Relevant bibliographies by topics / Exact and approximate inferences

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  2. Dissertations / Theses
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Academic literature on the topic 'Exact and approximate inferences'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Exact and approximate inferences"

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Wu, Lang. "Exact and Approximate Inferences for Nonlinear Mixed-Effects Models With Missing Covariates." Journal of the American Statistical Association 99, no. 467 (September 2004): 700–709. http://dx.doi.org/10.1198/016214504000001006.

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Mekhnacha, Kamel, Juan-Manuel Ahuactzin, Pierre Bessière, Emmanuel Mazer, and Linda Smail. "Exact and approximate inference in ProBT." Revue d'intelligence artificielle 21, no. 3 (June 12, 2007): 295–332. http://dx.doi.org/10.3166/ria.21.295-332.

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Akagi, Yasunori, Takuya Nishimura, Yusuke Tanaka, Takeshi Kurashima, and Hiroyuki Toda. "Exact and Efficient Inference for Collective Flow Diffusion Model via Minimum Convex Cost Flow Algorithm." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 3163–70. http://dx.doi.org/10.1609/aaai.v34i04.5713.

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Collective Flow Diffusion Model (CFDM) is a general framework to find the hidden movements underlying aggregated population data. The key procedure in CFDM analysis is MAP inference of hidden variables. Unfortunately, existing approaches fail to offer exact MAP inferences, only approximate versions, and take a lot of computation time when applied to large scale problems. In this paper, we propose an exact and efficient method for MAP inference in CFDM. Our key idea is formulating the MAP inference problem as a combinatorial optimization problem called Minimum Convex Cost Flow Problem (C-MCFP) with no approximation or continuous relaxation. On the basis of this formulation, we propose an efficient inference method that employs the C-MCFP algorithm as a subroutine. Our experiments on synthetic and real datasets show that the proposed method is effective both in single MAP inference and people flow estimation with EM algorithm.
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Abe, Takayuki, and Manabu Iwasaki. "EXACT AND APPROXIMATE INFERENCES FOR AN EXPONENTIAL MEAN FROM TYPE I CENSORED DATA." Bulletin of informatics and cybernetics 37 (December 2005): 31–39. http://dx.doi.org/10.5109/12589.

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YANG, HANN-PYI JAMES, and WEI-KEI SHIUE. "COMPARISON OF FAILURE INTENSITIES FROM TWO POISSON PROCESSES." International Journal of Reliability, Quality and Safety Engineering 02, no. 03 (September 1995): 235–43. http://dx.doi.org/10.1142/s0218539395000186.

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Statistical inferences for ratio and difference of intensities from two Poisson processes are reviewed. Both fixed time periods case and fixed number of failures case are considered. Exact results whenever available are described with emphasis on hypothesis testing procedures and confidence intervals construction. Some approximate confidence intervals are studied and simulation results indicate that these intervals are adequate even with small sample size.
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Karami, Md Jamil Hasan. "Assessing Goodness of Approximate Distributions for Inferences about Parameters in Nonlinear Regression Model." Dhaka University Journal of Science 71, no. 1 (May 29, 2023): 13–16. http://dx.doi.org/10.3329/dujs.v71i1.65267.

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It is often crucial to make inferences about parameters of a nonlinear regression model due to a dependency of Fisher information on the parameter being estimated. Here, the distribution of the relevant test statistic is not exact, but approximate. Therefore, similar conclusion, based on the values of different test statistics, may not be reached. This study shows, in this circumstance, how to come up with a nonlinear regression model that can be used for forecasting and other related purposes. The goodness of the approximate distributions, F and χ 2 , has been assessed to reach a correct decision. The simulation results show that the simulated probability of committing a type I error is very close to its true value in case of F distribution corresponding to F statistic. However, the χ 2 distribution does not do a similar job for the LRT statistic since the simulated type I error is quite larger. Dhaka Univ. J. Sci. 71(1): 13-16, 2023 (Jan)
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El-Sagheer, Rashad M., Taghreed M. Jawa, and Neveen Sayed-Ahmed. "Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme." Complexity 2021 (December 7, 2021): 1–11. http://dx.doi.org/10.1155/2021/9325928.

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In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.
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Lintusaari, Jarno, Paul Blomstedt, Tuomas Sivula, Michael U. Gutmann, Samuel Kaski, and Jukka Corander. "Resolving outbreak dynamics using approximate Bayesian computation for stochastic birth-death models." Wellcome Open Research 4 (January 25, 2019): 14. http://dx.doi.org/10.12688/wellcomeopenres.15048.1.

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Earlier research has suggested that approximate Bayesian computation (ABC) makes it possible to fit simulator-based intractable birth-death models to investigate communicable disease outbreak dynamics with accuracy comparable to that of exact Bayesian methods. However, recent findings have indicated that key parameters such as the reproductive number R may remain poorly identifiable with these models. Here we show that the identifiability issue can be resolved by taking into account disease-specific characteristics of the transmission process in closer detail. Using tuberculosis (TB) in the San Francisco Bay area as a case-study, we consider a model that generates genotype data from a mixture of three stochastic processes, each with their distinct dynamics and clear epidemiological interpretation. We show that our model allows for accurate posterior inferences about outbreak dynamics from aggregated annual case data with genotype information. As a by-product of the inference, the model provides an estimate of the infectious population size at the time the data was collected. The acquired estimate is approximately two orders of magnitude smaller compared to the assumptions made in the earlier related studies, and much better aligned with epidemiological knowledge about active TB prevalence. Similarly, the reproductive number R related to the primary underlying transmission process is estimated to be nearly three-fold compared with the previous estimates, which has a substantial impact on the interpretation of the fitted outbreak model.
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Lintusaari, Jarno, Paul Blomstedt, Brittany Rose, Tuomas Sivula, Michael U. Gutmann, Samuel Kaski, and Jukka Corander. "Resolving outbreak dynamics using approximate Bayesian computation for stochastic birth–death models." Wellcome Open Research 4 (August 30, 2019): 14. http://dx.doi.org/10.12688/wellcomeopenres.15048.2.

