text:
\section{Introduction}\label{section: introduction}
Recommendation system and ads click-trough rate (CTR) prediction both have profound impact on web-scale big data, and have been received a lot of attention in both academia and industrial community. In these systems, the critical problem is to predict the probability of clicks, which will be used to rank the candidate items or ads.

These problems have been successfully tackled by supervised learning methods, in which user profiles and item attributes are used as input features. The challenge is that, the data for web-scale recommendation systems is mostly discrete and categorical, resulting in an extreme large and sparse feature space to optimize. Feature sparsity of this kind is commonly handled by constructing feature interactions which are modeled by inner product of their low dimensional representations. In this so-called factorization machine model \cite{FM}, the naive inner product is not expressive enough for spurious or implicit feature interactions. Therefore, higher-order factorization machine \cite{HOFM} is proposed to learn higher-order feature interactions efficiently. On the other hand, deep learning based approaches have successfully enhanced the performance significantly because sophisticated feature interactions can be captured. Besides, another merit of the deep learning methods is that they can reduce human efforts in feature engineering. To name a few, DeepFM \cite{DeepFM} integrates the deep neural networks on top of the factorization machine, and the Deep \& Cross neural network (DCN) \cite{DCN} takes outer product of features at the element wise and vector wise level such that higher order feature interactions can be learned in an automatic and explicit fashion. In DCN, the order of interactions is determined by the number of multi-layer perceptron (MLP) layers. However, by using multiple layers of MLPs it is inefficient to learn multiplicative feature interactions. Therefore, in xDeepFM \cite{Xdeepfm} it is proposed to use convolution neural network to replace MLP.

In this paper, we re-examine the building block for these models: the inner product between feature representations. To this end, we propose to learn the low-dimensional representations in a hyperbolic geometry equipped with Lorentz distance, such that the triangle inequality for feature vectors could be violated. Our work is inspired by the work on collaborative metric learning (CML) \cite{cml}, where the inner product is replaced by the distance between feature vectors, but following a completely different path. As opposed to the work of CML, in which the authors argue that triangle inequality in a Euclidean space should be strictly obeyed, we propose to take advantage of the sign of the triangle inequality. Specifically, we construct our score function for feature interactions not by the inner product or distance between feature vectors, but by examining the triangle formed by them in a hyperbolic space. This reason for our approach is two-folded: (1) a hyperbolic space is intrinsically a lot more capacious than the Euclidean space; (2) the proposed score function will provide a robust objective function to learn fine-grained feature interactions. As a result, the embedding learned by this score function are therefore ready to use directly, just as the vanilla factorization machine. Our experiments on several benchmark datasets show that, even without using any deep learning layers on top of the embedding layer, the proposed approach will achieve the state-of-the-art performance with reducing up to 82.9\% in training parameters and 69.7\% in training time compared to the strong deep learning baselines such as DeepFM, DCN and xDeepFM.

\subsection{Our Contributions}
Overall, the primary contributions of this paper can be summarized as follows:
\begin{itemize}
    \item We propose to learn feature interactions with a score function measuring the validity of triangle inequalities. This score function is bounded and dimension agnostic, which opens up a novel viewpoint on learning the fine-grained structure of interacting features.
    \item We conduct extensive experiments on a wide range of real-world datasets. Our results demonstrate that LorentzFM achieves state-of-the-art performance, compared to existing deep learning approaches.
    \item We thoroughly investigate the number of training parameters and training time to understand its cost in resource.
\end{itemize}

\section{Why Learning Triangle Inequality?}\label{sec:background}
In this section, we first provide some technical background about hyperbolic geometry and Lorentz distance. With these definitions,  we will show that Lorentz distances for a triangle could violate triangle inequality. The motivation is to show how it is related to the metric learning in Euclidean space.

\subsection{Hyperbolic Geometry and Lorentz Distance}
Hyperbolic geometry aims to study non-Euclidean space with a constant negative curvature. Due to its negative curvature, hyperbolic geometry has very different properties compared to the Euclidean geometry.

First, the circumference and area of a circle in the hyperbolic space grow exponentially with the radius, as opposed to the linear and quadratic growth rate in Euclidean space. Therefore, the capacity of embeddings in the hyperbolic space of the same upper bound in radius is much larger than its Euclidean counterpart. Secondly, the triangle inequality Eq. \eqref{eq:triangle_ineq} with Lorentz distance defined in Eq. \eqref{eq:lorentz_distance} defined therein can be violated. This property enables us to characterize the pairwise relation between points in the hyperbolic space by the sign of the inequality.

There are several important models of hyperbolic space for computation purpose: the Poincar\'{e} ball model, the hyperboloid model, the Klein model and so on. These models all describe the same geometry and can be connected by transformations that preserve geometric properties of the hyperbolic space such as isometry. In the following, we only introduce the technical basics of the hyperboloid model, which will be used throughout the paper.

\subsubsection{Hyperboloid Model}
Let us define the Lorentzian inner product between $\mathbf{u}$, $\mathbf{v}\in\mathbb{R}^{n+1}$ as
\begin{equation}\label{eq:lorentz_inner_prod}
    \langle \mathbf{u}, \mathbf{v} \rangle_{\mathcal{L}}

    = -u_0 v_0 + \sum_{i=1}^nu_n v_n.
\end{equation}
The hyperboloid of dimension {\em n},  $\mathcal{H}^{n,\beta}\subseteq\mathbb{R}^{n+1}$ consists of the following set of points:
\begin{equation}\label{eq:hyperboloid}
    \mathcal{H}^{n,\beta} = \left\{\mathbf{x}\in\mathbb{R}^{n+1} : ||x||_{\mathcal{L}}^2 = -\beta, x_0 \geq \beta\right\},
\end{equation}
where $||\mathbf{x}||_{\mathcal{L}}^2 = \langle \mathbf{x}, \mathbf{x}\rangle_{\mathcal{L}}$ is the Lorentzian norm of the vector $\mathbf{x}$.  With this definition, for every vector $\mathbf{x}\in\mathcal{H}^{n,\beta}$, the component $x_0$ is not a free parameter, and is given by
\begin{equation}\label{eq: x_0}
    x_0 = \sqrt{\beta + \sum_{i=1}^n x_i^2}.
\end{equation}
The associated geodesic distance between two points is given as
\begin{equation}\label{eq:geodesic}
    d_{\ell}(\mathbf{u}, \mathbf{v}) = {\rm arccosh}(-\langle \mathbf{u}, \mathbf{v} \rangle_{\mathcal{L}} ).
\end{equation}
Note that the origin vector of the hyperboloid model $\mathcal{H}^{n,\beta}$ is $\mathbf{0}=(\beta,0,\dots,0)$, and its Lorentzian inner product with vector $\mathbf{x}$ is simply $\langle \mathbf{0}, \mathbf{x}\rangle_\mathcal{L} = -x_0 \leq \beta$.

When $\beta=1$, the model is called a \textit{unit} hyerboloid model, which will be used throughout the paper. Without introducing any confusions, we will simply call it hyperboloid model and use $\mathcal{H}^{n}$ to denote $\mathcal{H}^{n,1}$.

\subsubsection{Lorentz Distance} The squared Lorentz distance, or Lorentz distance in short, between $\mathbf{u}$, $\mathbf{v}\in\mathcal{H}^n$ is given by
\begin{equation}\label{eq:lorentz_distance}
     d^2_\mathcal{L}(\mathbf{u}, \mathbf{v}) = ||\mathbf{u} - \mathbf{v}||_{\mathcal{L}}^2 = -2 - 2\langle\mathbf{u}, \mathbf{v}\rangle_{\mathcal{L}}.
\end{equation}
It satisfies almost all axioms of Euclidean geometry but the triangle inequality, which is one of the most crucial geometric property with positive definitive Riemannian metric. It states that for any three points, $\mathbf{x}, \mathbf{y}$ and $\mathbf{z}$, any two pairwise distances $d(\cdot, \cdot)$ should be greater or equal to the remaining pairwise distance:
\begin{equation}\label{eq:triangle_ineq}
    d(\mathbf{x}, \mathbf{y}) \leq d(\mathbf{x}, \mathbf{z}) + d(\mathbf{z}, \mathbf{y}).
\end{equation}
In the hyperbolic space, the geodesic distance defined in Eq. \eqref{eq:geodesic} between three points also satisfies this property. However, the inequality could be violated with Lorentz distances, because the Riemannian metric is negative.  Consider the triangle formed by the origin $\mathbf{0}$ and other two points $\textbf{u}$ and $\textbf{v}$ in Figure \ref{figure:triangle}. When the two points are far apart on the opposite side of $x_1$ axis, the triangle inequality is violated. On the other hand, the triangle inequality holds if the two points are on the same side of $x_1$ axis.

\begin{figure}[t]
\begin{center}
\includegraphics[width=1\columnwidth]{triangle.pdf}
\end{center}
\caption{Visualization of the hyperboloid model $\mathcal{H}^2$. In this model, triangles could (a) violates Lorentz triangle inequality and (b) obeys triangle inequality for points on the hyperboloid.} \label{figure:triangle}
\end{figure}

\subsection{Learning Triangle Inequalities}

As pointed out in \citet{cml}, learning the distance in the embedding space rather than inner product has advantages to learn a fine-grained embedding space that could capture the representation not only for item-user interactions, but  also for item-item and user-user distances. Essentially, the so-called metric learning scheme is blessed by the constraint of triangle inequality.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=1\columnwidth]{model_2D.pdf}
\end{center}
\caption{The 2D landscape for the score function in the (a) triangle learning scheme ({\em e.g.}, Eq. \eqref{eq:triangle_inequality}) and (b) metric learning scheme using geodesic distance in a 2D hyperboloid model. } \label{figure:landscape}
\end{figure}

In contrast to collaborative metric learning scheme, we argue that the feature interaction between two points can be learned by the sign of the triangle inequality for Lorentz distance, instead of using the distance itself. Formally, our target score function is written as
\begin{equation}\label{eq:triangle_inequality}
    \mathcal{S}(\mathbf{x}, \mathbf{y}) = \frac{ d^2_{\mathcal{L}}(\mathbf{x}, \mathbf{y}) - d^2_{\mathcal{L}}(\mathbf{x}, \mathbf{0}) - d^2_{\mathcal{L}}(\mathbf{0}, \mathbf{y})}{\langle \mathbf{0}, \mathbf{x} \rangle_{\mathcal{L}} \langle \mathbf{0}, \mathbf{y}\rangle_{\mathcal{L}}},
\end{equation}
where $\mathbf{0} = (1, 0, \cdots, 0)$ is the origin. The nominator is simply the difference between the two sides of the triangle inequality, and the denominator is used to bound the score function.

