Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model, for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact and very efficient approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.Comment: 15 pages, 8 figure

STOICHIOMETRY OF RESPIRATORY STIMULATION, ACCUMULATION OF CA++ AND PHOSPHATE, AND OXIDATIVE PHOSPHORYLATION IN RAT LIVER MITOCHONDRIA.

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Bayesian parameter inference with stochastic solar dynamo models

Time-series of cosmogenic radionuclides stored in natural archives such as ice cores and tree rings are a proxy for solar magnetic activity on multi-millennial time-scales. Radionuclides data exhibit a number of interesting features such as intermittent stable cycles of high periods and Grand Minima. Although a lot of effort has gone into the development of sound physically based stochastic solar dynamo models, it is still largely unclear what are the underlying mechanisms that lead to the observed phenomena. Answering these questions requires quantitatively calibrating the models to the data and comparing performances of different models with the associated uncertainties in model parameters and predictions. Bayesian statistics is a consistent framework for parameter inference where knowledge about model parameters is expressed through probability distributions and updated using measured data. However, Bayesian inference with non-linear stochastic models can become computationally extremely expensive and it is therefore hardly ever applied. In recent years, sophisticated and scalable algorithms have emerged, which have the potential of making Bayesian inference for complex stochastic models feasible. We intend to investigate the power of Approximate Bayesian Computation (ABC) and Hamiltonian Monte Carlo (HMC) algorithms. We present our first inference results with stochastic solar dynamo models

Supersampling and network reconstruction of urban mobility

Understanding human mobility is of vital importance for urban planning, epidemiology, and many other fields that aim to draw policies from the activities of humans in space. Despite recent availability of large scale data sets related to human mobility such as GPS traces, mobile phone data, etc., it is still true that such data sets represent a subsample of the population of interest, and then might give an incomplete picture of the entire population in question. Notwithstanding the abundant usage of such inherently limited data sets, the impact of sampling biases on mobility patterns is unclear -- we do not have methods available to reliably infer mobility information from a limited data set. Here, we investigate the effects of sampling using a data set of millions of taxi movements in New York City. On the one hand, we show that mobility patterns are highly stable once an appropriate simple rescaling is applied to the data, implying negligible loss of information due to subsampling over long time scales. On the other hand, contrasting an appropriate null model on the weighted network of vehicle flows reveals distinctive features which need to be accounted for. Accordingly, we formulate a "supersampling" methodology which allows us to reliably extrapolate mobility data from a reduced sample and propose a number of network-based metrics to reliably assess its quality (and that of other human mobility models). Our approach provides a well founded way to exploit temporal patterns to save effort in recording mobility data, and opens the possibility to scale up data from limited records when information on the full system is needed.Comment: 14 pages, 4 figure

Simulation-based inference using surjective sequential neural likelihood estimation

We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel method for simulation-based inference in models where the evaluation of the likelihood function is not tractable and only a simulator that can generate synthetic data is available. SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function which allows for conventional Bayesian inference using either Markov chain Monte Carlo methods or variational inference. By embedding the data in a low-dimensional space, SSNL solves several issues previous likelihood-based methods had when applied to high-dimensional data sets that, for instance, contain non-informative data dimensions or lie along a lower-dimensional manifold. We evaluate SSNL on a wide variety of experiments and show that it generally outperforms contemporary methods used in simulation-based inference, for instance, on a challenging real-world example from astrophysics which models the magnetic field strength of the sun using a solar dynamo model

Pandemic impact on supply chains: strategies to minimize supply chain disruption

Working Paper del Departament d’Organització d’Empreses de la Universitat Politècnica de Catalunya.Covid-19 pandemic has challenged all the areas of living of people in the last year, supply chains were not excluded by it. Restriction measures, global health concerns and drastic-unreasonable demand changes were the main issues supply chains had and still have to face in the most globalized world ever seen. The aim of this work is to understand how the pandemic impacted in the supply chains, the first reactions of companies to minimize the disruption of the production, logistic and supply shock and finally the measures to be taken in order to prevent future problems. The question of this study is, in fact: how did supply chains react to pandemic and what can they do to be more resilient? To answer this question, in the first section we show the chronological development of the pandemic, starting from China’s outbreak and its expansion to the rest of the world, keeping in mind the economical context in which the event takes place. In the second section we first review literature on natural disasters, since it are the most similar events to a pandemic in terms of their effects. Moreover, in the third section we depict the suggestions to move to a more resilient management of the supply chain and the possible measures to be taken by supply chain managers. The focus will be on the improvements and weaknesses of current supply chain management techniques, such as Just-In-Time methodology, in-shoring possibilities and demand management. At this study publishing, supply chains are still struggling with uncertainty associated with the pandemic situation and need to change some of their features and strengthen others to prevent future disruptions. Future researches could take advantage of more specific and updated information on this topic.Preprin

Transience and constancy of interactions in a plant-frugivore network

Plant-animal mutualistic interactions such as frugivory and seed dispersal display great variation in time due to fluctuations in fruit abundance, animal abundance, and behavior. In particular, some species participate in interactions with other species only transiently, while other species are active for longer periods of time. Species with a longer period of activity are able to interact with more species, and thus engage in constant participation in an interaction network. Species with high constancy would thus be expected to help maintain the biodiversity of a community; however, the manner in which constant species link to their partners may be critical to species coexistence. Because species that interact with many partners concurrently could create more competition compared to those species that interact sequentially with many partners, evaluating the concurrence in an interaction network sheds light on how the network can maintain biodiversity. In this study, we investigate how phenological patterns of fruit production and frugivore presence affect the temporal variation of a plant-frugivore network, and focus on the manner in which high degree species collect their interactions over time. We found a clear separation of activity periods: most species appeared only briefly and participated in relatively few interactions, or showed activity for longer time periods and participated in more interactions. Species that were active for longer time periods often shifted interactions, resulting in a sequential collection of their partners in time, rather than concurrence. For the seed dispersal mutualism in particular, sequential accumulation of partners may allow plant species more opportunities to disperse their seeds compared to concurrence. We suggest that for temporally and spatially heterogeneous landscapes, sequential accumulation of partners would serve to reduce competition and facilitate coexistence of species. Copyright © 2013 Yang et al

Entangled symmetric states and copositive matrices

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions