text:
\section{Introduction}
Airborne Laser Scanning (ALS) is one of the most important remote sensing technologies that experience fast development~\cite{7907286,8082119,9112288}. ALS point clouds are advantageous over optical data in terms of various lighting conditions and shadows. It has become the most essential form of data at large spatial scales~\cite{8681075,8854321}. However, ALS point clouds contain irregularly distributed points with a series of attributes and have a complex data structure, which makes the point cloud semantic labeling challenging~\cite{wahabzada2015automated,grilli2017review}.

In recent years, deep learning models~\cite{lecun2015deep}, especially convolutional neural networks (CNNs), have been proved to be effective in feature extraction in an end-to-end fashion~\cite{litjens2017survey,deng2014tutorial,zhang2018survey}.
The CNNs also inspire researchers to tackle the challenging point cloud semantic labeling problems. However, traditional CNNs normally consist of 2D convolutional layers, which cannot directly adapt to the structure of 3D point clouds. Hence, 3D CNNs are applied on 2D contexts transformed from 3D point clouds~\cite{li2016vehicle,maturana20153d}, as is seen in VoxNet~\cite{7353481} and ShapeNets~\cite{wu20153d}. Other studies utilize multi-view CNNs to extract geometric features from multiple 2D rendering views of point clouds~\cite{boulch2017unstructured,caltagirone2017fast}. These volumetric CNNs and multi-view CNNs can only be applied to the transformed data from 3D point clouds, which would incur much information loss. The approach to address this issue would be to build a 3D model that can be directly applied to the structure of point clouds. Qi~\cite{qi2017pointnet} proposed a unique deep learning structure called PointNet, which utilizes a set of functions to obtain global features from point clouds. To capture local features and improve the generalizability of the model for pattern recognition tasks, Qi~\cite{qi2017pointnet++} further proposed a novel model called PointNet++.
More, DGCNN~\cite{wang2019dynamic} can extract local features of point clouds while maintaining permutation invariance. PointCONV~\cite{wu2019pointconv} can learn the weights of point clouds at different locations. KPConv~\cite{thomas2019kpconv} can get a matrix to perform feature updates based on the position of each point, and MS-PCNN~\cite{ma2019multi}, which is less sensitive to data distribution and computational power.
These methods integrate the preprocessing, training, and classification of the point clouds, which have been proven successful in various applications.

However, compared to the objects from indoor scenes, objects from the ALS point clouds exhibit greater variation even in objects from the same class~\cite{hsiao2004change}. For example, the geometric features of powerlines vary greatly in size and scale. Therefore, previous methods which adopt the extracted geometric features to classify powerlines are prone to misclassifications caused by the large variations of object shapes and scales~\cite{blomley20163d}.
And due to the irregularity of the point cloud distribution, most of the point clouds distributed along the boundaries of objects from different classes are mixed. The features of these point clouds are difficult to be extracted correctly and then used for semantic labeling. Moreover, there are scale differences between ALS point cloud classes; for example, the size and shape of cars do not vary as much as those of trees. But the perceptual field of the feature extraction layer of a CNN is fixed, which poses challenges in classifying objects varying in size and shape. The features captured by the same receptive field may not be able to classify either class well.
Therefore, the features extracted from the ALS point cloud need to be assigned different weights under different classes, and each point can be distinguished from the surrounding points.
The model should pay more attention to the feature extraction process of the points~\cite{nam2017dual}.

This research proposes a novel double self-attention convolutional network called the DAPnet to address the challenging issues laid out above.
The novel model is inspired by the self-attention mechanism~\cite{vaswani2017attention,nam2017dual}, which can produce different values depending on different keys, i.e., the relationship between the input features.
For ALS point clouds, the self-attention module can assign different weights to the features of each point, even if they are close to one another.
To be specific, we have designed a double self-attention module, which refers to the point attention module (PAM) and the group attention module (GAM), as the top feature extraction layer of the model.
The PAM constructs a matrix of key-value pairs based on the correlation between features of points in the same batch.
The extracted features are again assigned different weights under key-value pairs, which can effectively classify the surrounding points, especially those within the border areas.
As for the shape diversity problem in the same class, considering that sample points in a local region can constitute a local feature, so it's reasonable to divide them into different groups, where each group is a local feature belonging to an object. These different groups contain information about the shape of the object. Therefore, with our proposed GAM, we can redistribute weights among the features via these groups. This mechanism has been proved to be able to improve the final semantic labeling results.
The two attention modules process the extracted features in parallel, and the model fuses their output.
To obtain multiscale features, during the processing of the data, we also use multiscale radius to construct groups and directly connect the hierarchical features to the upsampling process by the skip-connection method. The
DAPnet can be directly applied to raw ALS point clouds without transformation.
The experimental results on the benchmark dataset show that our method can effectively and efficiently classify the point clouds by generating a state-of-the-art overall accuracy of 90.7\%, which is 5.5\% above the best benchmark.
Compared to the best benchmark methods, DAPnet also significantly improves the average F1 score to 82.3\%, up by 9.1\%. The ablation experiment shows that the double self-attention module improves the average per-class accuracy by 7\% at the same rate of model convergence.
The major contributions of this research can be summarized as follows:
\begin{itemize}
    \item The proposed DAPnet uses the PAM and the GAM to reassign weights to the extracted point cloud features. With these features, the model can effectively classify point clouds from boundaries or at different scales.
    \item The point attention module is beneficial for classifying areas with mixed point clouds by constructing a matrix of key-value pairs of extracted features and assigning different weights to the inputs.
    \item The group attention module enhances the correlation between groups of the same object by assigning different weights to the groups, which improves the classification accuracy for point clouds with diverse shape classes.
\end{itemize}

The remainder of this paper is organized into three sections. We present our method in Section \ref{methods}. The experimental results are presented in Section \ref{expriment}. We draw conclusions and detailed discussion for further work in Section \ref{conclusion}.

\section{Methods}
\label{methods}

\subsection{Data Preprocessing}

\begin{figure}[tbp]
    \begin{center}
    \includegraphics[scale=0.3]{figures/proc.png}
    \end{center}
    \caption{Demonstration of data processing. From left to right is the process of ALS point clouds in the area to regular input data.}
    \label{fig:proc}
\end{figure}

\begin{figure*}[htp]
    \begin{center}
    \includegraphics[scale=0.8]{figures/netGAI.png}
    \end{center}
    \caption{An overview of the double self-attention convolutional network named DAPnet}
    \label{fig:net}
\end{figure*}

Figure~\ref{fig:proc} shows the workflow of data preprocessing and normalization, which converts point clouds into regular batch input. Given an unordered 3D ALS point cloud $\{P_i | i = 1,2,...,n\} $ with $ P_i \in \mathbb{R}^d$. Each point $P_i$ is a vector $(x, y, z, int, ret, num) $ of its $(x, y, z)$ LiDAR-derived coordinates plus extra channels such as intensity, return number and number of returns, and corresponds to a reference label. For the training set, we obtain the length and width of the area based on the maximum and minimum coordinates. Then, a fixed-size block moves over the entire area, shifting a specified stride at each step.
Each block can overlap with adjacent ones, as the length of the stride could be less or equal to the block size. The entire area depicted by the dataset can be divided into multiple small blocks of the same size with different points.
The processed blocks then reconstitute a new dataset. The new dataset of $m$ blocks is $\{ P \} \rightarrow \{ B_j^{n_j} | j =1,2,...,m\}$, where $B_j^{n_j}$ is the representation of the $j$-th block of points and $n_j$ is the number of points in the corresponding block.
When the number of points in a block is below the threshold, we remove that block.
The settings of threshold and block size depend on point density and region size. According to our experimental results, a self-attention matrix with more than 250 points can effectively enhance the features of the points. So, when a block has less than 250 points, it is removed.
We apply a similar process to create the testing set without either reserving overlapping areas or removing blocks with insufficient points.

During the model training process, we randomly select blocks and use the min-max normalization method~\cite{jain2011min} to process the coordinates $(x, y, z)$ and intensity based on the point clouds in each block. Then at the block level, a fixed number of points are then randomly sampled. Therefore, for each block, we can obtain $\{ S_k^{n_k} | k =1,2,...,t\}$, where $S$ represents the sampled points, and $n_k$ is the number of samples at time $k$. When the number of point clouds of the block is less than the fixed number, we adopt the Bootstrap sample method~\cite{shao1994bootstrap} to sample enough points. As a result, the final dataset is $\{ P \} \rightarrow \{ S_k^{n_k} | k =1,2,...,t\}$.

\subsection{DAPnet}
\subsubsection{Method Overview}
The proposed DAPnet, a 3D point cloud semantic labeling model, consists of feature abstraction layers~\cite{qi2017pointnet++}, a PAM, a GAM, feature propagation layers, and a classifier as shown in Figure~\ref{fig:net}.

The feature abstraction layer is a feature extractor adapted to raw point clouds. It contains group sampling and convolutional layers, which can effectively extract hierarchical features. Group sampling divides all points into different groups to learn multiple local features, and convolutional layers extract features from the data via multi-size kernels. Compared to PointNet++, we use multiple sizes of groups for sampling while also concatenating all the features, by the skip-connection method, directly with the output of the corresponding feature propagation layer.
After the input data is processed from multiple feature abstraction layers, we can, in turn, obtain multiple features of points and groups as output.

Both as critical parts of the DAPnet, the proposed point and group attention modules are two types of self-attention modules. They assign different weights to the feature based on the relevance of the points or groups to the surrounding features, thus improving the performance of the semantic labeling.
These two modules process the output from the feature abstraction module in parallel.
In the PAM, especially for point clouds in the border area of the objects, features assigned different weights can better reflect their association with different classes. Similarly, an object usually corresponds to several groups of points. In the GAM, the weight assigned by the correlation between the groups shows whether they are of the same class. Finally, the enhanced features are the sum of values produced from the two modules.

Feature propagation is an upsampling operation that can use the learned features to retrieve the features of all input points. The upsampling process also concatenates the features on[from] the corresponding feature abstraction layer through the skip-connection method. Then, the neighboring points have similar features. The final results of feature propagation are sent to the classifier.

