do and also made sure there were enough props to support the operated on side. I felt welcomed and very supported to continue my Yoga and Pilates practice.
Just a very big thank you for conducting such an excellent class, my lungs feel so good, proper instruction of breathing, you are clear in your lessons, an absolute joy to be part of your classes.
My goal was to strengthen my back to rid myself of dreadful back pain I would experience daily. With a very cautious instructor, we embarked on improving my everyday life. Each week I attend class. If I miss it, I regret it.
Since doing Pilates consistently, I can live a normal life, work is no longer a struggle, I can go for bush walks without being in pain. I started to lose weight and tone up a little which wasn't the goal but was a great benefit. I am a happier person and genuinely love this form of workout.
I could go on forever about the way I have benefitted from doing Pilates. All I can say is try it and find out for yourself, because without help of Jes from 'Essence of my Heart',my life wouldn't be as good as it is.
After doing yoga and Pilates classes with Jes for the past four years, I have noticed some marked improvements in my overall health. When I first began doing yoga and Pilates with Jes it was more about just enjoying the classes but now I am realising that the cumulative effect of this kind of exercise and lifestyle has actually healed my body and improved my mind.
I am a working mother of four and in my early forties was faced with the depressing feeling that I was aging before my time, with low energy, sore joints and failing strength. Now, thanks to yoga and pilates with Jes, I have a whole new feeling of strength and wellness – mind and body. There is always the immediate reward of feeling great after each class but the long term effects are what I am valuing the most.
– Sue, 47 years young!
Jes is one of the truly beautiful people, her classes are amazing. She caters for all types, young, older, fit and not so fit, yet she makes us all feel comfortable with where we are at. Thank you Jess for giving us the opportunity to do these sorts of classes.
Jes's yoga classes are truly amazing. From a person who participates in a high level of physical activity each week, nothing more has helped my body than Jes's yoga classes. This practice has completely changed my body physically and mentally. Jes's kind nature makes everyone feel comfortable and welcome in her classes and her special touches makes it quite a unique experience. Her classes are of a high standard and she takes a lot of pride in her career.
Jes is always prepared and adapts her planning to meet us clients where we're at. Jes is the best yoga, Pilates, health and fitness teacher ever. Her knowledge and skill is incredible but even more than that, it is obvious that she passionately lives what she teaches. I love attending Jes's classes. I always walk away feeling great.
I took advantage of the mini massage special from Ed after my barre class. I was a little sore, so it was nice to have a massage, and I can say I thoroughly enjoyed it. Ed was very friendly and professional. I would absolutely recommend him, and look forward to my next massage.
Thanks for Pilates classic & Props, I love it, even though I can barely move, I feel great!! We are so lucky to have you in Warwick!