Academic literature on the topic 'Ill posed ODE'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Ill posed ODE.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Journal articles on the topic "Ill posed ODE"
1
Cebers, Andrejs, and Harijs Kalis. "NUMERICAL SIMULATION OF MAGNETIC DROPLET DYNAMICS IN A ROTATING FIELD." Mathematical Modelling and Analysis 18, no. 1 (February 1, 2013): 80–96. http://dx.doi.org/10.3846/13926292.2013.756835.
Full textAbstract:
Dynamics and hysteresis of an elongated droplet under the action of a rotating magnetic field is considered for mathematical modelling. The shape of droplet is found by regularization of the ill-posed initial–boundary value problem for nonlinear partial differential equation (PDE). It is shown that two methods of the regularization – introduction of small viscous bending torques and construction of monotonous continuous functions are equivalent. Their connection with the regularization of the ill-posed reverse problems for the parabolic equation of heat conduction is remarked. Spatial discretization is carried out by the finite difference scheme (FDS). Time evolution of numerical solutions is obtained using method of lines for solving a large system of ordinary differential equations (ODE).
2
Čiegis, Raimondas, and Andrej Bugajev. "Numerical approximation of one model of bacterial self-organization." Nonlinear Analysis: Modelling and Control 17, no. 3 (July 25, 2012): 253–70. http://dx.doi.org/10.15388/na.17.3.14054.
Full textAbstract:
This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of complicated solution patterns. In this paper we show that this chemotaxisdriven instability can be connected to the ill-posed problem defined by the backward in time diffusion process. The method of lines is used to construct robust numerical approximations. At the first step we approximate spatial derivatives in the PDE by applying approximations targeted for special physical processes described by differential equations. The obtained system of ODE is split into a system describing separately fast and slow physical processes and different implicit and explicit numerical solvers are constructed for each subproblem. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.
3
CAZENAVE, THIERRY, FLÁVIO DICKSTEIN, and FRED B. WEISSLER. "NON-REGULARITY IN HÖLDER AND SOBOLEV SPACES OF SOLUTIONS TO THE SEMILINEAR HEAT AND SCHRÖDINGER EQUATIONS." Nagoya Mathematical Journal 226 (September 9, 2016): 44–70. http://dx.doi.org/10.1017/nmj.2016.35.
Full textAbstract:
In this paper, we study the Cauchy problem for the semilinear heat and Schrödinger equations, with the nonlinear term $f(u)=\unicode[STIX]{x1D706}|u|^{\unicode[STIX]{x1D6FC}}u$. We show that low regularity of $f$ (i.e., $\unicode[STIX]{x1D6FC}>0$ but small) limits the regularity of any possible solution for a certain class of smooth initial data. We employ two different methods, which yield two different types of results. On the one hand, we consider the semilinear equation as a perturbation of the ODE $w_{t}=f(w)$. This yields, in particular, an optimal regularity result for the semilinear heat equation in Hölder spaces. In addition, this approach yields ill-posedness results for the nonlinear Schrödinger equation in certain $H^{s}$-spaces, which depend on the smallness of $\unicode[STIX]{x1D6FC}$ rather than the scaling properties of the equation. Our second method is to consider the semilinear equation as a perturbation of the linear equation via Duhamel’s formula. This yields, in particular, that if $\unicode[STIX]{x1D6FC}$ is sufficiently small and $N$ is sufficiently large, then the nonlinear heat equation is ill-posed in $H^{s}(\mathbb{R}^{N})$ for all $s\geqslant 0$.
4
Benaïchouche, Simon, Clément Legoff, Yann Guichoux, François Rousseau, and Ronan Fablet. "Unsupervised Reconstruction of Sea Surface Currents from AIS Maritime Traffic Data Using Trainable Variational Models." Remote Sensing 13, no. 16 (August 10, 2021): 3162. http://dx.doi.org/10.3390/rs13163162.
Full textAbstract:
The estimation of ocean dynamics is a key challenge for applications ranging from climate modeling to ship routing. State-of-the-art methods relying on satellite-derived altimetry data can hardly resolve spatial scales below ∼100 km. In this work we investigate the relevance of AIS data streams as a new mean for the estimation of the surface current velocities. Using a physics-informed observation model, we propose to solve the associated the ill-posed inverse problem using a trainable variational formulation. The latter exploits variational auto-encoders coupled with neural ODE to represent sea surface dynamics. We report numerical experiments on a real AIS dataset off South Africa in a highly dynamical ocean region. They support the relevance of the proposed learning-based AIS-driven approach to significantly improve the reconstruction of sea surface currents compared with state-of-the-art methods, including altimetry-based ones.