The final classifier realizes the classification of each point class, thereby achieving the semantic labeling of the ALS point clouds.

\subsubsection{Feature Abstraction Layer}
As the first part of the DAPnet, the feature abstraction layers aggregate points into groups at different hierarchies and progressively extract features at different layers.

For a given set of points $P = \{ p_1, p_2, …, p_N\}$, where $P$ is an $N \times D$ matrix. $N$ is the number of points, and $D$ is the number of dimensions of a point feature, such as coordinate, RGB, intensity, etc. For group sampling, in order to continuously measure the spatial distance at different layers, we transform the ALS point clouds $P$ to a $N \times (l+D)$ matrix, where $l$ represents the dimension of coordinates. And the spatial coordinate dimensions are not involved in the process of feature extraction.
We define $M=l+D$, so ALS point clouds can be $P^{N \times M}$.
In our study data, the $l=3$ and $D =6$. Thus, we denote the input points as $P^{N \times 9}$. Then, to make sure that the sampled group covers the entire object, we use iterative farthest point sampling (FPS)~\cite{eldar1997farthest} to find several major centroids, which means that during the iteration, each selected point is the farthest one from the rest. In this study, we used the $L_2$ distance to measure the spatial distance between two points. The sampled centroids are a subset of $P$, denoted as $\{p_{i_1}, p_{i_2}, …, p_{i_m} \}$. $i_m$ represents the index in $P$. Based on these centroids, we construct groups based on the ball query method~\cite{qi2017pointnet++} which can find all points within a fixed radius. In this step, we use the multiscale radius for grouping, taking into account the problem of sparse and dense point sampling. After group sampling, the input data become $P^{G\times S \times M}$, where $G$ represents the number of groups, and $S$ represents the fixed number of points in each group.

To extract features, we apply an 1-D convolutional operation on each group which is treated as a new object. The convolution results are normalized with Batch Normalization (BN)~\cite{ioffe2015batch} and put through the ReLU activation function~\cite{krizhevsky2012imagenet}, a non-linear operation. This process can be written mathematically as follows,
\begin{equation}

    f(\{p_1, p_2, ..., p_j\}) =  \text{ReLU}(\text{BN}_{k=1}^j( W \circ \{p_k\} + b)),
\end{equation}
where $\{p_1, p_2, ..., p_j\}$ is a group of points, and $\circ$ represents the 1-D convolutional operation. Next, we apply max pooling~\cite{murray2014generalized} over the output from the feature extraction, to extract global features.
Since each group can be treated as a part of an object, the extracted grouped features are the different local features of the object. The entire feature abstraction layer produces the output data, $P^{G \times S \times T}$, where $T$ represents the dimension of the features.

\begin{figure}[tp]
  \centering
  \subfigure[Point Attention Module]{
    \label{fig:pam}
    \includegraphics[scale=0.3]{figures/point.png}}
  \subfigure[Group Attention Module]{
    \label{fig:gam}
    \includegraphics[scale=0.3]{figures/group.png}}
  \caption{The details of the double self-attention module.}
  \label{fig:attention}
\end{figure}

\subsubsection{Point Attention Module}
The point clouds in the border area of the objects from different classes are difficult to classify because the points from two sides of the boundary may be mingled up. Therefore the features of these points need to have different weights for different classes. In the light of this idea, we design the PAM based on the self-attention mechanism~\cite{vaswani2017attention}. This mechanism can be briefly described as mapping queries to key-value pairs. Through the query in the key-value pair, the weight of the query under the corresponding key is obtained. Then we assign the weights to the corresponding query to get the output. The same query has different outputs under different keys. The PAM constructs key-value pairs based on the correlation between the features of adjacent point clouds. When the feature is input to the PAM, the outputs obtained by the key-value pair mapping are beneficial to model classification.

Taking the output $P^{G \times S \times T }$ from the feature abstraction as input, the process of the PAM is illustrated in Figure~\ref{fig:pam}. First, it constructs key-value pairs, which are derived from the input data under the self-attention mechanism.
We feed the output data into two convolutional layers respectively and achieve two outputs $A^{G \times S \times T}$ and $B^{G \times S \times T}$. Then the point features of each group are expanded into vectors. We reshape them to two matrices, $\mathbf{A}^{G \times J}$ and $\mathbf{B}^{G \times J}$, where $J$ is $S \times T$, and further transpose the matrix $A$. After the matrix multiplication $\mathbf{A}^\top \mathbf{B}$, we apply a softmax function~\cite{bouchard2011clustering} on the results to obtain the point attention matrix $\mathbf{U}^{J \times J}$ which is the key-value pairs as follows,
\begin{equation}
    \mathbf{U}_{j,i} =  \frac{ \text{exp} (s_{ij}) }{ \sum^J_{i=1} \sum^J_{j=1} \text{exp} (s_{ij})},
\end{equation}
where $s_{ij} \in \mathbf{A}^\top \mathbf{B}$. The $\mathbf{U}_{j,i}$ indicates that the $i^{th}$ feature impacts on $j^{th}$ feature.
A larger value between the two points indicates that they have a strong correlation. We also feed the previous output $P$ through a convolutional layer and achieve the output data $C^{G \times S \times T}$ to query.
We convert it to the matrix $\mathbf{C}^{G \times J}$ and multiply by the transpose of the point-attention matrix. The result is $\mathbf{C} \mathbf{U}^{\top} \in \mathbb{R}^{G \times J}$.
Then we reshape the result to $G \times S \times T$ and multiply a scale $\alpha$ to do an element-wise sum with the data $P$. The final result is the output of attention mechanism, which can be written mathematically as follows,
\begin{equation}
    \text{Out}_{\text{point}} =  \alpha \sum^J_{i=1}  \mathbf{U}_{j,i} \mathbf{C}_i + D_j,
\end{equation}
where $\alpha $ is the learnable scale parameter and initialized as 0. It can gradually assign more weight to the non-local features beyond the local neighborhood. The points have different weights, which is beneficial for classifying some mixed points in the border area. The final result $\text{Out}_{\text{point}}$ is a feature-enhanced output with the point attention matrix.

\begin{table*}[h]
\centering
\caption{The detailed operations of DAPnet}
\begin{tabular}{lccccl}
\hline
\multicolumn{1}{c}{Layer Name} & Input & Output & Operations & \# Kernels & \multicolumn{1}{c}{Note} \\ \hline
\multirow{4}{*}{Feature Abstraction} & $L_0$ & $L_1$ & Conv,Conv,Conv,Max & (32,32,64) &  \\
 & $L_1$ & $L_2$ & Conv,Conv,Conv,Max & (64,64,128) &  \\
 & $L_2$ & $L_3$ & Conv,Conv,Conv,Max & (128,128,256) &  \\
 & $L_3$ & $L_4$ & Conv,Conv,Conv,Max & (256,256,512) &  \\ \hline
\multirow{5}{*}{PAM} & $L_4$ & $L_5$ & Conv & 64 &  \\
 & $L_4$ & $L_6$ & Conv & 64 &  \\
 & $L_5$,$L_6$ & $L_7$ & Multiple,Softmax & - & key-value pairs \\
 & $L_4$ & $L_8$ & Conv & - & query \\
 & $L_4$,$L_7$,$L_8$ & $L_9$ & Multiple,Add & - & $\alpha$,output \\ \hline
\multirow{2}{*}{GAM} & $L_4$ & $L_{10}$ & Multiple,Softmax &  & key-value pairs \\
 & $L_4$,$L_{10}$ & \multicolumn{1}{l}{$L_{11}$} & Multiple,Sum &  & $\beta$,query,output \\ \hline
\multirow{4}{*}{Feature Propagation} & \begin{tabular}[c]{@{}c@{}}$L_3$,\\ $L_{9}$,$L_{11}$\end{tabular} & \multicolumn{1}{l}{$L_{12}$} & \begin{tabular}[c]{@{}c@{}}Sum,Concat,Interpolation,\\ Conv,Conv\end{tabular} & (256,256) &  \\
 & $L_2$,$L_{12}$ & \multicolumn{1}{l}{$L_{13}$} & \begin{tabular}[c]{@{}c@{}}Concat,Interpolation,\\ Conv,Conv\end{tabular} & (256,256) &  \\
 & $L_1$,$L_{13}$ & \multicolumn{1}{l}{$L_{14}$} & \begin{tabular}[c]{@{}c@{}}Concat,Interpolation,\\ Conv,Conv\end{tabular} & (256,128) &  \\
 & $L_{14}$ & \multicolumn{1}{l}{$L_{15}$} & Conv,Conv,Conv & (128,128,128) &  \\ \hline
\multirow{2}{*}{Classifier} & $L_{15}$ & \multicolumn{1}{l}{$\hat{c}$} & Conv & (128) &  \\
 & $\hat{c}$,$c$ & \multicolumn{1}{l}{$L_{16}$} & Softmax,Cross entropy &  &  \\ \hline
\end{tabular}
\label{tab:detail}
\end{table*}

\subsubsection{Group Attention Module}
Each group is sampled from the points around the centroid, and they almost cover the entire object. And groups from the same object have higher correlations, and each group contributes differently to the final semantic labeling result. To enhance the contribution of different groups, we designed the group focus [attention] module based on the relationship between groups.
Similarly, it also needs to construct queries, key-value pairs, and outputs. Different from the PAM, it does not require a convolution operation at the beginning since it can destroy the relationship between groups.

