text:
\section{Introduction}

Point clouds are widely employed as a popular 3D representation for objects and scenes. They are generated by most current acquisition techniques and 3D sensors, and used within well-studied application fields such as autonomous driving, archaeology, robotics, augmented reality, to name a few. Among these applications, shape recognition and segmentation are two fundamental tasks focusing on automatically recognizing and segmenting 3D objects or object parts  \cite{qi2017pointnet2,li2018pointcnn,pham2019jsis3d}.

The majority of 3D object recognition approaches are currently based on deep learning \cite{qi2017pointnet2,li2018pointcnn,su2015multi,esteves2019equivariant,wu20153d,qi2016volumetric}. Most of the point-based methods take positional information, such as point coordinates or normal vectors on aligned 3D objects, as inputs for the network, then learn deep features suitable for the task at hand. These methods now achieve state-of-the-art performance for 3D recognition. PointNet \cite{qi2017pointnet} firstly designed a network to process point clouds by taking point coordinates as inputs. Following works such as \cite{qi2017pointnet2,li2018pointcnn,xu2018spidercnn,wang2019dynamic,rao2019spherical} developed various convolution operations on point clouds which brought performance improvements. These advances justify that designing networks based on the positional information of 3D points on aligned object shapes is an effective way for shape recognition.

Nevertheless, in many scenarios such as, e.g., 6D pose estimation for robotics/AR \cite{Yimin2016A,Xiang2017PoseCNN} and CAD models \cite{HaraldTracking} in industrial environments, or analysis of molecules \cite{bero2014rotation,berenger2014a} where small scale objects are uncontrolled, a major limitation of above point-based methods is that they tend to be rotation-sensitive, and their performance drops dramatically when tested on shapes under arbitrary rotations in the 3D rotation group SO(3). A remedy for this is to develop robustness against rotations by augmenting training dataset with arbitrary rotations, e.g., the SO(3)/SO(3) mode in Spherical CNN~\cite{esteves2018learning}. However, it is not efficient to use data augmentation for learning rotation-invariance, since the enlarged dataset requires a large computational cost. Also, the developed robustness to rotations of the network will be up to the seen augmentations during training.

\begin{wrapfigure}{r}{0.55\textwidth}
\setlength{\abovecaptionskip}{0pt}
\setlength{\belowcaptionskip}{10pt}
\vspace{-15pt}
\includegraphics[width=0.55\textwidth]{figures/fgure_front_page.pdf}
\caption{The three circles highlight examples of local planar surfaces. Their center points are similar with geometric features~\cite{chen2019clusternet}, but distinguishable by point coordinates of selected pose as features in our approach. Features of each center point are shown in rows of tables.}
\label{fig:figure_front_page}
\vspace{-25pt}
\end{wrapfigure}
To deal with rotation-sensitivity, an alternative way is to represent shapes with geometric features such as distances and angles. Spherical CNN~\cite{esteves2018learning} and $a^3$SCNN~\cite{Liu2019DeepL3} are representative works that take distances and angles as spherical functions. They learn rotation-equivariant features by defining convolutions on spherical functions, and then aggregate features by global average pooling for rotation-invariance. Note that these representations are not rigorously rotation-invariant due to discretization on sphere. ClusterNet~\cite{chen2019clusternet} and RIConvNet~\cite{zhang2019rotation} also take rotation-invariant geometric features as inputs and design specific convolutions on local point cloudsan. However, directly transforming point coordinates to rotation-invariant geometric features may lose positional information of point cloud, which is essential to recognize 3D shapes when they are (roughly) aligned. For example, in Fig. \ref{fig:figure_front_page}, three local surfaces within the circles are flat surfaces belonging to different parts of two shapes. If we represent the center points of these local surfaces by geometric features (e.g., in ClusterNet~\cite{chen2019clusternet}) agnostic to their positional information, these features may not distinguish different parts of the same shape or different shapes.

To achieve rotation-invariant shape recognition with high accuracy, we propose a novel deep architecture by learning positional and relational features of point cloud. It takes both point coordinates and geometric features as network inputs, and achieves rotation-invariance by designing a \textit{Positional Feature Embedding block (PFE-block)} and a \textit{Relational Feature Embedding block (RFE-block)}, both of which are rotation-invariant. For both shape classification and segmentation, invariant features on point cloud guarantee that classification label of shape and segmentation label of each point are invariant to shape rotation.

It seems to be contradictory to learn rotation-invariant features with point coordinates as input. We design the PFE-block as composition of a pose expander, a pose selector and a positional feature extractor. The PFE-block is proven to be able to produce invariant features for points agnostic to shape rotations.  The pose expander maps the shape into a rotation-invariant pose space, then the pose selector selects a unique pose from the space, whose point coordinates are more  discriminative than geometric features as shown in Fig. \ref{fig:figure_front_page}. With this selected pose, we extract its positional features by a positional feature extractor. The RFE-block further enhances the deep feature representation of the point cloud with relational convolutions, where the weights are learned based on the relations of neighboring points. This block is also rotation-invariant.

As a summary, we propose two novel rotation-invariant network blocks and a deep hierarchical network jointly learning positional and relational features as shown in Fig. \ref{fig:pipleline}. Our network is one of the very few works that achieve rigorous rotation-invariance. For both point cloud shape classification and segmentation, we achieve state-of-the-art performances on commonly used benchmark datasets.

\section{Related Work}

\subsection{Point-based deep learning}
Point cloud is a basic representation for 3D shape, and point coordinates are taken as raw features by most point-based networks to carry out tasks on aligned shapes. PointNet~\cite{qi2017pointnet} is the first effort that takes point coordinates as raw features and embeds positional information of points to deep features followed by max-pooling to be a global shape descriptor. Afterwards, a series of works attempt to improve feature embedding by designing novel deep networks on point clouds. PointNet++~\cite{qi2017pointnet2} builds hierarchical architecture with PointNet as local encoder. More works such as SpiderCNN~\cite{xu2018spidercnn}, PointCNN~\cite{li2018pointcnn}, KCNet~\cite{shen2018mining}, PointConv \cite{wu2019pointconv}, RS-CNN~\cite{liu2019relation} learn point cloud features with various local convolutions starting from point coordinates or additional geometric features. Though these works have achieved state-of-the-art performance for various shape analysis tasks, they are sensitive to shape rotation. In our work, we build a novel network with building blocks being able to achieve rotation-invariance, but with positional raw features as inputs. Our network can explore and encode positional information of 3D shapes while precluding the disadvantage of rotation-sensitiveness.

\subsection{Rotation-robust representations}
There are several ways to improve rotation-robustness. Data augmentation by randomly rotating shapes in training set is widely applied in training 3D networks as in~\cite{qi2017pointnet,xu2018spidercnn}. Furthermore, transformer network~\cite{jaderberg2015spatial}  was generalized and utilized in 3D recognition \cite{qi2017pointnet,bas20173d,mukhaimar2019pl}. The transformer implicitly learns alignments among shapes either in 3D space or feature space which may reduce the impact of shape rotations. As shown in~\cite{chen2019clusternet}, these techniques commonly improved robustness but can not achieve rigorous invariance to rotations.

Rotation-invariant geometric features can be taken as network inputs. Traditionally, these hand-crafted features are widely utilized to represent 3D shapes in \cite{stein1992structural,sun2001surface,zhong2009intrinsic,rusu2009fast,tombari2010unique}, and further introduced as inputs of deep networks~\cite{chen2019clusternet,zhang2019rotation,deng2018ppf}. Most of them utilize distances and angles \cite{zhang2019rotation,deng2018ppf} and sine / cosin values of the angles \cite{chen2019clusternet} as raw point-wise features. They encode relations among points and achieve invariance to arbitrary shape rotations. However, the geometric features may lose discriminative clues that are contained in point positions / orientations.

Another way to achieve rotation-robustness is to learn rotation-equivariant features. \cite{thomas2018tensor} built filters on spherical harmonics and learned locally equivariant features to 3D rotations and translations. Group convolution~\cite{cohen2016group} is a generalized convolution to achieve rotation-equivariant feature learning based on rotation-group. This idea is extended to 3D domain \cite{worrall2018cubenet} with various discretized rotation-groups. Spherical CNN \cite{esteves2018learning} and $a^3$SCNN \cite{Liu2019DeepL3} defined group convolution on sphere  which can be taken as an approximation to infinite group SO(3). They also require the input of the networks to be rotation-equivariant if regarding features as functions over shapes. Commonly, these methods lead to rotation-robustness by global aggregation such as average-pooling or max-pooling, but rigorous rotation-invariance is not ensured due to the discretized rotation groups.

\begin{figure}[t]
\begin{center}
\includegraphics[width=1\linewidth]{figures/figure_pipeline.pdf}
\end{center}
\caption{PR-invNet consists of geometric feature extraction, positional feature embedding block, relational feature embedding block. PR-invNet is designed for classification and segmentation. Shape coarsening is not utilized in segmentation. }
\label{fig:pipleline}
\end{figure}

Instead of requiring rotation-invariant geometric features as inputs, our network can directly learn positional features from point coordinates as inputs while achieving rigorous rotation-invariance based on PFE-block. It embeds the input shape into a rotation-invariant pose space, from which we derive a discriminative pose by pose selector to be sent to positional feature extractor, and this operation is rotation-invariant and justified to be effective in experiments.