5
Bolshakov, V. I., V. M. Volchuk, and Yu I. Dubrov. "Regularization of One Conditionally Ill-Posed Problem of Extractive Metallurgy." METALLOFIZIKA I NOVEISHIE TEKHNOLOGII 40, no. 9 (December 5, 2018): 1165–71. http://dx.doi.org/10.15407/mfint.40.09.1165.
Full text
6
George, Santhosh. "Newton-Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems." Journal of Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/439316.
Full textAbstract:
Recently in the work of George, 2010, we considered a modified Gauss-Newton method for approximate solution of a nonlinear ill-posed operator equationF(x)=y, whereF:D(F)⊆X→Yis a nonlinear operator between the Hilbert spacesXandY. The analysis in George, 2010 was carried out using a majorizing sequence. In this paper, we consider also the modified Gauss-Newton method, but the convergence analysis and the error estimate are obtained by analyzing the odd and even terms of the sequence separately. We use the adaptive method in the work of Pereverzev and Schock, 2005 for choosing the regularization parameter. The optimality of this method is proved under a general source condition. A numerical example of nonlinear integral equation shows the performance of this procedure.
7
Ghawadri, Nizam, Norazak Senu, Firas Adel Fawzi, Fudziah Ismail, and Zarina Ibrahim. "Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation." Algorithms 12, no. 1 (December 29, 2018): 10. http://dx.doi.org/10.3390/a12010010.
Full textAbstract:
In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods.
8
Cao, Chongsheng, and Edriss S. Titi. "Regularity “in Large” for the 3D Salmon’s Planetary Geostrophic Model of Ocean Dynamics." Mathematics of Climate and Weather Forecasting 6, no. 1 (February 1, 2020): 1–15. http://dx.doi.org/10.1515/mcwf-2020-0001.
Full textAbstract:
AbstractIt is well known, by now, that the three-dimensional non-viscous planetary geostrophic model, with vertical hydrostatic balance and horizontal Rayleigh friction/damping, coupled to the heat diffusion and transport, is mathematically ill-posed. This is because the no-normal flow physical boundary condition implicitly produces an additional boundary condition for the temperature at the lateral boundary. This additional boundary condition is different, because of the Coriolis forcing term, than the no-heat-flux physical boundary condition. Consequently, the second order parabolic heat equation is over-determined with two different boundary conditions. In a previous work we proposed one remedy to this problem by introducing a fourth-order artificial hyper-diffusion to the heat transport equation and proved global regularity for the proposed model. A shortcoming of this higher-oder diffusion is the loss of the maximum/minimum principle for the heat equation. Another remedy for this problem was suggested by R. Salmon by introducing an additional Rayleigh-like friction/damping term for the vertical component of the velocity in the hydrostatic balance equation. In this paper we prove the global, for all time and all initial data, well-posedness of strong solutions to the three-dimensional Salmon’s planetary geostrophic model of ocean dynamics. That is, we show global existence, uniqueness and continuous dependence of the strong solutions on initial data for this model. Unlike the 3D viscous PG model, we are still unable to show the uniqueness of the weak solution. Notably, we also demonstrate in what sense the additional damping term, suggested by Salmon, annihilate the ill-posedness in the original system; consequently, it can be viewed as “regularizing” term that can possibly be used to regularize other related systems.
9
Rohrer, James E., Qassam Saeed, Samreen Saeed, William V. Esler, David Beggs, Phillip O. Periman, Paul Hancock, and Seah H. Lim. "Attitude towards Cancer Treatment in Patients Attending a Community Cancer Center." Blood 104, no. 11 (November 16, 2004): 3143. http://dx.doi.org/10.1182/blood.v104.11.3143.3143.