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Earlier research has suggested that approximate Bayesian computation (ABC) makes it possible to fit simulator-based intractable birth–death models to investigate communicable disease outbreak dynamics with accuracy comparable to that of exact Bayesian methods. However, recent findings have indicated that key parameters, such as the reproductive number R, may remain poorly identifiable with these models. Here we show that this identifiability issue can be resolved by taking into account disease-specific characteristics of the transmission process in closer detail. Using tuberculosis (TB) in the San Francisco Bay area as a case study, we consider a model that generates genotype data from a mixture of three stochastic processes, each with its own distinct dynamics and clear epidemiological interpretation. We show that our model allows for accurate posterior inferences about outbreak dynamics from aggregated annual case data with genotype information. As a byproduct of the inference, the model provides an estimate of the infectious population size at the time the data were collected. The acquired estimate is approximately two orders of magnitude smaller than assumed in earlier related studies, and it is much better aligned with epidemiological knowledge about active TB prevalence. Similarly, the reproductive number R related to the primary underlying transmission process is estimated to be nearly three times larger than previous estimates, which has a substantial impact on the interpretation of the fitted outbreak model.
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Shapovalova, Yuliya. "“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study." Entropy 23, no. 4 (April 15, 2021): 466. http://dx.doi.org/10.3390/e23040466.

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We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.
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Dissertations / Theses on the topic "Exact and approximate inferences"

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Ducamp, Gaspard. "PROCOP : probabilistic rules compilation and optimisation." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS090.

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Adoptées depuis plus de 20 ans par le monde de l’industrie, les règles métiers (business rules) offrent la possibilité à des utilisateurs non-informaticiens de définir des politiques de prise de décision de manière simple et intuitive. Pour faciliter leurs utilisations, des systèmes à base de règles, dits « systèmes de gestion des règles métier », ont été développés, séparant la logique métier de l’application informatique. S’ils sont adaptés pour traiter des données structurées et complètes, ils ne permettent pas aisément de travailler sur des données probabilistes. PROCOP (Probabilistic Rules Optimized and COmPilation) est une thèse proposant une nouvelle approche pour l’intégration de raisonnement probabiliste dans IBM Operational Decision Manager (ODM), le système de gestion des règles métier développé par IBM, notamment via l’introduction d’une notion de risque global sur l'évaluation des conditions d'exécution d'une action, complexifiant la phase de compilation du système mais augmentant l’expressivité des règles métiers. Diverses méthodes sont explorées, implémentées et comparées afin de permettre l'utilisation d'une telle capacité de raisonnement à large échelle, notamment afin de répondre aux problématiques liées à l'utilisation de modèles graphiques probabilistes dans des réseaux complexes
Widely adopted for more than 20 years in industrial fields, business rules offer the opportunity to non-IT users to define decision-making policies in a simple and intuitive way. To facilitate their use, rule-based systems, known as business rule management systems, have been developed, separating the business logic from the computer application. While they are suitable for processing structured and complete data, they do not easily allow working with probabilistic data. PROCOP (Probabilistic Rules Optimized and COmPilation) is a thesis proposing a new approach for the integration of probabilistic reasoning in IBM Operational Decision Manager (ODM), IBM's business rules management system, in particular through the introduction of a concept of global risk on the evaluation of the execution conditions of an action, complicating the compilation phase of the system but increasing the expressiveness of the business rules. Various methods are explored, implemented and compared in order to allow the use of such a powerful reasoning capacity on a large scale, in particular in order to answer the problems linked to the use of probabilistic graphical models in complex networks
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Tucker, Dewey S. (Dewey Stanton). "Stochastic realization theory for exact and approximate multiscale models." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/34468.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.
Includes bibliographical references (p. [245]-252).
The thesis provides a detailed analysis of the independence structure possessed by multiscale models and demonstrates that such an analysis provides important insight into the multiscale stochastic realization problem. Multiscale models constitute a broad class of probabilistic models which includes the well--known subclass of multiscale autoregressive (MAR) models. MAR models have proven useful in a variety of different application areas, due to the fact that they provide a rich set of tools for various signal processing tasks. In order to use these tools, however, a MAR or multiscale model must first be constructed to provide an accurate probabilistic description of the particular application at hand. This thesis addresses this issue of multiscale model identification or realization. Previous work in the area of MAR model identification has focused on developing algorithms which decorrelate certain subsets of random vectors in an effort to design an accurate model. In this thesis, we develop a set-theoretic and graph-theoretic framework for better understanding these types of realization algorithms and for the purpose of designing new such algorithms.
(cont.) The benefit of the framework developed here is that it separates the realization problem into two understandable parts - a dichotomy which helps to clarify the relationship between the exact realization problem, where a multiscale model is designed to exactly satisfy a probabilistic constraint, and the approximate realization problem, where the constraint is only approximately satisfied. The first part of our study focuses on developing a better understanding of the independence structure exhibited by multiscale models. As a result of this study, we are able to suggest a number of different sequential procedures for realizing exact multiscale models. The second part of our study focuses on approximate realization, where we define a relaxed version of the exact multiscale realization problem. We show that many of the ideas developed for the exact realization problem may be used to better understand the approximate realization problem and to develop algorithms for solving it. In particular, we propose an iterative procedure for solving the approximate realization problem, and we show that the parameterized version of this procedure is equivalent to the well-known EM algorithm. Finally, a specific algorithm is developed for realizing a multiscale model which matches the statistics of a Gaussian random process.
by Dewey S. Tucker.
Ph.D.
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Cabo, Nodar Marta. "Exact and approximate algorithms for the inventory routing problem." Thesis, University of Southampton, 2003. https://eprints.soton.ac.uk/50599/.

