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In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with standard incidence. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.
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Putra, Roni Tri, Sukatik, and Sri Nita. "Kestabilan Model Epidemi SEIR Dengan Laju Insidensi." Jurnal Ilmiah Poli Rekayasa 10, no. 2 (April 14, 2015): 74. http://dx.doi.org/10.30630/jipr.10.2.77.
In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with incidence rate. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.
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Putra, Roni Tri, and Quinoza Guvil. "Kestabilan Model Epidemi Dengan Laju Insidensi Jenuh." Jurnal Ilmiah Poli Rekayasa 13, no. 1 (October 16, 2017): 43. http://dx.doi.org/10.30630/jipr.13.1.64.
In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with saturated incidence. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.
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Szidarovsky, Ferenc, and Koji Okuguchi. "A non-differentiable input-output model." Mathematical Social Sciences 18, no. 2 (October 1989): 187–90. http://dx.doi.org/10.1016/0165-4896(89)90044-9.
In this paper, it will be studied existence and uniqueness solution of equilibrium points for a SEIR model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and uniqueness solution of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.
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Cho, Jin Seo, and Halbert White. "DIRECTIONALLY DIFFERENTIABLE ECONOMETRIC MODELS." Econometric Theory 34, no. 5 (August 22, 2017): 1101–31. http://dx.doi.org/10.1017/s0266466617000354.
The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.
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Swietojanski, Pawel, and Steve Renals. "Differentiable Pooling for Unsupervised Acoustic Model Adaptation." IEEE/ACM Transactions on Audio, Speech, and Language Processing 24, no. 10 (October 2016): 1773–84. http://dx.doi.org/10.1109/taslp.2016.2584700.
Agop, M., O. Niculescu, A. Timofte, L. Bibire, A. S. Ghenadi, A. Nicuta, C. Nejneru, and G. V. Munceleanu. "Non-Differentiable Mechanical Model and Its Implications." International Journal of Theoretical Physics 49, no. 7 (April 9, 2010): 1489–506. http://dx.doi.org/10.1007/s10773-010-0330-5.
Rokhlin, Dmitry B., and Anatoly Usov. "Rational taxation in an open access fishery model." Archives of Control Sciences 27, no. 1 (March 1, 2017): 5–27. http://dx.doi.org/10.1515/acsc-2017-0001.
Abstract We consider a model of fishery management, where n agents exploit a single population with strictly concave continuously differentiable growth function of Verhulst type. If the agent actions are coordinated and directed towards the maximization of the discounted cooperative revenue, then the biomass stabilizes at the level, defined by the well known “golden rule”. We show that for independent myopic harvesting agents such optimal (or ε-optimal) cooperative behavior can be stimulated by the proportional tax, depending on the resource stock, and equal to the marginal value function of the cooperative problem. To implement this taxation scheme we prove that the mentioned value function is strictly concave and continuously differentiable, although the instantaneous individual revenues may be neither concave nor differentiable.
Thesis (Ph.D.)--Tufts University, 2004. Adviser: Boris Hasselblatt. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 61-62). Access restricted to members of the Tufts University community. Also available via the World Wide Web;
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Collins, Jack T. "Simulation to reality and back: A robot's guide to crossing the reality gap." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/230537/1/Jack_Collins_Thesis.pdf.
Simulation is an indispensable technology within robotics; however, the reality gap prevents many simulated solutions from transferring perfectly to reality. This thesis investigates the reality gap within the context of robotic manipulation. We present studies that first quantify and then benchmark the reality gap when comparing popular robotic simulators to a real-world ground truth collected using motion capture. We then present a promising new method for overcoming the reality gap that employs an online sim-to-real approach that utilises differentiable physics to iteratively narrow the gap and improve the simulation environment using data collected from the real system.
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Ogden, Richard R. "Differential rotation and the geodynamo." Thesis, University of Glasgow, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264156.
Nagloo, Joel Chris Ronnie. "Model theory, algebra and differential equations." Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/6813/.
