We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect product extension. Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. We study in details two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown.

Chemo-dynamical N-body simulations are an essential tool for understanding the formation and evolution of galaxies. As the number of observationally determined stellar abundances continues to climb, these simulations are able to provide new constraints on the early star formaton history and chemical evolution inside both the Milky Way and Local Group dwarf galaxies. Here, we aim to reproduce the low α-element scatter observed in metal-poor stars. We first demonstrate that as stellar particles inside simulations drop below a mass threshold, increases in the resolution produce an unacceptably large scatter as one particle is no longer a good approximation of an entire stellar population. This threshold occurs at around 10 3 M , a mass limit easily reached in current (and future) simulations. By simulating the Sextans and Fornax dwarf spheroidal galaxies we show that this increase in scatter at high resolutions arises from stochastic supernovae explosions. In order to reduce this scatter down to the observed value, we show the necessity of introducing a metal mixing scheme into particle-based simulations. The impact of the method used to inject the metals into the surrounding gas is also discussed. We finally summarise the best approach for accurately reproducing the scatter in simulations of both Local Group dwarf galaxies and in the Milky Way.

The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, hierarchical, interregional structure with a highly specific laminar architecture. The last decade has seen the emergence of extensive new data sets on anatomy and connectivity at the whole brain scale, providing promising new directions for studies of cortical function that take into account the inseparability of whole-brain and microcircuit architectures. Here, we present a data-driven computational model of the anatomy of non-barrel primary somatosensory cortex of juvenile rat, which integrates whole-brain scale data while providing cellular and subcellular specificity. This multiscale integration was achieved by building the morphologically detailed model of cortical circuitry embedded within a volumetric, digital brain atlas. The model consists of 4.2 million morphologically detailed neurons belonging to 60 different morphological types, placed in the nonbarrel subregions of the Paxinos and Watson atlas. They are connected by 13.2 billion synapses determined by axo-dendritic overlap, comprising local connectivity and long-range connectivity defined by topographic mappings between subregions and laminar axonal projection profiles, both parameterized by whole brain data sets. Additionally, we incorporated core- and matrix-type thalamocortical projection systems, associated with sensory and higher-order extrinsic inputs, respectively. An analysis of the modeled synaptic connectivity revealed a highly nonrandom topology with substantial structural differences but also synergy between local and long-range connectivity. Long-range connections featured a more divergent structure with a comparatively small group of neurons serving as hubs to distribute excitation to far away locations. Taken together with analyses at different spatial granularities, these results support the notion that local and interregional connectivity exist on a spectrum of scales, rather than as separate and distinct networks, as is commonly assumed. Finally, we predicted how the emergence of primary sensory cortical maps is constrained by the anatomy of thalamo-cortical projections. A subvolume of the model comprising 211,712 neurons in the front limb, jaw, and dysgranular zone has been made freely and openly available to the community.

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in the large deformation diffeomorphic metric mapping framework for shape analysis and image registration. The stochasticity thereby models errors or uncertainties of the flow in following the prescribed deformation velocity. The approach is illustrated in the example of finitedimensional landmark manifolds, whose stochastic evolution is studied both via the Fokker-Planck equation and by numerical simulations. We derive two approaches for inferring parameters of the stochastic model from landmark configurations observed at discrete time points. The first of the two approaches matches moments of the FokkerPlanck equation to sample moments of the data, while the second approach employs an expectation-maximization based algorithm using a Monte Carlo bridge sampling scheme to optimise the data likelihood. We derive and numerically test the ability of the two approaches to infer the spatial correlation length of the underlying noise.