On a Generalization of the van der Waerden Theorem

For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial can be chosen from a given semigroup and one can prescribe the occurring powers. A multidimensional version is included.Comment: 5 page

Using Gap Symmetry and Structure to Reveal the Pairing Mechanism in Fe-based Superconductors

I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the interactions by small changes in pressure, doping or disorder. Thus, measurements of order parameter evolution with these parameters should enable a deeper understanding of the underlying interactions. I briefly review the "standard paradigm" for $s$-wave pairing in these systems, and then focus on developments in the past several years which have challenged this picture. I discuss the reasons for the apparent close competition between pairing in s- and d-wave channels, particularly in those systems where one type of Fermi surface pocket -- hole or electron -- is missing. Observation of a transition between $s$- and $d$-wave symmetry, possibly via a time reversal symmetry breaking "$s+id$" state, would provide an importantconfirmation of these ideas. Several proposals for detecting these novel phases are discussed, including the appearance of order parameter collective modes in Raman and optical conductivities. Transitions between two different types of $s$-wave states, involving various combinations of signs on Fermi surface pockets, can also proceed through a ${\cal T}$-breaking "$s+is$" state. I discuss recent work that suggests pairing may take place away from the Fermi level over a surprisingly large energy range, as well as the effect of glide plane symmetry of the Fe-based systems on the superconductivity, including various exotic, time and translational invariance breaking pair states that have been proposed. Finally, I address disorder issues, and the various ways systematic introduction of disorder can (and cannot) be used to extract information on gap symmetry and structure.Comment: 41 pp., Published in special focus issue of Comptes Rendus Physique (Paris) on recent progress in Fe-based Superconductivity. Full issue with 10 review articles available at http://www.sciencedirect.com/science/journal/16310705/17/1-

Active Expressions: Basic Building Blocks for Reactive Programming

Modern software development without reactive programming is hard to imagine. Reactive programming favors a wide class of contemporary software systems that respond to user input, network messages, and other events. While reactive programming is an active field of research, the implementation of reactive concepts remains challenging. In particular, change detection represents a hard but inevitable necessity when implementing reactive concepts. Typically, change detection mechanisms are not intended for reuse but are tightly coupled to the particular change resolution mechanism. As a result, developers often have to re-implement similar abstractions. A reusable primitive for change detection is still missing. To find a suitable primitive, we identify commonalities in existing reactive concepts. We discover a class of reactive concepts, state-based reactive concepts. All state-based reactive concepts share a common change detection mechanism: they detect changes in the evaluation result of an expression. On the basis of the identified common change detection mechanism, we propose active expressions as a reusable primitive. By abstracting the tedious implementation details of change detection, active expressions can ease the implementation of reactive programming concepts. We evaluate the design of active expressions by re-implementing a number of existing state-based reactive concepts using them. The resulting implementations highlight the expressiveness of active expressions. Active expressions enable the separation of essential from non-essential parts when reasoning about reactive programming concepts. By using active expressions as a primitive for change detection, developers of reactive language constructs and runtime support can now focus on the design of how application programmers should be able to react to change. Ultimately, we would like active expressions to encourage experiments with novel reactive programming concepts and with that to yield a wider variety of them to explore

Order Parameter "Holes" and Theory of Microwave Conductivity in YBCO

We propose that the low temperature discrepancy between simple d-wave models of the microwave conductivity and existing experiments on single crystals of YBCO can be resolved by including the scattering of quasiparticles from "holes" of the order parameter at impurity sites. Within a framework proposed previously, we find in particular excellent agreement with data of Hosseini et al. on slightly overdoped YBCO samples over the entire temperature range down to about 2-3K, and for a wide range of frequencies. Remaining discrepancies in the "universal" regime at very low temperatures are discussed.Comment: 5 pages, 3 PS figure