text:
\section{Introduction}
Network geometry is one of the most important features of real-world networks~\cite{boguna2021}, as it explains frequently observed network properties, including scale-invariance, high clustering, and overlapping community structures. The concept of geometry is intimately connected to the idea of similarity in networks, that two similar vertices are likely to connect. Typical examples are social networks, where people sharing the same interests or living in the same region are more likely to interact, or the world wide web, where webpages sharing similar contents are often linked. The similarity of vertices can be modeled through geometry in a random graph. More specifically, two individuals can be modeled as vertices in a geometric space, and their similarity is then associated with a small distance between them. This class of models is often called  geometric network models.

In the past decades, several geometric models have been introduced, aiming to model and understand real network properties~\cite{krioukov2010,bringmann2016,deijfen2013scale,serrano2008}. The simplest example of geometric models are the random geometric graphs \cite{penrose2003,dall2002}, where an underlying Euclidean space is fixed, and nodes within a given radius are connected. However, random geometric graphs fail to describe the typical scale-free nature of real-world networks, where many nodes of low degree coexist with a few nodes of extremely large degrees.
Instead, the hyperbolic space has been found to be extremely useful for modeling real-world networks~\cite{krioukov2010}, as it explains the heavy-tailed degree distributions that many networks posses, their efficient routing~\cite{blasius2018,kleinberg2007} and their community structures~\cite{faqeeh2018}. Interestingly, the hyperbolic model is equivalent to the renown $\mathbb{S}^1$ model, where nodes are uniformly distributed on the circle, and a soft constraint is assigned to the degrees~\cite{serrano2008}.
Recently, a very intuitive network model called geometric inhomogeneous random graph has been proposed as generalization of hyperbolic random graphs~\cite{bringmann2016}. GIRGs combine the essential real-world properties of the hyperbolic random graph with simpler mathematical formulations that make them mathematically more tractable than hyperbolic random graphs. In these models each vertex is positioned in a geometric space, and has a weight representing its genuine ability to attract connections. Then, the probability of a connection between two vertices in the GIRG is an increasing function of the weight of each vertex, and a decreasing function of a distance between them.

Although in many cases network geometry is a natural assumption, networks may not be directly endowed with a metric space, and in principle they could also not posses any kind of geometry.
Determining whether a given network has an underlying latent hyperbolic geometric space has been highlighted as a major open problem~\cite{boguna2021,smith2019}. Indeed, usually we can only observe the network connections, and not the network features which can cause geometry. The main question is then: can we assess whether these connections were formed by some underlying geometry?

It has often been assumed that high clustering, or a large amount of triangles, implies the presence of geometry~\cite{krioukov2016}. Intuitively,  in a geometric space, the triangle inequality ensures that two neighbors of a vertex are likely to be close to each other, and therefore likely to be connected. In fact, triangles are a powerful statistic to distinguish geometric and non-geometric networks, when assuming that the former can be endowed with an Euclidean space~\cite{devroye2011,gao2017,bubeck2016}.
In this paper however, we show that pure triangle counts, as well as the average clustering coefficient, have limitations in detecting geometry induced by hyperbolic spaces. In fact, network models without any source of geometry may contain the same amount of triangles as hyperbolic random graphs, and may have arbitrary large average clustering coefficients. This is essentially due to the trade-off between weights and geometry in the GIRG representation of the hyperbolic model: connections can either be formed between high-weight nodes, or between close--by nodes. When the degree distribution has a particularly heavy tail, this trade-off favors triangles formed by high weighted vertices. Therefore, the underlying geometry cannot always be detected by triangle counts or clustering coefficients.

In this work we develop a novel and powerful statistic called \emph{weighted triangles} to detect hyperbolic geometry in networks, where triangles are weighted based on how likely they are to be caused by geometry. Triangles that carry low evidence for geometry are discounted, so that our statistic is able to differentiate hyperbolic geometry from non-geometric networks in a regime where standard triangle counts or clustering coefficients are not~\cite{kolk2021,michielan2021}.
We also provide experimental evidence that weighted triangles can successfully detect a geometric nature of real-world networks

\section{Models}

In this paper, our benchmark model is the Geometric Inhomogeneous random graph (GIRG)~\cite{GIRG}. This is a powerful, but tractable, random graph model that generalizes the hyperbolic random graph defined by Krioukov et al. in~\cite{krioukov2010}. In the GIRG model, each vertex $i\in \{1,2,\ldots,n\}$ is equipped with a weight $h_i$ and a uniformly sampled position $x_i$ on a $d$-dimensional torus $[0,1]^d$ endowed with the infinity norm. Weights are sampled independently from the Pareto distribution, with density
\begin{equation}\label{eq:paretolaw}
    \rho(h)=K_1 h^{-\tau},
\end{equation}
for any $h > h_0 > 0$, where $K_1$ is the normalizing constant and $\tau\in(2,3)$. Two nodes $i$ and $j$, are then connected independently with probability
\begin{equation}\label{eq:edgeprobGIRG}
    p(h_i,h_j,x_i, x_j)=K_2 \min\left(\frac{h_ih_j}{\mu n} ||x_i - x_j||^{-d},1\right)^{\gamma},
\end{equation}
for some $\gamma>1$ and where $\mu$ denotes the average weight. The constant $K_2$ is a correction factor, which ensures that the expected degree of any vertex $i$ is proportional to its weight $h_i$ (see Appendix \ref{app:expgedreeGIRG}).

In its original formulation, Bringmann et al. \cite{bringmann2016} defined the GIRG as an entire class of models, where the connection probability \eqref{eq:edgeprobGIRG} is only required to hold asymptotically. Here we focus on a specific element of this class, to have a practical and tractable comparison with non-geometric models.
An important reason to study the GIRG is that for $d=1,\gamma=\infty$ it is asymptotically equivalent to the hyperbolic random graph, as shown in \cite{GIRG,komjathy2020}. Thus, the asymptotic results on the GIRG shown here are valid for the hyperbolic random graph as well.

To determine when geometry can be detected, we compare the GIRG to the inhomogeneous random graph (IRG). This model differs from the GIRG only in the sense that it is non-geometric. Specifically, the vertices now possess only weights $h_i$, sampled from the Pareto distribution as in \eqref{eq:paretolaw}, and are connected with probability
\begin{equation}\label{eq:edgeprobIRG}
    p(h_i,h_j)=\min\left(\frac{h_i h_j}{\mu n},1\right).
\end{equation}
The two models have the same weight, and degree distribution \cite{bollobas2007,hofstad2021b}, and  differ only in their connection probability through the presence of geometry. We will therefore show that under classical triangle-based statistics, these models cannot be distinguished, making it impossible to distinguish hyperbolic geometry from simple scale-free networks.