In this thesis, we applied ideas and techniques from model theory, to study the structure of the sets of solutions XII - XV I , in a differentially closed field, of the Painlevé equations. First we show that the generic XII - XV I , that is those with parameters in general positions, are strongly minimal and geometrically trivial. Then, we prove that the generic XII , XIV and XV are strictly disintegrated and that the generic XIII and XV I are ω-categorical. These results, already known for XI , are the culmination of the work started by P. Painlevé (over 100 years ago), the Japanese school and many others on transcendence and the Painlevé equations. We also look at the non generic second Painlevé equations and show that all the strongly minimal ones are geometrically trivial.
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Bjørneng, Bjørn. "How to increase the understanding of differentials by using the Casio-calculator model 9860 G I/II to solve differential equations." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79468.
The major aims of this paper are to present how we can improve the students understanding and involvement in mathematics by using a programming/graphic calculator. I will use differentials as examples such as differentiation ,integrals and differential equations, creating lines of slopes for differential equation of the type y’= f(x,y) . Find the solution of some differential equations by using regression and create the graph connected to the differential equation. As we have different approaches to solving a problem, it is a hope the students interest in mathematics will improve. The tools used will be programming, graphic commands as plot, f-line, etc. One goal is also to show how we can create small programs solving problems in mathematics. For many students this will be a stepping stone for further work with programming. The programs used can be copied using the program FA 124 that can be downloaded from Casios homepages. On request I can send you the programs.
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Kriwet, Gregor [Verfasser]. "Methods for Model Calibration and Design of Optimal Experiments for Partial Differential Equation Models / Gregor Kriwet." Aachen : Shaker, 2016. http://d-nb.info/1118258258/34.
Baldi, Guillaume. "Contributions à la modélisation procédurale de structures cellulaires stochastoques 2D et à leur génération par l'exemple." Electronic Thesis or Diss., Strasbourg, 2024. http://www.theses.fr/2024STRAD001.
La création de matériaux et de textures procéduraux demande une grande expertise et constitue un travail long, fastidieux et coûteux, c’est pourquoi on cherche à développer des outils permettant leur génération automatique à partir d’exemples en entrée fournis sous la forme d’images : on parle de modélisation procédurale inverse.Dans cette thèse, nous proposons un modèle procédural appelé Cellular Point Process Texture Basis Function (C-PPTBF) permettant de représenter des structures cellulaires stochastiques 2D, impliquant des fonctions différentiables par rapport à la plupart de leurs paramètres, ce qui rend possible l’estimation de ces paramètres à partir d’exemples sans recourir entièrement à des réseaux de neurones profonds. Nous avons mis en place une chaîne de traitement permettant d’estimer les paramètres de notre modèle à partir d’exemples de structures fournis sous la forme d’images binaires, combinant une estimation réalisée à l’aide d’un réseau de neurones convolutif entraîné sur des images produites avec notre modèle de C-PPTBF et une phase d’estimation par descente de gradient directement sur les paramètres du modèle procédural The creation of procedural materials and textures requires considerable expertise, and is time-consuming, tedious and costly. We are therefore looking to develop tools for the automatic generation of procedural textures and materials from input exemplars provided in the form of images: This is known as inverse procedural modeling.In this thesis, we propose a procedural model called Cellular Point Process Texture Basis Function (C-PPTBF) for representing 2D stochastic cellular structures, involving functions that are differentiable with respect to most of their parameters, making it possible to estimate these parameters from examples without resorting entirely to deep neural networks. We have set up a processing pipeline to estimate the parameters of our model from structural examples provided in the form of binary images, combining an estimation performed using a convolutional neural network trained on images produced with our C-PPTBF model and an estimation phase using gradient descent directly on the parameters of the procedural model
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Francia, Giulio. "Differential display application to a Melanoma model." Thesis, King's College London (University of London), 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300029.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 1987. Title as it appeared in the Massachusetts Institute of Technology Graduate List, June 1987: Differential game models of oligopoly. Bibliography: leaves 242-249. by Marco Hanig. Ph.D.
