The aim of the current research is to analyse and discover, in a real context, behaviours, reactions and modes of interaction of social actors (people) with the humanoid robot Pepper. Indeed, we wanted to observe in a real, highly frequented context, the reactions and interactions of people with Pepper, placed in a shop window, through a systematic observation approach. The most interesting aspects of this research will be illustrated, bearing in mind that this is a preliminary analysis, therefore, not yet definitively concluded.
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Problems from metric graph theory such as Metric Dimension, Geodetic Set, and Strong Metric Dimension have recently had a strong impact on the field of parameterized complexity by being the first problems in NP to admit double-exponential lower bounds in the treewidth, and even in the vertex cover number for the latter. We initiate the study of enumerating minimal solution sets for these problems and show that they are also of great interest in enumeration. More specifically, we show that enumerating minimal resolving sets in graphs and minimal geodetic sets in split graphs are equivalent to hypergraph dualization, arguably one of the most important open problems in algorithmic enumeration. This provides two new natural examples to a question that emerged in different works this last decade: for which vertex (or edge) set graph property $\Pi$ is the enumeration of minimal (or maximal) subsets satisfying $\Pi$ equivalent to hypergraph dualization? As only very few properties are known to fit within this context -- namely, properties related to minimal domination -- our results make significant progress in characterizing such properties, and provide new angles of approach for tackling hypergraph dualization. In a second step, we consider cases where our reductions do not apply, namely graphs with no long induced paths, and show these cases to be mainly tractable.
We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the trapezoidal rule and A-stable convolution quadrature is stated and analysed. Existence and regularity analysis of the continuous equations informs the stability and error analysis of the semi-discrete system. The error analysis includes the consideration of the singularity at $t = 0$ which is addressed by the use of a correction in the numerical scheme. Extensive numerical experiments confirm the theory.
An arc-search interior-point method is a type of interior-point methods that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov's restarting strategy that is well-known method to accelerate the gradient method with a momentum term. The first one generates a sequence of iterations in the neighborhood, and we prove that the convergence of the generated sequence to an optimal solution and the computation complexity is polynomial time. The second one incorporates the concept of the Mehrotra-type interior-point method to improve numerical performance. The numerical experiments demonstrate that the second one reduced the number of iterations and computational time. In particular, the average number of iterations was reduced compared to existing interior-point methods due to the momentum term.
Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. In this paper, we develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (XVAE), whose parameters are estimated via variational Bayes combined with deep learning. The XVAE can be used as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same statistical properties as the inputs, especially in the tail. As an aside, our approach also provides a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while also outperforming many spatial extremes models with a stationary dependence structure. To further demonstrate the computational power of the XVAE, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16703 grid cells. We find that the extremal dependence strength is weaker in the interior of Red Sea and it has decreased slightly over time.
Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which directly discretize Langevin dynamics to estimate expectations over the target distribution. We study the use of transport maps that approximately normalize a target distribution as a way to precondition and accelerate the convergence of Langevin dynamics. We show that in continuous time, when a transport map is applied to Langevin dynamics, the result is a Riemannian manifold Langevin dynamics (RMLD) with metric defined by the transport map. We also show that applying a transport map to an irreversibly-perturbed ULA results in a geometry-informed irreversible perturbation (GiIrr) of the original dynamics. These connections suggest more systematic ways of learning metrics and perturbations, and also yield alternative discretizations of the RMLD described by the map, which we study. Under appropriate conditions, these discretized processes can be endowed with non-asymptotic bounds describing convergence to the target distribution in 2-Wasserstein distance. Illustrative numerical results complement our theoretical claims.
Temporal analysis of products (TAP) reactors enable experiments that probe numerous kinetic processes within a single set of experimental data through variations in pulse intensity, delay, or temperature. Selecting additional TAP experiments often involves arbitrary selection of reaction conditions or the use of chemical intuition. To make experiment selection in TAP more robust, we explore the efficacy of model-based design of experiments (MBDoE) for precision in TAP reactor kinetic modeling. We successfully applied this approach to a case study of synthetic oxidative propane dehydrogenation (OPDH) that involves pulses of propane and oxygen. We found that experiments identified as optimal through the MBDoE for precision generally reduce parameter uncertainties to a higher degree than alternative experiments. The performance of MBDoE for model divergence was also explored for OPDH, with the relevant active sites (catalyst structure) being unknown. An experiment that maximized the divergence between the three proposed mechanisms was identified and led to clear mechanism discrimination. However, re-optimization of kinetic parameters eliminated the ability to discriminate. The findings yield insight into the prospects and limitations of MBDoE for TAP and transient kinetic experiments.