Full textAbstract:
Abstract A diagnosis of a cancer sometimes changes the priorities and perspective of an individual. Previous literature suggests that cancer patients were more likely to indicate support for cancer treatment than non-cancer patients, even when the treatment may not be curative and when the odds for cure are low. We have carried out a questionnaire study to evaluate the attitude towards cancer treatment of a convenience sample of individuals attending a community cancer center situated along the “Bible belt” of the USA. A total of 460 individuals were recruited (100 newly diagnosed cancer patients; 100 cancer patients in complete remission; 60 cancer patients with relapsed/refractory disease; 100 non-cancer patients and 100 care-givers of cancer patients). The overall questionnaire return rate was 88% (range 84–91%). We used Chi square tests in two-way tables to test for significance. When asked whether or not the subject will agree to treatment that might be associated with uncomfortable side-effects for a cancer with less than 10% cure rate, 63.1% of cancer patients responded positively when compared to 48.9% of non-cancer patients (p = 0.02). This difference is most notable when relapsed/refractory patients were compared to non-cancer patients (70.6% vs 4.9%) (odd ratio = 0.345) (p = 0.007). These results, therefore, indicate that the positive attitude of most cancer patients to high risk cancer treatment is observed even in a region heavily influenced by religion. Moreover, the preference for treatment is stronger when the patient is faced with a real issue, rather than a hypothetical choice. Therefore, patients should be given an opportunity to revise living wills and other documents after they have been diagnosed with cancer. The study next examined the attitude towards intervention for potentially fatal treatment-related complications. Cancer patients were marginally more likely to agree (69.8%) to intervention of the life-threatening complications than non-cancer patients (60.0%) (p = 0.09) even if their life expectancy from the cancer is only 6 months. However, these differences were no longer apparent if the complication has arisen from a cancer that has a cure rate of 30%. Younger patients were also more likely to agree to intervention of life-threatening complications than older patients whether the intervention was for a cancer with a life-expectancy of only 6 months (p=.002) or 30% cure rates (p=.0002). Our study therefore suggests that most cancer patients, even those in the ‘Bible belt” and especially those with relapsed/refractory disease, expect oncologists to treat their disease and treatment-related complications whether or not the intervention only produces low cure rates or prolongs their life marginally. However, older patients are more likely to decline treatment. We next compared the responses from cancer patient care-givers to cancer patients. There was no significant difference in the attitude towards treatment between cancer care-givers and cancer patients regardless of how the question was posed, suggesting that daily contact with cancer patients may have positively influenced the attitude of individuals to high risk cancer treatment. This result also suggests that, when the patients are seriously ill and unable to make decisions on treatment, the decision by the care-givers probably reflects that of the patients.
10
Elgindi, Tarek, and In-Jee Jeong. "On Singular Vortex Patches, I: Well-posedness Issues." Memoirs of the American Mathematical Society 283, no. 1400 (March 2023). http://dx.doi.org/10.1090/memo/1400.
Full textAbstract:
The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show that globally m m -fold symmetric vortex patches with corners emanating from the origin are globally well-posed in natural regularity classes as long as m ≥ 3. m\geq 3. In this case, all of the angles involved solve a closed ODE system which dictates the global-in-time dynamics of the corners and only depends on the initial locations and sizes of the corners. Along the way we obtain a global well-posedness result for a class of symmetric patches with boundary singular at the origin, which includes logarithmic spirals. On the ill-posedness side, we show that any other type of corner singularity in a vortex patch cannot evolve continuously in time except possibly when all corners involved have precisely the angle π 2 \frac {\pi }{2} for all time. Even in the case of vortex patches with corners of angle π 2 \frac {\pi }{2} or with corners which are only locally m m -fold symmetric, we prove that they are generically ill-posed. We expect that in these cases of ill-posedness, the vortex patches actually cusp immediately in a self-similar way and we derive some asymptotic models which may be useful in giving a more precise description of the dynamics. In a companion work from 2020 on singular vortex patches, we discuss the long-time behavior of symmetric vortex patches with corners and use them to construct patches on R 2 \mathbb {R}^2 with interesting dynamical behavior such as cusping and spiral formation in infinite time.
Dissertations / Theses on the topic "Ill posed ODE"
1
MARINO, LORENZO. "Regolarizzazione debole attraverso rumore di Lévy degenere e sue applicazioni." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2021. http://hdl.handle.net/10281/330542.
Full textAbstract:
Dopo un'introduzione generale sul fenomeno della regolarizzazione attraverso rumore in un contesto degenere, la prima parte di questa tesi si concentra nello stabilire le stime di Schauder, un strumento analitico utile per dimostrare anche il carattere ben posto di equazioni differenziali stocastiche (EDS), per due classi di equazioni di Kolmogorov sotto una condizione di tipo Hörmander debole, i cui coefficienti giacciono in opportuni spazi di Hölder anisotropi con multi-indici di regolarità.
La prima classe considera un sistema non lineare controllato da un operatore simmetrico ⍺-stabile che agisce solo su alcune componenti. Il nostro metodo di dimostrazione si basa su un approccio perturbativo basato su espansioni della parametrice progressiva tramite formule di tipo Duhamel. A causa delle scarse proprietà regolarizzanti date dal contesto degenere, sfruttiamo anche alcuni controlli sulle norme di Besov, per trattare la perturbazione non lineare.
Come estensione del primo modello, presentiamo anche delle stime di Schauder associate a un operatore di Ornstein-Uhlenbeck degenere guidato da una classe più ampia di operatori di tipo quasi-stabile, come quello stabile relativistico o quello di Lamperti. La dimostrazione di questo risultato si basa invece su un'analisi precisa del comportamento del semigruppo di Markov corrispondente tra spazi di Hölder anisotropici e alcune tecniche di interpolazione.
