Polynomial-time Solvable #CSP Problems via Algebraic Models and Pfaffian Circuits

A Pfaffian circuit is a tensor contraction network where the edges are labeled with changes of bases in such a way that a very specific set of combinatorial properties are satisfied. By modeling the permissible changes of bases as systems of polynomial equations, and then solving via computation, we are able to identify classes of 0/1 planar #CSP problems solvable in polynomial-time via the Pfaffian circuit evaluation theorem (a variant of L. Valiant's Holant Theorem). We present two different models of 0/1 variables, one that is possible under a homogeneous change of basis, and one that is possible under a heterogeneous change of basis only. We enumerate a series of 1,2,3, and 4-arity gates/cogates that represent constraints, and define a class of constraints that is possible under the assumption of a ``bridge" between two particular changes of bases. We discuss the issue of planarity of Pfaffian circuits, and demonstrate possible directions in algebraic computation for designing a Pfaffian tensor contraction network fragment that can simulate a swap gate/cogate. We conclude by developing the notion of a decomposable gate/cogate, and discuss the computational benefits of this definition

Report on Mini-conference on Sludge Disposal Alternatives in the Ocean off Southern California, 8 September 1976

The purpose of the conference was to review the status of our capability to predict the environmental effects of the disposal of digested sewage sludge in the ocean off the coast of Southern California. At present, the ocean disposal of sewage sludge is prohibited by State and Federal regulations. Ocean disposal of sludge, however, is a complex of many alternative combinations of what, where and how; and the environmental consequences of all such combinations have not yet been determined. There is, in fact, some evidence that at least one environmentally sound mode of sludge disposal in the ocean off the Southern California coast may exist. This is the trapping of sludge in the sediments of deep, nearshore ocean basins. such as the Santa Monica Basin. Details of this method are given in Section 3.3. p. 12. It is the philosophy of the Environmental Quality Laboratory to study and evaluate policy alternatives but not to be an advocate of one alternative or another. Some of the policies studied may be contrary to existing laws or regulations, but it is believed that there is a better chance for improvement in the laws or regulations if alternatives currently outside them are also studied. The conference was sponsored by the Environmental Quality Laboratory in the belief that sufficient information is now available to begin making reasonable estimates of the environmental consequences of existing or alternative ocean disposal methods in order to compare them to land-based disposal methods. The purpose of this report is not to publish the actual proceedings of the conference. but rather to act as a communications aid. It is intended to publicize the issues that were raised at the conference, to give the names and addresses of people who are involved in these issues, and to present abstracts and literature citations. The schedule of the conference is presented in the next section. It is followed by a section containing abstracts of current research by conference attendees along with reference lists supplied by them. The fourth section is a summary of the afternoon discussion sessions. The final section is a list of conference attendees with their mailing addresses

Marginal analysis of longitudinal count data in long sequences: Methods and applications to a driving study

Most of the available methods for longitudinal data analysis are designed and validated for the situation where the number of subjects is large and the number of observations per subject is relatively small. Motivated by the Naturalistic Teenage Driving Study (NTDS), which represents the exact opposite situation, we examine standard and propose new methodology for marginal analysis of longitudinal count data in a small number of very long sequences. We consider standard methods based on generalized estimating equations, under working independence or an appropriate correlation structure, and find them unsatisfactory for dealing with time-dependent covariates when the counts are low. For this situation, we explore a within-cluster resampling (WCR) approach that involves repeated analyses of random subsamples with a final analysis that synthesizes results across subsamples. This leads to a novel WCR method which operates on separated blocks within subjects and which performs better than all of the previously considered methods. The methods are applied to the NTDS data and evaluated in simulation experiments mimicking the NTDS.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS507 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section

PROGRAMMED EFFECTS OF SURFACE WATER PRICE LEVELS ON U.S. AGRICULTURAL WATER USE AND PRODUCTION PATTERNS

Resource /Energy Economics and Policy,

Editorial

No aspect of the practice of pediatric anesthesia is more essential than airway management. Pediatric anesthesiologists are the ‘go to’ specialists when infants and children with difficult airways present anywhere in the hospital. To our advantage, rapid technical advances have taken place during the past decades and the number of tools available to assist us in providing and maintaining a secure and stable airway has increased significantly. Until the 1970s tracheal intubation with a conventional laryngoscope or blind nasal intubation were the mainstays of establishing an artificial airway. The choice of endotracheal tubes was limited. During the past 20 years a remarkable assortment of equipment and novel techniques to facilitate optimal airway management have been developed. These include supraglottic airways, direct and fiberoptic laryngoscopes and transtracheal devices. Improved imaging of the airway prior to initiation of airway management, with CT and MRI, for example, and during airway manipulation and instrumentation, using fiberoptic cameras and portable video displays, is now widely used. While new developments in airway management have helped us improve the quality of care of our patients, new challenges have also arisen. Which techniques should we learn, teach and employ? Which endotracheal tubes should be utilized – uncuffed or cuffed, old or new design? Which of our patients need preoperative imaging of the airway and/or sleep studies? What are the risks of newer interventions, including novel airway devices and laser instruments

The Hopf Rings for KO and KU

We compute the mod two homology Hopf rings of the spectra KO and KU. The spaces in these spectra are the infinite classical groups and their coset spaces, and their homology was first calculated in the Cartan seminars, but the Hopf ring structure was first determined in the second author's unpublished PhD thesis. The presentation given here serves as an introduction to the first author's much more intricate work on the connective spectrum bo. The Hopf ring viewpoint turns out to be very convenient for understanding the homological effect of various maps between classical groups and fibrations of their connective covers.Comment: 20 pages; to appear in JPA

On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.Comment: 22 pages, 6 figure