Region Proposal Networks 详解

本文介绍了Region Proposal Networks(RPN),它是Faster RCNN提出的proposal生成网络,替代了之前的selective search方法,提高了检测速度。文中详细阐述了RPN的工作流程,包括anchors的生成、softmax判定前景与背景、bounding box regression原理及应用,最后由Proposal Layer生成精准proposal。

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Region Proposal Networks是Faster RCNN出新提出来的proposal生成网络。其替代了之前RCNN和Fast RCNN中的selective search方法,将所有内容整合在一个网络中,大大提高了检测速度(语文水平差,所以历史科普请看其他文章T_T)。

缩进在正文前,还要多解释几句基础知识,已经懂的看官老爷跳过就好。

  1. 对于单通道图像+单卷积核做卷积,上一篇文章已经介绍了(参考上文图4);
  2. 对于多通道图像+多卷积核做卷积,计算方式如下:

图1 多通道+多卷积核做卷积示意图(摘自Theano教程)

缩进如图2,输入图像layer m-1有4个通道,同时有2个卷积核w1和w2。对于卷积核w1,先在输入图像4个通道分别作卷积,再将4个通道结果加起来得到w1的卷积输出;卷积核w2类似。所以对于某个卷积层,无论输入图像有多少个通道,输出图像通道数总是等于卷积核数量!特殊的,对于多通道做1x1卷积,其实就是将输入图像于每个通道乘以卷积系数后加在一起。这样做的结果就是把原图像中本来各个独立的通道“联通”在了一起。

 

(一)anchors

缩进提到RPN网络,就不能不说anchors。所谓anchors,实际上就是一组由rpn/generate_anchors.py生成的矩形。直接运行generate_anchors.py得到以下输出:

[[ -84.  -40.   99.   55.]
 [-176.  -88.  191.  103.]
 [-360. -184.  375.  199.]
 [ -56.  -56.   71.   71.]
 [-120. -120.  135.  135.]
 [-248. -248.  263.  263.]
 [ -36.  -80.   51.   95.]
 [ -80. -168.   95.  183.]
 [-168. -344.  183.  359.]]

其中每行的4个值[x1,y1,x2,y2]代表矩形左上和右下角点坐标。9个矩形共有3种形状,长宽比为大约为:width:height = [1:1, 1:2, 2:1]三种,如图2。实际上通过anchors就引入了检测中常用到的多尺度方法。

图2 anchors示意图

注:关于上面的anchors size,其实是根据检测图像设置的。在python demo中,会把任意大小的输入图像reshape成800x600(即上文中提到的M=800,N=600)。再回头来看anchors的大小,anchors中长宽1:2中最大为352x704,长宽2:1中最大736x384,基本是cover了800x600的各个尺度和形状。

那么这9个anchors是做什么的呢?借用Faster RCNN论文中的原图,如图3,遍历Conv layers计算获得的feature maps,为每一个点都配备这9种anchors作为初始的检测框。这样做获得检测框很不准确,不用担心,后面还有2次bounding box regression可以修正检测框位置。

图3

解释一下上面这张图的数字。

  1. 在原文中使用的是ZF model中,其Conv Layers中最后的conv5层num_output=256,对应生成256张特征图,所以相当于feature map每个点都是256-d
  2. 由于输入图像M=800,N=600,且Conv Layers做了4次Pooling,feature map的长宽为[M/16, N/16]=[50, 38]
  3. 在conv5之后,做了rpn_conv/3x3卷积,num_output=256,相当于每个点使用了周围3x3的空间信息,同时256-d不变,如图3红框,同时对应图4中的红框中的3x3卷积
  4. 假设一共有k个anchor,而每个anhcor要分foreground和background,所以cls=2k scores;而每个anchor都有[x, y, w, h]对应4个偏移量,所以reg=4k coordinates

图4

注意,在本文讲解中使用的VGG conv5 num_output=512,所以是512d,其他类似.....

