Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz\'ekelyhidi we prove non-uniqueness for solutions in $L^\infty$ in space and time.Comment: 23 pages, 2 fugure

Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

Dealing with Missing Data and Uncertainty in the Context of Data Mining

Missing data is an issue in many real-world datasets yet robust methods for dealing with missing data appropriately still need development. In this paper we conduct an investigation of how some methods for handling missing data perform when the uncertainty increases. Using benchmark datasets from the UCI Machine Learning repository we generate datasets for our experimentation with increasing amounts of data Missing Completely At Random (MCAR) both at the attribute level and at the record level. We then apply four classification algorithms: C4.5, Random Forest, Naïve Bayes and Support Vector Machines (SVMs). We measure the performance of each classifiers on the basis of complete case analysis, simple imputation and then we study the performance of the algorithms that can handle missing data. We find that complete case analysis has a detrimental effect because it renders many datasets infeasible when missing data increases, particularly for high dimensional data. We find that increasing missing data does have a negative effect on the performance of all the algorithms tested but the different algorithms tested either using preprocessing in the form of simple imputation or handling the missing data do not show a significant difference in performance

Multiple Imputation Ensembles (MIE) for dealing with missing data

Missing data is a significant issue in many real-world datasets, yet there are no robust methods for dealing with it appropriately. In this paper, we propose a robust approach to dealing with missing data in classification problems: Multiple Imputation Ensembles (MIE). Our method integrates two approaches: multiple imputation and ensemble methods and compares two types of ensembles: bagging and stacking. We also propose a robust experimental set-up using 20 benchmark datasets from the UCI machine learning repository. For each dataset, we introduce increasing amounts of data Missing Completely at Random. Firstly, we use a number of single/multiple imputation methods to recover the missing values and then ensemble a number of different classifiers built on the imputed data. We assess the quality of the imputation by using dissimilarity measures. We also evaluate the MIE performance by comparing classification accuracy on the complete and imputed data. Furthermore, we use the accuracy of simple imputation as a benchmark for comparison. We find that our proposed approach combining multiple imputation with ensemble techniques outperform others, particularly as missing data increases

Lung resistance-related protein as a predictor of clinical outcome in advanced testicular germ-cell tumours

This study was undertaken to investigate the expression and predictive value for outcome of multidrug resistance-associated (MDR) proteins P-glycoprotein (Pgp), MRP1, BCRP, and LRP, in advanced testicular germ-cell tumours (TGCT). Paraffin-embedded sections from 56 previously untreated patients with metastatic TGCT were immunostained for Pgp, MRP1, BCRP, and LRP. All patients received platinum-based chemotherapy after orchidectomy. Immunostaining was related to clinicopathological parameters, response to chemotherapy, and outcome. Strong and intermediate expressions of the different MDR-related proteins were: 27 and 41% (Pgp), 54 and 37% (MRP1), 86 and 7% (BCRP), and 14 and 29% (LRP). P-glycoprotein and MRP1 associated, respectively, to low AFP (P=0.026) and high LDH levels (P=0.014), whereas LRP expression associated with high beta-hCG levels (P=0.003) and stage IV tumours (P=0.029). No correlation was found between Pgp, MRP1, and BCRP expression and response to chemotherapy and survival. In contrast, patients with LRP-positive tumours (strong or intermediate expression) had shorter progression-free (P=0.0006) and overall survival (P=0.0116) than LRP-negative patients, even after individual log-rank adjustments by statistically associated variables. Our data suggest that a positive LRP immunostaining at the time of diagnosis in metastatic TGCT is associated with an adverse clinical outcome

Transnational corporations and the challenge of biosphere stewardship

This is the author accepted manuscript. The final version is available from Nature Research via the DOI in this recordSustainability within planetary boundaries requires concerted action by individuals, governments, civil society and private actors. For the private sector, there is concern that the power exercised by transnational corporations generates, and is even central to, global environmental change. Here, we ask under which conditions transnational corporations could either hinder or promote a global shift towards sustainability. We show that a handful of transnational corporations have become a major force shaping the global intertwined system of people and planet. Transnational corporations in agriculture, forestry, seafood, cement, minerals and fossil energy cause environmental impacts and possess the ability to influence critical functions of the biosphere. We review evidence of current practices and identify six observed features of change towards 'corporate biosphere stewardship', with significant potential for upscaling. Actions by transnational corporations, if combined with effective public policies and improved governmental regulations, could substantially accelerate sustainability efforts.Beijer FoundationErling-Persson Family FoundationMarianne and Marcus Wallenberg FoundationWalton Family FoundationDavid and Lucile Packard FoundationGordon and Betty Moore FoundationMistra: The Swedish Foundation for Strategic Environmental Researc

Socio-Economic Instability and the Scaling of Energy Use with Population Size

The size of the human population is relevant to the development of a sustainable world, yet the forces setting growth or declines in the human population are poorly understood. Generally, population growth rates depend on whether new individuals compete for the same energy (leading to Malthusian or density-dependent growth) or help to generate new energy (leading to exponential and super-exponential growth). It has been hypothesized that exponential and super-exponential growth in humans has resulted from carrying capacity, which is in part determined by energy availability, keeping pace with or exceeding the rate of population growth. We evaluated the relationship between energy use and population size for countries with long records of both and the world as a whole to assess whether energy yields are consistent with the idea of an increasing carrying capacity. We find that on average energy use has indeed kept pace with population size over long time periods. We also show, however, that the energy-population scaling exponent plummets during, and its temporal variability increases preceding, periods of social, political, technological, and environmental change. We suggest that efforts to increase the reliability of future energy yields may be essential for stabilizing both population growth and the global socio-economic system

Short-Term Hurricane Impacts on a Neotropical Community of Marked Birds and Implications for Early-Stage Community Resilience

Populations in fragmented ecosystems risk extirpation through natural disasters, which must be endured rather than avoided. Managing communities for resilience is thus critical, but details are sketchy about the capacity for resilience and its associated properties in vertebrate communities. We studied short-term resilience in a community of individually marked birds, following this community through the catastrophic destruction of its forest habitat by Hurricane Iris in Belize, Central America. We sampled for 58 d immediately before the storm, 28 d beginning 11 d after Hurricane Iris, and for 69 d approximately one year later. Our data showed that the initial capacity for resilience was strong. Many banded individuals remained after the storm, although lower post-hurricane recapture rates revealed increased turnover among individuals. Changes occurred in community dynamics and in abundances among species and guilds. Survivors and immigrants both were critical components of resilience, but in a heterogeneous, species-specific manner. Delayed effects, including higher fat storage and increased species losses, were evident one year later

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ~6 x 10^{-9} Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.Comment: 165 pages, 40 figures, 16 tables; accepted for publication in Living Reviews in Relativit