A duality for Spin Verlinde spaces and Prym Theta functions

The paper proves canonical isomorphisms between Spin Verlinde spaces, that is, spaces of global sections of a determinant line bundle over the moduli space of semistable Spinn-bundles over a smooth projective curve C, and the dual spaces of theta functions over Prym varieties of unramified double covers of C

Tunable Assembly of Gold Nanorods in Polymer Solutions to Generate Controlled Nanostructured Materials

Gold nanorods grafted with short chain polymers are assembled into controlled open structures using polymer-induced depletion interactions and structurally characterized using small angle x-ray scattering. When the nanorod diameter is smaller than the radius of gyration of the depletant polymer, the depletion interaction depends solely on the correlation length of the polymer solution and not directly on the polymer molecular weight. As the polymer concentration increases, the stronger depletion interactions increasingly compress the grafted chains and push the gold nanorods closer together. By contrast, other structural characteristics such as the number of nearest neighbors and fractal dimension exhibit a non-monotonic dependence on polymer concentration. These parameters are maximal at intermediate concentrations, which are attributed to a crossover from reaction-limited to diffusion-limited aggregation. The control over structural properties of anisotropic nanoscale building blocks demonstrated here will be beneficial to designing and producing materials \emph{in situ} with specific direction-dependent nanoscale properties and provides a crucial route for advances in additive manufacturing

Molecular ruby: exploring the excited state landscape

The discovery of the highly NIR-luminescent molecular ruby [Cr(ddpd)2]3+ (ddpd = N,N′-dimethyl-N,N′-dipyridin-2-ylpyridine-2,6-diamine) has been a milestone in the development of earth-abundant luminophors and has led to important new impulses in the field of spin-flip emitters. Its favourable optical properties such as a high photoluminescence quantum yield and long excited state lifetime are traced back to a remarkable excited state landscape which has been investigated in great detail. This article summarises the results of these studies with the aim to create a coherent picture of the excited state ordering and the ultrafast as well as long-timescale dynamics. Additional experimental data is provided to fill in gaps left by previous reports

Active Learning with Partial Feedback

While many active learning papers assume that the learner can simply ask for a label and receive it, real annotation often presents a mismatch between the form of a label (say, one among many classes), and the form of an annotation (typically yes/no binary feedback). To annotate examples corpora for multiclass classification, we might need to ask multiple yes/no questions, exploiting a label hierarchy if one is available. To address this more realistic setting, we propose active learning with partial feedback (ALPF), where the learner must actively choose both which example to label and which binary question to ask. At each step, the learner selects an example, asking if it belongs to a chosen (possibly composite) class. Each answer eliminates some classes, leaving the learner with a partial label. The learner may then either ask more questions about the same example (until an exact label is uncovered) or move on immediately, leaving the first example partially labeled. Active learning with partial labels requires (i) a sampling strategy to choose (example, class) pairs, and (ii) learning from partial labels between rounds. Experiments on Tiny ImageNet demonstrate that our most effective method improves 26% (relative) in top-1 classification accuracy compared to i.i.d. baselines and standard active learners given 30% of the annotation budget that would be required (naively) to annotate the dataset. Moreover, ALPF-learners fully annotate TinyImageNet at 42% lower cost. Surprisingly, we observe that accounting for per-example annotation costs can alter the conventional wisdom that active learners should solicit labels for hard examples.Comment: ICLR 201