nondeterministic PDAs none of the above nonedeterministic F.pdf

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The document discusses different types of machines and their relative powers to recognize formal languages. Nondeterministic pushdown automata and nondeterministic finite state automata can recognize more languages than their deterministic counterparts. Deterministic Turing machines are more powerful than deterministic finite state automata and can recognize any formal language, but are less powerful than nondeterministic machines.

Education

nondeterministic PDA's
none of the above
nonedeterministic FSAs
deterministic FSAs
deterministic turning machines
least powerful machines that can recognize language of all C programs that don't go into an
infinite loop recognizes fewer languages than nondeterministic FSA's reads and writes characters
to and from an array can recognize any language least powerful machines that can recognize
language of all valid C programs named after Alan Turing these nondeterministic machines
recognize more languages than their deterministic counterparts corresponds with intuitive notion of
"algorithm" Type-2 Grammar, Context-free pushes and pops characters using a stack

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Non-native species management n-Native Species Management: 12. Explain two 'temporal' ways in which a species is determined to be 'native' or not native. 13. Using the coyote, grey wolf, red wolf example explain the spatial dynamics of the range changes in each species and the reasons for these range changes. Given this, explain why you think the coyote should be considered native or not in eastern North America? 14. Why is it sometimes unclear if a species is native or introduced? Given an example and explain why it is unclear for that species. 15. If we 'normalize' invasive alien species/area of a country - what geosraphloal pattern stands out regarding the proportion of invasive alien species? 16. What are the main invasion pathways by which species invade? Give 2 examples. 17. What ecological characteristics do most invasive species share? What is the one necessary requirement for an invasive species to be successful? 18. There are several factors associated with the likelihood of establishment for invasive species. What is the difference between the 'enemy release hypothesis' and 'the snowball effect'. Which of these processes are invasive deer in South America an example of? Briefly explain. 19. What 2 factors are generally responsible for high risk of invasion?20. What 2 factors are key to risk modeling? 21. In what ways can the introduction of invasive species be prevented? Give an example. 22. How do we know if an introduced species has become 'invasive' i.e., is spreading? 23. What are the aims of non-native species management? Give an example of successful eradication and an example of a mechanism of management..

Nonnative species management nNative Species Management 1.pdf

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Nora's utility function is given by U=ln(C)+ln(L), where U is utility, C is consumption, and L is leisure. The total time Nora has is T=1 and is a utility maximizer. Before the Covic pandemic, the wage rate is 10 , and Nora has no non-labor income. When the pandemic hit and part of the economy was locked down, Norats decreased to 8 . However, the government provided income support by sending out a non-labor income of 5 to everyone, including Nora. Nora still has a total amount of time T=1 for leisure and work during the pandemic. Which of the following statements is correct? Before the pandemic, Nora's labor supply is 0.2 . Before the pandemic, Nora spent time equal to 0.2 on leisure. Before the pandemic, Nora's consumption was 9 . During the pandemic, Nora's labor supply is 0.5 . During the pandemic, Nora was better off for having a higher utility level. During the pandemic, Nora's labor supply is unchanged becauses income effects were perfectly offset by the substitution effect from the wage drop..

Noras utility function is given by UlnC+lnL where U i.pdf

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(Noce it any boxes seem not applicable, leave blank.) "The following table, based on government data, shows the frequency distribution of births by day of the week for all regixered births in the United States in a recent year. Test the null hypothesis that all seven days of the week are equally likely for childbirth. Number of Births (in 10,000) by Day of the Week, United States Source: National vital Statistics Reports, 60 (1) (November 2, 2011). Tes Scatistici According to your table, the P-value is bounded by:.

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Nonprofit corporations are also called Select one: a. eleemosynary institutions b. Subchapter C corporations c. alien corporations d. private corporations Responsibilities of a corporation's boards of directors include all but which of the following? Select one: a. authorize or approve the payment of dividends b. authorize or approve the selection, supervision, and removal of officers c. authorize or approve the adoption, appeal, or amendment of the corporate bylaws d. authorize or approve day-to-day corporate management decisions.