\section{Triangle counts}

The most intuitive statistic to detect geometry is the triangle count in the network, $\triangle$. Indeed, one would expect a high number of triangles in geometric networks due to the triangle inequality.
The number of triangles in the IRG scales as $n^{3(3-\tau)/2}$~\cite{stegehuis2019}. In the GIRG on the other hand, the triangle count undergoes a phase transition: when $\tau < 7/3$ it scales as $n^{3(3-\tau)/2}$, and when $\tau > 7/3$ it scales as $n$~\cite{hofstad2021,blasius2018b,michielan2021}. Then, for small values of $\tau$, we cannot distinguish geometry from the triangle counts scaling, as in both models the number of triangles is proportional to $n^{3(3-\tau)/2}$.
In Figures \ref{fig:pure_triangles_models_large} and~\ref{fig:pure_triangles_models_small} we clearly see that when $\tau = 2.1$, the number of triangles in geometric and non-geometric models grow with the same scaling.

\begin{figure*}[htb]
\centering
\subfloat[$\tau = 2.9$ \label{fig:pure_triangles_models_large}]{\includegraphics[width=0.4\textwidth]{triangles_big_tau.png}}
\qquad
\subfloat[$\tau = 2.1$ \label{fig:pure_triangles_models_small}]{\includegraphics[width=0.4\textwidth]{triangles_small_tau.png}}

\subfloat[$\tau = 2.9$ \label{fig:average_clustering_models_large}]{\includegraphics[width=0.4\textwidth]{clustering_big_tau.png}}
\qquad
\subfloat[$\tau = 2.1$ \label{fig:average_clustering_models_small}]{\includegraphics[width=0.4\textwidth]{clustering_small_tau.png}}

\subfloat[$\tau = 2.9$]{\includegraphics[width=0.4\textwidth \label{fig:weighted_triangles_models_large}]{weighted_big_tau.png}}
\qquad
\subfloat[$\tau = 2.1$ \label{fig:weighted_triangles_models_small}]{\includegraphics[width=0.4\textwidth]{weighted_small_tau.png}}

\caption{Triangle counts, clustering coefficient and weighted triangles for the Inhomogeneous random graph (IRG) and Geometric Inhomogeneous random graph (GIRG). Dots are the averages over 100 samples of IRG and GIRG, against the number of vertices $n$. Grey lines are linear interpolations between dots. (a) When $\tau>7/3$, the number of triangles increases linearly in GIRG, but slower than linearly for IRG. (b) When $\tau <7/3$, the triangles in the non-geometric and geometric model share the same scaling. (c) When $\tau$ is large, $\overline{C}$ differs significantly between the non-geometric and geometric model. (d)  When $\tau$ is small, $\overline{C}$ is qualitatively similar in both models. (e) (f) $W$ is significantly different both for small and large values of $\tau$. In particular, in non-geometric models $W$ remains bounded below 1/6.}

\end{figure*}

Theoretically, even when $\tau$ is small, it could still be possible to distinguish geometric/non-geometric inhomogeneous models through triangle counts. Indeed, if the number of triangles is $\triangle = A n^{3(3-\tau)/2} (1 +o(1))$, we may be able to establish the correct underlying model, by identifying the leading order term $A$. To this end, we can use precise asymptotic results from our earlier work~\cite{stegehuis2019,michielan2021}:
\begin{itemize}
    \item In the IRG, \begin{equation*}
    \frac{\triangle}{n^{3(3-\tau)/2}} \stackrel{\P}{\longrightarrow} A_{\text{IRG}}.
\end{equation*}
    \item In the GIRG, when $\tau < 7/3$, \begin{equation*}
    \frac{\triangle}{n^{3(3-\tau)/2}} \stackrel{\P}{\longrightarrow} A_{\text{GIRG}}.
\end{equation*}
\end{itemize}
Here, $A_{\text{IRG}}$ and $A_{\text{GIRG}}$ are explicit constants that  depend on the parameters of the two models.
If these are all known, then the two models could be distinguished using the difference between $A_{\text{IRG}}$ and $A_{\text{GIRG}}$. However, in realistic situations, one observes a network only through its connections, while the possible underlying geometry of the network and the vertex weights are usually not known. Therefore, in practice, we cannot estimate the parameters of the underlying models, and thus it is impossible to establish whether the triangle count is close to $A_{\text{IRG}} n^{3(3-\tau)/2}$ or $A_{\text{GIRG}} n^{3(3-\tau)/2}$.

We conclude that the number of triangles is not a satisfactory statistic for inferring the hyperbolic geometry.

\section{Average clustering coefficient}
Another common network statistic to measure the tendency of the nodes to form triangles, is the clustering coefficient, which has also been ascribed to indicate a network geometry~\cite{krioukov2016}.

The average clustering coefficient captures the probability that two randomly chosen neighbors of a randomly chosen vertex are connected as well. Equivalently, it is the average fraction of realized triangles out of all possible triangles that include a randomly chosen vertex:
\begin{equation}
    \overline{C} = \frac{1}{n} \sum_{i \in V} C_i = \frac{1}{n} \sum_{i \in V} \frac{2 \triangle_i}{d_i(d_i-1)},
\end{equation}
where $\triangle_i$ is the number of triangles containing vertex $i$, and $d_i$ is the degree of vertex $i$. Typically, if the value of $\overline{C}$ does not vanish in $n$, then this is considered to be evidence for geometry.

The average clustering in GIRGs is $\Omega(1)$, that is, non-vanishing as $n$ increases~\cite{GIRG}. In particular, in hyperbolic random graphs, $\overline{C}$ converges in probability to a positive constant~\cite{fountoulakis2021}.
For the IRG on the other hand, $\overline{C}$ decays asymptotically, as $n^{\tau-2}\ln(n)$~\cite{colomer2012,hofstad2017b}. Even though $\overline{C}$ vanishes for large $n$, the decay of $\overline{C}$ is extremely slow when $\tau \approx 2$, as we can observe in Figure \ref{fig:average_clustering_models_large}. Thus, the average clustering coefficient is impractical to detect geometry when $\tau$ is small.

Even more importantly, in non-geometric models with a different heavy-tailed degree distribution, $\overline{C}$ can even be constant. For example, consider an inhomogeneous random graph with weights
\begin{equation*}
    h_i=\begin{cases}
    2, & \text{with probability }1-1/(\sqrt{\mu n}),\\
    \sqrt{\mu n}, & \text{with probability } 1/(\sqrt{\mu n}).
    \end{cases}
\end{equation*}
We show in Appendix \ref{app:2-type_model} that $\overline{C}=\Theta(1)$ in this IRG, even though the model does not contain any source of geometry. Hence, $\overline{C}$ too, is not a good statistic to distinguish between geometric and non-geometric networks.

\section{Weighted triangles}
We will now describe our proposed statistic that, contrary to standard clustering-based statistics, is able to detect hyperbolic geometry. This statistic is again triangle-based so that it has the same computational complexity as other clustering-based statistics. The difference between  our statistic and  the average clustering coefficient or triangle count, is that all triangles are weighted based on their evidence for geometry. Indeed, in a hyperbolic space, triangles can be formed because of popularity (high-degree vertices), or similarity (close--by vertices). Thus, we weigh each triangle, so that triangles which carry low evidence for geometry have low weight, and triangles which carry high evidence for being formed due to geometry have high weight.
More precisely, we define
\begin{equation}
    W := \sum_{\substack{i,j,k \in V \\ i<j<k}} \frac{1}{d_i d_j d_k}\mathbbm{1}_{\{(i,j,k) = \triangle\}},
\end{equation}
where $\mathbbm{1}_{\{(i,j,k) = \triangle\}}$ is the indicator function of the event that the vertices $i,j,k$ form a triangle in the network.
The intuition behind the weights $(d_id_jd_k)^{-1}$ is that, in non-geometric power-law models, a typical triangle is formed between vertices of high degrees \cite{hofstad2021}. Thus, when we \textit{discount} the triangles formed by high-degree vertices, $W$ remains small. On the other hand, in the GIRG, there is a large number of triangles formed by close--by vertices with small degrees. Therefore, $W$ is significantly greater for GIRGs than for IRGs.

Indeed, as we show in Appendix \ref{app:concentrationW},
\begin{equation*}
    W =
    \begin{cases}
    O(1), & \text{ w.h.p. in IRG},\\
    \Omega(n), & \text{ w.h.p. in GIRG}.
    \end{cases}
\end{equation*}
Thus, weighted triangles make a very powerful statistic to infer hyperbolic geometry: in the absence of geometry, the statistic remains bounded, while it scales at least linearly under a geometric model. Moreover, this different behaviour is independent of $\tau$. This is clearly seen in Figures \ref{fig:weighted_triangles_models_large} and~\ref{fig:weighted_triangles_models_small}, where $W$ shows different scaling in non-geometric/geometric models, regardless of $\tau$.

