Ages and Age Spreads in Young Stellar Clusters

I review progress towards understanding the time-scales of star and cluster formation and of the absolute ages of young stars. I focus in particular on the areas in which Francesco Palla made highly significant contributions - interpretation of the Hertzsprung-Russell diagrams of young clusters and the role of photospheric lithium as an age diagnostic.Comment: To appear in "Francesco's Legacy: Star Formation in Space and Time", Memorie della SAIt, in press. Eds. R. Cesaroni, E. Corbelli and D. Galli. 5p

The second iterate for the Navier-Stokes equation

We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak strong uniqueness for Koch-Tataru solutions; and finally an instability result in $B^{-1}_{\infty,q}$, for q>2.Comment: 13 page

Prethermalization and thermalization in models with weak integrability breaking

We study the effects of integrability breaking perturbations on the non-equilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalizations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalization group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalization plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalization plateaux towards thermal behaviour. We identify a time scale characterizing this cross-over.Comment: 9 pages, 4 figure

Numerical methods for one-dimensional aggregation equations

We focus in this work on the numerical discretization of the one dimensional aggregation equation \pa_t\rho + \pa_x (v\rho)=0, $v=a(W'*\rho)$, in the attractive case. Finite time blow up of smooth initial data occurs for potential $W$ having a Lipschitz singularity at the origin. A numerical discretization is proposed for which the convergence towards duality solutions of the aggregation equation is proved. It relies on a careful choice of the discretized macroscopic velocity $v$ in order to give a sense to the product $v \rho$. Moreover, using the same idea, we propose an asymptotic preserving scheme for a kinetic system in hyperbolic scaling converging towards the aggregation equation in hydrodynamical limit. Finally numerical simulations are provided to illustrate the results

The role of active movement in fungal ecology and community assembly

Movement ecology aims to provide common terminology and an integrative framework of movement research across all groups of organisms. Yet such work has focused on unitary organisms so far, and thus the important group of filamentous fungi has not been considered in this context. With the exception of spore dispersal, movement in filamentous fungi has not been integrated into the movement ecology field. At the same time, the field of fungal ecology has been advancing research on topics like informed growth, mycelial translocations, or fungal highways using its own terminology and frameworks, overlooking the theoretical developments within movement ecology. We provide a conceptual and terminological framework for interdisciplinary collaboration between these two disciplines, and show how both can benefit from closer links: We show how placing the knowledge from fungal biology and ecology into the framework of movement ecology can inspire both theoretical and empirical developments, eventually leading towards a better understanding of fungal ecology and community assembly. Conversely, by a greater focus on movement specificities of filamentous fungi, movement ecology stands to benefit from the challenge to evolve its concepts and terminology towards even greater universality. We show how our concept can be applied for other modular organisms (such as clonal plants and slime molds), and how this can lead towards comparative studies with the relationship between organismal movement and ecosystems in the focus

Post-Matrix Product State Methods: To tangent space and beyond

We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well defined quantum number. We present some new illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post matrix product methods.Comment: 40 pages, 8 figure

Intelligent Adaptive Curiosity: a source of Self-Development

This paper presents the mechanism of Intelligent Adaptive Curiosity. This is a drive which pushes the robot towards situations in which it maximizes its learning progress. It makes the robot focus on situations which are neither too predictable nor too unpredictable. This mechanism is a source of self-development for the robot: the complexity of its activity autonomously increases. Indeed, we show that it first spends time in situations which are easy to learn, then shifts progressively its attention to situations of increasing difficulty, avoiding situations in which nothing can be learnt