MCMICM文档格式.docx
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MCMICM文档格式.docx
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(2)duringanygivenintervaloftime?
(3)duringaparticulartimeofday?
Howdoesthenumberofpotentialconflictsarisingduringthoseperiodsaffectcomplexity?
Doesthepresenceofadditionalsoftwaretoolstoautomaticallypredictconflictsandalertthecontrollerreduceoraddtothecomplexity?
Inadditiontotheguidelinesforyourreport,writeasummary(nomorethantwopages)thattheFAAanalystcanpresenttoJaneGarvey,theFAAAdministrator,todefendyourconclusions.
问题是空中交通管制
致力于记忆的Machol患病,前任首席科学家罗伯特的美国联邦航空局。
提高安全性及减少空中交通管制人员的工作量,美国联邦航空局(FAA)正在考虑加入软件对空中交通管制系统,该系统将自动检测潜在的飞机的飞行路线冲突和警觉的控制器。
最后,在联邦航空局提出了以下问题。
要求:
有两架飞机飞行时,应在空间、空中交通管制人员考虑的对象是太近,需要干预呢?
空域部门是B部分,三维领空的空中交通管制人员控制。
任何领空的领域,我们如何衡量多么复杂,它是由空中交通负荷?
什么是复杂程度取决于数量,同时通过飞机。
(1),在任何一个瞬间吗?
(2)在任何给定的时间间隔内吗?
(三)在一个特定的时间吗?
如何产生一些潜在的冲突,那些时段影响复杂性呢?
是否存在额外的软件工具,自动预测控制器的冲突和警觉的复杂性,减少或增加吗?
此外,对你的指南,写出总结报告(不超过两页),美国联邦航空局分析师会呈现给简Garvey,联邦航空局管理员,保护你的结论。
ProblemBRadioChannelAssignments
Weseektomodeltheassignmentofradiochannelstoasymmetricnetworkoftransmitterlocationsoveralargeplanararea,soastoavoidinterference.Onebasicapproachistopartitiontheregionintoregularhexagonsinagrid(honeycomb-style),asshowninFigure1,whereatransmitterislocatedatthecenterofeachhexagon.
Anintervalofthefrequencyspectrumistobeallottedfortransmitterfrequencies.Theintervalwillbedividedintoregularlyspacedchannels,whichwerepresentbyintegers1,2,3….Eachtransmitterwillbeassignedonepositiveintegerchannel.Thesamechannelcanbeusedatmanylocations,providedthatinterferencefromnearbytransmittersisavoided.
Ourgoalistominimizethewidthoftheintervalinthefrequencyspectrumthatisneededtoassignchannelssubjecttosomeconstraints.Thisisachievedwiththeconceptofaspan.Thespanistheminimum,overallassignmentssatisfyingtheconstraints,ofthelargestchannelusedatanylocation.Itisnotrequiredthateverychannelsmallerthatthespanbeusedinanassignmentthatattainsthespan.
Letsbethelengthofsideofoneofthehexagons.Weconcentrateonthecasethattherearetwolevelsofinterference.
RequirementA:
Thereareseveralconstraintsonfrequencyassignments.First,notwotransmitterswithindistance4sofeachothercanbegiventhesamechannel.Second,duetospectralspreading,transmitterswithindistance2sofeachothermustnotbegivethesameoradjacentchannels:
Theirchannelsmustdifferbyatleast2.Undertheseconstraints,whatcanwesayaboutthespaninFigure1?
RequirementB:
RepeatRequirementA,assumingthegridintheexamplespreadsarbitrarilyfarinalldirections.
RequirementC:
RepeatRequirementsAandB,exceptassumenowmoregenerallythechannelsfortransmitterwithindistance2sdifferbyatleastsomegivenintegerk,whilethoseatdistanceatmost4smuststilldifferbyatleastone.Whatcanwesayaboutthespanandaboutefficientstrategiesfordesigningassignments,asafunctionofk?
RequirementD:
Considergeneralizationsoftheproblem,suchasseverallevelsofinterferenceorirregulartransmitterplacements.Whatotherfactorsmaybeimportanttoconsider?
RequirementE:
Writeanarticle(nomorethan2pages)forthelocalnewspaperexplainingyourfindings.
InterdisciplinaryContestinModeling
Elephants:
WhenisEnough,Enough?
"
Ultimately,ifahabitatisundesirablychangedbyelephants,thentheirremovalshouldbeconsidered-evenbyculling"
.NationalGeographic(EarthAlmanac)-December1999
AlargeNationalParkinSouthAfricacontainsapproximately11,000elephants.Managementpolicyrequiresahealthyenvironmentthatcanmaintainastableherdof11,000elephants.Eachyearparkrangerscounttheelephantpopulation.Duringthepast20yearswholeherdshavebeenremovedtokeepthepopulationascloseto11,000aspossible.Thisprocessinvolvedshooting(forthemostpart)andoccasionallyrelocatingapproximately600to800elephantsperyear.
Recently,therehasbeenapublicoutcryagainsttheshootingoftheseelephants.Inaddition,itisnolongerfeasibletorelocateevenasmallpopulationofelephantseachyears.Acontraceptivedart,however,hasbeendevelopedthatcanpreventamatureelephantcowfromconceivingforaperiodoftwoyears.