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Cruz, Jorge Carlos Ferreira Rodrigues da. "Constraint reasoning for differential models." Doctoral thesis, FCT - UNL, 2003. http://hdl.handle.net/10362/1061.
The basic motivation of this work was the integration of biophysical models within the interval constraints framework for decision support. Comparing the major features of biophysical models with the expressive power of the existing interval constraints framework, it was clear that the most important inadequacy was related with the representation of differential equations. System dynamics is often modelled through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focussed on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables. The application of the constraint propagation algorithm for pruning the variable domains, that is, the enforcement of local-consistency, turned out to be insufficient to support decision in practical problems that include differential equations. The domain pruning achieved is not, in general, sufficient to allow safe decisions and the main reason derives from the non-linearity of the differential equations. Consequently, a complementary goal of this work proposes a new strong consistency criterion, Global Hull-consistency, particularly suited to decision support with differential models, by presenting an adequate trade-of between domain pruning and computational effort. Several alternative algorithms are proposed for enforcing Global Hull-consistency and, due to their complexity, an effort was made to provide implementations able to supply any-time pruning results. Since the consistency criterion is dependent on the existence of canonical solutions, it is proposed a local search approach that can be integrated with constraint propagation in continuous domains and, in particular, with the enforcing algorithms for anticipating the finding of canonical solutions. The last goal of this work is the validation of the approach as an important contribution for the integration of biophysical models within decision support. Consequently, a prototype application that integrated all the proposed extensions to the interval constraints framework is developed and used for solving problems in different biophysical domains.
Duffie, Darrell. Asset pricing with stochastic differential utility. Toronto: Dept. of Economics and Institute for Policy Analysis, University of Toronto, 1991.
Jüngel, Ansgar, Raul Manasevich, Peter A. Markowich, and Henrik Shahgholian, eds. Nonlinear Differential Equation Models. Vienna: Springer Vienna, 2004. http://dx.doi.org/10.1007/978-3-7091-0609-9.
Li, Qiang. China’s Development Under a Differential Urbanization Model. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-13-9451-5.
Book chapters on the topic "Differentiable model":
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Meidani, Kazem, Igor Borovikov, Amir Barati Farimani, and Harold Chaput. "Inverse Lighting with Differentiable Physically-Based Model." In Lecture Notes in Computer Science, 286–300. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-44505-7_20.
Presta, Alberto, Attilio Fiandrotti, Enzo Tartaglione, and Marco Grangetto. "A Differentiable Entropy Model for Learned Image Compression." In Image Analysis and Processing – ICIAP 2023, 328–39. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43148-7_28.
Wilson, Paul, and Fabio Zanasi. "Categories of Differentiable Polynomial Circuits for Machine Learning." In Graph Transformation, 77–93. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09843-7_5.
AbstractReverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.
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Li, Long, Etienne Mémin, and Gilles Tissot. "Stochastic Parameterization with Dynamic Mode Decomposition." In Mathematics of Planet Earth, 179–93. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_11.
AbstractA physical stochastic parameterization is adopted in this work to account for the effects of the unresolved small-scale on the large-scale flow dynamics. This random model is based on a stochastic transport principle, which ensures a strong energy conservation. The dynamic mode decomposition (DMD) is performed on high-resolution data to learn a basis of the unresolved velocity field, on which the stochastic transport velocity is expressed. Time-harmonic property of DMD modes allows us to perform a clean separation between time-differentiable and time-decorrelated components. Such random scheme is assessed on a quasi-geostrophic (QG) model.
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Kolek, Stefan, Duc Anh Nguyen, Ron Levie, Joan Bruna, and Gitta Kutyniok. "A Rate-Distortion Framework for Explaining Black-Box Model Decisions." In xxAI - Beyond Explainable AI, 91–115. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04083-2_6.
AbstractWe present the Rate-Distortion Explanation (RDE) framework, a mathematically well-founded method for explaining black-box model decisions. The framework is based on perturbations of the target input signal and applies to any differentiable pre-trained model such as neural networks. Our experiments demonstrate the framework’s adaptability to diverse data modalities, particularly images, audio, and physical simulations of urban environments.