For the output $P$ of the feature abstraction, the process of the GAM is illustrated in Figure~\ref{fig:gam}. We directly reshape it to a $G \times J$ matrix $\mathbf{D}$. Then we perform a matrix multiplication between the matrix and the transpose matrix and a softmax function on the result to obtain the group attention matrix $V^{G \times G}$, whose elements are calculated with the following,
\begin{equation}
    \mathbf{V}_{j,i} =  \frac{ \text{exp}   ((\mathbf{D}\mathbf{D}^\top)_{ij}) }{ \sum^G_i \sum^G_j \text{exp} ((\mathbf{D}\mathbf{D}^\top)_{ij})}.
\end{equation}

$\mathbf{V}_{j,i}$ is the key-value pair for the GAM. It represents the relationship between groups. Then the reshaped output $D^{G \times J}$ multiple V with a scale $\beta$. Finally, we do an element-wise sum with the data $P$. The process can be written as follows:
\begin{equation}
    \text{Out}_{\text{group}} =  \beta \sum^G_{i=1}   \mathbf(V)_{j,i} \mathbf{D}_i + D_j,
\end{equation}
where $\beta$ is also initialized as 0. When each group adds the corresponding weights, the features can be boosted based on the relationship between groups. And the weights assigned according to the correlation between the groups are beneficial for objects with irregular shapes.

\subsubsection{Feature Propagation Layer}
Because the final feature-enhanced outputs from the point and group attention modules cannot be directly used to classify each point, the feature propagation layer generates features from the feature-enhanced outputs to each point.

Feature propagation is also a hierarchical process, which progressively generates features corresponding to all points layer by layer. First, we concatenate the summed outputs and the features of the previous feature abstraction layer through the skip-connection method to the input. Then we use the inverse distance weighted method~\cite{setianto2013comparison} based on k nearest neighbors (KNN)~\cite{fukunaga1975branch} to interpolate feature values of the points in each layer, as follows,

\begin{equation}
\label{eq:fp}
u(x) = \left\{ \begin{array}{ll}
\frac{\sum^N_{i=1} w_i (x) u_i}{\sum^N_{i=1}w_i(x)}, & \textrm{if $ w_i = \frac{1}{||x - x_i||^2} $ for all $i$}\\
u_i, & \textrm{if $w_i = 0$ \qquad for some $i$}
\end{array} \right.
\end{equation}

From Eq.~\ref{eq:fp}, we can find that points farther from the point $x$ have less weight. After the weight of each point is assigned, we perform a global normalization for all weights. Through the processing of all feature propagation layers, we can get each point score $\hat{c}$ and compare it with the corresponding label $c$ under the cross-entropy loss function~\cite{bosman2000negative}. Finally, we use the gradient descent algorithm~\cite{kingma2014adam} to update all model weights.

\subsection{Training parameters}
In this section, we introduce the architecture of the DAPnet. The details of the architecture are provided in Table~\ref{tab:detail}, including data flow, the main process of operation, and the number of convolutional kernels.

First, the DAPnet has 4 layers of feature abstraction. In each layer, the point clouds are divided by group sampling. We use 3 convolutional layers for feature extraction on these groups, and the number of convolution kernels is gradually increased.
After 3 convolutional layers, we apply max-pooling to obtain the global features of each group $L_1$. Then, for the final output $L_4$ of feature abstraction, we can get the enhanced feature results of $L_9$ and $L_{11}$ by the point and group attention modules. The following 4 layers are feature propagation. Except for the last layer, the input is concatenated to the output of the corresponding feature abstraction. Finally, by comparing the obtained score of all original points with the corresponding label $c$, the classifier performs classification.

\subsection{Benchmark Methods}
To compare benchmark methods on the ISPRS 3D Semantic Labeling Contest, we selected the following algorithms for a brief review based on performance, feature extraction methods, and other factors, with their abbreviations as method names.

\begin{table}[h]
\centering
\caption{The detail of the benchmark methods}
\label{tab:method}
\setlength{\tabcolsep}{0.5mm}{
\begin{tabular}{lccc}
\hline
Method & Transformation & Features & Classifier \\
\hline
IIS\_7 & Yes & Geometrical & $ - $ \\
UM & Yes & Geometrical & OvO classifier \\
HM\_1 & Yes  & Multiple Scales & RF \\
WhuY3 & Yes & Geometrical & Softmax \\
LUH & Yes & Multiple Scales & RF \\
RIT\_1 &  No  & Geometrical & Softmax \\
NANJ2 & Yes & Geometrical & Softmax \\
PointNet & No & Geometrical & Softmax \\
PointNet++ & No & Multiple Scales & Softmax \\
PointSIFT & No & Multiple Scales & Softmax \\
GAPHNet & No & Multiple Scales & Softmax \\
\hline
DAPnet &  No  & Multiple Scales & Softmax \\
\hline
\end{tabular}}
\end{table}

\begin{figure*}[!htbp]
    \begin{center}
    \includegraphics[scale=0.4]{figures/dataset.png}
    \end{center}
    \caption{3D point cloud acquired via airborne laser scanning.}
    \label{fig:data}
\end{figure*}

\begin{table*}[!htbp]
\centering
\caption{Number of 3D points per class.}
\label{tab:data}
\begin{tabular}{lcccccccccc}
\hline
Class        & power & low\_veg & imp\_surf & car   & fence\_hedge & roof    & fac    & shrub  & tree    & Total   \\ \hline
Training Set & 546   & 180,850  & 193,723   & 4,614 & 12,070       & 152,045 & 27,250 & 47,605 & 135,173 & 753,876 \\
Test Set     & 600   & 98,690   & 101,986   & 3,708 & 7,422        & 109,048 & 11,224 & 24,818 & 54,226  & 411,722 \\ \hline
\end{tabular}
\end{table*}

The differences between these benchmark methods mainly lie in three aspects, namely, data transformation, features, and classifier types. Table~\ref{tab:method} show the characteristics of the mentioned methods and our proposed method. The \textbf{IIS\_7}~\cite{2016A} method over-segments the LiDAR data into super voxels in terms of various attributes (i.e., shape, colors, intensity, etc.), and applies the spectral and geometrical feature extraction. The \textbf{UM}~\cite{2016Context} method combines various features including point-attributes, textural patterns, and geometric attributes to a one-vs-one classifier. The \textbf{HM\_1}~\cite{2017Semantische} method depends on the geometric features of a selection of neighborhoods. To conduct the classification, it adopts a Conditional Random Field (CRF)~\cite{finkel2008efficient} with a RF classifier. The \textbf{WhuY3}~\cite{yang2017convolutional} method transforms the 3D neighborhood features of point clouds to a 2D image and applies a CNN to extract the high-level representation of features. The \textbf{LUH}~\cite{2016HIERARCHICAL} method extends the Voxel Cloud Connectivity Segmentation~\cite{papon2013voxel}. It designs a two-layer hierarchical CRF framework to connect relationships, along with the Fast Point Feature Histograms (FPFH) features~\cite{rusu2009fast}. The \textbf{RIT\_1}~\cite{yousefhussien2018multi} method proposes a 1D-fully convolutional network extended from PointNet~\cite{qi2017pointnet} in an end-to-end fashion. The \textbf{NANJ2}~\cite{2018Classifying} method applies a multiscale CNN to learn the geometric features on a set of multiscale contextual images.
Furthermore, we also use PointNet, PointNet++~\cite{qi2017pointnet++}, PointSIFT~\cite{2018PointSIFT}, and GAPHNet~\cite{LI202026} for comparison.
These methods are based on CNNs and can be applied to the original point cloud data without transformation. They use the extracted features to achieve the classification of points through the softmax classifier. PointSIFT obtains scale invariance by encoding each point in 8 directions. GAPHNet also uses the attention mechanism to improve the performance of semantic labeling.
During the training process, we used the same data processing methods for PointNet and PointNet++.

\begin{figure*}[!htbp]
    \begin{center}
    \includegraphics[scale=0.83]{figures/cls-map.png}
    \end{center}
    \caption{The classification result and error map of DAPnet on the Vaihingen 3D test dataset. The block in the red box is enlarged to show the details}
    \label{fig:bench}
\end{figure*}

\begin{table*}[h]
\centering
\caption{The confusion matrix of DAPnet on the Vaihingen 3D test dataset with per-class precision, recall and F1 score (\%). The overall accuracy (OA) is 90.7\%.}
\setlength{\tabcolsep}{1.7mm}{
\begin{tabular}{lccccccccc}
\hline
Classes & power & low\_veg & imp\_surf & car & fence\_hedge & roof & fac & shrub & tree \\ \hline
power & \textbf{90.3} (542) & 0.2 (1) & 0.0 (0) & 0.0 (0) & 0.0 (0) & 4.7 (28) & 0.3 (2) & 0.3 (2) & 4.2 (25) \\
low\_veg & 0.0 (0) & \textbf{89.5} (88,357) & 6.6 (6,470) & 0.1 (73) & 0.1 (106) & 0.5 (452) & 0.1 (104) & 2.8 (2,767) & 0.4 (361) \\
imp\_surf & 0.0 (0) & 2.2 (2,279) & \textbf{97.3} (99,225) & 0.1 (114) & 0.0 (48) & 0.1 (126) & 0.0 (27) & 0.1 (145) & 0.0 (22) \\
car & 0.0 (0) & 1.9 (70) & 1.1 (40) & \textbf{90.2} (3,344) & 0.8 (28) & 1.6 (58) & 0.5 (20) & 3.7 (138) & 0.3 (10) \\
fence\_hedge & 0.0 (0) & 9.2 (683) & 1.8 (136) & 1.6 (122) & \textbf{41.1} (3,047) & 1.8 (132) & 1.2 (91) & 28.4 (2,109) & 14.8 (1,102) \\
roof & 0.1 (75) & 0.3 (361) & 0.1 (97) & 0.0 (5) & 0.0 (52) & \textbf{97.0} (105,750) & 0.4 (414) & 1.0 (1,045) & 1.1 (1,249) \\
fac & 0.1 (10) & 8.1 (912) & 0.9 (99) & 1.1 (121) & 0.3 (33) & 13.8 (1,548) & \textbf{62.0} (6,963) & 7.0 (787) & 6.7 (751) \\
shrub & 0.0 (1) & 11.6 (2,882) & 0.6 (141) & 0.5 (132) & 1.2 (309) & 2.6 (653) & 1.1 (275) & \textbf{74.0} (18,353) & 8.3 (2,072) \\
tree & 0.0 (10) & 2.2 (1,174) & 0.0 (16) & 0.1 (35) & 0.3 (142) & 1.6 (882) & 0.7 (356) & 6.9 (3,761) & \textbf{88.2} (47,850) \\ \hline
Precision & 85.0 & 91.4 & 93.4 & 84.7 & 80.9 & 96.5 & 84.4 & 63.1 & 89.5 \\
Recall & 90.3 & 89.5 & 97.3 & 90.2 & 41.1 & 97.0 & 62.0 & 74.0 & 88.2 \\
F1 score & 87.6 & 90.4 & 95.3 & 87.4 & 54.5 & 96.7 & 71.5 & 68.1 & 88.9 \\ \hline
\end{tabular}}
\label{tab:oa2}
\end{table*}

