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Mathematical Contest in Modeling (MCM/ICM) Summary Sheet
建模数学竞赛 (MCM/ICM) 摘要表

Can We Believe the Rumors Circulating about the Asian Giant Hornet?
我们能相信流传的关于亚洲大黄蜂的谣言吗?

Abstract  抽象

Summary The Asian giant hornet, an invasive pest, was discovered on Vancouver Island in British Columbia, Canada. Subsequently, many residents claimed to have witnessed the hornets, but the authenticity of these claims remains to be verified. To better assess the spread of the Asian giant hornet, we modeled ResNet to identify images and predict the likelihood of misclassification.
摘要 亚洲大黄蜂是一种入侵性害虫,是在加拿大不列颠哥伦比亚省的温哥华岛发现的。随后,许多居民声称目睹了大黄蜂,但这些说法的真实性仍有待核实。为了更好地评估亚洲大黄蜂的传播,我们对 ResNet 进行了建模以识别图像并预测错误分类的可能性。

For task(a), we modeled prediction system with Prophet and SARIMA based on the collected public reports, to predict the time - dependent spread characteristics of the Asian giant hornet. The MSLE of Model 1 reached 2.89, and the MAE of Model 2 reached 9.00, indicating good predictive performance of the models. Both models suggest that the number of Asian giant hornet nests exhibits a spiky peak - shaped trend over time. In August 2020, the number of Asian giant hornet nests reached its maximum value, during which their activity level was high. Their active period is from May to October, with a cycle of one year.
对于任务 (a),我们根据收集到的公开报告,使用 Prophet 和 SARIMA 对预测系统进行建模,以预测亚洲大黄蜂的时间依赖性传播特征。模型 1 的 MSLE 达到 2.89,模型 2 的 MAE 达到 9.00,表明模型具有良好的预测性能。这两个模型都表明,随着时间的推移,亚洲巨型大黄蜂巢的数量呈现出尖刺的峰值形状趋势。2020 年 8 月,亚洲大黄蜂巢的数量达到最大值,在此期间它们的活动水平很高。他们的活跃期是从 5 月到 10 月,以一年为周期。

For task(b), we utilized the pre - trained ResNet model and adjusted relevant parameters to identify 3,305 images provided by the public. By introducing functions such as the classification function, cross - entropy, and Adam optimization algorithm, we successfully trained the model, achieving an accuracy of 95.86 % 95.86 % 95.86%95.86 \%. This model can accurately distinguish between wasps and hornets based on images and evaluate the likelihood of misclassification.
对于任务 (b),我们利用预先训练的 ResNet 模型并调整相关参数,以识别公众提供的 3,305 张图像。通过引入分类函数、交叉熵和 Adam 优化算法等函数,我们成功地训练了模型,实现了 的准确率。 95.86 % 95.86 % 95.86%95.86 \% 该模型可以根据图像准确区分黄蜂和大黄蜂,并评估错误分类的可能性。

For task©, based on the models from Task 1 and Task 2, we performed a weighting process, assigning weights of 30 % 30 % 30%30 \% and 70 % 70 % 70%70 \% respectively. The newly generated model is used for classification to select the reports that are most likely to be positive sightings.
对于任务©,根据任务 1 和任务 2 中的模型,我们执行了加权过程,分别分配了 30 % 30 % 30%30 \% 和 的 70 % 70 % 70%70 \% 权重。新生成的模型用于分类,以选择最有可能是正面目击事件的报告。

For task(d) and task(e), when additional new reports are added, we can manipulate the ResNet to train a model with a larger dataset and increase the update frequency. When the evidence provided in a certain month shows that no correct cases of the Asian giant hornet have been observed, it is determined that this pest has been eradicated in Washington State.
对于 task(d) 和 task(e),当添加额外的新报告时,我们可以操纵 ResNet 来训练具有更大数据集的模型并提高更新频率。当某个月提供的证据显示没有观察到亚洲大黄蜂的正确案例时,可以确定这种害虫已在华盛顿州被根除。

Keywords: Prophet; FARIMA ; FARIMA ; FARIMA;\mathrm{FARIMA} ; ResNet;cross - entropy;Adam
关键词:先知; FARIMA ; FARIMA ; FARIMA;\mathrm{FARIMA} ; ResNet;cross - 熵;亚当

Can We Believe the Rumors Circulating about the Asian Giant Hornet?
我们能相信流传的关于亚洲大黄蜂的谣言吗?

Janury 16,7025  1月 16,7025

Contents  内容

1 Introduction … 2  1 引言 ...2
1.1 Background … 2  1.1 背景 ...2
1.2 Approach Overview … 2
1.2 方法概述 ...2

2 Basic Analysis of the problem … 3
2 问题的基本分析3

2.1 The Characters of the Asian Giant Hornet … 4
2.1 亚洲大黄蜂的特征 ...4

2.2 Further Analysis … 3
2.2 进一步分析 ...3

3 Model Assumptions and Notations … 4
3 模型假设和符号 ...4

3.1 Assumptions and Justifications … 4
3.1 假设和理由 ...4

3.2 Notations … 5  3.2 符号 ...5
4 Models … 6  4 型号 ...6
4.1 K - Means for prediction system … 6
4.1 K - 预测系统均值 ...6

4.2 Pronhet for prediction system … 6
4.2 Pronhet 用于预测系统 ...6

4.3 SARIMA for prediction system … 7
4.3 SARIMA 用于预测系统 ...7

4.4 ResNet … 7  4.4 ResNet ...7
4.5 Cross - Entropy for ResNet model … 8
4.5 交叉 - ResNet 模型的熵 ...8

4.6 Adam for ResNet model … 8
4.6 Adam for ResNet 模型 ...8

5 Results … 9  5 结果 ...9
5.1 Characteristic Curves Of the Asian Giant Hornet’s Spread Over Time … 9
5.1 亚洲大黄蜂随时间传播的特征曲线......9