\section{Method}

In this section, we introduce our rotation-invariant network, dubbed \textit{PR-InvNet}. It aims at deep positional and relational feature learning, based on, respectively, the PFE-block and RFE-block.
As in Fig. \ref{fig:pipleline}, it consists of several stages. The initial feature embedding stage is composed of geometric feature extraction and RFE-block.
The output features of the PFE and RFE blocks are max-pooled over point cloud and concatenated, then fed to a MLP for shape classification. For point cloud segmentation, we switch off shape coarsening operation, and the concatenated features of PFE-blocks and RFE-blocks are further concatenated with globally max-pooled features before being fed to MLP for point label prediction. Each stage is now detailed in the following.

\subsection{Geometric feature extraction} \label{geo_fea_section}
PR-invNet takes geometric features similar to \cite{chen2019clusternet} as additional raw input features complementary to point coordinates\footnote{Even without geometric features, our network would be still rotation-invariant.}. As shown in Fig. \ref{fig:geometric}, $c$ and $o$ are the centers of the global shape and a local patch respectively. To compute geometric features of point $o$, we first consider its neighboring points. The feature of each of its neighboring point $q$ is computed as $[|\overrightarrow{cq}|,|\overrightarrow{oq}|, cos(\alpha), cos(\beta)]$,  with $[\cdot]$ being the concatenation operation. Then we concatenate features of all neighboring points together with the distance of $|\overrightarrow{co}|$ as the geometric feature of point $o$, i.e.,
\begin{equation}
g_o = [|\overrightarrow{co}|,\{|\overrightarrow{cq}|,|\overrightarrow{oq}|, cos(\alpha), cos(\beta)\}_{q \in N(o)}],
\end{equation}
where $N(o)$ denotes set of neighboring points of $o$.
For simplicity, we denote it  as $\{g_i\}_{i=1}^N$ with $N$ as number of points. It can be noted that $g_i$ is rotation-invariant, please refer to supplemental material for proof.
In our work, for each given point, the above geometric features are extracted and concatenated over a multi-scale neighborhoods (three neighborhoods determined by Euclidean distance with 8, 16, 32 points), and 8 neighboring points are uniformly sampled at each scale. Then the geometric feature of each point is in length of $3\times4\times8+1 = 97$.

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.9\linewidth,height=0.8in]{figures/figure_geo_fea_extraction.pdf}
\end{center}
\caption{Illustration of geometric feature extraction for point $o$ which is based on distances and angles. See Sect. 3.1 for details.}
\label{fig:geometric}
\end{figure}

\subsection{Positional feature embedding block}

The PFE-block aims to perform rotation-invariant feature embedding by incorporating positional information encoded in point coordinates.
Since point coordinates are sensitive to shape rotations, one solution is to take all rotated versions (i.e., poses) of a shape into consideration, and fuse extracted features from them by global pooling. However, this is inefficient since there are infinite number of rotations in SO(3) to ensure rigorous rotation-invariance. We propose an idea that first maps input shape to a rotation-invariant pose space by \textit{pose expander}, then selects a  representative pose by \textit{pose selector}. Point coordinates of selected pose are utilized to extract positional features by \textit{feature extractor}.

\subsubsection{Pose expander.} The pose expander aims to map a shape to produce a rotation-invariant pose space.
Given a shape with point cloud $P\in  \mathcal{R}^{N\times 3}$, it is obvious that the pose space $\{\mathcal{T}_{g}P\}_{g \in SO(3)}$ containing all possible rotated shapes in SO(3) is rotation-invariant.
We aim to derive a compact pose space of input shape guaranteeing rotation-invariance. We achieve this by first normalizing the pose of each shape via Principal Components Analysis (PCA), then applying a discretized rotation-group in SO(3) to the normalized shape to derive a pose space.

\begin{wrapfigure}{r}{0.4\textwidth}
\vspace{-20pt}
\includegraphics[width=0.4\textwidth]{figures/figure_eigen_shape.pdf}
\caption{Two rotated versions of one shape may result in two symmetric and different poses by PCA.}
\label{fig:figure_eigen_shape}
\vspace{-20pt}
\end{wrapfigure}

We first apply PCA on the point coordinates of a shape to normalize its pose using a coordinate system composed of the three eigen-vectors. We indicate the normalized shape as $\widehat{P}$. Note that pose normalization by PCA is not injective. For example, eigen-decomposition may result in different signs of eigen-vectors, therefore results in different normalized shapes. In Fig. \ref{fig:figure_eigen_shape}, a shape with two rotated versions may produce two different normalized shapes, which are symmetric

To solve the ambiguity of PCA-normalized shape, we enumerate all possible signs of eigen-vectors, and construct a PCA-normalized pose space with eight normalized shapes based on a symmetric group $G_S$
\begin{equation}
G_S = \{g_{s} |g_{s} = \left[ \begin{array}{ccc}
x & ~0 & ~0\\
0& ~y & ~0\\
0 & ~0 & ~z
\end{array}
\right], x,y,z\in \{-1,1\}, s = 1,2,\cdots,8\},
\end{equation}
Then the PCA-normalized pose space is obtained as
\begin{equation}
H_S(P) = \{\widehat{P}g_s|g_s \in G_S \},
\label{eqn:h_s_p}
\end{equation}
where $H_S(P)$ contains eight possible PCA-normalized shapes corresponding to different possible signs of eigen-vectors, and this pose space is denoted as \textit{sym-space}. Theorem 1 proves that $H_S(P)$ is rotation-invariant for input shape $P$.

Though sym-space is rotation-invariant, PCA may not always well align the poses of different shapes even from the same category. We further expand the pose space from $H_S(P)$ to increase the possibility of containing aligned poses for different shapes. By discretizing SO(3) using limited representative rotations, we enlarge sym-space $H_S(P)$ to \textit{rot-space} $H_{SR}(P)$ using rotation group $G_R$ as
\begin{equation}
H_{SR}(P) = \{\widehat{P}g_s g_r| g_s \in G_S, g_r \in G_R\},
\label{eq:rotSpace}
\end{equation}
where $G_R$ can be any discretized subgroup of SO(3).  $H_{SR}(P)$  is also rotation-invariant for $P$ as proved by Theorem 1. Compared with $H_{S}(P)$, rot-space $H_{SR}(P)$ contains more poses with higher chances to include the same or similar poses of different shapes. In our implementation, we use rotation group $A_5$ , i.e., alternating group of a regular dodecahedron (or a regular icosahedron) \cite{zimmermann2011finite} to construct the rot-space. By deleting duplicate shapes, we finally map the shape with rotation set  $A_5\times Z_2$ into rot-space with 120 poses.

\subsubsection{Pose selector.}
Given a shape $P$, we have derived a rotation-invariant pose space $H_{SR}(P)$, i.e., the rot-space. One naive way is to extract features from different poses of the shape in pose space followed by orderless operations, e.g., average- or max-pooling, to aggregate features as a rotation-invariant representation for shape $P$. However, it is computationally intensive to extract features from multiple poses of shape.
We design a simple but effective method by selecting the most representative shape pose using a pose selector, and learn positional features from this single selected shape instead than from all shapes in pose space.

The pose selector is designed as a \textit{multi-head neural network} $\Psi(\cdot)$ over shape poses in $H_{SR}(P)$. We score each pose by
$
v_{s}=\Psi(\bar{P}_{s})$ for pose $ \bar{P}_{s}  \in H_{SR}(P),  \ s=1,\cdots,|H_{SR}(P)|
$.
$v_{s}\in  \mathcal{R}^{N_h}$ is a vector generated by $N_h$ heads of $\Psi(\cdot)$. In our implementation, $\Psi(\cdot)$ is designed as a simple network with a point-wise fully connected (FC) layer, a max-pooling layer over all points, followed by an additional FC layer and softmax with $N_h$ output scores for a point cloud. Similar to multi-head attention~\cite{vaswani2017attention}, the multiple elements in vector $v_{s}$ reflect the responses of $\bar{P}_{s}$ to different modes of the neural network.
For a shape pose $ \bar{P}_{s}$, its final score is set as the largest response in vector $v_{s}$, i.e.,
$\bar{v}_{s} = \text{max}\{v_{s}\}$,
and $\bar{v}_{s}$ is a scalar. Then the selected representative shape $\widetilde{P}$ from pose space $H_{SR}(P)$ for shape $P$ is the shape pose with the largest score

Theorem 1 proves that the sym-space, rot-space  and the selected pose are rotation-invariant to $P$ (please see supplementary material for proof).

\begin{theorem}
Denoting $P\in  \mathcal{R}^{N\times 3}$ as point cloud of a shape, its sym-space $H_S(P)$ in Eqn. (\ref{eqn:h_s_p})  and rot-space $H_{SR}(P)$ in Eqn. (\ref{eq:rotSpace}) are rotation-invariant for $P$, i.e., for rotated shape $Q = PR$ of $P$ with any rotation matrix $R\in  \mathcal{R}^{3\times 3}$, we have $H_S(P) = H_S(Q)$ and $H_{SR}(P) = H_{SR}(Q)$. Assuming the pose selector is injective, the selected pose of $P$ is rotation-invariant, i.e., $\widetilde{P}=\widetilde{Q}$.
\end{theorem}

\begin{figure}[t]
\begin{center}
\includegraphics[width=1\linewidth]{figures/figure_positional_block.pdf}
\end{center}
\caption{Overview of the PFE-block. It maps a shape to be rotation-invariant pose space, i.e., rot-space, then selects a discriminative pose via pose selector, followed by feature extractor. This block is rotation-invariant.}
\label{fig:pfe_block}
\end{figure}

\subsubsection{Feature extractor.}
With the selected shape pose $\widetilde{P} \in  \mathcal{R}^{N\times3}$ of input shape $P$, we can extract its point-wise features based on the point coordinates like the traditional point-based networks, e.g., \cite{qi2017pointnet2,li2018pointcnn,xu2018spidercnn}.
 Specifically, given point-wise coordinates $\tilde{p}_i$, geometric feature $g_i$ (extracted from input shape $P$), and already extracted point features $f_i$, we concatenate $[g_i,f_i,\tilde{p}_i]$ as point-wise input features for our feature extractor. Motivated by the structure of PointNet++\cite{qi2017pointnet2}, for each point $i$, its point feature is extracted as
\begin{equation}
f'_i =  \Gamma\left(\{[g_j,f_j,\tilde{p}_j]\}_{j \in N(i)}\right)
\label{eqn:feat_extr}
\end{equation}
where $ N(i)$ is the local neighborhood of point $i$ with $K$ points including point $i$. $\Gamma(\cdot)$ is the feature extractor, which is designed as a shared MLP for points, followed by max-pooling over neighborhood.
Fig. \ref{fig:pfe_block} shows the pipeline of the PFE-block. Since the selected pose is rotation-invariant to input shape by Theorem 1, its point coordinates $\tilde{p}_i$ are also rotation-invariant. Hence, features in Eqn.~(\ref{eqn:feat_extr}) are rotation-invariant because all inputs of $\Gamma$ are rotation-invariant.