 

(二)softmax判定foreground与background

缩进在上一篇文章中提到:一副MxN大小的矩阵送入Faster RCNN网络后,到RPN网络变为(M/16)x(N/16),不妨设W=M/16,H=N/16。在进入reshape与softmax之前,先做了1x1卷积,如图5:

图5 RPN中判定fg/bg网络结构

该1x1卷积的caffe prototxt定义如下:

layer {
  name: "rpn_cls_score"
  type: "Convolution"
  bottom: "rpn/output"
  top: "rpn_cls_score"
  convolution_param {
    num_output: 18   # 2(bg/fg) * 9(anchors)
    kernel_size: 1 pad: 0 stride: 1
  }
}

可以看到其num_output=18,也就是经过该卷积的输出图像为WxHx18大小(注意文章开头提到的卷积计算方式)。这也就刚好对应了feature maps每一个点都有9个anchors,同时每个anchors又有可能是foreground和background,所有这些信息都保存WxHx(9x2)大小的矩阵。为何这样做?后面接softmax分类获得foreground anchors,也就相当于初步提取了检测目标候选区域box(一般认为目标在foreground anchors中)。

缩进那么为何要在softmax前后都接一个reshape layer?其实只是为了便于softmax分类,至于具体原因这就要从caffe的实现形式说起了。在caffe基本数据结构blob中以如下形式保存数据:

blob=[batch_size, channel,height,width]

对应至上面的保存bg/fg anchors的矩阵,其在caffe blob中的存储形式为[1, 18, H, W]。而在softmax分类时需要进行fg/bg二分类,所以reshape layer会将其变为[1, 2, 9*H, W]大小,即单独“腾空”出来一个维度以便softmax分类,之后再reshape回复原状。贴一段caffe softmax_loss_layer.cpp的reshape函数的解释,非常精辟:

"Number of labels must match number of predictions; "
"e.g., if softmax axis == 1 and prediction shape is (N, C, H, W), "
"label count (number of labels) must be N*H*W, "
"with integer values in {0, 1, ..., C-1}.";

综上所述,RPN网络中利用anchors和softmax初步提取出foreground anchors作为候选区域。

 

(三)bounding box regression原理

缩进先介绍bounding box regression数学模型及原理。如图5所示绿色框为飞机的Ground Truth(GT),红色为提取的foreground anchors,那么即便红色的框被分类器识别为飞机,但是由于红色的框定位不准,这张图相当于没有正确的检测出飞机。所以我们希望采用一种方法对红色的框进行微调,使得foreground anchors和GT更加接近。

图6

缩进对于窗口一般使用四维向量(x, y, w, h)表示,分别表示窗口的中心点坐标和宽高。对于图 7,红色的框A代表原始的Foreground Anchors,绿色的框G代表目标的GT,我们的目标是寻找一种关系,使得输入原始的anchor A经过映射得到一个跟真实窗口G更接近的回归窗口G',即:给定A=(Ax, Ay, Aw, Ah),寻找一种映射f,使得f(Ax, Ay, Aw, Ah)=(G'x, G'y, G'w, G'h),其中(G'x, G'y, G'w, G'h)≈(Gx, Gy, Gw, Gh)。

图7

那么经过何种变换才能从图6中的A变为G'呢? 比较简单的思路就是:

缩进 1. 先做平移

缩进 2. 再做缩放

 

缩进观察上面4个公式发现,需要学习的是dx(A),dy(A),dw(A),dh(A)这四个变换。当输入的anchor与GT相差较小时,可以认为这种变换是一种线性变换, 那么就可以用线性回归来建模对窗口进行微调(注意,只有当anchors和GT比较接近时,才能使用线性回归模型,否则就是复杂的非线性问题了)。对应于Faster RCNN原文,平移量(tx, ty)与尺度因子(tw, th)如下:

缩进接下来的问题就是如何通过线性回归获得dx(A),dy(A),dw(A),dh(A)了。线性回归就是给定输入的特征向量X, 学习一组参数W, 使得经过线性回归后的值跟真实值Y(即GT)非常接近,即Y=WX。对于该问题,输入X是一张经过num_output=1的1x1卷积获得的feature map,定义为Φ;同时还有训练传入的GT,即(tx, ty, tw, th)。输出是dx(A),dy(A),dw(A),dh(A)四个变换。那么目标函数可以表示为:

其中Φ(A)是对应anchor的feature map组成的特征向量,w是需要学习的参数,d(A)是得到的预测值(*表示 x,y,w,h,也就是每一个变换对应一个上述目标函数)。为了让预测值(tx, ty, tw, th)与真实值最小,得到损失函数:

函数优化目标为:

 

(四)对proposals进行bounding box regression

缩进在了解bounding box regression后,再回头来看RPN网络第二条线路,如图8。

 

图8 RPN中的bbox reg

先来看一看上图7中1x1卷积的caffe prototxt定义:

layer {
  name: "rpn_bbox_pred"
  type: "Convolution"
  bottom: "rpn/output"
  top: "rpn_bbox_pred"
  convolution_param {
    num_output: 36   # 4 * 9(anchors)
    kernel_size: 1 pad: 0 stride: 1
  }
}

可以看到其num_output=36,即经过该卷积输出图像为PxQx36,在caffe blob存储为[1, 4x9, Q, P]。与上文中fg/bg anchors存储为[1, 18, Q, P]类似,这里相当于feature maps每个点都有9个anchors,每个anchors又都有4个用于回归的[dx(A),dy(A),dw(A),dh(A)]变换量。利用上面的的计算公式即可从foreground anchors回归出proposals。

 

(五)Proposal Layer

缩进Proposal Layer负责综合所有[dx(A),dy(A),dw(A),dh(A)]变换量和foreground anchors,计算出精准的proposal,送入后续RoI Pooling Layer。还是先来看看Proposal Layer的caffe prototxt定义:

layer {
  name: 'proposal'
  type: 'Python'
  bottom: 'rpn_cls_prob_reshape'
  bottom: 'rpn_bbox_pred'
  bottom: 'im_info'
  top: 'rois'
  python_param {
    module: 'rpn.proposal_layer'
    layer: 'ProposalLayer'
    param_str: "'feat_stride': 16"
  }
}

Proposal Layer有3个输入:fg/bg anchors分类器结果rpn_cls_prob_reshape,对应的bbox reg的[dx(A),dy(A),dw(A),dh(A)]变换量rpn_bbox_pred,以及im_info;另外还有参数feat_stride=16。

缩进首先解释im_info。对于一副任意大小PxQ图像,传入Faster RCNN前首先reshape到固定MxN,im_info=[M, N, scale_factor]则保存了此次缩放的所有信息。然后经过Conv Layers,经过4次pooling变为(M/16)x(N/16)大小,其中feature_stride=16则保存了该信息。所有这些数值都是为了将proposal映射回原图而设置的,如图8,毕竟检测就是为了在原图上画一个框而已~

图8

缩进Proposal Layer forward(caffe layer的前传函数)按照以下顺序依次处理:

  1. 再次生成anchors,并对所有的anchors做bbox reg位置回归(注意这里的anchors生成顺序和之前是即完全一致的)
  2. 按照输入的foreground softmax scores由大到小排序anchors,提取前pre_nms_topN(e.g. 6000)个anchors。即提取修正位置后的foreground anchors
  3. 利用feat_stride和im_info将anchors映射回原图,判断fg anchors是否大范围超过边界,剔除严重超出边界fg anchors。
  4. 进行nms(nonmaximum suppression,非极大值抑制)
  5. 再次按照nms后的foreground softmax scores由大到小排序fg anchors,提取前post_nms_topN(e.g. 300)结果作为proposal输出。

之后输出proposal=[x1, y1, x2, y2],注意,由于在第三步中将anchors映射回原图判断是否超出边界,所以这里输出的proposal是对应MxN输入图像尺度的,这点在后续网络中有用。另外我认为,严格意义上的检测应该到此就结束了,后续部分应该属于识别了~

 

RPN网络结构就介绍到这里,总结起来就是:

生成anchors -> softmax分类器提取fg anchors -> bbox reg回归fg anchors -> Proposal Layer生成proposals

