2019第八届数学中国数学建模国际赛(小美赛)赛题
Problem A(MCM)
Heat from radioactivity
Suppose we make a piece of radioactive material with a long half-life into a specific
shape. In this material, the nucleus releases a proton in a random direction
as it decays. We assume that the energy of the proton carrying is a constant.
Protons, when they pass through the dense material itself, release the energy
they carry and convert it into heat. The relationship between the proton’s energy
release rate and its travel distance in the material is in accordance with
the Bragg peak curve1, that is, most of the energy is released when it travels to
a certain constant distance. We put this material in water, and we can assume
the Bragg peak curve of the proton in water is the same as in the material.
The question is what shape is the material made to maximize the total energy
released by the proton in the material?
Problem B(MCM)
The Cold Air Outlet Design in a Data Center
This is a problem faced by air conditioning design in data centers. In some
data centers, computer cabinets are open and arranged in three or four rows in a
room. The cooled air enters the room through the main pipe and is divided into
three or four branch pipes. The outlet of the branch pipe can only be placed on
the ceiling, blowing down, and hot air is discharged from a hot air containment
at one side of the room. The outlet of each branch pipe should not exceed
three1. Due to the mixing of cold air and hot air, the utilization efficiency of
cold air is reduced. Therefore, we need to consider air flow to reduce the cooling
amount wasted in corridors and gaps.
We need to take into account the height of the ceiling, the height of the
cabinet and the typical heat output of different cabinets. We assume that the
total cooling capacity of the air conditioner can meet the requirements of the
operation of the equipment room. When we determine the layout of the cabinet,
how to set the position of the air conditioning air outlet is the best solution?
Problem C(ICM)
Predict the Time Required to Pass a Congested Road
Section
In the navigation software, the estimation of travel time is often an important
function. Existing navigation software often obtains real-time GPS data through
the taxies or the vehicles installed the software to determine the current road
conditions. In the case of severe traffic jams, the speed of the car is slow,
so the estimation of the speed is very inaccurate. The consequence is that the
accuracy of the estimated traffic jam time is very poor. The actual time required
is sometimes even several times to ten times different from the forecast time.
Our question is how to predict the time to pass the traffic jam? Please collect
the available data and build a more accurate model to solve this problem.
Problem D(ICM)
What is the Answer for Secure Elections?
With the U.S. heading into a pivotal election, little progress has been made on
ensuring the integrity of voting systemsa concern that retook the spotlight when
the 2016 presidential election ushered Donald Trump into theWhite House amid
allegations of foreign interference.
Existing voting systems do leave plenty of room for suspicion: Voter impersonation
is theoretically possible (although investigations haverepeatedlyfoundnegligible
rates for this in the U.S.); mail-in votes can bealtered or stolen;
election officials might count inaccurately; and nearly every electronic voting
machine hasprovedhackable. Not surprisingly, a Gallup poll published prior
to the 2016 election founda third of Americansdoubted votes would be tallied
properly.
Blockchain advocates say the technology addresses the root cause of voting
systems insecuritythe fact that voting can be controlled by a single person,
group or machine.Argentinas Net Party provides an example of what can go
wrong. The tiny political party fields candidates who promise to strictly follow
citizens bidding as expressed on an online polling platform. When its leaders
were pondering interparty alliances in early 2014, they put the decision to a vote
among party members. To their horror, they discovered database administrators
were selectively delaying new voter registrations until after the referendum,
skewing the participant pool toward the administrators preferred outcome.
Blockchain, the technology behind the bitcoin digital currency, is a decentralized
public ledger of transactions that no one person or company owns or
controls. Instead, every user can access the entire blockchain, and every transfer
of funds from one account to another is recorded in a secure and verifiable form
by using mathematical techniques borrowed from cryptography. With copies
of the blockchain scattered all over the planet, it is considered to be effectively
tamper-proof.
The challenges that bitcoin poses to law enforcement and international currency
controls have been widely discussed. But the blockchain ledger has uses
far beyond simple monetary transactions.
Perhaps the most encouraging benefit of blockchain technology is the incen-
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tive it creates for participants to work honestly where rules apply equally to
all. Bitcoin did lead to some famous abuses in trading of contraband, and some
nefarious applications of blockchain technology are probably inevitable. The
technology doesnt make theft impossible, just harder. But as an infrastructure
that improves societys public records repository and reinforces representative
and participatory legal and governance systems, blockchain technology has the
potential to enhance privacy, security and freedom of conveyance of datawhich
surely ranks up there with life, liberty and the pursuit of happiness.
Functionally, a blockchain is simply a convoluted database. Each entry in
Bitcoins database, for example, is a transaction in a digital ledger. The ledger
publicly lists all transactions to date, implicitly specifying who retains how
much money. What distinguishes a blockchain from conventional databases is
that it enables multiple parties to share a database without centralized control.
Most conventional databases have one authoritative computer that governs the
process of adding data. In a blockchain, that trusted gatekeeper is replaced by
computers all over the internet, each maintaining its own copy of the database.
These computers act as validators for new data: When Alice wants to send
money to Bob, she broadcasts the transaction to the validators, which must
confirm for themselves the transaction adheres to the blockchains rules (for
example, that Alice has not sent more bitcoins than she owns). Once a majority
of the network has accepted the transactions, they become the de facto consensus
history.
Although blockchains most prominent uses are monetary, there is no reason
they cannot store other types of dataand votes would seem an excellent fit. An
ideal voting system resists corruption by authorities or hackers and empowers
citizens and auditors to agree on an elections outcome. Conveniently, auditable
consensus among parties who do not fully trust one another is exactly what
blockchains offer.
Are Blockchains the Answer for Secure Elections?Probably Not.
Suppose you are a technical advisor of the general election inspection committee.
You should finish the following tasks:
1. Build an underlying design or set of algorithms to solve the problem of
online voting using blockchain technology.
2. Evaluate the possible problems of blockchain technology in solving voting
problems, and try to improve it.
3. Experts in both cybersecurity and voting see blockchains as needlessly
complicated, and no more secure than otheronlineballots. Is it possible to
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reduce the complexity of blockchain technology and improve security by
combining with other technologies?
4. Write a one-page technical note describing your new idea, algorithm, and
results.
Your submission should consist of:
• One-page Summary Sheet,
• One-page Technical Note,
• Your solution of no more than 30 pages, for a maximum of 32 pages with
your summary and technical note.
Note: Reference list and any appendices do not count toward the 32-page
limit and should appear after your completed solution.
哇谢谢真是太有用了太谢谢楼主了
太感谢楼主了
感谢博主发的题目
真的太太太有用了，这个网站做的非常好。
这个也太太有用啦，博主真是太用心了。
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