\subsection{Relational feature embedding block}
The relational feature embedding block (RFE-block) is specifically designed to explore and learn point features by modeling interactions of neighboring points.
For each point $i$, we aggregate the features of its local neighborhood with $K$ points including point $i$ by convolution. Assuming the neighboring points are indexed by $k$ sorted by increasing Euclidean distance to point $i$, and corresponding point features are $\{f_k \in  \mathcal{R}^{d}\}_{k=1}^{K}$, the updated feature $f'_i \in  \mathcal{R}^{d'}$ for point $i$ is
\begin{equation}
f'_{il} = \sum_{k \in N(i)}\sum_{j=1}^{d} f_{kj}W_{kjl},  \mbox{ for } l = 1,\cdots,d'
\label{eqn:conv}
\end{equation}
where $f_{kj}$ is the $j$-th feature channel of the $k$-th neighboring point, $f'_{il}$ is the $l$-th channel of the updated feature $f_i'$. $W_{kjl}$ is defined as
\begin{equation}
\begin{split}
& W_{kjl} =\Phi([C_k^{p},C_k^{g},C_k^{f},g_k])_{j}\Theta_{kjl},
\end{split}
\label{eqn:relation}
\end{equation}
where $C_k^p,C_k^g,C_k^f \in  \mathcal{R}^K$ are $K$-d vectors denoting correlations of centered point coordinates, geometric features, point features respectively between $k$-th point and all $K$ points in local neighborhood, followed by $l_2$-normalization. For example, for centered point coordinates, i.e., coordinates subtracted by that of center pixel $i$,
$C_k^p = \text{Normalize}([p_k^{\top}p_1,p_k^{\top}p_2,\cdots,p_k^{\top}p_K])$, where we use $p$ to represent the centered point coordinates.
$C_k^g,C_k^f$ are similarly defined as inner products of corresponding features.
$\Phi(\cdot)$ is modeled as MLP, embedding relationships of neighboring points to convolution weight with learnable parameters $\Theta_{kjl}$.
It is easy to verify that weights in Eqn.~(\ref{eqn:relation}) are rotation-invariant because the inputs of $\Phi$ are rotation-invariant defined by inner products.

\subsection{Network architecture}

PR-invNet is designed by concatenating rotation-invariant PFE-block and RFE-block. As shown in Fig. \ref{fig:pipleline}, given a shape, we first initialize the point-wise features by initial feature embedding, followed by three stages concatenating PFE-block and RFE-block to extract positional and relational features. For classification, we use an additional shape coarsening operation at each stage to construct a hierarchy of coarsened points, implemented by farthest point sampling with sampling rate of 1/2.
The intermediate features generated by PFE-blocks and RFE-blocks of different stages are concatenated and aggregated by a MLP set as two layers of FC+BN+ReLU+Dropout, followed by a FC to output confidence for shape categorization or  segmentation. The number of hidden units of the first two FCs are 512, 256, and dropout probability is 0.5. The number of neighboring points in Eqns. (\ref{eqn:feat_extr}-\ref{eqn:conv}) is 16.
For an input shape of PR-invNet, we conduct PCA to normalize shape pose only one time, and all PFE-blocks in different stages derive rot-space by Eqn.(\ref{eq:rotSpace}) starting from point cloud of this normalized pose or its coarsened point clouds.
More details of pose selector $\Psi$, feature extractor $\Gamma$, convolution filters $\Phi$, $\Theta$ in RFE-block are introduced in  supplementary material.

\iffalse
\begin{table}[h]
\caption{Network details on pose selector $\Psi$, feature extractor $\Gamma$, convolution filters $\Phi$, $\Theta$ in RFE-block. $\Psi$ is with same parameter size in all stages. Parameter sizes of others in initial stage and stages 1-3 are respectively listed separated by semicolons. }
\begin{center}
\begin{tabular}{|c|p{95pt}<{\centering} |p{120pt}<{\centering}|p{120pt}<{\centering}|}
\hline
&\multirow{2}{*}{Architecture} &\multicolumn{2}{c|}{Parameters size}\\
\cline{3-4}
& & Classification & Segmentation\\
\hline
\multirow{2}{*}{$\Psi$} &  MLP1$\rightarrow$Max-pooling $\rightarrow$MLP2$\rightarrow$Softmax & MLP1:(32,64) MLP2:(128,200) & MLP1:(32,64) MLP2:(128,200)\\
\hline
\multirow{2}{*}{$\Gamma$} &\multirow{2}{*}{MLP$\rightarrow$Max-pooling} &$-$;(64,64,64); (128,128,128);(256,256,256)& $-$;(128,128,128); (256,256,256);(512,512,512)\\
\hline
\multirow{2}{*}{$\Phi$} &\multirow{2}{*}{MLP} &(32,32);(64,64); (128,128);(256,256)&(128,128);(128,128); (256,256);(512,512)\\
\hline
\multirow{2}{*}{$\Theta$} &\multirow{2}{*}{Matrix} &$K$$\times$32$\times$32;$K$$\times$64$\times$64;
$K$$\times$128$\times$128;$K$$\times$256$\times$256 &$K$$\times$128$\times$128;$K$$\times$128$\times$128; $K$$\times$256$\times$256;$K$$\times$512$\times$512\\
\hline
\end{tabular}
\end{center}
\label{tab:network_details}
\end{table}
\fi

\section{Experimental results}
In this section we evaluate and compare with state-of-the-art methods for rotated shape classification and segmentation on the following 3D datasets.

\textbf{ModelNet40 \cite{wu20153d}} consists of 12,311  shapes from
40 categories, with 9,843 training and 2,468 test objects for shape classification.

\textbf{ShapenetCore55 \cite{savva2016shrec16}} contains two subsets: `normal', `perturbed', with aligned and randomly rotated shapes in $SO(3)$ respectively. 51,190 models are categorized into 55 classes with training, validation, test sets in ratios of 70\%, 10\%, 20\%. We uniformly sample points from the original mesh data for both subsets.

\textbf{ShapeNet part \cite{chang2015shapenet}} contains 16,880 shapes from 16 category of shapes, with 14,006 / 2,874 shapes for training / test, annotated with 50 parts.

Each shape is represented by 1024 points. To train our PR-invNet, we take Adam optimizer with initial learning rate, epoch number as 0.001, 250, and the learning rate is exponentially decayed with decay rate and decay step as 0.7, 200000. The batch size for shape classification and segmentation are 16 and 8 respectively. It takes 286.6ms, 672.1ms in one iteration for shape classification and segmentation respectively on a NVIDIA 1080 Ti GPU.

\subsection{3D shape classification}
We mainly compare with point-based methods and rotation-robust methods

\begin{table}[h]
\caption{Shape classification accuracy on ModelNet40 (in $\%$).}
\begin{center}
\begin{tabular}{p{1.5cm} |l  p{1.6cm}<{\centering}  p{1.6cm}<{\centering} p{1.6cm}<{\centering} p{1.6cm}<{\centering}}
\hline
&~Method & Input size  & z/z  & SO(3)/SO(3) & z/SO(3)\\
\hline
\multirow{10}{1cm}{Rotation-sensitive}
&~VoxNet \cite{maturana2015voxnet} & $30^3$ & 83.0 &  87.3  & - \\
&~SubVolSup \cite{qi2016volumetric}  & $30^3$ & 88.5   & 82.7 & 36.6\\
&~SubVolSup MO \cite{qi2016volumetric} & $30^3$ & 89.5 & 85.0&45.5  \\
&~MVCNN 12x \cite{su2015multi} & $12 \times 224^2$ & 89.5  & 77.6 & 70.1\\
&~MVCNN 80x \cite{su2015multi}  & $80 \times 224^2$ & 90.2  & 86.0& \textbf{81.5}\\
&~PointNet \cite{qi2017pointnet}& $1024 \times 3$ &  87.0 &80.3 & 12.8\\
&~PointNet++ \cite{qi2017pointnet2} & $1024 \times 3$ & 89.3 & 85.0 & 28.6  \\
&~PointCNN  \cite{li2018pointcnn} & $1024 \times 3$ & 91.3 & 84.5 & 41.2\\
&~DGCNN  \cite{wang2019dynamic}    & $1024 \times 3$ & \textbf{92.2} &   \textbf{81.1} &20.6  \\
\hline
\multirow{5}{1cm}{Rotation-robust}
&~Spherical CNN \cite{esteves2018learning} & $2 \times64 \times 64$ & 88.9&76.9 &86.9 \\
&~$a^3$SCNN \cite{Liu2019DeepL3} & $2\times 165 \times 65$ & \textbf{89.6} & 87.9 & 88.7\\
&~RIConvNet \cite{zhang2019rotation} & $1024 \times 3$ &86.5 &86.4 &86.4 \\
&~ClusterNet \cite{chen2019clusternet} & $1024 \times 3$ &87.1 &87.1 &87.1 \\
&~RRI-PointNet++ & $1024 \times 3$ & 79.4&79.4 &79.4 \\
&~Proposed & $1024 \times 3$ &  89.2 &\textbf{89.2} & \textbf{89.2}\\
\hline
\end{tabular}
\end{center}
\label{tab:modelnet40}
\end{table}