The advantage of using Eq. \eqref{eq:triangle_inequality} is that, the function is bounded in $[-0.5, 2]$ in all dimensions. Therefore, the score function is free from the curse of dimensionality, compared to the collaborative metric learning scheme. To illustrate the landscape of the function, we plot Eq. \eqref{eq:triangle_inequality} for two points in 2D  in Figure \ref{figure:landscape} (a). Because each point on the 2D hyperboloid has only one free parameter, we plot the landscape of the score function by setting the $x$-axis and $y$-axis corresponding to the free parameter of each point respectively in a 2D plane. We also plot the landscape for collaborative metric learning scheme using the geodesic distance defined in Eq. \eqref{eq:geodesic} in Figure \ref{figure:landscape} (b). By comparison, we can observe that the landscape for our approach is smooth and bounded, but the score function for collaborative metric learning scheme is unbounded. The bounded property is promising because the embedding vectors are free to be far away from the origin with a smooth growth in the score function.

\section{Lorentzian Factorization Machine}

In this section, we first give an overview of our proposed Lorentzian Factorization Machine or {\em LorentzFM} for short, named after learning the triangle inequality equipped with Lorentz distance. Next, we describe each component of the model in some greater details.
Finally, we present a detailed description of how to optimize the model.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.99\columnwidth]{architecture.pdf}
\end{center}
\caption{The architecture of LorentzFM. It comprises an input layer, a Lorentz embedding layer and a triangle pooling layer to aggregate feature interactions.} \label{figure:model_architecture}
\end{figure}

\subsection{Overview}

The goal of our approach is to map the original sparse features into a low-dimensional space. As shown in Figure \ref{figure:model_architecture}, our purposed method takes the sparse feature vector $\mathcal{V}_x$ as input, followed by a Lorentz embedding layer that projects all features into the same hyperbolic space. Next, we feed the embeddings of all fields into a novel triangle pooling layer, which is coined as an aggregation function of all feature pairs to measure the soft ``validness'' of triangle inequality in overall. Unlike the recent state-of-the-arts neural architectures built upon Euclidean embeddings, LorentzFM does not need any extra parameters. In particular, for given sparse input $\mathcal{V}_x$, the output of the pooling layer is the model output score:
\begin{equation}\label{eq: LFM}
    \hat{S}_{LFM}(\mathcal{V}_x) = \sum_{i,j=1,i\neq j}^d \mathcal{T}(\textbf{v}_i, \textbf{v}_j)x_i x_j,
\end{equation}
where $\textbf{v}_i, \textbf{v}_k \in \mathcal{H}^{n}$ are embedding vector for each input feature field, and $\mathcal{T(\cdot, \cdot)}$ is the feature interaction function. Although formally in Eq. \eqref{eq: LFM} the linear term is missing, it actually reappears in the pooling function, $\mathcal{T(\cdot, \cdot)}$, as shown later.

\subsection{Lorentz Embedding Layer}
The embedding layer is a lookup table to project sparse features to low-dimensional dense vectors in the Lorentz space. Formally, let $\textbf{v}^k\in\mathcal{H}^{n}$ be the embedding vector for the $k$-th feature, whereas the 0-th component is given by the constraint as Eq. \eqref{eq: x_0}.

In some cases, categorical features can be multi-valued. For example, the genre of movie ``Titanic'' could be either ``Drama'' or ``Romance''. We use multiple fields for these categorical features under a universal encoding and pad them with ``unknown'' tags to ensure each sample is aligned in feature dimension.

\subsection{Triangle Pooling Layer}
We then feed the embedding vectors into the triangle pooling layer, which is an aggregation function that converts a set of embedding vectors to one vector:
\begin{equation}\label{eq:triangle_pooling}
\begin{aligned}
    \mathcal{T}(\textbf{u}, \textbf{v}) &= \frac{d^2_{\mathcal{L}}(\textbf{u}, \textbf{v}) - d^2_{\mathcal{L}}(\textbf{0}, \textbf{u}) - d^2_{\mathcal{L}}(\textbf{0}, \textbf{v})}{2 \langle\textbf{0}, \textbf{u} \rangle_{\mathcal{L}} \langle\textbf{0}, \textbf{v} \rangle_{\mathcal{L}}} \\
    &= \frac{1 - \langle\textbf{u}, \textbf{v} \rangle_{\mathcal{L}}  - u_0 - v_0}{u_0 v_0} \\
    &= \underbrace{\frac{1 - \langle\textbf{u}, \textbf{v} \rangle_{\mathcal{L}} }{u_0 v_0}}_\text{\clap{interaction term}} - \underbrace{\left( \frac{1}{u_0} + \frac{1}{v_0} \right)}_\text{\clap{linear term}}.
\end{aligned}
\end{equation}
In the second line we use the definition of Lorentz distance and Lorentz inner product. Owing to the normalization denominator, the linear term emerges, as shown in the last line.

\subsection{Objective and Learning}
The objective function to optimize both recommendation system and CTR prediction is the binary cross-entropy (BCE):
\begin{equation}
    \argmin_{\theta} \sum_{i} -y_i \log (p_i) - (1 - y_i) \log (1 - p_i),
\end{equation}
where $p_i$s are the probabilities for the $i$-th sample input vector $\mathcal{V}_{x}^{(i)}$ and computed as $p_i = \sigma(\hat{S}_{LFM}(\mathcal{V}_{x}^{(i)}))$, and $y_i$s are the true labels. Even though Bayesian Personalized Ranking (BPR) loss \cite{bpr} proves to be useful in common recommendation systems, we do not use it because the BCE loss is sign-sensitive, which is the desired property, while the BPR loss is not.

The parameters of our model are learned by using Riemanian stochastic gradient descent (RSGD) \cite{Rsgd}. As shown by \citet{lorentz_model}, the parameters are updated by the following form
\begin{equation}
    \theta_{t+1} = \exp_{\theta_t}(-\eta \,{\rm grad} \, f(\theta_t)),
\end{equation}
where ${\rm grad}\,f(\theta_t)$ is the gradient defined in the Riemannian manifold and $\eta$ is the learning rate. The Riemanian gradient is obtained by multiplying the gradient in the Euclidean space by the Lorentz metric, and then performing an orthogonal projection onto the tangent space spanned by the current parameter set. Finally, the parameter update is given by the following exponential map
\begin{equation}
    \exp_{\theta_t} (\mathbf{x})=\cosh(||{\mathbf{v}}||_{\mathcal{L}}) \mathbf{x} + \sinh({||{\mathbf{v}}||_{\mathcal{L}}}) \frac{\mathbf{v}}{||
    \mathbf{v}||_{\mathcal{L}}}
\end{equation}
which maps a tangent vector $\mathbf{v}$ in the tangent space onto the Lorentz manifold. Details can be found in \citet{lorentz_model}.

Since the score function Eq. \eqref{eq:triangle_inequality} is bounded and dimension independent, it is not necessary to apply an $L_2$ regularization term over the embedding vector, because it will create a resisting gradient towards the origin of the hyperboloid model.

\section{Experiment}\label{section:experiment}
In this section, we evaluate LorentzFM with four real-word datasets. We aim to answer the following research questions:
\begin{itemize}
    \item \textbf{RQ1:} Compared with the state-of-the-art deep learning based methods, how does our method perform?
    \item \textbf{RQ2:} What is the resource cost for LorentzFM compared to existing deep learning based methods?
    \item \textbf{RQ3:} How can we interpret feature interactions learned by LorentzFM?
\end{itemize}

\begin{table}[ht]
\begin{center}
\begin{tabular}{lcccc}
\toprule
 & {Steam} & {MovieLens} & {KKBox} & {Avazu$^{\dagger}$}\tabularnewline
 \midrule
\#Samples & 1.23M & 573K &  2.67M & 40.4M\tabularnewline
\midrule
\#User Fields & 1 & 5& 7& --\tabularnewline
\#Item Fields & 11 & 7& 6& --\tabularnewline
\#Fields & 12 & 12 & 12 & 21 \tabularnewline
\midrule
\#Users & 26.6K & 6.0K & 21.1K & --\tabularnewline
\#Items & 5.9K & 3.1K & 9.3K & --\tabularnewline
\#Features & 46.2K & 9.4K & 38.2K & 972K \tabularnewline
\midrule
Sparsity & 99.22\% & 96.85\% & 98.64\% & -- \tabularnewline
\bottomrule
\end{tabular}
\caption{Statistics of datasets after data preprocessing. $^{\dagger}$ In Avazu dataset there are no explicit indicators for item ID and user IDs, so we leave the corresponding rows blank.}\label{table: data_stats}
\end{center}
\end{table}

\begin{table*}[ht]
\centering
\begin{tabular}{lccccccccccc}
\toprule
 & \multicolumn{3}{c}{Steam} & \multicolumn{3}{c}{MovieLens} & \multicolumn{3}{c}{KKBox} & \multicolumn{2}{c}{Avazu}\tabularnewline
\cmidrule(lr){2-4}
\cmidrule(lr){5-7}
\cmidrule(lr){8-10}
\cmidrule(lr){11-12}
 & MRR & HR@10 & NDCG & MRR & HR@10 & NDCG & MRR & HR@10 & NDCG & AUC & Logloss\tabularnewline
 \midrule
FM & 0.1042 & 0.1898 & 0.2376 & 0.0638 & 0.1258 & 0.1966 & 0.0578 & 0.0998 & 0.1735 & 0.7582 & 0.3920  \tabularnewline
NFM & 0.1213 & 0.2286 & 0.2591 & 0.0723 & 0.1446 & 0.2082 & 0.0586 & 0.1086 & 0.1779 & 0.7641 & 0.3884 \tabularnewline
DeepFM & 0.1284 & 0.2408 & 0.2664 & 0.0780 & 0.1548 & 0.2143 & 0.0637 & 0.1140 & 0.1843 & 0.7674 & 0.3864 \tabularnewline
xDeepFM & 0.1228 & 0.2316 & 0.2615 & \textbf{0.0791} & \textbf{0.1570} & \textbf{0.2156} & 0.0639 & 0.1148 & 0.1846 & 0.7677 & 0.3865 \tabularnewline
DCN & 0.1213 & 0.2261 & 0.2598 & 0.0749 & 0.1512 & 0.2119 & 0.0644 & 0.1136 & 0.1848 & 0.7677 & 0.3863 \tabularnewline
\midrule
LorentzFM & \textbf{0.1362} & \textbf{0.2592} & \textbf{0.2746} & 0.0780 & 0.1533 & 0.2129 & \textbf{0.0733} & \textbf{0.1295} & \textbf{0.1938} & \textbf{0.7775} & \textbf{0.3828} \tabularnewline
\bottomrule
\end{tabular}
\caption{Best performance of each model with fixed embedding size 10 on the test set.} \label{table:performance}
\end{table*}