We show how quantum-inspired 2d tensor networks can be used to efficiently and accurately simulate the largest quantum processors from IBM, namely Eagle (127 qubits), Osprey (433 qubits) and Condor (1121 qubits). We simulate the dynamics of a complex quantum many-body system -- specifically, the kicked Ising experiment considered recently by IBM in Nature 618, p. 500-505 (2023) -- using graph-based Projected Entangled Pair States (gPEPS), which was proposed by some of us in PRB 99, 195105 (2019). Our results show that simple tensor updates are already sufficient to achieve very large unprecedented accuracy with remarkably low computational resources for this model. Apart from simulating the original experiment for 127 qubits, we also extend our results to 433 and 1121 qubits, thus setting a benchmark for the newest IBM quantum machines. We also report accurate simulations for infinitely-many qubits. Our results show that gPEPS are a natural tool to efficiently simulate quantum computers with an underlying lattice-based qubit connectivity, such as all quantum processors based on superconducting qubits.
The aim of this study is to analyze the effect of serum metabolites on diabetic nephropathy (DN) and predict the prevalence of DN through a machine learning approach. The dataset consists of 548 patients from April 2018 to April 2019 in Second Affiliated Hospital of Dalian Medical University (SAHDMU). We select the optimal 38 features through a Least absolute shrinkage and selection operator (LASSO) regression model and a 10-fold cross-validation. We compare four machine learning algorithms, including eXtreme Gradient Boosting (XGB), random forest, decision tree and logistic regression, by AUC-ROC curves, decision curves, calibration curves. We quantify feature importance and interaction effects in the optimal predictive model by Shapley Additive exPlanations (SHAP) method. The XGB model has the best performance to screen for DN with the highest AUC value of 0.966. The XGB model also gains more clinical net benefits than others and the fitting degree is better. In addition, there are significant interactions between serum metabolites and duration of diabetes. We develop a predictive model by XGB algorithm to screen for DN. C2, C5DC, Tyr, Ser, Met, C24, C4DC, and Cys have great contribution in the model, and can possibly be biomarkers for DN.
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well-established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability of the partial differential equation (PDE) models that are requisite to capture spatial features inherent to many phenomena. The differential algebra approach to structural identifiability has recently been demonstrated to be applicable to several specific PDE models. In this brief article, we present general methodology for performing structural identifiability analysis on partially observed linear reaction-advection-diffusion (RAD) PDE models. We show that the differential algebra approach can always, in theory, be applied to linear RAD models. Moreover, despite the perceived complexity introduced by the addition of advection and diffusion terms, identifiability of spatial analogues of non-spatial models cannot decrease structural identifiability. Finally, we show that our approach can also be applied to a class of non-linear PDE models that are linear in the unobserved variables, and conclude by discussing future possibilities and computational cost of performing structural identifiability analysis on more general PDE models in mathematical biology.
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors with independent coordinates having ordinary smooth densities, we derive an inversion inequality relating the $L^1$-Wasserstein distance between two distributions of the signal to the $L^1$-distance between the corresponding mixture densities of the observations. This smoothing inequality outperforms existing inversion inequalities. As an application of the inversion inequality to the Bayesian framework, we consider $1$-Wasserstein deconvolution with Laplace noise in dimension one using a Dirichlet process mixture of normal densities as a prior measure on the mixing distribution (or distribution of the signal). We construct an adaptive approximation of the sampling density by convolving the Laplace density with a well-chosen mixture of normal densities and show that the posterior measure concentrates around the sampling density at a nearly minimax rate, up to a log-factor, in the $L^1$-distance. The same posterior law is also shown to automatically adapt to the unknown Sobolev regularity of the mixing density, thus leading to a new Bayesian adaptive estimation procedure for mixing distributions with regular densities under the $L^1$-Wasserstein metric. We illustrate utility of the inversion inequality also in a frequentist setting by showing that an appropriate isotone approximation of the classical kernel deconvolution estimator attains the minimax rate of convergence for $1$-Wasserstein deconvolution in any dimension $d\geq 1$, when only a tail condition is required on the latent mixing density and we derive sharp lower bounds for these problems
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