\textbf{\textit{ModelNet40.}} As done in Spherical CNN~\cite{esteves2018learning}, we compare in the following three modes. (1) Both training and test on data augmented by azimuthal rotation (z/z); (2) Training with azimuthal rotation and test with arbitrary rotation
(z/SO(3)); (3) Both training and test with arbitrary rotation augmented data
(SO(3)/SO(3)). The results are presented in Table \ref{tab:modelnet40}.
The traditional point-based methods, including PointNet \cite{qi2017pointnet}, PointNet++ \cite{qi2017pointnet2}, PointCNN \cite{li2018pointcnn}, DGCNN \cite{wang2019dynamic}, perform best in z/z mode, but decline sharply when testing on data augmented with arbitrary rotations (z/SO(3)). Though using arbitrarily augmented training data in SO(3)/SO(3) mode, their performances still drop with large gaps. For these rotation-robust methods including Spherical CNN  \cite{esteves2018learning}, $a^3$SCNN \cite{Liu2019DeepL3}, RIConvNet \cite{zhang2019rotation}, ClusterNet \cite{chen2019clusternet} and RRI\footnote{RRI is an essential part of ClusterNet, and the codes are provided by the authors.}-PointNet++, they are more robust in different modes. Considering that Spherical CNN and $a^3$SCNN rely on discretized angles in the sphere, they are not rigorously rotation-invariant and performance drops in modes (2)-(3). ClusterNet, RIConvNet and RRI-PointNet++ are rotation-invariant relying on input geometric features. Our PR-invNet is also rotation-invariant, and it achieves highest performance in modes (2-3) and second highest performance in mode (1) than all the rotation-robust methods, demonstrating its superiority for arbitrarily rotated shape classification.

\begin{table}[htbp]
\caption{Shape classification accuracy on ShapeNetCore55 (in $\%$). All the results of compared methods are achieved by running their code.}
\begin{center}
\begin{tabular}{p{1.3cm}| l  p{1.5cm}<{\centering}  p{1.5cm}<{\centering} p{1.5cm}<{\centering}}
\hline
&~Method           & Input size  &   Aligned & Perturbed\\
\hline
\multirow{5}{1cm}{Rotation-sensitive}
&~PointNet \cite{qi2017pointnet}      & 1024$\times$3 & 83.4 &74.6\\
&~PointNet++ \cite{qi2017pointnet2}   & 1024$\times$3 & 84.2 & 70.9\\
&~DGCNN  \cite{wang2019dynamic}      &  1024$\times$3   &  \textbf{86.3} & \textbf{74.1} \\
&~RS-CNN \cite{liu2019relation} & 1024$\times$3 & 85.9& 73.4\\
&~SpiderCNN \cite{xu2018spidercnn} & 1024$\times$3 & 79.8& 64.4\\
\hline
\multirow{4}{1cm}{Rotation-robust}
&~Spherical CNN \cite{esteves2018learning} & 2$\times64^2$ & 76.2 & 73.8\\
&~RIConvNet \cite{zhang2019rotation} & 1024$\times$3 & 78.5 & 76.9\\
&~RRI-PointNet++ & 1024$\times$3 & 70.8 & 67.9\\
&~Proposed & 1024$\times$3 & \textbf{78.9} & \textbf{77.6}\\
\hline
\end{tabular}
\end{center}
\label{tab:shapenetcore55}
\end{table}

\textbf{\textit{ShapeNetCore55.}}  We compare with point-based methods including PointNet \cite{qi2017pointnet}, PointNet++ \cite{qi2017pointnet2}, DGCNN \cite{wang2019dynamic}, RS-CNN \cite{liu2019relation}, SpiderCNN \cite{xu2018spidercnn}, and also rotation-robust Spherical CNN~\cite{esteves2018learning} and rotation-invariant RIConvNet \cite{zhang2019rotation}, RRI-PointNet++. The results are presented in Table \ref{tab:shapenetcore55}.
As shown in Table \ref{tab:shapenetcore55}, we achieve best performance in both aligned and perturbed datasets, compared with Spherical CNN, RIConvNet and RRI-PointNet++. Among all methods, we achieve highest accuracy on the perturbed dataset.

\subsection{3D shape segmentation}

\begin{table}[t]
\caption{Shape segmentation mIoU on ShapeNet part segmentation dataset (in $\%$).}
\begin{center}
\begin{tabular}{p{1.5cm}| p{2.7cm} p{2.3cm} p{1.4cm}  p{2.0cm}<{\centering} p{2.0cm}<{\centering}}
\hline
&~Method   & Input &  z/z & SO(3)/SO(3) & z/SO(3)\\
\hline
\multirow{5}{1cm}{Rotation-sensitive}
&~PointNet \cite{qi2017pointnet}      & xyz &76.2& 74.4 &37.8\\
&~PointNet++  \cite{qi2017pointnet2}  & xyz+normal &80.7 & \textbf{76.7} & \textbf{48.2}\\
&~PointCNN  \cite{li2018pointcnn}     & xyz &81.5 &71.4  &34.7 \\
&~DGCNN   \cite{wang2019dynamic}     &  xyz &78.8 &  73.3& 37.4\\
&~SpiderCNN \cite{xu2018spidercnn} & xyz+normal & \textbf{81.8} & 72.3& 42.9\\
\hline
\multirow{2}{1cm}{Rotation-robust}
&~RIConvNet \cite{zhang2019rotation} & xyz &75.6 & 75.5& 75.3\\
&~Proposed & xyz & \textbf{79.4} & \textbf{79.4} &\textbf{79.4}\\
\hline
\end{tabular}
\end{center}
\label{tab:shape_segmentation_iou}
\end{table}

\begin{wrapfigure}{r}{0.5\textwidth}
\vspace{-20pt}
\includegraphics[width=0.5\textwidth]{figures/figure_show_seg_new.pdf}
\caption{Shape segmentation results. }
\label{fig:figure_show_seg}
\vspace{-15pt}
\end{wrapfigure}
We next apply PR-invNet to point cloud segmentation to predict the part label of each point. We use the same experimental settings as RIConvNet~\cite{zhang2019rotation}, and mean per-class IoU (mIoU, $\%$) are presented in Table \ref{tab:shape_segmentation_iou}. Compared with all rotation-sensitive point-based methods and rotation-robust methods, our PR-invNet outperforms them significantly in both SO(3)/SO(3) and z/SO(3) modes, i.e., more than $2.7\%$ and  $4.1\%$ mIoU improvements. We also report the per-class IoU for above settings in z/SO(3), SO(3)/SO(3) modes respectively in the supplemental material, and our PR-invNet achieves better performance than the rotation-robust RIConvNet on all categories.
In Fig. \ref{fig:figure_show_seg}, we show the segmentation results in z/SO(3) mode of several objects as well as the corresponding ground truth labels, and our predictions labels are reasonable and close to ground truth.

\makeatletter\def\@captype{table}\makeatother
\begin{minipage}{.65\textwidth}
\centering
\caption{Classification accuracy on ModelNet40 (\%).}
\vspace{10pt}
\label{tab:every_operation}
\begin{tabular}{l  p{1.0cm}<{\centering}  p{1.0cm}<{\centering} p{1.0cm}<{\centering} p{1.0cm}<{\centering}}
\hline
\multirow{2}{*}{~Method}     & Geo-fea  &   PFE-block & RFE-block & \multirow{2}{*}{Acc.}\\
\hline
~PR-invNet-noGeo & $\times$&$\surd$ &$\surd$ & 88.2\\
~PR-invNet-noPFE & $\surd$& $\times$&$\surd$ & 87.8\\
~PR-invNet-noRFE & $\surd$&$\surd$ & $\times$& 88.0\\
~PR-invNet &$\surd$ &$\surd$ &$\surd$ & \textbf{89.2}\\
\hline
\end{tabular}
\end{minipage}
\makeatletter\def\@captype{figure}\makeatother
\begin{minipage}{0.32\textwidth}
\centering
\includegraphics[width=3.3cm]{figures/figure_different_hierarchy.pdf}
\caption{Stage numbers.}
\label{fig:different_hierarchy}
\end{minipage}

\subsection{Ablation study}
In this section, we conduct ablation study on ModelNet40 to justify the effects of our network design, and also test the robustness of PR-invNet to noises.

\textit{\textbf{Effect of proposed blocks.}}
To evaluate the effectiveness of geometric feature extraction, PFE-block, and RFE-block, we conduct experiments that utilize networks without above blocks respectively, i.e., PR-invNet-noGeo, PR-invNet-noPFE, PR-invNet-noRFE, on ModelNet40, and present the experiment results in Table \ref{tab:every_operation}. Compared with PR-invNet, the networks of PR-invNet-noGeo, PR-invNet-noPFE, PR-invNet-noRFE achieve lower performance, demonstrating the need for each component. Note that all networks of above variants are also rigorously rotation-invariant, and they also achieve better performance than most of the rotation-sensitive and rotation-robust methods whose results are presented in Table \ref{tab:modelnet40} in the SO(3)/SO(3) and z/SO(3) modes.

