Hydrodynamic models of a cepheid atmosphere

A method for including the solution of the transfer equation in a standard Henyey type hydrodynamic code was developed. This modified Henyey method was used in an implicit hydrodynamic code to compute deep envelope models of a classical Cepheid with a period of 12(d) including radiative transfer effects in the optically thin zones. It was found that the velocity gradients in the atmosphere are not responsible for the large microturbulent velocities observed in Cepheids but may be responsible for the occurrence of supersonic microturbulence. It was found that the splitting of the cores of the strong lines is due to shock induced temperature inversions in the line forming region. The adopted light, color, and velocity curves were used to study three methods frequently used to determine the mean radii of Cepheids. It is concluded that an accuracy of 10% is possible only if high quality observations are used

Enhanced Operational Semantics in Systems Biology

We are faced with a great challenge: the cross-fertilization between the fields of formal methods for concurrency, in the computer science domain, and systems biology in the biological realm

Percolation of satisfiability in finite dimensions

The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though there is a logical connectivity transition. In part of the disconnected phase, rare regions lead to a divergent running time for optimization algorithms. The thermodynamic ground state for the NP-hard two-dimensional maximum-satisfiability problem is typically unique. These results have implications for the computational study of disordered materials.Comment: 4 pages, 4 fig

Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Turbulence-plankton interactions : a new cartoon

Author Posting. © John Wiley & Sons, 2009. This is the author's version of the work. It is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Marine Ecology 30 (2009): 133-150, doi:10.1111/j.1439-0485.2009.00288.x.Climate change will alter turbulence intensity, motivating greater attention to mechanisms of turbulence effects on organisms. Many analytic and analog models used to simulate and assess effects of turbulence on plankton rely on a one-dimensional simplification of the dissipative scales of turbulence, i.e., simple, steady, uniaxial shears, as produced in Couette vessels. There shear rates are constant and spatially uniform, and hence so is vorticity. Studies in such Couette flows have greatly informed, spotlighting stable orientations of nonspherical particles and predictable, periodic, rotational motions of steadily sheared particles in Jeffery orbits that steepen concentration gradients around nutrient-absorbing phytoplankton and other chemically (re)active particles. Over the last decade, however, turbulence research within fluid dynamics has focused on the structure of dissipative vortices in space and time and on spatially and temporally varying 2 vorticity fields in particular. Because steadily and spatially uniformly sheared flows are exceptional, so therefore are stable orientations for particles in turbulent flows. Vorticity gradients, finite net diffusion of vorticity and small radii of curvature of streamlines are ubiquitous features of turbulent vortices at dissipation scales that are explicitly excluded from simple, steady Couette flows. All of these flow components contribute instabilities that cause rotational motions of particles and so are important to simulate in future laboratory devices designed to assess effects of turbulence on nutrient uptake, particle coagulation and predatorprey encounter in the plankton. The Burgers vortex retains these signature features of turbulence and provides a simplified “cartoon” of vortex structure and dynamics that nevertheless obeys the Navier-Stokes equations. Moreover, this idealization closely resembles many dissipative vortices observed in both the laboratory and the field as well as in direct numerical simulations of turbulence. It is simple enough to allow both simulation in numerical models and fabrication of analog devices that selectively reproduce its features. Exercise of such numerical and analog models promises additional insights into mechanisms of turbulence effects on passive trajectories and local accumulations of both living and nonliving particles, into solute exchange with living and nonliving particles and into more subtle influences on sensory processes and swimming trajectories of plankton, including demersal organisms and settling larvae in turbulent bottom boundary layers. The literature on biological consequences of vortical turbulence has focused primarily on the smallest, Kolmogorov-scale vortices of length scale η. Theoretical dissipation spectra and direct numerical simulation, however, indicate that typical dissipative vortices with radii of 7η to 8η, peak azimuthal speeds of order 1 cm s-1 and lifetimes of order 10 s as a minimum (and much longer for moderate pelagic turbulence intensities) deserve new attention in studies of biological effects of turbulence.This research was supported by collaborative U.S. National Science Foundation grant (OCE- 0724744) to Jumars and Karp-Boss

Validation of the particle size distribution obtained with the laser in-situ scattering and transmission (LISST) meter in flow-through mode

High spatial and temporal resolution estimates of the particle size distribution (PSD) in the surface ocean can enable improved understanding of biogeochemistry and ecosystem dynamics. Oceanic PSD measurements remain rare due to the time-consuming, manual sampling methods of common particle sizing instruments. Here, we evaluate the utility of measuring particle size data at high spatial resolution with a commercially-available submersible laser di raction particle sizer (LISST-100X, Sequoia Scientific), operating in an automated mode with continuously flowing seawater. The LISST PSD agreed reasonably well with discrete PSD measurements obtained with a Coulter Counter and data from the flow-through sampling Imaging Flow-Cytobot, validating our methodology. Total particulate area and Volume derived from the LISST PSD agreed well with beam-attenuation and particulate organic carbon respectively, further validating the LISST PSD. Furthermore, When compared to the measured spectral characteristics of particulate beam attenuation, we find a significant correlation. However, no significant relationship between the PSD and spectral particulate backscattering was found

Scaling Limits for Internal Aggregation Models with Multiple Sources

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in R^d. In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in v2: added "least action principle" (Lemma 3.2); small corrections in section 4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version); expanded section 6.

Complex networks theory for analyzing metabolic networks

One of the main tasks of post-genomic informatics is to systematically investigate all molecules and their interactions within a living cell so as to understand how these molecules and the interactions between them relate to the function of the organism, while networks are appropriate abstract description of all kinds of interactions. In the past few years, great achievement has been made in developing theory of complex networks for revealing the organizing principles that govern the formation and evolution of various complex biological, technological and social networks. This paper reviews the accomplishments in constructing genome-based metabolic networks and describes how the theory of complex networks is applied to analyze metabolic networks.Comment: 13 pages, 2 figure

Determining the Solution Space of Vertex-Cover by Interactions and Backbones

To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, which has a direct correspondence to the solution space of Vertex-cover. By this algorithm, the whole solution space can be obtained strictly when there is no leaf-removal core on the graph and the odd cycles of unfrozen nodes bring great obstacles to its efficiency. Besides, this algorithm possesses favorable exactness and has good performance on random instances even with high average degrees. The interaction with the algorithm provides a new viewpoint to solve Vertex-cover, which will have a wide range of applications to different types of graphs, better usage of which can lower the computational complexity for solving Vertex-cover