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Nomuras Integration of Lehman Brothers Assets in Asia and Europe Mike W. Peng, University of Texas at Dallas The Opportunity of a Lifetime In September 2008, Lehman Brothers went bankrupt. Britains Barclay Capital bought Lehmans North America operations for $3.75 billion. Lehmans assets in Asia and Europe were purchased by Nomura for the bargain-basement price of $200 million. Founded in 1925, Nomura is the oldest and largest securities brokerage and investment banking firm in Japan. Although Nomura had operated in 30 countries prior to the Lehman deal in 2008, it had always been known as a significant but still primarily regional (Asian) player in the big league of the financial services industry. In addition to Lehman, the list of elite investment banking firms in early 2008 would include Goldman Sachs, Morgan Stanley, Bear Stearns, JP Morgan, and Citigroup of the United States; Credit Suisse and UBS of Switzerland; and Deutsche Bank of Germany. No one would include Nomura in this group. Nomura viewed itself primarily as an Asian version of Merrill Lynch. The tumultuous 2008 left Bear Stearns dead first, Lehman second, and all of the firms in the big league named above in deep financial trouble. To Nomura, this became the opportunity of a lifetime. Within a lightning 24 hours, CEO Kenichi Watanabe decided to acquire Lehmans remnants in Asia and Europe. Some of the Lehman assets were dirt cheap. For example, its French investment banking operations were sold to Nomura for only one euro (that is, 1!). Overall, by cherry-picking Lehmans Asia and Europe operations and adding 8,000 employees who tripled Nomuras size outside Japan, Nomura transformed itself into a global heavyweight overnight. The question was: Does Nomura have what it takes to make this acquisition a success? Integration Challenges The answer was a decisive No! from Nomuras investors, who drove its shares down by 70% by 2012. Since the purchase price seemed reasonable and there was little evidence that Nomura overpaid, the biggest challenge was post acquisition integration, merging a hard-charging New York investment bank with a hierarchical Japanese firm that still largely practices lifetime employment. Clearly, Lehmans most valuable, rare, and hard-to-imitate assets are its talents. To ensure that Nomura retained most of the ex-Lehman talents, Nomura set aside a compensation pool of $1 billion (five times the acquisition price) and guaranteed all ex-Lehman employees who chose to stay with Nomura not only their jobs, but also their 2007 pay level (including bonuses) for three years. About 95% of them accepted Nomuras offer. Given the ferociousness of the financial meltdown in 20082009 (which, if you remember, was triggered by Lehmans collapse), many employees at other firms that were not bankrupt lost their jobs. The fact that Nomura guaranteed both jobs and pay levels was widely appreciated by ex-Lehman employees who otherwise would have been devastated. Instead, acquiring Leh.

Nomuras Integration of Lehman Brothers Assets in Asia and .pdf

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Non random sampling offers the best chance of choosing a sample that accurately represents the population from which it was selected True False Random sampling offers the best chance of choosing a sample that accurately represents the population from which it was selected True False A population has parameters and a sample has statistics True False A population has statistics and a sample has parameters True False Availability or convenience sampling is a type of random sampling True False.