Sfruttando un approccio della parametrice retrograda, la seconda parte di questa tesi
cerca di stabilire il carattere ben posto in senso debole per una catena degenere di EDS guidate dalla stessa classe di processi quasi-stabili, sotto le assunzioni di regolarità di Hölder minime per i coefficienti. Come corollario del nostro metodo, presentiamo anche stime di tipo Krylov di interesse indipendente per il processo canonico sottostante. Infine, sottolineiamo attraverso opportuni controesempi che esiste effettivamente una soglia (quasi) ottimale sugli esponenti di regolarità che garantiscono il carattere ben posto debole per l'EDS.
In relazione ad alcune applicazioni meccaniche per delle dinamiche cinetiche con attrito, concludiamo studiando la stabilità delle perturbazioni del secondo ordine per operatori degeneri di Kolmogorov nelle norme Lp e Hölder.After a general introduction about the regularization by noise phenomenon in the degenerate setting, the first part of this thesis focuses at establishing the Schauder estimates, a useful analytical tool to prove also the well-posedness of stochastic differential equations (SDEs), for two different classes of Kolmogorov equations under a weak Hörmander-like condition, whose coefficients lie in suitable anisotropic Hölder spaces with multi-indices of regularity. The first class considers a nonlinear system controlled by a symmetric ⍺-stable operator acting only on some components. Our method of proof relies on a perturbative approach based on forward parametrix expansions through Duhamel-type formulas. Due to the low regularizing properties given by the degenerate setting, we also exploit some controls on Besov norms, in order to deal with the non-linear perturbation. As an extension of the first one, we also present Schauder estimates associated with a degenerate Ornstein-Uhlenbeck operator driven by a larger class of ⍺-stable-like operators, like the relativistic or the Lamperti stable one. The proof of this result relies instead on a precise analysis of the behaviour of the associated Markov semigroup between anisotropic Hölder spaces and some interpolation techniques. Exploiting a backward parametrix approach, the second part of this thesis aims at establishing the well-posedness in a weak sense of a degenerate chain of SDEs driven by the same class of ⍺-stable-like processes, under the assumptions of the minimal Hölder regularity on the coefficients. As a by-product of our method, we also present Krylov-type estimates of independent interest for the associated canonical process. Finally, we emphasize through suitable counter-examples that there exists indeed an (almost) sharp threshold on the regularity exponents ensuring the weak well-posedness for the SDE. In connection with some mechanical applications for kinetic dynamics with friction, we conclude by investigating the stability of second-order perturbations for degenerate Kolmogorov operators in Lp and Hölder norms.
Books on the topic "Ill posed ODE"
1
Manchak, Sarah M., and Robert D. Morgan. Offenders with Mental Illness in Prison. Edited by John Wooldredge and Paula Smith. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199948154.013.26.
Full textAbstract:
This essay describes trends in the number of mentally disordered offenders in prison and the unique challenges posed by them in terms of prison management and service delivery. The essay first explores why persons with mental illnesses are overrepresented in the criminal justice system, then discusses efforts to rehabilitate this population should not take place within the prison environment (and, if they do, what changes in current practices are necessary to adapt to the prison setting). How the challenges posed by mentally ill inmates are managed is also covered, with critical discussions of these strategies. Finally, an analysis of the changes that are needed to improve conditions for inmates with mental illness in prisons is presented, with a description of one promising program for treating these offenders. Suggestions for future research with this population that will help inform and improve prison conditions for offenders with mental illness are also provided.
2
Diran, Ingrid. Antonio Negri. Edinburgh University Press, 2018. http://dx.doi.org/10.3366/edinburgh/9781474423632.003.0029.
Full textAbstract:
Agamben describes his posture as a reader as one of seeking a text’s Entwicklungsfähigkeit, or capacity for elaboration.1 In examining Agamben’s practices of reading, we can attend to the opposite phenomenon: the counter-elaboration that a text, in having being read by the philosopher, performs upon Agamben’s own thought. This reciprocal elaboration might constitute a paradigm for Agamben’s use of reading, according to his own idiosyncratic definition of use as an event in the middle voice, in which (according to a definition of Benveniste) the subject ‘effects an action only in affecting itself (il effectue en s’affectant)’ (UB 28). With this definition in mind, we could say that Agamben effects a text (he writes) only to the extent that he is also affected by another text (he reads). This is why Agamben’s position as a reader proves particularly important to any assessment of his work, quite aside from the problem of influence or intellectual genealogy. For this same reason, however, assessing Agamben’s relation to Antonio Negri – a figure with whom, by most measures, he is at odds – poses an unexpected challenge: how can Agamben’s thought be a use of Negri? Answering this question means not only assessing the critical distance between the two thinkers, but also taking this distance as a measure, in the Spinozan sense, of mutual affection.
Book chapters on the topic "Ill posed ODE"
1
James, Carolyn. "Risk-Taking and Risk Management." In A Renaissance Marriage, 92–112. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780199681211.003.0006.