\subsection{Datasets and Preprocessing}
We use Steam, MovieLens and KKBox datasets to evaluate the recommendation task and Avazu dataset for the CTR task. The datasets are briefly described as follows.
\begin{itemize}
\item \textbf{Steam}\footnote{\url{http://cseweb.ucsd.edu/~jmcauley/datasets.html#steam_data}} is a dataset crawled from Steam database, which includes rich information such as users' playing hours, games' price, category and publisher \textit{etc}. We keep positive samples by setting the threshold of playing hours to 100.
\item \textbf{MovieLens}\footnote{\url{https://grouplens.org/datasets/movielens/1m/}} is a set of benchmark datasets for evaluating recommendation algorithms. We use the MovieLens 1M version and keep samples with ratings above 3.
\item \textbf{KKBox}\footnote{\url{https://www.kaggle.com/c/kkbox-music-recommendation-challenge}} dataset is adopted from the WSDM cup 2018 Challenge provided by the music streaming service KKBox. This dataset includes demographic information about the users and structured meta data about the songs. The original dataset has a binary label and we only keep the positive samples.
\item \textbf{Avazu}\footnote{\url{https://www.kaggle.com/c/avazu-ctr-prediction}} is an ads click-through dataset with more than 40 millions instances. It consists of 10 days of ad click-through data with only sparse features.
\end{itemize}

For the three recommendation datasets we process the dataset as follows: (1) keeping only positive ratings as described above and filter the \{KKBox, Steam, MovieLens\} dataset to \{20, 20, 5\}-core setting; (2) randomly splitting \{10K, 10K\} samples for \{validation, testing\}, and the rest as training set. For the Avazu dataset, we remove the timestamp field and then replace features less than 5 times by a universal ``unknown'' tag.  We randomly select 80\% samples for training and, 10\% for validation and 10\% for testing. Data statistics are shown in Table \ref{table: data_stats}.

\begin{figure*}[ht]
\begin{center}
\includegraphics[width=1.8\columnwidth]{baseline.pdf}
\end{center}
\caption{Performance comparison on the test set {\em w.r.t.} different embedding sizes for the Steam dataset.} \label{figure:dim_performance}
\end{figure*}

\subsection{Experiment Settings}
\subsubsection{Evaluation Metrics}
For each positive user-item pair in the recommendation task, we calculate the following three ranking metrics to evaluate the performance over {\em all} unobserved samples:
\begin{itemize}
    \item \textbf{MRR} is the average of the reciprocal ranks of the test items by their scores over the entire ranking list.
    \item \textbf{HR@10} measures the relative orders among positive and negatives within the top 10 of the ranking list.
    \item \textbf{NDCG} accounts for the position of the test items by assigning higher scores to top ranks over the entire ranking list.
\end{itemize}
For the CTR prediction task, we use {AUC} (Area Under the ROC curve) and {logloss} (binary cross-entropy) for evaluation. AUC measures the probability that an instance prediction will be ranked a higher score to a randomly chosen negative item, and in contrast logloss measures the distance between the predicted score and the ground truth label for each sample.

\subsubsection{Compared Baselines}
We consider the following models are our baselines:
\begin{itemize}
\item \textbf{FM} \cite{FM} combines the second-order feature interaction as well as a first order term.
\item \textbf{NFM} \cite{NFM}  can learn implicit high-order features by stacking MLP on top of the FM model.
\item \textbf{DCN} \cite{DCN}  concatenates MLP and Cross Network, which takes outer product of concatenated feature vector at bit-wise level. It can extract both the implicit and explicit high-order features.
\item \textbf{DeepFM} \cite{DeepFM}  combines the FM model and deep MLP to get the low and high-order features.
\item \textbf{xDeepFM} \cite{Xdeepfm} takes out product at the vector-wise level and applies the convolution layers to get the high-order explicit and implicit features.
\end{itemize}

\begin{table*}[ht]
\begin{center}
\begin{tabular}{lcccccccc}
\toprule
 & \multicolumn{4}{c}{\# Training Parameters}
 & \multicolumn{4}{c}{Training Time per Epoch (seconds)} \tabularnewline
 \cmidrule(lr){2-5}
\cmidrule(lr){6-9}
 & Steam & MovieLens & KKBox & Avazu & Steam & MovieLens & KKBox & Avazu \tabularnewline
 \midrule
FM & 507k & 103k & 420k & 10.68M & 124.0 & 82.4 & 648.3 & 312.1 \tabularnewline
NFM & 519k & 115k & 432k & 11.36M & 158.7 & 87.7 & 746.6 & 478.2 \tabularnewline
DeepFM & 717k & 313k & 634k & 11.10M & 159.2 & 87.1 & 693.3 & 450.7 \tabularnewline
xDeepFM & 865k & 498k & 808k & 11.46M & 391.0 & 223.4 & 1340.2 & 1459.8 \tabularnewline
DCN & 530k & 126k & 444k & 11.24M & 152.6 & 62.16 & 666.8 & 547.2 \tabularnewline
\midrule
LorentzFM & 415k & 85k & 344k & 8.75M & 160.7 & 67.6 & 664.2 & 522.2 \tabularnewline
$-\Delta$\%  & 21.8\%  & 82.9\% & 57.4\% & 22.1\% & -8.1\% & 69.7\% & 50.4\% & 4.6\% \tabularnewline
\bottomrule
\end{tabular}
\caption{Number of training parameters and training time per epoch according to the best performance in Table  \ref{table:performance}. The last row corresponds to the reduced percentage in training parameters or training time of LorentzFM, compared to the best performed baseline.}\label{table:cost_compare}
\end{center}
\end{table*}

\subsection{Training Details}
We implement LorentzFM and all baselines in PyTorch\footnote{\url{https://pytorch.org/}} \cite{pytorch}, and for each model the reported performance is given by performing grid search over the hyper-parameters on the validation set, with early stopping at 20 epochs.  The embedding size is set to 10 for all models for fair comparisons.
For the recommendation task, for each-item pair in the training set, we randomly sample 10 unobserved items together with the given user as negative samples. MRR is the metric for early stopping. For the CTR task, we use the original binary labels for training, and logloss is monitored for early stopping .

\textbf{LorentzFM Details}  Burn-in period is set to 25 epochs. For the recommendation task, we tune the learning rate $\in$ [0.05, 0.1, 0.2, 0.3] with RSGD and batch size $\in$ [64, 128, 256, 512]. For the CTR prediction task, the learning rate is tuned $\in$ [0.1, 0.2, 0.3] and batch size is set to 4096.

\textbf{Baselines Details}  The loss function is BPR loss for the recommendation task and BCE loss for the CTR task. We tune the dropout rate $p \in \{0,\,0.1,\dots,\,0.5\}$, the MLP layers $\in$ [[512, 256], [400, 400], [100, 100]], and the batch size $\in$ [64, 128, 256, 512].
Learning rate is set to 0.001 with Adam optimizer \cite{Adam}. We use an $L_2$ regularization with $\lambda=10^{-5}$. For the CTR prediction task, all hyper-parameters except for the embedding size are set identical to the original paper.

\subsection{Performance Comparison (RQ1)}
Table \ref{table:performance} reports our experiment results of each individual model on the four datasets with fixed embedding size 10. For each dataset, all the deep learning methods (NFM, DeepFM, xDeepFM and DCN) substantially outperform FM. It is expected because additional neural net layers built on top of the second-order feature interaction layer will incorporate higher-order feature interactions. The performance between these deep learning models are close upon fine-tuning over the hyper-parameters. Surprisingly, LorentzFM achieves even better results compared to these deep learning models significantly except for the MovieLens dataset. We observe that in MovieLens the number of sparse features is 5-100 times smaller than the other three datasets, which reflects that LorentzFM is especially powerful when the data is extremely sparse.

In order to understand the impact of embedding size on LorentzFM as well as the compared baselines, we conduct control experiments on the Steam dataset by holding the best hyper-parameter settings for each model in Table \ref{table:performance}, while varying the embedding size $\in[5,\,10,\,15,\,20]$. Figure \ref{figure:dim_performance} demonstrates that in general the performance of all models increases with embedding size except for FM. Note that the performance of LorentzFM surpasses over other deep learning methods at embedding size $\in [10,\,15,\,20]$.

\subsection{Resource Cost Comparison (RQ2)}
Table \ref{table:cost_compare} compares the amount of training parameters and the training time per epoch between LorentzFM and the best tuned baselines. In order to compare the training time fairly, we use the same batch size for each model. The number of training parameters for LorentzFM is 9 times feature size, because the zeroth component of each embedding vector is not a free parameter. In the last row of Table \ref{table:cost_compare}, we show the reduced percentage of the corresponding training parameters and training time when LorentzFM is compared with the best performing baseline. Because LorentzFM does not need any deep learning layers on top of the triangle pooling layer, it could reduce up to 82.9\% training parameters and 69.7\% in training time compared to xDeepFM.

\subsection{Case Study (RQ3)}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=1.\columnwidth]{case.pdf}
\end{center}
\caption{Visualization of the heatmap of score functions from LorentzFM for (a) a positive sample and (b) a negative sample, and from FM for the same (c) positive sample and (d) negative sample.} \label{figure:case_study}
\end{figure}

The fine-grained feature interactions are the essence for LorentzFM to outperform deep learning models. Therefore, it is expected that the structure of the feature interactions is capable to explain the human behavior. To demonstrate this, we sample a typical user (user ID ``76561198071045315'') whose almost \textit{all} positive ratings are free in price from the Steam dataset. We then plot the heatmap of feature interaction score of a positive item and a negative item from the test set for both LorentzFM and FM. The result is shown in Figure \ref{figure:case_study}, in which we mask the diagonal elements. From the heatmap we observe the following:

\begin{itemize}
    \item For the positive sample, the game is free of charge. The feature interaction score between ``UserID'' and ``Price'' learned by LorentzFM is highlighted with score 0.4, indicating that price free is strongly preferred by the user, see Figure \ref{figure:case_study} (a). However, as shown in Figure \ref{figure:case_study} (c), the information about this fine structure is missing in the heatmap for FM, because the inner product between the embedding of this ``UserID'' and ``Price'' is -0.14.
    \item For the negative sample, the price of the game is \$14.99. In this case, the score learned by LorentzFM between ``UserID' and ``Price'' is the most negative among others, as shown in Figure \ref{figure:case_study} (b), meaning that the negative sample is recognized mostly due to its price. On the other hand, the inner product between ``UserID'' and ``Price'' is not dominating for FM.
\end{itemize}
This case study shows that compared to FM, the interactions between feature pairs learned from LorentzFM are more informatively related to the underlying facts according to the sign and the magnitude of the pairwise score.

\section{Related Work}\label{section: related_work}

Factorization machine (FM) \cite{FM} and field-aware factorization machine (FFM) \cite{FFM} are two of the most well-known models for both recommendation systems and CTR predictions. FM models the sparse feature interactions by learning latent factors, and FFM introduced field aware factors to increase the model capacity and expressiveness. However, FFM consumes huge memory due to its field awareness and henceforth its scalability is restricted. Therefore, higher-order factorization machine \cite{HOFM} is proposed to model feature interactions beyond quadratic level.

