Neuropsychological Testing and Machine Learning Distinguish Alzheimer’s Disease from Other Causes for Cognitive Impairment

With promising results in recent treatment trials for Alzheimer’s disease (AD), it becomes increasingly important to distinguish AD at early stages from other causes for cognitive impairment. However, existing diagnostic methods are either invasive (lumbar punctures, PET) or inaccurate Magnetic Resonance Imaging (MRI). This study investigates the potential of neuropsychological testing (NPT) to specifically identify those patients with possible AD among a sample of 158 patients with Mild Cognitive Impairment (MCI) or dementia for various causes. Patients were divided into an early stage and a late stage group according to their Mini Mental State Examination (MMSE) score and labeled as AD or non-AD patients based on a post-mortem validated threshold of the ratio between total tau and beta amyloid in the cerebrospinal fluid (CSF; Total tau/Aβ(1–42) ratio, TB ratio). All patients completed the established Consortium to Establish a Registry for Alzheimer’s Disease—Neuropsychological Assessment Battery (CERAD-NAB) test battery and two additional newly-developed neuropsychological tests (recollection and verbal comprehension) that aimed at carving out specific Alzheimer-typical deficits. Based on these test results, an underlying AD (pathologically increased TB ratio) was predicted with a machine learning algorithm. To this end, the algorithm was trained in each case on all patients except the one to predict (leave-one-out validation). In the total group, 82% of the patients could be correctly identified as AD or non-AD. In the early group with small general cognitive impairment, classification accuracy was increased to 89%. NPT thus seems to be capable of discriminating between AD patients and patients with cognitive impairment due to other neurodegenerative or vascular causes with a high accuracy, and may be used for screening in clinical routine and drug studies, especially in the early course of this disease

Hybrid Bifurcations and Stable Periodic Coexistence for Competing Predators

We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a line of equilibria with an exchange point of normal stability vanishes. Our main result is the existence and stability criteria of periodic orbits that bifurcate from breaking a line of equilibria. As an application, we obtain stable periodic coexistent solutions in an ecosystem for two competing predators with Holling's type II functional response

On the Reliability of Diffusion Neuroimaging

Over the last years, diffusion imaging techniques like DTI, DSI or Q-Ball received increasin

Blow-up in komplexer Zeit

Scalar reaction-diffusion type partial differential equations (PDE) exhibit a phenomenon called blow-up. A solution blows-up in finite time if it ceases to exist in the solutions space, i.e. the norm grows to infinite. On the other hand, in reaction-diffusion type PDE there exists the notion of global attractor, the maximal compact invariant set, that attracts all bounded solutions. In this thesis we study a hidden kinship between solutions in the global attractor and blow-up solutions in analytic PDEs by allowing for complex time. \\\ In the first chapter we prove that heteroclinic orbits in one-dimensional unstable manifolds are accompanied by blow-up solutions. Furthermore, we study in more detail the quadratic nonlinear heat equation \ u_t = u_{xx} + u^2, \ and the heteroclinic orbit starting from the unique positive equilibrium. In this setting we show, that blow-up solution can be continued back to the real axis after the blow-up, but continuations along different time paths do not coincide. The proof relies on analyticity of unstable manifolds. This does not hold for center manifolds. In the second chapter we show that in special cases we can continue one-dimensional center manifolds of PDEs to sectors in the complex plane. \\\ Using the result of the second chapter, we prove the existence of blow-up solutions of PDEs in the presence of one-dimensional non-degenerate center manifolds.Skalare partielle reaktions-diffusions Differentialgleichungen (PDE) weisen das Phänomen des \enquote{blow-ups} auf. Eine Lösung \enquote{blows-up} in endlicher Zeit, falls sie aufhört im Lösungsraum der PDE zu existieren, also die Norm gegen unendlich geht. Auf der anderen Seite existieren globale Attraktoren - sie sind die maximale, kompakte und invariante Menge, die alle beschränkten Lösungen anzieht. In der vorliegenden Arbeit untersuchen wir den Zusammenhang des globalen Attraktors und \enquote{blow-up} in analytischen PDEs durch die Benutzung von komplexer Zeit. In dem ersten Kapitel zeigen wir, dass heterokline Lösungen auf eindimensionalen instabilen Mannigfaltigkeiten zusammen mit einem \enquote{blow-up} Orbit kommen. Wir studieren weiterhin die quadratische nichtlineare Wärmeleitungsgleichung \ u_t = u_{xx} + u^2, \ und den heteroklinen Orbit, der von dem eindeutigen Gleichgewicht startet. In diesem Beispiel sind wir in der Lage zu zeigen, dass der \enquote{blow-up} Orbit durch die komplexe Zeit am \enquote{blow-up} Zeitpunkt vorbei zurück auf die reelle Zeitachse fortgesetzt werden kann. Allerdings müssen die Fortsetzungen entlang verschiedener komplexer Zeit Pfade nicht übereinstimmen. Der Beweis benutzt die Analytizität der instabilen Mannigfaltigkeit. Zentrumsmannigfaltigkeiten hingegen sind nicht analytisch. Dennoch können wir im zweiten Kapitel zeigen, dass sich eindimensionale PDE Zentrumsmannigfaltigkeiten in speziellen Fällen in Sektoren der komplexen Ebene fortsetzen lassen. \\\ In dem dritten Kapitel zeigen wir unter der Verwendung der Resultate des zweiten Kapitels die Existenz von \enquote{blow- up} Lösungen auf eindimensionalen Zentrumsmannigfaltigkeiten

Correction: Psychotic Experiences and Overhasty Inferences Are Related to Maladaptive Learning.

[This corrects the article DOI: 10.1371/journal.pcbi.1005328.]