Full textAbstract:
This chapter explores the ways in which gender shaped the respective approaches to political decision-making by the marquis and his wife. I argue that while the delegated nature of her authority encouraged Isabella to keep her emotions strictly in check and to be prudent in a diplomatic setting, Francesco was far more erratic. On the one hand, he adopted strategies of temporizing, prevarication, and swift changes of allegiance to hedge his bets politically, seen by contemporaries as intrinsically female vices, on the other, he indulged in reckless and competitive behaviour designed to display his masculine courage and princely disdain for caution. Together the couple evaded the dangers posed by the second French descent and the fall of Milan to Louis XII, but it was Isabella’s prudence that neutralized the ill-considered risk-taking of her husband.
2
D'Avy, Jacob, Wei-Wen Hsu, Chung-Hao Chen, Andreas F. Koschan, and Mongi Abidi. "An Efficient Method for Optimizing Segmentation Parameters." In Emerging Technologies in Intelligent Applications for Image and Video Processing, 29–47. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9685-3.ch002.
Full textAbstract:
Segmenting an image into meaningful regions is an important step in many computer vision applications such as facial recognition, target tracking and medical image analysis. Because image segmentation is an ill-posed problem, parameters are needed to constrain the solution to one that is suitable for a given application. For a user, setting parameter values is often unintuitive. We present a method for automating segmentation parameter selection using an efficient search method to optimize a segmentation objective function. Efficiency is improved by utilizing prior knowledge about the relationship between a segmentation parameter and the objective function terms. An adaptive sampling of the search space is created which focuses on areas that are more likely to contain a minimum. When compared to parameter optimization approaches based on genetic algorithm, Tabu search, and multi-locus hill climbing the proposed method was able to achieve equivalent optimization results with an average of 25% fewer objective function evaluations.
3
Buttu, Diana, and Féilim Ó. hAdhmaill. "International Humanitarian Law: protecting rights and promoting welfare during war?" In International Human Rights, Social Policy & Global, 77–90. Policy Press, 2020. http://dx.doi.org/10.1332/policypress/9781447349211.003.0007.
Full textAbstract:
Chapter 6 discusses the historical development of universal human rights protections during warfare through the establishment of International Humanitarian Law. It critically assesses the challenges posed to such protections by powerful states, geo-political considerations and the changing nature of war and conflict. It examines the operation of the International Criminal Court, the role of the UN Security Council and the geo-political manipulation of the UN by the USA and others, using the case of the Israel/Palestine conflict as but one example. In a world where most armed conflicts now involve non-state actors and casualties are overwhelmingly civilians, it also critically assesses attempts to reform IHL through, for example, the 1977 Protocols and the limitations of such reform.
4
Lepoutre, Maxime. "The Problem of Fragmentation." In Democratic Speech in Divided Times, 188–213. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198869757.003.0008.
Full textAbstract:
This chapter assesses the challenge that social and spatial fragmentation poses for inclusive public discourse. This fragmentation impedes democratic speech by keeping people apart, by fuelling intergroup ill will, and by amplifying intergroup inequalities. To address this problem, the chapter recommends adopting ‘integrative’ policies aimed at desegregating social and political groups. Integrative policies, however, remain deeply controversial. For one thing, they may appear to violate people’s freedom of association. And, in particular, such policies seemingly overlook the important interest that members of historically oppressed groups have in residential self-segregation. But, properly understood, integrative measures in fact need not jeopardize these interests. First, integrative policies create meaningful associative opportunities even as they restrict others. Second, integrating a system of public discourse does not require integrating all sites in that system. Doing so therefore leaves space for historically oppressed groups to engage in a meaningful measure of residential self-segregation.
5
Wong, Frank F. "The Search for American Liberal Education." In Rethinking Liberal Education. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195097726.003.0007.
Full textAbstract:
When Charles William Eliot launched his radical reforms at Harvard in the late 1870s, he was convinced that the fixed curriculum, based on English liberal education models, was ill-suited to the democratic spirit, the cultural diversity, and the rapidly changing circumstances in America. By introducing the free elective system, he hoped to develop in students the habits of self-reliance that he regarded as essential to the American democratic system. Seventy years later, in a post-World War II climate of concern about the "unifying purpose and idea" for American education, Harvard issued a new version of liberal education in its famous Redbook. To address the new American circumstances, these reforms reduced rather than increased choices for students. These benchmarks of American higher education notwithstanding, the final chapter of a widely respected study by Bruce Kimball, published in 1986, opens with the observation that there is no "distinctively American view of liberal education. This observation contains an irony that raises interesting and significant questions. After such high-profile efforts as those made at Harvard, why is there no clear model of American liberal education? And if there is no such model, do we need to develop one, especially in the context of the dramatic changes affecting American society today—changes that in many ways are more radical than those faced by Charles William Eliot? Why, in this latest round of debates about the core curriculum in our colleges and universities, has the issue been posed in terms of the primacy and purity of Western civilization rather than in terms of the adequacy of our educational models to address the realities of America in the late twentieth century? These questions are even more striking when one considers the almost complete reversal of roles and the dramatic changes in orientation that have occurred in the relationship between the United States and its cultural ancestors in the Anglo-European world.