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Nestl'de ERP ve Deiim Ynetimi vaka almas analizi Vaka incelemesini okuyun ve sorular yantlayn: SAP ile 200 milyon $'lk bir szleme ve danmanlk hizmetleri ve bakm iin 80 milyon $'dan fazla bir szleme imzaladktan bir yl sonra, Londra'daki HSBC menkul kymetleri Nestl tavsiyelerini drd SA hisse senedi. Kurumsal Kaynak Planlamas (ERP) projesi muhtemelen uzun vadeli faydalar salayacak olsa da, projenin irket zerinde ksa vadeli etkisinin ne olaca merak ediliyordu. Nestl Company'nin hedefi, dnyann nde gelen beslenme, salk ve zindelik irketi olarak bir i kurmaktr. irket, 1867 ylnda Henri Nestl'nin bebekler iin ilk stl mamay gelitirmesi ve bir komunun ocuunun hayatn kurtarmasyla kuruldu. Nestl'nin genel merkezi Vevey, svire'de olup dnya apnda ofisleri bulunmaktadr. irket, ikolata ve ekerlemelerin yan sra, balca markalaryla da tannmaktadr. Markalar Nestl ABD altnda birletirildi ve yeniden organize edildi, ancak blmler hala corafi olarak dank genel merkezlere sahipti ve kendi i kararlarn zerk bir ekilde alyordu. Ayrca, irket genelindeki eitli sistemleri ve sreleri incelemekle grevli bir ekip, birok sorunlu fazlalk buldu. rnein Nestl USA markalar ayn satcya vanilya iin yirmi dokuz farkl fiyat dyordu. Nestl ABD Bakan Yardmcs ve CIO'su Jeri Dunn, "Her tesis satcdan vanilya alr ve satc da alabildiini dnd her eyi alrd. Ve kontrol edemememizin nedeni, her blmn ve her fabrikann vanilyaya cannn istedii ad vermesidir. Yani siz buna 1234 diyebilirsiniz ve arkasnda tam bir spesifikasyon olabilir ve ben buna 7778 diyebilirim. Karlatrma imkanmz yoktu. Dunn ve ekibi, her marka iin maliyet tasarrufu ve grup satn alma gc salayacak teknoloji standartlar ve ortak sistemler nerdi. Dunn daha sonra dnya apndaki Nestl projeleri iin ortak bir metodolojinin uygulanmasn kolaylatrmak iin svire'ye gitti, ancak iki yl sonra CIO olarak Amerika'ya dndnde, tavsiyelerinden yalnzca birkann yerine getirildiini grd. Dunn'n hatrlad gibi, "Ekibim standartlar belirleyebilirdi, ancak uygulamann kullanma sunulmas iletmelerin keyfine kalm bir eydi." Dunn'n eyaletlere dn, ABD bakan ve CEO'su Joe Weller'in tm bireysel markalar skca entegre olmu tek bir irkette birletirme vizyonunu takip etti. irketin durumu hakknda dnen Dunn, Ne kadar irkin olduunu bildiklerini sanmyorum. Dokuz farkl defteri kebirimiz ve yirmi sekiz mteri giri noktamz vard. Birden fazla satn alma sistemimiz vard. Belirli bir satcyla ne kadar hacim yaptmza dair hibir fikrimiz yoktu nk her fabrika kendi frn satc ustalarn kurdu ve kendi bana satn ald. Dunn ve finans, tedarik zinciri, datm ve satn alma departmanlarndan bir grup ynetici, Nestl'nin neyi doru yaptn ve nelerin iyiletirilebileceini incelemek iin bir kilit payda ekibi oluturdu. Bulgularn Joe Weller ve dier st dzey yneticilere sunmalar iin onlara yaklak iki saat verildi, ancak toplant tm gn ald. Payda ekibin plan, uygulanmas ila be yl srecek bir mihenk ta projesi olarak SAP'yi ieriyordu. Dunn'n iaret ettii gibi, Bunun bir i sreci yeniden dzenlemesi olacan ve i yapma eklinizi.

Nestlde ERP ve Deiim Ynetimi vaka almas analizi Vaka i.pdf

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No question providing a table that passes This is wha.pdf

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No puedo dejar de toser: un estudio de caso sobre el sistema respiratorio Mike est sentado en su suite de entrenamiento atltico sintiendo pena por s mismo. Se mud del sur de California para jugar ftbol en la Universidad del Norte de Minnesota (NMU) como un jugador altamente reclutado. Todo iba bien hasta que se enferm de un terrible resfriado. Pronto se recuper, pero ahora se encuentra con una tos seca persistente y dificultad para recuperar el aliento cada vez que se esfuerza, que es todos los das! Tambin nota que ha empeorado a medida que el clima se ha vuelto ms fro. Para empeorar las cosas, Mike se siente y parece estar fuera de forma, por lo que su entrenador lo ha estado criticando por perseverar. Unos das despus, Mike le cuenta su historia a JP, el entrenador atltico principal de NMU. Estoy pensando que mi resfriado est regresando, o algo ms est mal conmigo. Cuando estoy pasando el rato, como ahora, me siento bien. Pero tan pronto como empiezo a correr me quedo sin aliento y no puedo dejar de toser. JP escucha los sonidos respiratorios de Mike con su estetoscopio, pero no escucha nada anormal. Entonces le dice a Mike que regrese tan pronto como regresen los sntomas durante la prctica de ftbol. Veinte minutos despus, Mike est de vuelta en la sala de entrenamiento atltico, con sibilancias audibles, tos y dificultad para respirar. El mdico del equipo, el Dr. McInnis, se encuentra all y realiza un examen fsico completo. Tambin realiza pruebas de funcin pulmonar con Mike mediante espirometra, incluida una capacidad vital forzada (FVC) y un volumen espiratorio forzado en un segundo (FEV1). Le indica a Mike que tome una inhalacin mxima y luego exhale lo ms fuerte y mximamente posible en el espirmetro. Segn sus hallazgos, el Dr. McInnis le dice a Mike que cree que est experimentando una broncoconstriccin inducida por el fro (tambin llamada asma inducida por el fro), que empeora con el esfuerzo. El mdico le explica a Mike que su reciente infeccin de las vas respiratorias superiores probablemente inflam sus vas respiratorias, hacindolas hipersensibles y reactivas a los irritantes, como el fro y el esfuerzo fsico. Cuando Mike hace ejercicio en las fras tardes otoales de Minnesota, sus sensibles vas respiratorias se contraen temporalmente, causando los sntomas que est experimentando. El asma es casi siempre una condicin reversible. El Dr. McInnis prescribe dos bocanadas de un inhalador de albuterol, para usar 10 minutos antes de una sesin de ejercicio en el fro. Preguntas para pensar: 1. Describa la relacin entre la presin intrapulmonar, la presin atmosfrica y el flujo de aire durante la inspiracin y espiracin normales, haciendo referencia a la ley de Boyle. 2. La resistencia vara en las vas respiratorias de conduccin de Mike. Usando su comprensin de la anatoma respiratoria, explique en qu parte de sus vas respiratorias la resistencia es mayor y por qu. 3. Varios factores fsicos que influyen en la eficiencia de la ventilacin pulmonar son la disten.

