2021 American Collegiate Mathematical Contest in Modeling
Problem C confirms the wasp's buzz
Reproduction of the original title:
In September 2019, a swarm (also known as the Asian giant wasp) was discovered on Vancouver Island, British Columbia, Canada. The nest was quickly destroyed, but word of the incident quickly spread throughout the region. Since then, there have been more cases in neighboring Washington state Several confirmed pest sightings, as well as a large number of false sightings. See Figure 1 below for detection maps, wasp watches, and public sight. Hornets are the largest species of wasp in the world, and nest occurrences are alarming.
Additionally , Giant hornets are predators of European honeybees, invading and destroying their nests. A small number of giant hornets are able to destroy entire colonies of European honeybees in a short period of time. At the same time, they are voracious predators of other insects and are considered agricultural pests.
This The wasp life cycle is similar to that of many other wasps. A fertilized queen emerges in the spring and starts a new colony. In the fall, the new queen leaves the nest and will spend the winter in the soil waiting for spring. The range of a new queen is estimated to be 30 km to establish her nest. More detailed information on the Asian giant hornet is included in the issue annex and is also available online. The
presence of the Asian giant hornet would cause a great deal of anxiety due to the potentially severe impact on local bee populations. Established in Washington State A hotline and a website have been established for people to report sightings of these hornets. Based on these reports from the public, the state must decide how to prioritize its limited resources in order to follow up with more investigations. While some reports have been identified as , but many other sightings turned out to be other types of insects. The
main questions in this question are "how do we interpret the data provided by public reports?" and "what strategies can we use to prioritize Additional investigations into these public reports?"
Your paper should explore and address the following aspects:
treatment and discussion whether it is possible to predict the spread of this pest over time, and with what precision.
Most reported sightings incidents of mistaking other wasps for Hornets. Use only the provided dataset files and (possibly) the provided image files to create, analyze and discuss models that predict the likelihood of misclassification. Use your model to discuss your classification
analysis How to lead to a priority investigation Report the most likely positive findings.
Address how to update your model, given more new reports over time, and how often updates should occur.
Using your model, what would constitute evidence that the pest has been eradicated in Washington State?
Finally, your report should include a two-page memo summarizing your results to the Washington State Department of Agriculture.
Overview of the overall solution process (abstract)
The presence of wasp citrus in Washington State could have potentially negative impacts on local ecology. Given the limited resources of government agencies, researchers need to develop strategies for analyzing the investigative priorities of these wasp public sighting reports. The specific task is divided into 5 questions.
For question 1, we need to integrate the biological characteristics of the wasp and the data characteristics provided by the title to establish a growth and proliferation model of the wasp population. First, based on the logistics model, the establishment of the basic growth model of the wasp colony was completed on the basis of changes in environmental factors such as temperature and living habits. Afterwards, we used the Gaussian distribution function to describe the probability of natural events to simulate the spatio-temporal location of each sighting, and built wasp colony reproduction and prediction models in order to analyze the probability of sightings. This is because we fully consider that sighting reports do not fully represent the exact location of wasp populations, and their occurrence has a certain degree of randomness. The spatiotemporal location of events builds a wasp colony reproduction and prediction model. In the simulation of the positive ID data distribution of the data set by the model, the simulated distribution is relatively close to the actual data point distribution. Based on the distance relationship between the earliest occurrence point of the targeting event and each occurrence point, a fitting accuracy analysis method is established. In validation, the fitting accuracy was about 84.6% for correct witness reports.
Regarding question 2, in order to make full use of various data in the dataset, we divide the dataset into three dimensions: spatio-temporal data, text, and images. Afterwards, we use the growth-diffusion model to analyze spatio-temporal data, build an LDA-based text classification model for text analysis, and build a CNN-based image analysis model. The results of the validation of the individual models show that the analysis predicts the likelihood of classifying a dataset requires a synthesis of the various types of data provided in the dataset. Therefore, we synthesized the prediction confidence level independently given by the 3D model, and weighted it according to the effective information of each dimension, and completed the 3D comprehensive data analysis and prediction model. The model obtained a goodness of fit of 92.86% (positive ID) and 85.22% (negative ID) in the fit of the existing data. For each data point, the model's predictions are also well explained.
For question 3, we used the prediction confidence obtained by the model of question 2, and divided the data into six levels of S, A, B, C, D, and E according to the confidence interval. S rank is the highest rank. The higher the level, the higher the investigation priority of the sighting report.
For problem 4, we propose an incremental model update method based on the forgetting factor. When updated with new wasp sighting reports, the model calculates the defined forgetting factor and updates the original training data. The test shows that the updated method improves the goodness of fit of the model by 10.68% (negative ID), and can self-correct the prediction results to a certain extent.
Regarding question 5, we propose three conditions that can prove the eradication of wasps based on various factors. We use the data from 2019-2020 for analysis and demonstration, which proves the correctness of the evaluation criteria. Finally, we predict the development trend of events in 2021.
The model established in this paper has high comprehensiveness and accuracy. Additionally, it can impart confidence in the predictions of each data point, optimizing researchers' strategies for analyzing survey reports. At the same time, we provided the Washington State Department of Agriculture with a two-page memo.
