Milnor’s Conjecture on Monotonicity of Topological Entropy: results and questions

This note discusses Milnor’s conjecture on monotonicity of entropy and gives a short exposition of the ideas used in its proof which was obtained in joint work with Henk Bruin, see [BvS09]. At the end of this note we explore some related conjectures and questions

Decay of correlations in one-dimensional dynamics

We consider multimodal C3 interval maps f satisfying a summability condition on the derivatives Dn along the critical orbits which implies the existence of an absolutely continuous f-invariant probability measure mu. If f is non-renormalizable, mu is mixing and we show that the speed of mixing (decay of correlations) is strongly related to the rate of growth of the sequence (Dn) as n → infinity. We also give sufficient conditions for mu to satisfy the Central Limit Theorem. This applies for example to the quadratic Fibonacci map which is shown to have subexponential decay of correlations.</p

Robustness of ergodic properties of non-autonomous piecewise expanding maps

Recently, there has been an increasing interest in non-autonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map results in statistical behaviour close to that of . We show this fact in the case of piecewise regular expanding maps. In particular, we impose conditions on perturbations of this class of maps that include situations slightly more general than what has been considered so far, and prove that these are stochastically stable in the usual sense. We then prove that the evolution of a given distribution of mass under composition of time-dependent perturbations (arbitrarily—rather than randomly—chosen at each step) close to a given map remains close to the invariant mass distribution of . Moreover, for almost every point, Birkhoff averages along trajectories do not fluctuate wildly. This result complements recent results on memory loss for non-autonomous dynamical systems

Restraint, disinhibition and food-related processing bias

This study examined associations between restraint, disinhibition and food-related processing bias (FPB, assessed by the emotional Stroop task) in males and females in the UK, Greece and Iran. Results showed high restraint was associated with higher FPB. However, high restrained current dieters showed lower FPB that high restrained non-dieters. There was no significant difference in FPB for those showing high versus low disinhibition. Results are discussed in relation to theories of incentive salience and current concerns

Minder en anders Bemesten: Voordelen van maaimeststoffen voor teelt van najaarsspinazie - Resultaten veldproef Joost van Strien, in Ens, 2009

In 2009 heeft het Louis Bolk Instituut onderzoek verricht naar het gebruik van versgemaaide en ingekuilde maaimeststoffen voor de bemesting van najaarspinazie op het bedrijf van Joost van Strien in Ens in de Noord Oost Polder. Maaimeststoffen zijn een innovatief teeltsysteem (het zgn. “cut-and-carry” systeem) waarbij gemaaide grasklaver of luzerne, gewassen die als bodemverbeteraar een essentiële rol in de gewasrotatie vormen, direct op eigen bedrijf worden ingezet als hulpmest stof i.pv. deze te verkopen als veevoer. Wij concluderen dat door gebruik van het systeem dat op het bedrijf van Joost van Strien is ontwikkeld, doelgericht gebruik kan worden gemaakt van meerjarige vlinderbloemige gewassen. Hierdoor worden zowel het bodemleven en bodemkwaliteit bevorderd terwijl de afhankelijkheid van biologische akkerbouw van externe dierlijke meststoffen sterk wordt verminderd door het sluiten van interne nutriëntenkringlopen. Door het gebruik van meerjarige en diepwortelende vlinderbloemige gewassen zoals luzerne of gras klaver kan er stikstof uit de atmosfeer op een klimaatneutrale manier worden gebonden terwijl nutriënten uit diepere bodem ook opnieuw beschikbaar komen voor hoogrenderende gewassen

Revealing dynamics, communities and criticality from data

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behaviour for parameter ranges for which no data on the system is available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an {}, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behaviour of such networks can be decomposed in terms of an emergent deterministic component and a {} term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. { We illustrate this approach on synthetic time-series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. } We reconstruct the community structure by analysing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range

COmplexome Profiling ALignment (COPAL) reveals remodeling of mitochondrial protein complexes in Barth syndrome

Item does not contain fulltextMOTIVATION: Complexome profiling combines native gel electrophoresis with mass spectrometry to obtain the inventory, composition and abundance of multiprotein assemblies in an organelle. Applying complexome profiling to determine the effect of a mutation on protein complexes requires separating technical and biological variations from the variations caused by that mutation. RESULTS: We have developed the COmplexome Profiling ALignment (COPAL) tool that aligns multiple complexome profiles with each other. It includes the abundance profiles of all proteins on two gels, using a multi-dimensional implementation of the dynamic time warping algorithm to align the gels. Subsequent progressive alignment allows us to align multiple profiles with each other. We tested COPAL on complexome profiles from control mitochondria and from Barth syndrome (BTHS) mitochondria, which have a mutation in tafazzin gene that is involved in remodeling the inner mitochondrial membrane phospholipid cardiolipin. By comparing the variation between BTHS mitochondria and controls with the variation among either, we assessed the effects of BTHS on the abundance profiles of individual proteins. Combining those profiles with gene set enrichment analysis allows detecting significantly affected protein complexes. Most of the significantly affected protein complexes are located in the inner mitochondrial membrane (mitochondrial contact site and cristae organizing system, prohibitins), or are attached to it (the large ribosomal subunit). AVAILABILITY AND IMPLEMENTATION: COPAL is written in python and is available from http://github.com/cmbi/copal. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online

Multicomponent dynamical systems: SRB measures and phase transitions

We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various definitions of SRB measures are considered as well.Comment: 13 pages, LaTeX 2