It is interesting to observe that the average clustering coefficient can be seen as a specific way of weighing triangles as well:
\begin{equation}\label{eq:nCapprox}
\begin{split}
    &n\overline{C} = \sum_{\substack{i,j,k \in V \\ i<j<k}} \left[\frac{1}{\binom{d_i}{2}} + \frac{1}{\binom{d_j}{2}} + \frac{1}{\binom{d_k}{2}}\right] \mathbbm{1}_{\{i,j,k = \triangle\}}\\
    &\approx n \overline{C}_h : = \sum_{\substack{i,j,k \in V \\ i<j<k}} 2 \left( \frac{1}{h_i^2} + \frac{1}{h_j^2} + \frac{1}{h_k^2} \right) \mathbbm{1}_{\{i,j,k = \triangle\}}.
\end{split}
\end{equation}
On the other hand,
\begin{equation}\label{eq:Wapprox}
    W \approx W_h := \sum_{\substack{i,j,k \in V \\ i<j<k}} \frac{1}{h_i h_j h_k} \mathbbm{1}_{\{i,j,k = \triangle\}}.
\end{equation}
By~\cite{hofstad2021,blasius2018b,michielan2021}, triangles containing high-weighted vertices are likely to appear in scale-free models regardless of the geometry of the system. Thus, an effective statistic for geometry detection should discount triangles formed by high-degree vertices. From \eqref{eq:nCapprox} and \eqref{eq:Wapprox} we see that such discounting occurs in both $n\overline{C}_h$ and $W_h$.
However, in $W_h$, the factor $1/(h_i h_j h_k)$ is small as soon as {\it at least one} of the three vertices has high weight. On the contrary,  in $n\overline{C}_h$, the factor $1/h_i^2 + 1/h_j^2 + 1/h_k^2$ is small if and only if {\it all three vertices} have high weights. Therefore, $W$ discounts triangles formed by high-weight vertices more effectively than $n \overline{C}$ does. Indeed, Appendix~\ref{app:2-type_model} shows that the average clustering coefficient may also be constant for non-geometric networks, while weighted triangles are able to detect the non-geometric nature of the underlying network. This makes weighted triangles $W$ a better geometry detector than the average clustering coefficient.

\section{Real-world networks}
We will now investigate the performance of our statistic on real-world data.
As our statistic was designed to infer hyperbolic geometry, we focus only on networks with a heavy-tailed degree distribution.
Furthermore, we investigate data sets that contain  multiple snapshots of different sizes of the same network, to compare the theoretical scaling of $W$ with the scaling found in the data. These networks are described in detail in Table \ref{tab:realnetworks}.
\begin{table}[b]
\caption{\label{tab:realnetworks}
Overview of the data sets. \textit{ArXiv collab} collects coauthorships between scientists posting preprints on the Condensed Matter E-Print Archive, from 1999 to 2005 \cite{newman2001}; \textit{CAIDA AS} contains the CAIDA autonomous systems relationship, from January 2004 to November 2007 \cite{caida_as}; \textit{Gnutella p2p} collects all Gnutella peer-to-peer file sharing connections from August 2002 \cite{matei2002}.}
\begin{ruledtabular}
\begin{tabular}{ccc}
\textrm{Name}&
\textrm{\# snapshots}&
\textrm{avg. $n$ per snapshot}\\
\colrule
ArXiv collab \cite{newman2001} & 3 & 29437\\
CAIDA AS \cite{caida_as} & 122 & 22550 \\
Gnutella p2p \cite{matei2002} & 8 & 22811\\
\end{tabular}
\end{ruledtabular}
\end{table}

Figure \ref{fig:real_networks} shows the behavior of triangle counts $\triangle$, the average clustering coefficient $\overline{C}$ and weighted triangles $W$.

\begin{figure*}[ht]
\centering
\subfloat[ArXiv collab]{\includegraphics[height=11cm]{arxiv_collab.png}}
\hspace{0.3cm}
\subfloat[CAIDA AS]{\includegraphics[height=11cm]{caida_as.png}}
\hspace{0.3cm}
\subfloat[Gnutella p2p]{\includegraphics[height=11cm]{gnutella.png}}
\caption{Triangle counts $\triangle$ (blue), average clustering coefficient $\overline{C}$ (orange), and weighted triangles $W$ (green), computed for the data sets: (a) ArXiv collaboration (cond-mat); (b) CAIDA autonomous systems relationship; (c) gnutella peer-to-peer connections. The red line is the simple linear regression of $W$.}
\label{fig:real_networks}
\end{figure*}

In all three data sets, $W$ behaves roughly linearly in $n$, as our theoretical analysis predicts for geometric networks. The clustering coefficient as well as the pure triangle counts on the other hand, has more erratic behavior that is difficult to interpret. We will now discuss the results for each network in some more detail.

$W$ grows linearly for the ArXiv collaboration networks (Figure \ref{fig:real_networks}a): this suggests that geometry is present in the network. This corresponds to an intuition that ArXiv collaborations have a natural geometric structure: researchers working in the same group, region, or country are more likely to write a paper together. Moreover, a collaboration between two researchers is more likely if they work on similar topics.

The average clustering coefficient $\overline{C}$ is rather small for the CAIDA AS networks (Figure~\ref{fig:real_networks}b), and it seems to be decreasing, as the network size increases. On the other hand, the weighted triangles show a linear growth, revealing a source of geometry, that, in fact, is consistent with the domain knowledge about this network. Indeed, interactions between autonomous systems occur through peering or transit.  An important part of peer selection is the following: internet service providers (ISPs) have a set of \textit{points-of-presence}, that are the locations where they have routers/servers and related equipment/personnel across the world. An ISP can  peer with another ISP only at locations where both have a point-of-presence. Such location-dependent connectivity rules naturally suggest the presence of an implicit geometry in the network formation.

Lastly, the Gnutella peer-to-peer networks (Figure \ref{fig:real_networks}c) show an extremely small average clustering coefficient, failing to detect geometry.
On the contrary, the weighted triangles reveal geometry, as $W$ increases linearly with the network size. Indeed, it is reasonable to expect a geometric structure in this network because peer-to-peer file transfers are more likely between users who share similar interests. Then, we could construct an hidden metric space, by embedding users into this space according to their interests.

Overall, the plots in Figure \ref{fig:real_networks} suggest that weighted triangles can be an effective statistic to detect geometry in real-world networks.

\section{Conclusion and discussion}

In this paper we have analyzed in detail different methods to detect hyperbolic geometry in networks, when only the connections of the network are known. For theoretical purposes, we used the IRG and GIRG as benchmark models, on which we established analytical results. In both random graph models, the probability of connection depends on the popularity features of individuals vertices, expressed through their weights, so that the empirical degree distribution is power law with parameter $\tau$. However, GIRG also models  similarity of individuals, by locating the graph vertices randomly in a $d$-dimensional torus endowed with a metric.

First, we have established that triangle counts and the average clustering coefficient have serious limitations in detecting the presence of geometry when the degree distribution has a particular heavy tail (when $\tau<7/3$). Using numerical simulations we confirmed these limitations, by comparing the number of triangles and the average clustering coefficient in different models.

Next, we have introduced a new statistic, weighted triangles $W$, that effectively discounts triangles formed by high degree vertices. The underlying intuition is that such triangles carry low evidence for geometry because they are common in power law networks with or without an underlying geometric space. Our main  result states that $W$ is a suitable statistic for detecting geometry, because, asymptotically in the network size, $W$ remains bounded in IRGs, while it grows linearly in GIRGs. Numerical experiments on the real-world data show a remarkable agreement with this analysis, and confirm the high potential of the $W$ statistic for uncovering a hidden network geometry.