Model assumptions:
To simplify our model and remove complexity, we make the following main assumptions in this paper. Assumption .1 The hives are distributed in a certain area around the positive witness location. Since the data presented only reported the occurrence of the sighting, based on the habits of the wasp citrus, we assumed that the wasp that was correctly sighted came from an area surrounding the event site. This assumption allows the model to better fit the distribution of data points.
Hypothesis 2 provides data that includes anthropogenic influence on the colony. From the analysis of this problem, it can be seen that the witness event data of vespa citrus in the data cannot fully represent the natural growth and spread of vespa citrus. Because the Vespa citrus group has the advantage of invasive species, the eradication of Vespa citrus in Washington State also requires the intervention of human factors, and it is impossible to grow completely naturally.
Hypothesis 3 Over a certain period of time, climate change will not have a large impact on wasp colonies. This assumption is made to simplify the calculation of the model and to eliminate the influence of unknown factors on the model.
The data provided by Hypothesis 4 is true and reliable to a certain extent. Because the model we built is based on the data provided by the subject, only the high validity of the data can guarantee the high reliability of the model.
Question restatement:
In September 2019, a colony of wasps (also known as Asian giant hornets) was discovered on Vancouver Island, British Columbia, Canada. News of the incident quickly spread throughout the region. Since then, there have been several confirmed pest sightings in neighboring Washington state, as well as many false sightings. Vespas are the largest species of bumblebee in the world, and the emergence of nests is astounding. They are voracious predators of other insects and are considered agricultural pests. Meanwhile, more detailed information on the Asian giant hornet is included in the question annex and can also be found online.
Because of the potentially severe impact of wasp citrus, Washington state has created a helpline and a website for people to report sightings of these hornets, and must decide how to prioritize its limited resources to follow up with additional investigations.
Build a mathematical model to address and discuss the spread of this pest over time and assess the level of precision.
Using only the provided dataset files and (possibly) provided image files, build a model to analyze, discuss and predict the likelihood of misclassification.
Use this model to discuss how triage analysis leads to prioritized investigation of reports that are most likely to be positive sightings.
Build a way to update the model and provide other new reports over time, and discuss update frequency.
Resolve evidence that this pest has been eradicated in Washington State.
Model establishment and solution Overall paper thumbnail
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Part of the program code: (code and documentation not free)
import torch
import torch . nn as nn
class AutoEncoder ( nn . Module ):
def __init__ ( self ):
super ( AutoEncoder , self ) . __init__ ()
self . DownSampling = nn . Sequential (
nn . Conv2d (3 , 6 , 3 , 1 , 1 ) , nn . ReLU () ,
nn . BatchNorm2d ( 6) , nn . MaxPool2d ( 2) ,
nn . Conv2d (6 , 12 , 3 , 1 , 1 ) , nn . ReLU () ,
nn . BatchNorm2d ( 12 ) , nn . MaxPool2d (2 ) ,
nn . Conv2d ( 12 , 24 , 3 , 1 , 1 ) , nn . ReLU () ,
nn . BatchNorm2d ( 24 ) , nn . MaxPool2d (2 ) ,
nn . Conv2d ( 24 , 48 , 3 , 1 , 1 ) , nn . ReLU () ,
nn . BatchNorm2d ( 48 ) , nn . MaxPool2d (2 ) ,
)
self . UpSampling = nn . Sequential (
nn . Conv2d ( 48 , 24 , 3 , 1 , 1 ) ,
nn . ConvTranspose2d ( 24 , 24 , 3 , 2 , 1 , 1 ) , nn . ReLU () ,
nn . Conv2d ( 24 , 12 , 3 , 1 , 1 ) ,
nn . ConvTranspose2d ( 12 , 12 , 3 , 2 , 1 , 1 ) , nn . ReLU () ,
nn . Conv2d ( 12 , 6 , 3 , 1 , 1 ) ,
nn . ConvTranspose2d (6 , 6 , 3 , 2 , 1 , 1) , nn . ReLU () ,
nn . Conv2d (6 , 3 , 3 , 1 , 1 ) ,
nn . ConvTranspose2d (3 , 3 , 3 , 2 , 1 , 1) ,
)
def forward ( self , x ):
return self . DownSampling ( x ) , self . UpSampling ( self . DownSampling ( x) )
import torch
import torch . nn as nn
class CNN ( nn . Module ):
def __init__ ( self ):
super ( CNN , self ) . __init__ ()
self . conv = nn . Sequential (
nn . Conv2d ( 48 , 96 , 3 , 1 , 1 ) , nn . ReLU () ,
nn . BatchNorm2d ( 96 ) , nn . MaxPool2d (2 ) ,
nn . Conv2d ( 96 , 192 , 3 , 1 , 1) , nn . ReLU () ,
nn . BatchNorm2d ( 192 ) , nn . MaxPool2d ( 2 ) ,
)
self . out = nn . Sequential (
nn . Linear ( 3072 , 128 ) , nn . Dropout ( 0 . 25 ) , nn . ReLU () ,
nn . Linear ( 128 , 2 ) , nn . Softmax ( dim =1 ) ,
)
def forward ( self , x ):
return self . out ( self . conv ( x ). view ( x. shape [0], -1 )