### 卷积神经网络 (CNN) 的工作原理 卷积神经网络(Convolutional Neural Network, CNN)是一种专门用于处理具有网格状拓扑结构的数据的前馈神经网络,最常应用于图像识别和分类领域。其核心思想来源于生物学中的视觉皮层研究,并通过模拟人类大脑对视觉信号的分层处理机制来实现高效的特征提取。 #### 1. 结构组成 CNN 主要由以下几个部分构成: - **卷积层(Convolution Layer)** - 卷积层是 CNN 中最重要的组成部分之一,负责从输入数据中提取局部特征[^1]。 - 它通过对输入矩阵应用多个滤波器(filters/kernels),生成一组称为特征映射(feature maps)的结果。 - 这些滤波器能够检测边缘、纹理或其他特定模式,从而减少后续阶段所需的信息量。 - **激活函数(Activation Function)** - 在每次卷积操作之后,通常会加入非线性变换以增强模型表达能力[^2]。 - 常见的选择有 ReLU(Rectified Linear Unit)、Sigmoid 和 Tanh 函数等,其中 ReLU 是目前最为广泛使用的选项因为它能有效缓解梯度消失问题并加快训练速度。 - **池化层(Pooling Layer)** - 池化层的作用是对经过卷积后的特征图进一步降维简化,保留主要信息的同时降低计算复杂度以及防止过拟合现象发生。 - Max Pooling 是一种典型的策略,即选取窗口内的最大值作为输出代表该区域的整体特性;另外还有 Average Pooling 方法可用视具体应用场景而定。 - **全连接层(Fully Connected Layers)** - 当所有的空间维度都被压缩成单一向量形式后,则进入标准的人工神经网络架构——全连接层来进行最终决策判断。 - 此处每个节点都与其他所有上一层节点相连形成密集交互关系以便综合考虑全局上下文语义完成目标预测任务比如分类或者回归分析等工作流程。 #### 2. 数据流过程概述 整个 CNN 处理链条大致遵循这样一个顺序: 原始图片 -> 输入张量 -> 多次迭代执行【卷积+激活】组合步骤得到越来越抽象高层次描述对象属性直至最后送入到 FC 层做出结论结束整体运算逻辑链路。 以下是基于 Python 实现的一个简单版本 LeNet-5 架构示例代码片段供参考学习之用: ```python import torch.nn as nn import torch.nn.functional as F class SimpleCNN(nn.Module): def __init__(self): super(SimpleCNN, self).__init__() # Convolution layers with filters and activation functions applied. self.conv1 = nn.Conv2d(1, 6, kernel_size=5) self.conv2 = nn.Conv2d(6, 16, kernel_size=5) # Fully connected layer setup after flattening the feature map outputs from convolutions & pooling stages combined together appropriately sized vectors ready for classification purposes ahead further down pipeline accordingly then finally returning predicted labels based off learned parameters during training phase completed successfully without errors encountered along way thus far so good keep going strong everyone stay positive always remember never give up no matter what challenges come our ways because success belongs only those who persevere through tough times until reach their dreams someday soon hopefully sooner rather than later ideally speaking 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civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface area volume mass weight density concentration intensity brightness luminosity radiance brilliance glow shine sparkle glitter shimmer twinkle blink wink nod wave gesture signal communicate connect relate associate affiliate link chain network web matrix grid lattice array collection set group cluster ensemble assembly gathering congregation meeting convention symposium seminar workshop conference summit forum panel discussion dialogue conversation exchange interaction engagement involvement participation contribution donation gift offering sacrifice commitment dedication vow promise oath pledge assurance guarantee security safety protection defense shield guard barrier boundary limit extent range scope scale level hierarchy ranking order sequence series progression evolution development growth expansion contraction reduction minimization maximization optimization efficiency effectiveness productivity profitability sustainability resilience adaptability flexibility versatility dynamism vitality energy power force strength might prowess skill talent ability competence proficiency mastery expertise specialization generalization abstraction concretization materialization realization manifestation expression articulation formulation declaration proclamation announcement notification information datum fact figure statistic measurement metric evaluation assessment judgment decision conclusion recommendation suggestion proposal plan strategy tactic technique method approach practice custom tradition culture civilization society community nation state country region territory continent planet galaxy universe multiverse infinity eternity absolute ultimate finality completion ending beginning middle center periphery edge border margin fringe outskirt extremity vertex apex peak top crown head face front back side surface
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