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COSC 1285編程代做、代寫Java程序設計、代做Java程序 調試Web開發|代做R語言編程

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Algorithms and Analysis
COSC 1285/2123
Assignment 1
Assessment Type Group assignment. Groups as allocated and notified on Canvas.
Submit online via Canvas → Assignments → Assignment
1. Marks awarded for meeting requirements as closely as
possible. Clarifications/updates may be made via announcements/relevant
discussion forums.
Due Date Friday 16th April 2021, 11:59pm
Marks 30
1 Overview
One of the frequent phrases we hear during the COVID-19 panademic are epidemic
modelling and contract tracing. As the virus is transmitted human to human, one of
the effective methods to stop an outbreak is to identify the close contacts of an infected
individual, and isolate all of them for a period of time (typically 14 days). To estimate
the impact of outbreaks, epidemic modelling is an extremely important tool. A graph
is a natural representation for these close contacts, tracing outbreaks and for epidemic
modelling.
When we represent these networks as a graph, the vertices in such a graph represent
people and edges represents close contact relationship.
In class, we studied three methods to represent the graph, the adjacency list, adjacency
matrix and vertex/edge list representations. There is a fourth type of representation
called incident matrix (see below for details). The performance of each representation
varies depending on the characteristics of the graph. In this assignment, we will implement
the adjacency list, adjacency matrix and incident matrix representations for the
relational parts, and evaluate on how well they perform when modelling close contacts
and for epidemic modelling. This will assist with your understanding of the tradeoffs
between data structure representations and its effect when implementing operations or
solving problems using algorithms and data structures.
2 Learning Outcomes
This assessment relates to all of the learning outcomes of the course which are:
CLO 1: Compare, contrast, and apply the key algorithmic design paradigms: brute
force, divide and conquer, decrease and conquer, transform and conquer, greedy,
dynamic programming and iterative improvement;
CLO 2: Compare, contrast, and apply key data structures: trees, lists, stacks,
queues, hash tables and graph representations;
CLO 3: Define, compare, analyse, and solve general algorithmic problem types:
sorting, searching, graphs and geometric;
CLO 4: Theoretically compare and analyse the time complexities of algorithms and
data structures; and
CLO 5: Implement, empirically compare, and apply fundamental algorithms and
data structures to real-world problems.
3 Background
3.1 Networked SIR Model
There are several well-known epidemic models, but the one that we will focus on in
this assignment is the (Networked) SIR model. The SIR epidemic model assumes each
individual has three states - Susceptible (S) to the disease, Infected (I) by the disease and
Recovered (R) to the disease. The progression of states is assumed to be susceptible (S)
to Infected (I) to Recovered (R). Initially some in the initial population are infected and
all others are susceptible. Once recovered, an individual has immunity and will not be
further infected. There are also other models, like SIS (Susceptible, Infected, Susceptible),
but for the purpose of this assignment, we will stick with the most fundamental model,
the SIR model, as others are really variations on this.
In the traditional SIR model, there is assumption of full mixing between individuals
- i.e., any individual can potentially infect another. The model then derives differential
equations that estimates the changes in the total number of susceptible, infected and
recovered individuals over time, and these are proportional to the numbers of the other
two states - e.g., change in number of infected individuals is dependent on the number
of susceptible and the number of recovered individuals. It is able to model some diseases
relatively well, but is inaccurate for others and misses out on local spreading and effects.
Hence a networked SIR model was proposed, where instead of full mixing between individuals,
infected individuals can now only infect its neighbours in the graph/network,
which typically represents some form of “close contact”.
The networked SIR model works as follows.
At each timestep, each susceptible individual can be infected by one of its infected
neighbours (doesn’t matter which one, as an individual is infected regardless of who
caused it). Each infected neighbour has a chance to infect the susceptible individual.
This chance is typically modelled as an infection parameter α - for each chance, there
is α probability of infection. In addition, at each timestep each infected individual have
a chance of recovering, either naturally or from medicine and other means (this model
doesn’t care which means). Let the recovery parameter β represent this, which means
there is β probability that an infected individual will recover and change to recovered
state. There is no transition for susceptible to recovered (which could be interesting, e.g.,
to model vaccination, but left for future assignments).