\textit{\textbf{Effect of stage number.}}
To  evaluate the effect of number of stages in PR-invNet, we compare performance of PR-invNet-$i$ with $i=0,1,2,\cdots,5$, and $i$ denotes number of stages excluding initial feature embedding stage. As shown in Fig. \ref{fig:different_hierarchy}, network with 3 stages achieve the highest accuracy. Deeper architectures have larger capacity but marginally decreased performances. This phenomenon was also observed in other graph CNNs~\cite{li2019deepgcns}, and training of deeper networks on point clouds deserves to be more investigated in future work.

\begin{figure}[t]
\centering
\begin{minipage}[t]{0.32\textwidth}
\centering
\includegraphics[width=3.3cm]{figures/figure_different_rotation.pdf}
\caption{Rotation groups.}
\label{fig:different_rotation}
\end{minipage}
\begin{minipage}[t]{.32\textwidth}
\centering
\includegraphics[width=3.3cm]{figures/figure_different_head.pdf}
\caption{Head numbers.}
\label{fig:diff_head}
\end{minipage}
\begin{minipage}[t]{0.32\textwidth}
\centering
\includegraphics[width=3.4cm]{figures/figure_different_noise.pdf}
\caption{Noise levels.}
\label{fig:different_noise}
\end{minipage}
\end{figure}

\textit{\textbf{Design of global shape feature.}} As shown in Fig. \ref{fig:pipleline}, learned features from all PFE-blocks and RFE-blocks are aggregated by MLP for classification. We evaluate PR-invNet-PFE and PR-invNet-RFE that only utilize features from PFE-blocks and RFE-blocks respectively, achieving $88.5\%$, $87.4\%$ classification accuracies on ModelNet40. Result using only features of the last RFE-block is $88.3\%$.
This demonstrates that concatenating all features of PFE-block and RFE-block is more effective.

\textit{\textbf{Effect of PCA-normalization and rot-space.}}
In PR-invNet, we take PCA to normalize shape as network input. We also conduct experiments with networks without PCA-normalization and only with PCA (without using sym-space and rot-space), i.e.,  PR-invNet-noPCA, PR-invNet-PCA. Their classification accuracies in ModelNet40 with z/z mode are $90.0\%$ and $89.1\%$ respectively, but drop to $44.3\%, 74.8\%$ in z/SO(3) mode, which are not rotation-invariant. In SO(3)/SO(3), our pose selector over rot-space upon PCA($89.2\%$) outperforms pure PCA for alignment($88.3\%$). Removing both PCA and pose selector achieves $87.3\%$, showing our pose selection is more effective than PCA.

\textit{\textbf{Effect of rotation group $G_R$.}}
In pose expander of PFE-block, we use the rotation group $G_R$ to construct rot-space, which is taken as alternating group $A_5$ of a regular dodecahedron (or icosahedron). Other alternating (symmetry) group can also be used, such as identity group ($I_R$), or $A_4$, $S_4$ \cite{zimmermann2011finite} respectively corresponding to regular tetrahedron, cube (or octahedron). The classification accuracies using these groups are in Fig. \ref{fig:different_rotation}. Compared with other groups, $A_5$ has the maximum number of elements, resulting in largest rot-space and achieves the highest accuracy. Operating on this largest space, the pose selector has more probability to select a better pose for shape recognition.

\textit{\textbf{Effect of pose selector.}}
In PFE-block, we use a pose selector to select the representative shape pose in rot-space. However, we can also extract features from all shapes from rot-space and then perform max-pooling or average-pooling over them to aggregate features. We compare our pose selector with these aggregation methods and present the classification accuracy and computational cost in Table \ref{tab:different_aggregation}. Since it is infeasible to extract features from all shapes in rot-space containing 120 poses, we compare these variants on the sym-space containing eight shape poses, i.e., rot-space with identity rotation group. We experiment with batch size 12, and as shown in Table \ref{tab:different_aggregation}, our pose selection method achieves higher performance while needing less GPU memory and computational time.

\textit{\textbf{Effect of head number in $\Psi$.}}
For pose selector $\Psi$, we design it as a multi-head neural network, which has 200 heads. We conduct experiments to demonstrate the effect of head numbers. As shown in Fig. \ref{fig:diff_head}, the $\Psi$ with head number as 200 achieves higher performance. Note that $\Psi$ with multi-heads all achieve better accuracies than that with one head.

\begin{table}
\begin{minipage}{0.48\linewidth}
\centering
\caption{Cla. Acc.  on ModelNet40.}
\label{tab:different_aggregation}
\begin{tabular}{l  p{1cm}<{\centering}  p{1cm}<{\centering} p{1cm}<{\centering} }
\hline
\multirow{2}{*}{Method} & Acc. (\%) & Memory (GB) & Time (ms)\\
\hline
Average-pooling & 88.1 & 10.2 & 496.5 \\
Max-pooling &  88.3 &10.2 & 512.3 \\
Proposed & \textbf{88.5} & \textbf{4.4} & \textbf{251.0}\\
\hline
\end{tabular}
\end{minipage}
\begin{minipage}{0.48\linewidth}
\centering
\caption{Cla. Acc.  on ModelNet40 (\%).}
\label{tab:every_relations}
\begin{tabular}{l  p{0.5cm}<{\centering}  p{0.5cm}<{\centering} p{0.5cm}<{\centering} p{0.5cm}<{\centering} p{0.5cm}<{\centering}}
\hline
~Method      & $C^p_k$  &   $C^g_k$ & $C^f_k$ & $g_k$ & Acc.\\
\hline
~PR-invNet-P &$\times$&$\surd$&$\surd$ & $\surd$& 88.1\\
~PR-invNet-G &$\surd$&$\times$&$\surd$ & $\surd$& 88.8\\
~PR-invNet-F &$\surd$&$\surd$&$\times$& $\surd$& 89.9\\
~PR-invNet-g &$\surd$&$\surd$&$\surd$& $\times$ & 88.5\\
~PR-invNet &$\surd$ &$\surd$ &$\surd$& $\surd$ & \textbf{89.2}\\
\hline
\end{tabular}
\end{minipage}
\end{table}

\textit{\textbf{Design of RFE-block.}}
In RFE-block, we design convolution filters based on three terms, i.e., the relations of point position, geometric feature, and point feature in Eqn. (\ref{eqn:relation}). In Table \ref{tab:every_relations}, we show our networks using only one of these terms, resulting in networks of PR-invNet-P, PR-invNet-G, PR-invNet-F respectively. We also present result of PR-invNet-g only using geometric feature in Eqn. (\ref{eqn:relation}). Their classification accuracies are all inferior compared with full version.
We also conduct experiment that without normalization in Eqn. (\ref{eqn:relation}), achieving classification accuracy as $88.6\%$.

\textit{\textbf{Robustness to noise.}}
We train PR-invNet on ModelNet40 training dataset and test it on test data with various levels of noise under the z/SO(3) mode. We add Gaussian noise with different standard deviation (Std) on each point (coordinates within a unit ball) independently. The overall classification accuracies are in Fig. \ref{fig:different_noise}. PR-invNet keeps robustness under noise with Std of $0.01$.

\begin{figure}
\begin{center}
\includegraphics[width=0.85\linewidth]{figures/figure_show_centers.pdf}
\end{center}
\caption{Illustration of selected shapes corresponding to different heads in multi-head score network. Shapes in a box highlighted by same color correspond to same head.}
\label{fig:figure_show_centers}
\end{figure}

\textit{\textbf{Visualization for pose selector.}}
In PFE-block, we design multi-head score network $\Psi$ to select a pose from rot-space $H_{SR}(P)$ based on scoring each shape pose by its maximum score belonging to multiple heads. Therefore the selected pose from rot-space corresponds to a certain head. Here we illustrate selected shape poses organized by corresponding heads highlighted in different colors in Fig. \ref{fig:figure_show_centers}. We observe that shapes  corresponding to each head have similar poses. The multi-head score network may enable to learn to align the shapes to clusters of poses using heads in multi-head score network.

\section{Conclusions}
In this work, we focus on rotation-invariant deep network design on point clouds by proposing two rotation-invariant network blocks. The constructed PR-invNet was extensively justified to be effective for rotated 3D shape classification and segmentation. In future work, we are interested to deeply investigate pose alignment capability of PFE-block, and further improve the network architecture.

\textbf{Acknowledgement.} This work was supported by NSFC (11971373, 11690011, U1811461, 61721002) and National Key R\&{D} Program 2018AAA0102201.

\bibliographystyle{splncs}

redpajama_set_name: RedPajamaArXiv


text:
<?php

declare(strict_types=1);

namespace Eelly\SDK\Pay\Service;

use Eelly\SDK\Pay\DTO\SubjectAdjustDTO;

/**
 * 会计科目日核算
 *
 * @author zhangyingdi<zhangyingdi@eelly.net>
 */
interface SubjectAdjustInterface
{

    /**
     * 根据结算日期跟科目代码,获取会计科目日核算记录
     *
     * @param string $subjectCode 科目代码
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     *
     * @author zhangyingdi<zhangyingdi@eelly.net>
     * @since  2017-11-20
     */
    public function getSubjectAdjust(string $subjectCode, string $workDate): SubjectAdjustDTO;
}

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Afro-Americans in New York Life and History is an academic journal organized and distributed by Buffalo, New York's Afro-American Historical Association of the Niagara Frontier.