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No publique esto como "respondido" si NO lo responde... la ltima persona lo public como respondido y no respondi las preguntas. gracias. DENNIS TIENE UNA MALA SEMANA DA UNO: LUNES 10:00 a.m En el taller de ABC Manufacturing, Dennis, un empleado afroamericano de 52 aos, tiene la siguiente conversacin con una compaera de trabajo hispana, Rosa, y su jefe, Bryce: DENNIS: Oye, Rosa, conoces a mi amigo Jimmy, que trabaja en Core Enterprises? ROSA: S, es el tipo que hace el mismo trabajo que nosotros. DENNIS: S, tiene exactamente el mismo trabajo. Bueno, l y yo estbamos hablando de negocios y dej escapar cunto dinero gana. Quieres adivinar? ROSA: No. DENNIS: $50,000! ROSA: Dlares? DENNIS: No, siclos! S, dlares. Adems, tiene tres semanas de vacaciones pagadas. Adems, potencial de bonificacin de cinco mil dlares y su seguro de salud es increble! ROSA: Qu?! Estamos perdiendo el tiempo. Tenemos que pensar en formar un sindicato. DENNIS: Cuntame sobre eso. Cuando le dije a Jimmy cunto dinero gano, se ri tanto que pens que se le saldra la cerveza por la nariz. Dijo que estamos recibiendo salarios de esclavos y que si estuviramos en cualquier otra empresa, estaramos ganando mucho ms dinero. BRYCE: Hola, chicos, de qu estn hablando? DENNIS: Nada, Bryce. Solo poltica. BRYCE: Escucha, sabes que no me gusta que hables de sueldo. Provoca problemas y va en contra de nuestra poltica. 13:00 En su hora de almuerzo, Dennis revisa el correo electrnico de su empresa, donde encuentra un correo electrnico de Jimmy. Adjunto al correo electrnico hay una foto de una mujer desnuda con una leyenda divertida. Dennis lo reenva a sus amigos varones en el departamento de envos de ABC. Se produce un intercambio de correo electrnico "solo para adultos" entre los destinatarios del correo electrnico. Este tipo de actividad no es nueva para Dennis. Durante su descanso, Dennis tambin hace una llamada telefnica a Brad Hoffa, el representante sindical de la Federacin Internacional de Personas que Trabajan, preguntando sobre posibles elecciones sindicales en ABC Manufacturing. DA DOS: MARTES 11:30 am Durante una reunin de personal sobre cuotas de produccin, que incluye a Bryce, Rosa y otros trabajadores, Dennis saca a relucir el tema de los salarios. Surge la siguiente conversacin: DENNIS: Bryce, tengo un amigo que trabaja en Core Enterprises. Usted los conoce? BRYCE: Por supuesto, son nuestra competencia ms dura. DENIS: Correcto. Entonces, este amigo mo hace bsicamente el mismo trabajo que yo, y dej escapar cunto dinero gana. Todos los que estamos aqu merecemos un aumento! BRYCE: Bueno, Dennis, no creo que este sea el momento apropiado para discutir eso. Entonces, continuando, si alguien puede mirar la columna 3 en el pizarrn. . . DENNIS: Rosa, cunto ganas? ROSA: $38,000. DENNIS: Ja, muy mal. Los muchachos y yo ganamos $42,000, y siguen siendo salarios de esclavos. Rosa, incluso tienes antigedad sobre nosotros. Qu tienes que decir a eso, Bryce? Realmente eres un nazi! BRYCE: Espera, Den.