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Janiczek, John, Parth Thaker, Gautam Dasarathy, Christopher S. Edwards, Philip Christensen, and Suren Jayasuriya. "Differentiable Programming for Hyperspectral Unmixing Using a Physics-Based Dispersion Model." In Computer Vision – ECCV 2020, 649–66. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58583-9_39.
Millard, Matthew, David Franklin, and Walter Herzog. "A Continuous and Differentiable Mechanical Model of Muscle Force and Impedance." In Biosystems & Biorobotics, 262–66. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01887-0_50.
Ascoli, Alon, Ronald Tetzlaff, and Leon Chua. "Continuous and Differentiable Approximation of a TaO Memristor Model for Robust Numerical Simulations." In Emergent Complexity from Nonlinearity, in Physics, Engineering and the Life Sciences, 61–69. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-47810-4_6.
Wei, Xian, Yangyu Xu, Yanhui Huang, Hairong Lv, Hai Lan, Mingsong Chen, and Xuan Tang. "Learning Extremely Lightweight and Robust Model with Differentiable Constraints on Sparsity and Condition Number." In Lecture Notes in Computer Science, 690–707. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19772-7_40.
Ouala, Said, Pierre Tandeo, Bertrand Chapron, Fabrice Collard, and Ronan Fablet. "End-to-End Kalman Filter in a High Dimensional Linear Embedding of the Observations." In Mathematics of Planet Earth, 211–21. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_13.
AbstractData assimilation techniques are the state-of-the-art approaches in the reconstruction of a spatio-temporal geophysical state such as the atmosphere or the ocean. These methods rely on a numerical model that fills the spatial and temporal gaps in the observational network. Unfortunately, limitations regarding the uncertainty of the state estimate may arise when considering the restriction of the data assimilation problems to a small subset of observations, as encountered for instance in ocean surface reconstruction. These limitations motivated the exploration of reconstruction techniques that do not rely on numerical models. In this context, the increasing availability of geophysical observations and model simulations motivates the exploitation of machine learning tools to tackle the reconstruction of ocean surface variables. In this work, we formulate sea surface spatio-temporal reconstruction problems as state space Bayesian smoothing problems with unknown augmented linear dynamics. The solution of the smoothing problem, given by the Kalman smoother, is written in a differentiable framework which allows, given some training data, to optimize the parameters of the state space model.
Conference papers on the topic "Differentiable model":
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Kotary, James, Vincenzo Di Vito, and Ferdinando Fioretto. "Differentiable Model Selection for Ensemble Learning." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/217.
Model selection is a strategy aimed at creating accurate and robust models by identifying the optimal model for classifying any particular input sample. This paper proposes a novel framework for differentiable selection of groups of models by integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning with a strategy that learns to combine the predictions of appropriately selected pre-trained ensemble models. It does so by modeling the ensemble learning task as a differentiable selection program trained end-to-end over a pretrained ensemble to optimize task performance. The proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of classification tasks.
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Vishniakou, Ivan, and Johannes D. Seelig. "Differentiable Model-based Adaptive Optics for Microscopy." In Computational Optical Sensing and Imaging. Washington, D.C.: OSA, 2021. http://dx.doi.org/10.1364/cosi.2021.cm1a.3.
Bern, James M., Yannick Schnider, Pol Banzet, Nitish Kumar, and Stelian Coros. "Soft Robot Control With a Learned Differentiable Model." In 2020 3rd IEEE International Conference on Soft Robotics (RoboSoft). IEEE, 2020. http://dx.doi.org/10.1109/robosoft48309.2020.9116011.
Pilault, Jonathan, Can Liu, Mohit Bansal, and Markus Dreyer. "On Conditional and Compositional Language Model Differentiable Prompting." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/460.