\begin{table*}[!h]
\centering
\caption{The comparison between DAPnet and other methods on Vaihingen 3D test dataset. The per-class F1 score, the average F1 scores (Avg. F1), and the overall accuracy (OA). (\%)}
\setlength{\tabcolsep}{3mm}{
\begin{tabular}{lccccccccccc}
\hline
Method & power & low\_veg & imp\_surf & car & fence\_hedge & roof & fac & shrub & tree & Avg. F1 & OA\\ \hline
IIS\_7 & 54.4 & 65.2 & 85.0 & 57.9 & 28.9 & 90.9 & — & 39.5 & 75.6 & 55.3 & 76.2\\
UM & 46.1 & 79.0 & 89.1 & 47.7 & 5.2 & 92.0 & 52.7 & 40.9 & 77.9 & 58.9 & 80.8\\
HM\_1 & 69.8 & 73.8 & 91.5 & 58.2 & 29.9 & 91.6 & 54.7 & 47.8 & 80.2 & 66.4 & 80.5\\
WhuY3 & 37.1 & 81.4 & 90.1 & 63.4 & 23.9 & 93.4 & 47.5 & 39.9 & 78.0 & 61.6 & 82.3\\
LUH & 59.6 & 77.5 & 91.1 & 73.1 & 34.0 & 94.2 & \textbf{56.3} & 46.6 & \textbf{83.1} & 68.4 & 81.6\\
RIT\_1 & 37.5 & 77.9 & 91.5 & 73.4 & 18.0 & 94.0 & 49.3 & 45.9 & 82.5 & 63.3 & 81.6\\
NANJ2 & 62.0 & \textbf{88.8} & 91.2 & 66.7 & \textbf{40.7} & 93.6 & 42.6 & 55.9 & 82.6 & 69.3 & \textbf{85.2} \\
PointNet & 43.6 & 80.4 & 87.8 & 47.3 & 21.6 & 81.9 & 28.7 & 38.5 & 64.5 & 54.9 & 75.1\\
PointNet++ & 71.4 & 84.9 & 91.6 & 73.9 & 36.2 & 90.4 & 51.9 & 50.5 & 75.9 & 69.6 & 84.2\\
PointSIFT & 73.3 & 77.4 & 91.7 & 70.4 & 33.8 & 93.7 & 51.1 & 53.6 & 80.6 & 68.8 & 82.7 \\
GAPHNet& \textbf{77.5} & 78.9 & \textbf{94.0} & \textbf{74.2} & 35.3 & \textbf{95.0} & 52.3 & \textbf{57.6} & 82.1 & \textbf{73.2} & 84.5 \\\hline
DAPnet & \textbf{87.6} & \textbf{90.4} & \textbf{95.3} & \textbf{87.4} & \textbf{54.5} & \textbf{96.7} & \textbf{71.5} & \textbf{68.1} & \textbf{88.9} & \textbf{82.3} & 90.7\\ \hline
\end{tabular}}
\label{tab:ben_f1}
\end{table*}

\section{Experiment}
\label{expriment}
\subsection{Dataset}
The Vaihingen dataset has been proposed within the scope of the ISPRS test project on urban classification ~\cite{cramer2010dgpf,niemeyer2014contextual}, and it is the benchmark dataset for ISPRS 3D semantic labeling.
More details about this dataset could be found on the ISPRS website\footnote{http://www2.isprs.org/commissions/comm3/wg4/3d-semantic-labeling.html}.
In detail, the ALS point cloud dataset consists of 1,165,598 points and is divided into two areas for training and testing. There are a total of 753,876 training points and 411,722 test points. The training area is mainly residential, with detached houses and high-rise buildings. The test area is located in the center of Vaihingen and has dense and complex buildings. We aim to discern the following 9 object classes with the model, including Powerline (power), Low Vegetation (low\_veg), Impervious Surfaces (im\_surf), Car, Fence/Hedge (fence\_hedge), Roof, Facade (fac), Shrub and Tree. Each point in the point clouds contains LiDAR-derived (x, y, z) coordinates, backscattered intensity, return number, number of returns, and reference label. The training and test areas are demonstrated in Figure~\ref{fig:data}, and the class distribution of the training and test sets are shown in Table~\ref{tab:data}.

We also use the dataset of the 2019 IEEE GRSS Data Fusion Contest 3D point cloud classification challenge~\footnote{https://competitions.codalab.org/competitions/20217} (DFC 3D) to validate the generalization ability of the DAPnet. This dataset is also an ALS point cloud dataset, captured in Jacksonville, Florida, and Omaha, Nebraska.
The DFC 3D dataset has 6 classes, which are Ground, High Vegetation/Trees (high\_veg), Building Roof (building), Water, Elevated Road/Bridge, and Unlabeled.
Every point is also a vector $(x, y, z, int, ret, num) $.

\subsection{Implementation Details}
We implemented the DAPnet with the PyTorch framework. To process the data, We choose 30$\times$30m as the block size and 10 as the stride. In each block, we sample 1024 points so that those blocks contain the same number of points. The number of groups for the group sampling of the feature abstraction layer are 256, 128, 64, and 32, which correspond to the sampling radius of 0.1, 0.2, 0.4, and 0.8. The multi-scale sampling radii are [0.05, 0.1], [0.1, 0.2], [0.2, 0.4], and [0.4, 0.8] respectively. A batch size of 16 and the maximum epoch of 200 are set for model training. The Adam optimizer~\cite{kingma2014adam} with a momentum of 0.9 and a decaying rate of 0.0001 is used. In terms of the learning rate policy, we use polynomial decay, where the learning rate is monotonically decreasing as the model training progress by iterations. The learning rate at the $i$-th iteration in polynomial decay is given by Equation~\ref{eq:lr},
\begin{equation}
    lr_{i} = (lr_{1}-lr_{I}) \times (1 - \frac{i}{I})^{0.7} + lr_{terminal}
    \label{eq:lr}
\end{equation}
where the initial learning rate $lr_{1}$ is set to 0.001, and the learning rate $lr_{I}$ at the last iteration $I$ is set to $1e^{-5}$ for model training.
The evaluation metrics of per-class accuracy, precision, recall, and F1-score are calculated using the ISPRS 3D Semantic Labeling Contest dataset. The source codes are available at Github\footnote{https://github.com/RayleighChen/point-attention}.

\subsection{Classification Results}

Table~\ref{tab:oa2} shows the confusion matrix of the DAPnet model. The overall accuracy is 90.7\%, and the model achieves over 90\% accuracy on classes of powerline, impervious surface, car, and roof.
Objects from these classes usually have fixed shapes, and the DAPnet can process the ALS point clouds of these well.
However, the model has not been effective in terms of accuracy in classifying fence/hedge (41.1\%), facade (62.0\%), and shrub (74.0\%). Ineffectiveness in the worst-performing class, fence/hedge, can be attributed to diverse shapes, plus those point clouds tend to be mixed with objects from other classes.
Objects wrongfully classified as fence/hedge are mainly in shrub and tree classes, at 28.4\% and 14.8\%. Shrubs and trees bear great similarity to objects in fence/hedge in terms of height, topological features, and spectral reflectance, and the precision for classifying them is high at 84.7\%, indicating that the DAPnet is less likely to wrongly classify shrub and tree as the fence/hedge.
On the other hand, many facade points are misclassified as roofs because of the similarity between the two classes, while roof points are rarely misclassified by DAPnet as the facade class.
The result reveals that DAPnet has excellent performance for classes with fixed shapes and also shows good precision for classes with diverse shapes.

The classification results and error maps of the DAPnet are shown in Figure~\ref{fig:bench}.
The DAPnet can correctly classify ALS point clouds in most areas, especially where the impervious surface and roof are mixed. Nonetheless, the classification error in areas of mixed shrubs and trees is large according to the error map. When point clouds have similar features, and their constituent objects have irregular shapes and intermixed points at the same time, DAPnet is unable to classify these points correctly.
In the classification map, we zoomed in on the semantic labeling results for an area. This area contains impervious surfaces, roofs, low vegetation, and trees. According to the corresponding error map, the DAPnet has only misclassified a small number of low vegetation and tree points. Still, the DAPnet has demonstrated itself to do well in classifying impervious surfaces, roofs, and most of the low vegetation and trees. The power of the DAPnet has been manifest in those promising results.

\subsection{Performance Evaluation}
Table~\ref{tab:ben_f1} shows the F1 score of our method and the benchmark methods. The DAPnet produces a 9.1\% higher average F1 scores than the best benchmark method.
The DAPnet attains the best overall accuracy (90.7\%), which is 5.5\% higher than the best benchmark. While the edge of the overall accuracy is high, the DAPnet also prevails at per class F1 score with an average improvement of 8.1\% compared to the best benchmark of each class.
For powerline, car, fence/hence, facade, and shrub classes, the improvement is even more significant than the best benchmark, at an average percentage of 12.6\%, where the facade class has improved the most 15.2\%. The classes of powerline, car and fence/hedge have a limited number of training samples according to Table~\ref{tab:data}, but the significant increase in F1 scores with the DAPnet shows that the model performs well even with a small number of samples.
With this considerable improvement, the DAPnet achieves a new start-of-the-art performance.