History and background
Founded in 1977, the journal's mission statement informs readers that its purpose is "to publish analytical, historical, and descriptive articles dealing with the life and history of Afro-Americans in New York State." The Articles featured, deal with methodology and trends in local and regional African-American studies, historical and current. Additionally, documents are frequently published that have historical significance to the African-American in the state of New York, specifically. Finally, book reviews are published pertaining to aspects of the life, history, and culture of people of African descent and race relations.

At the time of the journal's first publication, the success of Alex Haley's novel Roots: The Saga of an American Family (1976) had created an immense, new found interest in the African-American community for the discovery, preservation, and presentation of the often-overlooked rich cultural heritage that African Americans had established in the United States.

Relevance
The plight of African Americans in the United States in the 20th and 21st centuries can be connected to many different issues.  The barriers of racism, economics and politics have greatly contributed to the oppression of people of color. These barriers continue to do so today. Whether purposefully or unknowingly actions in today's world due to these have left scars on society that have yet to heal. Afro-Americans in New York Life and History has played an important role in merging academic and community perspectives of African-American history and culture.

Editors and Board of Directors
As of July 2013, Seneca Vaught, professor of history and African Studies at Kennesaw State University, is the journal's Editor, aided by Associate Editors Clarence Williams of CUNY, Lillian Williams of SUNY at Buffalo, and Oscar R. Williams of SUNY at Albany. A variety of scholars who are interested in furthering the field of African-American history serve as Contributing Editors.

In addition to Editorial supervision, the twenty-three member Board of Directors that oversees the Afro-American Historical Association of the Niagara Frontier also has input into the operation and contents of the journal.

Notable issues
The issues concerning this journal are aimed towards African Americans in New York, with prevalent issues brought to light and discussed in the volumes of Afro-Americans in New York Life and History.
In 2005, the New York Historical Society held an exhibition titled Slavery in New York. An issue regarding Slavery in Albany, New York by Oscar Williams, Vol. 34, No. 2 (July 2010) emphasized that slavery was not limited to the south. In 1991, human remains by construction workers in lower Manhattan raised awareness of the African Burial Ground, where slaves in New York City were buried. Slavery was practiced into the 19th century. Most studies on slavery in New York have mentioned other New York cities sparingly. There is a failure on an understanding that slavery was widespread throughout New York. The capital, Albany, houses a special relationship of slavery beginning with the establishment of the Dutch West India Company in 1621.

Another issue arose in regards to African-American prisoners as passive citizens. Themis Chronopoulos' article "Political Power and Passive Citizenship: The Implications of Considering African American Prisoners as Residents of Rural New York State Districts" explains how African-American prisoners who used to live in New York City were transferred to a rural prison, which has had critical political implications. This movement of prisoners has allowed more conservative legislators to hold a political office. State law dictates that prisoners have no rights but are still being accounted for in the population. Consequently, these conservative legislators have been generally hostile in regards to African Americans and their interest. If it was not for the urban population of upstate New York, numerous senate districts would have to be redrawn due to a lack of number of residents. The Republican Party would not be able to dominate the New York State Senate and downstate New York would be more politically powerful.

Scholarship
The Carter G. Woodson essay contest is a scholarship awarded to students, ranging from grades 4-12, that show significant ability in writing. These essays are themed and students must be a resident from the western New York area. Cash prizes and certificates are presented to the winner. The winners' essays will be published in Historically Speaking and read at the African American History Program.

References

External links

Publications established in 1977
Area studies journals
Black studies publications


text:
About Rich Koslowski
"About Rich"…Yes, folks, this is quite possibly the most exciting portion of the Rich Koslowski website.
I was born in Milwaukee, Wisconsin in 1967 and have lived in the Milwaukee area ever since (minus the ten wonderful years we lived in sunny Aptos, CA).
I graduated from Menomonee Falls High School in 1985. My education as a young lad was an exercise in seeing just how little I could actually do and still pass. I was the classic "underachiever" and "class clown."
Overall I had a fantastic childhood and had a great group of friends, most of whom I still see on a regular basis to this day.
My parents owned their own grocery store where I worked in the Meat Department. I met a lot of great people working there and the experience was invaluable. I hated it at the time, of course, but looking back I realize what an invaluable tool it was for me in shaping who I am today. My father was the most hard-working individual I've ever seen. He taught me about work ethic and pride. He is also, I should add, a world champion in the culinary art of sausage making! Not bad for a guy who had to quit school in the seventh grade because of a little episode known as World War II.
I earned an Associate's Degree in Commercial Art at Milwaukee Area Technical College in 1988 and parlayed that into a meaningless job as a "dust spotter" at a local photo lab. The job totally blew but I met my wife, Sandy, there so I guess the experience wasn't a total loss.
Rich Koslowski at drawing desk
From there I went on to working as an animator at a small studio in Franksville, WI called Animagination. We worked on television commercials, instructional videos and a few children's books. It was through Animagination (say that ten times fast!) and my good buddy, the owner Art Mawhinney, that I got my first comic book gig working on Sonic The Hedgehog published by Archie Comics. We were doing storyboarding for the t.v. show and it led us to Archie in a roundabout way. Not your typical way of breaking into comics, but it worked and I was thrilled! I still work as an Inker for Archie to this day. Yes, I can pretty much ink Jughead in my sleep.
Comics was, and still is, my first love as an artist. It was always my dream growing up to work in this wonderful business. So landing the gig at Archie was a dream come true.
In addition to working in the field as an Inker at Archie I also worked in a comic book store for a while here in Milwaukee. It was at this store, Collector's Edge, working under the tutelage of the enigmatic owner, Jef Parker, that we found ourselves discussing the fact that a certain amount of our customers were found to be lacking in certain…social skills. We commented that it would be nice if they had some sort of "handbook" to aide them in their fruitless hopes of attracting female companionship. Hence, I set about creating said "handbook" in the form of my own self-published comic book entitled, How To Pick Up Girls If You're A Comic Book Geek, in 1997. A one-shot, full-color, 40 page comic that I had to take a home equity loan out to get it printed. I had no idea if it would sell, or not, but I absolutely felt compelled to produce this comic. I was thrilled to see the results. The book was a bona fide hit and I decided shortly thereafter to make it into an ongoing series entitled The 3 Geeks. The 3 Geeks was expanded in format in 1999 when I was nominated for three Eisner Awards and the title became Geeksville. Image Comics also published it for a while. A full-color issue called "Jim's Jerky" was a highlight, including a free chunk of beef jerky with the comic.
For me The 3 Geeks comic is all about fun. I always try my best to make that comic innovative, fresh and fun.
In 2001 I decided to finally produce a book I had been tinkering with for years. A book about the cartoon industry called Three Fingers. A dark comedy told in a documentary style about "cartoon actors" in the 30s and 40s and the barriers they faced in a prejudicial Hollywood. I approached Chris Staros of Top Shelf Productions with my proposal and he sent me a contract a few days later.
In 2002 Three Fingers the graphic novel was released to much hoopla and fanfare! I was incredibly proud of that day, that book, and the critical praise it received. In 2003 it was nominated for the Harvey Award, the Ursa Major Award and the Ignatz Award for "Best Graphic Novel." It won the coveted Ignatz brick––quite possibly the coolest award in the history of awards.
In 2005 I did another graphic novel with Top Shelf entitled The King––my take on the whole Elvis Presley phenomenon. The King was also well received by the fans and critics and has had several foreign editions published; another proud moment in my career.
In 2007 my Illustrated Screen Novel, The List, was self-published. A twisted holiday tale. It is currently "being shopped" to Hollywood studios. Fingers crossed. In 2010 I collaborated with writer, JD Arnold on the graphic novel, BB Wolf and the Three LPs, my third book with Top Shelf. I have several new projects in the works and enjoy painting oil portraits in my spare time. Stay tuned… And, oh yeah!…my muse is my Stella Rose. My delightful daughter who provides me with most of my inspiration!
– R
Rich Koslowski at Drawing Desk, Ink Sketch

