Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy

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

Large-scale literature mining to assess the relation between anti-cancer drugs and cancer types

Background:There is a huge body of scientific literature describing the relation between tumor types and anti-cancer drugs. The vast amount of scientific literature makes it impossible for researchers and physicians to extract all relevant information manually.Methods:In order to cope with the large amount of literature we applied an automated text mining approach to assess the relations between 30 most frequent cancer types and 270 anti-cancer drugs. We applied two different approaches, a classical text mining based on named entity recognition and an AI-based approach employing word embeddings. The consistency of literature mining results was validated with 3 independent methods: first, using data from FDA approvals, second, using experimentally measured IC-50 cell line data and third, using clinical patient survival data.Results:We demonstrated that the automated text mining was able to successfully assess the relation between cancer types and anti-cancer drugs. All validation methods showed a good correspondence between the results from literature mining and independent confirmatory approaches. The relation between most frequent cancer types and drugs employed for their treatment were visualized in a large heatmap. All results are accessible in an interactive web-based knowledge base using the following link: https://knowledgebase.microdiscovery.de/heatmap.Conclusions:Our approach is able to assess the relations between compounds and cancer types in an automated manner. Both, cancer types and compounds could be grouped into different clusters. Researchers can use the inter-active knowledge base to inspect the presented results and follow their own research questions, for example the identification of novel indication areas for known drugs

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

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