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NO NECESITO EXPLICAR P1 El iPhone 11 vino con la caracters.pdf

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No es necesario que expliques, solo elige la respuesta correcta. 13 - En 2008, el estudiante canadiense Christopher Charles estaba trabajando en la zona rural de Camboya, viviendo en una tpica casa camboyana sobre pilotes. No tena electricidad, ni agua corriente y, dice, mucho tiempo para sentarse y pensar. "Estaba observando la prevalencia de la anemia y la infeccin parasitaria en la regin y comenc a descubrir este enorme problema sobre el que nadie estaba haciendo nada", en Camboya. La anemia es una enfermedad que est relacionada con niveles bajos de hierro en la sangre y casi la mitad de la poblacin de Camboya la padece. Charles decidi que quera hacer algo. Las personas han estado agregando hierro a sus alimentos a travs de ollas de hierro durante aos, y otros toman suplementos. As que a Charles se le ocurri lo que pens que era una alternativa simple: dar a los aldeanos pequeos bloques de hierro para que los colocaran en sus ollas. El hierro se libera lentamente a medida que el agua hierve y tambin se libera en los alimentos cocinados en ella. Charles dice que al principio la gente los odiaba. Pensaron que eran feos y que les rayaran las ollas, as que las convirtieron en topes para puertas. Pero l sigui en ello. Luego vino su "momento Eureka" cultural, cuando se dio cuenta de que en la Camboya rural casi todo gira en torno al pescado. La gente gana dinero pescando, son una gran parte de la dieta jemer, su folclore, incluso su moneda, el riel, lleva el nombre de un pez. "Y me top con este tipo de pez que se llama Try Kantrop y est asociado con la suerte en el folclore de la aldea, por lo que tena el beneficio adicional de ser atractivo y resonaba con la gente en un sentido de suerte, buena salud y bienestar. ", dice Carlos. "Y realmente ayud a vender la idea a los camboyanos con los que estaba trabajando y lograr que se involucraran en el proyecto". Y naci Lucky Iron Fish. Y espera convencer a los escpticos de la comunidad cientfica y aumentar el cofre de guerra de $ 1.2 millones que la compaa ya ha recaudado. Mientras tanto, la compaa Lucky Iron Fish comenz a comercializar su pescado a fines del ao pasado aqu en Camboya, en el extranjero y en lnea. "Obviamente, muchos turistas los compran porque son un hermoso recuerdo de Camboya y tienen una gran historia detrs de ellos, pero la gente tambin los ha estado comprando porque tienen a alguien en la familia que est anmico", dice. Han vendido lo suficiente, tanto aqu como en su mayora en lnea, que la compaa ahora est regalando varios miles a sus socios de ONG. Qu tipo de estrategia de adaptacin se ejemplifica mejor en el artculo anterior? A - Externalizacin B - Innovacin C - Enfoque D-Variacin 14- Los productos de Apple se disean en California pero se ensamblan en China. Los trabajadores de Foxconn trabajan seis das, doce horas al da y ganan menos de $17 por da. 23.000 trabajadores trabajan en la lnea de montaje (solo 50 ciudades de EE. UU. son lo suficientemente grandes como para proporcionar .

No es necesario que expliques solo elige la respuesta corre.pdf

saravanan544051

No Hand WRITING please 200 words minimum this is a discuss.pdf

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No Dox 24hr+ Dox You design some constructs, put them in a virus, and infect cells. You then do immunofluorescence staining to visualize the presence of Cas9. The results are shown above. If the secondary antibody you used is a green goat anti rat secondary antibody, what kind of primary antibody did you use? Goat anti Cas9 primary antibody Rat anti Cas9 primary antibody Goat anti Dox primary antibody Rat anti Dox primary antibody.

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no additional information provided PART 2, EXERCISE B - Stratum contours from outcrop traces This map shows the outcrop pattern for a deformed sedimentary layer. The stippling denotes the map region where one finds rocks underlain by layer at the surface, and the continuous dark line gives the trace of the bottom of the bed. In unstippled areas, the bottom of the bed was eroded away. 1. Draw and label stratum contours for the base of the layer. 2. Use the stratum contours to determine whether the structure represented on the map is an anticline, syncline, plunging anticline, etc. Neatly label the structure on the top of the map!.