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In this thesis we develop exact and approximate algorithms for the inventory routing problem (IRP). The inventory routing problem is one of deciding an optimal delivery policy for a set of customers through a given planning period. Customers can hold inventory and do not need deliveries every day. Deliveries are carried out by a fleet of homogeneous vehicles that must be routed to travel a minimum distance while visiting all customers scheduled for that day. Decisions concern which customers to be visited and how much to deliver to each of them must be taken. A new formulation for the IRP is presented as a mixed integer programming model. This new approach allows split deliveries so customers can receive the inventory through more than one vehicle during the same day. It also seeks periodic solutions through a given planning period. Although throughout our research the planning period is fixed, all algorithms presented in this thesis can be applied to any length of the planning period. Special cases for this problem are also considered and optimal polynomial algorithms have been developed. We develop four constructive heuristics for the inventory routing problem. These heuristics are based on a schedule-first route-second approach. First, a decision is made on which customers to visit each day, and how much inventory they should receive on each delivery. Then, a vehicle routing problem is solved for each day to perform the deliveries to the customers. Several experiments are carried out to compare the performance of each heuristic. An iterated local search method is then applied to the best solution obtained with these heuristics. The local search is based on node interchange and aims to reduce the number of routes per day as well as the total distance travelled. Extensive computational tests are carried out to asses the effectiveness of this local search procedure.
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Ahern, Zeke Alexander. "Exact and approximate optimisation for strategic bus network planning." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/206458/1/Zeke_Ahern_Thesis.pdf.

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This thesis contributes to the area of transportation network design at the strategic level, considering objectives for the passenger and operator. The main goal of the research is to improve the existing methods by developing new and more rigorous approaches to integrating route choice, service frequency and adequately accounting for passenger waiting time. An exact model was developed: providing a concise non-ambiguous description to the problem. Case study problem instances found that exact methods implemented by commercial solvers are not scalable for practical problems. Therefore, meta-heuristics were presented to find near-optimal solutions efficiently and demonstrate the practicality of the model in the real-world.
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Markovsky, Ivan. "Exact and approximate modeling of linear systems : a behavioral approach /." Philadelphia, Pa. : Society for Industrial and Applied Mathematics, 2006. http://www.loc.gov/catdir/enhancements/fy0708/2005057537-d.html.

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Taylor, Michael. "Exact and approximate epidemic models on networks : theory and applications." Thesis, University of Sussex, 2013. http://sro.sussex.ac.uk/id/eprint/45258/.

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This thesis is concerned with modelling the spread of diseases amongst host populations and the epidemics that result from this process. We are primarily interested in how networks can be used to model the various heterogeneities observable in real-world populations. Firstly, we start with the full system of Kolmogorov/master equations for a simple Susceptible-Infected-Susceptible (SIS) type epidemic on an arbitrary contact network. From this general framework, we rigorously derive sets of ODEs that describe the exact dynamics of the expected number of individuals and pairs of individuals. We proceed to use moment closure techniques to close these hierarchical systems of ODEs, by approximating higher order moments in terms of lower order moments. We prove that the simple first order mean-field approximation becomes exact in the limit of a large, fully-connected network. We then investigate how well two different pairwise approximations capture the topological features of theoretical networks generated using different algorithms. We then introduce the effective degree modelling framework and propose a model for SIS epidemics on dynamic contact networks by accounting for random link activation and deletion. We show that results from the resulting set of ODEs agrees well with results from stochastic simulations, both in describing the evolution of the network and the disease. Furthermore, we derive an analytic calculation of the stability of the disease-free steady state and explore the validity of such a measure in the context of a dynamically evolving contact network. Finally, we move on to derive a system of ODEs that describes the interacting dynamics of a disease and information relating to the disease. We allow individuals to become responsive in light of received information and, thus, reduce the rate at which they become infected. We consider the effectiveness of different routes of information transmission (such as peer-to-peer communication or mass media campaigns) in slowing or preventing the spread of a disease. Finally, we use a range of modelling techniques to investigate the spread of disease within sheep flocks. We use field data to construct weighted contact networks for flocks of sheep to account for seasonal changes of the flock structure as lambs are born and eventually become weaned. We construct a range of network and ODE models that are designed to investigate the effect of link-weight heterogeneity on the spread of disease.
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Igwe, Tobenna. "An empirical study on computation of exact and approximate equilibria." Thesis, University of Liverpool, 2018. http://livrepository.liverpool.ac.uk/3016935/.