Prompts have been shown to be an effective method to adapt a frozen Pretrained Language Model (PLM) to perform well on downstream tasks. Prompts can be represented by a human-engineered word sequence or by a learned continuous embedding. In this work, we investigate conditional and compositional differentiable prompting. We propose a new model, Prompt Production System (ProPS), which learns to transform task instructions or input metadata, into continuous prompts that elicit task-specific outputs from the PLM. Our model uses a modular network structure based on our neural formulation of Production Systems, which allows the model to learn discrete rules -- neural functions that learn to specialize in transforming particular prompt input patterns, making it suitable for compositional transfer learning and few-shot learning. We present extensive empirical and theoretical analysis and show that ProPS consistently surpasses other PLM adaptation techniques, and often improves upon fully fine-tuned models, on compositional generalization tasks, controllable summarization and multilingual translation, while needing fewer trainable parameters.
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Lutter, Michael, Johannes Silberbauer, Joe Watson, and Jan Peters. "Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning." In 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2021. http://dx.doi.org/10.1109/icra48506.2021.9561805.
Zhi, Bowen, Alisha Sharma, Dmitry N. Zotkin, and Ramani Duraiswami. "A Differentiable Image Source Model for Room Acoustics Optimization." In 2023 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA). IEEE, 2023. http://dx.doi.org/10.1109/waspaa58266.2023.10248140.
Wang, Zhuoer, Yicheng Wang, Ziwei Zhu, and James Caverlee. "Unsupervised Candidate Answer Extraction through Differentiable Masker-Reconstructor Model." In Findings of the Association for Computational Linguistics: EMNLP 2023. Stroudsburg, PA, USA: Association for Computational Linguistics, 2023. http://dx.doi.org/10.18653/v1/2023.findings-emnlp.379.
Richard, Gaël, Pierre Chouteau, and Bernardo Torres. "A Fully Differentiable Model for Unsupervised Singing Voice Separation." In ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2024. http://dx.doi.org/10.1109/icassp48485.2024.10447244.
Tschiatschek, Sebastian, Aytunc Sahin, and Andreas Krause. "Differentiable Submodular Maximization." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/379.
We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial nature, submodular functions can be maximized approximately with strong theoretical guarantees in polynomial time. Typically, learning the submodular function and optimization of that function are treated separately, i.e. the function is first learned using a proxy objective and subsequently maximized. In contrast, we show how to perform learning and optimization jointly. By interpreting the output of greedy maximization algorithms as distributions over sequences of items and smoothening these distributions, we obtain a differentiable objective. In this way, we can differentiate through the maximization algorithms and optimize the model to work well with the optimization algorithm. We theoretically characterize the error made by our approach, yielding insights into the tradeoff of smoothness and accuracy. We demonstrate the effectiveness of our approach for jointly learning and optimizing on synthetic maxcut data, and on real world applications such as product recommendation and image collection summarization.
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Hong, Charles, Qijing Huang, Grace Dinh, Mahesh Subedar, and Yakun Sophia Shao. "DOSA: Differentiable Model-Based One-Loop Search for DNN Accelerators." In MICRO '23: 56th Annual IEEE/ACM International Symposium on Microarchitecture. New York, NY, USA: ACM, 2023. http://dx.doi.org/10.1145/3613424.3623797.
Urban, Nathan. Black-Box Neural System Identificationand Differentiable Programming to Improve Earth System Model PredictionsFebruary. Office of Scientific and Technical Information (OSTI), March 2021. http://dx.doi.org/10.2172/1769681.
Otrok, Christopher, Huigang Chen, Alessandro Rebucci, Gianluca Benigno, and Eric R. Young. Optimal Policy for Macro-Financial Stability. Inter-American Development Bank, December 2012. http://dx.doi.org/10.18235/0011440.