The research community of CTR prediction recently pays more attention to the deep learning models, due to their strong capabilities in feature extraction. Wide \& Deep model was initially introduced for jointly training wide linear models and deep neural networks to capture both shallow and deep representations. However, these advances still require manual efforts for feature engineering in advance of model training stage. DeepFM \cite{DeepFM}, Neural FM \cite{NFM} and Deep \& Cross Network \cite{DCN} are representative models to combine low-order and high-order feature interactions to improve the performance in CTR in an automatic manner. Product-based Neural Networks \cite{pnn} tries to capture high-order feature interactions by involving a product layer on top of the embedding layer. Apart from the advances in model architectures, attention mechanism, which first appears in neural machine translation models to learn a weighted sum of model outputs, also finds its impact for CTR and recommendation systems. Works that incorporate attention mechanism include Deep Interest Network \cite{DIN}, Attentional Factorization Machine \cite{afm} and AutoInt \cite{AutoINT}.

Traditional research on recommendation system tries to learn latent factors for user and items based on their preferences \cite{prob_mf,dl_cf}. In these works, learning latent factors by factorizing the interaction matrix is equivalent to using Euclidean inner product of embeddings of user, item and their side information. Our work is inspired by the seminal paper collaborative metric learning \cite{cml} which argues that inner product formulation will result in violation of triangle inequality in Euclidean space. The authors propose to learn not only user-item, but also user-user and item-item distances. This idea is later on generalized to use hyperbolic distance \cite{hyper_rec,scalable_hyper_rec} for recommendation systems, accompanied by the recent advances in hyperbolic representation learning and hyperbolic neural networks \cite{Poincare_embedding,lorentz_model,hyper_entail_cone,Tradeoff_hyperbolic,Lorentz_distance_learning,Hyperbolic_attention_network,radam}. While hyperbolic representation seems eminent over Euclidean representations in many applications, especially for problems with underlying hierarchical structures, previous study focus on learning the distances rather than the violation of triangle inequalities in terms of Lorentz distance. Besides, another type of approach to model feature interactions is to replace the inner product in the FM by circular correlation or circular convolution, as shown in \citet{holo_fm}.

\section{Conclusion}
In this paper, we present a lightweight yet effective model named LorentzFM for recommendation and CTR prediction tasks. We propose a new score function by characterizing if the triangle inequality for Lorentz distance is violated or not in the hyperboloid model. Our model is advantageous with its capability in modeling feature interactions with the underlying geometry, without using any deep learning layers. Empirical experiment results on four real-world benchmark dataset show that LorentzFM achieves the state-of-the-art performance, outperforming multiple existing deep learning baselines, while using fewer training parameters and less training time.

\section{Acknowledgements}
The authors thanks Vivian Tian, Alan Lu, Hua
Yang and Xiaoyuan Wu for their supports, and anonymous reviewers for their valuable comments.

\bigskip

redpajama_set_name: RedPajamaArXiv


The MIT Sloan School of Management recently hosted an alumni webinar featuring ShiftGear Partner (+ MIT Professor) Nelson Repenning. Repenning shared an overview on Dynamic Work Design with brief case studies and the research behind the principles.
To extend the reach of the principles, MIT shared the webinar link with ShiftGear.


text:
Tribulus terrestris L.
Tribulus lanuginosus L. Tribulus saharae A. Chev. Tribulus terrestris var. sericeus Andersson ex Svenson. [1]
English Tadjaroft , gokhru, nerunji, puncture vine, gokshura [2]
Thailand khokkrasun (central); naam krasung, naam din (northern) [3]
Vietnam t[aaj]t l[ee], b[aj]ch t[aaj]t l[ee], gai ma v[uw][ow]ng [3]
Tribulus terrestris is native of the Mediterranean region, now widespread throughout the world from 35°S to 47°N, often as a noxious weed. It is not recorded as a weed in Central or South America, South-East Asia or western Africa. [3]
T. terrestris has the prostate, flat stems radiate from the crown to a diameter of up to a metre. They grow in horizontal patches unless growing in shade where they tend to grow taller. T. terrestris produces flowers that are measuring 5 mm to 10 mm wide with yellow petals. The flowers produce a fruit that is composed of four or five sections or nutlets which have sharp spines. The carpals of the fruit resemble the cloven hoof of a cow. [2][3]
T. terrestris has been reported to contain terrestrosins A, B, C, D, E; alkaloids; Sterols including β-sitosterol, campesterol, stigmasterol; flavinoids; terrestiamide, tannins, tribol, spirostanol saponins. [4][5][6]
Fruit and root. Occasionally the stem is used as an astringent. [4]
In the variety of African traditional medical systems, the most concentrated usage of T. terrestris occurs in the Central Saharan region of the continent. As it is throughout the rest of its natural habitat, one of the most common uses of T. terrestris is that of an aphrodisiac. In Algeria, one popular application of T. terrestris as an aphrodisiac is an infusion of the fruit ingested. In West Africa, it is more common for the fruits to be ingested alone to achieve the same effect. [3] In other cases, the whole plant is decocted and ingested. [7] In cases of certain sexually transmitted diseases, namely gonorrhea, the roots are boiled in water, and then ingested throughout the day. [8]
Another very common usage of T. terrestris is as a gastrointestinal aide. In cases of diarrhea, the leaves and twigs are often used to alleviate symptoms. In some cases, leafy twigs are macerated and combined with herbs into a sauce which is eaten with meals. [7] In other cases, a leaf tea is ingested. [3] T. terrestris is also considered in some African traditional medical systems to be a very effective diuretic. Fruit extracts of T. terrestris have been used and thought to be both diuretic and stimulant. [9]
T. terrestris has been found in laboratory studies to possess antifungal and antibacterial properties. In one study this herb was tested against 11 species of pathogenic and non-pathogenic microorganisms. Extracts from all parts of the plant were tested and all demonstrated antimicrobial activity against most of the 11 organisms. Of the plant parts tested, the most active against both Gram-negative and Gram-positive bacteria was ethanol extract from the fruits. This same extract also demonstrated anti-fungal activity against C. albicans. [10] An in vitro study examined the anti-fungal activity of eight saponins from T. terrestris against six fluconazole-resistant yeasts. The results demonstrated effective antifungal activity for two of the saponins (TTS-12 and TTS-15) against several candidal species. [11] Additional research has supported these findings. [12]
Research has continued into the cytotoxic properties of T. terrestris against several types of cancer cell lines. One of the active principles of this herb, spirostanol glycoside, demonstrated a broad range of anticancer activity against multiple areas. [12] In one study, saponins from T. terrestris were examined against liver cancer cell lines. The saponins demonstrated cytotoxic activity against the liver cancer cells through apoptosi. [13] In an in-vitro study, saponins were examined against renal carcinoma cells and again, the results indicated that the saponins decreased the number of cancer cells though apoptosis. [14] The method by which this action takes place is thought to involve up- and down-regulation of polyamines' homeostasis, suppression of proliferation, and inducing apoptosis. [15]
T. terrestris is also often used in the treatment of hypertension and in heart disease. [16] In one fairly large study of over 400 patients with coronary heart disease, saponins from T. terrestris demonstrated the action of dilating coronary artery and improving coronary circulation and demonstrated more positive effects on improving ECG of myocardial ischemia than patients in a control group taking Yufen Ningxin Pian. Researchers concluded that this herb has the potential to be an ideal treatment for angina pectoris as it produces no adverse side effects on hepatic and renal functions even when taken over a long period of time. [17]
T. terrestris is also used as anaphrodisiac, primarily in males and, due to its ability increase certain sexual hormones, it has been used in mild cases of erectile dysfunction. [18][19]
T. terrestris is also marketed as a dietary supplement to improve endurance and strength during exercise. Not only has this not been substantiated, but there have been numerous studies that have shown negative results for this application. [20][21] There have also been reports of increased incidence of gynaecomastia in male body builders. [22]
T. terrestris is also often used in the treatment of hypertension and in heart disease. In one fairly large study of over 400 patients with coronary heart disease, saponins from T. terrestris demonstrated the action of dilating coronary artery and improving coronary circulation and demonstrated more positive effects on improving ECG of myocardial ischemia than patients in a control group taking Yufen Ningxin Pian. Researchers concluded that this herb has the potential to be an ideal treatment for angina pectoris as it produces no adverse side effects on hepatic and renal functions even when taken over a long period of time. [20]
Based on pharmacology, use with caution if taking hormonal medications such as estrogen, progesterone and testosterone. [14][15]
Dosage Range
5-1g dried fruit powder as directed. [2]
Most Common Dosage
250 mg extract of fruit standardized to contain 40% saponins. [2]
The Plant List. Ver1.1. Tribulus terrestris L. [homepage on the Internet]. c2013 [updated 2012 Apr 18; cited 2016 Jan 15]. Available from: http://www.theplantlist.org/tpl1.1/search?q=Tribulus+terrestris
Kapoor LD. CRC Handbook of Ayurvedic medicinal plants. Boca Raton, Florida: CRC Press, 1990; p. 325.
Chuakul W, Soonthornchareonnon N, Ruangsomboon O. Tribulus terrestris L. In: van Valkenburg JLCH, Bunyapraphatsara N, editors. Plant Resources of South-East Asia No. 12(2): Medicinal and poisonous plants 2. Leiden, Netherlands: Backhuys Publisher, 2001; p. 562
Conrad J, Dinchev D, Klaiber I, Mika S, Kostova I, Kraus W. A novel furostanol saponin from Tribulus terrestris of Bulgarian origin. Fitoterapia. 2004;75(2):117-122.
Huang JW, Tan CH, Jiang SH, Zhu DY. Terrestrinins A and B, two new steroid saponins from Tribulus terrestris. J Asian Nat Prod Res. 2003;5(4):285-290.
De Combarieu E, Fuzzati N, Lovati M, Mercalli E. Furostanol saponins from Tribulus terrestris. Fitoterapia. 2003;74(6):583-591.
Neuwinger HD. African traditional medicine: A dictionary of plant use and applications. Stuttgart, Germany: Medpharm Gmbh Scientific Publishers, 2000; p. 338-339.
Samuelsson G, Farah MH, Claeson P, et al. Inventory of plants used in traditional medicine in Somalia. IV. Plants of the families Passifloraceae-Zygophyllaceae. J Ethnopharmacol. 1993;38(1):1-29.
Kerharo J, Adam JG. La Pharmacopée sénégalaise traditionnelle: Plantes médicinales et toxiques. Paris, France: Vigot Publishing; 1974.
Al-Bayati FA, Al-Mola HF. Antibacterial and antifungal activities of different parts of Tribulus terrestris L. growing in Iraq. J Zhejiang Univ Sci B. 2008;9(2):154-159.
Zhang JD, Cao YB, Xu Z, et al. In vitro and in vivo antifungal activities of the eight steroid saponins from Tribulus terrestris L. with potent activity against fluconazole-resistant fungal pathogens. Biol Pharm Bull. 2005;28(12):2211-2215.
Bedir E, Khan IA, Walker LA. Biologically active steroidal glycosides from Tribulus terrestris. Pharmazie. 2002;57(7):491-493.
Sun B, Qu WJ, Zhang XL, Yang HJ, Zhuang XY, Zhang P. Investigation on inhibitory and apoptosis-inducing effects of saponins from Tribulus terrestris on hepatoma cell line BEL-7402. Zhongguo Zhong Yao Za Zhi. 2004;29(7):681-684.
Yang HJ, Qu WJ, Sun B. Experimental study of saponins from Tribulus terrestris on renal carcinoma cell line. Zhongguo Zhong Yao Za Zhi. 2005;30(16):1271-1274.
Neychev VK, Nikolova E, Zhelev N, Mitev VI. Saponins from Tribulus terrestris L are less toxic for normal human fibroblasts than for many cancer lines: influence on apoptosis and proliferation. Exp Biol Med (Maywood). 2007;232(1):126-133.
Premila MS. Ayurvedic herbs: A clinical guide to the healing plants of traditional indian medicine. Binghamton, New York: The Hayworth Press; 2006.
Wang B, Ma L, Liu T. 406 cases of angina pectoris in coronary heart disease treated with saponin of Tribulus terrestris. Zhong Xi Yi Jie He Za Zhi. 1990;10(2):85-87, 68.
Gauthaman K, Ganesan AP, Prasad RN. Sexual effects of puncturevine (Tribulus terrestris) extract (protodioscin): an evaluation using a rat model. J Altern Complement Med. 2003; 9(2): 257-265
Gauthaman K, Ganesan AP. The hormonal effects of Tribulus Terrestris and its role in the management of male erectile dysfunction and evaluation using primates, rabbit and rat. Phytomedicine. 2008;15(1-2):44-54
Neychev VK, Mitev VI. The aphrodisiac herb Tribulus terrestris does not influence the androgen production in young men. J Ethnopharmacol. 2005;101(1-3):319-323.
Rogerson S, Riches CJ, Jennings C, Weatherby RP, Meir RA, Marshall-Gradisnik SM. The effect of five weeks of Tribulus terrestris supplementation on muscle strength and body composition during preseason training in elite rugby league players. J Strength Cond Res. 2007;21(2):348-353.
Jameel JK, Kneeshaw PJ, Rao VS, Drew PJ. Gynaecomastia and the plant product "Tribulis terrestris". Breast. 2004;13(5):428-430.

