Generalized Permutohedra from Probabilistic Graphical Models

A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. There is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models and also for mixed graphical models containing undirected, directed and bidirected edges, we give a construction of this polytope, up to equivalence of normal fans, as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models.Comment: Appendix B is expanded. Final version to appear in SIAM J. Discrete Mat

Multisite Weather Generators Using Bayesian Networks: An Illustrative Case Study for Precipitation Occurrence

ABSTRACT: Many existing approaches for multisite weather generation try to capture several statistics of the observed data (e.g. pairwise correlations) in order to generate spatially and temporarily consistent series. In this work we analyse the application of Bayesian networks to this problem, focusing on precipitation occurrence and considering a simple case study to illustrate the potential of this new approach. We use Bayesian networks to approximate the multi-variate (-site) probability distribution of observed gauge data, which is factorized according to the relevant (marginal and conditional) dependencies. This factorization allows the simulation of synthetic samples from the multivariate distribution, thus providing a sound and promising methodology for multisite precipitation series generation.We acknowledge funding provided by the project MULTI‐SDM (CGL2015‐ 66583‐R, MINECO/FEDER)

Current-induced cooling phenomenon in a two-dimensional electron gas under a magnetic field

We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential phi and the temperature T in a 2DEG enclosed in a square area surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with phi_{left} < phi_{right} and T_{left} =T_{right}), using a pair of nonlinear Poisson equations (for phi and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.Comment: 25 pages, 7 figure

Fault Trees from Data: Efficient Learning with an Evolutionary Algorithm

Cyber-physical systems come with increasingly complex architectures and failure modes, which complicates the task of obtaining accurate system reliability models. At the same time, with the emergence of the (industrial) Internet-of-Things, systems are more and more often being monitored via advanced sensor systems. These sensors produce large amounts of data about the components' failure behaviour, and can, therefore, be fruitfully exploited to learn reliability models automatically. This paper presents an effective algorithm for learning a prominent class of reliability models, namely fault trees, from observational data. Our algorithm is evolutionary in nature; i.e., is an iterative, population-based, randomized search method among fault-tree structures that are increasingly more consistent with the observational data. We have evaluated our method on a large number of case studies, both on synthetic data, and industrial data. Our experiments show that our algorithm outperforms other methods and provides near-optimal results.Comment: This paper is an extended version of the SETTA 2019 paper, Springer-Verla

The Use of Case Study Competitions to Prepare Students for the World of Work

As we continue into the new millennium, it is imperative that educational institutions equip graduates with the knowledge and skills that are increasingly needed and valued by business and industry. In this article, the authors argue that the case study approach and, specifically, case study competitions constitute an ideal pedagogical strategy for achieving this objective in an effective and efficient manner, with resulting benefits for both students and employers

An Experimental Comparison of Hybrid Algorithms for Bayesian Network Structure Learning

International audienceWe present a novel hybrid algorithm for Bayesian network structure learning, called Hybrid HPC (H2PC). It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. It is based on a subroutine called HPC, that combines ideas from incremental and divide-and-conquer constraint-based methods to learn the parents and children of a target variable. We conduct an experimental comparison of H2PC against Max-Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning, on several benchmarks with various data sizes. Our extensive experiments show that H2PC outperforms MMHC both in terms of goodness of fit to new data and in terms of the quality of the network structure itself, which is closer to the true dependence structure of the data. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available

Evidence of Novel Quasiparticles in a Strongly Interacting Two-Dimensional Electron System: Giant Thermopower and Metallic Behaviour

We report thermopower ($S$) and electrical resistivity ($\rho_{2DES}$) measurements in low-density (10$^{14}$ m$^{-2}$), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We observe at temperatures $\lesssim$ 0.7 K a linearly growing $S$ as a function of temperature indicating metal-like behaviour. Interestingly this metallicity is not Drude-like, showing several unusual characteristics: i) the magnitude of $S$ exceeds the Mott prediction valid for non-interacting metallic 2DESs at similar carrier densities by over two orders of magnitude; and ii) $\rho_{2DES}$ in this regime is two orders of magnitude greater than the quantum of resistance $h/e^2$ and shows very little temperature-dependence. We provide evidence suggesting that these observations arise due to the formation of novel quasiparticles in the 2DES that are not electron-like. Finally, $\rho_{2DES}$ and $S$ show an intriguing decoupling in their density-dependence, the latter showing striking oscillations and even sign changes that are completely absent in the resistivity.Comment: QFS2012 Conference proceedings, Journal of Low Temperature Physics, accepted (figure and discussion added upon referee suggestions

The retirement experiences of elite female gymnasts: Self identity and the physical self

This study explored experiences of retirement from elite sport among a sample of retired female gymnasts. Given the young age at which female gymnasts begin and end their sport careers, particular attention was afforded to the role of identity and the physical self in the process of adaptation. Retrospective, semi-structured interviews were conducted and interview transcripts analyzed using interpretative phenomenological analysis. Analysis indicated that retirement from gymnastics engendered adjustment difficulties for six of the seven participants. Identity loss was particularly salient, and for two gymnasts, physical changes associated with retirement were a further source of distress. The challenge of athletic retirement was intensified because the gymnasts had heavily invested in sport during adolescence, a period demarcated for the pursuit of an identity. Furthermore, their retirement coincided with a time when adolescents typically undergo profound changes physiologically. Practical suggestions to facilitate athletes' disengagement from sport are discussed