Compared to algorithms that use multiscale features (HM\_1, LUH, PointNet++, PointSIFT, and GAPHNet), DAPnet achieves the best performance on classes at different scales. The incorporation of point and group attention modules allows these multiscale features to contribute better to the results of semantic labeling under the corresponding key-value pair matrix. While both opt for attention mechanism, the DAPnet still maintains an edge over the GAPHNet. In classes such as car, fence/hence, and facade, the per-class F1 score of the DAPnet performs at least 13\% higher than the GAPHNet. The attention module constructed upon the correlation between points and groups can be better used for semantic labeling of point clouds.

\begin{table}[!htbp]
\centering
\caption{The comparison between DAPnet and other methods on DFC 3D test dataset. (\%)}
\begin{tabular}{lccccc}
\hline
Model & ground & high\_veg & building & others & Avg. F1 \\ \hline
PointNet & 14.2 & 31.7 & 13.3 & 11.4 & 19.7 \\
PointNet++ & 15.5 & 45.7 & 28.2 & 23.1 & 29.8 \\
PointSIFT & 14.1 & 46.9 & 29.8 & 15.2 & 30.3 \\
GAPHNet & 20.8 & 76.5 & 35.7 & 25.2 & 44.3 \\
DAPnet & \textbf{21.6} & \textbf{78.3} & \textbf{40.3} & \textbf{26.6} & \textbf{46.7} \\ \hline
\end{tabular}
\label{tab:transfer}
\end{table}

\begin{figure*}[!htbp]
    \begin{center}
    \includegraphics[scale=0.83]{figures/diff.jpg}
    \end{center}
    \caption{The qualitative classification results of different models. Circled parts are areas where the results disagree significantly with one another.}
    \label{fig:diff}
\end{figure*}

\begin{table*}[!h]
\centering
\caption{The comparison of performances using different strategies. (\%)}
\setlength{\tabcolsep}{3mm}{
\begin{tabular}{lccccccccccc}
\hline
Method & power & low\_veg & imp\_surf & car & fence\_hedge & roof & fac & shrub & tree & Avg. F1 & OA \\ \hline

DAPnet(BASE) &77.7 & 87.1 & 91.5 & 72.7 & 45.6 & 88.1 & 60.4 & 56.1 & 80.8 & 73.3 & 84.5 \\ \hline
DAPnet(M) & 81.7 & 87.2 & 93.0 & 75.3 & 50.6 & 90.7 & 63.7 & 57.9 & 82.3 & 75.8 & 86.0  \\
DAPnet(G) & 76.8 & 87.4 & 92.2 & 75.8 & 51.2 & 90.6 & 64.2 & 60.0 & 83.7 & 75.8 & 86.1  \\
DAPnet(GM) & 85.9 & 87.8 & 92.5 & 79.3 & 53.8 & 93.7 & 68.2 & 63.9 & 84.6 & 78.8 & 87.6  \\
DAPnet(P) & 85.5 & 86.9 & 93.1 & 76.8 & 51.1 & 93.5 & 69.2 & 57.4 & 86.2 & 77.8 & 87.3  \\
DAPnet(PM) & 87.4 & 88.9 & 92.7 & 81.8 & 54.4 & 94.8 & 71.4 & 58.5 & 87.2 & 79.7 & 88.3  \\
DAPnet(PG) & 87.6 & 90.4 & 94.7 & 85.9 & 53.4 & 96.2 & 70.3 & 67.9 & 88.2 & 81.6 & 90.2 \\  \hline
DAPnet(PGM) & 87.6 & 90.4 & 95.3 & 87.4 & 54.5 & 96.7 & 71.5 & 68.1 & 88.9 & 82.3 & 90.7  \\
 \hline
\end{tabular}}
\label{tab:abl}
\end{table*}

\subsection{Generalization Analysis}
In order to validate the generalization ability of the DAPnet, we have used the same experimental strategy as the GAPHNet. The DAPnet trained on the Vaihingen 3D dataset is directly used to predict semantic labels for the DFC 3D dataset without retraining.
Considering that the classes of the two datasets are different, we also adopt the same strategy~\cite{LI202026} and use the trained model, mapping the predicted impervious surface to ground, shrubs, and trees to high vegetation, roofs and facades to buildings, and the rest to others. Here we mainly analyze the classification results of these three classes on the DFC 3D dataset.

We select 16 point cloud files (16,641,946 points) out of 110 files into the validation set.
We compared the experimental results with several other methods for the per-class F1 scores as shown in Table~\ref{tab:transfer}. In this transferred task, the DAPnet still obtained the best results. All of these methods use multiscale features, but the models that employ the attention mechanism have remarkable advantages in performance over those that do not. On high vegetation, both the GAPHNet and the DAPnet using the attention mechanism even outperform the other methods by more than 30\%. The incorporation of the attention module improves the generalization ability of the models. Compared to the GAPHNet, the improvement of DAPnet is not as significant as on the Vaihingen 3D dataset. We believe this is because the shape of objects in these classes is not complex, and the point clouds around object boundaries are more distinct and have fewer mix-ups between points from different classes. So even though the overall performance of the two models is close, we believe the DAPnet can be applied to more scenarios, and its best performance on the DFC 3D dataset attests to its good generalization ability.

\subsection{Ablation Study}
In order to verify the effectiveness of attention modules and the multi-radius group sampling method employed in the DAPnet, we have conducted an ablation study to compare different strategies by the incorporation or the removal of modules. These strategies build upon the model with the basic configuration (BASE), i.e., neither any attention modules are added, nor the multi-radius group sampling is used. Other strategies incorporate different modules and methods, including the PAM (P), the GAM (G), or multi-radius group sampling (M) and the combinations among them. The radius values of choice in the group sampling are in [0.1, 0.2, 0.4, 0.8]. The results are shown in Table~\ref{tab:abl}, with the strategies represented by the concatenation of incorporated module notations. The DAPnet(PGM) is the full version of our proposed model.

Through Table~\ref{tab:abl}, we can infer the effect of different modules by comparing pairs of related strategies. For starters, the effect of the point and group attention module combined can be evidenced in the fact that the DAPnet(PG) has achieved higher overall accuracy than the DAPnet(BASE) and that the overall accuracy of DAPnet(PGM) is also higher than the DAPnet(M). By comparing DAPnet(P) or DAPnet(G) to the DAPnet(BASE), we learn that the overall accuracy of the model improves even when only one of the PAM and the GAM is added to the model.
Whereas for the three operations, P, G, and M, the PAM has exerted a most significant improvement on the model, and their impact on the per-class F1 scores varies.
For example, for powerline, the F1 score of DAPnet(P) is higher than that of DAPnet(G), while for low vegetation and shrubs, the F1 score of DAPnet(P) is lower than that of DAPnet(G).
The GAM is beneficial for classes with diverse shapes, while the PAM is beneficial for point clouds at the boundary areas between objects of different classes where points easily blend. However, for the overall performance of the model, the PAM attributes greater improvement than the GAM.
To summarize, with the double attention modules, the DAPnet can obtain the best results.

\subsection{Visualization of results}

\begin{figure}[tp]
    \begin{center}
    \includegraphics[scale=1.0]{figures/models.jpg}
    \end{center}
    \caption{The training phases of loss and overall accuracy from different models.}
    \label{fig:loss}
\end{figure}

In order to qualitatively analyze the performance of the models with or without the PAM and the GAM,
Figure~\ref{fig:diff} shows the classification results of 3 random blocks in the test set under DAPnet(M) and DAPnet(PGM). These blocks contain point clouds of multiple classes, and we have marked the areas with large differences among classification results with red circles. The proposed DAPnet(PGM) both yielded good results. For the mixed areas of roofs and trees and the areas of shrubs and low vegetation, DAPnet(PGM) can classify point clouds well compared to DAPnet(M).
The correct classification of a large number of these points improves the classification performance of DAPnet, which show that DAPnet performs better with the irregular format and the border issue.
We also plot the loss and overall accuracies for DAPnet(BASE) and DAPnet(PGM), as shown in Figure~\ref{fig:loss}. We find that both DAPnet(BASE) and DAPnet(PGM) converge at approximately 100 epochs. Incorporating the double self-attention module reduces the loss and improves the overall accuracy of the model, which demonstrates the effectiveness of the double self-attention module.

\subsection{Discussion}
In the experiment, our method obtains an overall accuracy of 90.7\% using the ISPRS 3D Semantic Labeling data, which outperforms the state-of-the-art benchmark. Our model also achieves a better per-class F1 score (average +3.4\%) than the best per-class F1 scores among the benchmark methods. In particular, the accuracies of powerline and car have improved by 10.1\% and 13.2\% respectively. Through ablation experiments, we find that the two different attention modules perform differently over classes. Compared with the strategy without any attention module, the double self-attention module has significantly improved the results of various classes, especially car and shrub, which have improved by more than 10.0\%. The GAM enhances the
F1 scores of about 3\% on the classes of car, facade, and shrub, while the PAM enhances the F1 scores by 5\% in the classes of powerline, car, facade, and tree.
We find that the marginal benefit of adding the PAM is greater than the marginal benefit of adding the GAM. When the model only uses the GAM, the model performance is similar to the model using only a multiscale radius group sampling method. However, the PAM performs best when used together with the GAM.
The ablation experiments show that the strategy of adding the double self-attention module is the best in terms of both overall accuracy and the per-class F1 scores.

\section{Conclusion}
\label{conclusion}
This study proposes a novel model called the DAPnet by using a double self-attention module to classify point cloud objects of various shapes and scales. The double self-attention module consists of point and group attention modules.
The PAM effectively solves the point cloud classification problem for multiple classes in a mixed area by assigning new weights to the extracted features through the relationship between points. The GAM, on the other hand, solves the point cloud classification problem of classes with diverse shapes through the relationship between different groups.
Under the PAM and the GAM, the DAPnet performs well and also has good generalization ability.

However, the DAPnet also has the following limitations: (1) In data preprocessing, the feature extraction of point clouds is limited by the block size and the sampling number of points. When the scale or shape of the object is larger than the block, it is difficult for the model to get good features. (2) In some areas with mixed objects from different classes, such as the roof and impervious surfaces, there are still many problems with their predicted semantic labels.
This might be because the features assigned new weights by the attention module make the model classification biased. (3) We also notice that our method and the benchmark methods have low F1 scores on the fence class. The features of these classes may be more difficult to extract than the others.
In our future work, we would break through the limitations to get better performance.

