A closed formula for the number of convex permutominoes

In this paper we determine a closed formula for the number of convex permutominoes of size n. We reach this goal by providing a recursive generation of all convex permutominoes of size n+1 from the objects of size n, according to the ECO method, and then translating this construction into a system of functional equations satisfied by the generating function of convex permutominoes. As a consequence we easily obtain also the enumeration of some classes of convex polyominoes, including stack and directed convex permutominoes

Exact bosonization of the Ising model

We present exact combinatorial versions of bosonization identities, which equate the product of two Ising correlators with a free field (bosonic) correlator. The role of the discrete free field is played by the height function of an associated bipartite dimer model. Some applications to the asymptotic analysis of Ising correlators are discussed.Comment: 35 page

Representation of conformal maps by rational functions

The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times faster, to represent the maps by rational functions computed by the AAA algorithm. To justify this claim, first we prove a theorem establishing root-exponential convergence of rational approximations near corners in a conformal map, generalizing a result of D. J. Newman in 1964. This leads to the new algorithm for approximating conformal maps of polygons. Then we turn to smooth domains and prove a sequence of four theorems establishing that in any conformal map of the unit circle onto a region with a long and slender part, there must be a singularity or loss of univalence exponentially close to the boundary, and polynomial approximations cannot be accurate unless of exponentially high degree. This motivates the application of the new algorithm to smooth domains, where it is again found to be highly effective

Permutations defining convex permutominoes

"Vegeu el resum a l'inici del document del fitxer adjunt"

Robust Fluid Processing Networks

Fluid models provide a tractable and useful approach in approximating multiclass processing networks. However, they ignore the inherent stochasticity in arrival and service processes. To address this shortcoming, we develop a robust fluid approach to the control of processing networks. We provide insights into the mathematical structure, modeling power, tractability, and performance of the resulting model. Specifically, we show that the robust fluid model preserves the computational tractability of the classical fluid problem and retains its original structure. From the robust fluid model, we derive a (scheduling) policy that regulates how fluid from various classes is processed at the servers of the network. We present simulation results to compare the performance of our policies to several commonly used traditional methods. The results demonstrate that our robust fluid policies are near-optimal (when the optimal can be computed) and outperform policies obtained directly from the fluid model and heuristic alternatives (when it is computationally intractable to compute the optimal).National Science Foundation (U.S.) (Grant CNS-1239021)National Science Foundation (U.S.) (Grant IIS-1237022)United States. Army Research Office (Grant W911NF-11-1-0227)United States. Army Research Office (Grant W911NF-12-1-0390)United States. Office of Naval Research (Grant N00014-10-1-0952

Introduction: The Third International Conference on Epigenetic Robotics

This paper summarizes the paper and poster contributions to the Third International Workshop on Epigenetic Robotics. The focus of this workshop is on the cross-disciplinary interaction of developmental psychology and robotics. Namely, the general goal in this area is to create robotic models of the psychological development of various behaviors. The term "epigenetic" is used in much the same sense as the term "developmental" and while we could call our topic "developmental robotics", developmental robotics can be seen as having a broader interdisciplinary emphasis. Our focus in this workshop is on the interaction of developmental psychology and robotics and we use the phrase "epigenetic robotics" to capture this focus

Further paleomagnetic evidence for oroclinal rotation in the central folded Appalachians from the Bloomsburg and the Mauch Chunk Formations

Renewed paleomagnetic investigations of red beds of the Upper Silurian Bloomsburg and the Lower Carboniferous Mauch Chunk Formations were undertaken with the objective of obtaining evidence regarding the possibility of oroclinal bending as contributing to the arcuate structural trend of the Pennsylvania salient. These formations crop out on both limbs of the salient and earlier, but less definitive paleomagnetic studies on these units indicate that early acquired magnetizations can be recovered. Oriented samples were obtained from nine sites on the southern limb of the salient and eight sites from the northern limb in the Bloomsburg. The natural remanent magnetizations are multivectorial, dominated by a component (B) with a distributed spectrum of unblocking temperatures ranging up to 670°C, and a component (C) with a higher and very discrete distribution of unblocking temperatures. The B component is uniformly of reverse polarity, shows a statistically significant synfolding character, and represents a Late Paleozoic remagnetization. The C component passes fold tests with normal and reverse polarity site means. The C component directions from the southern limb (345.1°/-31.6°) and the northern limb (359.3°/-29.7°) are significantly different in declination (14.2°±10.4°) but not in inclination (1.9°±9°). Samples were also analyzed from seven additional sites in the Mauch Chunk on the southern limb of the salient. Inclusion of these new data gives a revised estimate of the difference between southern and northern limb mean directions of prefolding magnetizations in the Mauch Chunk of 23.3°±12.5 in declination and 4.8°±11° in inclination. Paleomagnetic data from the Bloomsburg, Mauch Chunk, and revised results recently reported for the Upper Devonian Catskill Formation together indicate 22.8°±11.9° of relative rotation, accounting for approximately half the present change in structural trend around the Pennsylvania salient. The oroclinal rotation can be regarded as a tightening of a less arcuate depositional package that developed across a basement reentrant, to achieve a curvature closer to that of the earlier zigzag continental margin outline