A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Defining correctness conditions for concurrent objects in multicore architectures

Correctness of concurrent objects is defined in terms of conditions that determine allowable relationships between histories of a concurrent object and those of the corresponding sequential object. Numerous correctness conditions have been proposed over the years, and more have been proposed recently as the algorithms implementing concurrent objects have been adapted to cope with multicore processors with relaxed memory architectures. We present a formal framework for defining correctness conditions for multicore architectures, covering both standard conditions for totally ordered memory and newer conditions for relaxed memory, which allows them to be expressed in uniform manner, simplifying comparison. Our framework distinguishes between order and commitment properties, which in turn enables a hierarchy of correctness conditions to be established. We consider the Total Store Order (TSO) memory model in detail, formalise known conditions for TSO using our framework, and develop sequentially consistent variations of these. We present a work-stealing deque for TSO memory that is not linearizable, but is correct with respect to these new conditions. Using our framework, we identify a new non-blocking compositional condition, fence consistency, which lies between known conditions for TSO, and aims to capture the intention of a programmer-specified fence

Telescope Time Without Tears: A Distributed Approach to Peer Review

The procedure that is currently employed to allocate time on telescopes is horribly onerous on those unfortunate astronomers who serve on the committees that administer the process, and is in danger of complete collapse as the number of applications steadily increases. Here, an alternative is presented, whereby the task is distributed around the astronomical community, with a suitable mechanism design established to steer the outcome toward awarding this precious resource to those projects where there is a consensus across the community that the science is most exciting and innovative.Comment: 9 pages, accepted for publication in Astronomy & Geophysic

Regional Dispersal of Daphnia lumholtzi in North America Inferred from ISSR Genetic Markers

The exotic zooplankter Daphnia lumholtzi is believed to have been introduced into Fairfield Lake, TX in 1983. Since introduction, D. lumholtzi has spread throughout the Midwest and Southeast United States. Due to its large head and tail spines, it may be less susceptible than native species to predation and therefore pose a threat to aquatic ecosystems. Development of management practices calls for study of the dispersal and potential impact of D. lumholtzi on invaded ecosystems. Inter-simple sequence repeat (ISSR) markers were used in an effort to determine dispersal patterns of D. lumholtzi. Previous studies have shown that ISSRs possess sufficient levels of variability to reveal relationships at the population level. My objectives were to i) examine the utility of ISSRs in defining clonal groups within and across populations of D. lumholtzi, ii) look for genetic variation that may imply alternative sources of introduction of D. lumholtzi into North America and, iii) assess dispersal patterns of D. lumholtzi across parts of North America. Analysis included populations from Illinois, Kentucky, and Tennessee, as well as the population at Fairfield Lake, Texas. Eighteen primers were screened and two were found to be variable with respect to the D. lumholtzi populations sampled. The primers BECKY (CA)7YC and OMAR (GAG)5RC produced a total of 812 ISSR fragments of which 677 (83%) were polymorphic. Overall similarity of individuals inferred from presence/absence of bands was used to draw conclusions about D. lumholtzi populations. Cluster analysis (UPGMA) of ISSR banding patterns revealed a potential presence of two clonal lineages within the Fairfield Lake population and a large amount of genetic variation within and across all other populations sampled. Observed high levels of genetic variation in all populations except Fairfield Lake, suggests that Fairfield Lake is not the source population as is widely accepted. Furthermore, it appears that the genotypes present at Fairfield Lake are a subset of the numerous genotypes present in the other populations analyzed. If Fairfield Lake is in fact the source of introduction of D. lumholtzi into North America, my data suggest dispersal of D. lumholtzi across the U.S. resembles a stepping stone model of dispersal with one (or several) long distance dispersal event(s) originating at Fairfield Lake followed by several short distance dispersals

Recent oceanographic investigations in the Gulf of California

Results of seven hydrographic cruises into the Gulf of California during 1956 and 1957 show that the water mass there is characteristic of Equatorial Pacific water though modified by intensive evaporation in surface layers. The combination of wind regime and complicated topographical features plays a predominant role in circulation, upwelling, distribution of temperature, and other hydrographic factors. Seasonal changes are large...

Characterizing spiral arm and interarm star formation

Interarm star formation contributes significantly to a galaxy's star formation budget, and provides an opportunity to study stellar birthplaces unperturbed by spiral arm dynamics. Using optical integral field spectroscopy of the nearby galaxy NGC 628 with VLT/MUSE, we construct Halpha maps including detailed corrections for dust extinction and stellar absorption to identify 391 HII regions at 35pc resolution over 12 kpc^2. Using tracers sensitive to the underlying gravitational potential, we associate HII regions with either arm (271) or interarm (120) environments. Using our full spectral coverage of each region, we find that most HII region physical properties (luminosity, size, metallicity, ionization parameter) are independent of environment. We calculate the fraction of Halpha luminosity due to the diffuse ionized gas (DIG) background contaminating each HII region, and find the DIG surface brightness to be higher within HII regions compared to the surroundings, and slightly higher within arm HII regions. Use of the temperature sensitive [SII]/Halpha line ratio map instead of the Halpha surface brightness to identify HII region boundaries does not change this result. Using the dust attenuation as a tracer of the gas, we find depletion times consistent with previous work (2 x 10^9 yr) with no differences between the arm and interarm, however this is very sensitive to the DIG correction. Unlike molecular clouds, which can be dynamically affected by the galactic environment, we see fairly consistent HII region properties in both arm and interarm environments. This suggests either a difference in arm star formation and feedback, or a decoupling of dense star forming clumps from the more extended surrounding molecular gas.Comment: 10 pages, 4 figures, 1 table, accepted for publication in Ap

Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

Budget feasible mechanisms on matroids

Motivated by many practical applications, in this paper we study budget feasible mechanisms where the goal is to procure independent sets from matroids. More specifically, we are given a matroid =(,) where each ground (indivisible) element is a selfish agent. The cost of each element (i.e., for selling the item or performing a service) is only known to the element itself. There is a buyer with a budget having additive valuations over the set of elements E. The goal is to design an incentive compatible (truthful) budget feasible mechanism which procures an independent set of the matroid under the given budget that yields the largest value possible to the buyer. Our result is a deterministic, polynomial-time, individually rational, truthful and budget feasible mechanism with 4-approximation to the optimal independent set. Then, we extend our mechanism to the setting of matroid intersections in which the goal is to procure common independent sets from multiple matroids. We show that, given a polynomial time deterministic blackbox that returns -approximation solutions to the matroid intersection problem, there exists a deterministic, polynomial time, individually rational, truthful and budget feasible mechanism with (3+1) -approximation to the optimal common independent set

Fermionic Zero Modes on Domain Walls

We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the absence of the Majorana mass terms, the equations are solvable analytically. In the case of massless fermions a zero energy solution exists and we show that although this mode is not discretely normalizable it is Dirac delta function normalizable and should be viewed as part of a continuum spectrum rather than as an isolated zero mode.Comment: 6 pages, 3 figures, matches version published in PR

Modulating pulse solutions for quasilinear wave equations

This paper presents an existence proof for symmetric modulating pulse solutions of a quasilinear wave equation. Modulating pulse solutions consist of a pulse-like envelope advancing in the laboratory frame and modulating an underlying wave-train; they are also referred to as "moving breathers" since they are time-periodic in a moving frame of reference. The problem is formulated as an infinite-dimensional dynamical system with two stable, two unstable and infinitely many neutral directions. Using a partial normal form and a generalisation of local invariant-manifold theory to the quasilinear setting we prove the existence of modulating pulses on arbitrarily large, but finite domains in space and time