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The computation of Nash equilibria is one of the central topics in game theory, which has received much attention from a theoretical point of view. Studies have shown that the problem of finding a Nash equilibrium is PPAD-complete, which implies that we are unlikely to find a polynomial-time algorithm for this problem. Naturally, this has led to a line of work studying the complexity of finding approximate Nash equilibria. This thesis examines the computation of such approximate Nash equilibria within several classes of games from an empirical perspective. In this thesis, we address the computation of approximate Nash equilibria in bimatrix and polymatrix games. For both of these game classes, we provide a library of implementations of algorithms for the computation of exact and approximate Nash equilibria, as well as a suite of game generators which were used as a base for our empirical analysis of the algorithms. We investigate the trade-off between quality of approximation produced by the algorithms and the expected runtime. We provide some insight into the inner workings of the state-of-the-art algorithm for computing ε-Nash equilibria, presenting worst-case examples found for our provided suite of game generators. We then show lower bounds on these algorithms. In the case of polymatrix games, we generate this lower bound from a real-world application of game theory. For bimatrix games, we provide a robust means of generating lower bounds for approximation algorithms with the use of genetic algorithms.
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Diaz, Bobillo Ignacio Javier. "The general ℓ₁ optimal multiblock problem : exact and approximate solutions." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/12798.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1992.
Includes bibliographical references (leaves 119-123).
by Ignacio Javier Diaz-Bobillo.
Ph.D.
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Hassan, Abdeljabbar Hassan Mohammed Albarra. "Parallel Scheduling in the Cloud Systems : Approximate and Exact Methods." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0223/document.

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Cette thèse porte sur la résolution exacte et heuristique de plusieurs problèmes ayant des applications dans le domaine de l'Informatique dématérialisé (cloud computing). L'Informatique dématérialisée est un domaine en plein extension qui consiste à mutualiser les machines/serveurs en définissant des machines virtuelles représentant des fractions des machines/serveurs. Il est nécessaire d'apporter des solutions algorithmiques performantes en termes de temps de calcul et de qualité des solutions. Dans cette thèse, nous nous sommes intéressés dans un premier temps au problème d'ordonnancement sur plusieurs machines (les machines virtuelles) avec contraintes de précédence, c.-à-d., que certaines tâches ne peuvent s'exécuter que si d'autres sont déjà finies. Ces contraintes représentent une subdivision des tâches en sous tâches pouvant s'exécuter sur plusieurs machines virtuelles. Nous avons proposé plusieurs algorithmes génétiques permettant de trouver rapidement une bonne solution réalisable. Nous les avons comparés avec les meilleurs algorithmes génétiques de la littérature et avons défini les types d'instances où les solutions trouvées sont meilleures avec notre algorithme. Dans un deuxième temps, nous avons modélisé ce problème à l'aide de la programmation linéaire en nombres entiers permettant de résoudre à l'optimum les plus petites instances. Nous avons proposé de nouvelles inégalités valides permettant d'améliorer les performances de notre modèle. Nous avons aussi comparé cette modélisation avec plusieurs formulations trouvées dans la littérature. Dans un troisième temps, nous avons analysé de manière approfondie la sous-structure du sous-graphe d'intervalle ne possédant pas de clique de taille donnée. Nous avons étudié le polytope associé à cette sous-structure et nous avons montré que les facettes que nous avons trouvées sont valides pour le problème d'ordonnancement sur plusieurs machines avec contraintes de précédence mais elles le sont aussi pour tout problème d'ordonnancement sur plusieurs machines. Nous avons étendu la modélisation permettant de résoudre le précédent problème afin de résoudre le problème d'ordonnancement sur plusieurs machines avec des contraintes disjonctives entre les tâches, c.-à-d., que certaines tâches ne peuvent s'exécuter en même temps que d'autres. Ces contraintes représentent le partage de ressources critiques ne pouvant pas être utilisées par plusieurs tâches. Nous avons proposé des algorithmes de séparation afin d'insérer de manière dynamique nos facettes dans la résolution du problème puis avons développé un algorithme de type Branch-and-Cut. Nous avons analysé les résultats obtenus afin de déterminer les inégalités les plus intéressantes afin de résoudre ce problème. Enfin dans le dernier chapitre, nous nous sommes intéressés au problème d'ordonnancement d'atelier généralisé ainsi que la version plus classique d'ordonnancement d'atelier (open shop). En effet, le problème d'ordonnancement d'atelier généralisé est aussi un cas particulier du problème d'ordonnancement sur plusieurs machines avec des contraintes disjonctives entre les tâches. Nous avons proposé une formulation à l'aide de la programmation mathématique pour résoudre ces deux problèmes et nous avons proposé plusieurs familles d'inégalités valides permettant d'améliorer les performances de notre algorithme. Nous avons aussi pu utiliser les contraintes définies précédemment afin d'améliorer les performances pour le problème d'ordonnancement d'atelier généralisé. Nous avons fini par tester notre modèle amélioré sur les instances classiques de la littérature pour le problème d'ordonnancement d'atelier. Nous obtenons de bons résultats permettant d'être plus rapide sur certaines instances
The Cloud Computing appears as a strong concept to share costs and resources related to the use of end-users. As a consequence, several related models exist and are widely used (IaaS, PaaS, SaaS. . .). In this context, our research focused on the design of new methodologies and algorithms to optimize performances using the scheduling and combinatorial theories. We were interested in the performance optimization of a Cloud Computing environment where the resources are heterogeneous (operators, machines, processors...) but limited. Several scheduling problems have been addressed in this thesis. Our objective was to build advanced algorithms by taking into account all these additional specificities of such an environment and by ensuring the performance of solutions. Generally, the scheduling function consists in organizing activities in a specific system imposing some rules to respect. The scheduling problems are essential in the management of projects, but also for a wide set of real systems (telecommunication, computer science, transportation, production...). More generally, solving a scheduling problem can be reduced to the organization and the synchronization of a set of activities (jobs or tasks) by exploiting the available capacities (resources). This execution has to respect different technical rules (constraints) and to provide the maximum of effectiveness (according to a set of criteria). Most of these problems belong to the NP-Hard problems class for which the majority of computer scientists do not expect the existence of a polynomial exact algorithm unless P=NP. Thus, the study of these problems is particularly interesting at the scientific level in addition to their high practical relevance. In particular, we aimed to build new efficient combinatorial methods for solving parallel-machine scheduling problems where resources have different speeds and tasks are linked by precedence constraints. In our work we studied two methodological approaches to solve the problem under the consideration : exact and meta-heuristic methods. We studied three scheduling problems, where the problem of task scheduling in cloud environment can be generalized as unrelated parallel machines, and open shop scheduling problem with different constraints. For solving the problem of unrelated parallel machines with precedence constraints, we proposed a novel genetic-based task scheduling algorithms in order to minimize maximum completion time (makespan). These algorithms combined the genetic algorithm approach with different techniques and batching rules such as list scheduling (LS) and earliest completion time (ECT). We reviewed, evaluated and compared the proposed algorithms against one of the well-known genetic algorithms available in the literature, which has been proposed for the task scheduling problem on heterogeneous computing systems. Moreover, this comparison has been extended to an existing greedy search method, and to an exact formulation based on basic integer linear programming. The proposed genetic algorithms show a good performance dominating the evaluated methods in terms of problems' sizes and time complexity for large benchmark sets of instances. We also extended three existing mathematical formulations to derive an exact solution for this problem. These mathematical formulations were validated and compared to each other by extensive computational experiments. Moreover, we proposed an integer linear programming formulations for solving unrelated parallel machine scheduling with precedence/disjunctive constraints, this model based on the intervaland m-clique free graphs with an exponential number of constraints. We developed a Branch-and-Cut algorithm, where the separation problems are based on graph algorithms. [...]
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Almoustafa, Samira. "Distance-constrained vehicle routing problem : exact and approximate solution (mathematical programming)." Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/7640.