6
Assan, Never. "Goat - a Sustainable and Holistic Approach in Addressing Triple Challenges of Gender Inequality, Climate Change Effects, Food and Nutrition Insecurity in Rural Communities of Sub Saharan Africa." In Goat Science - Environment, Health and Economy [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96408.
Full textAbstract:
Goat-centered approach can transform rural agrarian households and communities toward gender inclusive climate change adaptation in agriculture to enhance food security and nutrition in Sub Saharan Africa. Gender inequality, climate change effect and food and nutrition insecurity are the most defining and deeply intertwined socio-economic and environmental challenges in rural communities in sub Saharan Africa. This chapter offers an overview of potentiality of goat rearing as a sustainable and holistic approach in addressing triple challenges of gender inequality, climate change effects and food and nutrition insecurity in rural communities. The failure to address gender inequality and deal with the climate change effect has thrown the Sub-Saharan Africa into a state of perpetual food scarcity due to compromised food production, consequently condemning the rural communities and its people to extreme poverty and nutrition insecurity. Because of this scenario, a number of both internal and external development agencies, have put several measures in place to alleviate the situation, which has for long preyed upon the region and continues to frustrate food stability in the region. The total failure of the previous autonomously attempt to address the triple challenges of gender inequality, climate change effects and food and nutrition insecurity at the household level give ground to prominence on the endorsement of more sustainable and multifaceted approaches. A proposition is made that goat rearing is one such initiative, which combines the empowerment of women in agriculture to ensure availability of the basic food needs of the household, while sustaining animal production due to goat’s adaptability to the climate induced harsh environmental conditions. The goat centered multifactorial approach to address the triple challenges is focused on the exploitation of the interlinkages among these socio-economic and environmental ills. The major assumption is that goat rearing in rural economies simultaneously curtails the risk of food and nutrition insecurity by acting as an entry point of gender equality, while leveraging on the opportunities that goat rearing will effectively offset adversities posed by the climate change effect. In most instances, women are potentially more vulnerable compared to men as they directly experience the ponderous effects of climate change in agricultural production, in turn compromising food and nutrition security. Goat rearing is central in the removal of systemic barriers that hold women back from equal participation in agriculture, by broadening their socio-economic opportunities, hence, playing a significant role in agricultural value-chains. The goat-rearing sustainability concept is based on establishing and maintaining the circumstances under which people and nature can subsist in productive harmony, that allow fulfilling the social, economic, and other requirements of present and future generations. Despite the climate change adverse effects, the goat population has continued to proliferate in harshest agro-ecological regions, which demonstrate that goats have managed to adapt to the current unfriendly climate induced environmental conditions. It is assumed that promoting goat rearing will narrow the gender equality gap between men and women, and enhance the participation of women in agriculture, hence, improving productivity, and food and nutrition security. Goats due to their numerical population advantage and deeply embedment in rural communities have constantly contributed to rural poor resource farmers’ livelihoods in many ways, and their contributions tend to be significant. This chapter offers an overview of potentiality of goat rearing as a sustainable and holistic approach in addressing triple challenges of gender inequality, climate change effects and food insecurity in rural communities of Sub Saharan Africa.
Conference papers on the topic "Ill posed ODE"
1
Agarwal, Harish, Amit Kale, Srikanth Akkaram, Mahadevan Balasubramaniam, Susan Ebacher, and Paul Gilleberto. "Inverse Modeling Techniques for Application to Engine Transient Performance Data Matching." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-51313.
Full textAbstract:
A framework demonstrating the application of inverse modeling technology for engine performance data matching is presented. Transient aero-thermodynamic cycle models are used to simulate engine performance and control characteristics over the entire flight envelope. These models are used not only for engine design and certification but also to provide performance guarantees to the customer and for engine diagnostics. Therefore, it is extremely important that these models are able to accurately predict the performance metrics of interest. Accuracy of these models can be improved by fine-tuning model parameters so that the model output best matches the flight test data. The performance of an aircraft engine is fine tuned from several sensor observations, e.g. exhaust gas temperature, fuel flow, and fan speed. These observations vary with parameters like power level, core speed and operating conditions like altitude, inlet conditions (temperature and pressure), and Mach number, and are used in conjunction with a transient performance simulation model to assess engine performance. This is normally achieved through an iterative manual approach that requires a lot of expert judgment. Simulating transient performance characteristics often requires an engineer to estimate model parameters by matching model response to engine sensor data. Such an estimation problem can be posed using inverse modeling technology. One of the main challenges in the application of inverse modeling for parameter estimation is that the problem can be ill-posed that leads to instability and non-uniqueness of the solution. The inverse method employed here for parameter estimation provides a solution for both well-posed and ill-posed problems. Sensitivity analysis can be used to better pose the data-matching problem. Singular value decomposition (SVD) technique is used to address the ill-posed nature of the inverse problem, which is solved as a finite dimensional non-linear optimization problem. Typically, the transient response is highly nonlinear and it may not be possible to match the whole transient simultaneously. This paper extends the framework on transient inverse modeling developed in [1] for engine transient performance applications. Variable weighting mechanism allows providing different weights to different sensors. This helps in better control on data matching, identify drift in parameter values over time, and point towards incorrect modeling assumptions. The application of the inverse methodology is demonstrated on a single spool non-afterburning engine and a commercial aviation engine model.