\section*{ACKNOWLEDGEMENTS}\label{ACKNOWLEDGEMENTS}

This work was supported by the National Natural Science Foundation of China (grant numbers 41871364, 41871276, 41871302, and 41861048). This work was carried out in part using computing resources at the High Performance Computing Center of Central South University.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


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Rick Kash and Dimitri Panayotopoulos Join IRI Board of Directors
By ZAMarketing@iriworldwide.co.za | 12 September 2019 Email
Veteran Consumer Goods Professionals to Enhance IRI's Ability to Drive Sustainable Competitive Advantage for Clients
IRI®, a global leader in big data, predictive analytics and forward-looking insights for consumer, retail and media companies, today announced that Rick Kash and Dimitri Panayotopoulos will join the company's Board of Directors, effective immediately. IRI is a portfolio company of Vestar Capital Partners and New Mountain Capital.
"We are very pleased to have Rick and Dimitri — two highly accomplished consumer goods professionals who are well respected in the industry — join the IRI board," said Jeffrey Ansell, chairman of IRI and a Vestar senior advisor. "Both Rick and Dimitri bring deep insight, knowledge and specialized expertise uniquely suited to IRI's business, and I look forward to their contributions in driving IRI's next phase of growth."
"I know IRI well and have long respected the company's consistent, leading-edge innovations in the fast-moving predictive analytics sector," said Mr. Kash. "I look forward to working closely alongside the rest of the Board to support IRI's strategic initiatives and being part of this exciting company's future in this dynamic field."
"Successful brand-building and marketing demand the sophisticated, groundbreaking services and solutions offered by IRI," said Mr. Panayotopoulos. "I am enthusiastic about working with the IRI team as we continue to enhance and refine analytics that anticipate competitive trends for our clients."
"Our new directors have exceptional experience building brands and businesses via leveraging insights, analytics and the right strategic choices," said Andrew Appel, president and chief executive officer of IRI. "We look forward to working with them to further IRI's mission of driving sustainable competitive advantage for our clients."
Rick Kash
Rick Kash is the founder and former chairman and CEO of Cambridge Consulting Group, one of the world's preeminent growth-strategy consulting firms, which was acquired by Nielsen Holdings Plc in 2009. Kash joined Nielsen at the time of the acquisition, ultimately serving as vice chairman of Nielsen. Since leaving Nielsen in 2016, Kash, who currently serves as a director of Simply Good Foods, has served on a variety of corporate and nonprofit boards. He is also currently affiliated with Vestar as a director of Woodstream, another Vestar portfolio company.
Kash founded two cancer research companies in partnership with Harvard University. His book, "How Companies Win," was selected by Fortune magazine as the most important book for business leaders to read in 2011.
From 1995-2010, Kash was one of 36 elected members of the U.S. Senate Business Forum, a group of businesspeople selected by U.S. senators to advise senators and Cabinet members on the economy and U.S. business performance. A native of Chicago, Kash received a Doctor of Humane Letters degree from DePaul University in 2017.
Dimitri Panayotopoulos
Dimitri Panayotopoulos is a former vice chairman of The Procter & Gamble Company, where he had responsibility for the full portfolio of P&G's brands and business units and more than $80 billion of global revenues. He brings deep experience in driving growth, innovation and executional excellence. Following his 37-year career at P&G, which spanned many of its international operations, he became a senior advisor at Boston Consulting Group.
Panayotopoulos' distinguished career at P&G included positions in advertising and marketing before moving on to various country manager positions. He led successful initiatives in China that resulted in a multibillion-dollar P&G business and also managed P&G's 110-country market-development organization in Central and Eastern Europe, the Middle East and Africa and spearheaded the creation of a unified approach to building brands and businesses in those markets. After being named Group President of Global Fabric Care, Panayotopoulos helped build Downy, Lenor, and Gain into billion-dollar brands. Panayotopoulos resides in Switzerland and serves on the boards of British American Tobacco Company and JBS Foods International. He also served on the board of Logitech International until earlier this year.
About the IRI Partner Ecosystem
IRI fundamentally believes that delivering differentiated growth for clients requires deep, highly integrated partnering with a variety of best-of-breed companies. As such, IRI works closely with a broad range of industry leaders across multiple industries and sectors to create innovative joint solutions, services and access to capabilities to help its clients more effectively collaborate and compete in their various markets and exceed their growth objectives. IRI is committed to its partnership philosophy and continues to actively enhance its open ecosystem of partners through alliances, joint ventures, acquisitions and affiliations. The IRI Partner Ecosystem includes such leading companies as 84.51°, Adobe, The Boston Consulting Group, Clavis Insights, comScore, Data Plus Math, Dynata, Edison, Experian, GfK, Gigwalk, Google, Ipsos, Jumpshot, Mastercard Advisors, MaxPoint, Ogury, Omnicom, One Click Retail, Oracle, Pinterest, Simulmedia, SPINS, Univision, Viant, and others.
About IRI
IRI is a leading provider of big data, predictive analytics and forward-looking insights that help CPG, OTC health care organizations, retailers, financial services and media companies grow their businesses. A confluence of major external events — a change in consumer buying habits, big data coming into its own, advanced analytics and personalized consumer activation — is leading to a seismic shift in drivers of success in all industries. With the largest repository of purchase, media, social, causal and loyalty data, all integrated on an on-demand, cloud-based technology platform, IRI is empowering the personalization revolution, helping to guide its more than 5,000 clients around the world in their quests to remain relentlessly relevant, capture market share, connect with consumers, collaborate with key constituents and deliver market-leading growth. For more information, visit www.iriworldwide.com.
Shelley Hughes
Email: Shelley.Hughes@IRIworldwide.com
FMCG 6
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AgroAtlas - Relatives - Distribution area of sterile oat (Avena sterilis).
Distribution area of sterile oat (Avena sterilis).
Map was created using maps of scale 1:2,000,000-1:11,250,000.
"Alber.s Equal Area Conic for the USSR", 9, 1001, 7, 100, 0, 44, 68, 0, 0.
Vector map consisting of 1 base and 3 thematic layers. The distribution area of the species is represented by polygons and points.
Points represent sites at which herbarium specimens of the species have been found and species locations cited in published references. The general distribution area was created by generalizing information on distribution of the species.
The map was created using herbarium data and published maps from Grossheim.s monograph, "Flora of the Caucasus" (1939).
In the former USSR, the species is found among crops of summer cultures and on desert badlands in the lower mountain belt of Central Asia.
Grossheim A.A. 1939. Flora of the Caucasus. V.2. Polypodiaceae - Gramineae. Baku, Publishing house AzFaN. 587 pages.
All rights on the map and its descriptions belong to its author.
Copyright on the photos belongs to Dzyubenko E.


text:
Contact MSBA
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Mississippi School Boards Association Names Denotris Jackson as First Female, African-American Executive Director
Ridgeland, MS (August 17, 2020) — The Executive Committee of the Mississippi School Boards Association (MSBA) has named Denotris Jackson as the new Executive Director. She replaced Dr. Mike Waldrop who retired in July after being employed with the Association for 20 years. Jackson is the first female, first African-American, and first board member to serve as Executive Director.
"During this history-making era of MSBA, I am excited to welcome Denotris Jackson as the executive director of MSBA," said MSBA Board President Jan Vaughn. "Without a doubt, her input and contributions to MSBA will continue to move us forward. We look forward to a long and successful journey under her leadership."
Jackson joined MSBA in 2007, and during her tenure has served as Assistant Executive Director, Director of Policy/Advocacy, and Director of Board Development. She was also appointed to two terms on the high-performing Clinton Public School District Board of Trustees and on the MSBA Board of Directors. She held various leadership positions on both boards, including serving as President of each. She also holds the distinction of being the first school board member to be employed at MSBA.
"I am grateful for the opportunity to continue to serve the MSBA members," said MSBA Executive Director Denotris Jackson. "The MSBA Board of Directors is committed to student success through effective school board governance. I look forward to building upon MSBA's strong reputation as a resource for Mississippi K-12 educators, key legislators, and partners."
Under Jackson's leadership, MSBA created the Prospective Superintendent Leadership Academy (PSLA), a professional development program designed to prepare potential candidates for superintendent positions in Mississippi's public schools. Jackson also oversaw the development of OAgendas, the electronic board meeting service, and the Technology and Branding departments. She was instrumental in the design and development of the MSBA Online Policy program, online training programs, and MSBA mobile app. Jackson serves on the association's training faculty, has written school board member continuing education training modules, and has presented at state, regional, and national conferences. She also serves on the association's Superintendent Search Committee.
Jackson's background includes 10 years of Early Childhood Administration in both the private and public sectors. She also worked for nine years in real estate sales and marketing with RE/MAX Real Estate Group. Her public school experience includes working in the Business Office of the Clinton Public School District.
Jackson is active in her church, Greater Bethlehem Temple, where she serves as a Sunday School Teacher, choir member, and education committee member. She is the 2017 recipient of the Mississippi College Educator Advocate Award, the 2017-18 Delta Kappa Gamma Society International Red Rose Award, and the 2016 Friend of Education award presented by the Mississippi Association of School Administrators. Jackson is an Associate member of the Junior Auxiliary of Clinton, having served as a Crown Club Advisor mentoring high school girls in community service and chairing several projects.
Jackson is a graduate of Clinton High School and Jackson State University, where she received a bachelor's degree in childcare and family science and a master's degree in early childhood education. She is a graduate of Leadership Clinton and the Disney Business Institute. She is also an instructor at the Southeast Bible College.
Jackson, a resident of Clinton, MS, and her husband, Kenneth, have five adult children and four grandchildren.
Thursday, January 21, 2021 MISSISSIPPI SCHOOL BOARDS ASSOCIATION
Office: 380 Zurich Drive, Ridgeland, MS 39157
Mail: PO Box 203, Clinton, MS 39060
Phone: 601-924-2001 Fax:601-924-2002 Toll Free:888-367-6722


