Добірка наукової літератури з теми "Monotone bounded integration"

In this work, we propose a definition of comonotonicity for elements of [Formula: see text], i.e. bounded self-adjoint operators defined over a complex Hilbert space [Formula: see text]. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of [Formula: see text] that generalizes quantum expectations. We characterize Choquet expectations as the real-valued functionals over [Formula: see text] which are comonotonic additive, [Formula: see text]-monotone, and normalized.

In this paper, we study a dynamically consistent numerical method for the approximation of a nonlinear integro-differential equation modeling an epidemic with age of infection. The discrete scheme is based on direct quadrature methods with Gregory convolution weights and preserves, with no restrictive conditions on the step-length of integration h, some of the essential properties of the continuous system. In particular, the numerical solution is positive and bounded and, in cases of interest in applications, it is monotone. We prove an order of convergence theorem and show by numerical experiments that the discrete final size tends to its continuous equivalent as h tends to zero.

In this paper, we study the problem of selecting a subset from a ground set to maximize a monotone objective function f such that a monotone cost function c is bounded by an upper limit. State-of-the-art algorithms include the generalized greedy algorithm and POMC. The former is an efficient fixed time algorithm, but the performance is limited by the greedy nature. The latter is an anytime algorithm that can find better subsets using more time, but without any polynomial-time approximation guarantee. In this paper, we propose a new anytime algorithm EAMC, which employs a simple evolutionary algorithm to optimize a surrogate objective integrating f and c. We prove that EAMC achieves the best known approximation guarantee in polynomial expected running time. Experimental results on the applications of maximum coverage, influence maximization and sensor placement show the excellent performance of EAMC.

There are several generalized linear mixed models to combine direct and indirect evidence on several diagnostic tests from related but independent diagnostic studies simultaneously also known as network meta-analysis. The popularity of these models is due to the attractive features of the normal distribution and the availability of statistical software to obtain parameter estimates. However, modeling the latent sensitivity and specificity using the normal distribution after transformation is neither natural nor computationally convenient. In this article, we develop a meta-analytic model based on the bivariate beta distribution, allowing to obtain improved and direct estimates for the global sensitivities and specificities of all tests involved, and taking into account simultaneously the intrinsic correlation between sensitivity and specificity and the overdispersion due to repeated measures. Using the beta distribution in regression has the following advantages, that the probabilities are modeled in their proper scale rather than a monotonic transform of the probabilities. Secondly, the model is flexible as it allows for asymmetry often present in the distribution of bounded variables such as proportions, which is the case with sparse data common in meta-analysis. Thirdly, the model provides parameters with direct meaningful interpretation since further integration is not necessary to obtain the meta-analytic estimates.

A VLSI chip is fabricated by integrating several rectangular circuit blocks on a 2D silicon floor. The circuit blocks are assumed to be placed isothetically and the netlist attached to each block is given. For wire routing, the terminals belonging to the same net are to be electrically interconnected using conducting paths. A staircase channel is an empty polygonal region on the silicon floor bounded by two monotonically increasing (or decreasing) staircase paths from one corner of the floor to its diagonally opposite corner. The staircase paths are defined by the boundaries of the blocks. In this paper, the problem of determining a monotone staircase channel on the floorplan is considered such that the number of distinct nets whose terminals lie on both sides of the channel, is minimized. Two polynomial-time algorithms are presented based on the network flow paradigm. First, the simple two-terminal net model is considered, i.e., each net is assumed to connect exactly two blocks, for which an O(n×k) time algorithm is proposed, where n and k are respectively the number of blocks and nets on the floor. Next, the algorithm is extended to the more realistic case of multi-terminal net problem. The time complexity of the latter algorithm is O((n+k)×T), where T is the total number of terminals attached to all nets in the floorplan. Solutions to these problems are useful in modeling the repeater block placement that arises in interconnect-driven floorplanning for deep-submicron VLSI physical design. It is also an important problem in context to the classical global routing, where channels are used as routing space on silicon.

The aim of this article is to find a geometric and physical interpretation of fractional order derivatives for a general class of functions defined over a bounded or unbounded domain. We show theoretically and geometrically that the absolute value of the fractional derivative value of a function is inversely proportional to the area of the triangle. Further, we prove geometrically that the fractional derivatives are inversely proportional to the classical integration in some sense. The established results are verified numerically for non‐monotonic, trigonometric, and power functions. Further, this article establishes a significant connection between the area of the projected fence and the area of triangles. As the area of triangles decreases, the area of the projected fence increases, and vice versa. We calculate the turning points of the fractional derivative values of different functions with respect to order , including non‐monotonic, trigonometric, and power functions. In particular, we demonstrate that for the power function , with being a positive real number, the value is a turning point when . However, for , the turning point shifts to the left of point and shifts to the right of point for We discuss the physical interpretation of fractional order derivatives in terms of fractional divergence. We present some applications of fractional tangent lines in the field of numerical analysis.