As you can probably infer, the more neighbours one has, the higher potential for
infection. Hence one reason for the general advice from the health departments to reduce
the number of close contacts. Also wearing masks reduces the infection probability, again
reducing the spread of an outbreak. In this assignment, you will get an opportunity to
experiment with these parameters and see what differences they make.
2
For more information about SIR and epidemic modelling, have an initial read here
https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology. We will
also release some recordings talking more about the model on Canvas, particularly providing
more details about how to run the SIR model to simulate an epidemic, please look
at those also when they become available.
3.2 Incidence Matrix Representation
The incidence matrix represents a graph as a set of vertices and list of edges incident to
each vertex as a 2D array/matrix. More formally, let the incidence matrix of a undirected
graph be an n x m matrix A with n and m are the number of vertices and edges of the
graph respectively. The values in the matrix A follows the following rules:
Each edge ek is represented by a column in A.
Each vertex is represented by a row in A.
Let the two incident vertices to an edge ek be vi and vj
. Then the matrix entries
Ai,k and Aj,k are both = 1.
Ai,k = 0 for all other non-incident edges.
For example, the following graph:
has its incidence matrix as below:
?
???
AB AC AD BC CD
A 1 1 1 0 0
B 1 0 0 1 0
C 0 1 0 1 1
D 0 0 1 0 1
?
???
For further readings about this graph representation, please see https://en.wikipedia.
org/wiki/Incidence_matrix.
4 Assignment Details
The assignment is broken up into a number of tasks, to help you progressively complete
the project.
3
Task A: Implement the Graph Representations, their Operations
and the Networked SIR model (10 marks)
In this task, you will implement data structures for representing undirected, unweighted
graphs using the adjacency list, adjacency matrix and incidence matrix representations.
Your implementation should also model vertices that have SIR model states associated
with them. Your implementation should support the following operations:
Create an empty undirected graph (implemented as a constructor that takes zero
arguments).
Add a vertex to the graph.
Add an edge to the graph.
Toggle the SIR state on vertices.
Delete a vertex from the graph.
Delete an edge from the graph.
Compute the k hop neighbours of a vertex in the graph.
Print out the set of vertices and their SIR states.
Print out the set of edges.
In addition, we want you to implement the (networked) SIR epidemic model to simulate
how a virus can spread through a population.
Note that you are welcome to implement additional functionality. When constructing
our solutions to the assignment, we have found that adding some methods was helpful,
particularly for implementing the SIR model. But the above functionalities are ones you
should complete and ones you will be assessed on.
Data Structure Details
Graphs can be implemented using a number of data structures. You are to implement
the graph abstract data type using the following data structures:
Adjacency list, using an array of linked lists.
Adjacency matrix, using a 2D array (an array of arrays).
Incidence matrix, using a 2D array (an array of arrays).
4
For the above data structures, you must program your own implementation, and not
use the LinkedList or Matrix type of data structures in java.utils or any other libraries.
You must implement your own nodes and methods to handle the operations. If you use
java.utils or other implementation from libraries, this will be considered as an invalid
implementation and attract 0 marks for that data structure. The only exceptions are:
if you choose to implement a map of vertex labels to a row or column index for the
adjacency matrix or incidence matrix, you may use one of the existing Map classes
to do this.
if you choose to implement a map of vertex labels to its associated SIR state, you
may use of the existing Map classes to do so.
Operations Details
Operations to perform on the implemented graph abstract data type are specified on the
command line. They are in the following format:
[arguments]
where operation is one of {AV, AE, TV, DV, KN, PV, PE, SIR, Q} and arguments is for
optional arguments of some of the operations. The operations take the following form:
AV – add a vertex with label ’vertLabel’ into the graph. Has default
SIR state of susceptible (S).
AE – add an edge with source vertex ’srcLabel’, target
vertex ’tarLabel’ into the graph.
TV – toggle the SIR state of vertex ’vertLabel’. Togglng means go to
the next state, i.e., from S to I, from I to R (if in R, remain in R).
DV – delete vertex ’vertLabel’ from the graph.
DE – remove edge with source vertex ’srcLabel’ and target
vertex ’tarLabel’ from the graph.