redpajama_set_name: RedPajamaCommonCrawl


text:
Bangla Phone Secure CA
বাংলা English
SSLDigital Certificate
PKI TokenSigning Tool
CCA CertificateBPSCA CertificateSearch CertificateCRLCPSCA License
FAQRoot Certificate InstallerSSL SupportDigital Certificate HelpToken ManagerToken Driver
What is a digital certificate?
A digital certificate is an electronic "passport" that allows a person, computer or organization to exchange information securely. A digital certificate may also be referred to as a public key certificate. Just like a passport, a digital certificate provides identifying information, is forgery resistant and can be verified because it was issued by an official, trusted agency. The certificate contains the name of the certificate holder, a serial number, expiration dates, a copy of the certificate holder's public key (used for encrypting messages and digital signatures) and the digital signature of the certificate-issuing authority (CA) so that a recipient can verify that the certificate is real.
What are certificates used for?
Certificates are used primarily to verify the identity of a person or device, authenticate a service, or encrypt files.
You can use Digital Signature Certificates for the following:
For sending and receiving digitally signed and encrypted emails .
For carrying out secure web-based transactions, or to identify other participants of web-based transactions.
In eTendering, eProcurement, Income Tax [for e-filling income tax returns] applications and also in many other applications.
For signing and verifying documents like Word,Excel,PDF,etc.
For signing and verifying executables (e.g. .exe) so that you can be sure the .exe you are attempting to run is from your trusted publisher
It plays a vital role in creating a paperless office
Why do I need digital certificates?
A digital certificate authenticates your identity electronically. It also provides you with a high level of security for your online transactions by ensuring absolute privacy of the information exchanged using a digital certificate. You can use certificates to encrypt information such that only the intended recipient can read it. You can digitally sign information to assure the recipient that it has not been changed in transit, and also verify your identity as the sender of the message
A Digital Signature Certificate explicitly associates the identity of an individual/device with a pair of electronic keys - public and private keys - and this association is endorsed by the CA. The certificate contains information about a user's identity (for example, their name, pincode, country, email address, the date the certificate was issued and the name of the Certifying Authority that issued it). These keys complement each other in that one does not function in the absence of the other. They are used by browsers and servers to encrypt and decrypt information regarding the identity of the certificate user during information exchange processes. The private key is stored on the user's computer hard disk or on an external device such as a token. The user retains control of the private key; it can only be used with the issued password. The public key is disseminated with the encrypted information. The authentication process fails if either one of these keys in not available or do not match. This means that the encrypted data cannot be decrypted and therefore, is inaccessible to unauthorized parties.
A digital signature is an electronic form of a signature that can be used to authenticate the identity of the sender of a message or the signer of a document, and also ensure that the original content of the message or document that has been sent is unchanged. Digital signatures are easily transportable and cannot be imitated by someone else. The ability to ensure that the original signed message arrived means that the sender cannot easily disclaim it later.
What is a crypto token or security token?
A security token (or sometimes a hardware token, authentication token, USB token, cryptographic token, software token, virtual token, or key fob) is a hardware device that an authorized user of computer services is given to ease authentication. Whenever you apply for a certificate, upon request, BPSCA may provide you a crypto token which will have your certificates stored. This token will be necessary for signing.
Copyright © Bangla Phone Secure CA Powered by Commlink Info Tech Ltd. Home Site Map


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text:
Stay Home Hunts
Virtual Holiday Hunt
Kids Virtual Scavenger Hunts
Mini Hunts!
Downtown Dallas
Indoor Hunts
UT Dallas
Buzzered!
Free Hunts for Charities
Book a Hunt
Custom Hunts
Hunt in a Box
I was reading an article about Stevie Wonder recently when I learned something that delighted me. Turns out, Stevie wrote his incredible song "I Wish" just after a Motown company picnic. Stevie said "I had such a good time at the picnic that I went to Crystal Recording Stud io right afterward and the vibe came right to my mind — running at the picnic, the contests, we all participated."
So we're clear, he went to a work event and had so much fun that he went back to work -- and his output was astounding. How's that for a lesson? Happy employees make great things.
There's another lesson in that song, and while it's hinted at my Stevie's quote, it's really made clear in the music itself. It's about participation. Listen to the way the musicians flirt with chaos. Hear those gleeful arpeggios tumbling upwards and downwards, those instruments gamboling all around each other but never collapsing, like expert contestants in a three-legged race. Now that's teamwork. When people of different styles collaborate, they can make music. Team bonding is all about that -- learning people's skills and how to work together.
The lyrics, too, are joyful. The song's a nostalgic celebration of childhood, inspired by the euphoria of play. Heck, there's even a few whoops and hollers, just for the fun of it! So yeah, get out there and have a little joy! Play for a while.
When we create scavenger hunts, we're careful to offer a diverse experience that allows everyone to have fun, regardless of their speciality, their role, or their title. "I wish those days could come back once more," Stevie sings, and we know what he means. We try to embody that spirit of childhood play when we take groups out on hunts. I guess you could say we like creating a little sense of Wonder.
Editor's note: OK, ok. It should be acknowledged that a lot of you may have first heard this song when Will Smith sampled it for the title song from his movie Wild Wild West. If thinking of that song put you in a bit of a frontier mood, you should definitely check out our scavenger hunt in Grapevine, inspired by the desperados and rough riders who called the town home.
Here's a puzzle inspired by the classic series Reading Rainbow. In the list of authors above, each is name colored according to the title of a book he or she wrote. For example, if you saw "Steven Crane" in red letters, that's a clue to The Red Badge of Courage. When you're ready for the answers, take a look, it's in this post, way down the page! (And If you'd like more puzzles like this, consider booking a scavenger hunt with DFW Scavenger Hunt!)
Nathaniel Hawthorne - The Scarlet Letter
Tom Clancy - The Hunt for Red October
Anthony Burgess - A Clockwork Orange
Dr. Seuss - Green Eggs and Ham
Fannie Flagg - Fried Green Tomatoes at the Whistle Stop Cafe
Walter Mosely - Devil in a Blue Dress
Alice Walker - The Color Purple
Oscar Wilde - The Picture of Dorian Gray
E.L. James - Fifty Shades of Grey
Mark Bowden - Black Hawk Down
Donald J. Sobol - Encyclopedia Brown (many editions)
214-702-9612 | dfwscavengerhunt@gmail.com


text:
Until November 17th 2019 we worshipped in a building in the centre of Isleham village which had its 200th birthday seven years ago; parking in the area was limited and internal space restricted our activities. Our vision was not just to solve these problems, but to build a new church centre to accommodate future generations.
Our previous building was dated but it provided the facilities which met our needs through that 200 plus years. As society and requirements have changed and developed, our building was no longer able to meet all of our needs today.
Our vision was to have a Christian centre which would provide an attractive social meeting place, just like other community venues provide; a place where people would want to meet together.
Fundamentally we are a church and part of the expression of our life together was to have a place of worship and dignity, where we could embrace traditional values in a changing world in a relevant way.
Artists Impression


The signs and symptoms associated with the condition largely depend on if the cancer is 'functioning' (producing hormones) or 'nonfunctioning' (not producing hormones) and which hormones are present in excess. In most cases, the underlying cause of the condition is unknown. However, certain genetic conditions such as multiple endocrine neoplasia type 2, Li-Fraumeni syndrome, Von Hippel-Lindau syndrome, neurofibromatosis type I, and Carney complex are associated with an increased risk of developing adrenal tumors and cancer. Treatment may include a combination of surgery, hormone therapy, chemotherapy and radiation therapy.
ClinicalTrials.gov lists trials that are related to Adrenal cancer. Click on the link to go to ClinicalTrials.gov to read descriptions of these studies.
The American Cancer Society provides more information on Adrenal cancer.
Mayo Clinic has an information page on Adrenal cancer.
PubMed is a searchable database of medical literature and lists journal articles that discuss Adrenal cancer. Click on the link to view a sample search on this topic.
Adrenal Gland Tumor. The American Society of Clinical Oncology. March 2016; http://www.cancer.net/cancer-types/adrenal-gland-tumor/introduction.
Adrenal Carcinoma. Medscape Reference. January 2017; http://emedicine.medscape.com/article/276264-overview.
Adrenal Cancer. Mayo Clinic. December 2015; http://www.mayoclinic.org/diseases-conditions/adrenal-cancer/home/ovc-20165296.


April 2, 2015 in News, Photo Essays.
October 14, 2014 in News, Photo Essays.
Mr Austine Manzi makes back packs out of upcycled water bottles.
May 11, 2014 in Photo Essays.
April 25, 2014 in Photo Essays.
March 27, 2014 in Photo Essays.
March 22, 2014 in Photo Essays.
March 21, 2014 in Photo Essays.


text:
https://apnews.com/article/2093aed062e2450ea0cb6c1032b60766
US to shut down Idaho nuclear waste processing project
By KEITH RIDLERDecember 9, 2018 GMT
FILE - In this May 11, 2015 file photo, nuclear waste is stored in underground containers at the Idaho National Laboratory near Idaho Falls, Idaho. Federal officials will shut down a nuclear waste treatment project at the site after determining it would not be economically feasible to bring in radioactive waste from other states. The U.S. Department of Energy in documents made public this week says the Advanced Mixed Waste Treatment Project that employs 650 workers will end next year. Officials say workers are wrapping up processing radioactive waste at the department's 890-square-mile (2,300-square-kilometer) site that includes the Idaho National Laboratory. (AP Photo/Keith Ridler, File)
BOISE, Idaho (AP) — Federal officials will shut down an Idaho nuclear waste treatment project after determining it would not be economically feasible to bring in radioactive waste from other states.
The U.S. Department of Energy in documents made public this week said the Advanced Mixed Waste Treatment Project that employs 650 workers will end next year.
Officials said workers are wrapping up processing 85,000 cubic yards (65,000 cubic meters) of radioactive waste at the department's 890-square-mile (2,300-square-kilometer) site that includes the Idaho National Laboratory.
A $500 million treatment plant handles transuranic waste that includes work clothing, rags, machine parts and tools that have been contaminated with plutonium and other radioactive elements. The U.S. Nuclear Regulatory Commission says transuranic wastes take much longer to decay and are the most radioactive hazard in high-level waste after 1,000 years.
The Energy Department said that before the cleanup began, Idaho had the largest stockpile of transuranic waste of any of the agency's facilities. Court battles between Idaho and the federal government culminated with a 1995 agreement requiring the Energy Department to clean up the Idaho site.
The Idaho treatment plant compacts the transuranic waste, making it easier to ship and put into long-term storage at the Waste Isolation Pilot Plant in New Mexico.
Federal officials earlier this year floated the idea of keeping the $500 million treatment plant running in Idaho with waste from other states. The bulk of that would have been 8,000 cubic yards (6,100 cubic meters) of radioactive waste from a former nuclear weapons production area in Hanford in eastern Washington.
Local officials and politicians generally supported the idea because of the good-paying jobs. The Snake River Alliance, an Idaho-based nuclear watchdog group, said it had concerns the nuclear waste brought to Idaho would never leave.
A 38-page economic analysis the Department of Energy completed in August and released this week found "it does not appear to be cost effective due to packaging and transportation challenges in shipping waste" to Idaho.
"As work at the facility will continue into 2019, no immediate workforce impacts are anticipated," the agency said in an email to The Associated Press on Friday. The Energy Department "recognizes the contribution of this facility and its employees to DOE's cleanup mission and looks forward to applying the knowledge gained and experience of the workforce to other key activities at the Idaho site."
The agency said it would also consider voluntary separation incentives for workers.
With the Idaho treatment plant scheduled to shut down, it's not clear how the transuranic waste at Hanford and other sites will be dealt with.
The Energy Department "will continue to work to ensure a path forward for packaging and certification of TRU (transuranic) waste at Hanford and other sites," the agency said in the email to the AP.
The Post Register first reported the closure.