Three (!) months ago, we moved into our Hamburg apartment and are now (!) finally the proud owners of a kitchen. Amen! Did we suffer from hunger during this time? No, of course not.
To be honest, it was fine, maybe even too good!? But don´t get me wrong: I would personally never be able to live without a kitchen.
But I must say that I did notice that online platforms for grocery delivery are getting increasingly better and could lead to a change of paradigm. While we mostly cook and sometimes order food nowadays, food delivery could become the standard in the future and we will only cook ourselves on special occasions. Regarding special occasions, I can add the following aspect: if real restaurant visits become a daily thing, they lose their appeal at the latest after three weeks and become annoying. After a long day of work or on a lazy weekend, people really yearn for their own four walls and intimacy. Even though the very friendly Lieferhelden actually never bother anyone with their short delivery.
For a long time, I avoided delivery services because you had to wait for up to an hour and then I often only received lukewarm pizza. Foodora proved me wrong and can let the customer know the exact delivery time with a real-time tracker and tracing options and can show the respective location of the delivery. I know how long the delivery time will be and can plan accordingly. This way, it is possible that no more than 20 minutes pass from placing an order to the delivery – perfect, if you are really hungry and as impatient as me. If you place orders regularly, the delivery fee is even dropped, so that there is no disadvantage to going to a restaurant. And the best thing: the food is still steaming hot when I open it. I can track my order because the route and the exact location are displayed. The system learns from my orders and suggests according menus and offers.
With Amazon prime now, I can even order additional individual food products, which I know and value from my local retailers. This way, there will be no surprise in the bag. And I can select time slots outside of the normal business hours for the delivery. This is especially convenient when you are on a business trip and otherwise an empty refrigerator is waiting for you at home.This brings me to the further digitalization of the kitchen, which I will use from now on. Nowadays, people cook via an app, meaning that they already turn on their oven for a casserole from the office. With the Home Connect App I control my Bosch oven. Via this app, a glance at your smartphone at the supermarket tells you what is missing in the refrigerator for lunch. Of course, it is connected like the rest of the smart kitchen. The exhaust hood and stove are already communicating with each other.
This way, not only the kitchen steam actually created by cooking is exhausted – more often via downdraft ventilation directly on the stovetop. Sensors make sure that the water doesn´t boil over anymore when cooking pasta and the steak doesn´t burn in the pan. This way, cooking is even more fun and simply takes care of the annoying part for me.
Jury ADC Festival 2018: Allein unter Männern.


Tonight, instead of my usual routine of preparing for ROTC and going to bed early, I'm going to watch three of my sorority sisters perform in a play called Top Girls! They've been rehearsing for several weeks now, and a big group of us are excited to support them. We're all prepared with our bouquets!
Visions and Voices is USC's university-wide arts and humanities initiative that features a wide variety of events organized by USC faculty and schools. The events range from Operas to talks by professors and discussions with famous playwrights. This is a great opportunity for students of all majors to develop an appreciation for various cultures and diversity.
This particular event focuses on the role of women in society and what it means to be a successful woman across ages and generations. Thankfully, it also includes some comedy. Now that I've seen the play, I can finish this post: it was really entertaining! It had just the right mix of interesting historical allusion and modern comedy. I could definitely see why my friends got picked for the parts they played—their personalities definitely showed in their characters. What a great way to spend a Thursday night!
The setting for the first scene, a dinner party!
So excited to watch my friends perform!


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broad day, a photo by eL hue V on Flickr.
Big Blue 2, a photo by eL hue V on Flickr.
at the request of the building owner and Jersey City Mural Arts Program we filled in some bricks with a bit more color, 90 ft of it. Thanks again to Dylan Evans for the spot. Thanks to Vitamin Water for the hook ups.
burlap, a photo by eL hue V on Flickr.
calm, a photo by eL hue V on Flickr.
faded, a photo by eL hue V on Flickr.
Jersey Fresh 2011, a photo by eL hue V on Flickr.
tucked away, a photo by eL hue V on Flickr.
0721091040.jpg, a photo by eL hue V on Flickr.
sketchwall, a photo by eL hue V on Flickr.


text:
Die Saison 1948 war die 15. Spielzeit der Serie A1, der höchsten italienischen Eishockeyspielklasse. Meister wurde zum insgesamt zehnten Mal in der Vereinsgeschichte der Hockey Club Milano.

Modus
Die Sieger dreier Hauptrundengruppen traten in einer Qualifikationsrunde gegeneinander an. Der Sieger spielte gegen die für das Halbfinale gesetzte Mannschaft SG Cortina. Der Gewinner des Halbfinales durfte gegen den für das Finale gesetzten HC Milano spielen.

Hauptrunde

Gruppe A

Gruppe B

Gruppe C

Qualifikationsrunde

Sp = Spiele, S = Siege, U = unentschieden, N = Niederlagen

Playoffs

Halbfinale

Finale

Meistermannschaft
Giancarlo Bucchetti – Giancarlo Bulgheroni – Ignazio Dionisi – Arnaldo Fabris – Vincenzo Fardella – Aldo Federici – Umberto Gerli – Dino Innocenti – Costanzo Mongini – Franco Rossi – Giannantonio Zopegni

Weblinks
 Spielzeit bei hockeytime.net (italienisch)

1948
Eishockeyveranstaltung 1948

redpajama_set_name: RedPajamaWikipedia


text:
Holland & Knight Commemorates Founding Partner Chesterfield Smith's 100th Birthday with Major Gift to Legal Services of Greater Miami
MIAMI (July 27, 2017) – Friday, July 28 marks the 100th anniversary of the birth of Chesterfield Smith, the founding partner of Holland & Knight. To mark the occasion, Holland & Knight has announced a major gift of $100,000 to Legal Services of Greater Miami, Inc. to continue the legacy of Mr. Smith, a legendary lawyer and vocal advocate for pro bono legal services for the poor.
During his long career, Mr. Smith promoted his commitment to pro bono and continually challenged the legal profession to "Do Good!". In 1999, Legal Services dedicated its office building as the Chesterfield Smith Center for Equal Justice in honor of Mr. Smith's role as chair of the Legal Services Campaign for Justice, which raised funds to purchase the building.
"We could think of no better way to honor Chesterfield's memory than to ensure that his adopted hometown of Miami would continue to benefit from the great work of Legal Services," said Steven Sonberg, Holland & Knight's managing partner. "Access to the legal system is a critical issue in our community, and we hope that our contribution will help those in desperate need."
"Holland & Knight has always been a leader in the legal profession," said Legal Services executive director Marcia K. Cypen. "We are so very grateful to the firm for this extraordinary lead gift to our Building the Cornerstone Campaign. The firm's vision and philanthropic leadership will make a lasting impact in our community for generations to come."
Legal Services of Greater Miami is a non-profit organization providing free civil legal services for vulnerable members of the community with nowhere else to turn for help, including women, children, seniors, veterans returning from combat, people with disabilities, low-wage workers and the homeless.
The gift will help ensure that our most vulnerable neighbors will have representation in our civil justice system. The representation provided by the Legal Services staff will protect their rights to safe, affordable, decent housing and access to health care.
Holland & Knight has had a long partnership with Legal Services. Partner Tiffani Lee currently serves on the board of directors. Partner Tracy Nichols served as co-chair and Rodolfo Sorondo and Wifredo Ferrer serve on the Building the Cornerstone Campaign committee. Partner Bill Bloom also provided pro bono real estate services to the organization during its recent headquarters relocation.
Steven Sonberg
Related Office
Latest News and Headlines


Our case, Chad Lee v. Thomas Stanley Kaczmarczyk et al., made headlines on TMZ. http://www.tmz.com/2008/12/10/hypnotist-victim-jazzercises-away-pain-suffering/ Our client, Chad Lee, was called out of the audience to participate in a hypnotist entertainment show at Harrah's in Las Vegas. After being hypnotized, our client was instructed that when he heard the words "Harrah's Hotel and Casino," he was to run off the elevated stage, with a stick horse between his legs, yelling "Hi Ho Silver." The announcer said "Harrah's Hotel and Casino" and our client followed his instructions and ran off the elevated stage and fractured his foot. The case settled for a Confidential Six Figure Amount.


text:
Scientists Create New Maps Depicting Potential Worldwide Coral Bleaching By 2056
by Underwatertimes.com News Service - February 25, 2013 20:04 EST
Scientists: Coral Bleaching Increases Chances Of Coral Disease; 'Both Related To Prolonged Thermal Stress'
NOAA Declares Third Ever Global Coral Bleaching Event; Bleaching Intensifies In Hawaii, High Ocean Temperatures Threaten Caribbean Corals
Massive Coral Bleaching Could Decimate SE Asia's Coral Triangle This Winter
UN Report: Aquaculture Has Potential To Cut Poverty, Combat Food Insecurity; 'The Greatest Potential To Produce More Fish'
Research: Tiny Polyps Gorge Themselves to Survive Coral Bleaching
In a new study, scientists predict more frequent and severe coral bleaching events. Credit: Thomas Vignaud
MIAMI, Florida -- In a study published today in Nature Climate Change researchers used the latest emissions scenarios and climate models to show how varying levels of carbon emissions are likely to result in more frequent and severe coral bleaching events.
Large-scale 'mass' bleaching events on coral reefs are caused by higher-than-normal sea temperatures. High temperatures make light toxic to the algae that reside within the corals. The algae, called 'zooxanthellae', provide food and give corals their bright colors. When the algae are expelled or retained but in low densities, the corals can starve and eventually die. Bleaching events caused a reported 16 percent loss of the world's coral reefs in 1998 according to the Global Coral Reef Monitoring Network.
If carbon emissions stay on the current path most of the world's coral reefs (74 percent) are projected to experience coral bleaching conditions annually by 2045, results of the study show. The study used climate model ensembles from the upcoming Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC).
Around a quarter of coral reefs are likely to experience bleaching events annually five or more years earlier than the median year, and these reefs in northwestern Australia, Papau New Guinea, and some equatorial Pacific islands like Tokelau, may require urgent attention, researchers warn.
"Coral reefs in parts of the western Indian Ocean, French Polynesia and the southern Great Barrier Reef, have been identified as temporary refugia from rising sea surface temperatures," said Ruben van Hooidonk, Ph.D., from the Cooperative Institute for Marine and Atmospheric Studies (CIMAS) at the University of Miami and NOAA's Atlantic Oceanographic and Meteorological Laboratory. "These locations are not projected to experience bleaching events annually until five or more years later than the median year of 2040, with one reef location in the Austral Islands of French Polynesia protected from the onset of annual coral bleaching conditions until 2056."
The findings emphasize that without significant reductions in emissions most coral reefs are at risk, according to the study. A reduction of carbon emissions would delay annual bleaching events more than two decades in nearly a quarter (23 percent) of the world's reef areas, the research shows.
"Our projections indicate that nearly all coral reef locations would experience annual bleaching later than 2040 under scenarios with lower greenhouse gas emissions." said Jeffrey Maynard, Ph.D., from the Centre de Recherches Insulaires et Observatoire de l'Environnement (CRIOBE) in Moorea, French Polynesia. "For 394 reef locations (of 1707 used in the study) this amounts to at least two more decades in which some reefs might conceivably be able to improve their capacity to adapt to the projected changes."
"More so than any result to date, this highlights and quantifies the potential benefits for reefs of reducing emissions in terms of reduced exposure to stressful reef temperatures."
"This study represents the most up-to-date understanding of spatial variability in the effects of rising temperatures on coral reefs on a global scale," said researcher Serge Planes, Ph.D., also from the French research institute CRIOBE in French Polynesia.
The researchers involved in the study all concur that projections that combine the threats posed to reefs by increases in sea temperature and ocean acidification will further resolve where temporary refugia may exist.


