Thick Soergel calculus in type A

Let R be the polynomial ring in n variables, acted on by the symmetric group S_n. Soergel constructed a full monoidal subcategory of R-bimodules which categorifies the Hecke algebra, whose objects are now known as Soergel bimodules. Soergel bimodules can be described as summands of Bott-Samelson bimodules (attached to sequences of simple reflections), or as summands of generalized Bott-Samelson bimodules (attached to sequences of parabolic subgroups). A diagrammatic presentation of the category of Bott-Samelson bimodules was given by the author and Khovanov in previous work. In this paper, we extend it to a presentation of the category of generalized Bott-Samelson bimodules. We also diagrammatically categorify the representations of the Hecke algebra which are induced from trivial representations of parabolic subgroups. The main tool is an explicit description of the idempotent which picks out a generalized Bott-Samelson bimodule as a summand inside a Bott-Samelson bimodule. This description uses a detailed analysis of the reduced expression graph of the longest element of S_n, and the semi-orientation on this graph given by the higher Bruhat order of Manin and Schechtman.Comment: Changed title. Expanded the exposition of the main proof. This paper relies extensively on color figure

Dynamic Composite Data Physicalization Using Wheeled Micro-Robots

This paper introduces dynamic composite physicalizations, a new class of physical visualizations that use collections of self-propelled objects to represent data. Dynamic composite physicalizations can be used both to give physical form to well-known interactive visualization techniques, and to explore new visualizations and interaction paradigms. We first propose a design space characterizing composite physicalizations based on previous work in the fields of Information Visualization and Human Computer Interaction. We illustrate dynamic composite physicalizations in two scenarios demonstrating potential benefits for collaboration and decision making, as well as new opportunities for physical interaction. We then describe our implementation using wheeled micro-robots capable of locating themselves and sensing user input, before discussing limitations and opportunities for future work

Towards a Minimal Stabilizer ZX-calculus

The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only if these two diagrams represent the same quantum evolution or quantum state. We previously showed that the stabilizer ZX-calculus can be simplified by reducing the number of rewrite rules, without losing the property of completeness [Backens, Perdrix & Wang, EPTCS 236:1--20, 2017]. Here, we show that most of the remaining rules of the language are indeed necessary. We do however leave as an open question the necessity of two rules. These include, surprisingly, the bialgebra rule, which is an axiomatisation of complementarity, the cornerstone of the ZX-calculus. Furthermore, we show that a weaker ambient category -- a braided autonomous category instead of the usual compact closed category -- is sufficient to recover the meta rule 'only connectivity matters', even without assuming any symmetries of the generators.Comment: 29 pages, minor updates for v

High-capacity preconscious processing in concurrent groupings of colored dots.

Grouping is a perceptual process in which a subset of stimulus components (a group) is selected for a subsequent-typically implicit-perceptual computation. Grouping is a critical precursor to segmenting objects from the background and ultimately to object recognition. Here, we study grouping by color. We present subjects with 300-ms exposures of 12 dots colored with the same but unknown identical color interspersed among 14 dots of seven different colors. To indicate grouping, subjects point-click the remembered centroid ("center of gravity") of the set of homogeneous dots, of heterogeneous dots, or of all dots. Subjects accurately judge all of these centroids. Furthermore, after a single stimulus exposure, subjects can judge both the heterogeneous and homogeneous centroids, that is, subjects simultaneously group by similarity and by dissimilarity. The centroid paradigm reveals the relative weight of each dot among targets and distractors to the underlying grouping process, offering a more detailed, quantitative description of grouping than was previously possible. A change detection experiment reveals that conscious memory contains less than two dots and their locations, whereas an ideal detector would have to perfectly process at least 15 of 26 dots to match the subjects' centroid judgments-indicating an extraordinary capacity for preconscious grouping. A different color set yielded identical results. Grouping theories that rely on predefined feature maps would fail to explain these results. Rather, the results indicate that preconscious grouping is automatic, flexible, and rapid, and a far more complex process than previously believed

Fabrication and tuning of plasmonic optical nanoantennas around droplet epitaxy quantum dots by cathodoluminescence

We use cathodoluminescence to locate droplet epitaxy quantum dots with a precision $\lesssim$ nm before fabricating nanoantennas in their vicinity by electron-beam lithography. Cathodoluminescence is further used to evidence the effect of the antennas as a function of their length on the light emitted by the dot. Experimental results are in good agreement with numerical simulations of the structures