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The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing problem into a travelling salesman problem and uses the assignment problem as a lower bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational experiments show that we are able to exactly solve large test instances with up to 1000 customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups of instances. We wanted to determine how far the difference is between the best feasible solution obtained by VNS and the value of optimal solution in order to use the output of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions.
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Books on the topic "Exact and approximate inferences"

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Reinhard, Klette, ed. Euclidean shortest paths: Exact or approximate algorithms. London: Springer-Verlag, 2011.

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Queueing networks with blocking: Exact and approximate solutions. New York: Oxford University Press, 1994.

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Chang, Yin-Wen. Exact and Approximate Methods for Machine Translation Decoding. [New York, N.Y.?]: [publisher not identified], 2015.

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Ivan, Markovsky, ed. Exact and approximate modeling of linear systems: A behavioral approach. Philadelphia: Society for Industrial and Applied Mathematics, 2006.

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Kiss, Istvan Z. Mathematics of Epidemics on Networks: From Exact to Approximate Models. Cham: Springer International Publishing, 2017.

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Chen, Hsing-Ta. Delving Into Dissipative Quantum Dynamics: From Approximate to Numerically Exact Approaches. [New York, N.Y.?]: [publisher not identified], 2016.

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Glowinski, R. Exact and approximate controllability for distributed parameter systems: A numerical approach. New York: Cambridge University Press, 2008.

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Hartley, T. T. Exact and approximate solutions to the oblique shock equations for real-time applications. [Akron, Ohio: University of Akron, Electrical Engineering Dept., 1991.

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Burstein, Joseph. Exact numerical solutions of nonlinear differential equations, short algorithms: After three centuries of approximate methods. Boston: Metrics Press, 2002.

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Klette, Reinhard, and Fajie Li. Euclidean Shortest Paths: Exact or Approximate Algorithms. Springer London, Limited, 2014.

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Book chapters on the topic "Exact and approximate inferences"

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Kwatra, Saloni, and Vicenç Torra. "Empirical Evaluation of Synthetic Data Created by Generative Models via Attribute Inference Attack." In IFIP Advances in Information and Communication Technology, 282–91. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57978-3_18.

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AbstractThe disclosure risk of synthetic/artificial data is still being determined. Studies show that synthetic data generation techniques generate similar data to the original data and sometimes even the exact original data. Therefore, publishing synthetic datasets can endanger the privacy of users. In our work, we study the synthetic data generated from different synthetic data generation techniques, including the most recent diffusion models. We perform a disclosure risk assessment of synthetic datasets via an attribute inference attack, in which an attacker has access to a subset of publicly available features and at least one synthesized dataset, and the aim is to infer the sensitive features unknown to the attacker. We also compute the predictive accuracy and F1 score of the random forest classifier trained on several synthetic datasets. For sensitive categorical features, we show that Attribute Inference Attack is not highly feasible or successful. In contrast, for continuous attributes, we can have an approximate inference. This holds true for the synthetic datasets derived from Diffusion models, GANs, and DPGANs, which shows that we can only have approximated Attribute Inference, not the exact Attribute Inference.
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Azzolini, Damiano, Elena Bellodi, and Fabrizio Riguzzi. "Approximate Inference in Probabilistic Answer Set Programming for Statistical Probabilities." In AIxIA 2022 – Advances in Artificial Intelligence, 33–46. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27181-6_3.