For practical applications, it would be interesting to provide some rule of thumb, how large $W$ should be to signal geometry. In Appendix~\ref{app:W_IRG} we obtain that $\Exp{W} = O(1)$, in IRGs. Then from Markov's inequality it follows that for sufficiently large $n$,
    \begin{equation*}
        \Prob{W \geq n^\alpha} \leq \frac{1}{ n^{\alpha-\varepsilon}} \to 0
    \end{equation*}
    for any $0<\varepsilon<\alpha<1$. Furthermore, in GIRGs, we have that $\Exp{W} = \Omega(n)$, while $\operatorname{Var}(W)=O(n)$ (see Appendices \ref{app:W_GIRG}-\ref{app:varianceW}). Hence, from Chebyshev's inequality, we get
    \begin{equation*}
        \Prob{W \leq \sqrt{n}} \to 0
    \end{equation*}
    in the large network limit. This suggests $\sqrt{n}$ as a possible threshold for $W$ to detect geometry. However, if $n$ is not sufficiently large, this asymptotic approach could fail. Indeed, even though $W = \Omega(n)$ in GIRGs, the leading order term can be very small. For example, in Figure \ref{fig:real_networks}c, for $n = 50000$, the estimated $W$ is still smaller than 2. In fact, a smaller cutoff of for example $n^{0.1}$ seems to work better. These empirical observations require further investigations. Based on  our results that $W$ is an asymptotically powerful statistic, designing statistical tests for finite $n$ is a natural next step in the quest of detecting network geometry.