This paper studies whether policymakers should wait to intervene until a financial crisis strikes or rather act in a preemptive manner. This question is examined in a relatively simple dynamic stochastic general equilibrium model in which crises are endogenous events induced by the presence of an occasionally binding borrowing constraint as in Mendoza (2010). First, the paper shows that the same set of taxes that replicates the constrained social planner allocation could be used optimally by a Ramsey planner to achieve the first best unconstrained equilibrium: in both cases without any precautionary intervention. Second, the paper shows that the extent to which policymakers should intervene in a preemptive manner depends critically on the set of policy tools available and what these instruments can achieve when a crisis strikes. For example, in the context of the model, it is found that, if the policy tools are constrained so that the first best cannot be achieved and the policymaker has access to only one tax instrument, it is always desirable to intervene before the crisis regardless of the instrument used. If, however, the policymaker has access to two instruments, it is optimal to act only during crisis times. Third and finally, the paper proposes a computational algorithm to solve Markov-perfect optimal policy for problems in which the policy function is not differentiable.
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Miller, Jonah Maxwell. The Differential Equations That Model Diseases. Office of Scientific and Technical Information (OSTI), March 2020. http://dx.doi.org/10.2172/1606334.
Díaz Alvarado, Carlos, Ugo Panizza, and Alejandro Izquierdo. Fiscal Sustainability in Emerging Market Countries with an Application to Ecuador. Inter-American Development Bank, August 2004. http://dx.doi.org/10.18235/0010831.
This paper surveys the recent literature on fiscal sustainability, with particular emphasis on emerging market countries. It discusses the main elements that differentiate emerging market countries from industrial countries and then discusses how probabilistic models can help to evaluate fiscal sustainability in an uncertain environment. Based on this discussion, the paper uses Ecuador to illustrate an application of the probabilistic model, and of the framework to evaluate the impact of shocks to current account financing on sustainability.
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Childers, David, Jesús Fernández-Villaverde, Jesse Perla, Christopher Rackauckas, and Peifan Wu. Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation. Cambridge, MA: National Bureau of Economic Research, October 2022. http://dx.doi.org/10.3386/w30573.
Petra, Noei, and Georg Stadler. Model Variational Inverse Problems Governed by Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, March 2011. http://dx.doi.org/10.21236/ada555315.
Schramm, Harrison C., and Nedialko B. Dimitrov. Differential Equation Models for Sharp Threshold Dynamics. Fort Belvoir, VA: Defense Technical Information Center, August 2012. http://dx.doi.org/10.21236/ada567671.
He, Xihua. PR-015-113601-R02 Validation of Internal Corrosion Threat Models for Dry Natural Gas Pipelines. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), August 2015. http://dx.doi.org/10.55274/r0010914.
This report documents the verification and validation (of the probabilistic models developed previously to predict internal corrosion (IC) threats in nominally dry natural gas pipelines. Model uncertainty quantification showed that "low temperature, high pressure" posed the greatest IC threat. To validate the model, actual measurements were compared to model-predicted wall loss. The comparison included information from an IC failure, investigated by the National Transportation Safety Board (NTSB), with in-line inspection (ILI) data sets from five pipeline operators. Two of the pipeline operator data sets showed wall loss measurements either evenly distributed at all locations around the circumfer-ence of the pipe or predominantly at the top of the pipe. These measurements agreed with negligible wall loss predicted by the model. Two other operator data sets measured significant wall loss occurring at the bottom of the pipe. These measurements agreed with non-negligible risk of IC also predicted by the mod-el. The 5th operator data set confirmed the analysis of ILI data uncertainty and corroborated the validation results. For the NTSB investigated failure, the model prediction is in good agreement with the post-failure examination because the model predicted a very high IC risk for this pipeline that failed. This validation provides increased confidence that the previously developed models can differentiate between negligible and non-negligible wall loss occurring in a dry natural gas pipeline.
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Doyle, Wendy S. K., David C. Thompson, and Philippe Pierre Pebay. A data storage model for novel partial differential equation descretizations. Office of Scientific and Technical Information (OSTI), April 2007. http://dx.doi.org/10.2172/907817.
Mocan, H. Naci, Stephen Billups, and Jody Overland. A Dynamic Model of Differential Human Capital and Criminal Activity. Cambridge, MA: National Bureau of Economic Research, March 2000. http://dx.doi.org/10.3386/w7584.