Ce manuscrit se concentre sur l'optimisation Bayésienne d'un modèle d'appréciation quantitative des risques microbiologiques (AQRM) dans le cadre du projet ArtiSaneFood soutenu par l'Union européenne. L'objectif est d'établir des stratégies de bio-intervention efficaces pour les fabricants de fromage au lait cru en France, en s'appuyant sur trois types de travaux : 1) le développement d'un modèle AQRM multipathogène pour un fromage de type pâte molle au lait cru, 2) étudier des méthodes d'intégration monotone pour l'estimation des sorties du modèle AQRM et 3) la conception d'un algorithme d'optimisation Bayésienne adapté à un simulateur stochastique et coûteux.Dans la première partie, nous proposons un modèle AQRM multipathogène construit sur la base d'études existantes (voir, par exemple, Bonifait et al., 2021, Perrin et al., 2014, Sanaa et al., 2004, Strickland et al., 2023). Ce modèle est conçu pour estimer l'impact des maladies d'origine alimentaire sur la santé publique, causées par des agents pathogènes tels que Escherichia coli entérohémorragiques (EHEC), Salmonella et Listeria monocytogenes, potentiellement présents dans le fromage de type pâte molle au lait cru. Ce modèle “farm-to-fork” intègre les mesure de maitrise liées aux tests microbiologiques du lait et du fromage, permettant d'estimer les coûts associés aux interventions. Une implémentation du modèle AQRM pour EHEC est fournie en R et dans le cadre FSKX (Basak et al., under review). La deuxième partie de ce manuscrit explore l'application potentielle de méthodes d'intégration séquentielle, exploitant les propriétés de monotonie et de bornage des sorties du simulateur. Nous menons une revue de littérature approfondie sur les méthodes d'intégration existantes (voir, par exemple, Kiefer, 1957, Novak, 1992), et examinons les résultats théoriques concernant leur convergence. Notre contribution comprend la proposition d'améliorations à ces méthodes et la discussion des défis associés à leur application dans le domaine de l'AQRM.Dans la dernière partie de ce manuscrit, nous proposons un algorithme Bayésien d'optimisation multiobjectif pour estimer les entrées optimales de Pareto d'un simulateur stochastique et coûteux en calcul. L'approche proposée est motivée par le principe de “Stepwise Uncertainty Reduction” (SUR) (voir, par exemple, Vazquez and Bect, 2009, Vazquez and Martinez, 2006, Villemonteix et al., 2007), avec un critère d'échantillonnage basé sur weighted integrated mean squared error (w-IMSE). Nous présentons une évaluation numérique comparant l'algorithme proposé avec PALS (Pareto Active Learning for Stochastic simulators) (Barracosa et al., 2021), sur un ensemble de problèmes de test bi-objectifs. Nous proposons également une extension (Basak et al., 2022a) de l'algorithme PALS, adaptée au cas d'application de l'AQRM
This manuscript focuses on Bayesian optimization of a quantitative microbiological risk assessment (QMRA) model, in the context of the European project ArtiSaneFood, supported by the PRIMA program. The primary goal is to establish efficient bio-intervention strategies for cheese producers in France.This work is divided into three broad directions: 1) development and implementation of a multipathogen QMRA model for raw milk soft cheese, 2) studying monotone integration methods for estimating outputs of the QMRA model, and 3) designing a Bayesian optimization algorithm tailored for a stochastic and computationally expensive simulator.In the first part we propose a multipathogen QMRA model, built upon existing studies in the literature (see, e.g., Bonifait et al., 2021, Perrin et al., 2014, Sanaa et al., 2004, Strickland et al., 2023). This model estimates the impact of foodborne illnesses on public health, caused by pathogenic STEC, Salmonella and Listeria monocytogenes, which can potentially be present in raw milk soft cheese. This farm-to-fork model also implements the intervention strategies related to mlik and cheese testing, which allows to estimate the cost of intervention. An implementation of the QMRA model for STEC is provided in R and in the FSKX framework (Basak et al., under review). The second part of this manuscript investigates the potential application of sequential integration methods, leveraging the monotonicity and boundedness properties of the simulator outputs. We conduct a comprehensive literature review on existing integration methods (see, e.g., Kiefer, 1957, Novak, 1992), and delve into the theoretical findings regarding their convergence. Our contribution includes proposing enhancements to these methods and discussion on the challenges associated with their application in the QMRA domain.In the final part of this manuscript, we propose a Bayesian multiobjective optimization algorithm for estimating the Pareto optimal inputs of a stochastic and computationally expensive simulator. The proposed approach is motivated by the principle of Stepwise Uncertainty Reduction (SUR) (see, e.g., Vazquezand Bect, 2009, Vazquez and Martinez, 2006, Villemonteix et al., 2007), with a weighted integrated mean squared error (w-IMSE) based sampling criterion, focused on the estimation of the Pareto front. A numerical benchmark is presented, comparing the proposed algorithm with PALS (Pareto Active Learning for Stochastic simulators) (Barracosa et al., 2021), over a set of bi-objective test problems. We also propose an extension (Basak et al., 2022a) of the PALS algorithm, tailored to the QMRA application case

Recent applications of description logics (DLs) strongly suggest the integration of non-monotonic features into DLs, with particular attention to defeasible inheritance. However, the existing non-monotonic extensions of DLs are usually based on default logic or autoepistemic logic, and have to be seriously restricted in expressive power to preserve the decidability of reasoning. In particular, such DLs allow the modelling of defeasible inheritance only in a very restricted form, where non-monotonic reasoning is limited to individuals that are explicitly identified by constants in the knowledge base. In this paper, we consider non-monotonic extensions of expressive DLs based on circumscription. We prove that reasoning in such DLs is decidable even without the usual, strong restrictions in expressive power. We pinpoint the exact computational complexity of reasoning as complete for NPNEXP and NEXPNP, depending on whether or not the number of minimized and fixed predicates is assumed to be bounded by a constant. These results assume that only concept names (and no role names) can be minimized and fixed during minimization. On the other hand, we show that fixing role names during minimization makes reasoning undecidable.