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Abstract“Type 1” statements were introduced by Halpern in 1990 with the goal to represent statistical information about a domain of interest. These are of the form “x% of the elements share the same property”. The recently proposed language PASTA (Probabilistic Answer set programming for STAtistical probabilities) extends Probabilistic Logic Programs under the Distribution Semantics and allows the definition of this type of statements. To perform exact inference, PASTA programs are converted into probabilistic answer set programs under the Credal Semantics. However, this algorithm is infeasible for scenarios when more than a few random variables are involved. Here, we propose several algorithms to perform both conditional and unconditional approximate inference in PASTA programs and test them on different benchmarks. The results show that approximate algorithms scale to hundreds of variables and thus can manage real world domains.
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Muhamed, Aashiq, Sriram Srinivasan, Choon-Hui Teo, Qingjun Cui, Belinda Zeng, Trishul Chilimbi, and S. V. N. Vishwanathan. "Web-Scale Semantic Product Search with Large Language Models." In Advances in Knowledge Discovery and Data Mining, 73–85. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33380-4_6.

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AbstractDense embedding-based semantic matching is widely used in e-commerce product search to address the shortcomings of lexical matching such as sensitivity to spelling variants. The recent advances in BERT-like language model encoders, have however, not found their way to realtime search due to the strict inference latency requirement imposed on e-commerce websites. While bi-encoder BERT architectures enable fast approximate nearest neighbor search, training them effectively on query-product data remains a challenge due to training instabilities and the persistent generalization gap with cross-encoders. In this work, we propose a four-stage training procedure to leverage large BERT-like models for product search while preserving low inference latency. We introduce query-product interaction pre-finetuning to effectively pretrain BERT bi-encoders for matching and improve generalization. Through offline experiments on an e-commerce product dataset, we show that a distilled small BERT-based model (75M params) trained using our approach improves the search relevance metric by up to 23% over a baseline DSSM-based model with similar inference latency. The small model only suffers a 3% drop in relevance metric compared to the 20x larger teacher. We also show using online A/B tests at scale, that our approach improves over the production model in exact and substitute products retrieved.
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Tsurkov, Vladimir. "Exact and Approximate Aggregation." In Large-scale Optimization — Problems and Methods, 1–76. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-3243-6_1.

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Cygan, Marek, and Marcin Pilipczuk. "Exact and Approximate Bandwidth." In Automata, Languages and Programming, 304–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02927-1_26.

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Godbole, Anant P., Sanjay Khunger, and Esther Ososanya. "Exact and Approximate Hypercube Reliabilities." In Runs and Patterns in Probability, 163–72. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4613-3635-8_10.

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Helgaker, Trygve, Poul Jørgensen, and Jeppe Olsen. "Exact and Approximate Wave Functions." In Molecular Electronic-Structure Theory, 107–41. Chichester, UK: John Wiley & Sons, Ltd, 2014. http://dx.doi.org/10.1002/9781119019572.ch4.

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Elad, Michael. "From Exact to Approximate Solutions." In Sparse and Redundant Representations, 79–109. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7011-4_5.

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Alon, Noga, and Shai Gutner. "Balanced Hashing, Color Coding and Approximate Counting." In Parameterized and Exact Computation, 1–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-11269-0_1.

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Dodson, M. M. "Abstract Exact and Approximate Sampling Theorems." In New Perspectives on Approximation and Sampling Theory, 1–21. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08801-3_1.

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Conference papers on the topic "Exact and approximate inferences"

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Marinescu, Radu, Haifeng Qian, Alexander Gray, Debarun Bhattacharjya, Francisco Barahona, Tian Gao, and Ryan Riegel. "Approximate Inference in Logical Credal Networks." 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.2023/632.

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The Logical Credal Network or LCN is a recent probabilistic logic designed for effective aggregation and reasoning over multiple sources of imprecise knowledge. An LCN specifies a set of probability distributions over all interpretations of a set of logical formulas for which marginal and conditional probability bounds on their truth values are known. Inference in LCNs involves the exact solution of a non-convex non-linear program defined over an exponentially large number of non-negative real valued variables and, therefore, is limited to relatively small problems. In this paper, we present ARIEL -- a novel iterative message-passing scheme for approximate inference in LCNs. Inspired by classical belief propagation for graphical models, our method propagates messages that involve solving considerably smaller local non-linear programs. Experiments on several classes of LCNs demonstrate clearly that ARIEL yields high quality solutions compared with exact inference and scales to much larger problems than previously considered.
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van Bremen, Timothy, and Ondrej Kuzelka. "Approximate Weighted First-Order Model Counting: Exploiting Fast Approximate Model Counters and Symmetry." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/587.

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We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count of a sentence given an unweighted first-order model counting oracle. The algorithm has applications to inference in a variety of first-order probabilistic representations, such as Markov logic networks and probabilistic logic programs. Crucially for many applications, no assumptions are made on the form of the input sentence. Instead, the algorithm makes use of the symmetry inherent in the problem by imposing cardinality constraints on the number of possible true groundings of a sentence's literals. Realising the first-order model counting oracle in practice using the approximate hashing-based model counter ApproxMC3, we show how our algorithm is competitive with existing approximate and exact techniques for inference in first-order probabilistic models. We additionally provide PAC guarantees on the accuracy of the bounds generated.
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Lee, K. David, Eric Wiesenfeld, and Andrew Gelfand. "Statistical comparison of a hybrid approach with approximate and exact inference models for Fusion 2+." In Defense and Security Symposium, edited by Ivan Kadar. SPIE, 2007. http://dx.doi.org/10.1117/12.717398.

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Lee, Nian-Ze, Yen-Shi Wang, and Jie-Hong R. Jiang. "Solving Stochastic Boolean Satisfiability under Random-Exist Quantification." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/96.

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Stochastic Boolean Satisfiability (SSAT) is a powerful formalism to represent computational problems with uncertainly, such as belief network inference and propositional probabilistic planning. Solving SSAT formulas lies in the same complexity class (PSPACE-complete) as solving Quantified Boolean Formula (QBF). While many endeavors have been made to enhance QBF solving, SSAT has drawn relatively less attention in recent years. This paper focuses on random-exist quantified SSAT formulas, and proposes an algorithm combining binary decision diagram (BDD), logic synthesis, and modern SAT techniques to improve computational efficiency. Unlike prior exact SSAT algorithms, the proposed method can be easily modified to solve approximate SSAT by deriving upper and lower bounds of satisfying probability. Experimental results show that our method outperforms the state-of-the-art algorithm on random k-CNF formulas and has effective application to approximate SSAT on circuit benchmarks.
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Tian, Zheng, Ying Wen, Zhichen Gong, Faiz Punakkath, Shihao Zou, and Jun Wang. "A Regularized Opponent Model with Maximum Entropy Objective." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/85.

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In a single-agent setting, reinforcement learning (RL) tasks can be cast into an inference problem by introducing a binary random variable o, which stands for the "optimality". In this paper, we redefine the binary random variable o in multi-agent setting and formalize multi-agent reinforcement learning (MARL) as probabilistic inference. We derive a variational lower bound of the likelihood of achieving the optimality and name it as Regularized Opponent Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel perspective on opponent modeling and show how it can improve the performance of training agents theoretically and empirically in cooperative games. To optimize ROMMEO, we first introduce a tabular Q-iteration method ROMMEO-Q with proof of convergence. We extend the exact algorithm to complex environments by proposing an approximate version, ROMMEO-AC. We evaluate these two algorithms on the challenging iterated matrix game and differential game respectively and show that they can outperform strong MARL baselines.
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Allphin, Devin, and Joshua Hamel. "A Parallel Offline CFD and Closed-Form Approximation Strategy for Computationally Efficient Analysis of Complex Fluid Flows." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38691.

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Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flow variables. This artificial relationship-building technique, called meta-modeling or surrogate/offline approximation, uses design of experiments (DOE) theory to efficiently approximate non-physical coupling between the variables of interest in a fluid flow analysis problem. By mathematically approximating these variables, DOE methods can effectively reduce the required quantity of CFD simulations, freeing computational resources for other analytical focuses. An idealized interpretation of a fluid flow problem can also be employed to create suitably accurate approximations of fluid flow variables for the purposes of engineering analysis. When used in parallel with a meta-modeling approximation, a closed-form approximation can provide useful feedback concerning proper construction, suitability, or even necessity of an offline approximation tool. It also provides a short-circuit pathway for further reducing the overall computational demands of a fluid flow analysis, again freeing resources for otherwise unsuitable resource expenditures. To validate these inferences, a design optimization problem was presented requiring the inexpensive estimation of aerodynamic forces applied to a valve operating on a simulated piston-cylinder heat engine. The determination of these forces was to be found using parallel surrogate and exact approximation methods, thus evidencing the comparative benefits of this technique. For the offline approximation, latin hypercube sampling (LHS) was used for design space filling across four independent design variable degrees of freedom (DOF). Flow solutions at the mapped test sites were converged using STAR-CCM+ with aerodynamic forces from the CFD models then functionally approximated using Kriging interpolation. For the closed-form approximation, the problem was interpreted as an ideal 2-D converging-diverging (C-D) nozzle, where aerodynamic forces were directly mapped by application of the Euler equation solutions for isentropic compression/expansion. A cost-weighting procedure was finally established for creating model-selective discretionary logic, with a synthesized parallel simulation resource summary provided.
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Jha, Chandan Kumar, and Joycee Mekie. "SEDA - Single Exact Dual Approximate Adders for Approximate Processors." In DAC '19: The 56th Annual Design Automation Conference 2019. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3316781.3322475.

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Yeredor, Arie. "On hybrid exact-approximate joint diagonalization." In 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2009. http://dx.doi.org/10.1109/camsap.2009.5413271.

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Huber, Mark. "Exact sampling and approximate counting techniques." In the thirtieth annual ACM symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/276698.276709.

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Piper, John E. "Exact and approximate time-shift operators." In SPIE Defense, Security, and Sensing, edited by Edmund G. Zelnio and Frederick D. Garber. SPIE, 2009. http://dx.doi.org/10.1117/12.818196.

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Reports on the topic "Exact and approximate inferences"

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Mobley, Curtis D. Ecosystem Predictions with Approximate vs. Exact Light Fields. Fort Belvoir, VA: Defense Technical Information Center, March 2009. http://dx.doi.org/10.21236/ada495652.

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Mobley, Curtis D. Ecosystem Predictions with Approximate vs. Exact Light Fields. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada519107.

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Boland, Matthew R. Examination of the Use of Exact Versus Approximate Phase Weights on the Performance of a Synthetic Aperture Sonar System. Fort Belvoir, VA: Defense Technical Information Center, March 2003. http://dx.doi.org/10.21236/ada414590.