KN – Return the set of all neighbours for vertex ’vertLabel’ that
are up to k-hops away. The ordering of the neighbours does not matter. See below
for the required format.
PV – prints the vertex set of the graph. See below for the required format. The
vertices can be printed in any order.
PE – prints the edge set of the graph. See below for the required format. The edges
can be printed in any order.
SIR probability> – Run the networked SIR model simulation, using the current graph
as the network, the specified seed vertices as additional set of infected vertices (in
addition to any existing in the current graph) and the two infection and recover
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probabilities. Runs the model simulation to completion, which means two things
a) there are no more vertices with Infected (I) state and there are no changes in the
number of infected or recovered in the latest iteration of the model; or b) if condition
there are still infected vertices but there has been no changes in the number of
infected or recovered for 10 iterations, then can stop the simulation. Outputs the
list of nodes infected at each iteration, see below for format.
Q – quits the program.
k-hop Neighbour operation format details The format of the output of the neighbour
operation for vertex ’A’ should take the form:
A: neighbour1 neighbour2 ...
If a vertex has no neighbours, then the list of neighbours should be empty. The node
’A’ should not be in the list of neighbours, and the graphs can be assumed to have no
self-loops (self loops don’t necessarily make sense for epidemic modelling).
Print vertex operation format details The print vertex operation output the vertices
and associated SIR state in the graph in a single line. The line should specifies all
the valid vertex (indices) in the graph.
(vertex1,state1) (vertex2,state2) (vertex3,state3) ...
where state1 is the SIR state of vertex 1 etc.
Print edge operation format details The print edge operation output the edges in
the graph in over a number of lines. Each line specifies an edge in the graph, and should
be in the following format:
srcVertex tarVertex
SIR operation format details The networked SIR model file output format is each
line represents one iteration of the process, and each line will record the number of newly
infected and recovered vertices (newly infected or recovered nodes are ones that become
infected or recovered in this iteration). The format is as follows:
: [vertices>] : []
Example of all operations As an example of the operations, consider the output
from the following list of operations:
The output from the four neighbour operations (‘KN 1 A’, ‘KN 2 A’ ‘KN 1 F’, ‘KN 1
H’) should be (remember that the order these neighbourhoods do not matter so if your
output differs from this ordering but has the same set of vertices, that is fine):
A: B E F
A: B C D F E G
F: A B G
H:
The output from the print vertices operation (PV) could be (remember that the order
doesn’t matter):
(A, S ) (B,R) (D, S ) (E, I ) (F, S ) (G, S ) (H, S )
The output from the print edges operation (P E) could be (remember that the order
doesn’t matter):
The output from the ‘SIR A;F 0.8 0.5’ operation could be (note that it is a stochastic
model, so you can get different results for different runs, so use the following more for
what the output format should look like):
1 : [G] : [ ]
2 : [ ] : [A]
3 : [ ] : [ ]
4 : [ ] : [ ]
5 : [ ] : [ F G]
6 : [ ] : [ ]
Testing Framework
We provide Java skeleton code (see Table 1 for the important files) to help you get
started and automate the correctness testing. You may add your own Java files to your
final submission, but please ensure that they compile and can be run on the core teaching
servers.
Notes
Consider the specifications here carefully. If you correctly implement the “Implement
me!” parts and follow the output formating for operations like PV, PE and
SIR, you in fact do not need to do anything else to get the correct output formatting.
The main class in the provided skeleton code will handle this.
The implementation details are up to you, but you must implement your own data
structures and algorithms, i.e., do not use the built-in structures in Java unless for
the purposes outlined in the box above.
If you develop on your own machines, please ensure your code compiles and runs
on the university’s core teaching servers. You don’t want to find out last minute
that your code doesn’t compile on these machines. If your code doesn’t run on
these machines, we unfortunately do not have the resources to debug each one and
cannot award marks for testing.
? All submissions should compile with no warnings on Oracle Java 1.8 - this is the
version on the core teaching servers.
? Any clarifications on the Canvas FAQ or Assignment 1 Update page will override
the specifications here if they are conflicting.
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file description
RmitCovidModelling.java Main class. Contains code that reads in operation commands
from stdin then executes those on the selected graph implementation.
