Unsupervised Learning of Invariance Transformations

The need for large amounts of training data in modern machine learning is one of the biggest challenges of the field. Compared to the brain, current artificial algorithms are much less capable of learning invariance transformations and employing them to extrapolate knowledge from small sample sets. It has recently been proposed that the brain might encode perceptual invariances as approximate graph symmetries in the network of synaptic connections. Such symmetries may arise naturally through a biologically plausible process of unsupervised Hebbian learning. In the present paper, we illustrate this proposal on numerical examples, showing that invariance transformations can indeed be recovered from the structure of recurrent synaptic connections which form within a layer of feature detector neurons via a simple Hebbian learning rule. In order to numerically recover the invariance transformations from the resulting recurrent network, we develop a general algorithmic framework for finding approximate graph automorphisms. We discuss how this framework can be used to find approximate automorphisms in weighted graphs in general

Pharmacological and optical activation of TrkB in Parvalbumin interneurons regulate intrinsic states to orchestrate cortical plasticity

Elevated states of brain plasticity typical for critical periods of early postnatal life can be reinstated in the adult brain through interventions, such as antidepressant treatment and environmental enrichment, and induced plasticity may be critical for the antidepressant action. Parvalbumin-positive (PV) interneurons regulate the closure of developmental critical periods and can alternate between high and low plasticity states in response to experience in adulthood. We now show that PV plasticity states and cortical networks are regulated through the activation of TrkB neurotrophin receptors. Visual cortical plasticity induced by fluoxetine, a widely prescribed selective serotonin reuptake inhibitor (SSRI) antidepressant, was lost in mice with reduced expression of TrkB in PV interneurons. Conversely, optogenetic gain-of-function studies revealed that activation of an optically activatable TrkB (optoTrkB) specifically in PV interneurons switches adult cortical networks into a state of elevated plasticity within minutes by decreasing the intrinsic excitability of PV interneurons, recapitulating the effects of fluoxetine. TrkB activation shifted cortical networks towards a low PV configuration, promoting oscillatory synchrony, increased excitatory-inhibitory balance, and ocular dominance plasticity. OptoTrkB activation promotes the phosphorylation of Kv3.1 channels and reduces the expression of Kv3.2 mRNA providing a mechanism for the lower excitability. In addition, decreased expression and puncta of Synaptotagmin2 (Syt2), a presynaptic marker of PV interneurons involved in Ca2+-dependent neurotransmitter release, suggests lower inputs onto pyramidal neurons suppressing feed-forward inhibition. Together, the results provide mechanistic insights into how TrkB activation in PV interneurons orchestrates the activity of cortical networks and mediating antidepressant responses in the adult brain.Peer reviewe

A high-order Boris integrator

This work introduces the high-order Boris-SDC method for integrating the equations of motion for electrically charged particles in electric and magnetic fields. Boris-SDC relies on a combination of the Boris-integrator with spectral deferred corrections (SDC). SDC can be considered as preconditioned Picard iteration to compute the stages of a collocation method. In this interpretation, inverting the preconditioner corresponds to a sweep with a low-order method. In Boris-SDC, the Boris method, a second-order Lorentz force integrator based on velocity-Verlet, is used as a sweeper/preconditioner. The presented method provides a generic way to extend the classical Boris integrator, which is widely used in essentially all particle-based plasma physics simulations involving magnetic fields, to a high-order method. Stability, convergence order and conservation properties of the method are demonstrated for different simulation setups. Boris-SDC reproduces the expected high order of convergence for a single particle and for the center-of-mass of a particle cloud in a Penning trap and shows good long-term energy stability

High-resolution Simulations of Strongly Coupled Coulomb Systems with a Parallel Tree Code

Despite intense research, the properties of strongly coupled Coulomb systems have not yet been completely understood. However, with the advent of Free Electron Lasers with wavelengths reaching down to tenths of nanometers and intensities beyond 10$^{16 W}$/cm$^{−2}$ during the last years, it has become possible to experimentally probe the warm dense matter regime up to solid densities. Now, systems that can be studied are reaching from hot, low-density plasmas of fusion research to cold dense solids that are dominated by quantum-mechanical effects and strong correlations. Their consistent theoretical description requires a multitude of effects to be considered. In particular, strong correlations pose significant difficulties here. Computer simulations provide a tool for bridging between experiments and theory as they do not suffer from these complications. The experimentally accessible optical and transport properties in plasmas are primarily featured by the electronic subsystem, such as its collective behavior and interaction with the ionic background, i. e. Coulomb collisions. In this work the collisional behavior of warm dense bulk matter and collective effects in nano plasmas are investigated by means of molecular dynamics simulations. To this end, simulation experiments performed earlier on electronic resonances in metallic nano clusters are extended to significantly larger systems. The observed complex resonance structure is analyzed using a newly introduced spatially resolved spectral diagnostic. As a second field of study, the bulk collision frequency as the key parameter for optical and transport properties in warm dense matter is evaluated in a generalized Drude approach for a hydrogen-like plasma. Here, the combined high-field and strong coupling regime that is only scarcely covered by theoretical models is of primary interest. To solve the underlying N-body problem for both applications, a highly parallel Barnes- Hut tree code is utilized and considerably extended with respect to functionality, versatility, and scalability. With its new excellent scalability to hundred thousands of processors and simulation setups consisting of up to billions of particles and its support for periodic boundary conditions with an efficient and precise real-space approach it delivers highly resolved results and is prepared for further studies on the warm dense matter regime. Here, its unique predictive capabilities can finally be used for connecting to real-world experiments

A hybrid biological neural network model for solving problems in cognitive planning

A variety of behaviors, like spatial navigation or bodily motion, can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of empirical findings about the mammalian neocortex and hippocampus. The neurons and synaptic connections in the model represent structures that can result from self-organization into a cognitive map via Hebbian learning, i.e. into a graph in which each neuron represents a point of some abstract task-relevant manifold and the recurrent connections encode a distance metric on the manifold. Graph traversal problems are solved by wave-like activation patterns which travel through the recurrent network and guide a localized peak of activity onto a path from some starting position to a target state