5.2 Recognition system based on ResNet … 11
5.2 基于 ResNet 的识别系统 ...11

5.3 Integrated Model … 12
5.3 集成模型12

6 Sensitivity Analysis of Models … 13
6 模型的敏感性分析 ...13

7 Strengths and Weaknesses … 16
7 优点和缺点 ...16

7.1 Strengths … 16  7.1 优势 ...16
7.2 Weaknesses … 18  7.2 弱点 ...18
8 Future Plans … 20
8 未来计划 ...20

1 Introduction  1 引言

1.1 Background  1.1 背景

The Asian giant hornet, also serves as the world’s largest species of wasp, is a voracious predator of other insects that are considered agricultural pests. As predators of European honeybees, they can reproduce rapidly and destroy European honeybee colonies in a short time. Currently, nests of this pest have been discovered on Vancouver Island in British Columbia, Canada, and the potential harm it poses has caused public anxiety. However, the accuracy of the public’s sighting photos and reports remains lacking. Given limited resources, it is crucial to effectively find accurate sighting evidence.
亚洲大黄蜂也是世界上最大的黄蜂物种,是其他被认为是农业害虫的昆虫的贪婪捕食者。作为欧洲蜜蜂的捕食者,它们可以迅速繁殖并在短时间内摧毁欧洲蜜蜂群。目前,在加拿大不列颠哥伦比亚省的温哥华岛发现了这种害虫的巢穴,它带来的潜在危害引起了公众的焦虑。然而,公众的目击照片和报告仍然缺乏准确性。在资源有限的情况下,有效找到准确的目击证据至关重要。
The State of Washington has established a helpline and a website. Our team, in an attempt to find a solution, is faced with the following problems:
华盛顿州已经建立了一条求助热线和一个网站。我们的团队在寻找解决方案的过程中,遇到了以下问题:
  1. Predict the spread of the Asian giant hornet over time and determine the level of precision.
    预测亚洲大黄蜂随时间推移的传播并确定精度级别。
  2. Create a model to predict the likelihood of misclassification in the sighting files based on the provided data.
    创建一个模型,以根据提供的数据预测瞄准文件中错误分类的可能性。
  3. Analyze how the model can identify the positive sighting reports that should be prioritized for investigation.
    分析模型如何识别应优先调查的阳性目击报告。
  4. Determine how the model can be updated in case of additional reports and what the update frequency should be.
    确定在有其他报表的情况下如何更新模型以及更新频率应该是多少。
  5. Use the established model to determine what evidence would prove that the Asian giant hornet has been eradicated in the State of Washington.
    使用已建立的模型来确定哪些证据可以证明亚洲大黄蜂已在华盛顿州被根除。

1.2 Approach Overview  1.2 方法概述

In this paper, we try to model a prediction system to analyze eyewitness documents and evaluate their accuracy. Our main contributions are as follows:
在本文中,我们尝试对预测系统进行建模,以分析目击者文件并评估其准确性。我们的主要贡献如下:
  1. Based on the data about Asian giant hornets from Pennsylvania State University, we determined the characteristics of this type of hornet. We established two models, Prophet and SARIMA, to analyze the time - dependent spreading characteristics of this pest. Moreover, we plotted the fitting curves and the distribution maps of the time - evolving regions, and provided the accuracy of the two models.
    根据宾夕法尼亚州立大学关于亚洲巨型大黄蜂的数据,我们确定了这种大黄蜂的特征。我们建立了两个模型,Prophet 和 SARIMA,来分析这种害虫的时间依赖性传播特征。此外,我们绘制了时间演变区域的拟合曲线和分布图,并提供了两个模型的准确性。
  2. We utilized the pre - trained ResNet model, combined with the cross - entropy and the Adam optimization algorithm, to adjust and optimize the model, generating the main model for this problem. This model is capable of image recognition and can distinguish between positive and negative examples.
    我们利用预先训练的 ResNet 模型,结合交叉熵和 Adam 优化算法,对模型进行调整和优化,生成了这个问题的主模型。该模型能够进行图像识别,并且可以区分正面和负面示例。
  3. On the basis of the main model, we introduced the Prophet and SARIMA models and weighted them, obtaining a model that takes into account both the spreading characteristics of the Asian giant hornets themselves and the sighting patterns of local residents. This model can screen out the positive sighting reports that should be investigated first.
    在主模型的基础上,我们引入了 Prophet 和 SARIMA 模型并对其进行加权,得到了一个既考虑了亚洲大黄蜂本身的传播特征又考虑了当地居民的观察模式的模型。该模型可以筛选出应首先调查的阳性目击报告。
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