redpajama_set_name: RedPajamaArXiv


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NEWS ALERT Community Foundation Updates Name and Public Identity
Community Foundation Updates Name and Public Identity
Sunshine Coast Foundation Changes Name but Not Mission
Wendy Francis
Nearly two decades after its creation, the Sunshine Coast Community Foundation is changing its name and refreshing its public identity. As of October 16th, the organization will be known as the 'Sunshine Coast Foundation'.
"We are not as well known as we ought to be for the work that we do, and many people confuse us with other local organizations having similar names," said Foundation Board Chair Manjit Kang. "We feel that 'Sunshine Coast Foundation' clearly communicates who we are and the focus of our efforts."
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It also established a COVID-19 Emergency Relief Fund that is supporting organizations who are struggling because of the pandemic. So far, it has awarded more than $114,000 from that fund, and is still accepting both donations and applications.
The Sunshine Coast Foundation will remain a part of the national network of community foundations. A new website is in creation and will be launched soon. Visitors to the current site www.sccfoundation.com will be directed to the new site once it is operational. Please contact the foundation with any questions or for more information at 604.741.7360.
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text:
STATE OF WEST BENGAL V. MIR MOHAMMAD OMAR & ORS, 2000 C Cr.LR (SC) 469:[2000] INSC 454 (29 August 2000)
22.	The post-mortem report made by PW-30 (Dr. Debabrata Choudhury) shows that the victim was murdered. He noticed as many as 45 injuries on the dead body which included fracture of 5 ribs (2 to 6 ) on he left side towards sternal end, fracture of some of he fingers and extravasaion of blood on he night side of occipital region and also on he situs of the rib fractures. The remaining injuries included a few lacerated wounds, contustions and aberrations. There was just one minor incised wound on he left pinna. The right lung was congested. The doctor opined that death of that deceased had resulted from multiple injuries and injuries of vital organs and I was homicidal in naure.
23.	The trial court made a fallacious conclusion regarding the death of the deceased on the premise that the public prosecutor did not elicit from the doctor as to whether the injuries were sufficient in the ordinary course of nature to cause death. The Sessions Judge concluded thus on the said issue: "There being no evidence on record to show that the injuries were sufficient in the ordinary course of nature to cause death, it cannot be said that the injuries noticed by the autopsy surgeon (PW-30) were responsible for causing the death of the deceased Mahesh." No doubt it would have been of advantage to the court if the public prosecutor had put the said question to the doctor when he was examined. But mere omission to put that question is not enough for the court to reach a wrong conclusion. Though not an expert as PW-30, the Sessions Judge himself would have been an experienced judicial officer. Looking at the injuries he himself could have deduced whether those injuries were sufficient in the ordinary course of nature to cause death. No sensible man with some idea regarding the features of homicidal cases would come to a different conclusion from the injuries indicated above, the details of which have been stated by the doctor (PW-30) in his evidence.
24	We have no doubt that homicidal death of Mahesh had happened on the same night of his abduction. Now we have to deal with another crucial issue. Having found that Mahesh was abducted by the accused in order to murder him and he was in fact really murdered very soon thereafter can the accused escape from the penal consequences of such murder.
31.	The abductors have not given any explanation as to what happened to Mahesh after he was abducted by them. But the learned Sessions Judge after referring to the law on circumstantial evidence concluded thus: "On a careful analysis and appreciation of the evidence I think that there is a missing link in the chain of events after the deceased was last seen together with the accused persons and the discovery of the dead body of the deceased at Islamia Hospital. Therefore, the conclusion seems irresistible that the prosecution has failed to establish the charge of murder against the accused persons beyond any reasonable doubt." The pristine rule that the burden of proof is on the prosecution to prove the guilt of the accused should not be taken as a fossilised doctrine as though it admits no process of intelligent reasoning. The doctrine of presumption is not alien to the above rule, nor would it impair the temper of the rule. On the other hand, if the traditional rule relating to burden of proof of the prosecution is allowed to be wrapped in pedantic coverage the offenders in serious offences would be the major beneficiaries, and the society would be the casualty.
34	When it is proved to the satisfaction of the court that Mahesh was abducted by the accused and they took him out of that area, the accused alone knew what happened to him until he was with them. If he was found murdered within a short time after the abduction the permitted reasoning process would enable the court to draw the presumption that the accused have murdered him. Such inference can be disrupted if accused would tell the court what else happened to Mahesh at least until he was in their custody.
LAST SEEN TOGETHER AND EXTRA JUDICIAL CONFESSION.
CRIMINAL APPELLATE JURISDICTION
CRIMINAL APPEAL NO. 180 OF 2001
Chattar Singh and Anr. ..Appellants
State of Haryana ..Respondent
( Also reported in AIR 2009 SC 378 )
Dr. ARIJIT PASAYAT, J.
BRIEF FACTS OF THE CASE
1. Challenge in this appeal is to the judgment of a Division Bench of the Punjab and Haryana High Court upholding the conviction of appellant No.1-Chattar Singh (hereinafter referred to as `A-1') for offence punishable under Section 302 of the Indian Penal Code, 1860. He was also convicted for offence punishable under Section 201 and Section 498A IPC. Different sentences were imposed for the said offences. Appellant-Mange Ram (hereinafter referred to as `A-2') was convicted for offence punishable under Section 498A IPC and was sentenced to undergo RI for two years and to pay a fine of Rs.2,000/-. The conviction recorded by learned Additional Sessions Judge, Rohtak, was confirmed by Division Bench of the High Court as also the sentences for both the appellants.
2. Background facts giving rise to the prosecution are as follows:
A young girl, namely, Guddi (hereinafter referred to as the `deceased') aged about 26 years, belonged to village Nimly in district Bhiwani in Haryana. Her marriage was performed with Chattar Singh, A-1, son of Mange Ram, A-2 of village Sahlawas, in district Rohtak, in the year 1990. Both the families are agriculturists. A daughter, namely, Poonam (deceased no.2) was born from this wedlock.
Dead bodies of Guddi and that of the infant daughter Poonam in the posture that the latter was in the armpit of Guddi were found in a well of village Sahalwas on the morning of 17.2.1993. Jeet Singh, father of the deceased made an application Ex.PO on 16.2.1993, a day earlier that his daughter was missing, before SI Ashok Kumar, PW-12, the then Station House Officer, Police Station, Sahlawas and on its basis formal FIR Ex.PN was recorded. On 17.2.1993 he inspected the spot and prepared rough site plan Ex.PCC. He got the dead bodies of the deceased photographed by Varinder Singh, Photographer, PW.14. Ex.PJJ/l to 8 are the photographs and Ex.PJJ/9 to 14 and Ex.PZ/7 and 8 are their negatives. Zile Singh, PW.9, also took photographs Ex.PZ/7 to 12 and the negatives are Ex.PZ/1 to 6. The Investigating Officer prepared inquest reports Ex.PB and PD. He also prepared rough site plan of the place of recovery of dead
bodies Ex.PDD. The dead bodies were taken out from the well and were despatched for post mortem. On 28.2.1993, Chattar Singh and Mange Ram accused were produced by Babu Lal, Sarpanch of the village before the Investigating officer who were arrested. On interrogation by the Investigating Officer on 1.3.1993, Chattar Singh accused made a disclosure statement Ex.PFF and in pursuance thereof got recovered Chuni (Scarf)
from the specified place which were taken into possession vide memo Ex.PFF/1. He also prepared rough site plan Ex.PFF/2 of the place of recovery. However, the statement made by Jeet Singh, PW.3, the father of the deceased contained the allegations that Chattar Singh (husband) and Mange Ram (father-in-law) of the deceased as well as Rajesh and Vijay Singh along with their wives Bimla and Bala respectively who were maltreating his daughter were demanding Rs.50,000/- as a part of dowry and only on fulfilment of that condition the daughter could remain in peace. He allegedly borrowed a sum of Rs.50,000/- from one Badan Singh, PW.8, and paid the amount to the accused persons. He also claimed that he gave various other amounts, valuables and articles on various occasions and it was, therefore, that since this amount was given at least 25 days earlier to the occurrence, after the birth of the child when Guddi had stayed only for a short period prior to the occurrence at the place of her in-laws. So, there was one version of the complainant, father of the deceased, that the dispute which led to the death of the deceased was the demand of dowry. However, during further investigation of the case, it transpired that extra judicial confession was allegedly made by Chattar Singh and Mange Ram accused that they were suspecting illicit relation of the deceased Guddi with some person and that she had conceived a child from that person and the child was delivered at her parents' place. Therefore, on account of that stigma being cast on the family of the accused, they did not think that it was befitting their prestige that Guddi should be allowed to stay with them and they have done her and the infant child to death and asked the Sarpanch Babu Lal to help them in the matter. A similar extra judicial confession was allegedly made before Dial Singh, PW.5, Om Singh, PW.6 and Ms.Viney Bhardwaj, P.W.10, a Reader in the Department of History who was the Secretary of one Mahila Dakshita Samiti and the Samiti had approached the accused persons in the village where Mange Ram made an extra judicial confession that his son Chattar Singh had done the deceased to death, because of infidelity of the deceased.
10. There is no doubt that conviction can be based solely on circumstantial evidence but it should be tested by the touch- stone of law relating to circumstantial evidence laid down by the this Court as far back as in 1952.
11. In Hanumant Govind Nargundkar and Anr. V. State of Madhya Pradesh, (AIR 1952 SC 343), wherein it was observed thus:
"It is well to remember that in cases where the evidence is of a circumstantial nature, the circumstances from which the conclusion of guilt is to be drawn should be in the first instance be fully established and all the facts so established should be consistent only with the hypothesis of the guilt of the accused. Again, the circumstances should be of a conclusive nature and tendency and they should be such as to exclude every hypothesis but the one proposed to be proved. In other words, there must be a chain of evidence so far complete as not to leave any reasonable ground for a conclusion consistent with the innocence of the accused and it must be such s to show that within all human probability the act must have been done by the accused."
12. A reference may be made to a later decision in Sharad Birdhichand Sarda v. State of Maharashtra, (AIR 1984 SC 1622). Therein, while dealing with circumstantial evidence, it has been held that onus was on the prosecution to prove that
the chain is complete and the infirmity of lacuna in prosecution cannot be cured by false defence or plea. The conditions precedent in the words of this Court, before conviction could be based on circumstantial evidence, must be fully established. They are:
the circumstances from which the conclusion of guilt is to be drawn should be fully established. The circumstances concerned `must' or `should' and not `may be' established;
the facts so established should be consistent only with the hypothesis of the guilt of the accused, that is to say, they should not be explainable on any other hypothesis except that the accused is guilty;
the circumstances should be of a conclusive nature and tendency;
they should exclude every possible hypothesis except the one to be proved; and
there must be a chain of evidence so complete as not to leave any reasonable ground for the conclusion consistent with the innocence of the accused and must show that in all human probability the act must hav been done by the accused.
These aspects were highlighted in State of Rajasthan v. Raja Ram (2003 (8) SCC 180), State of Haryana v. Jagbir Singh and Anr. (2003 (11) SCC 261) and Kusuma Ankama Rao v State of A.P. (Criminal Appeal No.185/2005 disposed of on 7.7.2008)
14. So far as the last seen aspect is concerned it is necessary to take note of two decisions of this court. In State of U.P. v. Satish [2005 (3) SCC 114] it was noted as follows:
"22. The last seen theory comes into play where the time-gap between the point of time when the accused and the deceased were seen last alive and when the deceased is found dead is so small that possibility of any person other than the accused being the author of the crime becomes impossible. It would be difficult in some cases to positively establish that the deceased was last seen with the accused when there is a long gap and possibility of other persons coming in between exists. In the absence of any other positive evidence to conclude that the accused and the deceased were last seen together, it would be hazardous to come to a conclusion of guilt in those cases. In this case there is positive evidence that the deceased and the accused were seen together by witnesses PWs. 3 and 5, in addition to the evidence of PW-2."
15. In Ramreddy Rajeshkhanna Reddy v. State of A.P. [2006 (10) SCC 172] it was noted as follows:
"27. The last-seen theory, furthermore, comes into play where the time gap between the point of time when the accused and the deceased were last seen alive and the deceased is found dead is so small that possibility of any person other than the accused being the author of the crime becomes impossible. Even in such a case the courts should look for some corroboration". (See also Bodh Raj v. State of J&K (2002(8) SCC 45).)" .
16. A similar view was also taken in Jaswant Gir v. State of Punjab [2005(12) SCC 438] and Kusuma Ankama Rao's case (supra).
EXTRA JUDICIAL CONFESSION.
17. Confessions may be divided into two classes i.e. judicial and extra-judicial. Judicial confessions are those which are made before a Magistrate or a court in the course of judicial proceedings. Extra-judicial confessions are those which are made by the party elsewhere than before a Magistrate or court. Extra-judicial confessions are generally those that are made by a party to or before a private individual which includes even a judicial officer in his private capacity. It also includes a Magistrate who is not especially empowered to record confessions under Section 164 of the Code of Criminal Procedure, 1973 (for short the `Code') or a Magistrate so empowered but receiving the confession at a stage when Section 164 of the Code does not apply. As to extra-judicial confessions, two questions arise: (i) were they made voluntarily? and (ii) are they true? As the section enacts, a confession made by an accused person is irrelevant in
criminal proceedings, if the making of the confession appears to the court to have been caused by any inducement, threat or promise, (1) having reference to the charge against the accused person, (2) proceeding from a person in authority, and (3) sufficient, in the opinion of the court to give the accused person grounds which would appear to him reasonable for supposing that by making it he would gain any advantage or avoid any evil of a temporal nature in reference to the proceedings against him. It follows that a confession would be voluntary if it is made by the accused in a fit state of mind, and if it is not caused by any inducement, threat or promise which has reference to the charge against him, proceeding from a person in authority. It would not be involuntary, if the inducement, (a) does not have reference to the charge against the accused person; or (b) it does not proceed from a person in authority; or (c) it is not sufficient, in the opinion of the court to give the accused person grounds which would appear to him reasonable for supposing that, by making it, he would gain any advantage or avoid any evil of a temporal nature in reference to the proceedings against him. Whether or not the confession was voluntary would depend upon the facts and circumstances of each case, judged in the light of Section 24 of the Indian Evidence Act, 1872 (in short `Evidence Act'). The law is clear that a confession cannot be used against an accused person unless the court is satisfied that it was voluntary and at that stage the question whether it is true or false does not arise. If the facts and circumstances surrounding the making of a confession appear to cast a doubt on the veracity or voluntariness of the confession, the court may refuse to act upon the confession, even if it is admissible in evidence. One important question, in regard to which the court has to be satisfied with is, whether when the accused made the confession, he was a free man or his movements were controlled by the police either by themselves or through some other agency employed by them for the purpose of securing such a confession. The question whether a confession is voluntary or not is always a question of fact. All the factors and all the circumstances of the case, including the important factors of the time given for reflection, scope of the accused getting a feeling of threat, inducement or promise, must be considered before deciding whether the court is satisfied that in its opinion the impression caused by the inducement, threat or promise, if any, has been fully removed. A free and voluntary confession is deserving of the highest credit, because it is presumed to flow from the highest sense of guilt. (See R. v. Warickshall) It is not to be conceived that a man would be induced to make a free and voluntary confession of guilt, so contrary to the feelings and principles of human nature, if the facts confessed were not true. Deliberate and voluntary confessions of guilt, if clearly proved, are among the most effectual proofs in law. An involuntary confession is one which is not the result of the free will of the maker of it. So where the statement is made as a result of harassment and continuous interrogation for several hours after the person is treated as an offender and accused, such statement must be regarded as involuntary. The inducement may take the form of a promise or of a threat, and often the inducement involves both promise and threat, a promise of forgiveness if disclosure is made and threat of prosecution if it is not. (See Woodroffe's Evidence, 9th Edn., p. 284.) A promise is always attached to the confession alternative while a threat is always attached to the silence alternative; thus, in one case the prisoner is measuring the net advantage of the promise, minus the general undesirability of a false confession, as against the present unsatisfactory situation; while in the other case he is measuring the net advantages of the present satisfactory situation, minus the general undesirability of the confession against the threatened harm. It must be borne in mind that every inducement, threat or promise does not vitiate a confession. Since the object of the rule is to exclude only those confessions which are testimonially untrustworthy, the inducement, threat or promise must be such as is calculated to lead to an untrue confession. On the aforesaid analysis the court is to determine the absence or presence of an inducement, promise etc. or its sufficiency and how or in what measure it worked on the mind of the accused. If the inducement, promise or threat is sufficient in the opinion of the court, to give the accused person grounds which would appear to him reasonable for supposing that by making it he would gain any advantage or avoid any evil, it is enough to exclude the confession. The words "appear to him" in the last part of the section refer to the mentality of the accused.
18. An extra-judicial confession, if voluntary and true and made in a fit state of mind, can be relied upon by the court. The confession will have to be proved like any other fact. The value of the evidence as to confession, like any other evidence, depends upon the veracity of the witness to whom it has been made. The value of the evidence as to the confession depends on the reliability of the witness who gives the evidence. It is not open to any court to start with a presumption that extra-judicial confession is a weak type of evidence. It would depend on the nature of the circumstances, the time when the
confession was made and the credibility of the witnesses who speak to such a confession. Such a confession can be relied upon and conviction can be founded thereon if the evidence about the confession comes from the mouth of witnesses who appear to be unbiased, not even remotely inimical to the accused, and in respect of whom nothing is brought out which may tend to indicate that he may have a motive of attributing an untruthful statement to the accused, the words spoken to by the witness are clear, unambiguous and unmistakably convey that the accused is the perpetrator of the crime and nothing is omitted by the witness which may militate against it. After subjecting the evidence of the witness to a rigorous test on the touchstone of credibility, the extra-judicial confession can be accepted and can be the basis of a conviction if it passes the test of credibility.
19. So far as the extra judicial confession of A-2 before PWs 5 and 6 is concerned that actually is not of much relevance in view of Section 30 of Evidence Act. The stress in the said provision is on the joint trial for the same offence. In the instant case A-2 was not tried for Section 302 IPC. Therefore, his confession if any is of no consequence. But the extra judicial confession before PW-10 which has been relied upon by both the trial Court and the High Court cannot be lost sight of.
20. In view of the evidence led, the inevitable conclusion is that the conviction recorded by the trial Court and upheld by the High Court does not suffer from any infirmity to warrant interference. However, considering the age of A-2 the sentence is reduced to the period already undergone which is nearly one year so far as A-2 is concerned. Except the modification of sentence so far as A-2 is concerned the appeal is dismissed. The bail bonds executed so far as A-2 is concerned shall stand discharged. So far as A-1 is concerned he shall surrender to custody forthwith to serve the remainder of sentence.
(Dr. ARIJIT PASAYAT) ....................J.
(Dr. MUKUNDAKAM SHARMA).....J.
New Delhi,