redpajama_set_name: RedPajamaCommonCrawl


text:
using System.ComponentModel.DataAnnotations;
using System.ComponentModel.DataAnnotations.Schema;
using TrackableEntities.Client;

namespace WebApiSample.Shared.Entities.Models
{
    [Table("Customer")]
    public partial class Customer : EntityBase
    {
        public Customer()
        {
            Orders = new ChangeTrackingCollection<Order>();
        }

        [StringLength(5)]
		public string CustomerId
		{
			get { return _CustomerId; }
			set
			{
				if (Equals(value, _CustomerId)) return;
				_CustomerId = value;
				NotifyPropertyChanged();
			}
		}
		private string _CustomerId;

        [Required]
        [StringLength(40)]
		public string CompanyName
		{
			get { return _CompanyName; }
			set
			{
				if (Equals(value, _CompanyName)) return;
				_CompanyName = value;
				NotifyPropertyChanged();
			}
		}
		private string _CompanyName;

        [StringLength(30)]
		public string ContactName
		{
			get { return _ContactName; }
			set
			{
				if (Equals(value, _ContactName)) return;
				_ContactName = value;
				NotifyPropertyChanged();
			}
		}
		private string _ContactName;

        [StringLength(15)]
		public string City
		{
			get { return _City; }
			set
			{
				if (Equals(value, _City)) return;
				_City = value;
				NotifyPropertyChanged();
			}
		}
		private string _City;

        [StringLength(15)]
		public string Country
		{
			get { return _Country; }
			set
			{
				if (Equals(value, _Country)) return;
				_Country = value;
				NotifyPropertyChanged();
			}
		}
		private string _Country;

		public CustomerSetting CustomerSetting
		{
			get { return _CustomerSetting; }
			set
			{
				if (Equals(value, _CustomerSetting)) return;
				_CustomerSetting = value;
				CustomerSettingChangeTracker = _CustomerSetting == null ? null
					: new ChangeTrackingCollection<CustomerSetting> { _CustomerSetting };
				NotifyPropertyChanged();
			}
		}
		private CustomerSetting _CustomerSetting;
		private ChangeTrackingCollection<CustomerSetting> CustomerSettingChangeTracker { get; set; }

		public ChangeTrackingCollection<Order> Orders
		{
			get { return _Orders; }
			set
			{
				if (Equals(value, _Orders)) return;
				_Orders = value;
				NotifyPropertyChanged();
			}
		}
		private ChangeTrackingCollection<Order> _Orders;
    }
}

redpajama_set_name: RedPajamaGithub


text:
DAY6 is for everybody
A spot of affordable luxury in an old Manila racetrack
The Hippodrome Bar has nightly live entertainment featuring well-known local artists and foreign performers.
Winford Manila Resort and Casino hosts families whose kids love its innovative swimming pool
By: Linda B. Bolido Philippine Daily Inquirer / 05:05 AM July 20, 2019
Regardless of Winford Manila Resort and Casino's industry ranking, its hotel manager, Ryan Rabe, promises guests a five-star experience—whether for a staycation, or for a day or night of fun and games.
Built in 2016, Winford may still be unfamiliar to people south of the Pasig River, but seems to be gaining popularity among guests who've been there.
These include families with young children wanting a respite from their domestic routine, but unwilling to make a long, exhausting trip out of Metro Manila.
People on the north side of the Pasig now mark milestones or celebrate special occasions at Winford. Several schools in or around the University Belt also look no further than Winford as venue for their social events. It is, after all, the only hotel of top quality that is nearest to them.
Ryan Rabe, Winford Manila Resort and Casino manager
On a recent weekend, Winford—designed by Recio & Casas and occupying 7,510 square meters of the old San Lazaro Hippodrome—hosted families with young children who wanted to enjoy its amenities including the innovative swimming pool.
It was also the venue for a big event which, one of the guests was overheard saying, was organized by the National Teachers College.
Gaming enthusiasts and cockfighting and bingo fans have also been finding their way to Winford.
Winford's rooms are generously proportioned.
The 22-story Winford, the first hotel venture of the Manila Jockey Club, is one of several commercial and residential establishments that have risen on what was once the San Lazaro racetrack in Manila's Santa Cruz district.
The old racetrack is now a mixed-use development known as the San Lazaro Tourism and Business Park. A number of property developers have established their presence.
Right across is an SM mall. The Ayala group has a condo building and may soon be joined by other developers.
Although it has the character of a luxury hotel, Winford's rates of its 128 rooms and executive suites are not expensive. And unlike most new hotels, Winford's rooms, including the bathrooms, are spacious.
An executive suite has two sinks in the bathroom, and a toilet in the receiving area to keep the privacy of the sleeping quarters.
The hotel has four food and beverage outlets. Choi's Garden—an executive of another hotel says it's among the better Chinese restaurants in a hotel—serves authentic Cantonese food and is the largest of the Choi's Garden chain in Metro Manila with seating for 300 guests and a presidential room for functions.
Copa de Manila is a Spanish-Filipino restaurant, while the Hippodrome Bar and Lounge, a nod to the racetrack, is the entertainment venue.
Children and adults have hours of fun in this innovative pool designed like a fountain.
Rabe says the hotel features live entertainment every night. A recent performer was "American Idol" finalist Jessica Sanchez.
The Pool Bar on the 11th floor lets guests enjoy the innovative pool. A project of DQA Environmental Design, the pool has water flowing from several pipes built into a low wall that children love to soak in.
On the fourth floor is the ballroom that can accommodate 700 guests. Although used for weddings, birthdays and other occasions, it also has facilities for MICE (meetings, incentives, conventions and exhibitions), a major marketing thrust of the government's Tourism Promotions Board.
Winford can be a convenient starting point to explore Manila's historic, religious and cultural sites. Vintage churches like the Minor Basilica of the Black Nazarene (Quiapo), Our Lady of the Pillar Parish Church (Santa Cruz), San Sebastián, Saint Jude, and Our Lady of Montserrat in San Beda, as well as bargain centers (Tutuban, Divisoria and Chinatown) are only a few minutes away. Public utility jeepneys, tricycles and the LRT are options for those who don't want to drive through Manila traffic.
Huge metallic roses and a modern chandelier lend the reception area a distinctive look.
There's a shuttle service to Lucky Chinatown, which is next door to the retail mecca 168 Mall. Shuttle is also available to and from points in Caloocan and Quezon cities and other parts of Metro Manila and Bulacan province.
Also accessible is the Dangwa Flower Market, and Bambang, a popular source of reasonably priced medical equipment and supplies. —CONTRIBUTED
Winford Manila Resort and Casino is on MJC Drive, Santa Cruz, Manila; tel. 5282300; winfordmanila.com
Recio + CasasRyan RabeSan Lazaro HippodromeWinford Manila Resort and Casino
racosta
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When Q'ero shaman Don Francisco takes the 'iron bird' from Peru to visit the 'brothers and sisters in the North,' he is besieged by requests to perform despachos (the ceremony by which prayers may be actualized) and to administer the nine rites of the Munay-Ki (the q'ero rites of passage). So I was not surprised when I was asked to film Don Francisco explaining the importance of the Munay-Ki for a global audience.
2) the Spanish so that we could easily create subtitles later.
This sounded simple, but Don Francisco would answer and then quickly look at Mauricio for approval. I opened my big mouth and suggested through Mauricio that Don Francisco keep looking at the camera lens. The video below picks it up as I begin to call for action and Mauricio reminds Don Francisco to look at the camera, and not the translator.
As Mauricio translated my request, Don Francisco 'broke character' and gave the response of toleration: "Yeh, Yeh Yeh." He then proceeded to answer the question "Why is the Munay-Ki important?" as if he were never interrupted.
and prayers of the participants of a despacho. I was ready to put the microphone on Don Francisco and turned to him on the bench — he was gone!
Don Francisco returned smiling with these massive kintus, which are usually the size of coca or bay leaves.