HereissomeinformationaboutthePark:
·
Thereisverylittleemigrationorimmigrationofelephants.
Thegenderratioisverycloseto1:
1andcontrolmeasureshaveendeavoredtomaintainparity.
Thegenderratioofnewborncalvesisalsoabout1:
1.Twinsarebornabout1.35%ofthetime.
Cowsfirstconceivebetweentheagesof10and12andproduce,onaverage,acalfevery3.5yearsuntiltheyreachanageofabout60.Gestationisapproximately22months.
Thecontraceptivedartcausesanelephantcowtocomeintooestruseverymonth(butnotconceiving).Elephantsusuallyhavecourtshiponlyoncein3.5years,sothemonthlycyclecancauseadditionalstress.
Acowcanbedartedeveryyearwithoutadditionaldetrimentaleffects.Amatureelephantcowwillnotbeabletoconceivefor2yearsafterthelastdaring.
Between70%and80%ofnewborncalvessurvivetoage1year.Thereafter,thesurvivalrateisuniformacrossallagesandisveryhigh(over95%),untilaboutage60;
itisagoodassumptionthatelephantsdiebeforereachingage70.
ThereisnohuntingandnegligiblepoachinginthePark.
Theparkmanagementhasaroughdatafileoftheapproximateagesandgenderoftheelephantstheyhavetransportedoutoftheregionduringthepast2years.Thisdataisavailableonwebsite:
2000data.xls.UnfortunatelynodataisavailablefortheelephantsthathavebeenshotorremaininthePark.
Youroveralltaskistodevelopandusemodelstoinvestigatehowthecontraceptivedartmightbeusedforpopulationcontrol.Specifically.
Task1:
Developanduseamodeltospeculateaboutthelikelysurvivalrateforelephantsaged2to60.Alsospeculateaboutthecurrentagestructureoftheelephantpopulation.
Task2:
Estimatehowmanycowswouldneedtothedartedeachyeartokeepthepopulationfixedatapproximately11,000elephants.Showhowtheuncertaintyinthedataatyourdisposalaffectsyourestimate.Commentonanychangesintheagestructureofthepopulationandhowhismightaffecttourists.(Youmaywantolookaheadabout30-60years.)
无线信道分配问题,B
我们寻求的无线电频道模型对对称网络的一个大平面发射机地点,以避免干扰。
一个基本的方法是分割成定期六角形网格中(honeycomb-style),如图1所示,在一个变送器地处每一个六边形。
间隔频率是那种发射机的频率。
幕间休息时将被分为定期间隔渠道,我们代表以整数1、2、3…。
每台发射机将指派一个正整数频道。
同样的通道可用在很多地方,避免干扰器附近。
我们的目标是最小宽度的区间的频谱分配通道,不需要一定的约束。
这是一段的概念。
跨距是最小的,在满足约束的条件下,所有的任务中最大的通道用于任何位置。
这并不是必需的,每一个小的跨度被用于一个作业,获跨度。
让我们成为长度的六角形的。
我们专注于案件有两个层次的干扰。
有几个限制对频率的作业。
首先,没有两器内彼此之间的距离4s可以获得相同的频道。
第二,由于内传播,发射机的光谱彼此之间的距离两秒不得给同一或邻近信道:
他们的通道上必须至少两种。
在这些限制,我们又能说些什么关于跨在图1?
重复,B网格的假设条件的例子中任意传播到四面八方。
要求丙级:
重复要求A和B,除非假定现在更一般的渠道不同距离两秒内由发射机至少某些给定的整数k,而那些在距离至多4s仍然必须至少有一个不同。
我们能说什么,有效的跨策略设计作业,作为一种功能的k?
考虑概括的问题,如不同层级的干扰或不规则的发射机安置。
其它因素可能是非常重要的考虑?
写一篇(不超过2页)为当地报纸上发现解释你。
2000ICMContestProblemElephants:
“Ultimately,ifahabitatisundesirablychangedbyelephants,thentheirremovalshouldbeconsidered–evenbyculling.”NationalGeographic(EarthAlmanac)–December1999
Recently,therehasbeenapublicoutcryagainsttheshootingoftheseelephants.Inaddition,itisnolongerfeasibletorelocateevenasmallpopulationofelephantseachyear.Acontraceptivedart,how-ever,hasbeendevelopedthatcanpreventamatureelephantcowfromconceivingforaperiodoftwoyears.
HereissomeinformationabouttheelephantsinthePark:
∙Thereisverylittleemigrationorimmigrationofelephants.
∙Thegenderratioisverycloseto1:
1andcontrolmeasureshaveendeavoredtomaintainparity.
∙Thegenderratioofnewborncalvesisalsoabout1:
1.Twinsarebornabout1.35%ofthetime.
∙Cowsfirstconceivebetweentheagesof10and12andproduce,onaverage,acalfevery3.5yearsuntiltheyreachanageofabout60.Gestationisapproximately22months.
∙Thecontraceptivedartcausesanelephantcowtocomeintooestruseverymonth(butnotconceiving).Elephantsusuallyhavecourtshiponlyoncein3.5years,sothemonthlycyclec
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