2
Damean, Nicolae A. "Computational Removing of Electrical Resistance Measurement Error Caused by Thermic Effects." In ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium collocated with the ASME 1995 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/cie1995-0770.
Full textAbstract:
Abstract Thermic behaviour of electrical resistor passed by a constant DC is analysed both theoretical and numerical. This problem, a ill-posed one is changed in a well-posed one solving a parameter identification problem. The last problem is the principal subject of this paper. Numerical simulations presented here correspond to resistance temperature detector Pt-100. They lead to improving of resistance measurement error (and of temperature certainly for this particular case) through computational removing of error caused by thermic effects.
3
Sun, Xiaopeng, Muxingzi Li, Tianyu He, and Lubin Fan. "Enhance Image as You Like with Unpaired Learning." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/140.
Full textAbstract:
Low-light image enhancement exhibits an ill-posed nature, as a given image may have many enhanced versions, yet recent studies focus on building a deterministic mapping from input to an enhanced version. In contrast, we propose a lightweight one-path conditional generative adversarial network (cGAN) to learn a one-to-many relation from low-light to normal-light image space, given only sets of low- and normal-light training images without any correspondence. By formulating this ill-posed problem as a modulation code learning task, our network learns to generate a collection of enhanced images from a given input conditioned on various reference images. Therefore our inference model easily adapts to various user preferences, provided with a few favorable photos from each user. Our model achieves competitive visual and quantitative results on par with fully supervised methods on both noisy and clean datasets, while being 6 to 10 times lighter than state-of-the-art generative adversarial networks (GANs) approaches.
4
Poggio, Tomaso. "Parallel Processes in Early Vision: from the computational structure to algorithms and parallel hardware." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/optcomp.1985.ma3.
Full textAbstract:
One of the best definitions of early vision is that it is inverse optics — a set of computational problems that both machines and biological organisms have to solve. While in classical optics the problem is to determine the images of physical objects, vision is confronted with the inverse problem of recovering three-dimensional shape from the light distribution in the image. Most processes of early vision such as stereomatching, computation of motion and all the “structure from" processes can be regarded as solutions to inverse problems. This common characteristic of early vision can be formalized: most early vision problems are “ill-posed problems" in the sense of Hadamard. In this article we will first review a new framework suggested by Poggio and Torre (1984). They suggested that the mathematical theory developed for regularizing ill-posed problems leads in a natural way to the solution of early vision problems in terms of variational principles of a certain class. They argued that this is a new theoretical framework for some of the variational solutions already obtained in the analysis of early vision processes. They also showed how several other problems in early vision can be approached and solved. Thus the computational, ill-posed nature of early vision problems dictates a specific class of algorithms for solving them, based on variational principles of a certain class. It is natural to consider next which classes of parallel hardware may efficiently implement regularization algorithms. We are especially interested in implementations that are suggestive for biology. I will thus review a model of computation proposed by Poggio and Koch (1984) that maps easily into biologically plausible mechanisms. They showed that a natural way of implementing variational principles of the regularization type is to use electrical, chemical or neuronal networks. They also showed how to derive specific networks for solving several low-level vision problems, such as the computation of visual motion and edge detection.
5
Groetsch, C. W., and Martin Hanke. "Regularization of Some One-Dimensional Inverse Problems for Identification of Nonlinear Surface Phenomena." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0657.
Full textAbstract:
Abstract A simple numerical method for some one-dimensional inverse problems of model identification type arising in nonlinear heat transfer is discussed. The essence of the method is to express the nonlinearity in terms of an integro-differential operator, the values of which are approximated by a linear spline technique. The inverse problems are mildly ill-posed and therefore call for regularization when data errors are present. A general technique for stabilization of unbounded operators may be applied to regularize the process and a specific regularization technique is illustrated on a model problem.