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Background: A good friend of Sara's.
Basic: A friend of Sara and one of Rociel's first victims.
Information: Ruri has fallen in love with Setsuna by the beginning of the story, and Sara reluctantly agrees to try to set her up with Setsuna . While it is still being set up, Ruri comes across Katan , who shows her the game "Angel Sanctuary". Setsuna arrives then, shoving Katan away, and tells Ruri how much better she looks without her glasses on - this gives Ruri hope for a relationship with him, and Sara brings the two to an old chapel to try to get them together (though she personally didn't want them to be together, she was trying for the sake of her friend). To try to awaken Alexiel , Katan attacks the church, and Setsuna leaps ot protect Sara , leaving Ruri unprotected. Her eyes are severely damaged, and she ends up blind, with bandages over her eyes. During this time she uses the game Angel Sanctuary, and slowly has her soul sucked up to be used by Rociel. She is granted sight just long enough to see Rociel , and then her body and soul are both swallowed up by Rociel , and her form is used by Rociel to get to Sara and Setsuna - neither of them the wiser.


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text:
Q: Nsetools API's not working when deployed on ec2 instance I am planning to use nsetools library with python to get top gainers and top losers.
the code is working fine on local and getting me all the information but when I deployed same code on ec2 instance the code nse.get_top_gainers() is getting timed out.

A: Seems like NSE blocked the access from VM's and the cloud machines.

redpajama_set_name: RedPajamaStackExchange


After a three-hour community-wide meeting at Marlboro College last week, students, faculty and staff decided not to ban cell phones from the small rural campus. Students dropped their resolution restricting cell phones to private quarters in return for a promise from cell phone-owning students not to use them. Good call.


They frame your face and enhance your look. However, keeping those the fast-growing hair in order and maintaining a shape that works for your face can be a grueling practice, especially if you have sensitive skin.
Cue Giselle Soto, the brow specialist behind Normani Kordei, Nazanin Mandi, Alina Baraz and Ryan Destiny's perfect arches.
"Most of the time my clients request their eyebrows to be shaped anywhere from the day of to about three to four days before the red carpet event," she told E! News. "My clients come to me for my expertise in eyebrow shaping and fill in their eyebrows. Even with clients that have make up artists on staff, will still request for me to handle the makeup on their eyebrows."
With the hectic schedules of many of her clients, however, she can't always be there to perfect their brows prior to events. Thus, the beauty pro shared her advice to maintaining the shape if you can't make it to your pro.
"In between sessions, I suggest that they keep the eyebrow hairs brushed up, utilize castor oil to help keep the hair healthy and keep a great brow gel," she said.
For brow gel, the pro continued, "Make sure when choosing the right color to use for you, always chose a color that is one shade lighter than your actual skin color," calling Gimme Brow Gel by Benefit Cosmetics as her go-to.
Beyond these tips, the former Fifth Harmony star actually has a special routine that's fit for her very full brows: "Normani comes in every two weeks for service. She is a 'tweeze-only' client for eyebrow shaping because of sensitive skin. She has very full eyebrows that does not require a make up fill in. After brow shaping, if anything, we apply a light coat of brow gel."


text:
package com.yogee.zhebuy.modules.ebuy.entity;

import com.yogee.zhebuy.common.persistence.EbuyEntity;
import org.hibernate.validator.constraints.Length;
import java.util.Date;
import com.fasterxml.jackson.annotation.JsonFormat;

