查看: 14458|回复: 6

2022年第十一届认证杯数学中国数学建模国际赛（小美赛）赛题发布

[复制链接]

字体大小: 正常放大

ilikenba

1万主题	49 听众	2万积分

TA的每日心情

	奋斗 2024-6-23 05:14

签到天数: 1043 天

[LV.10]以坛为家III

群组: 万里江山

群组: sas讨论小组

群组: 长盛证券理财有限公司

群组: C 语言讨论组

群组: Matlab讨论组

电梯直达

1^#

发表于 2022-12-2 08:01 |只看该作者 |倒序浏览

|招呼Ta 关注Ta

2022小美赛赛题的移动云盘下载地址
https://caiyun.139.com/m/i?0F5CJAMhGgSJx

2022
Certifificate Authority Cup International Mathematical Contest Modeling
http://mcm.tzmcm.cn
Problem A (MCM)
How Pterosaurs Fly
Pterosaurs is an extinct clade of flflying reptiles in the order, Pterosauria. They
existed during most of the Mesozoic: from the Late Triassic to the end of
the Cretaceous. Pterosaurs are the earliest vertebrates known to have evolved
powered flflight. Their wings were formed by a membrane of skin, muscle, and
other tissues stretching from the ankles to a dramatically lengthened fourth
fifinger[1].
There were two major types of pterosaurs. Basal pterosaurs were smaller
animals with fully toothed jaws and long tails usually. Their wide wing mem
branes probably included and connected the hind legs. On the ground, they
would have had an awkward sprawling posture, but their joint anatomy and
strong claws would have made them effffective climbers, and they may have lived
in trees. Basal pterosaurs were insectivores or predators of small vertebrates.
Later pterosaurs (pterodactyloids) evolved many sizes, shapes, and lifestyles.
Pterodactyloids had narrower wings with free hind limbs, highly reduced tails,
and long necks with large heads. On the ground, pterodactyloids walked well on
all four limbs with an upright posture, standing plantigrade on the hind feet and
folding the wing fifinger upward to walk on the three-fifingered “hand”. The fossil
trackways show at least some species were able to run and wade or swim[2].
Pterosaurs sported coats of hair-like fifilaments known as pycnofifibers, which
covered their bodies and parts of their wings[3]. In life, pterosaurs would have
had smooth or flfluffffy coats that did not resemble bird feathers. Earlier sug
gestions were that pterosaurs were largely cold-blooded gliding animals, de
riving warmth from the environment like modern lizards, rather than burning
calories. However, later studies have shown that they may be warm-blooded
(endothermic), active animals. The respiratory system had effiffifficient unidirec
tional “flflow-through” breathing using air sacs, which hollowed out their bones
to an extreme extent. Pterosaurs spanned a wide range of adult sizes, from
the very small anurognathids to the largest known flflying creatures, including
Quetzalcoatlus and Hatzegopteryx[4][5], which reached wingspans of at least
nine metres. The combination of endothermy, a good oxygen supply and strong
1muscles made pterosaurs powerful and capable flflyers.
The mechanics of pterosaur flflight are not completely understood or modeled
at this time. Katsufumi Sato did calculations using modern birds and concluded
that it was impossible for a pterosaur to stay aloft[6]. In the book Posture,
Locomotion, and Paleoecology of Pterosaurs it is theorized that they were able
to flfly due to the oxygen-rich, dense atmosphere of the Late Cretaceous period[7].
However, both Sato and the authors of Posture, Locomotion, and Paleoecology
of Pterosaurs based their research on the now-outdated theories of pterosaurs
being seabird-like, and the size limit does not apply to terrestrial pterosaurs,
such as azhdarchids and tapejarids. Furthermore, Darren Naish concluded that
atmospheric difffferences between the present and the Mesozoic were not needed
for the giant size of pterosaurs[8].
Another issue that has been diffiffifficult to understand is how they took offff.
If pterosaurs were cold-blooded animals, it was unclear how the larger ones
of enormous size, with an ineffiffifficient cold-blooded metabolism, could manage
a bird-like takeoffff strategy, using only the hind limbs to generate thrust for
getting airborne. Later research shows them instead as being warm-blooded
and having powerful flflight muscles, and using the flflight muscles for walking as
quadrupeds[9]. Mark Witton of the University of Portsmouth and Mike Habib of
Johns Hopkins University suggested that pterosaurs used a vaulting mechanism
to obtain flflight[10]. The tremendous power of their winged forelimbs would
enable them to take offff with ease[9]. Once aloft, pterosaurs could reach speeds
of up to 120 km/h and travel thousands of kilometres[10].
Your team are asked to develop a reasonable mathematical model of the
flflight process of at least one large pterosaur based on fossil measurements and
to answer the following questions.
1. For your selected pterosaur species, estimate its average speed during nor
mal flflight.
2. For your selected pterosaur species, estimate its wing-flflap frequency during
normal flflight.
3. Study how large pterosaurs take offff; is it possible for them to take offff like
birds on flflat ground or on water? Explain the reasons quantitatively.
References
[1] Elgin RA, Hone DW, Frey E (2011). The Extent of the Pterosaur Flight
Membrane. Acta Palaeontologica Polonica. 56 (1): 99-111.
2[2] Mark Witton. Terrestrial Locomotion.
https://pterosaur.net/terrestrial locomotion.php
[3] Laura Geggel. It’s Offiffifficial: Those Flying Reptiles Called Pterosaurs
Were Covered in Fluffffy Feathers. https://www.livescience.com/64324-
pterosaurs-had-feathers.html
[4] Wang, X.; Kellner, A.W.A.; Zhou, Z.; Campos, D.A. (2008). Discovery of a
rare arboreal forest-dwelling flflying reptile (Pterosauria, Pterodactyloidea)
from China. Proceedings of the National Academy of Sciences. 105 (6):
1983-87.
[5] Buffffetaut E, Grigorescu D, Csiki Z. A new giant pterosaur with a robust
skull from the latest cretaceous of Romania. Naturwissenschaften. 89 (4):
180-84.
[6] Devin Powell. Were pterosaurs too big to flfly?
https://www.newscientist.com/article/mg20026763-800-were-pterosaurs
too-big-to-flfly/
[7] Templin, R. J.; Chatterjee, Sankar. Posture, locomotion, and paleoecology
of pterosaurs. Boulder, Colo: Geological Society of America. p. 60.
[8] Naish, Darren. Pterosaurs breathed in bird-like fashion and had inflflatable
air sacs in their wings.
https://scienceblogs.com/tetrapodzoology/2009/02/18/pterosaur
breathing-air-sacs
[9] Mark Witton. Why pterosaurs weren’t so scary after all.
https://www.theguardian.com/science/2013/aug/11/pterosaurs-fossils
research-mark-witton
[10] Jeffff Hecht. Did giant pterosaurs vault aloft like vampire bats?
https://www.newscientist.com/article/dn19724-did-giant-pterosaurs
vault-aloft-like-vampire-bats/