Please note that Pick Up Times are between the hours of 7:00am & 4:30pm EST Monday through Friday, excluding University Holidays and closings. Property must be paid for and removed within 5 business days of auction close.
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text:
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We chart a course through the Drake Passage and along the Antarctic Peninsula with the ambition of crossing the Antarctic Circle. The farther south we go, the more sea ice we are likely to encounter, along with incredible wildlife and awe-inspiring scenery. Should we arrive at 66°33'S, we'll join the small band of explorers that can claim they have made it this far south.
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Itinerary Overview
Day 1: Arrival
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Day 15: Disembarkation
Download Itinerary
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No need to stress about missed connections or flight delays as you arrive with plenty of time to unwind and enjoy the beautiful Arakur Resort & Spa or spend time discovering the southernmost city in the world, Ushuaia.
Day 2, Ushuaia
Explore the sights of Ushuaia such as the museums and Argentinean leather markets or continue relaxing at the hotel. Attend the optional evening briefing for the opportunity to ask questions and meet some of your fellow travelers.
Day 3, Embarkation
Spend your morning exploring Ushuaia or unwinding at the resort until our mid-afternoon transfer to the ship. Our Expedition Team and ship staff will greet you on board, followed by a safety and orientation briefing and Captain's welcome dinner.
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Join our Polar Experts as they teach you about everything Antarctic, from wildlife to history; participate in our renowned Citizen Science program; or sit back and take in this fabled journey while catching exciting glimpses of wildlife. Grab your binoculars to identify the many seabirds that follow the ship as we cross the Antarctic Convergence into Antarctic waters and noticeably cooler temperatures.
Day 6, South Shetland Islands
The volcanic South Shetland Islands offer amazing abundance and beauty, so we'll hop into our inflatable Zodiac boats and spend as much time as possible exploring. Be prepared to marvel up close at nature's glory!
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Day 7-9, Antarctic Circle
Heading south across the Bransfield Strait, we sail towards the Antarctic Circle. From our most southern point (south of the Antarctic Circle), we'll start making our way back north, cruising through the narrow channels of the Antarctic Peninsula.
Day 10-12, Peninsula
Heading north, we'll explore any number of picturesque bays and famed harbors, maneuvering through majestic channels as we travel the wildlife-rich waters. There are great opportunities to stop at several active scientific bases and historic landing sites as we spot numerous species of penguins, seals, and whales along the rugged coastlines and in the sea.
Day 13-14, Drake Passage
We leave this magical place and make our way north, once again crossing the legendary Drake Passage. We have one last hurrah as we celebrate the conclusion of our expedition with a special slideshow and a final meal together.
Day 15, Ushuaia Disembarkation
With huge smiles on weary, content faces, we disembark in the morning, letting you catch a flight to Buenos Aires or stay in Ushuaia for more sights and adventure.
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*Camping is not available on all departures.
CITIZEN SCIENCE Included
PHOTOGRAPHY Included
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Prices quoted are per-person based on double/triple occupancy.
A limited number of twin suites may be sold for single occupancy at 1.7 times the twin rate.
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The most experienced team on land, water, or ice
World class marine biologists, environmental scientists, ornithologists, and modern day explorers are all part of our expedition team - highly experienced, synced to your needs and interests, and with safety always top of mind. More than a team, though, this is a tight knit family. Most of us voyage together year after year, all share a deep love for Antarctica, and all take immense pleasure in making your trip one you'll never forget.
Polar Latitudes is one of the few operators that require all operational staff to be certified as crew under the International Maritime Organization's STCW standards. Furthermore, we are the first polar operator to adopt the Polar Tourism Guides Association (PTGA) guide qualification framework, a world first in training and certifying polar guides in the skills and experience required for our unique industry. Read more about why you should consider choosing PTGA accredited guides here.
Check out some of our amazing Expedition Staff below!
Expedition Team changes for each departure and is composed of at least one of each of the roles below.
Team details are sent via email approximately 90 days prior to departure.
Hayley Shephard
Director of Expedition Operations
Hannah Lawson
Nate Small
Pablo Brandeman
Assistant Expedition Leader
Mariela Cornejo
Passenger Service Manager
Conny Bartl
Seb Coulthard
Antarctic Historian
Bob Gilmore
Citizen Science Coordinator
Annette Bombosch, PhD
Jeff Reynolds
Jim Gardner
Tracy Allen
Marty Garwood
Sophie Ballagh
Kayak Guide
Ewan Blyth
Assistant Kayak Guide
Steve Schellenberg
Ben Osborne
Photography Coach
Mathew Farrell
Will Rogan
Adam Rheborg
Tim Warren
Randy Bulicka
Dr. Dan Schual-Berke
Falcon Scott
Hella Martens
Ashley Hamilton
Kurtis Randall
Silver medalist in the 2017 World Guide Awards, Hayley has spent 13 years adventuring in Antarctica, and still feels privileged to walk amongst the penguins, float on a sea of bergy bits, or await the surface of a Humpback while surrounded by glaciers, icebergs and rugged mountain peaks. Hayley's motto is, "Live your dreams, follow your passions."
In BC, Canada, Hayley keeps in the company of Orca and Humpback whales, Grizzly and Black bears. She relishes in the Polar bear and Beluga whale capital of the world working as a guide in Churchill, Manitoba. Originally from the Kapiti Coast in New Zealand, she now calls Vancouver Island home. In her spare time, Hayley likes to take extended sea kayaking adventures around Vancouver Island and Haida Gwaii. She once attempted the world's first solo sea kayak journey around South Georgia Island to help raise awareness for the Albatross, about which a book and documentary were made.
Hayley looks forward to sharing with you her passion, admiration and respect for this polar region. It will change you. Are you ready?
Hannah has a particular love of birdlife and marine mammals and has been sharing her thrill for the natural world working aboard Expedition Ships in remote regions since 1999.
A zoology student at the University of Liverpool, England, Hannah changed direction after graduation and worked as a wildlife artist and mural painter in Africa for several years. On her return to the UK she gained a Masters in Natural History Illustration from the Royal College of Art in London. During her student years she spent her time doing practical conservation projects as a leader with British Trust for Conservation Volunteers.
She is now able to divide her time between doing artwork from her studio in England and working as a wildlife guide, zodiac driver and expedition leader. She visits the Antarctic peninsula and South Georgia annually in the Austral summer and then heads north to cruise the shoreline of the UK, Norway and the Arctic, swapping penguin sightings for polar bears, and sketching, photographing and learning about the lives of the creatures she sees along the way.
For the past few years he has been immersed in the polar world. He makes his annual migration between Antarctica and the Arctic, following the arctic terns around the world every year. Having done nearly 70 trips (and still counting) in the Polar Regions, he is always grateful to be discovering the last vast wildernesses left on this planet and is passionate to share the experience with you. He is enthusiastic about all sorts of wildlife, though is convinced that he has close relatives that are whales, and his third cousin happens to be in the auk family.
When he's not gallivanting near the poles, you will probably find him wandering the warmer climes of the planet (15 Celsius being plenty warm), seeking out more adventures and playing with light in photography.
Born in Bariloche, North Argentinean Patagonia, Pablo was introduced to outdoors and tourism as a small child. He moved to Ushuaia in 1996 and shortly after made his way into Expedition Cruising as an Assistant Expedition Leader.
Pablo has done over 140 trips to the Antarctic Peninsula, South Georgia, Falklands, Ross Sea and other locations around the Southern Ocean, and has worn all the different hats: Zodiac Driver, Logistics, Camp Master, Lecturer, Expedition Leader, Assistant Expedition Leader, and Kayak Operations. In 2010 he organized and led the Four Desserts marathon on board the Antarctic Dream.
He enjoys glacier hikes, snowshoeing, skiing, snowboarding, rock climbing and wakeboarding. After taking the last boat up on the hook, he likes to play the guitar and sing at the bar, and has many tales to tell about the explorers and history of this remote area.
Now in her fifth Antarctic season, Mariela spends her winters in her home town of Ushuaia teaching alpine skiing and snowboarding, guiding snowmobile excursions, and leading snowshoeing and cross-country skiing adventures.
In her spare time, she likes to sing, dance, and read about the earliest explorers to this land. Mariela is dedicated to ensuring that clients have the best combination of service and fun!
Conny has been an outdoors person all of her life growing up at the feet of the German Alps. Having spent her childhood skiing and mountaineering in local regions it was the crucial adventures across the neighboring borders that indoctrinated her great love of travel. This deep passion led Conny abroad at the youthful age of 16 where she would complete her bachelor's and master's degrees in Business in the U.S. and Hong Kong respectively. From there, Conny has followed a successful career in Sales & Marketing within international luxury hotels, living and working in Asia, Australia and New Zealand.
Conny's enthusiasm and passion for Antarctica was born after embarking on her first expedition cruise, aboard our very own Hebridean Sky. Witnessing Antarctica's breathtaking majesty and untouched beauty first-hand, as well as experiencing close encounters with Antarctica's wildlife, changed her profoundly as a person – a change that has led her to seek a new career within this precious and humbling part of the world. With her bubbly personality, abundant energy and her infectious nature as a people-person she is looking forward to making every future passenger's journey their "trip of a lifetime".
Over the last fifteen years, Seb has worked at the sharp end of maritime aviation with previous jobs spanning half the globe. The Royal Navy exposed him to some of the most inhospitable regions of the world. In 2009, Seb landed on the shores of South Georgia for the first time and stood before the grave of his personal hero: Sir Ernest Shackleton.
In January 2013, he joined the 'Shackleton Epic' team, which became the first expedition in history to faithfully recreate Sir Ernest Shackleton's small boat voyage across the Southern Ocean – with precisely the same equipment as Shackleton himself. From the clothing to the boat, the sextant, the reindeer skin blankets, and of course the starvation diet.
When he is not onboard ship lecturing, or climbing a mountain, he can be found in Scotland with his wife and children sailing the world's most faithful seaworthy replica of Shackleton's lifeboat. The boat was built with the sole purpose of keeping the great polar explorers legacy alive though adventure sailing excursions.
Seb is an accomplished aeronautical engineer, Fellow of the Royal Geographical Society, former GB Chapter Chair for The Explorers Club, joint recipient of the Royal Institute of Navigation Certificate of Achievement, and a joint Royal Yachting Association and Union Internationale Motonautique powerboat world record holder.
Ever since he could crawl, Bob has been drawn to the natural world. His passion for nature has led him to develop an evolving Citizen Science program, allowing guests on board to help scientists around the world learn how climate change is affecting the Antarctic Continent.
Hailing from Chicago, and holding a degree in Forestry, Bob initially spent his summers as the Lead Wilderness Ranger on the north face of Mount Hood for the US Forest Service and his winters at McMurdo Station in Antarctica working for the US Antarctic Program. While there he helped with logistics at South Pole Station for scientists who were researching everything from the natural anti-freeze found in the fish populations, to drilling ice-core samples to determine historical climate fluctuations.
In 2004, Bob decided to share the experiences and knowledge he gained in his 4 seasons with the USAP by joining expedition life as a guide and interpreter within the realm of Glaciology and Geology. He's been rolling through the Drake Passage and exploring the Antarctic Peninsula ever since.
Bob is one of the few people who have managed to reach both the North and South Poles. When not in the Polar Regions, Bob continues exploring and resides in the Rocky Mountains near Aspen, Colorado spending his time hiking, fly fishing, camping and whitewater rafting.
Born in Germany, Annette studied Marine Biology and obtained a Masters in Marine Conservation in New Zealand. There, she had the once-in-a-lifetime chance to visit Antarctica as part of a postgraduate certificate offered by the University in Christchurch. Camping at the base of Mount Erebus – the same region used as base camp by early explorers such as Scott and Shackleton – Annette caught the "polar bug". Returning from New Zealand, she conducted her PhD at the German Polar Research Institute. Here, she studied the habitat suitability of Antarctic whales and participated in several multi-week expeditions to the Southern Ocean on board the German research icebreaker RV Polarstern.
Annette has been working on various expedition cruises to Svalbard, Greenland, the North Pole, the Falklands, South Georgia and Antarctica. For Annette, visiting South Georgia is one of the very special moments in life, given its history of whaling and polar exploration. Annette speaks German and English and is looking forward to spending her Antarctic summer with you, sharing her passion for marine mammals day and night.
While Jeff was at summer camp as a child, a jellyfish stung him and changed the course of his life. He realized just how mysterious the oceans were, and couldn't wait to learn more. Now Jeff is a marine biologist and his extensive experience includes classifying the biodiversity of glass sponge reefs off Canada's west coast using video footage with world expert Dr. Verena Tunnicliffe, conducting fish and marine mammal surveys, and helping to biologically classify Alaska's entire shoreline.
Jeff not only enjoys the hunt for a good whale sighting but also enjoys the small critters that make up the base of the food chain. They are especially important because they sustain the large marine mammals that visit Antarctica's waters to feed each year.
An avid sailor, scuba diver and photographer, Jeff has worked in and on the ocean since 2007 and, no matter what the temperature or weather brings, you'll always see him smiling when he's on or near the ocean with camera in hand.
Jeff works on various expedition cruises exploring Canada's rugged west coast and southeast Alaska. The Antarctic was a dream of his to explore since he first learned of the vastly unknown icy continent in elementary school from a National Geographic magazine. He is very excited to be able to share his knowledge and passion for the marine world with you!
As a University-based educator, researcher and administrator for many decades, Jim has had the opportunity to work in and explore many of the high mountain areas and some of the polar regions of the Earth. 2018-19 is his fifth season in Antarctica and the Southern Ocean. His specialties include weather and climate, surface geology and landforms, glaciers and other forms of snow and ice, and natural hazards and disasters.
Now "retired" and living in Victoria, British Columbia, Jim continues to teach field courses in mountain and coastal environments, assist graduate students, and publish in the scientific media. Being part of the PL Expedition Team has added a new dimension to his experience as an educator and scientist, and has enhanced other aspects of his life.
Though his areas of speciality focus on inanimate objects and processes of the environment, life experience has taught him that their meaning and significance rests in the animate world, including that of people. This, he attempts to convey in his presentations and musings. Being a bit of a fossil age-wise, gives him a certain advantage in bringing those locked in the stone of the Antarctic to life. Though the past is important in understanding the present and future, his most memorable experiences all relate to the immediate sounds, devoid of engines, chatter and the click of cameras, coming from birds and other animals, calving glaciers, crunching ice floes, breaking waves and wind.
Tracy is deeply passionate about learning, teaching, and educational travel. He believes that isolated, hostile, and largely uninhabited Antarctica is central to understanding how the world works and our impact upon it.
A Professor of Environmental Science and Physical Geography at the State University of New York, College at Oneonta, Tracy's research interests are focused on rivers, lakes, glaciers, geomorphology, and environmental change. His love for cold climates grew out of investigation and exploration in Arctic and mountain environments. He has spent summers working and teaching on the Bering Glacier in Alaska and has canoed thousands of miles on Arctic rivers.
Synonymous with education, adventure travel is a means to achieve personal and professional growth. From an early age, Tracy would strike out from the Blue Ridge of Virginia to discover nature, mountains, and, eventually, other countries. Since then, he has backpacked throughout nearly all countries on Earth – from Mount Kilimanjaro in Tanzania to Mount Everest in Tibet and Nepal and from Machu Picchu in Peru to Pagan in Myanmar. At each location, he explores natural processes and human/environment relations. Tracy travels simply, with backpack, tent, and sleeping bag. When asked about his wanderlust, various intellectual motivations surface, but the deep-seated reality is that he has an adventurous spirit.
Born in Sydney, Australia, Marty's love of the ocean led him to a degree in Marine Science, extensive SCUBA qualifications, and a very hands-on job as Head Penguin Keeper at the Sydney Aquarium. While he did have some very unique experiences (try being a foster parent to penguin chicks!) seeing penguins in their natural environment is his ultimate thrill. He will never forget being greeted by a party of King Penguins at the largest colony in the world on the shores of South Georgia Island.
As a marine biologist Marty's passion for ocean animals extends beyond the polar regions having worked with a wide range of sharks, fish, reptiles, birds and mammals. Coming from Australia this also means he has worked directly with the most venomous snake, spider, octopus and fish on the planet. Marty practices free diving in an attempt to spend as long underwater in one breath as the penguins do.
Sophie's background is in guiding and instructing around the world in remote outdoor locations. With her expertise in trip planning, logistics and navigation as well as risk management and group management across a range of pursuits, she is a well-rounded outdoor professional. She shares her passion with clients and students for beautiful wild places. Sophie has an interest in fitness and health and also anything relating to the outdoors. Whether it be navigation, maps or weather, kayaking and rock climbing, she is happy to share her knowledge and tell tales of endless adventures.
As a young boy growing up in one of the "gateway's to Antarctica", the island of Tasmania, he was besotted by this far away magical land of ice. He had heard the stories, seen the photos and met those that had survived the "Big White." And so it became that as a guide he needed to one day, somehow, get himself to the bottom of the earth.
Ewan speaks English, Spanish, and some basic Japanese.
Steve has been guiding tours and expeditions all over the British Columbian coast. He has led history, photography, and even a painting tour! His adventurous pursuit of work in the wild has allowed him to guide on the Barrier Reef cays and the whitewater rivers of Belize, as well as along New Zealand's beautiful South Island coastline. In addition to guiding kayaking and zodiac tours in Antarctica, he also takes guests hiking to photograph the polar bears of Hudson Bay, in the Canadian arctic.
Steve enjoys his spare time cruising on his sailboard, surfing, hiking and finding wildlife and landscapes to photograph. Always prepared to crack a smile, Steve will be looking forward to helping you explore the Antarctic and the Southern Ocean.
In 2007, Ben was overall winner of the "Wildlife Photographer of the Year" competition and won the "Creative Visions of Nature" category. His work was recognized by the Royal Photographic Society in 2008 through the award of an Honorary Fellowship.
With two zoology degrees, Ben initially worked as a scientist before switching to full-time photography. He spent 18 months working for the British Antarctic Survey on Bird Island (South Georgia) researching wandering albatrosses and monitoring major seabird and mammal populations. Two years later he spent 9 months on a yacht surveying wildlife on South Georgia and the Antarctic Peninsula. These experiences (and a career change) culminated with a 4-month commission from National Geographic magazine shooting images for a major feature about Antarctica.
Following a chance conversation on a sacred mountain in China, Ben became involved in the ground-breaking BBC series about Antarctica, "Life in the Freezer". He shot editorial stills for the series book and photographed the presenter Sir David Attenborough on location. Since then Ben has worked regularly with BBC film crews, shooting publicity and editorial stills for major wildlife series including "Blue Planet" and "Planet Earth".
From his early years growing up on the edge of the Atlantic in rural Newfoundland, Philip has had a keen sense of adventure and a love of wild places. He studied Biology and Environmental Sciences before shifting gears to pursue a growing passion for mountaineering. For 10 years he worked as an instructor in mountain skills in the Vancouver Island Alps.
Philip blends his love of the outdoors, adventure, and photography in his work instructing, guiding and collaborating with several adventure tourism businesses. So it's no surprise that Philip joins Polar Latitudes as one of our Expedition Photographers. Philip has a knack for explaining some of the more technical aspects of digital photography in plain terms and is always happy to share tricks and tips, or just talking camera-shop! When asked about his favorite thing about the Antarctic he says "it's the light, there's so much of it, and it's so beautiful and clear".
Mathew became enamored with the world's wild places from an early age. It was this love of out-of-the way places that led him to pick up a camera and share his experiences. Those early motives morphed into a love a photography itself, and a career in telling stories with light. Things have gone full circle, with photography calling Mathew back to the mountains where he started.
When he's not working on expeditions as a photography coach or shooting documentaries, Mathew works as a newspaper photographer, and in film and television. When he takes a break from cameras, he heads back to the wilderness anyway, climbing, surfing, fly fishing or mountain biking.
A current graduate professor in photography, Will has been teaching and showing professionally for over 15 years. He is excited to bring his love of nature, adventure, and photography to Antarctica.
His photography career has taken him to numerous places around the world including Hiroshima, Columbia, Taiwan, Paris and Antwerp. His work has been exhibited in museums and galleries internationally. He currently shows with galleries in San Francisco and Tokyo, and lives on a boat in the San Francisco Bay with his wife and two daughters.
Will has walked slacklines over the Grand Canyon, trad climbed around the High Sierras, and backpacked extensively with his family around the Western US.
Born in Sweden, he worked in the USA, Thailand and Japan with many different and unorthodox professions. He discovered a passion for travel, and dedicated himself to visiting the most exciting places on the planet before he retired. This led him to the Expedition Tourism business, which is now his full-time profession, while he freelances as a wildlife and travel writer.
Adam is a wonderful lecturer on wildlife, photography and polar history and is a great source of many exciting stories about the places we visit.
Tim is a Southern Ocean native from the port town of Hobart, Tasmania. As the base of the Australian Antarctic Division and departure point for some of the most well known Antarctic expeditions, Tim grew up wanting to experience the polar regions for himself. After his first season with Polar Latitudes, he knew he was hooked.
Tim's area of expertise is leading adventure travel groups into remote and challenging areas. He has been guiding expedition sea kayak trips both in his native country and overseas for more than 10 years. He has also worked extensively as an aquatics trainer and instructor with various educational intuitions and brings this passion into every group he takes on the water.
A lover of all things to do with alpine environments and water Tim loves to be in these elements and share them with others. When not in the Antarctica, you'll find Tim in the Sierra Nevada mountains where he teaches swift water rescue and Wilderness First Aid courses.
During childhood, Randy learned how to play various instruments and how to conduct orchestras. At Brno University he studied engineering but quickly discovered music was the only thing he was interested in.
As a One Man Band, Randy worked in German, Swiss and Austrian Spa Hotels & Alpine Ski resorts. During his off time, he developed a passion for skiing and became a certified ski instructor.
Since 2006 Randy has been working aboard the finest European River Cruise vessels on Rhine, Main and Danube, entertaining his passengers with a wide repertoire of Jazz, Rock & Roll, Blues, Oldies and the Best of the Top Charts.
Dr. Dan studied medicine in New York City, completed residency in Portland, OR, and eventually settled in the greater Seattle area. He is an actively practicing emergency physician boarded in Emergency Medicine with many long years of emergency medicine experience. He is responsible for coordinating our onboard doctors and medical supplies.
Every Polar Latitudes voyage has a currently-practicing and English-speaking doctor experienced in Emergency medicine. Medical services are available 24 hours a day, and a doctor accompanies passengers on all shore landings.
As Captain Scott's only grandson and the son of Sir Peter Scott, well-known wildlife conservationist, founder of the Wildfowl and Wetlands Trust, and co-founder of the WWF, Falcon was brought up at the Slimbridge Wildfowl Trust with his two sisters. As a child, he traveled widely with his parents during holidays, including expeditions to Africa and to the Arctic.
As a young man, Falcon took up a career in civil engineering. Later a passion for architecture and art took him into building unusual and creative projects in the domestic sector, and building many unique houses, a vocation he still loves to indulge in. He built his own stone house in Argyll, Scotland where he now lives with his wife and family, and
runs a self-catering holiday business renting luxury log cabins which he also built himself. Falcon has always loved being outdoors and exploring wild places, and between building things has traveled to many places. He especially loves the remote parts of Scotland near his home, and has explored the mountains and sea lochs over many years using his own small motor boat, sailing with friends, and on foot climbing most of the mountains.
In 2012 Falcon joined the international team to work as a Heritage Carpenter on the conservation of his Grandfather's iconic Terra Nova Hut at Cape Evans for the NZ Antarctic Heritage Trust. The experience was deeply moving for him, and re-vitalized his interest in the family connection to Antarctica. The beauty of Antarctica has inspired him to develop his artistic flair and he now loves to paint the wildlife and landscapes.
Born in The Netherlands, and raised by adventurous parents, Hella became infected with the travel virus and a deep fascination for animal behavior and the natural world early in her childhood. When 5 years old she drew and wrote a small booklet on the life of an Orca family, unaware of the life journey she would embark on 20 years later.
A BSc. degree in Wildlife Management, Policy and Education led her into the realm of the oceans' giants. Passionate about the threats our natural world and its inhabitants are facing, she is convinced that education is the most powerful tool to create ambassadors for the natural world. Since 2004 Hella has surveyed marine mammals in the Scottish Hebridean Isles, studied Pilot whales in the Canary Islands, Killer whales in BC, Canada, Bottlenose dolphins in Australia and Humpback whales in Mexico. She has worked as a naturalist in New Zealand, and lived and worked in the Azores for 4 years as a whale watching guide and lecturer. Here she experienced a life altering encounter with a Blue whale, that she will be more than happy to share with those keen to listen. Hella has also been trained and contracted as an offshore marine mammal observer in the seismic industry.
In 2016 her biologist's dream was fulfilled by being able to explore the polar regions of our planet. Hella has spent two polar winters guiding whale watching and northern light excursions in Northern Norway and now divides her year between guiding expedition cruises to the European and Russian Arctic and to Antarctica as a lecturer in marine mammal biology, and zodiac driver. When she's not on an expedition ship, Hella is still occasionally working as marine naturalist in the Azores, Norway or elsewhere. She spends her free time traveling, outdoors or enjoying the peace and quiet of the French countryside with her family and furry creatures.
Ashley is an adventurer, outdoor educator, and traveler who lives for exploring the natural world and meeting new people. Her passion for the outdoors began in Niagara On The Lake, Ontario where she was born and spent almost every summer day mountain biking, swimming, and canoeing. Her thirst for adventure continued through University where she led social justice programs abroad for young adults to Morocco, India, and Belize.
She is a certified teacher with a science degree specializing in Kinesiology, Biology, and Psychology and has spent the past eight years working with inner-city youth from Toronto teaching and directing at an outdoor experiential school.
Currently she spends her summers on the BC coast, leading educational sea kayak expeditions through various regions of the Pacific Northwest, such as the Broughton Archipelago, Johnstone Strait, and the Great Bear Rainforest, in the great company of Orca, Humpback whales, and so many more magnificent creatures. In the winters, she works in the snowy wonderlands of Northern Ontario developing educational programs and leading dog sledding expeditions working alongside her incredible team of Alaskan huskies. In her spare time, she loves trail running, playing guitar and piano, mountain biking, and cooking delicious meals with friends.
Kurtis is excited to be one of your kayak guides on board! Hailing from a small town outside of Ottawa, Canada, most of his time growing up was spent playing on the lakes, rivers and in the forests of beautiful shield country in Ontario. Kurtis has been working in the outdoors as a sea kayak and canoe guide for over a decade. He spends his year in the polar regions; the austral summer around the Antarctic peninsula playing among the ice and the Boreal summer in the Canadian arctic and sub-arctic leading multi-week canoe and sea kayak expeditions on some of Canada's remote northern rivers. In 2014, he had the opportunity to be part of the successful search for the infamous Erebus and Terror in the Northwest passage, Sir John Franklin's lost vessels.
In addition to guiding, Kurtis studied Geology in University, following a passion for the natural world and landscapes, with particular interests in earth systems and mineralogy. He is happy to talk and share some knowledge over a cup of tea in the lounge, not only on geology but on all things natural science. His biggest passion is living and playing in the outdoors and sharing those experiences with you.
A world-class small ship experience
Seaventure features a 1-A Super ice class rating — the highest ice class awarded to passenger vessels. The ship offers all outside-facing staterooms (some with balconies) and beautifully appointed dining areas, as well as al fresco dining on the Lido deck when weather permits.
Seaventure also offers a heated saltwater pool on the top deck, a sauna and fitness center, and a dedicated Citizen Science lab.
Club/Bar
Heated Salt-Water Pool
All Voyages Include:
Two Hotel Nights
Alcoholic and Non-Alcoholic Beverages
Certified Emergency MD and Clinic
World Class Cuisine and Live Entertainment
Complimentary Coffee/Tea station
Voyage Photographer
Dedicated Passenger Service Manager
Complimentary Expedition Jacket
Ship Facilities:
Two Elevators serving all passenger decks
Library with computers
Fitness Center and Sauna
Heated salt-water swimming pool
Citizen Science Laboratory
includes balcony
Veranda (Twin Setup)
All Staterooms Feature:
Exterior views
Sitting area with chairs or sofa and table
Complimentary Mini-Bar
Safe to store your valuables
Independent temperature controls
Luxury toiletries
View Deck Plan
Adventures in Antarctica
Celebrating Antarctica
Christmas in Antarctica
Holidays in Antarctica
FSG from Puerto Madryn
FSG from Ushuaia
Reverse FSG
Shackleton's Final Quest
White River Jct, VT 05001
© 2017-2020 | Polar Latitudes
© 2017-2020 | Polar Latitudes | PO Box 1227 | White River Jct, VT 05001
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Drawing will be held May 1, 2021
Valid for trip cost only on new bookings to the Antarctic
Trip must be purchased within one year of award date
Travel must be completed within two years of award date
Trip must be booked directly with Polar Latitudes, cannot be redeemed via third party
Can only be combined with Early Booking Discount, cannot be combined with any other offer
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The folks at WHOI would love to tell you more about the whale scientists on this trip and the important research you'll be a part of!
For details please contact Alison Kline at whalevoyage@whoi.edu or 508-289-2335
Welcome to Polar Latitudes!


