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Classical dynamics from self-consistency equations in quantum mechanics
Get PDFDuring the last three decades, P. Bóna has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence of macroscopic classical dynamics from microscopic quantum processes. We propose here a new mathematical approach to Bona's one, with much brother domain of applicability. It highlights the central role of self-consistency. This leads to a mathematical framework in which the classical and quantum worlds are naturally entangled. We build a Poisson bracket for the polynomial functions on the hermitian weak∗ continuous functionals on any C∗-algebra. This is reminiscent of a well-known construction for finite-dimensional Lie algebras. We then restrict this Poisson bracket to states of this C∗-algebra, by taking quotients with respect to Poisson ideals. This leads to densely defined symmetric derivations on the commutative C∗-algebras of real-valued functions on the set of states. Up to a closure, these are proven to generate C0-groups of contractions. As a matter of fact, in general commutative C∗-algebras, even the closableness of unbounded symmetric derivations is a non-trivial issue. Some new mathematical concepts are introduced, which are possibly interesting by themselves: the convex weak ∗ Gâteaux derivative, state-dependent C∗-dynamical systems and the weak∗-Hausdorff hypertopology, a new hypertopology used to prove, among other things, that convex weak∗-compact sets generically have weak∗-dense extreme boundary in infinite dimension. Our recent results on macroscopic dynamical properties of lattice-fermion and quantum-spin systems with long-range, or mean-field, interactions corroborate the relevance of the general approach we present here. Note that the present paper is an extended version of the published one.This work was supported by CNPq (Grant No. 309723/2020-5); FAPESP (Grant No. 2017/22340-9); the Basque Government through the BERC 2022-2025 program; the Spanish Ministry of Science, Innovation and Universities (BCAM Severo Ochoa accreditation Grant Nos. SEV-2017-0718 and PID2020-112948GB-I00); and the COST Action CA18232 financed by the European Cooperation in Science and Technology (COST)
Minimax Classification under Concept Drift with Multidimensional Adaptation and Performance Guarantees
Get PDFThe statistical characteristics of instance-label pairs often change with time in practical scenarios of supervised classification. Conventional learning techniques adapt to such concept drift accounting for a scalar rate of change by means
of a carefully chosen learning rate, forgetting factor, or window size. However, the time changes in common scenarios are multidimensional, i.e., different statistical characteristics often change in a different manner. This paper presents adaptive minimax risk classifiers (AMRCs) that account for multidimensional time changes by means of a multivariate and high-order tracking
of the time-varying underlying distribution. In addition, differently from conventional techniques, AMRCs can provide computable tight performance guarantees. Experiments on multiple benchmark datasets show the classification improvement of AMRCs compared to the state-of-the-art and the reliability of the presented performance guarantees.Ramon y Cajal Grant RYC-2016-19383
BCAM’s Severo Ochoa Excellence Accreditation SEV-2017-0718, the Spanish Ministry of Economic Affairs and Digital Transformation
through Project IA4TES MIA.2021.M04.0008,
and by the Basque Government through the
IT-1504-22, and BERC 2022-2025 programmes
1D Painless Multi-level Automatic Goal-Oriented h and p Adaptive Strategies Using a Pseudo-Dual Operator
Get PDFThe main idea of our Goal-Oriented Adaptive (GOA) strategy is based on performing global and uniform h- or p-refinements (for h- and p-adaptivity, respectively) followed by a coarsening step, where some basis functions are removed according to their estimated importance. Many Goal-Oriented Adaptive strategies represent the error in a Quantity of Interest (QoI) in terms of the bilinear form and the solution of the direct and adjoint problems. However, this is unfeasible when solving indefinite or non-symmetric problems since symmetric and positive definite forms are needed to define the inner product that guides the refinements. In this work, we provide a Goal-Oriented Adaptive (h- or p-) strategy whose error in the QoI is represented in another bilinear symmetric positive definite form than the one given by the adjoint problem. For that purpose, our Finite Element implementation employs a multi-level hierarchical data structure that imposes Dirichlet homogeneous nodes to avoid the so-called hanging nodes. We illustrate the convergence of the proposed approach for 1D Helmholtz and convection-dominated problems
Uniform Lech's inequality
Get PDFLet (R,m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, this set is bounded above by a finite constant depending only on M. The lower bound extends a classical inequality of Lech, and the upper bound answers a question of Stückrad–Vogel in the affirmative. As an application, we obtain results on uniform behavior of the lengths of Koszul homology moduleLa Caixa Junior Leader Postdoctoral Fellowship “LCF/BQ/PI21/11830033”.