2022
Certifificate Authority Cup International Mathematical Contest Modeling
http://mcm.tzmcm.cn
Problem B (MCM)
The Genetic Process of Sequences
Sequence homology is the biological homology between DNA, RNA, or protein
sequences, defifined in terms of shared ancestry in the evolutionary history of
life[1]. Homology among DNA, RNA, or proteins is typically inferred from their
nucleotide or amino acid sequence similarity. Signifificant similarity is strong
evidence that two sequences are related by evolutionary changes from a common
ancestral sequence[2].
Consider the genetic process of a RNA sequence, in which mutations in nu
cleotide bases occur by chance. For simplicity, we assume the sequence mutation
arise due to the presence of change (transition or transversion), insertion and
deletion of a single base. So we can measure the distance of two sequences by
the amount of mutation points. Multiple base sequences that are close together
can form a family, and they are considered homologous.
Your team are asked to develop a reasonable mathematical model to com
plete the following problems.
1. Please design an algorithm that quickly measures the distance between
two suffiffifficiently long(> 103 bases) base sequences.
2. Please evaluate the complexity and accuracy of the algorithm reliably, and
design suitable examples to illustrate it.
3. If multiple base sequences in a family have evolved from a common an
cestral sequence, design an effiffifficient algorithm to determine the ancestral
sequence, and map the genealogical tree.
References
[1] Koonin EV. “Orthologs, paralogs, and evolutionary genomics”. Annual Re
view of Genetics. 39: 30938, 2005.
[2] Reeck GR, de Han C, Teller DC, Doolittle RF, Fitch WM, Dickerson RE,
et al. “Homology” in proteins and nucleic acids: a terminology muddle and
a way out of it. Cell. 50 (5): 667, 1987.

