TY - CONF
AB - The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a sense that they depend only on the symmetry class of the matrix and otherwise are independent of the details of the distribution. We present the recent solution to this half-century old conjecture. We explain how stochastic tools, such as the Dyson Brownian motion, and PDE ideas, such as De Giorgi-Nash-Moser regularity theory, were combined in the solution. We also show related results for log-gases that represent a universal model for strongly correlated systems. Finally, in the spirit of Wigner’s original vision, we discuss the extensions of these universality results to more realistic physical systems such as random band matrices.
AU - Erdös, László
ID - 1507
TI - Random matrices, log-gases and Hölder regularity
VL - 3
ER -
TY - CONF
AB - We present a rigorous derivation of the BCS gap equation for superfluid fermionic gases with point interactions. Our starting point is the BCS energy functional, whose minimizer we investigate in the limit when the range of the interaction potential goes to zero.
AU - Bräunlich, Gerhard
AU - Hainzl, Christian
AU - Seiringer, Robert
ID - 1516
T2 - Proceedings of the QMath12 Conference
TI - On the BCS gap equation for superfluid fermionic gases
ER -
TY - JOUR
AB - Ammonium is the major nitrogen source in some plant ecosystems but is toxic at high concentrations, especially when available as the exclusive nitrogen source. Ammonium stress rapidly leads to various metabolic and hormonal imbalances that ultimately inhibit root and shoot growth in many plant species, including Arabidopsis thaliana (L.) Heynh. To identify molecular and genetic factors involved in seedling survival with prolonged exclusive NH4+ nutrition, a transcriptomic analysis with microarrays was used. Substantial transcriptional differences were most pronounced in (NH4)2SO4-grown seedlings, compared with plants grown on KNO3 or NH4NO3. Consistent with previous physiological analyses, major differences in the expression modules of photosynthesis-related genes, an altered mitochondrial metabolism, differential expression of the primary NH4+ assimilation, alteration of transporter gene expression and crucial changes in cell wall biosynthesis were found. A major difference in plant hormone responses, particularly of auxin but not cytokinin, was striking. The activity of the DR5::GUS reporter revealed a dramatically decreased auxin response in (NH4)2SO4-grown primary roots. The impaired root growth on (NH4)2SO4 was partially rescued by exogenous auxin or in specific mutants in the auxin pathway. The data suggest that NH4+-induced nutritional and metabolic imbalances can be partially overcome by elevated auxin levels.
AU - Yang, Huaiyu
AU - Von Der Fecht Bartenbach, Jenny
AU - Friml, Jirí
AU - Lohmann, Jan
AU - Neuhäuser, Benjamin
AU - Ludewig, Uwe
ID - 1532
IS - 3
JF - Functional Plant Biology
TI - Auxin-modulated root growth inhibition in Arabidopsis thaliana seedlings with ammonium as the sole nitrogen source
VL - 42
ER -
TY - JOUR
AB - We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations.
AU - Guerrero, Paul
AU - Jeschke, Stefan
AU - Wimmer, Michael
AU - Wonka, Peter
ID - 1629
IS - 2
JF - ACM Transactions on Graphics
TI - Edit propagation using geometric relationship functions
VL - 33
ER -
TY - CONF
AB - We extend the notion of verifiable random functions (VRF) to constrained VRFs, which generalize the concept of constrained pseudorandom functions, put forward by Boneh and Waters (Asiacrypt’13), and independently by Kiayias et al. (CCS’13) and Boyle et al. (PKC’14), who call them delegatable PRFs and functional PRFs, respectively. In a standard VRF the secret key sk allows one to evaluate a pseudorandom function at any point of its domain; in addition, it enables computation of a non-interactive proof that the function value was computed correctly. In a constrained VRF from the key sk one can derive constrained keys skS for subsets S of the domain, which allow computation of function values and proofs only at points in S. After formally defining constrained VRFs, we derive instantiations from the multilinear-maps-based constrained PRFs by Boneh and Waters, yielding a VRF with constrained keys for any set that can be decided by a polynomial-size circuit. Our VRFs have the same function values as the Boneh-Waters PRFs and are proved secure under the same hardness assumption, showing that verifiability comes at no cost. Constrained (functional) VRFs were stated as an open problem by Boyle et al.
AU - Fuchsbauer, Georg
ED - Abdalla, Michel
ED - De Prisco, Roberto
ID - 1643
T2 - SCN 2014
TI - Constrained Verifiable Random Functions
VL - 8642
ER -