PID2021-125052NA-I0
Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking
Get PDFIn this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone
A self-organizing weighted optimization based framework for large-scale multi-objective optimization
Get PDFThe solving of large-scale multi-objective optimization problem (LSMOP) has become a hot research topic in evolutionary computation. To better solve this problem, this paper proposes a self-organizing weighted optimization based framework, denoted S-WOF, for addressing LSMOPs. Compared to the original framework, there are two main improvements in our work. Firstly, S-WOF simplifies the evolutionary stage into one stage, in which the evaluating numbers of weighted based optimization and normal optimization approaches are adaptively adjusted based on the current evolutionary state. Specifically, regarding the evaluating number for weighted based optimization (i.e., t1), it is larger when the population is in the exploitation state, which aims to accelerate the convergence speed, while t1 is diminishing when the population is switching to the exploration state, in which more attentions are put on the diversity maintenance. On the other hand, regarding the evaluating number for original optimization (i.e., t2), which shows an opposite trend to t1, it is small during the exploitation stage but gradually increases later. In this way, a dynamic trade-off between convergence and diversity is achieved in S-WOF. Secondly, to further improve the search ability in the large-scale decision space, an efficient competitive swarm optimizer (CSO) is implemented in S-WOF, which shows efficiency for solving LSMOPs. Finally, the experimental results have validated the superiority of S-WOF over several state-of-the-art large-scale evolutionary algorithms
An Ensemble Surrogate-Based Framework for Expensive Multiobjective Evolutionary Optimization
Get PDFSurrogate-assisted evolutionary algorithms (SAEAs) have become very popular for tackling computationally expensive multiobjective optimization problems (EMOPs), as the surrogate models in SAEAs can approximate EMOPs well, thereby reducing the time cost of the optimization process. However, with the increased number of decision variables in EMOPs, the prediction accuracy of surrogate models will deteriorate, which inevitably worsens the performance of SAEAs. To deal with this issue, this article suggests an ensemble surrogate-based framework for tackling EMOPs. In this framework, a global surrogate model is trained under the entire search space to explore the global area, while a number of surrogate submodels are trained under different search subspaces to exploit the subarea, so as to enhance the prediction accuracy and reliability. Moreover, a new infill sampling criterion is designed based on a set of reference vectors to select promising samples for training the models. To validate the generality and effectiveness of our framework, three state-of-the-art evolutionary algorithms [nondominated sorting genetic algorithm III (NSGA-III), multiobjective evolutionary algorithm based on decomposition with differential evolution (MOEA/D-DE) and reference vector-guided evolutionary algorithm (RVEA)] are embedded, which significantly improve their performance for solving most of the test EMOPs adopted in this article. When compared to some competitive SAEAs for solving EMOPs with up to 30 decision variables, the experimental results also validate the advantages of our approach in most cases
A high-resolution fuel type mapping procedure based on satellite imagery and neural networks: Updating fuel maps for wildfire simulators
Get PDFA major limitation in the simulation of forest fires involves the proper characterization of the surface vegetation over the study area, based on land cover maps. Unfortunately, these maps may be outdated, with areas where vegetation is either not documented or inaccurately portrayed. These limitations may impair the predictions of wildfire simulators or the design of risk maps and prevention plans. This study proposes a complete procedure for fuel type classification using satellite imagery and fully-connected neural networks. Specifically, our work is based on pixel- based processing cells, generating high-resolution maps. The field study is located in the Northeast of Castilla y Leo ́n, a central Spanish region, and the Rothermel criteria was followed for the fuel classification. The results record an accuracy of close to 78% on the test sets for the two studied settings, improving on the results reported in previous studies and ratifying the robustness of our approach. Additionally, the confusion matrix analysis and the per-class statistics computed confirm good reliability for all fuel types in a cross-validation framework. The predicted maps can be used on wildfire simulators through GIS tools.BERC 2022–2025
PID2019-107685RB-I00
European Regional Development Fund (ERDF) and the Department of Education of the regional government, the Junta of Castilla y Leo ́n, (Grant contract SA089P20);
the European Union’s Horizon 2020 – Research and Innovation Framework Program under Grant agreement ID 101036926
The role of asymmetric prediction losses in smart charging of electric vehicles
Get PDFClimate change prompts humanity to look for decarbonisation opportunities, and a viable option is to supply electric vehicles with renewable energy. The stochastic nature of charging demand and renewable generation requires intelligent charging driven by predictions of charging behaviour. The conventional prediction models of charging behaviour usually minimise the quadratic loss function. Moreover, the adequacy of predictions is almost solely evaluated by accuracy measures, disregarding the consequences of prediction losses in an application context. Here, we study the role of asymmetric prediction losses which enable balancing the over- and under-predictions and adjust predictions to smart charging algorithms. Using the main classes of machine learning methods, we trained prediction models of the connection duration and compared their performance for various asymmetries of the loss function. In addition, we proposed a methodological approach to quantify the consequences of prediction losses on the performance of selected archetypal smart charging schemes. In concrete situations, we demonstrated that an appropriately selected degree of the loss function asymmetry is crucial as it almost doubles the price range where the smart charging is beneficial, and increases the extent to which the charging demand is satisfied up to 40%. Additionally, the proposed methods improve charging fairness since the distribution of unmet charging demand across vehicles becomes more homogeneous.IA4TES MIA.2021.M04.000
SHOULD I STAY OR SHOULD I GO? ZERO-SIZE JUMPS IN RANDOM WALKS FOR LÉVY FLIGHTS
Get PDFWe study Markovian continuous-time random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in zero. The significance of this result is two-fold: i) with regard to the probabilistic derivation of the fractional diffusion equation and also ii) with regard to the concept of site fidelity in the framework of Lévy-like motion for wild animals.Severo Ochoa SEV-2017-071