text:
Jeep,Mopar
Truck Thursday: Mopar ready to customize the all-new 2020 Jeep® Gladiator
Design,Engineering,Jeep
Wrangler Wednesday: All-new 2018 Jeep® Wrangler ready for the holidays
Wrangler Wednesday: The all-new 2018 Jeep® Wrangler features brighter headlamps, "Star Wars" inspiration
All-new 2018 Jeep® Wrangler Rubicon
Design,Engineering,Jeep | May 16 2018
Wrangler Wednesday: Testing the all-new 2018 Jeep® Wrangler to the ends of the Earth
When it came time to take the next step in the development of the all-new 2018 Jeep Wrangler from the drawing board to actually testing the latest version of the iconic vehicle, a test track just would not do.
For more than seven decades, the Jeep Wrangler has been known for its rugged, go-anywhere versatility. Thus, a sanitized, boring and controlled environment would not be the proper venue to test the capabilities of the latest version of the Wrangler.
To do this, the engineers took the vehicle for months at a time to the blistering cold of Alaska and scorching Arizona heat for extreme-weather testing. They also took it through the Northern Michigan mud and the Rubicon Trail.
Additionally, as the popularity of the Wrangler has spread around the globe, the newest version of the Wrangler underwent testing around the world in countries such as China, Brazil, India, Australia, New Zealand and Italy.
All-new 2018 Jeep® Wrangler Sahara
When all the miles were tallied, the all-new Wrangler underwent more than 3.9 million miles of testing. This was one of the highest number of miles of testing ever for any FCA US vehicle. It was also something that was necessary for a vehicle with the pedigree of the Wrangler.
"When we were designing, developing and engineering the next generation Wrangler, there were a few things that we knew," said Mike Manley, Head of Jeep Brand. "We had to be absolutely authentic to what Wrangler stands for: that's its capability, its versatility, the whole sense of being able to do more tomorrow than you've done today. We knew that and our fans had told us that. We had to stay true to that."
Learn more about the capabilities of the all-new Wrangler by visiting the Jeep website.
all new 2018 jeep wranglerEdward CardenasJeepJeep WranglerMike ManleyTesting
Edward Cardenas
Hello from the Motor City! I'm Edward Cardenas and I'm multimedia editor for Stellantis. As a lifelong Detroiter, I have been surrounded by the automotive industry. I've had members of my immediate and extended family work in the industry. I've covered it as a journalist and advocated for it as
Hello from the Motor City! I'm Edward Cardenas and I'm multimedia editor for Stellantis. As a lifelong Detroiter, I have been surrounded by the automotive industry. I've had members of my immediate and extended family work in the industry. I've covered it as a journalist and advocated for it as a communications professional. I have also experienced the thrills of the industry while riding in a race car at nearly 200 miles per hour. Having this breadth of experience, I look forward to drawing upon my experiences to bring a wide range of stories, photos and videos about Chrysler, FIAT and Alfa Romeo to Stellantis Digital Media. When I'm not covering my brands, I'm spending time with my wife and two boys.
Get where you're going and everywhere in between with the Uconnect 4C navigation system
2019 Ram 1500 takes lighting to new level of impact, design


"MINÄ TEIN TÄMÄN", a performance video by Finnish artists JENNY SUHONEN, ANNA USCHANOV and Kana Ohashi (Camera and editing).
The video was exhibited in Vapaan Taidekoulun lopputyönäyttely 2012, Finland.
MINÄ TEIN TÄMÄN ( "I made this") from yutakana on Vimeo.


On Tuesday, April 9, 2019, Summit Elementary opened its new playground for use.
Ten students each raised $100 or more for the school's Playground Read-a-thon, earning a pizza lunch with Principal Dr. Julie Haake and the privilege of being the first students to use the playground.
In the afternoon, all classes got to enjoy the new playground and the sunny spring weather.
Summit Principal Dr. Julie Haake thanked her predecessor as principal, Mr. David Stroot, along with CUSD 10 Superintendent Dr. Robert Green and Buildings & Grounds Director Mike Hollingshead for moving the playground project from dream to completion.
Click HERE to watch a highlight video of the playground's first visitors.


text:
Q: How to prevent the copy of XML documentation files in a release mode build? I have a Visual Studio 2010 project which references some third-party components. Their assemblies are accompanied by XML documentation files, which are useful for us (and only us) developers. And whenever the project is built (either in Debug or Release modes) these XML files are copied to the build directory.
I can't seem to find a setting or switch to disable the copy of those XML files to the build directory, either within Visual Studio or though MSBuild. A post-build script may be an option, but a smelly one. Any ideas? Thank you.

A: When you build a project the .xml/.pdb files are gathered through the ResolveAssemblyReference task. When ResolveAssemblyReference is called it is passed a list of file extensions for related files. That list of file extensions is captured in the MSBuild property AllowedReferenceRelatedFileExtensions. By default that list will contain ".pdb;.xml".
If you want to exclude all related reference files from being picked up then just override the value of the property to something which related files won't have extensions of. For example you can set AllowedReferenceRelatedFileExtensions to "-".
You can also customize the list of file which are returned by that. If you only want to find only .pdb files then you will need to pass in AllowedReferenceRelatedFileExtensions=".pdb". In that case any references which have .pdb file next to the .dll/.exe they will be copied as well. You can also use this to copy other related files which may not end in .pdb/.xml. For example if you have a referenced assembly named, MyAssembly.dll and in that same folder there exists MyAssembly.pdb and MyAssembly.foo  If you set AllowedReferenceRelatedFileExtensions=".pdb;.foo" then both the .pdb and .foo file will be copied to the output directory.

A: Visual studio project file has the same format as any msbuild file. So you can manually add the condition into corresponding section to not copy your xml files if configuration name is 'Release'.
It should be changing
<ItemGroup>

to
<ItemGroup Condition="'$(CONFIG)'=='RELEASE'">

or something like this.

A: If the .xml/.pdb are marked as build-action "Content" (etc), you can change them to "None". You should also ensure they copy-to-build-output is false.
Are both of those set?

A: What is the problem with having the XML files get copied into the folder on release builds?  It seems to me that this is fine and that the real problem is with the code that picks up files to place them in the installer.  Picking up third party dlls from your own bin\release folder is not a good practice in my opinion.  I'd have my installer pick up third party dlls from their own folder in my source tree.

A: The setting is in the Properties of the project in question, under the "Build" tab, uncheck "XML documentation file". It's also an MSBuild property called <DocumentationFile> under the applicable <PropertyGroup> for your build configuration in the .*proj file.

redpajama_set_name: RedPajamaStackExchange


Happy Monday friends! I hope you all had a great weekend and enjoyed some yummy Super Bowl snacks! We had a productive weekend and had a date night on Friday that I'm sharing tomorrow, but I officially have a new favorite restaurant in NYC! Jon and I watched the game at home and had some healthy buffalo chicken dip and made some guilt free pizzas.
This week is officially the start of my busy season and I'm determined to maintain my sanity and health. One of my goals is to always meal prep so that I don't just eat a bunch of junk when I'm burning the midnight oil. I like to joke that I don't want to gain the tax season ten. This week I made my Dig Inn bowl, and I'm so thankful to have Jon to help me with my meal preps.
My other goal this busy season is to go to yoga once a week. There is a class on Tuesday mornings in my building so it's extremely convenient. I haven't been to yoga in over a year and have really felt the difference. I also don't stretch very regularly so yoga is such a great complement to my lifting. I also love the mental benefits of yoga too, that's definitely needed with the stress of busy season.


text:
Мариэль Нордман (; род. , Монпелье) — французская . Жена скрипача Патриса Фонтанарозы.

Биография
Начинала своё музыкальное образование как пианистка, однако после встречи в 1951 году с Лили Ласкин обратилась к арфе.

Широко концертирует соло и в ансамбле (унаследовав, в частности, от Ласкин дуэт с Жаном Пьером Рампалем), а также выступает со своеобразными музыкальными шоу, в рамках которых сочетает игру на арфе с танцем, пантомимой, комическими репризами.

Специально для Нордман сочинения для арфы писали выдающиеся композиторы разных стран, в том числе Эдисон Денисов.

Ссылки
 Официальный сайт
 Marielle Nordmann на сайте Allmusic

Академические музыканты Франции


text:
is a district located in Toyama Prefecture, Japan.

As of 2003, the district has an estimated population of 49,118 and a density of 77.09 persons per km2. The total area is 637.19 km2.

Towns and villages
The district has two towns:

 Asahi
 Nyūzen

History

Mergers
 On March 31, 2006 - The town of Unazuki merged with the old city of Kurobe to form the new city of Kurobe.

Districts in Toyama Prefecture