2022
Certifificate Authority Cup International Mathematical Contest Modeling
http://mcm.tzmcm.cn
Problem C (ICM)
Classify Human Activities
One important aspect of human behavior understanding is the recognition and
monitoring of daily activities. A wearable activity recognition system can im
prove the quality of life in many critical areas, such as ambulatory monitor
ing, home-based rehabilitation, and fall detection. Inertial sensor based activ
ity recognition systems are used in monitoring and observation of the elderly
remotely by personal alarm systems[1], detection and classifification of falls[2],
medical diagnosis and treatment[3], monitoring children remotely at home or in
school, rehabilitation and physical therapy , biomechanics research, ergonomics,
sports science, ballet and dance, animation, fifilm making, TV, live entertain
ment, virtual reality, and computer games[4]. We try to use miniature inertial
sensors and magnetometers positioned on difffferent parts of the body to classify
human activities, the following data were obtained.
Each of the 19 activities is performed by eight subjects (4 female, 4 male,
between the ages 20 and 30) for 5 minutes. Total signal duration is 5 minutes
for each activity of each subject. The subjects are asked to perform the activ
ities in their own style and were not restricted on how the activities should be
performed. For this reason, there are inter-subject variations in the speeds and
amplitudes of some activities.
Sensor units are calibrated to acquire data at 25 Hz sampling frequency.
The 5-min signals are divided into 5-sec segments so that 480(= 60 × 8) signal
segments are obtained for each activity.
The 19 activities are:
1. Sitting (A1);
2. Standing (A2);
3. Lying on back (A3);
4. Lying on right side (A4);
5. Ascending stairs (A5);
16. Descending stairs (A6);
7. Standing in an elevator still (A7);
8. Moving around in an elevator (A8);
9. Walking in a parking lot (A9);
10. Walking on a treadmill with a speed of 4 km/h in flflat position and 15 deg
inclined positions (A10);
11. Walking on a treadmill with a speed of 4 km/h in 15 deg inclined positions
(A11);
12. Running on a treadmill with a speed of 8 km/h (A12);
13. Exercising on a stepper (A13);
14. Exercising on a cross trainer (A14);
15. Cycling on an exercise bike in horizontal position (A15);
16. Cycling on an exercise bike in vertical position (A16);
17. Rowing (A17);
18. Jumping (A18);
19. Playing basketball (A19).
Your team are asked to develop a reasonable mathematical model to solve
the following problems.
1. Please design a set of features and an effiffifficient algorithm in order to classify
the 19 types of human actions from the data of these body-worn sensors.
2. Because of the high cost of the data, we need to make the model have
a good generalization ability with a limited data set. We need to study
and evaluate this problem specififically. Please design a feasible method to
evaluate the generalization ability of your model.
3. Please study and overcome the overfifitting problem so that your classififi-
cation algorithm can be widely used on the problem of people’s action
classifification.
The complete data can be downloaded through the following link:
https://caiyun.139.com/m/i?0F5CJUOrpy8oq
2Appendix: File structure
• 19 activities (a)
• 8 subjects (p)
• 60 segments (s)
• 5 units on torso (T), right arm (RA), left arm (LA), right leg (RL), left
leg (LL)
• 9 sensors on each unit (x, y, z accelerometers, x, y, z gyroscopes, x, y, z
magnetometers)
Folders a01, a02, ..., a19 contain data recorded from the 19 activities.
For each activity, the subfolders p1, p2, ..., p8 contain data from each of the
8 subjects.
In each subfolder, there are 60 text fifiles s01, s02, ..., s60, one for each
segment.
In each text fifile, there are 5 units × 9 sensors = 45 columns and 5 sec × 25
Hz = 125 rows.
Each column contains the 125 samples of data acquired from one of the
sensors of one of the units over a period of 5 sec.
Each row contains data acquired from all of the 45 sensor axes at a particular
sampling instant separated by commas.
Columns 1-45 correspond to:
• T_xacc, T_yacc, T_zacc, T_xgyro, ..., T_ymag, T_zmag,
• RA_xacc, RA_yacc, RA_zacc, RA_xgyro, ..., RA_ymag, RA_zmag,
• LA_xacc, LA_yacc, LA_zacc, LA_xgyro, ..., LA_ymag, LA_zmag,
• RL_xacc, RL_yacc, RL_zacc, RL_xgyro, ..., RL_ymag, RL_zmag,
• LL_xacc, LL_yacc, LL_zacc, LL_xgyro, ..., LL_ymag, LL_zmag.
Therefore,
• columns 1-9 correspond to the sensors in unit 1 (T),
• columns 10-18 correspond to the sensors in unit 2 (RA),
• columns 19-27 correspond to the sensors in unit 3 (LA),
• columns 28-36 correspond to the sensors in unit 4 (RL),
• columns 37-45 correspond to the sensors in unit 5 (LL).
3References
[1] Mathie M.J., Celler B.G., Lovell N.H., Coster A.C.F. Classifification of basic
daily movements using a triaxial accelerometer. Med. Biol. Eng. Comput.
42(5), 679-687, 2004
[2] Kangas M., Konttila A., Lindgren P., Winblad I., Ja¨msa¨ T. Comparison of
low-complexity fall detection algorithms for body attached accelerometers.
Gait Posture 28(2), 285-291, 2008
[3] Wu W.H., Bui A.A.T., Batalin M.A., Liu D., Kaiser W.J. Incremental diag
nosis method for intelligent wearable sensor system. IEEE T. Inf. Technol.
B. 11(5), 553-562, 2007
[4] Shiratori T., Hodgins J.K. Accelerometer-based user interfaces for the con
trol of a physically simulated character. ACM T. Graphic. 27(5), 2008