/**
 * 爆品展示Entity
 * @author jackqth
 * @version 2017-06-02
 */
public class EbuyHotItem extends EbuyEntity<EbuyHotItem> {

	private static final long serialVersionUID = 1L;
	private Long item;		// 商品id
	private String auditStatus;		// 审核状态
	private Long operator;		// 审批操作人
	private Date auditTime;		// 审批操作时间
	private Date gmtCreate;		// 创建时间
	private Date gmtModified;		// 最后修改时间

	public EbuyHotItem() {
		super();
	}

	public EbuyHotItem(String id){
		super(id);
	}

	public Long getItem() {
		return item;
	}

	public void setItem(Long item) {
		this.item = item;
	}

	@Length(min=0, max=1, message="审核状态长度必须介于 0 和 1 之间")
	public String getAuditStatus() {
		return auditStatus;
	}

	public void setAuditStatus(String auditStatus) {
		this.auditStatus = auditStatus;
	}

	public Long getOperator() {
		return operator;
	}

	public void setOperator(Long operator) {
		this.operator = operator;
	}

	@JsonFormat(pattern = "yyyy-MM-dd HH:mm:ss")
	public Date getAuditTime() {
		return auditTime;
	}

	public void setAuditTime(Date auditTime) {
		this.auditTime = auditTime;
	}

	@JsonFormat(pattern = "yyyy-MM-dd HH:mm:ss")
	public Date getgmtCreate() {
		return gmtCreate;
	}

	public void setgmtCreate(Date gmtCreate) {
		this.gmtCreate = gmtCreate;
	}

	@JsonFormat(pattern = "yyyy-MM-dd HH:mm:ss")
	public Date getGmtModified() {
		return gmtModified;
	}

	public void setGmtModified(Date gmtModified) {
		this.gmtModified = gmtModified;
	}

}

redpajama_set_name: RedPajamaGithub


text:
Home » Movies & TV » Jason Momoa reveals new suit for 'Aquaman and the Lost Kingdom'
Jason Momoa reveals new suit for 'Aquaman and the Lost Kingdom'
Posted on September 7, 2021 by Aiya Rodjel
After dropping Sweet Girl on Netflix and ongoing promotion of the high-anticipated epic ensemble movie Dune, Jason Momoa has another Hollywood project you might have heard of: the sequel to the 2018 blockbuster hit Aquaman named Aquaman and the Long Kingdom.
And guess what? It looks like the Atlantian king is getting a darker costume, as per PhilStarLife.com. The actor posted two photos on his Instagram page: the first photo showed him in the classic green and orange costume reminiscent of Aquaman's original comic book look. The second photo features Momoa in a sleeker and darker stealth suit with armor.
A post shared by Jason Momoa (@prideofgypsies)
The 42-year old star is currently filming the movie in London and is definitely hyping up the fandom at it. The upcoming DC Extended Universe (DCEU) movie also stars Amber Heard as Mera, alongside Patrick Wilson as Orm/Ocean Master, Dolph Lundgren as King Nereus, and Yahya Abdul-Mateen II as David Kane/Black Manta.
So what should fans expect from the next installment in Aquaman/Arthur Curry's story? Well, according to the film's director, James Wan, the sequel touches on his horror roots. "Aquaman 2 is very heavily inspired by Planet of the Vampires," Wan said. "You can take the boy out of horror, but you can never take the horror out of the boy."
Wan said the change in tone for the film comes "partially because they were not familiar with the comic book, which deals in this very lurid, strange world."
"People were taken aback that I didn't throw all that stuff away and make a dark, heavy film. But I didn't feel that would have been right for it. So with the second film, I feel it will be easier for people to accept where we go because I've already laid the foundation," Wan said.
Sounds exciting, right? Aquaman and the Lost Kingdom is slated for a December 2022 release. Let's hope Filipinos can catch the movie in the cinemas by then.
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WATCH: GMA's Latest "Voltes V: Legacy" Reel Earns Approval of Anime's Original Producer
'Arcane' finally topples 'Squid Game' as Netflix's most-watched show


text:
(function () {
  'use strict';
  angular.module('com.module.browser', []);
})();


The use of ancillaries and accessories other than those recommended in the operating instructions could lead to an increased risk of personal injury for you. Q Before first use Q Charging the rechargeable battery on the device (see Fig. D) note: The battery is supplied partially charged. Charge the battery for at least three hours before first use. You can charge the Li-Ion battery at any time without risk of shortening battery life. Interrupting the charging process does not damage the battery.
Avant de lire le mode d'emploi, ouvrez la page contenant les illustrations et familiarisez-vous ensuite avec toutes les fonctions de l'appareil. Prima di leggere aprire la pagina con le immagini e prendere confidenza con le diverse funzioni dell'apparecchio. Vouw voor het lezen de pagina met de afbeeldingen open en maak u vertrouwd met alle functies van het apparaat. Antes de comecar a ler abra na pagina com as imagens e, de seguida, familiarize-se com todas as funcoes do aparelho. X18VKomperna.


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ORLANDO, Fla., March 26, 2019 /PRNewswire/ -- Tupperware Brands Corporation (NYSE: TUP) will release its first quarter 2019 results on Wednesday, April 24, 2019 , prior to the opening of the market, followed by a conference call at 8:30 a.
The most recent short interest data was recently released for the 01/15/2019 settlement date, and Tupperware Brands Corp is one of the most shorted stocks of the Russell 3000, based on 5.36 "days to cover" versus the median component at 4.81. There are a number of ways to look at short data, but one metric that we find particularly useful is the "days to cover" because it considers both the total shares short and the average daily volume of shares typically traded.
Tupperware is too cheap to pass up.
Fourth-quarter sales fall 14%, and the dividend is slashed by 60%.
- Fourth quarter sales down 14% versus last year and 7% in local currency+.
Investors in Tupperware Brands Corp saw new options begin trading this week, for the February 15th expiration. At Stock Options Channel, our YieldBoost formula has looked up and down the TUP options chain for the new February 15th contracts and identified one put and one call contract of particular interest.
In recent trading, shares of Tupperware Brands Corp have crossed above the average analyst 12-month target price of $35.67, changing hands for $35.77/share. When a stock reaches the target an analyst has set, the analyst logically has two ways to react: downgrade on valuation, or, re-adjust their target price to a higher level.
The most recent short interest data was recently released for the 10/15/2018 settlement date, and Tupperware Brands Corp is one of the most shorted stocks of the Russell 3000, based on 6.34 "days to cover" versus the median component at 4.82. There are a number of ways to look at short data, but one metric that we find particularly useful is the "days to cover" because it considers both the total shares short and the average daily volume of shares typically traded.
Investors in Tupperware Brands Corp saw new options begin trading this week, for the December 21st expiration. At Stock Options Channel, our YieldBoost formula has looked up and down the TUP options chain for the new December 21st contracts and identified one put and one call contract of particular interest.
Plasticware firm's stock is down 50% since January, making its yield attractive.
The most recent short interest data was recently released for the 06/15/2018 settlement date, and Tupperware Brands Corp is one of the most shorted stocks of the Russell 3000, based on 6.56 "days to cover" versus the median component at 4.34. There are a number of ways to look at short data, but one metric that we find particularly useful is the "days to cover" because it considers both the total shares short and the average daily volume of shares typically traded.
Investors in Tupperware Brands Corp saw new options begin trading this week, for the August 17th expiration. At Stock Options Channel, our YieldBoost formula has looked up and down the TUP options chain for the new August 17th contracts and identified one put and one call contract of particular interest.
Investors in Tupperware Brands Corp saw new options begin trading today, for the January 2019 expiration. One of the key inputs that goes into the price an option buyer is willing to pay, is the time value, so with 242 days until expiration the newly trading contracts represent a possible opportunity for sellers of puts or calls to achieve a higher premium than would be available for the contracts with a closer expiration.
Investors in Tupperware Brands Corp saw new options begin trading this week, for the June 15th expiration. At Stock Options Channel, our YieldBoost formula has looked up and down the TUP options chain for the new June 15th contracts and identified one put and one call contract of particular interest.
Looking at options trading activity among components of the Russell 3000 index, there is noteworthy activity today in Tupperware Brands Corp , where a total volume of 4,747 contracts has been traded thus far today, a contract volume which is representative of approximately 474,700 underlying shares (given that every 1 contract represents 100 underlying shares). That number works out to 51% of TUP's average daily trading volume over the past month, of 931,060 shares.
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Tupperware: Value Trap Or Putting The Blame On The Previous CEO?