My new collection inspired by the concept the book of Ursula Priess (Sturz durch alle Spiegel) in some sentences in the book. Because it is about the relationship between daughter and father and that the subject is that more girls experience it. Sometimes these experiences are exactly the same whether you live in Iran, whether in other countries. And with the death of the father, for many years in the minds of girls is reviewed.
I also use in this collection of my paintings.
"Aber später, später sterbe ich gerne, schreibst Du, dass sie [die kleine Ursel] gesagt habe, während sie malte, mit stiller Lust."
"Eine der drei Damen, sehe ich, trägt goldene Ohrclips, halbkugelförmig – exakt wie jene, die Max mir damals geschenkt hat. "[…] Ich verstand ihn damals nicht, sein Geschenk zeigte mir: Er hat keine Ahnung, was mir gefällt und was mich schmückt."
"Warum aber hatte er mir Perlen geschenkt? Perlen entsprachen ihm nicht, und auch mir nicht."
My method is that I take pictures at first to the main subject, then with my paintings I create the desired spaces. Then I collage the pictures on my paintings. And finally, the particular elements of the image referre to the text of the book, such as the "brush" in the first photo, the "clips ear" in the second photo and "pearl" in the third photo.
Sometimes I take a picture and then I see main subject suddenly in my mind in another space. In this collection I have tried to portray these spaces.


