Minimal failure probability for ceramic design via shape control

We consider the probability of failure for components made of brittle mate- rials under one time application of a load as introduced by Weibull and Batdorf - Crosse and more recently studied by NASA and the STAU cooperation as an objective functional in shape optimization and prove the existence of optimal shapes in the class of shapes with a uniform cone property. The corresponding integrand of the objective functional has convexity properties that allow to derive lower-semicontinuity according to Fujii (Opt. Th. Appl. 1988). These properties require less restrictive regularity assumptions for the boundaries and state functions compared to [arXiv:1210.4954]. Thereby, the weak formulation of linear elasticity can be kept for the abstract setting for shape optimization as presented in the book by Haslinger and Maekinen

Bimodal activation of different neuron classes with the spectrally red-shifted channelrhodopsin chimera C1V1 in Caenorhabditis elegans

The C. elegans nervous system is particularly well suited for optogenetic analyses of circuit function: Essentially all connections have been mapped, and light can be directed at the neuron of interest in the freely moving, transparent animals, while behavior is observed. Thus, different nodes of a neuronal network can be probed for their role in controlling a particular behavior, using different optogenetic tools for photo-activation or –inhibition, which respond to different colors of light. As neurons may act in concert or in opposing ways to affect a behavior, one would further like to excite these neurons concomitantly, yet independent of each other. In addition to the blue-light activated Channelrhodopsin-2 (ChR2), spectrally red-shifted ChR variants have been explored recently. Here, we establish the green-light activated ChR chimera C1V1 (from Chlamydomonas and Volvox ChR1′s) for use in C. elegans. We surveyed a number of red-shifted ChRs, and found that C1V1-ET/ET (E122T; E162T) works most reliable in C. elegans, with 540–580 nm excitation, which leaves ChR2 silent. However, as C1V1-ET/ET is very light sensitive, it still becomes activated when ChR2 is stimulated, even at 400 nm. Thus, we generated a highly efficient blue ChR2, the H134R; T159C double mutant (ChR2-HR/TC). Both proteins can be used in the same animal, in different neurons, to independently control each cell type with light, enabling a further level of complexity in circuit analyses

A Convenient Infinite Dimensional Framework for Generative Adversarial Learning

In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional theoretical framework for generative adversarial learning. Assuming the class of uniformly bounded $k$-times $\alpha$-H\"older differentiable and uniformly positive densities, we show that the Rosenblatt transformation induces an optimal generator, which is realizable in the hypothesis space of $\alpha$-H\"older differentiable generators. With a consistent definition of the hypothesis space of discriminators, we further show that in our framework the Jensen-Shannon divergence between the distribution induced by the generator from the adversarial learning procedure and the data generating distribution converges to zero. Under sufficiently strict regularity assumptions on the density of the data generating process, we also provide rates of convergence based on concentration and chaining