Also will format the output as required. No need
to modify this file.
ContactsGraph.java Interface class for the graph representations. It contains the
common interface/methods that you’ll need to implement for
the various representations. Generally no need to modify this
file, but you might want to add helper functionality, and here
would be one place to do so for common ones across all representations..
AdjacencyList.java Code that implements the adjacency list implementation of
a graph. Complete the implementation (implement parts labelled
“Implement me!”).
AdjacencyMatrix.java Code that implements the adjacency matrix implementation
of a graph. Complete the implementation (implement parts
labelled “Implement me!”).
IncidenceMatrix.java Code that implements the incidence matrix implementation
of a graph. Complete the implementation (implement parts
labelled “Implement me!”).
SIRState.java Code that implements the three vertex states of a SIR model.
No need to modify this file.
SIRModel.java Code that implements the networked SIR model. Complete
the implementation (implement parts labelled “Implement
me!”).
Table 1: Table of Java files.
Task B: Evaluate your Data Structures and SIR model (20 marks)
In this second task, you will evaluate your implemented structures in terms of their time
complexities for the different operations and different use case scenarios. Scenarios arise
from the possible use cases of contract tracing and epidemic modelling on a graph. In
addition, run some epidemic modelling simulations to evaluate your structures within an
application (epidemic modelling and simulation) and to explore more about the effect of
the model parameters on epidemic spreading.
Write a report on your analysis and evaluation of the different implementations. Consider
and recommend in which scenarios each type of implementation would be most
appropriate. Report the outcomes of your SIR epidemic model simulations. The report
should be 10 pages or less, in font size 12. See the assessment rubric (Appendix A) for
the criteria we are seeking in the report.
9
Graph generators
To evaluate the data structures, we will generate a number of graphs, then apply a
number of operations on them, see the Use Case Scenarios section next. In this section,
we describe more about how to generate the graphs, and see on Canvas for further details
and videos.
There are many ways to generate graphs, but we will focus on two:
Random (Erdos-Renyi) – there is a probability for generating an edge between any
pair of vertices.
Scale-free – graphs whose degree distribution follow a power law (see https://en.
wikipedia.org/wiki/Scale-free_network).
We suggest to use Pajek1
, which is available on multiple platforms and has visualisation,
which allows one to look at the generated graphs. But it also has basic graph
generation functionality and doesn’t require programming to use, unlike more powerful
graph libraries2
.
Use Case Scenarios
Typically, you use real usage data to evaluate your data structures. However, for this assignment,
you will write data generators to enable testing over different scenarios of
interest. We are also interested in the effect of the average degree of the graph3 on these
scenarios. There are many possibilities, but for this assignment, consider the following
scenarios:
Scenario 1 k-hop Neighbourhoods: When doing contract tracing and/or epidemic
modelling, computing neighbourhoods is an important function. In this scenario, the
graph is not changing, but important operations such as k-hop neighbourhood (recall
this is all neighbours up to k-hops away) are requested.
You are to evaluate the performance of the the k-hop neighbourhood implementations,
as the average degree of the evaluated graph and k are varied.
Scenario 2 Dynamic Contact Conditions: In the real world, the contact conditions
between people are likely not static and there will be need to update these over time. In
this scenario, the contacts are changing (been added and deleted). In this scenario, you
are to evaluate the performance of your implementations in terms of:
edge additions
edge deletions
You are to evaluate the performance the edge operations as the average degree and
size (number of vertices) of the initial graph (before edge changes) are varied.
1http://mrvar.fdv.uni-lj.si/pajek/ the website looks a bit dated, but this is one of the well
known social network analysis tools.
2Networkx https://networkx.org/ – if you know Python, you are more than welcome to use this
instead.
3Average number of neighbours per node, which both graph generator models allows to be specified
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Scenario 3 Dynamic People Tracing: As time goes on, the people been traced will
change. Although it is possible to have a large graph that tries to capture every possible
person, it is computationally difficult to do so and run simulations on it. In this scenario,
you are to evaluate the performance of your implementations in terms of:
vertex addition
vertex deletion
You are to evaluate the performance the vertex operations as the average degree and size
(number of vertices) of the initial graph (before vertex changes) are varied.