text:
Wife Shares Story Of Actor Husband's Relapse After Her Miscarriage
by Christine Organ
Image via Jamie McCarthy/Getty Images/ Instagram
Jonathan Rhys Meyers' wife opened up about recent miscarriage, saying it may have triggered her husband's relapse
Actress Mara Lane, wife of Jonathan Rhys Meyers, shared sad news of the couple's recent miscarriage in an Instagram post over the weekend, acknowledging its impact on her husband's struggles with sobriety.
"With much sadness, we open our hearts to share that J and I lost our second child, who was baking in the oven," she wrote. "Child was very very much wanted (right now especially by J, so he took the news particularly not so well) and we are still working with coping skills over here… when life throws us curve balls such as these."
https://www.instagram.com/p/BY1_pAWDZkx/
Lane acknowledged her husband's challenging past and his ongoing struggle with addiction — along with the impact this "curve ball" had on his health and sobriety.
"Depression is a real concern from past abuse as well as alcoholism which he was born with," she wrote. "He has been able to turn any ugliness and hurt in his life into art and is the strongest person I know. I do not know anyone who has been through what he has been through and reached his level of successes."
But as often goes with the recovery process, she said that sometimes it's two steps forward, one step back. Her poignant post cuts to an often undiscussed reality of miscarriage — the emotional toll hits fathers too. Hard. Even though they may not be the one dealing with the physical impact of a miscarriage, they grieve too. It is a loss not just for the mom, but for the couple and the family.
Meyers was recently thrust into the spotlight when a paparazzo snapped photos of him drunk at a Dublin airport.
"I feel that whomever took photos of my husband was slightly in the wrong and was concerned for the wrong reasons but … it's ok," she wrote. "It's ok. Maybe you have/had a family to feed and need/needed money? I don't know. We forgive you."
She reassured fans, friends and family that Meyers is safe and working toward recovery with a sober living companion and bodyguard until he can get into a hospital closer to home.
The couple's first child, Wolf, was born last December.
https://www.instagram.com/p/BTvg7enjMDW/?taken-by=thelionandthelambchop
"Life is life," she concluded. "Life is beautiful. Life is tough sometimes though so let's try not looking down at someone unless we intend on helping them up."


i bought the game on steam and i play on an ultrawide monitor at 3440x1440.
Unfortunately right from the start, i'm not able to see what happen in the game, because it happen at the bottom of the screen,hidden outside the play area. If i play in windowed mode everything goes back to normal, but the windows is very small.
Is there a way to force the game to start in 2560x1440? i don't mind play with black border, at least it would be fullscreen.
Hi vfizzotti, I don't know what brand of monitor you're using (you never said) but can't you set the display to 2560x1440 manually via some control panel ON the monitor itself?
at least it would be fullscreen.
manipulate the game's resolution, google that up.
if not try looking for software similiar to that one.
Like Sleepyuser said, i was searching for a way to manually manipulate the game's resolution. I tried using the custom commands on the steam launch options, but for this game they are not working, it overrides them.
Your English is MUCHO better than my Italian!
Augurandovi un sano e prospero anno nuovo.