Benjamin Guenoun, MD(a), Firass El Hajj, MD(b), David Biau, PhD(b), Philippe Anract, PhD(b), Jean-Pierre Courpied, PhD(b).
The Journal of Arthroplasty. 2015 Jan; 30(1):141-4.
CT (computed tomography) scan measurements were performed using the ORS Visual software.


A gated entrance and long meandering drive through nature welcome you to Maracoté - a world class waterfront estate that will capture the hearts of many. It is situated on 23.5 acres with 2,200 linear feet of oceanfront near the entrance to BC's Desolation Sound, home to some of the worlds best boating, fishing and natural beauty. This gorgeous family estate is comprised of a stunning architecturally designed main residence, a caretakers cottage, numerous guest houses and outbuildings, magnificent gardens and vegetable garden, scenic walking trails and a private 60ft dock. Beautifully crafted over two years, the 4 bedroom/5 bathroom main residence boasts over 8,400sf of living space highlighted by huge vaulted ceilings providing large amounts of natural light, sumptuous Master Suite with an impressive bathroom and a private terrace with ocean views, edge grain fir radiant heated floors, an in demand custom chef's kitchen, oversized sized office, a wine enthusiasts cellar and a games room and gym. Gorgeous paths and perennial gardens surround the home and lead you to a 50x20 in ground pool with private patios over looking the coastline.


At CES 2011, Sony announced that their new Bravia HDTVs will have access to Time Warner Cable Video-On-Demand without a cable receiver. This is a most unusual development for a cable operator to provide their content over IP services, but it makes sense considering they make a lot of money renting movies, and they have secured rental windows for their service making new releases available 28 days before rental kiosks.
There isn't a lot of detail about this partnership yet, but I am assuming this will only be provided to Time Warner Cable subscribers – at least initially. They don't want to give away their strong VOD leverage to satellite subscribers. It also makes sense that they would want to gain VOD sales from subscribers without cable receivers. Certainly they understand a lot of people are giving up their DVRs in favor of IP services like Hulu and Netflix.
Following Sony's announcement, Samsung also announced partnerships with both Time Warner Cable and Comcast to bring VOD to their HDTVs and Galaxy Tab. The Galaxy Tab features sound similar to the Xfinity Remote for iPad, and should include seamless sharing of video back and forth between the TV and tablet.
There is more information from Samsung than from Sony concerning their partnership. It is confirmed the cable VOD will be available to cable subscribers. They also announced a cool feature that allows content recorded on a DVR (presumably the Samsung DVR) to be played on a Samsung HDTV in the home connected to the local network.
These are very exciting announcements. The converged home is closer and more affordable than we know.
LAS VEGAS, Jan. 6, 2011-Samsung Electronics Co., Ltd. and Time Warner Cable shared the stage today at the International Consumer Electronics Show to announce a collaboration that will allow Time Warner Cable customers to access their cable subscriptions on the Samsung Smart TV and Samsung Galaxy Tab in their homes. Time Warner Cable Chairman and CEO Glenn Britt joined Samsung Visual Display President Boo-Keun Yoon on stage during Mr. Yoon's keynote speech, where the two companies jointly announced the collaboration and demonstrated the services.
Available as an app within Samsung's application storefront, the Time Warner Cable service ultimately will give Time Warner Cable's subscribers access to all of their cable channels directly on Samsung smart TVs and Galaxy Tab in the home. All of the content can be consumed through Samsung's award-winning LED, LCD and Plasma smart TV line-up, which delivers a high-quality, visual enhanced and connected entertainment experience to the home.
In addition to watching live TV on the Smart TV and Tab, Mr. Britt demonstrated the capability for Time Warner Cable customers to access recorded content from a DVR elsewhere in the home directly on the Samsung Smart TV, without the need for a connected set-top box. This creates a multi-room viewing experience that doesn't require multiple set-top boxes in homes that have more than one connected TV.
The Time Warner Cable applications will be demonstrated at the Samsung booth in the Central Hall at the International Consumer Electronics Show, Jan. 6-9, 2011.
Time Warner Cable anticipates beginning to offer the apps commercially on Samsung devices later this year.
Time Warner Cable is the second-largest cable operator in the U.S., with technologically advanced, well-clustered systems located mainly in five geographic areas – New York State (including New York City), the Carolinas, Ohio, southern California (including Los Angeles) and Texas. Time Warner Cable serves more than 14 million customers who subscribe to one or more of its video, high-speed data and voice services. Time Warner Cable Business Class offers a suite of phone, Internet, Ethernet and cable television services to businesses of all sizes. Time Warner Cable Media Sales, the advertising arm of Time Warner Cable, offers national, regional and local companies innovative advertising solutions that are targeted and affordable. More information about the services of Time Warner Cable is available at www.timewarnercable.com, www.twcbc.com and www.twcmediasales.com.
LAS VEGAS – January 6, 2011 – Today at the International Consumer Electronics (CES) Show, Samsung Electronics Co, Ltd., and Comcast Corporation (Nasdaq: CMCSA, CMCSK) jointly announced the companies' partnership to continue to revolutionize the way consumers access content and watch television with Xfinity TV. For the first time on a connected TV, the new Xfinity TV service will offer a rich, Web-like interface, enabling simpler navigation and the ability to seamlessly search across TV, DVR recordings, and video on demand among tens of thousands of content choices. A sleek graphics-rich display will guide the viewer to their favorite programming.
The partnership will also deliver a customized and integrated multi-platform viewing experience on Samsung Smart TVs and the Androidâ"¢ powered Samsung Galaxy Tab. On the tablet, the Xfinity TV experience is a virtual television guide and a mobile video player all in one. Xfinity TV digital customers will be able to browse, discover and sort video content, search for their favorite programs, change the channel on a Samsung Smart TV in real time, and program DVRs. In addition, they will be able to watch streaming TV shows and movies On Demand directly on the tablet, and access that content across multiple devices. The service's roadmap includes the ability to begin watching a favorite movie on the Samsung Galaxy Tab, then pause the movie and resume watching it on a Samsung Smart TV from the exact moment it was paused, and vice versa.
The Xfinity TV service was unveiled today at the International Consumer Electronics Show by Comcast Chairman and CEO Brian L. Roberts during a keynote speech by Boo-Keun Yoon, President of Samsung's Visual Display Business, and will also be demonstrated at the Samsung booth in the Central Hall.
The Xfinity TV experience will be distributed later this year on the Samsung Smart TVs and on the application store for the Galaxy products interacting through the Comcast set top box, giving consumers yet another access point for discovering and connecting to Comcast Xfinity TV services. Content can be watched through Samsung's award-winning LED, LCD and PDP TV products that reflect the company's commitment to delivering consumers high-quality, visually enhanced and connected entertainment experiences in their home.
Xfinity is a great website, lots of content, but that is just what it is.. content. TV Everywhere needs to be everywhere you are and needs to be what you pay for, not just the VOD side, but LIVE TV. Understandable they are still working on it and it will be end of the year. When I started working at DISH Network I purchased a sling adapter to go with my 722k receiver. Now that is true TV Everyhere, the monthly TV I pay for and my DVR's, if I want content I can go to the sites as well, xfinity, hulu, Dish Online, there are more. But they are just content.