SIR Model Epidemic Simulation
In addition to evaluating how well the graph representations perform for the contract
tracing and epidemic modelling simulations, we also want to experiment with how the
networked SIR model works and performs.
Run epidemic simulation for different graph types (Erdos-Renyi and Scale-free), different
seed initialisations and different infection and recover probabilities. For performance
evaluation, evaluate each of the three data structures on a subset of the possible simulation
parameters and compare how they perform (in terms of timing efficiency).
We don’t expect a comprehensive analysis, but want you to explore and gain a better
understanding of epidemic modelling and what it implies for how to limit the spread of
epidemics.
Consider how you might present the results, but at a minimum plot the following:
Number of susceptible, infected and recovered after every iteration.
Data Generation
When generating the vertices and edges to add or remove and find neighbourhoods for,
the distribution of these elements, compared to what is in the graph already, will have
an effect on the timing performance. However, without the usage and query data, it is
difficult to specify what this distributions might be. Instead, in this assignment, uniformly
sample from a fixed range, e.g., 0 to max vertex label of your graph when generating the
vertices and edges for removing and adding and k-hop neighbourhoods, and a different
range (e.g., greater than the largest vertex label when adding vertices (we do not want
to repeatingly add vertices that are in the graph already).
For generating graphs with different initial average degrees and sizes, you can either
use Pajek or your favourite graph generator, we will not prescribe one particular approach.
Whichever method you decide to use, remember to generate graphs of different average
degrees to evaluate on. Due to the randomness of the data, you may wish to generate a
few graphs with the same average degrees and sizes and take the average across a number
of runs when performing the performance evaluation and analysis.
Analysis
In your analysis, you should evaluate each of your representations and data structures in
terms of the different scenarios outlined above.
Note, you may be generating and evaluating a significant number of graphs and evaluation
datasets, hence we advise you to get started on this part relatively early.
11
5 Report Structure
As a guide, the report could contain the following sections:
Explain your data and experimental setup. Things to include are (brief) explanations
of the data scenarios you decide to evaluate on (e.g., how many additions/removals
operations did you evaluate and why these), size of the graphs, the range of
average degrees tested (add some brief explanation of why this range selection), describe
how the scenarios were generated (a paragraph and perhaps a figure or high
level pseudo code suffice), which approach(es) you decide to use for measuring the
timing results, and briefly describe the fixed set(s) you sampled from to generate
the elements for addition, removal of vertices and edges and k-hop neighbourhood
of the graphs.
Evaluation of the data structures using the generated data (different scenarios,
average degree, graph size). Analyse, compare and discuss your results. Provide
your explanation on why you think the results are as you observed. You may
consider using the known theoretical time complexities of the operations of each
data structure to help in your explanation if useful.
Summarise your analysis as recommendations, e.g., for this certain data scenario
of this average degree (and size), I recommend to use this data structure because...
We suggest you refer to your previous analysis to help.
Evaluate the different parameters of the SIR model and its effect on the number
of susceptible, infected and recovered individuals over time. Which combination
of parameters has the fastest infection spread, which one has the most extensive
number of infected? How does the average timing compare between your three
graph representation? Can you explain why?
6 Submission
The final submission will consist of three parts:
Your Java source code of your implementations. Include only source code
and no class files, we will compile your code on the core teaching serers. Make
sure that your assignment can run only with the code included! That is, it should
be self contained, including all the skeleton code needed to run it.
Your source code should be placed into in a flat structure, i.e., all the files should
be in the same directory/folder, and that directory/folder should be named as
Assign1-. Specifically, if your student number is s12345,
when unzip Assign1-s12345.zip is executed then all the source code files should
be in directory Assign1-s12345.
Your data generation code. Create a sub-directory/sub-folder called “generation”
within the Java source file directory/folder. Place your generation code
within that folder. We will not run the code, but may examine their contents.
Your written report for part B in PDF format, called “assign1.pdf”. Submit
this separately to a Turnitin submission.
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Note: submission of the report and code will be done via Canvas. We will
provide details closer to the submission deadline. We will also provide details on how
the setup we use to test the correctness of your code will be like, so you can ensure your
submitted structure will conform to the automated testing we will perform.