Contrary to critics of legalized marijuana, a new report indicates that pot reform has led to a decrease in illegal shipments of the herb through the U.S. Postal Service – just another piece of evidence proving that prohibition is the root of felonious drug activity in the Land of the Free.
The U.S. News and World Report recently collected statistics from the U.S. Postal Inspection Service, which shows a significant decrease in people shipping marijuana through the mail since Colorado and Washington established taxed and regulated cannabis markets. In fact, Uncle Sam noticed a 12 percent reduction in this federal offense in 2014, as well as an equal decrease in pot poundage seized by postal inspectors.
Although marijuana continues to be made legal on a statewide basis across the country, the federal government still considers weed to be one of the most dangerous drugs in the world. It is for that reason that shipping even the smallest amount of the herb through the U.S. Postal Service is considered a criminal offense that is prosecuted at the federal level. The Postal Inspection Agency is the law enforcement branch charged with bringing the hammer down in such cases.
"We investigate any and all suspicious packages that contain illegal narcotics," Lori McCallister, the postal inspector's national spokesperson, told U.S. News.
Although the recent decline in pot shipments through the U.S. Mail may not seem important enough to make a fuss, marijuana activists suggest that it provides us with a glimpse into the demise of the back market drug trade in the event that prohibition is repealed.
"Most of the shipping that's being done is by people in the illicit market, and those are the people we're trying to get out of business," said Diane Goldstein, who serves as an executive board member with Law Enforcement Against Prohibition.
Interestingly, the Drug Enforcement Administration also reports a decline in marijuana seizures since legal pot markets began to surface in America. In 2014, the DEA took control of less black market marijuana than they have in almost 30 years.
However, the Rocky Mountain High Intensity Drug Trafficking Area, which is the drug enforcement watchdog for Colorado, Utah and Wyoming, claims that regardless of the reports from the USPIS and the DEA, they have noticed an increase in marijuana shipments coming from Colorado. Yet, McCallister told U.S. News that not only are these claims inaccurate, but they were likely padded in an attempt to maintain the agency's federal funding.
The U.S. Postal Inspection Service busted over 2,000 people in 2014 for sending controlled substances through the mail. The agency claims to aggressively prosecute such cases, even those committed in states that have legalized the leaf. In other words, it is still considered a federal crime in Colorado to ship weed to a friend or family member living within the state.


text:
Q: Assign dynamic string in a list to variables in functions I have 2 lists:
datastr={0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 2., 0., \
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., \
0., 0., 0., 0., 0., 0., 0.};

dataB={548.29, 94.16, -322.15, -573.56, 495.01, 82.28, "eta11", "eta12", \
"eta13", "eta14", 307.53, -394.29, "eta15", 259.65, -245.74, "eta16", \
625.45, 738.91, 809.55, 2173.72, 3018.17, 122.09, 440.24, 340.35, \
"eta17", 740.92, 1317.23, 483.88, 675.24, "eta18", "eta19", "eta110", \
"eta111", "eta112", "eta113", "eta114", "eta115", "eta116", "eta117", \
"eta118", "eta119"}

I then do a summary of the multiple of the 2 lists and have:
etaa = (Total[dataJ*datastr])

I got:
etaa = -0.199 + 2. "eta26"

I want to set the "eta26" as a variables in a function
Funt[T_,eta26_]:=  (-0.199 + 2. "eta26")*T^2 +  "eta26"

The function Funt[T_,eta26_] is fitted to an experimental data set having values of the Funt and T to find value for the eta26.
Could you please suggest me how to extract the "eta26" in a list and set them as a variable in a Function as give above.
Thank and regards,
Anh

A: You can do that using rules:
Funt[T_, eta26_] := (-0.199 + 2. "eta26")*T^2 + "eta26" /. "eta26" -> eta26
Funt[2, 3]

26.204

A: Convert the strings to symbols using ToExpression.
expr = ToExpression@dataB;
etaa = Total[expr*datastr]
(* 94.16 + 2. eta16 *)

redpajama_set_name: RedPajamaStackExchange


WASHINGTON, October 2, 2017 – After much consultation with members of Congress, President Trump has proposed a massive tax cut designed to stimulate the economy so that economic growth will increase. The Democrats have denounced the plan, saying that it won't necessarily grow the economy nor will it add jobs or benefit the middle class. The Democrats are spreading pure mythology.
Myth number one: The GOP tax cuts benefit the wealthy and not the middle class. Democrats argue that high-income earners could see a $25,000 reduction in taxes while middle-class income earners will see only a few hundred dollars.
Let's say Trump wants to be fair and cut taxes for all Americans by 10 percent. A wealthy person currently earns $1,000,000 and pays federal income taxes of $250,000. A middle-class person earns $60,000 per year and pays $4,000 in federal taxes.
If Trump cuts taxes by 10 percent for everyone, the wealthy person gets a $25,000 (10 percent of the $250,000) tax cut while the average person gets $400 (10 percent of $4,000). Since the high-income earner pays 60 times more in taxes, his tax cut will be 60 times greater than the average.
It is simply impossible to "significantly" cut taxes for people who pay very little tax.
Additionally, in 2001 President Bush cut all tax rates by 10 percent for a 10-year period. In 2012, President Obama made those lower rates permanent for everyone except the highest income earners who saw their tax rate increase from 36 to 39.6 percent.
Trump wants to return that larger increase to its earlier 36 percent rate plus provide a slight additional tax break to this wage class, so he set his proposed top rate at 35 percent.
Myth number two: Cutting corporate tax rates won't create jobs. While the data indicate that after every previous major tax cut, economic activity increased and the unemployment rate fell, Trump's opponents say that may not happen, claiming corporations could decide to use the extra income to pay larger dividends to stockholders and/or repurchase shares of outstanding stock.
That is actually somewhat true. When there are no good investments for corporations, they increase dividends and sometimes re-purchase their own shares, thus reducing the float and thus lowering the shares' price-earnings ratio. That can frequently induce current shareholders to increase their positions in the stock; or, should those stockholders spot better or or more aggressive investment opportunities in other stocks or sectors, they will re-invest the money back into the economy by purchasing shares of growth companies.
Whether the corporation invests to expand and add jobs, or stockholders invest in their existing position or invest their profits in other corporations that expand and add jobs, economic expansion will occur and jobs will be added.
Myth number three: Lower class tax rates are increasing. Trump wants to reduce the over all number of tax brackets, so he is combining the current 10 percent bracket with the current 16 percent bracket to create a single 12 percent bracket. Since the standard deduction is significantly increased in the President's plan, lower income earners will pay a higher rate on their taxable income; but, they likely will pay less in total taxes since the amount of taxable income will be lowered.
In other words, a person today would pay 10 percent on taxable income of $20,000, or $2,000. By raising the standard deduction by $6,000, that same person's taxable income would be only $14,000. So, 12 percent of $14,000 means the tax bill would be $1,680, a saving of $320, which is more than a 10 percent tax cut. This key distinction has been ignored by Democrats and the media alike.
Further, as low-income earners find better opportunities in a growing economy, their income would increase. Instead of paying a 16 percent tax on that new income, only 12 percent would be charged.
Myth number four: Eliminated estate taxes benefits the wealthy. The reality is that the wealthy set up trusts to own assets. In turn, the trust still owns the assets no matter who receives the asset's income. In other words, the wealthy minimize their federal estate tax by transferring asset ownership prior to death.
High estate taxes are paid mostly by the upper middle and middle classes. Trump wants to allow people who have earned income, paid taxes and accumulated wealth to pass that wealth on to their heirs without allowing the government to force the heirs sell some assets to pay estate taxes.
After every major tax decrease, economic activity has increased. Usually by the second year of reduced taxes, tax revenue has increased and the rate of increase was higher than before the tax cut was enacted. The deficit problem occurs because spending has skyrocketed.
Ultimately, after Clinton's capital gains tax rate cut, his administration's budget carried a surplus, not a deficit, for four years running.
Since annual economic growth has not exceeded 3 percent since 2005 – which is the longest period of economic stagnation in US history – it is critical that Trump's tax plan is passed, allowing America's annual growth to reach 3 or 4 percent or better. That would provide more opportunity for all Americans, reduce unemployment, raise wages, increase incomes, reduce government spending on social programs and eventually reduce social problems as well.
Aside from Trump's opposition, which consistently misrepresents the effects of Trump's tax cut plan, who who else could possibly oppose such positive outcomes?
*Cartoon by Branco. Used with permission and by arrangement with ComicallyIncorrect.