Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Singular and regular solutions of a non-linear parabolic system

We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$. For dimensions $n>4$ we present strong numerical evidence supporting existence of blow-up solutions. Moreover, using the same techniques we numerically confirm a conjecture of Lepin regarding existence of self-similar singular solutions to a semi-linear heat equation.Comment: 16 page

Independent analysis of the orbits of Pioneer 10 and 11

Independently developed orbit determination software is used to analyze the orbits of Pioneer 10 and 11 using Doppler data. The analysis takes into account the gravitational fields of the Sun and planets using the latest JPL ephemerides, accurate station locations, signal propagation delays (e.g., the Shapiro delay, atmospheric effects), the spacecrafts' spin, and maneuvers. New to this analysis is the ability to utilize telemetry data for spin, maneuvers, and other on-board systematic effects. Using data that was analyzed in prior JPL studies, the anomalous acceleration of the two spacecraft is confirmed. We are also able to put limits on any secondary acceleration (i.e., jerk) terms. The tools that were developed will be used in the upcoming analysis of recently recovered Pioneer 10 and 11 Doppler data files.Comment: 22 pages, 5 figures; accepted for publication in IJMP

A Cognitive Model of an Epistemic Community: Mapping the Dynamics of Shallow Lake Ecosystems

We used fuzzy cognitive mapping (FCM) to develop a generic shallow lake ecosystem model by augmenting the individual cognitive maps drawn by 8 scientists working in the area of shallow lake ecology. We calculated graph theoretical indices of the individual cognitive maps and the collective cognitive map produced by augmentation. The graph theoretical indices revealed internal cycles showing non-linear dynamics in the shallow lake ecosystem. The ecological processes were organized democratically without a top-down hierarchical structure. The steady state condition of the generic model was a characteristic turbid shallow lake ecosystem since there were no dynamic environmental changes that could cause shifts between a turbid and a clearwater state, and the generic model indicated that only a dynamic disturbance regime could maintain the clearwater state. The model developed herein captured the empirical behavior of shallow lakes, and contained the basic model of the Alternative Stable States Theory. In addition, our model expanded the basic model by quantifying the relative effects of connections and by extending it. In our expanded model we ran 4 simulations: harvesting submerged plants, nutrient reduction, fish removal without nutrient reduction, and biomanipulation. Only biomanipulation, which included fish removal and nutrient reduction, had the potential to shift the turbid state into clearwater state. The structure and relationships in the generic model as well as the outcomes of the management simulations were supported by actual field studies in shallow lake ecosystems. Thus, fuzzy cognitive mapping methodology enabled us to understand the complex structure of shallow lake ecosystems as a whole and obtain a valid generic model based on tacit knowledge of experts in the field.Comment: 24 pages, 5 Figure

A systematic review and meta-analysis of 271 PCDH19-variant individuals identifies psychiatric comorbidities, and association of seizure onset and disease severity

Epilepsy and Mental Retardation Limited to Females (EFMR) is an infantile onset disorder characterized by clusters of seizures. EFMR is due to mutations in the X-chromosome gene PCDH19, and is underpinned by cellular mosaicism due to X-chromosome inactivation in females or somatic mutation in males. This review characterizes the neuropsychiatric profile of this disorder and examines the association of clinical and molecular factors with neuropsychiatric outcomes. Data were extracted from 38 peer-reviewed original articles including 271 individual cases. We found that seizure onset ≤12 months was significantly associated (p = 4.127 × 10⁻⁷) with more severe intellectual disability, compared with onset >12 months. We identified two recurrent variants p.Asn340Ser and p.Tyr366Leufs*10 occurring in 25 (20 unrelated) and 30 (11 unrelated) cases, respectively. PCDH19 mutations were associated with psychiatric comorbidities in approximately 60% of females, 80% of affected mosaic males, and reported in nine hemizygous males. Hyperactive, autistic, and obsessive-compulsive features were most frequently reported. There were no genotype-phenotype associations in the individuals with recurrent variants or the group overall. Age at seizure onset can be used to provide more informative prognostic counseling.Kristy L Kolc, Lynette G Sadleir, Ingrid E Scheffer, Atma Ivancevic, Rachel Roberts, Duyen H Pham, Jozef Gec

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Modeling resilience and sustainability in ancient agricultural systems

The reasons why people adopt unsustainable agricultural practices, and the ultimate environmental implications of those practices, remain incompletely understood in the present world. Archaeology, however, offers unique datasets on coincident cultural and ecological change, and their social and environmental effects. This article applies concepts derived from ecological resilience thinking to assess the sustainability of agricultural practices as a result of long-term interactions between political, economic, and environmental systems. Using the urban center of Gordion, in central Turkey, as a case study, it is possible to identify mismatched social and ecological processes on temporal, spatial, and organizational scales, which help to resolve thresholds of resilience. Results of this analysis implicate temporal and spatial mismatches as a cause for local environmental degradation, and increasing extralocal economic pressures as an ultimate cause for the adoption of unsustainable land-use practices. This analysis suggests that a research approach that integrates environmental archaeology with a resilience perspective has considerable potential for explicating regional patterns of agricultural change and environmental degradation in the past

Early multidrug resistance, defined by changes in intracellular doxorubicin distribution, independent of P-glycoprotein.

Resistance to multiple antitumour drugs, mostly antibiotics or alkaloids, has been associated with a cellular plasma membrane P-glycoprotein (Pgp), causing energy-dependent transport of drugs out of cells. However, in many common chemotherapy resistant human cancers there is no overexpression of Pgp, which could explain drug resistance. In order to characterise early steps in multidrug resistance we have derived a series of P-glycoprotein-positive (Pgp/+) and P-glycoprotein-negative (Pgp/-) multidrug resistant cell lines, from a human non-small cell lung cancer cell line, SW-1573, by stepwise selection with increasing concentrations of doxorubicin. These cells were exposed to doxorubicin and its fluorescence in nucleus (N) and cytoplasm (C) was quantified with laserscan microscopy and image analysis. The fluorescence N/C ratio in parent cells was 3.8 and decreased both in Pgp/+ and Pgp/- cells with increasing selection pressure to 1.2-2.6 for cells with a resistance factor of 7-17. N/C ratios could be restored partly with verapamil only in Pgp/+ cells. N/C ratio measurements may define a general Pgp-independent type of defense of mammalian cells against certain anticancer agents which may precede Pgp expression in early doxorubicin resistance

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