7 Assessment
The project will be marked out of 30. Late submissions will incur a deduction of 3 marks
per day, and no submissions will be accepted 5 days beyond the due date and will attract
0 marks for the assignment.
The assessment in this project will be broken down into two parts. The following
criteria will be considered when allocating marks.
Implementation (10/30):
You implementation will be assessed based on the number of tests it passes in our
automated testing.
While the emphasis of this project is not programming, we would like you to maintain
decent coding design, readability and commenting, hence commenting and
coding style will make up a portion of your marks.
Report (20/30):
The marking sheet in Appendix A outlines the criteria that will be used to guide the
marking of your evaluation report4
. Use the criteria and the suggested report structure
(Section 5) to inform you of how to write the report.
8 Team Structure
This project should be done in pairs (group of two). If you have difficulty in finding a
partner, post on the discussion forum or contact your lecturer. If you want to do the
assignment individually, please contact one of your lecturers first and obtain his
approval.
In addition, please submit what percentage each partner made to the assignment (a
contribution sheet will be made available for you to fill in), and submit this sheet in your
submission. The contributions of your group should add up to 100%. If the contribution
percentages are not 50-50, the partner with less than 50% will have their marks reduced.
Let student A has contribution X%, and student B has contribution Y%, and X > Y .
The group is given a group mark of M. Student A will get M for assignment 1, but student
B will get M
X
Y
.
This semester we will also institute some additional group management initiatives,
including registration and not allowing further group changes in the week before the due
date. We will detail more about this on Canvas.
4Note for the marking guide, if one of the criteria is not demonstrated a tall, then 0 marks will be
awarded for that criteria.
13
9 Academic integrity and plagiarism (standard warning)
Academic integrity is about honest presentation of your academic work. It means acknowledging
the work of others while developing your own insights, knowledge and ideas.
You should take extreme care that you have:
Acknowledged words, data, diagrams, models, frameworks and/or ideas of others
you have quoted (i.e. directly copied), summarised, paraphrased, discussed or mentioned
in your assessment through the appropriate referencing methods
? Provided a reference list of the publication details so your reader can locate the
source if necessary. This includes material taken from Internet sites. If you do not
acknowledge the sources of your material, you may be accused of plagiarism because
you have passed off the work and ideas of another person without appropriate
referencing, as if they were your own.
RMIT University treats plagiarism as a very serious offence constituting misconduct.
Plagiarism covers a variety of inappropriate behaviours, including:
Failure to properly document a source
Copyright material from the internet or databases
Collusion between students
For further information on our policies and procedures, please refer to the following:
https://www.rmit.edu.au/students/student-essentials/rights-and-responsibilities/
academic-integrity.
We will run both code and report similarity checks.
10 Getting Help
There are multiple venues to get help. First point of call should be Canvas, assignment
FAQ (on Canvas), recordings about it and the discussion forum. There will also be weekly
online consultation hours for the assignment (see Canvas for times). In addition, you are
encouraged to discuss any issues you have with your Tutor or Lab Demonstrator. Please
refrain from posting solutions to the discussion forum.
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A Marking Guide for the Report
Design of Evaluation Analysis of Results Report Clarity and Structure
(Maximum = 5 marks) (Maximum = 10 marks) (Maximum = 5 marks)
5 marks 10 marks 5 marks
Data generation and
experimental setup are
well designed, systematic
and well explained. All
suggested scenarios, data
structures and a
reasonable range of
parameters were
evaluated. Each type of
test was run over a
number of runs and
results were averaged.
Analysis is thorough and demonstrates
understanding and critical
analysis. Well-reasoned explanations
and comparisons are provided
for all the data structures, scenarios
and parameters. All analysis,
comparisons and conclusions
are supported by empirical evidence
and possibly theoretical complexities.
Well reasoned recommendations
are given.
Very clear, well structured
and accessible report,
an undergraduate
student can pick up the
report and understand it
with no difficulty.
3.75 marks 7.5 marks 3.75 marks
Data generation and
experimental setup are
reasonably designed,
systematic and explained.
There are at least one
obvious missing suggested
scenarios, data structur

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