6
Nickerson, Brendon M., and Anriëtte Bekker. "A Comparison of Inverse Models for the Estimation of Ice-Induced Propeller Moments on a Polar Vessel." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-62755.
Full textAbstract:
Abstract Full-scale measurements were conducted on the port side propulsion shaft the S.A. Agulhas II during the 2019 SCALE Spring Cruise. The measurements included the shaft torque captured at two separate measurement locations, and the shaft rotational speed at one measurement location. The ice-induced propeller moments are estimated from the full-scale shaft responses using two inverse models. The first is a published discrete lumped mass model that relies on regularization due to the inverse problem being ill-posed. This model is only able to make use of the propulsion shaft torque as inputs. The second model is new and employs modal superposition to represent the propulsion shaft as a combination of continuous modes, resulting in a well-posed problem. This new model requires the additional measurement of the shaft rotational speed for the inverse solution. The continuous model is shown to be more consistent and efficient, which allows its use in real-time monitoring of propeller moments.
7
Orlande, Helcio R. B. "Inverse Problems in Heat Transfer: New Trends on Solution Methodologies and Applications." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-23349.
Full textAbstract:
Systematic methods for the solution of inverse problems have developed significantly during the last twenty years and have become a powerful tool for analysis and design in engineering. Inverse analysis is nowadays a common practice in which the groups involved with experiments and numerical simulation synergistically collaborate throughout the research work, in order to obtain the maximum of information regarding the physical problem under study. Inverse problems are mathematically classified as ill-posed, that is, their solutions do not satisfy either one of the requirements of existence, uniqueness or stability. The solution approaches generally consist of the reformulation of the inverse problem in terms of an approximate well-posed problem. In this paper we briefly review various approaches for the solution of inverse problems, including those based on classical regularization techniques and those based on the Bayesian statistics. Applications of inverse problems are then presented for cases of practical interest, such as the characterization of non-homogeneous materials and the prediction of the temperature field in oil pipelines.
8
DeLillo, Thomas K., Tomasz Hrycak, and Nicolas Valdivia. "Iterative Regularization Methods for Inverse Problems in Acoustics." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32730.
Full textAbstract:
We consider the use of conjugate-gradient-like iterative methods for the solution of integral equations arising from an inverse problem in acoustics in a bounded three dimensional region. The inverse problem is the computation of the normal velocities on the boundary of a region from pressure measurements on an interior surface. The pressure satisfies the Helmholtz equation in the region. Two formulations are considered: one based on the representation of pressures by a single layer potential and the other based on the Helmholtz-Kirchhoff integral equation. Both formulations can be used to approximate the Neumann Green’s function as an alternative. The integral equations are all ill-posed and are discretized by a boundary element method. The resulting liner systems are ill-conditoned and a (smooth) regularized solutions must be sought. Two regularization rules, including a new one, for conjugate-gradient-like methods are applied and found to have advantages over a standard method based on the truncated singular value decomposition using generalized cross validation. Due to the occurence of multiple singular values for our integral operators, conjugate gradient methods compute the optimal solution in the first few iterations and prove to be particularly fast for these large scale acoustics problems.
9
Eichmann, George, and Mihajlo Stojancic. "Direct constrained linear associative memory inverse filter." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.tup5.
Full textAbstract:
The recognition of signals and images degraded by a linear low-pass degradation operator, even in the absence of any measurement noise, is an ill-posed problem. Based on a new constrained associative memory (CAM) method, the reconstruction (restoration) for an arbitrary binary object from an image, either linearly degraded by a linear shift-invariant (LSI) or shift-variant (LSV) degradation operator, in the presence of strong noise, is achieved. Using an appropriate training set of signals, related ideally to a perfect degradation operator inverse, the CAM method yields a general, in the form of a 2-D array of coefficients, one-step impulsive-type (spiking) inverse filter. Computer simulation results of the reconstruction of 1-D and 2-D signals and images, degraded by LSI and LSV systems, in the presence of strong noise are presented.
10
Kersten, Daniel, and David C. Knill. "Reflectance estimation and lightness constancy: a probabilistic approach." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.thc2.
Full textAbstract:
The image of a natural scene can be considered a product of reflectance and effective illumination functions. One goal of image understanding is the estimation of the reflectance and illumination from image luminance data. Human observers are remarkably good at inferring reflectance changes from an image. One well-known aspect of this ability is lightness constancy. However, because there are two unknowns for every data point in the image, this problem is ill-posed, and it does not have a unique solution without prior constraints on the class of reflectance and illumination functions. We use Markov random fields to model and thereby constrain the class of reflectance and illumination functions. Our computational goal is taken to be the maximization of the posterior distribution of the reflectance and illumination conditional on the image. This goal is achieved using stochastic relaxation. This approach provides a general framework for quantifying the computational theory apart from specific algorithmic implementations for a number of problems of early vision.