Cyclic sieving, rotation, and geometric representation theory

We study rotation of invariant vectors in tensor products of minuscule representations. We define a combinatorial notion of rotation of minuscule Littelmann paths. Using affine Grassmannians, we show that this rotation action is realized geometrically as rotation of components of the Satake fibre. As a consequence, we have a basis for invariant spaces which is permuted by rotation (up to global sign). Finally, we diagonalize the rotation operator by showing that its eigenspaces are given by intersection homology of quiver varieties. As a consequence, we generalize Rhoades' work on the cyclic sieving phenomenon.Comment: 16 page

Buildings, spiders, and geometric Satake

Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).Comment: 49 pages; revised and to appear in Compositio Mathematic

Bioluminescence, photophysical, computational and molecular docking studies of fully conformationally restricted enamine infraluciferin

A new rationally designed fully rotationally restricted luciferin has been synthesised. This synthetic luciferin, based upon the structure of infraluciferin, has two intramolecular H-bonds to reduce degrees of freedom, an amine group to enhance ICT process, and an alkenyl group to increase π-conjugation. In the spectroscopic measurements and computational calculations, enamine luciferin showed more red-shifted absorption and fluorescence emission than LH2 and iLH2. With PpyWT luciferase enamine luciferin gave bioluminescence at 564 nm which is similar to LH2 at 561 nm. Further investigation by docking studies revealed that the emission wavelength of enamine luciferin might be attributed to the unwanted twisted structure caused by Asp531 within the enzyme. With mutant luciferase FlucRed, the major emission peak was shifted to 606 nm, a distinct shoulder above 700 nm, and 21% of its spectrum located in the nIR range

Smartphone-based multicolor bioluminescent 3D spheroid biosensors for monitoring inflammatory activity

Whole-cell biosensors present many advantages, including being able to monitor the toxicity and bioavailability of chemicals; cells grown in traditional 2D cultures, however, do not reproduce the complexity of in vivo physiology. In the last years, 3D cell-culture models have garnered great attention due to their capability to better mimic in vivo cellular responses to external stimuli, providing excellent model living organisms. In order to obtain a predictive, sensitive, and robust yet low-cost 3D cell biosensor, we developed a smartphone-based bioluminescent 3D cell biosensor platform for effect-based analysis. We exploited the Nuclear Factor-kappa B (NF-kB) signal transduction pathway, which is induced by several types of stressors and is involved in the regulation of cell-cycle/growth, inflammation, apoptosis, and immunity. The smartphone-based biosensor relies on immobilized HEK293 spheroids genetically engineered with powerful red- and green-emitting luciferases utilized as inflammation and viability reporters. It provides a limit of detection for Tumor Necrosis Factor (TNF\u3b1) of 0.15\u202f\ub1\u202f0.05\u202fng/mL and could be a useful tool to initially screen environmental samples or other compounds on-site, especially for additional more accurate chemical analyses

Disorder-Driven Pretransitional Tweed in Martensitic Transformations

Defying the conventional wisdom regarding first--order transitions, {\it solid--solid displacive transformations} are often accompanied by pronounced pretransitional phenomena. Generally, these phenomena are indicative of some mesoscopic lattice deformation that ``anticipates'' the upcoming phase transition. Among these precursive effects is the observation of the so-called ``tweed'' pattern in transmission electron microscopy in a wide variety of materials. We have investigated the tweed deformation in a two dimensional model system, and found that it arises because the compositional disorder intrinsic to any alloy conspires with the natural geometric constraints of the lattice to produce a frustrated, glassy phase. The predicted phase diagram and glassy behavior have been verified by numerical simulations, and diffraction patterns of simulated systems are found to compare well with experimental data. Analytically comparing to alternative models of strain-disorder coupling, we show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in uuencoded format. Three other figures available via anonymous ftp

The Effects of Forest Fuel-Reduction Treatments in the United States

The current conditions of many seasonally dry forests in the western and southern United States, especially those that once experienced low- to moderate-intensity fire regimes, leave them uncharacteristically susceptible to high-severity wildfire. Both prescribed fire and its mechanical surrogates are generally successful in meeting short-term fuel-reduction objectives such that treated stands are more resilient to high-intensity wildfire. Most available evidence suggests that these objectives are typically accomplished with few unintended consequences, since most ecosystem components (vegetation, soils, wildlife, bark beetles, carbon sequestration) exhibit very subtle effects or no measurable effects at all. Although mechanical treatments do not serve as complete surrogates for fire, their application can help mitigate costs and liability in some areas. Desired treatment effects on fire hazards are transient, which indicates that after fuel-reduction management starts, managers need to be persistent with repeated treatment, especially in the faster-growing forests in the southern United States.Keywords: wildfire, forest conservation, forest management, fire surrogates, fire ecolog