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Zarrieß, Benjamin, and Anni-Yasmin Turhan. Most Specific Generalizations w.r.t. General EL-TBoxes. Technische Universität Dresden, 2013. http://dx.doi.org/10.25368/2022.196.

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In the area of Description Logics the least common subsumer (lcs) and the most specific concept (msc) are inferences that generalize a set of concepts or an individual, respectively, into a single concept. If computed w.r.t. a general EL-TBox neither the lcs nor the msc need to exist. So far in this setting no exact conditions for the existence of lcs- or msc-concepts are known. This report provides necessary and suffcient conditions for the existence of these two kinds of concepts. For the lcs of a fixed number of concepts and the msc we show decidability of the existence in PTime and polynomial bounds on the maximal roledepth of the lcs- and msc-concepts. The latter allows to compute the lcs and the msc, respectively.
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Baader, Franz, and Oliver Fernández Gil. Decidability and Complexity of Threshold Description Logics Induced by Concept Similarity Measures. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.229.

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In a recent research paper, we have proposed an extension of the lightweight Description Logic (DL) EL in which concepts can be defined in an approximate way. To this purpose, the notion of a graded membership function m, which instead of a Boolean membership value 0 or 1 yields a membership degree from the interval [0; 1], was introduced. Threshold concepts can then, for example, require that an individual belongs to a concept C with degree at least 0:8. Reasoning in the threshold DL T EL(m) obtained this way of course depends on the employed graded membership function m. The paper defines a specific such function, called deg, and determines the exact complexity of reasoning in T EL(deg). In addition, it shows how concept similarity measures (CSMs) ~ satisfying certain properties can be used to define graded membership functions m~, but it does not investigate the complexity of reasoning in the induced threshold DLs T EL(m~). In the present paper, we start filling this gap. In particular, we show that computability of ~ implies decidability of T EL(m~), and we introduce a class of CSMs for which reasoning in the induced threshold DLs has the same complexity as in T EL(deg).
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Allegheny woodrat and eastern small-footed bat inventory: White Rocks ? Cumberland Gap National Historical Park. National Park Service, 2024. http://dx.doi.org/10.36967/2302513.

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Surveys were conducted for the presence of Allegheny woodrats, eastern small-footed bats, and their habitat within Sample Units surrounding potential climbing routes on the White Rocks cliff of Cumberland Gap National Historical Park. White Rocks is a 200-300ft south facing cliff along the Virginia- Kentucky border that contains the typical habitat requirements of both species: rock ledges, outcrops, or a network of fissures and crevices surrounded by forested habitat. The eastern small-footed bat uses this type of habitat primarily during the summer months for roosting while the Allegheny woodrat is present year-round building nests within deep crevices. The eastern small-footed bat is listed as threatened in Kentucky and both are considered Species of Greatest Conservation Need in Virginia. The rock-climbing community has approached the National Park Service with interest in opening the cliff to recreational climbing. The results of this survey will be used to assess impacts to the species and aid in the studies required for the potential development of a formal climbing management plan. Surveys were conducted from August 24 to September 3, 2021, and included searches of the cliff face via rappelling, ground searches of suitable habitat surrounding the rim and base of the climbing routes, and noninvasive woodrat camera trap and bat acoustic surveys. Suitable eastern small-footed bat and Allegheny woodrat habitat was documented along all eleven potential climbing routes, and results of the acoustic and camera trap surveys confirmed the presence of both species. Surveyors did not observe roosting bats during visual encounter surveys, so we cannot confirm they are roosting along the specific climbing routes. It is likely they are using or could use the habitat at some point given their presence at the site. Surveyors did not observe obvious sign of woodrat presence, perhaps due to the complexity of the cliff habitat, but woodrats were captured at 32 of 37 (86%) camera sites. Video of woodrat activity at sites F3-C3, MF-C3, and CC-C1 confirm that these cameras were placed at crevices actively used by woodrats for caching food. Woodrat activity was captured on the first night at nearly half of the camera sites (40%) and within all Sample Units except SU-4. This suggests that the rim and/or base of most climbing routes are at or near core activity centers. Detection data was fitted to occupancy models to estimate probabilities of site occupancy and detection. Consistent with observations of woodrat activity detection probabilities and na?ve estimates of occupancy indicate woodrats are active at both the rim and base throughout the white rocks area. Design constraints, however, make it difficult to make strong inferences about factors affecting occupancy at the site or to predict occupancy at unsampled areas of the White Rocks cliff. Detection probabilities were high in all Sample Units especially after the first night of detection and were positively associated with habitat. However, these variables had little to do with site occupancy rates and are not very informative for predicting the influence of climbing activities on Allegheny woodrats. Research on the effects of rock climbing to roosting bats and Allegheny woodrats is lacking, but it has the potential to negatively impact these species both directly and indirectly. Directly through disturbance or harm to roosting bats or woodrats during climbing activities and indirectly through degradation of the cliff face and loss of suitable habitat. Whether climbing activities negatively affect the population of either species may depend on the amount of suitable habitat in areas where climbing does not occur and the extent of climbing activities. Suitable habitat does not appear to be a limiting factor at the site and the White Rocks cliff area extends beyond the potential climbing areas. These and other factors such as the presence of other species of concern should be considered when evaluating alternatives to continue climbing closures or consider opening the cliff to recreational climbing with protection measures. Measures that may reduce the impact of climbing activities on these species include additional surveys to determine exact roosting or nesting areas, restrictions on the amount and timing of climbing activities, restrictions on actions that degrade or remove vegetation from the rock surface, and education about the presence of these species at the site.
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