2022
Certifificate Authority Cup International Mathematical Contest Modeling
http://mcm.tzmcm.cn
Problem D (ICM)
Whether Wildlife Trade Should Be Banned for a Long
Time
Wild-animal markets are the suspected origin of the current outbreak and the
2002 SARS outbreak, And eating wild meat is thought to have been a source
of the Ebola virus in Africa. Chinas top law-making body has permanently
tightened rules on trading wildlife in the wake of the coronavirus outbreak,
which is thought to have originated in a wild-animal market in Wuhan. Some
scientists speculate that the emergency measure will be lifted once the outbreak
ends.
How the trade in wildlife products should be regulated in the long term?
Some researchers want a total ban on wildlife trade, without exceptions, whereas
others say sustainable trade of some animals is possible and benefificial for peo
ple who rely on it for their livelihoods. Banning wild meat consumption could
cost the Chinese economy 50 billion yuan (US $ 7.1 billion) and put one mil
lion people out of a job, according to estimates from the non-profifit Society of
Entrepreneurs and Ecology in Beijing.
A team led by Shi Zheng-Li and Cui Jie of the Wuhan Institute of Virology
in China, chasing the origin of the deadly SARS virus, have fifinally found their
smoking gun in 2017. In a remote cave in Yunnan province, virologists have
identifified a single population of horseshoe bats that harbours virus strains with
all the genetic building blocks of the one that jumped to humans in 2002, killing
almost 800 people around the world. The killer strain could easily have arisen
from such a bat population, the researchers report in PLoS Pathogens on 30
November, 2017. Another outstanding question is how a virus from bats in
Yunnan could travel to animals and humans around 1,000 kilometres away in
Guangdong, without causing any suspected cases in Yunnan itself. Wildlife
trade is the answer. Although wild animals are cooked at high temperature
when eating, some viruses are diffiffifficult to survive, humans may come into contact
with animal secretions in the wildlife market. They warn that the ingredients
are in place for a similar disease to emerge again.
Wildlife trade has many negative effffects, with the most important ones being:
1Figure 1: Masked palm civets sold in markets in China were linked to the SARS
outbreak in 2002.Credit: Matthew Maran/NPL
• Decline and extinction of populations
• Introduction of invasive species
• Spread of new diseases to humans
We use the CITES trade database as source for my data. This database
contains more than 20 million records of trade and is openly accessible. The
appendix is the data on mammal trade from 1990 to 2021, and the complete
database can also be obtained through the following link:
https://caiyun.139.com/m/i?0F5CKACoDDpEJ
Requirements Your team are asked to build reasonable mathematical mod
els, analyze the data, and solve the following problems:
1. Which wildlife groups and species are traded the most (in terms of live
animals taken from the wild)?
2. What are the main purposes for trade of these animals?
3. How has the trade changed over the past two decades (2003-2022)?
4. Whether the wildlife trade is related to the epidemic situation of major
infectious diseases?
25. Do you agree with banning on wildlife trade for a long time? Whether it
will have a great impact on the economy and society, and why?
6. Write a letter to the relevant departments of the US government to explain
your views and policy suggestions.