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Nkleozom yeniden modelleme kompleksleri, replikasyon ve transkripsiyonun gereklemesine izin vermek zere histon oktamerlerinden DNA'nn gevemesi iin nemlidir. Aadaki zelliklerden hangisi nkleozom yeniden modelleme komplekslerini tanmlar? C. ATP genellikle yeniden ekillenmeye enerji salamak iin kullanlr. B. Kompleksler, spesifik DNA dizilerine balanabilir. C. Kompleksler, spesifik modifiye edilmi histon kalntlarna balanabilir. D. DNA, DNA'nn histonlara balanmasndaki genel bir konformasyonel deiiklikle yeniden ekillendirilebilir. E. Bunlarn hepsi dorudur..

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saravanan544051

Niteliksel faktrler doas gerei finansal deildir, ancak ynetimin karar verirken dikkate almas nemlidir. alm olduunuz (veya aina olduunuz) bir irketi dnerek, ynetimin karar vermesi iin nemli olabilecek niteliksel faktr tanmlayn. Ardndan, her birini nem srasna gre deerlendirin. Deerlendirmenize gre, nitel faktrlerin nicel sonulara ar basaca bir durumu gerekelendirin. Ak ol. Portfy aktiviteleri kendi kendini yanstacandan, ltfen portfolyo atamasn aadakilere baladnzdan emin olun: ************* Referanslar ve metin ii alnt******************.

Niteliksel faktrler doas gerei finansal deildir ancak yne.pdf

saravanan544051

Negro = 40 puntos Gris = 20 puntos Blanco = 0 puntos 7) Suponga que los boletos de lotera de $1 tienen las siguientes probabilidades: 1 en 5 para ganar un boleto gratis (valor $1), 1 en 100 para ganar $5, 1 en 100,000 para ganar $1000 y 1 en 10 millones para ganar $1 milln. Cul es el valor esperado de un billete de lotera? (Nota: los ganadores no recuperan el $ 1 que gastaron en el boleto). Es ms fcil pensar en este como similar a la primera forma en que Ben resolvi el ejemplo de los dados en clase..

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Poster to be presented at Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2024, Kaust, Saudi Arabia, https://cemse.kaust.edu.sa/stochnum/events/event/snsl-workshop-2024. In this work we have considered a setting that mimics the Henry problem \cite{Simpson2003,Simpson04_Henry}, modeling seawater intrusion into a 2D coastal aquifer. The pure water recharge from the ``land side'' resists the salinisation of the aquifer due to the influx of saline water through the ``sea side'', thereby achieving some equilibrium in the salt concentration. In our setting, following \cite{GRILLO2010}, we consider a fracture on the sea side that significantly increases the permeability of the porous medium. The flow and transport essentially depend on the geological parameters of the porous medium, including the fracture. We investigated the effects of various uncertainties on saltwater intrusion. We assumed uncertainties in the fracture width, the porosity of the bulk medium, its permeability and the pure water recharge from the land side. The porosity and permeability were modeled by random fields, the recharge by a random but periodic intensity and the thickness by a random variable. We calculated the mean and variance of the salt mass fraction, which is also uncertain. The main question we investigated in this work was how well the MLMC method can be used to compute statistics of different QoIs. We found that the answer depends on the choice of the QoI. First, not every QoI requires a hierarchy of meshes and MLMC. Second, MLMC requires stable convergence rates for $\EXP{g_{\ell} - g_{\ell-1}}$ and $\Var{g_{\ell} - g_{\ell-1}}$. These rates should be independent of $\ell$. If these convergence rates vary for different $\ell$, then it will be hard to estimate $L$ and $m_{\ell}$, and MLMC will either not work or be suboptimal. We were not able to get stable convergence rates for all levels $\ell=1,\ldots,5$ when the QoI was an integral as in \eqref{eq:integral_box}. We found that for $\ell=1,\ldots 4$ and $\ell=5$ the rate $\alpha$ was different. Further investigation is needed to find the reason for this. Another difficulty is the dependence on time, i.e. the number of levels $L$ and the number of sums $m_{\ell}$ depend on $t$. At the beginning the variability is small, then it increases, and after the process of mixing salt and fresh water has stopped, the variance decreases again. The number of random samples required at each level was estimated by calculating the decay of the variances and the computational cost for each level. These estimates depend on the minimisation function in the MLMC algorithm. To achieve the efficiency of the MLMC approach presented in this work, it is essential that the complexity of the numerical solution of each random realisation is proportional to the number of grid vertices on the grid levels.

$Poster_density_driven_with_fracture_MLMC.pdf$ $Poster_density_driven_with_fracture_MLMC.pdf$

Poster_density_driven_with_fracture_MLMC.pdf

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